/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 },
it remains to prove termination of the 99-rule system
{ 0 0 0 0 1 2 0 2 0 1 2 2 1 1 1 1 1 0 2 2 ⟶ 0 2 0 0 1 0 1 0 0 2 0 0 2 0 2 1 1 0 1 2 ,
  0 0 0 1 0 2 0 2 1 2 0 1 1 2 1 1 2 2 1 1 ⟶ 0 1 2 0 2 2 1 1 1 0 1 0 2 1 2 1 2 1 2 1 ,
  0 0 0 1 2 0 2 2 1 1 0 1 0 1 2 0 1 1 1 1 ⟶ 0 1 2 0 1 2 1 0 1 0 1 0 2 0 1 1 1 1 0 2 ,
  0 0 0 2 0 0 0 2 1 2 2 1 1 0 0 0 1 1 1 2 ⟶ 0 2 2 1 0 1 0 2 2 2 1 1 2 0 0 0 0 0 1 2 ,
  0 0 0 2 1 2 2 0 1 1 0 0 1 1 2 1 0 2 2 1 ⟶ 0 2 0 1 1 2 0 1 2 1 2 1 0 2 2 0 2 0 1 0 ,
  0 0 0 2 2 1 1 2 2 0 0 2 1 2 0 1 1 0 2 2 ⟶ 0 2 2 2 1 0 0 2 1 2 1 2 1 2 1 1 1 2 0 2 ,
  0 0 1 0 0 1 1 2 1 1 2 2 1 1 2 2 1 1 0 2 ⟶ 0 1 1 0 0 2 0 0 2 0 2 1 1 1 1 1 0 2 0 2 ,
  0 0 1 0 1 0 2 0 0 1 2 1 1 2 2 2 1 0 2 1 ⟶ 0 2 1 0 1 0 0 0 2 0 0 1 2 0 2 1 0 0 2 0 ,
  0 0 1 0 1 2 2 2 1 1 2 1 2 1 0 2 0 1 2 0 ⟶ 0 2 0 1 1 2 2 2 1 0 0 2 1 0 0 0 0 2 0 2 ,
  0 0 1 0 2 0 2 1 1 1 0 0 0 2 2 1 2 1 1 2 ⟶ 0 2 0 0 2 2 0 2 1 1 2 1 2 1 0 2 2 0 2 0 ,
  0 0 1 0 2 1 2 2 2 2 0 1 2 0 1 1 2 2 0 2 ⟶ 0 0 2 1 1 0 0 2 2 2 0 1 2 2 0 1 2 2 0 2 ,
  0 0 1 0 2 2 1 2 0 0 1 1 2 2 2 1 1 2 1 1 ⟶ 0 2 0 2 2 0 0 1 2 0 2 0 0 1 1 0 0 2 1 1 ,
  0 0 1 0 2 2 2 2 1 0 2 1 0 2 2 0 1 1 2 1 ⟶ 0 0 1 0 0 0 0 2 2 2 2 0 0 0 1 0 0 2 1 1 ,
  0 0 1 1 0 2 2 1 1 1 1 1 2 0 2 1 0 2 2 1 ⟶ 0 2 0 1 1 0 1 2 2 2 0 0 2 2 2 0 2 0 0 0 ,
  0 0 1 1 1 1 0 2 2 2 2 1 1 2 2 2 1 1 2 1 ⟶ 0 1 0 0 1 1 2 2 0 2 2 0 2 0 0 0 2 2 1 1 ,
  0 0 1 2 0 1 2 0 1 1 1 0 2 2 1 0 2 1 1 2 ⟶ 0 1 2 2 0 2 2 2 1 0 1 2 2 1 0 0 1 1 1 2 ,
  0 0 1 2 2 0 1 1 2 0 0 2 2 1 0 2 1 2 1 0 ⟶ 0 2 2 0 2 0 2 1 0 2 0 0 2 2 1 0 0 0 2 0 ,
  0 0 1 2 2 1 0 1 1 1 0 0 1 2 1 2 2 2 0 2 ⟶ 0 1 1 2 2 0 0 2 0 2 2 0 0 1 0 0 0 0 0 0 ,
  0 0 1 2 2 1 1 0 2 2 2 0 1 1 1 1 0 1 2 1 ⟶ 0 1 2 2 0 1 1 1 2 0 2 0 0 1 2 0 2 1 2 0 ,
  0 0 2 0 0 0 2 1 2 2 2 1 1 1 0 2 1 1 0 0 ⟶ 0 2 0 1 2 0 1 2 0 1 0 1 2 2 1 2 1 0 0 0 ,
  0 0 2 0 1 1 2 0 2 1 0 2 2 1 1 0 1 2 0 1 ⟶ 0 1 2 0 2 0 1 0 1 2 1 0 0 2 2 1 0 1 0 1 ,
  0 0 2 0 1 2 2 0 0 1 2 2 0 0 2 2 1 1 0 1 ⟶ 0 0 1 2 0 0 1 1 0 2 0 2 0 0 0 0 0 2 0 1 ,
  0 0 2 0 2 1 1 2 1 1 1 1 1 0 1 1 1 2 2 1 ⟶ 0 2 0 0 2 1 1 2 2 0 2 0 1 2 2 2 1 1 1 2 ,
  0 0 2 1 0 1 0 0 2 0 1 1 0 2 0 2 2 2 2 0 ⟶ 0 2 2 0 0 0 2 1 0 0 0 1 1 2 0 1 1 0 0 0 ,
  0 0 2 1 1 0 2 2 1 1 1 1 2 2 0 0 2 1 0 0 ⟶ 0 2 2 1 1 1 2 1 0 1 2 1 2 1 1 2 1 0 0 0 ,
  0 0 2 2 0 0 1 0 2 2 1 1 2 2 1 0 2 2 0 1 ⟶ 0 2 0 2 2 1 0 0 2 2 1 2 1 1 0 0 2 0 2 1 ,
  0 0 2 2 0 1 0 2 1 2 1 1 2 2 2 1 1 2 0 2 ⟶ 0 0 1 2 1 2 1 2 1 2 0 1 2 1 0 0 0 1 2 0 ,
  0 0 2 2 1 1 1 0 1 0 1 0 1 2 2 2 1 2 0 0 ⟶ 0 1 0 2 0 2 2 1 0 1 0 2 1 2 1 0 1 1 1 2 ,
  0 0 2 2 1 2 0 1 2 2 0 1 0 0 0 2 2 0 0 0 ⟶ 0 0 0 0 2 0 0 0 2 2 2 0 2 0 1 0 1 0 0 0 ,
  0 0 2 2 2 0 1 0 1 1 1 0 1 0 0 0 1 1 2 0 ⟶ 0 2 0 2 2 2 2 0 2 2 1 0 0 0 0 0 0 2 0 0 ,
  0 1 0 0 1 0 2 1 2 2 1 2 2 1 1 1 1 2 2 1 ⟶ 0 0 1 1 1 0 1 0 0 0 2 2 1 1 2 0 0 2 1 2 ,
  0 1 0 0 1 1 1 0 1 1 2 1 1 1 2 2 1 2 2 1 ⟶ 0 0 1 1 1 2 1 0 2 0 0 0 1 2 2 0 0 1 1 1 ,
  0 1 0 0 2 2 0 1 2 2 1 2 1 0 1 2 2 2 1 0 ⟶ 0 0 2 2 0 2 2 2 1 0 2 1 2 0 2 2 0 0 2 2 ,
  0 1 0 0 2 2 0 2 2 1 2 1 2 1 1 0 0 2 2 2 ⟶ 0 2 0 1 2 1 0 1 0 0 0 0 0 0 2 0 1 0 2 1 ,
  0 1 0 1 0 1 1 0 0 0 1 0 2 1 1 2 0 1 0 1 ⟶ 0 0 2 1 1 0 0 2 0 2 1 0 1 1 0 2 2 0 1 2 ,
  0 1 0 1 1 1 1 2 0 2 2 2 2 2 2 1 0 2 0 1 ⟶ 0 0 0 2 2 1 0 0 1 2 1 0 2 2 1 0 0 2 2 1 ,
  0 1 0 1 1 2 1 0 0 0 2 2 2 1 2 1 2 1 0 2 ⟶ 0 1 0 0 2 2 1 2 1 0 1 0 0 0 2 0 0 2 1 2 ,
  0 1 0 1 1 2 2 0 0 0 2 2 2 1 1 0 1 1 1 1 ⟶ 0 0 2 2 2 2 2 2 1 1 0 1 2 2 0 1 2 0 2 1 ,
  0 1 0 1 1 2 2 1 0 1 2 1 1 0 1 2 0 2 0 2 ⟶ 0 2 0 1 0 1 1 0 0 1 0 2 0 0 0 2 2 0 2 0 ,
  0 1 0 1 2 1 1 1 0 0 1 1 2 2 2 0 2 0 1 2 ⟶ 0 2 1 1 2 1 0 2 0 1 1 0 2 0 1 0 2 2 0 2 ,
  0 1 0 1 2 1 1 1 2 2 0 2 1 1 2 1 2 0 2 1 ⟶ 0 2 1 2 0 0 2 1 2 2 1 2 1 2 0 2 0 0 2 1 ,
  0 1 0 2 0 0 1 2 2 2 1 2 2 2 0 0 0 1 2 2 ⟶ 0 1 0 1 1 2 1 0 0 1 0 0 2 2 2 1 0 2 0 0 ,
  0 1 0 2 0 2 1 1 1 0 1 2 2 0 2 0 1 1 2 0 ⟶ 0 0 1 2 0 0 0 0 0 0 1 1 0 2 0 2 1 2 1 0 ,
  0 1 0 2 1 1 1 0 2 2 1 1 1 1 2 0 2 1 0 0 ⟶ 0 2 1 0 2 0 0 1 2 2 0 0 0 1 1 1 1 0 2 2 ,
  0 1 0 2 2 1 1 0 1 0 2 2 1 0 2 0 1 0 1 1 ⟶ 0 1 2 0 0 2 2 0 0 0 0 2 1 2 1 0 1 2 0 2 ,
  0 1 0 2 2 2 1 2 1 1 1 2 1 0 2 1 1 1 0 1 ⟶ 0 0 1 2 2 2 1 0 0 1 1 2 1 1 2 0 0 1 2 0 ,
  0 1 1 0 0 2 0 2 1 1 1 2 1 2 1 0 0 1 1 1 ⟶ 0 1 0 0 2 2 0 0 2 2 0 2 0 0 1 2 1 0 1 2 ,
  0 1 1 0 1 0 2 1 1 2 2 0 2 0 2 0 2 2 0 1 ⟶ 0 2 0 2 1 0 0 1 2 2 1 2 2 1 2 2 1 2 2 0 ,
  0 1 1 0 1 1 1 1 2 0 2 0 2 2 2 0 0 0 2 1 ⟶ 0 1 0 1 2 2 2 0 2 2 1 1 2 2 2 0 0 0 1 0 ,
  0 1 1 0 1 2 1 2 0 2 2 1 0 0 2 0 1 0 1 1 ⟶ 0 0 0 1 2 0 2 2 2 0 1 0 1 2 1 1 1 0 2 0 ,
  0 1 1 0 2 0 2 1 2 1 2 2 0 2 1 2 2 1 1 0 ⟶ 0 2 0 1 1 1 0 1 0 1 2 0 2 2 1 0 2 0 0 2 ,
  0 1 1 0 2 1 1 0 0 1 1 1 2 2 2 0 2 0 0 2 ⟶ 0 1 2 1 0 2 1 0 1 2 2 2 0 0 2 0 2 2 1 2 ,
  0 1 1 0 2 1 2 1 1 0 1 1 2 1 0 1 0 1 1 1 ⟶ 0 1 1 1 2 1 2 2 0 1 1 0 2 2 0 0 2 1 0 2 ,
  0 1 1 0 2 2 0 1 2 2 2 0 2 2 1 2 1 2 1 0 ⟶ 0 0 2 0 0 2 0 2 1 0 2 2 2 0 0 0 2 1 1 2 ,
  0 1 1 1 1 1 1 2 2 0 2 0 2 2 0 2 1 0 1 0 ⟶ 0 2 0 1 1 0 2 0 0 1 1 2 0 1 0 0 1 0 2 0 ,
  0 1 1 1 1 2 0 0 0 2 2 2 2 1 0 2 2 2 0 1 ⟶ 0 2 0 0 0 1 2 0 1 2 2 2 1 2 1 1 1 2 1 2 ,
  0 1 1 1 2 2 1 2 1 1 1 0 0 1 1 1 2 1 1 0 ⟶ 0 0 1 0 2 0 1 1 1 2 0 2 1 2 2 0 2 1 2 1 ,
  0 1 1 2 0 1 0 0 1 2 0 2 1 0 0 0 0 2 0 1 ⟶ 0 0 2 1 2 2 2 1 2 1 0 0 0 2 2 1 0 1 2 0 ,
  0 1 1 2 0 2 0 2 2 1 1 2 0 1 2 2 0 1 0 0 ⟶ 0 1 2 0 0 0 2 1 2 0 1 2 2 2 2 0 1 1 0 1 ,
  0 1 1 2 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 ⟶ 0 0 0 1 0 1 0 1 1 1 2 0 1 2 2 0 2 2 0 2 ,
  0 1 1 2 2 2 2 1 0 2 0 0 1 2 2 1 2 2 2 2 ⟶ 0 1 0 0 2 0 0 1 2 1 2 0 1 2 2 1 0 2 0 2 ,
  0 1 2 0 0 1 2 0 2 0 0 1 0 2 0 0 2 1 2 0 ⟶ 0 2 1 2 0 0 0 2 0 0 2 1 2 2 0 2 2 0 0 0 ,
  0 1 2 0 0 2 1 1 0 2 1 0 1 1 1 0 1 1 0 0 ⟶ 0 0 0 2 0 1 1 2 2 0 2 0 0 2 1 0 0 2 1 1 ,
  0 1 2 0 1 0 2 0 2 1 2 2 1 1 1 2 0 1 2 1 ⟶ 0 0 2 2 2 0 0 0 1 0 0 0 0 2 1 2 1 1 2 1 ,
  0 1 2 0 2 0 0 2 1 1 1 2 2 0 0 0 2 0 0 0 ⟶ 0 1 0 0 2 1 0 1 1 0 1 2 2 0 1 2 1 0 1 0 ,
  0 1 2 1 0 1 2 2 1 1 0 0 1 1 2 2 1 0 1 1 ⟶ 0 2 2 2 0 2 0 2 0 1 2 1 2 2 2 1 0 0 1 0 ,
  0 1 2 2 0 1 1 1 2 1 0 0 2 0 1 2 2 0 1 2 ⟶ 0 2 0 0 2 0 2 2 1 0 1 1 1 0 2 0 1 2 0 0 ,
  0 1 2 2 2 0 0 2 0 1 2 1 0 1 0 0 2 0 0 2 ⟶ 0 0 0 1 2 0 2 1 2 2 0 0 0 1 0 1 0 0 1 2 ,
  0 1 2 2 2 2 2 2 2 1 0 2 2 1 1 2 1 2 1 1 ⟶ 0 2 1 0 2 1 0 1 2 0 0 0 1 2 0 0 0 0 0 1 ,
  0 2 0 0 0 2 1 1 0 2 2 1 1 0 0 0 0 1 0 0 ⟶ 0 0 2 1 0 0 0 2 2 2 2 0 0 2 0 2 1 2 1 2 ,
  0 2 0 0 1 0 2 1 0 2 2 0 1 0 2 1 2 1 1 2 ⟶ 0 2 1 0 2 1 0 2 1 2 1 0 1 2 0 1 0 0 0 0 ,
  0 2 0 1 1 0 1 1 1 0 1 0 0 2 1 0 2 2 2 0 ⟶ 0 2 2 2 0 0 2 0 0 2 0 1 2 1 2 2 1 2 1 2 ,
  0 2 0 1 1 1 0 1 2 2 0 2 0 2 0 2 1 2 0 1 ⟶ 0 2 2 0 1 2 2 2 2 1 0 2 1 2 0 0 2 2 2 1 ,
  0 2 0 1 2 1 1 1 1 2 0 2 1 2 0 1 2 2 0 1 ⟶ 0 1 1 1 1 2 1 0 0 1 1 0 2 1 0 0 2 0 0 1 ,
  0 2 0 2 0 2 0 2 1 1 0 2 1 1 1 1 2 0 2 0 ⟶ 0 1 0 2 1 2 1 1 0 0 2 2 2 0 0 1 2 2 0 0 ,
  0 2 0 2 0 2 1 2 2 0 1 1 1 2 1 1 0 2 0 1 ⟶ 0 2 0 0 1 1 1 0 2 1 1 2 0 0 0 2 2 1 1 0 ,
  0 2 0 2 1 0 0 1 2 0 2 0 1 0 1 1 1 2 2 1 ⟶ 0 0 1 0 1 0 1 1 2 1 0 0 0 1 2 2 2 0 1 0 ,
  0 2 0 2 1 1 2 0 0 0 2 1 2 1 2 0 0 1 2 0 ⟶ 0 2 2 0 1 2 0 1 0 0 0 0 2 1 0 0 0 0 1 2 ,
  0 2 0 2 1 2 1 2 2 0 2 1 1 1 2 1 1 1 1 1 ⟶ 0 1 1 1 0 2 1 0 1 2 1 0 0 0 2 1 1 2 0 1 ,
  0 2 1 0 1 2 2 0 0 1 2 0 2 2 2 2 2 2 1 1 ⟶ 0 0 0 1 2 2 0 0 0 1 2 0 0 0 2 2 0 1 0 2 ,
  0 2 1 1 0 2 1 1 1 1 2 2 0 1 1 1 2 2 1 1 ⟶ 0 0 2 0 0 1 0 2 2 1 0 1 1 0 0 2 0 2 2 1 ,
  0 2 1 1 1 0 0 1 2 1 2 1 1 2 0 2 1 0 1 2 ⟶ 0 1 0 1 0 2 0 0 0 1 1 1 2 0 0 0 1 2 2 2 ,
  0 2 1 1 1 0 2 1 1 0 1 0 2 2 0 0 2 0 2 1 ⟶ 0 1 0 1 2 2 2 1 1 0 2 2 1 2 0 0 0 0 2 1 ,
  0 2 1 1 1 1 0 0 0 0 2 1 2 0 0 2 1 0 2 1 ⟶ 0 0 0 1 0 1 1 2 0 2 0 0 2 2 2 2 1 0 2 1 ,
  0 2 1 1 1 2 2 0 0 0 2 1 0 1 2 2 1 0 2 0 ⟶ 0 1 0 1 0 0 0 1 0 2 1 1 0 0 2 1 2 0 2 1 ,
  0 2 1 1 2 0 2 2 2 0 1 2 0 2 0 2 2 0 0 1 ⟶ 0 0 2 1 2 0 0 0 2 0 1 2 2 2 1 0 1 1 1 0 ,
  0 2 1 1 2 1 2 2 2 0 0 1 0 2 1 1 1 2 2 0 ⟶ 0 0 0 2 1 0 1 2 1 2 1 1 1 2 0 0 0 1 1 0 ,
  0 2 1 2 0 1 1 1 2 0 1 1 2 1 2 0 2 0 2 0 ⟶ 0 1 2 1 1 0 1 1 2 1 2 0 1 0 1 2 2 0 2 2 ,
  0 2 1 2 0 1 1 2 2 0 1 1 0 1 2 1 0 0 0 1 ⟶ 0 0 1 0 0 2 0 2 0 1 2 1 0 0 0 1 0 0 2 1 ,
  0 2 2 0 0 2 1 0 2 0 2 0 2 0 1 1 2 2 1 0 ⟶ 0 2 0 0 0 0 0 0 1 2 0 1 2 2 0 1 0 1 0 1 ,
  0 2 2 0 1 2 2 0 1 1 2 1 1 2 2 2 1 0 1 2 ⟶ 0 2 1 0 0 0 2 0 1 1 1 0 1 0 2 2 1 1 2 2 ,
  0 2 2 0 2 0 1 1 2 2 2 0 2 2 0 2 0 1 2 0 ⟶ 0 1 1 0 0 0 2 0 0 1 1 1 0 1 1 0 0 0 0 2 ,
  0 2 2 1 0 0 1 1 2 0 2 2 0 1 1 2 2 1 0 0 ⟶ 0 2 1 0 2 2 0 0 0 0 0 1 2 1 0 1 1 2 1 1 ,
  0 2 2 1 1 1 1 0 0 1 0 1 0 2 2 1 1 2 2 1 ⟶ 0 2 2 2 0 2 2 1 1 2 2 2 2 0 2 0 0 2 0 2 ,
  0 2 2 1 1 2 0 1 0 1 0 2 0 1 0 1 0 2 1 1 ⟶ 0 1 1 0 0 1 1 0 0 2 2 1 1 2 2 0 0 0 2 0 ,
  0 2 2 1 1 2 2 1 0 2 1 2 1 1 2 2 2 0 2 0 ⟶ 0 2 1 2 2 2 1 0 0 1 0 0 0 1 2 1 1 2 2 1 ,
  0 2 2 1 2 0 1 1 0 0 1 1 2 0 1 1 0 2 2 2 ⟶ 0 2 2 2 0 2 0 0 2 2 0 0 2 1 1 0 0 2 1 1 ,
  0 2 2 2 2 1 0 0 0 2 2 1 0 1 1 1 0 1 2 2 ⟶ 0 0 2 2 0 2 0 2 0 1 1 2 0 0 0 0 2 1 1 2 ,
  1 2 2 0 2 0 2 1 2 1 2 1 0 0 1 0 0 2 0 1 ⟶ 1 0 1 2 0 1 0 0 1 0 0 0 2 1 0 0 1 0 0 2 }

The system was reversed.

After renaming modulo the bijection { 2 ↦ 0, 0 ↦ 1, 1 ↦ 2 },
it remains to prove termination of the 99-rule system
{ 0 0 1 2 2 2 2 2 0 0 2 1 0 1 0 2 1 1 1 1 ⟶ 0 2 1 2 2 0 1 0 1 1 0 1 1 2 1 2 1 1 0 1 ,
  2 2 0 0 2 2 0 2 2 1 0 2 0 1 0 1 2 1 1 1 ⟶ 2 0 2 0 2 0 2 0 1 2 1 2 2 2 0 0 1 0 2 1 ,
  2 2 2 2 1 0 2 1 2 1 2 2 0 0 1 0 2 1 1 1 ⟶ 0 1 2 2 2 2 1 0 1 2 1 2 1 2 0 2 1 0 2 1 ,
  0 2 2 2 1 1 1 2 2 0 0 2 0 1 1 1 0 1 1 1 ⟶ 0 2 1 1 1 1 1 0 2 2 0 0 0 1 2 1 2 0 0 1 ,
  2 0 0 1 2 0 2 2 1 1 2 2 1 0 0 2 0 1 1 1 ⟶ 1 2 1 0 1 0 0 1 2 0 2 0 2 1 0 2 2 1 0 1 ,
  0 0 1 2 2 1 0 2 0 1 1 0 0 2 2 0 0 1 1 1 ⟶ 0 1 0 2 2 2 0 2 0 2 0 2 0 1 1 2 0 0 0 1 ,
  0 1 2 2 0 0 2 2 0 0 2 2 0 2 2 1 1 2 1 1 ⟶ 0 1 0 1 2 2 2 2 2 0 1 0 1 1 0 1 1 2 2 1 ,
  2 0 1 2 0 0 0 2 2 0 2 1 1 0 1 2 1 2 1 1 ⟶ 1 0 1 1 2 0 1 0 2 1 1 0 1 1 1 2 1 2 0 1 ,
  1 0 2 1 0 1 2 0 2 0 2 2 0 0 0 2 1 2 1 1 ⟶ 0 1 0 1 1 1 1 2 0 1 1 2 0 0 0 2 2 1 0 1 ,
  0 2 2 0 2 0 0 1 1 1 2 2 2 0 1 0 1 2 1 1 ⟶ 1 0 1 0 0 1 2 0 2 0 2 2 0 1 0 0 1 1 0 1 ,
  0 1 0 0 2 2 1 0 2 1 0 0 0 0 2 0 1 2 1 1 ⟶ 0 1 0 0 2 1 0 0 2 1 0 0 0 1 1 2 2 0 1 1 ,
  2 2 0 2 2 0 0 0 2 2 1 1 0 2 0 0 1 2 1 1 ⟶ 2 2 0 1 1 2 2 1 1 0 1 0 2 1 1 0 0 1 0 1 ,
  2 0 2 2 1 0 0 1 2 0 1 2 0 0 0 0 1 2 1 1 ⟶ 2 2 0 1 1 2 1 1 1 0 0 0 0 1 1 1 1 2 1 1 ,
  2 0 0 1 2 0 1 0 2 2 2 2 2 0 0 1 2 2 1 1 ⟶ 1 1 1 0 1 0 0 0 1 1 0 0 0 2 1 2 2 1 0 1 ,
  2 0 2 2 0 0 0 2 2 0 0 0 0 1 2 2 2 2 1 1 ⟶ 2 2 0 0 1 1 1 0 1 0 0 1 0 0 2 2 1 1 2 1 ,
  0 2 2 0 1 2 0 0 1 2 2 2 1 0 2 1 0 2 1 1 ⟶ 0 2 2 2 1 1 2 0 0 2 1 2 0 0 0 1 0 0 2 1 ,
  1 2 0 2 0 1 2 0 0 1 1 0 2 2 1 0 0 2 1 1 ⟶ 1 0 1 1 1 2 0 0 1 1 0 1 2 0 1 0 1 0 0 1 ,
  0 1 0 0 0 2 0 2 1 1 2 2 2 1 2 0 0 2 1 1 ⟶ 1 1 1 1 1 1 2 1 1 0 0 1 0 1 1 0 0 2 2 1 ,
  2 0 2 1 2 2 2 2 1 0 0 0 1 2 2 0 0 2 1 1 ⟶ 1 0 2 0 1 0 2 1 1 0 1 0 2 2 2 1 0 0 2 1 ,
  1 1 2 2 0 1 2 2 2 0 0 0 2 0 1 1 1 0 1 1 ⟶ 1 1 1 2 0 2 0 0 2 1 2 1 0 2 1 0 2 1 0 1 ,
  2 1 0 2 1 2 2 0 0 1 2 0 1 0 2 2 1 0 1 1 ⟶ 2 1 2 1 2 0 0 1 1 2 0 2 1 2 1 0 1 0 2 1 ,
  2 1 2 2 0 0 1 1 0 0 2 1 1 0 0 2 1 0 1 1 ⟶ 2 1 0 1 1 1 1 1 0 1 0 1 2 2 1 1 0 2 1 1 ,
  2 0 0 2 2 2 1 2 2 2 2 2 0 2 2 0 1 0 1 1 ⟶ 0 2 2 2 0 0 0 2 1 0 1 0 0 2 2 0 1 1 0 1 ,
  1 0 0 0 0 1 0 1 2 2 1 0 1 1 2 1 2 0 1 1 ⟶ 1 1 1 2 2 1 0 2 2 1 1 1 2 0 1 1 1 0 0 1 ,
  1 1 2 0 1 1 0 0 2 2 2 2 0 0 1 2 2 0 1 1 ⟶ 1 1 1 2 0 2 2 0 2 0 2 1 2 0 2 2 2 0 0 1 ,
  2 1 0 0 1 2 0 0 2 2 0 0 1 2 1 1 0 0 1 1 ⟶ 2 0 1 0 1 1 2 2 0 2 0 0 1 1 2 0 0 1 0 1 ,
  0 1 0 2 2 0 0 0 2 2 0 2 0 1 2 1 0 0 1 1 ⟶ 1 0 2 1 1 1 2 0 2 1 0 2 0 2 0 2 0 2 1 1 ,
  1 1 0 2 0 0 0 2 1 2 1 2 1 2 2 2 0 0 1 1 ⟶ 0 2 2 2 1 2 0 2 0 1 2 1 2 0 0 1 0 1 2 1 ,
  1 1 1 0 0 1 1 1 2 1 0 0 2 1 0 2 0 0 1 1 ⟶ 1 1 1 2 1 2 1 0 1 0 0 0 1 1 1 0 1 1 1 1 ,
  1 0 2 2 1 1 1 2 1 2 2 2 1 2 1 0 0 0 1 1 ⟶ 1 1 0 1 1 1 1 1 1 2 0 0 1 0 0 0 0 1 0 1 ,
  2 0 0 2 2 2 2 0 0 2 0 0 2 0 1 2 1 1 2 1 ⟶ 0 2 0 1 1 0 2 2 0 0 1 1 1 2 1 2 2 2 1 1 ,
  2 0 0 2 0 0 2 2 2 0 2 2 1 2 2 2 1 1 2 1 ⟶ 2 2 2 1 1 0 0 2 1 1 1 0 1 2 0 2 2 2 1 1 ,
  1 2 0 0 0 2 1 2 0 2 0 0 2 1 0 0 1 1 2 1 ⟶ 0 0 1 1 0 0 1 0 2 0 1 2 0 0 0 1 0 0 1 1 ,
  0 0 0 1 1 2 2 0 2 0 2 0 0 1 0 0 1 1 2 1 ⟶ 2 0 1 2 1 0 1 1 1 1 1 1 2 1 2 0 2 1 0 1 ,
  2 1 2 1 0 2 2 0 1 2 1 1 1 2 2 1 2 1 2 1 ⟶ 0 2 1 0 0 1 2 2 1 2 0 1 0 1 1 2 2 0 1 1 ,
  2 1 0 1 2 0 0 0 0 0 0 1 0 2 2 2 2 1 2 1 ⟶ 2 0 0 1 1 2 0 0 1 2 0 2 1 1 2 0 0 1 1 1 ,
  0 1 2 0 2 0 2 0 0 0 1 1 1 2 0 2 2 1 2 1 ⟶ 0 2 0 1 1 0 1 1 1 2 1 2 0 2 0 0 1 1 2 1 ,
  2 2 2 2 1 2 2 0 0 0 1 1 1 0 0 2 2 1 2 1 ⟶ 2 0 1 0 2 1 0 0 2 1 2 2 0 0 0 0 0 0 1 1 ,
  0 1 0 1 0 2 1 2 2 0 2 1 2 0 0 2 2 1 2 1 ⟶ 1 0 1 0 0 1 1 1 0 1 2 1 1 2 2 1 2 1 0 1 ,
  0 2 1 0 1 0 0 0 2 2 1 1 2 2 2 0 2 1 2 1 ⟶ 0 1 0 0 1 2 1 0 1 2 2 1 0 1 2 0 2 2 0 1 ,
  2 0 1 0 2 0 2 2 0 1 0 0 2 2 2 0 2 1 2 1 ⟶ 2 0 1 1 0 1 0 2 0 2 0 0 2 0 1 1 0 2 0 1 ,
  0 0 2 1 1 1 0 0 0 2 0 0 0 2 1 1 0 1 2 1 ⟶ 1 1 0 1 2 0 0 0 1 1 2 1 1 2 0 2 2 1 2 1 ,
  1 0 2 2 1 0 1 0 0 2 1 2 2 2 0 1 0 1 2 1 ⟶ 1 2 0 2 0 1 0 1 2 2 1 1 1 1 1 1 0 2 1 1 ,
  1 1 2 0 1 0 2 2 2 2 0 0 1 2 2 2 0 1 2 1 ⟶ 0 0 1 2 2 2 2 1 1 1 0 0 2 1 1 0 1 2 0 1 ,
  2 2 1 2 1 0 1 2 0 0 1 2 1 2 2 0 0 1 2 1 ⟶ 0 1 0 2 1 2 0 2 0 1 1 1 1 0 0 1 1 0 2 1 ,
  2 1 2 2 2 0 1 2 0 2 2 2 0 2 0 0 0 1 2 1 ⟶ 1 0 2 1 1 0 2 2 0 2 2 1 1 2 0 0 0 2 1 1 ,
  2 2 2 1 1 2 0 2 0 2 2 2 0 1 0 1 1 2 2 1 ⟶ 0 2 1 2 0 2 1 1 0 1 0 0 1 1 0 0 1 1 2 1 ,
  2 1 0 0 1 0 1 0 1 0 0 2 2 0 1 2 1 2 2 1 ⟶ 1 0 0 2 0 0 2 0 0 2 0 0 2 1 1 2 0 1 0 1 ,
  2 0 1 1 1 0 0 0 1 0 1 0 2 2 2 2 1 2 2 1 ⟶ 1 2 1 1 1 0 0 0 2 2 0 0 1 0 0 0 2 1 2 1 ,
  2 2 1 2 1 0 1 1 2 0 0 1 0 2 0 2 1 2 2 1 ⟶ 1 0 1 2 2 2 0 2 1 2 1 0 0 0 1 0 2 1 1 1 ,
  1 2 2 0 0 2 0 1 0 0 2 0 2 0 1 0 1 2 2 1 ⟶ 0 1 1 0 1 2 0 0 1 0 2 1 2 1 2 2 2 1 0 1 ,
  0 1 1 0 1 0 0 0 2 2 2 1 1 2 2 0 1 2 2 1 ⟶ 0 2 0 0 1 0 1 1 0 0 0 2 1 2 0 1 2 0 2 1 ,
  2 2 2 1 2 1 2 0 2 2 1 2 2 0 2 0 1 2 2 1 ⟶ 0 1 2 0 1 1 0 0 1 2 2 1 0 0 2 0 2 2 2 1 ,
  1 2 0 2 0 2 0 0 1 0 0 0 2 1 0 0 1 2 2 1 ⟶ 0 2 2 0 1 1 1 0 0 0 1 2 0 1 0 1 1 0 1 1 ,
  1 2 1 2 0 1 0 0 1 0 1 0 0 2 2 2 2 2 2 1 ⟶ 1 0 1 2 1 1 2 1 0 2 2 1 1 0 1 2 2 1 0 1 ,
  2 1 0 0 0 1 2 0 0 0 0 1 1 1 0 2 2 2 2 1 ⟶ 0 2 0 2 2 2 0 2 0 0 0 2 1 0 2 1 1 1 0 1 ,
  1 2 2 0 2 2 2 1 1 2 2 2 0 2 0 0 2 2 2 1 ⟶ 2 0 2 0 1 0 0 2 0 1 0 2 2 2 1 0 1 2 1 1 ,
  2 1 0 1 1 1 1 2 0 1 0 2 1 1 2 1 0 2 2 1 ⟶ 1 0 2 1 2 0 0 1 1 1 2 0 2 0 0 0 2 0 1 1 ,
  1 1 2 1 0 0 2 1 0 2 2 0 0 1 0 1 0 2 2 1 ⟶ 2 1 2 2 1 0 0 0 0 2 1 0 2 0 1 1 1 0 2 1 ,
  1 2 2 1 2 1 2 2 1 1 1 1 2 2 2 2 0 2 2 1 ⟶ 0 1 0 0 1 0 0 2 1 0 2 2 2 1 2 1 2 1 1 1 ,
  0 0 0 0 2 0 0 2 1 1 0 1 2 0 0 0 0 2 2 1 ⟶ 0 1 0 1 2 0 0 2 1 0 2 0 2 1 1 0 1 1 2 1 ,
  1 0 2 0 1 1 0 1 2 1 1 0 1 0 2 1 1 0 2 1 ⟶ 1 1 1 0 0 1 0 0 2 0 1 1 0 1 1 1 0 2 0 1 ,
  1 1 2 2 1 2 2 2 1 2 0 1 2 2 0 1 1 0 2 1 ⟶ 2 2 0 1 1 2 0 1 1 0 1 0 0 2 2 1 0 1 1 1 ,
  2 0 2 1 0 2 2 2 0 0 2 0 1 0 1 2 1 0 2 1 ⟶ 2 0 2 2 0 2 0 1 1 1 1 2 1 1 1 0 0 0 1 1 ,
  1 1 1 0 1 1 1 0 0 2 2 2 0 1 1 0 1 0 2 1 ⟶ 1 2 1 2 0 2 1 0 0 2 1 2 2 1 2 0 1 1 2 1 ,
  2 2 1 2 0 0 2 2 1 1 2 2 0 0 2 1 2 0 2 1 ⟶ 1 2 1 1 2 0 0 0 2 0 2 1 0 1 0 1 0 0 0 1 ,
  0 2 1 0 0 2 1 0 1 1 2 0 2 2 2 1 0 0 2 1 ⟶ 1 1 0 2 1 0 1 2 2 2 1 2 0 0 1 0 1 1 0 1 ,
  0 1 1 0 1 1 2 1 2 0 2 1 0 1 1 0 0 0 2 1 ⟶ 0 2 1 1 2 1 2 1 1 1 0 0 2 0 1 0 2 1 1 1 ,
  2 2 0 2 0 2 2 0 0 1 2 0 0 0 0 0 0 0 2 1 ⟶ 2 1 1 1 1 1 0 2 1 1 1 0 2 1 2 0 1 2 0 1 ,
  1 1 2 1 1 1 1 2 2 0 0 1 2 2 0 1 1 1 0 1 ⟶ 0 2 0 2 0 1 0 1 1 0 0 0 0 1 1 1 2 0 1 1 ,
  0 2 2 0 2 0 1 2 1 0 0 1 2 0 1 2 1 1 0 1 ⟶ 1 1 1 1 2 1 0 2 1 2 0 2 0 1 2 0 1 2 0 1 ,
  1 0 0 0 1 2 0 1 1 2 1 2 2 2 1 2 2 1 0 1 ⟶ 0 2 0 2 0 0 2 0 2 1 0 1 1 0 1 1 0 0 0 1 ,
  2 1 0 2 0 1 0 1 0 1 0 0 2 1 2 2 2 1 0 1 ⟶ 2 0 0 0 1 1 0 2 0 1 2 0 0 0 0 2 1 0 0 1 ,
  2 1 0 0 2 1 0 2 0 1 0 2 2 2 2 0 2 1 0 1 ⟶ 2 1 1 0 1 1 2 0 1 2 2 1 1 2 0 2 2 2 2 1 ,
  1 0 1 0 2 2 2 2 0 1 2 2 0 1 0 1 0 1 0 1 ⟶ 1 1 0 0 2 1 1 0 0 0 1 1 2 2 0 2 0 1 2 1 ,
  2 1 0 1 2 2 0 2 2 2 1 0 0 2 0 1 0 1 0 1 ⟶ 1 2 2 0 0 1 1 1 0 2 2 0 1 2 2 2 1 1 0 1 ,
  2 0 0 2 2 2 1 2 1 0 1 0 2 1 1 2 0 1 0 1 ⟶ 1 2 1 0 0 0 2 1 1 1 2 0 2 2 1 2 1 2 1 1 ,
  1 0 2 1 1 0 2 0 2 0 1 1 1 0 2 2 0 1 0 1 ⟶ 0 2 1 1 1 1 2 0 1 1 1 1 2 1 0 2 1 0 0 1 ,
  2 2 2 2 2 0 2 2 2 0 1 0 0 2 0 2 0 1 0 1 ⟶ 2 1 0 2 2 0 1 1 1 2 0 2 1 2 0 1 2 2 2 1 ,
  2 2 0 0 0 0 0 0 1 0 2 1 1 0 0 2 1 2 0 1 ⟶ 0 1 2 1 0 0 1 1 1 0 2 1 1 1 0 0 2 1 1 1 ,
  2 2 0 0 2 2 2 1 0 0 2 2 2 2 0 1 2 2 0 1 ⟶ 2 0 0 1 0 1 1 2 2 1 2 0 0 1 2 1 1 0 1 1 ,
  0 2 1 2 0 1 0 2 2 0 2 0 2 1 1 2 2 2 0 1 ⟶ 0 0 0 2 1 1 1 0 2 2 2 1 1 1 0 1 2 1 2 1 ,
  2 0 1 0 1 1 0 0 1 2 1 2 2 0 1 2 2 2 0 1 ⟶ 2 0 1 1 1 1 0 2 0 0 1 2 2 0 0 0 2 1 2 1 ,
  2 0 1 2 0 1 1 0 2 0 1 1 1 1 2 2 2 2 0 1 ⟶ 2 0 1 2 0 0 0 0 1 1 0 1 0 2 2 1 2 1 1 1 ,
  1 0 1 2 0 0 2 1 2 0 1 1 1 0 0 2 2 2 0 1 ⟶ 2 0 1 0 2 0 1 1 2 2 0 1 2 1 1 1 2 1 2 1 ,
  2 1 1 0 0 1 0 1 0 2 1 0 0 0 1 0 2 2 0 1 ⟶ 1 2 2 2 1 2 0 0 0 2 1 0 1 1 1 0 2 0 1 1 ,
  1 0 0 2 2 2 0 1 2 1 1 0 0 0 2 0 2 2 0 1 ⟶ 1 2 2 1 1 1 0 2 2 2 0 2 0 2 1 2 0 1 1 1 ,
  1 0 1 0 1 0 2 0 2 2 1 0 2 2 2 1 0 2 0 1 ⟶ 0 0 1 0 0 2 1 2 1 0 2 0 2 2 1 2 2 0 2 1 ,
  2 1 1 1 2 0 2 1 2 2 1 0 0 2 2 1 0 2 0 1 ⟶ 2 0 1 1 2 1 1 1 2 0 2 1 0 1 0 1 1 2 1 1 ,
  1 2 0 0 2 2 1 0 1 0 1 0 1 2 0 1 1 0 0 1 ⟶ 2 1 2 1 2 1 0 0 2 1 0 2 1 1 1 1 1 1 0 1 ,
  0 2 1 2 0 0 0 2 2 0 2 2 1 0 0 2 1 0 0 1 ⟶ 0 0 2 2 0 0 1 2 1 2 2 2 1 0 1 1 1 2 0 1 ,
  1 0 2 1 0 1 0 0 1 0 0 0 2 2 1 0 1 0 0 1 ⟶ 0 1 1 1 1 2 2 1 2 2 2 1 1 0 1 1 1 2 2 1 ,
  1 1 2 0 0 2 2 1 0 0 1 0 2 2 1 1 2 0 0 1 ⟶ 2 2 0 2 2 1 2 0 2 1 1 1 1 1 0 0 1 2 0 1 ,
  2 0 0 2 2 0 0 1 2 1 2 1 1 2 2 2 2 0 0 1 ⟶ 0 1 0 1 1 0 1 0 0 0 0 2 2 0 0 1 0 0 0 1 ,
  2 2 0 1 2 1 2 1 0 1 2 1 2 1 0 2 2 0 0 1 ⟶ 1 0 1 1 1 0 0 2 2 0 0 1 1 2 2 1 1 2 2 1 ,
  1 0 1 0 0 0 2 2 0 2 0 1 2 0 0 2 2 0 0 1 ⟶ 2 0 0 2 2 0 2 1 1 1 2 1 1 2 0 0 0 2 0 1 ,
  0 0 0 1 2 2 1 0 2 2 1 1 2 2 1 0 2 0 0 1 ⟶ 2 2 0 1 1 2 2 0 1 1 0 0 1 1 0 1 0 0 0 1 ,
  0 0 2 1 2 2 2 1 2 0 0 1 1 1 2 0 0 0 0 1 ⟶ 0 2 2 0 1 1 1 1 0 2 2 1 0 1 0 1 0 0 1 1 ,
  2 1 0 1 1 2 1 1 2 0 2 0 2 0 1 0 1 0 0 2 ⟶ 0 1 1 2 1 1 2 0 1 1 1 2 1 1 2 1 0 2 1 2 }

Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,2) ↦ 3, (2,0) ↦ 4, (0,2) ↦ 5, (2,1) ↦ 6, (1,0) ↦ 7, (1,1) ↦ 8, (1,4) ↦ 9, (3,0) ↦ 10, (3,2) ↦ 11, (3,1) ↦ 12, (2,4) ↦ 13 },
it remains to prove termination of the 1584-rule system
{ 0 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 7 ⟶ 0 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 7 ,
  0 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 8 ⟶ 0 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 8 ,
  0 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 2 ⟶ 0 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 2 ,
  0 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 9 ⟶ 0 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 9 ,
  7 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 7 ⟶ 7 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 7 ,
  7 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 8 ⟶ 7 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 8 ,
  7 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 2 ⟶ 7 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 2 ,
  7 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 9 ⟶ 7 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 9 ,
  4 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 7 ⟶ 4 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 7 ,
  4 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 8 ⟶ 4 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 8 ,
  4 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 2 ⟶ 4 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 2 ,
  4 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 9 ⟶ 4 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 9 ,
  10 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 7 ⟶ 10 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 7 ,
  10 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 8 ⟶ 10 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 8 ,
  10 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 2 ⟶ 10 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 2 ,
  10 0 1 2 3 3 3 3 4 0 5 6 7 1 7 5 6 8 8 8 9 ⟶ 10 5 6 2 3 4 1 7 1 8 7 1 8 2 6 2 6 8 7 1 9 ,
  5 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 7 ⟶ 5 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 7 ,
  5 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 8 ⟶ 5 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 8 ,
  5 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 2 ⟶ 5 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 2 ,
  5 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 9 ⟶ 5 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 9 ,
  2 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 7 ⟶ 2 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 7 ,
  2 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 8 ⟶ 2 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 8 ,
  2 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 2 ⟶ 2 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 2 ,
  2 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 9 ⟶ 2 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 9 ,
  3 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 7 ⟶ 3 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 7 ,
  3 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 8 ⟶ 3 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 8 ,
  3 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 2 ⟶ 3 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 2 ,
  3 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 9 ⟶ 3 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 9 ,
  11 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 7 ⟶ 11 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 7 ,
  11 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 8 ⟶ 11 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 8 ,
  11 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 2 ⟶ 11 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 2 ,
  11 3 4 0 5 3 4 5 3 6 7 5 4 1 7 1 2 6 8 8 9 ⟶ 11 4 5 4 5 4 5 4 1 2 6 2 3 3 4 0 1 7 5 6 9 ,
  5 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 7 ⟶ 0 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 7 ,
  5 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 8 ⟶ 0 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 8 ,
  5 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 2 ⟶ 0 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 2 ,
  5 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 9 ⟶ 0 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 9 ,
  2 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 7 ⟶ 7 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 7 ,
  2 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 8 ⟶ 7 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 8 ,
  2 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 2 ⟶ 7 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 2 ,
  2 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 9 ⟶ 7 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 9 ,
  3 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 7 ⟶ 4 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 7 ,
  3 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 8 ⟶ 4 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 8 ,
  3 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 2 ⟶ 4 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 2 ,
  3 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 9 ⟶ 4 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 9 ,
  11 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 7 ⟶ 10 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 7 ,
  11 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 8 ⟶ 10 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 8 ,
  11 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 2 ⟶ 10 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 2 ,
  11 3 3 3 6 7 5 6 2 6 2 3 4 0 1 7 5 6 8 8 9 ⟶ 10 1 2 3 3 3 6 7 1 2 6 2 6 2 4 5 6 7 5 6 9 ,
  0 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 7 ⟶ 0 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 7 ,
  0 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 8 ⟶ 0 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 8 ,
  0 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 2 ⟶ 0 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 2 ,
  0 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 9 ⟶ 0 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 9 ,
  7 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 7 ⟶ 7 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 7 ,
  7 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 8 ⟶ 7 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 8 ,
  7 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 2 ⟶ 7 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 2 ,
  7 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 9 ⟶ 7 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 9 ,
  4 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 7 ⟶ 4 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 7 ,
  4 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 8 ⟶ 4 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 8 ,
  4 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 2 ⟶ 4 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 2 ,
  4 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 9 ⟶ 4 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 9 ,
  10 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 7 ⟶ 10 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 7 ,
  10 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 8 ⟶ 10 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 8 ,
  10 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 2 ⟶ 10 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 2 ,
  10 5 3 3 6 8 8 2 3 4 0 5 4 1 8 8 7 1 8 8 9 ⟶ 10 5 6 8 8 8 8 7 5 3 4 0 0 1 2 6 2 4 0 1 9 ,
  5 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 7 ⟶ 1 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 7 ,
  5 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 8 ⟶ 1 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 8 ,
  5 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 2 ⟶ 1 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 2 ,
  5 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 9 ⟶ 1 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 9 ,
  2 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 7 ⟶ 8 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 7 ,
  2 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 8 ⟶ 8 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 8 ,
  2 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 2 ⟶ 8 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 2 ,
  2 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 9 ⟶ 8 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 9 ,
  3 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 7 ⟶ 6 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 7 ,
  3 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 8 ⟶ 6 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 8 ,
  3 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 2 ⟶ 6 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 2 ,
  3 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 9 ⟶ 6 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 9 ,
  11 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 7 ⟶ 12 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 7 ,
  11 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 8 ⟶ 12 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 8 ,
  11 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 2 ⟶ 12 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 2 ,
  11 4 0 1 2 4 5 3 6 8 2 3 6 7 0 5 4 1 8 8 9 ⟶ 12 2 6 7 1 7 0 1 2 4 5 4 5 6 7 5 3 6 7 1 9 ,
  0 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 7 ⟶ 0 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 7 ,
  0 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 8 ⟶ 0 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 8 ,
  0 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 2 ⟶ 0 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 2 ,
  0 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 9 ⟶ 0 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 9 ,
  7 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 7 ⟶ 7 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 7 ,
  7 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 8 ⟶ 7 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 8 ,
  7 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 2 ⟶ 7 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 2 ,
  7 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 9 ⟶ 7 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 9 ,
  4 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 7 ⟶ 4 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 7 ,
  4 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 8 ⟶ 4 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 8 ,
  4 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 2 ⟶ 4 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 2 ,
  4 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 9 ⟶ 4 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 9 ,
  10 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 7 ⟶ 10 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 7 ,
  10 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 8 ⟶ 10 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 8 ,
  10 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 2 ⟶ 10 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 2 ,
  10 0 1 2 3 6 7 5 4 1 8 7 0 5 3 4 0 1 8 8 9 ⟶ 10 1 7 5 3 3 4 5 4 5 4 5 4 1 8 2 4 0 0 1 9 ,
  0 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 7 ⟶ 0 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 7 ,
  0 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 8 ⟶ 0 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 8 ,
  0 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 2 ⟶ 0 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 2 ,
  0 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 9 ⟶ 0 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 9 ,
  7 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 7 ⟶ 7 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 7 ,
  7 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 8 ⟶ 7 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 8 ,
  7 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 2 ⟶ 7 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 2 ,
  7 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 9 ⟶ 7 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 9 ,
  4 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 7 ⟶ 4 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 7 ,
  4 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 8 ⟶ 4 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 8 ,
  4 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 2 ⟶ 4 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 2 ,
  4 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 9 ⟶ 4 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 9 ,
  10 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 7 ⟶ 10 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 7 ,
  10 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 8 ⟶ 10 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 8 ,
  10 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 2 ⟶ 10 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 2 ,
  10 1 2 3 4 0 5 3 4 0 5 3 4 5 3 6 8 2 6 8 9 ⟶ 10 1 7 1 2 3 3 3 3 4 1 7 1 8 7 1 8 2 3 6 9 ,
  5 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 7 ⟶ 1 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 7 ,
  5 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 8 ⟶ 1 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 8 ,
  5 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 2 ⟶ 1 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 2 ,
  5 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 9 ⟶ 1 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 9 ,
  2 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 7 ⟶ 8 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 7 ,
  2 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 8 ⟶ 8 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 8 ,
  2 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 2 ⟶ 8 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 2 ,
  2 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 9 ⟶ 8 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 9 ,
  3 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 7 ⟶ 6 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 7 ,
  3 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 8 ⟶ 6 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 8 ,
  3 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 2 ⟶ 6 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 2 ,
  3 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 9 ⟶ 6 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 9 ,
  11 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 7 ⟶ 12 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 7 ,
  11 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 8 ⟶ 12 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 8 ,
  11 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 2 ⟶ 12 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 2 ,
  11 4 1 2 4 0 0 5 3 4 5 6 8 7 1 2 6 2 6 8 9 ⟶ 12 7 1 8 2 4 1 7 5 6 8 7 1 8 8 2 6 2 4 1 9 ,
  1 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 7 ⟶ 0 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 7 ,
  1 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 8 ⟶ 0 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 8 ,
  1 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 2 ⟶ 0 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 2 ,
  1 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 9 ⟶ 0 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 9 ,
  8 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 7 ⟶ 7 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 7 ,
  8 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 8 ⟶ 7 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 8 ,
  8 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 2 ⟶ 7 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 2 ,
  8 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 9 ⟶ 7 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 9 ,
  6 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 7 ⟶ 4 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 7 ,
  6 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 8 ⟶ 4 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 8 ,
  6 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 2 ⟶ 4 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 2 ,
  6 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 9 ⟶ 4 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 9 ,
  12 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 7 ⟶ 10 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 7 ,
  12 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 8 ⟶ 10 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 8 ,
  12 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 2 ⟶ 10 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 2 ,
  12 7 5 6 7 1 2 4 5 4 5 3 4 0 0 5 6 2 6 8 9 ⟶ 10 1 7 1 8 8 8 2 4 1 8 2 4 0 0 5 3 6 7 1 9 ,
  0 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 7 ⟶ 1 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 7 ,
  0 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 8 ⟶ 1 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 8 ,
  0 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 2 ⟶ 1 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 2 ,
  0 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 9 ⟶ 1 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 9 ,
  7 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 7 ⟶ 8 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 7 ,
  7 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 8 ⟶ 8 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 8 ,
  7 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 2 ⟶ 8 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 2 ,
  7 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 9 ⟶ 8 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 9 ,
  4 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 7 ⟶ 6 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 7 ,
  4 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 8 ⟶ 6 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 8 ,
  4 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 2 ⟶ 6 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 2 ,
  4 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 9 ⟶ 6 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 9 ,
  10 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 7 ⟶ 12 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 7 ,
  10 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 8 ⟶ 12 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 8 ,
  10 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 2 ⟶ 12 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 2 ,
  10 5 3 4 5 4 0 1 8 8 2 3 3 4 1 7 1 2 6 8 9 ⟶ 12 7 1 7 0 1 2 4 5 4 5 3 4 1 7 0 1 8 7 1 9 ,
  0 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 7 ⟶ 0 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 7 ,
  0 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 8 ⟶ 0 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 8 ,
  0 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 2 ⟶ 0 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 2 ,
  0 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 9 ⟶ 0 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 9 ,
  7 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 7 ⟶ 7 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 7 ,
  7 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 8 ⟶ 7 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 8 ,
  7 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 2 ⟶ 7 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 2 ,
  7 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 9 ⟶ 7 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 9 ,
  4 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 7 ⟶ 4 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 7 ,
  4 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 8 ⟶ 4 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 8 ,
  4 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 2 ⟶ 4 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 2 ,
  4 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 9 ⟶ 4 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 9 ,
  10 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 7 ⟶ 10 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 7 ,
  10 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 8 ⟶ 10 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 8 ,
  10 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 2 ⟶ 10 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 2 ,
  10 1 7 0 5 3 6 7 5 6 7 0 0 0 5 4 1 2 6 8 9 ⟶ 10 1 7 0 5 6 7 0 5 6 7 0 0 1 8 2 3 4 1 8 9 ,
  5 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 7 ⟶ 5 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 7 ,
  5 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 8 ⟶ 5 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 8 ,
  5 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 2 ⟶ 5 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 2 ,
  5 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 9 ⟶ 5 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 9 ,
  2 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 7 ⟶ 2 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 7 ,
  2 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 8 ⟶ 2 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 8 ,
  2 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 2 ⟶ 2 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 2 ,
  2 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 9 ⟶ 2 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 9 ,
  3 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 7 ⟶ 3 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 7 ,
  3 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 8 ⟶ 3 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 8 ,
  3 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 2 ⟶ 3 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 2 ,
  3 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 9 ⟶ 3 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 9 ,
  11 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 7 ⟶ 11 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 7 ,
  11 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 8 ⟶ 11 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 8 ,
  11 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 2 ⟶ 11 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 2 ,
  11 3 4 5 3 4 0 0 5 3 6 8 7 5 4 0 1 2 6 8 9 ⟶ 11 3 4 1 8 2 3 6 8 7 1 7 5 6 8 7 0 1 7 1 9 ,
  5 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 7 ⟶ 5 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 7 ,
  5 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 8 ⟶ 5 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 8 ,
  5 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 2 ⟶ 5 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 2 ,
  5 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 9 ⟶ 5 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 9 ,
  2 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 7 ⟶ 2 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 7 ,
  2 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 8 ⟶ 2 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 8 ,
  2 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 2 ⟶ 2 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 2 ,
  2 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 9 ⟶ 2 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 9 ,
  3 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 7 ⟶ 3 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 7 ,
  3 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 8 ⟶ 3 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 8 ,
  3 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 2 ⟶ 3 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 2 ,
  3 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 9 ⟶ 3 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 9 ,
  11 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 7 ⟶ 11 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 7 ,
  11 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 8 ⟶ 11 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 8 ,
  11 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 2 ⟶ 11 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 2 ,
  11 4 5 3 6 7 0 1 2 4 1 2 4 0 0 0 1 2 6 8 9 ⟶ 11 3 4 1 8 2 6 8 8 7 0 0 0 1 8 8 8 2 6 8 9 ,
  5 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 7 ⟶ 1 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 7 ,
  5 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 8 ⟶ 1 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 8 ,
  5 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 2 ⟶ 1 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 2 ,
  5 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 9 ⟶ 1 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 9 ,
  2 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 7 ⟶ 8 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 7 ,
  2 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 8 ⟶ 8 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 8 ,
  2 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 2 ⟶ 8 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 2 ,
  2 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 9 ⟶ 8 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 9 ,
  3 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 7 ⟶ 6 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 7 ,
  3 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 8 ⟶ 6 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 8 ,
  3 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 2 ⟶ 6 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 2 ,
  3 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 9 ⟶ 6 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 9 ,
  11 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 7 ⟶ 12 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 7 ,
  11 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 8 ⟶ 12 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 8 ,
  11 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 2 ⟶ 12 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 2 ,
  11 4 0 1 2 4 1 7 5 3 3 3 3 4 0 1 2 3 6 8 9 ⟶ 12 8 8 7 1 7 0 0 1 8 7 0 0 5 6 2 3 6 7 1 9 ,
  5 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 7 ⟶ 5 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 7 ,
  5 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 8 ⟶ 5 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 8 ,
  5 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 2 ⟶ 5 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 2 ,
  5 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 9 ⟶ 5 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 9 ,
  2 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 7 ⟶ 2 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 7 ,
  2 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 8 ⟶ 2 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 8 ,
  2 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 2 ⟶ 2 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 2 ,
  2 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 9 ⟶ 2 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 9 ,
  3 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 7 ⟶ 3 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 7 ,
  3 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 8 ⟶ 3 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 8 ,
  3 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 2 ⟶ 3 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 2 ,
  3 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 9 ⟶ 3 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 9 ,
  11 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 7 ⟶ 11 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 7 ,
  11 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 8 ⟶ 11 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 8 ,
  11 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 2 ⟶ 11 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 2 ,
  11 4 5 3 4 0 0 5 3 4 0 0 0 1 2 3 3 3 6 8 9 ⟶ 11 3 4 0 1 8 8 7 1 7 0 1 7 0 5 3 6 8 2 6 9 ,
  0 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 7 ⟶ 0 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 7 ,
  0 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 8 ⟶ 0 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 8 ,
  0 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 2 ⟶ 0 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 2 ,
  0 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 9 ⟶ 0 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 9 ,
  7 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 7 ⟶ 7 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 7 ,
  7 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 8 ⟶ 7 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 8 ,
  7 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 2 ⟶ 7 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 2 ,
  7 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 9 ⟶ 7 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 9 ,
  4 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 7 ⟶ 4 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 7 ,
  4 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 8 ⟶ 4 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 8 ,
  4 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 2 ⟶ 4 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 2 ,
  4 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 9 ⟶ 4 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 9 ,
  10 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 7 ⟶ 10 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 7 ,
  10 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 8 ⟶ 10 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 8 ,
  10 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 2 ⟶ 10 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 2 ,
  10 5 3 4 1 2 4 0 1 2 3 3 6 7 5 6 7 5 6 8 9 ⟶ 10 5 3 3 6 8 2 4 0 5 6 2 4 0 0 1 7 0 5 6 9 ,
  1 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 7 ⟶ 1 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 7 ,
  1 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 8 ⟶ 1 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 8 ,
  1 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 2 ⟶ 1 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 2 ,
  1 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 9 ⟶ 1 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 9 ,
  8 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 7 ⟶ 8 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 7 ,
  8 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 8 ⟶ 8 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 8 ,
  8 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 2 ⟶ 8 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 2 ,
  8 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 9 ⟶ 8 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 9 ,
  6 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 7 ⟶ 6 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 7 ,
  6 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 8 ⟶ 6 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 8 ,
  6 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 2 ⟶ 6 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 2 ,
  6 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 9 ⟶ 6 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 9 ,
  12 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 7 ⟶ 12 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 7 ,
  12 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 8 ⟶ 12 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 8 ,
  12 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 2 ⟶ 12 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 2 ,
  12 2 4 5 4 1 2 4 0 1 8 7 5 3 6 7 0 5 6 8 9 ⟶ 12 7 1 8 8 2 4 0 1 8 7 1 2 4 1 7 1 7 0 1 9 ,
  0 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 7 ⟶ 1 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 7 ,
  0 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 8 ⟶ 1 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 8 ,
  0 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 2 ⟶ 1 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 2 ,
  0 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 9 ⟶ 1 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 9 ,
  7 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 7 ⟶ 8 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 7 ,
  7 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 8 ⟶ 8 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 8 ,
  7 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 2 ⟶ 8 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 2 ,
  7 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 9 ⟶ 8 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 9 ,
  4 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 7 ⟶ 6 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 7 ,
  4 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 8 ⟶ 6 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 8 ,
  4 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 2 ⟶ 6 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 2 ,
  4 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 9 ⟶ 6 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 9 ,
  10 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 7 ⟶ 12 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 7 ,
  10 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 8 ⟶ 12 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 8 ,
  10 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 2 ⟶ 12 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 2 ,
  10 1 7 0 0 5 4 5 6 8 2 3 3 6 2 4 0 5 6 8 9 ⟶ 12 8 8 8 8 8 2 6 8 7 0 1 7 1 8 7 0 5 3 6 9 ,
  5 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 7 ⟶ 1 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 7 ,
  5 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 8 ⟶ 1 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 8 ,
  5 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 2 ⟶ 1 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 2 ,
  5 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 9 ⟶ 1 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 9 ,
  2 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 7 ⟶ 8 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 7 ,
  2 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 8 ⟶ 8 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 8 ,
  2 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 2 ⟶ 8 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 2 ,
  2 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 9 ⟶ 8 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 9 ,
  3 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 7 ⟶ 6 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 7 ,
  3 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 8 ⟶ 6 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 8 ,
  3 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 2 ⟶ 6 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 2 ,
  3 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 9 ⟶ 6 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 9 ,
  11 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 7 ⟶ 12 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 7 ,
  11 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 8 ⟶ 12 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 8 ,
  11 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 2 ⟶ 12 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 2 ,
  11 4 5 6 2 3 3 3 6 7 0 0 1 2 3 4 0 5 6 8 9 ⟶ 12 7 5 4 1 7 5 6 8 7 1 7 5 3 3 6 7 0 5 6 9 ,
  1 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 7 ⟶ 1 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 7 ,
  1 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 8 ⟶ 1 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 8 ,
  1 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 2 ⟶ 1 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 2 ,
  1 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 9 ⟶ 1 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 9 ,
  8 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 7 ⟶ 8 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 7 ,
  8 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 8 ⟶ 8 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 8 ,
  8 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 2 ⟶ 8 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 2 ,
  8 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 9 ⟶ 8 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 9 ,
  6 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 7 ⟶ 6 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 7 ,
  6 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 8 ⟶ 6 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 8 ,
  6 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 2 ⟶ 6 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 2 ,
  6 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 9 ⟶ 6 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 9 ,
  12 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 7 ⟶ 12 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 7 ,
  12 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 8 ⟶ 12 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 8 ,
  12 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 2 ⟶ 12 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 2 ,
  12 8 2 3 4 1 2 3 3 4 0 0 5 4 1 8 8 7 1 8 9 ⟶ 12 8 8 2 4 5 4 0 5 6 2 6 7 5 6 7 5 6 7 1 9 ,
  5 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 7 ⟶ 5 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 7 ,
  5 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 8 ⟶ 5 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 8 ,
  5 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 2 ⟶ 5 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 2 ,
  5 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 9 ⟶ 5 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 9 ,
  2 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 7 ⟶ 2 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 7 ,
  2 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 8 ⟶ 2 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 8 ,
  2 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 2 ⟶ 2 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 2 ,
  2 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 9 ⟶ 2 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 9 ,
  3 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 7 ⟶ 3 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 7 ,
  3 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 8 ⟶ 3 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 8 ,
  3 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 2 ⟶ 3 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 2 ,
  3 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 9 ⟶ 3 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 9 ,
  11 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 7 ⟶ 11 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 7 ,
  11 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 8 ⟶ 11 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 8 ,
  11 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 2 ⟶ 11 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 2 ,
  11 6 7 5 6 2 3 4 0 1 2 4 1 7 5 3 6 7 1 8 9 ⟶ 11 6 2 6 2 4 0 1 8 2 4 5 6 2 6 7 1 7 5 6 9 ,
  5 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 7 ⟶ 5 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 7 ,
  5 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 8 ⟶ 5 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 8 ,
  5 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 2 ⟶ 5 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 2 ,
  5 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 9 ⟶ 5 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 9 ,
  2 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 7 ⟶ 2 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 7 ,
  2 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 8 ⟶ 2 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 8 ,
  2 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 2 ⟶ 2 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 2 ,
  2 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 9 ⟶ 2 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 9 ,
  3 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 7 ⟶ 3 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 7 ,
  3 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 8 ⟶ 3 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 8 ,
  3 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 2 ⟶ 3 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 2 ,
  3 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 9 ⟶ 3 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 9 ,
  11 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 7 ⟶ 11 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 7 ,
  11 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 8 ⟶ 11 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 8 ,
  11 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 2 ⟶ 11 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 2 ,
  11 6 2 3 4 0 1 8 7 0 5 6 8 7 0 5 6 7 1 8 9 ⟶ 11 6 7 1 8 8 8 8 7 1 7 1 2 3 6 8 7 5 6 8 9 ,
  5 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 7 ⟶ 0 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 7 ,
  5 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 8 ⟶ 0 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 8 ,
  5 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 2 ⟶ 0 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 2 ,
  5 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 9 ⟶ 0 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 9 ,
  2 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 7 ⟶ 7 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 7 ,
  2 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 8 ⟶ 7 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 8 ,
  2 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 2 ⟶ 7 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 2 ,
  2 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 9 ⟶ 7 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 9 ,
  3 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 7 ⟶ 4 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 7 ,
  3 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 8 ⟶ 4 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 8 ,
  3 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 2 ⟶ 4 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 2 ,
  3 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 9 ⟶ 4 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 9 ,
  11 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 7 ⟶ 10 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 7 ,
  11 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 8 ⟶ 10 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 8 ,
  11 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 2 ⟶ 10 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 2 ,
  11 4 0 5 3 3 6 2 3 3 3 3 4 5 3 4 1 7 1 8 9 ⟶ 10 5 3 3 4 0 0 5 6 7 1 7 0 5 3 4 1 8 7 1 9 ,
  1 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 7 ⟶ 1 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 7 ,
  1 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 8 ⟶ 1 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 8 ,
  1 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 2 ⟶ 1 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 2 ,
  1 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 9 ⟶ 1 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 9 ,
  8 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 7 ⟶ 8 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 7 ,
  8 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 8 ⟶ 8 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 8 ,
  8 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 2 ⟶ 8 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 2 ,
  8 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 9 ⟶ 8 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 9 ,
  6 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 7 ⟶ 6 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 7 ,
  6 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 8 ⟶ 6 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 8 ,
  6 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 2 ⟶ 6 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 2 ,
  6 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 9 ⟶ 6 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 9 ,
  12 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 7 ⟶ 12 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 7 ,
  12 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 8 ⟶ 12 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 8 ,
  12 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 2 ⟶ 12 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 2 ,
  12 7 0 0 0 1 7 1 2 3 6 7 1 8 2 6 2 4 1 8 9 ⟶ 12 8 8 2 3 6 7 5 3 6 8 8 2 4 1 8 8 7 0 1 9 ,
  1 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 7 ⟶ 1 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 7 ,
  1 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 8 ⟶ 1 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 8 ,
  1 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 2 ⟶ 1 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 2 ,
  1 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 9 ⟶ 1 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 9 ,
  8 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 7 ⟶ 8 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 7 ,
  8 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 8 ⟶ 8 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 8 ,
  8 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 2 ⟶ 8 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 2 ,
  8 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 9 ⟶ 8 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 9 ,
  6 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 7 ⟶ 6 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 7 ,
  6 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 8 ⟶ 6 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 8 ,
  6 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 2 ⟶ 6 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 2 ,
  6 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 9 ⟶ 6 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 9 ,
  12 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 7 ⟶ 12 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 7 ,
  12 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 8 ⟶ 12 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 8 ,
  12 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 2 ⟶ 12 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 2 ,
  12 8 2 4 1 8 7 0 5 3 3 3 4 0 1 2 3 4 1 8 9 ⟶ 12 8 8 2 4 5 3 4 5 4 5 6 2 4 5 3 3 4 0 1 9 ,
  5 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 7 ⟶ 5 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 7 ,
  5 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 8 ⟶ 5 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 8 ,
  5 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 2 ⟶ 5 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 2 ,
  5 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 9 ⟶ 5 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 9 ,
  2 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 7 ⟶ 2 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 7 ,
  2 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 8 ⟶ 2 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 8 ,
  2 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 2 ⟶ 2 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 2 ,
  2 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 9 ⟶ 2 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 9 ,
  3 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 7 ⟶ 3 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 7 ,
  3 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 8 ⟶ 3 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 8 ,
  3 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 2 ⟶ 3 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 2 ,
  3 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 9 ⟶ 3 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 9 ,
  11 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 7 ⟶ 11 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 7 ,
  11 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 8 ⟶ 11 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 8 ,
  11 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 2 ⟶ 11 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 2 ,
  11 6 7 0 1 2 4 0 5 3 4 0 1 2 6 8 7 0 1 8 9 ⟶ 11 4 1 7 1 8 2 3 4 5 4 0 1 8 2 4 0 1 7 1 9 ,
  0 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 7 ⟶ 1 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 7 ,
  0 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 8 ⟶ 1 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 8 ,
  0 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 2 ⟶ 1 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 2 ,
  0 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 9 ⟶ 1 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 9 ,
  7 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 7 ⟶ 8 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 7 ,
  7 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 8 ⟶ 8 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 8 ,
  7 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 2 ⟶ 8 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 2 ,
  7 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 9 ⟶ 8 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 9 ,
  4 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 7 ⟶ 6 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 7 ,
  4 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 8 ⟶ 6 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 8 ,
  4 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 2 ⟶ 6 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 2 ,
  4 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 9 ⟶ 6 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 9 ,
  10 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 7 ⟶ 12 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 7 ,
  10 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 8 ⟶ 12 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 8 ,
  10 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 2 ⟶ 12 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 2 ,
  10 1 7 5 3 4 0 0 5 3 4 5 4 1 2 6 7 0 1 8 9 ⟶ 12 7 5 6 8 8 2 4 5 6 7 5 4 5 4 5 4 5 6 8 9 ,
  1 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 7 ⟶ 0 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 7 ,
  1 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 8 ⟶ 0 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 8 ,
  1 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 2 ⟶ 0 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 2 ,
  1 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 9 ⟶ 0 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 9 ,
  8 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 7 ⟶ 7 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 7 ,
  8 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 8 ⟶ 7 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 8 ,
  8 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 2 ⟶ 7 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 2 ,
  8 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 9 ⟶ 7 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 9 ,
  6 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 7 ⟶ 4 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 7 ,
  6 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 8 ⟶ 4 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 8 ,
  6 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 2 ⟶ 4 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 2 ,
  6 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 9 ⟶ 4 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 9 ,
  12 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 7 ⟶ 10 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 7 ,
  12 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 8 ⟶ 10 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 8 ,
  12 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 2 ⟶ 10 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 2 ,
  12 8 7 5 4 0 0 5 6 2 6 2 6 2 3 3 4 0 1 8 9 ⟶ 10 5 3 3 6 2 4 5 4 1 2 6 2 4 0 1 7 1 2 6 9 ,
  1 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 7 ⟶ 1 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 7 ,
  1 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 8 ⟶ 1 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 8 ,
  1 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 2 ⟶ 1 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 2 ,
  1 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 9 ⟶ 1 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 9 ,
  8 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 7 ⟶ 8 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 7 ,
  8 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 8 ⟶ 8 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 8 ,
  8 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 2 ⟶ 8 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 2 ,
  8 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 9 ⟶ 8 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 9 ,
  6 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 7 ⟶ 6 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 7 ,
  6 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 8 ⟶ 6 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 8 ,
  6 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 2 ⟶ 6 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 2 ,
  6 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 9 ⟶ 6 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 9 ,
  12 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 7 ⟶ 12 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 7 ,
  12 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 8 ⟶ 12 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 8 ,
  12 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 2 ⟶ 12 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 2 ,
  12 8 8 7 0 1 8 8 2 6 7 0 5 6 7 5 4 0 1 8 9 ⟶ 12 8 8 2 6 2 6 7 1 7 0 0 1 8 8 7 1 8 8 8 9 ,
  1 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 7 ⟶ 1 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 7 ,
  1 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 8 ⟶ 1 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 8 ,
  1 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 2 ⟶ 1 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 2 ,
  1 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 9 ⟶ 1 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 9 ,
  8 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 7 ⟶ 8 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 7 ,
  8 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 8 ⟶ 8 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 8 ,
  8 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 2 ⟶ 8 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 2 ,
  8 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 9 ⟶ 8 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 9 ,
  6 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 7 ⟶ 6 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 7 ,
  6 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 8 ⟶ 6 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 8 ,
  6 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 2 ⟶ 6 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 2 ,
  6 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 9 ⟶ 6 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 9 ,
  12 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 7 ⟶ 12 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 7 ,
  12 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 8 ⟶ 12 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 8 ,
  12 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 2 ⟶ 12 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 2 ,
  12 7 5 3 6 8 8 2 6 2 3 3 6 2 6 7 0 0 1 8 9 ⟶ 12 8 7 1 8 8 8 8 8 2 4 0 1 7 0 0 0 1 7 1 9 ,
  5 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 7 ⟶ 0 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 7 ,
  5 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 8 ⟶ 0 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 8 ,
  5 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 2 ⟶ 0 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 2 ,
  5 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 9 ⟶ 0 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 9 ,
  2 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 7 ⟶ 7 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 7 ,
  2 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 8 ⟶ 7 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 8 ,
  2 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 2 ⟶ 7 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 2 ,
  2 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 9 ⟶ 7 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 9 ,
  3 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 7 ⟶ 4 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 7 ,
  3 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 8 ⟶ 4 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 8 ,
  3 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 2 ⟶ 4 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 2 ,
  3 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 9 ⟶ 4 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 9 ,
  11 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 7 ⟶ 10 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 7 ,
  11 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 8 ⟶ 10 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 8 ,
  11 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 2 ⟶ 10 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 2 ,
  11 4 0 5 3 3 3 4 0 5 4 0 5 4 1 2 6 8 2 6 9 ⟶ 10 5 4 1 8 7 5 3 4 0 1 8 8 2 6 2 3 3 6 8 9 ,
  5 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 7 ⟶ 5 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 7 ,
  5 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 8 ⟶ 5 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 8 ,
  5 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 2 ⟶ 5 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 2 ,
  5 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 9 ⟶ 5 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 9 ,
  2 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 7 ⟶ 2 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 7 ,
  2 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 8 ⟶ 2 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 8 ,
  2 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 2 ⟶ 2 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 2 ,
  2 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 9 ⟶ 2 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 9 ,
  3 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 7 ⟶ 3 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 7 ,
  3 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 8 ⟶ 3 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 8 ,
  3 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 2 ⟶ 3 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 2 ,
  3 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 9 ⟶ 3 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 9 ,
  11 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 7 ⟶ 11 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 7 ,
  11 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 8 ⟶ 11 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 8 ,
  11 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 2 ⟶ 11 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 2 ,
  11 4 0 5 4 0 5 3 3 4 5 3 6 2 3 3 6 8 2 6 9 ⟶ 11 3 3 6 8 7 0 5 6 8 8 7 1 2 4 5 3 3 6 8 9 ,
  1 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 7 ⟶ 0 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 7 ,
  1 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 8 ⟶ 0 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 8 ,
  1 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 2 ⟶ 0 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 2 ,
  1 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 9 ⟶ 0 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 9 ,
  8 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 7 ⟶ 7 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 7 ,
  8 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 8 ⟶ 7 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 8 ,
  8 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 2 ⟶ 7 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 2 ,
  8 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 9 ⟶ 7 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 9 ,
  6 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 7 ⟶ 4 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 7 ,
  6 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 8 ⟶ 4 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 8 ,
  6 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 2 ⟶ 4 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 2 ,
  6 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 9 ⟶ 4 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 9 ,
  12 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 7 ⟶ 10 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 7 ,
  12 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 8 ⟶ 10 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 8 ,
  12 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 2 ⟶ 10 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 2 ,
  12 2 4 0 0 5 6 2 4 5 4 0 5 6 7 0 1 8 2 6 9 ⟶ 10 0 1 8 7 0 1 7 5 4 1 2 4 0 0 1 7 0 1 8 9 ,
  0 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 7 ⟶ 5 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 7 ,
  0 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 8 ⟶ 5 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 8 ,
  0 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 2 ⟶ 5 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 2 ,
  0 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 9 ⟶ 5 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 9 ,
  7 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 7 ⟶ 2 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 7 ,
  7 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 8 ⟶ 2 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 8 ,
  7 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 2 ⟶ 2 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 2 ,
  7 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 9 ⟶ 2 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 9 ,
  4 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 7 ⟶ 3 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 7 ,
  4 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 8 ⟶ 3 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 8 ,
  4 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 2 ⟶ 3 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 2 ,
  4 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 9 ⟶ 3 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 9 ,
  10 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 7 ⟶ 11 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 7 ,
  10 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 8 ⟶ 11 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 8 ,
  10 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 2 ⟶ 11 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 2 ,
  10 0 0 1 8 2 3 4 5 4 5 4 0 1 7 0 1 8 2 6 9 ⟶ 11 4 1 2 6 7 1 8 8 8 8 8 2 6 2 4 5 6 7 1 9 ,
  5 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 7 ⟶ 0 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 7 ,
  5 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 8 ⟶ 0 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 8 ,
  5 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 2 ⟶ 0 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 2 ,
  5 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 9 ⟶ 0 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 9 ,
  2 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 7 ⟶ 7 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 7 ,
  2 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 8 ⟶ 7 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 8 ,
  2 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 2 ⟶ 7 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 2 ,
  2 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 9 ⟶ 7 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 9 ,
  3 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 7 ⟶ 4 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 7 ,
  3 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 8 ⟶ 4 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 8 ,
  3 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 2 ⟶ 4 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 2 ,
  3 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 9 ⟶ 4 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 9 ,
  11 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 7 ⟶ 10 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 7 ,
  11 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 8 ⟶ 10 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 8 ,
  11 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 2 ⟶ 10 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 2 ,
  11 6 2 6 7 5 3 4 1 2 6 8 8 2 3 6 2 6 2 6 9 ⟶ 10 5 6 7 0 1 2 3 6 2 4 1 7 1 8 2 3 4 1 8 9 ,
  5 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 7 ⟶ 5 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 7 ,
  5 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 8 ⟶ 5 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 8 ,
  5 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 2 ⟶ 5 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 2 ,
  5 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 9 ⟶ 5 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 9 ,
  2 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 7 ⟶ 2 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 7 ,
  2 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 8 ⟶ 2 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 8 ,
  2 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 2 ⟶ 2 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 2 ,
  2 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 9 ⟶ 2 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 9 ,
  3 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 7 ⟶ 3 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 7 ,
  3 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 8 ⟶ 3 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 8 ,
  3 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 2 ⟶ 3 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 2 ,
  3 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 9 ⟶ 3 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 9 ,
  11 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 7 ⟶ 11 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 7 ,
  11 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 8 ⟶ 11 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 8 ,
  11 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 2 ⟶ 11 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 2 ,
  11 6 7 1 2 4 0 0 0 0 0 1 7 5 3 3 3 6 2 6 9 ⟶ 11 4 0 1 8 2 4 0 1 2 4 5 6 8 2 4 0 1 8 8 9 ,
  0 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 7 ⟶ 0 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 7 ,
  0 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 8 ⟶ 0 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 8 ,
  0 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 2 ⟶ 0 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 2 ,
  0 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 9 ⟶ 0 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 9 ,
  7 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 7 ⟶ 7 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 7 ,
  7 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 8 ⟶ 7 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 8 ,
  7 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 2 ⟶ 7 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 2 ,
  7 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 9 ⟶ 7 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 9 ,
  4 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 7 ⟶ 4 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 7 ,
  4 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 8 ⟶ 4 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 8 ,
  4 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 2 ⟶ 4 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 2 ,
  4 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 9 ⟶ 4 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 9 ,
  10 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 7 ⟶ 10 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 7 ,
  10 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 8 ⟶ 10 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 8 ,
  10 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 2 ⟶ 10 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 2 ,
  10 1 2 4 5 4 5 4 0 0 1 8 8 2 4 5 3 6 2 6 9 ⟶ 10 5 4 1 8 7 1 8 8 2 6 2 4 5 4 0 1 8 2 6 9 ,
  5 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 7 ⟶ 5 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 7 ,
  5 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 8 ⟶ 5 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 8 ,
  5 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 2 ⟶ 5 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 2 ,
  5 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 9 ⟶ 5 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 9 ,
  2 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 7 ⟶ 2 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 7 ,
  2 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 8 ⟶ 2 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 8 ,
  2 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 2 ⟶ 2 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 2 ,
  2 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 9 ⟶ 2 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 9 ,
  3 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 7 ⟶ 3 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 7 ,
  3 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 8 ⟶ 3 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 8 ,
  3 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 2 ⟶ 3 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 2 ,
  3 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 9 ⟶ 3 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 9 ,
  11 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 7 ⟶ 11 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 7 ,
  11 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 8 ⟶ 11 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 8 ,
  11 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 2 ⟶ 11 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 2 ,
  11 3 3 3 6 2 3 4 0 0 1 8 8 7 0 5 3 6 2 6 9 ⟶ 11 4 1 7 5 6 7 0 5 6 2 3 4 0 0 0 0 0 1 8 9 ,
  0 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 7 ⟶ 1 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 7 ,
  0 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 8 ⟶ 1 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 8 ,
  0 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 2 ⟶ 1 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 2 ,
  0 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 9 ⟶ 1 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 9 ,
  7 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 7 ⟶ 8 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 7 ,
  7 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 8 ⟶ 8 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 8 ,
  7 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 2 ⟶ 8 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 2 ,
  7 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 9 ⟶ 8 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 9 ,
  4 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 7 ⟶ 6 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 7 ,
  4 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 8 ⟶ 6 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 8 ,
  4 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 2 ⟶ 6 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 2 ,
  4 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 9 ⟶ 6 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 9 ,
  10 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 7 ⟶ 12 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 7 ,
  10 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 8 ⟶ 12 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 8 ,
  10 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 2 ⟶ 12 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 2 ,
  10 1 7 1 7 5 6 2 3 4 5 6 2 4 0 5 3 6 2 6 9 ⟶ 12 7 1 7 0 1 8 8 7 1 2 6 8 2 3 6 2 6 7 1 9 ,
  0 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 7 ⟶ 0 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 7 ,
  0 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 8 ⟶ 0 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 8 ,
  0 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 2 ⟶ 0 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 2 ,
  0 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 9 ⟶ 0 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 9 ,
  7 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 7 ⟶ 7 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 7 ,
  7 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 8 ⟶ 7 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 8 ,
  7 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 2 ⟶ 7 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 2 ,
  7 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 9 ⟶ 7 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 9 ,
  4 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 7 ⟶ 4 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 7 ,
  4 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 8 ⟶ 4 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 8 ,
  4 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 2 ⟶ 4 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 2 ,
  4 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 9 ⟶ 4 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 9 ,
  10 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 7 ⟶ 10 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 7 ,
  10 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 8 ⟶ 10 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 8 ,
  10 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 2 ⟶ 10 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 2 ,
  10 5 6 7 1 7 0 0 5 3 6 8 2 3 3 4 5 6 2 6 9 ⟶ 10 1 7 0 1 2 6 7 1 2 3 6 7 1 2 4 5 3 4 1 9 ,
  5 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 7 ⟶ 5 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 7 ,
  5 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 8 ⟶ 5 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 8 ,
  5 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 2 ⟶ 5 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 2 ,
  5 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 9 ⟶ 5 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 9 ,
  2 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 7 ⟶ 2 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 7 ,
  2 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 8 ⟶ 2 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 8 ,
  2 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 2 ⟶ 2 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 2 ,
  2 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 9 ⟶ 2 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 9 ,
  3 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 7 ⟶ 3 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 7 ,
  3 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 8 ⟶ 3 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 8 ,
  3 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 2 ⟶ 3 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 2 ,
  3 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 9 ⟶ 3 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 9 ,
  11 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 7 ⟶ 11 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 7 ,
  11 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 8 ⟶ 11 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 8 ,
  11 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 2 ⟶ 11 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 2 ,
  11 4 1 7 5 4 5 3 4 1 7 0 5 3 3 4 5 6 2 6 9 ⟶ 11 4 1 8 7 1 7 5 4 5 4 0 5 4 1 8 7 5 4 1 9 ,
  0 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 7 ⟶ 1 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 7 ,
  0 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 8 ⟶ 1 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 8 ,
  0 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 2 ⟶ 1 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 2 ,
  0 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 9 ⟶ 1 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 9 ,
  7 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 7 ⟶ 8 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 7 ,
  7 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 8 ⟶ 8 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 8 ,
  7 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 2 ⟶ 8 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 2 ,
  7 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 9 ⟶ 8 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 9 ,
  4 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 7 ⟶ 6 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 7 ,
  4 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 8 ⟶ 6 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 8 ,
  4 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 2 ⟶ 6 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 2 ,
  4 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 9 ⟶ 6 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 9 ,
  10 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 7 ⟶ 12 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 7 ,
  10 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 8 ⟶ 12 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 8 ,
  10 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 2 ⟶ 12 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 2 ,
  10 0 5 6 8 8 7 0 0 5 4 0 0 5 6 8 7 1 2 6 9 ⟶ 12 8 7 1 2 4 0 0 1 8 2 6 8 2 4 5 3 6 2 6 9 ,
  1 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 7 ⟶ 1 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 7 ,
  1 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 8 ⟶ 1 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 8 ,
  1 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 2 ⟶ 1 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 2 ,
  1 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 9 ⟶ 1 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 9 ,
  8 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 7 ⟶ 8 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 7 ,
  8 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 8 ⟶ 8 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 8 ,
  8 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 2 ⟶ 8 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 2 ,
  8 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 9 ⟶ 8 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 9 ,
  6 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 7 ⟶ 6 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 7 ,
  6 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 8 ⟶ 6 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 8 ,
  6 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 2 ⟶ 6 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 2 ,
  6 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 9 ⟶ 6 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 9 ,
  12 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 7 ⟶ 12 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 7 ,
  12 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 8 ⟶ 12 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 8 ,
  12 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 2 ⟶ 12 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 2 ,
  12 7 5 3 6 7 1 7 0 5 6 2 3 3 4 1 7 1 2 6 9 ⟶ 12 2 4 5 4 1 7 1 2 3 6 8 8 8 8 8 7 5 6 8 9 ,
  1 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 7 ⟶ 0 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 7 ,
  1 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 8 ⟶ 0 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 8 ,
  1 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 2 ⟶ 0 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 2 ,
  1 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 9 ⟶ 0 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 9 ,
  8 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 7 ⟶ 7 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 7 ,
  8 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 8 ⟶ 7 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 8 ,
  8 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 2 ⟶ 7 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 2 ,
  8 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 9 ⟶ 7 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 9 ,
  6 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 7 ⟶ 4 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 7 ,
  6 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 8 ⟶ 4 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 8 ,
  6 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 2 ⟶ 4 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 2 ,
  6 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 9 ⟶ 4 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 9 ,
  12 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 7 ⟶ 10 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 7 ,
  12 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 8 ⟶ 10 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 8 ,
  12 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 2 ⟶ 10 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 2 ,
  12 8 2 4 1 7 5 3 3 3 4 0 1 2 3 3 4 1 2 6 9 ⟶ 10 0 1 2 3 3 3 6 8 8 7 0 5 6 8 7 1 2 4 1 9 ,
  5 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 7 ⟶ 0 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 7 ,
  5 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 8 ⟶ 0 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 8 ,
  5 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 2 ⟶ 0 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 2 ,
  5 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 9 ⟶ 0 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 9 ,
  2 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 7 ⟶ 7 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 7 ,
  2 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 8 ⟶ 7 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 8 ,
  2 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 2 ⟶ 7 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 2 ,
  2 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 9 ⟶ 7 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 9 ,
  3 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 7 ⟶ 4 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 7 ,
  3 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 8 ⟶ 4 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 8 ,
  3 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 2 ⟶ 4 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 2 ,
  3 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 9 ⟶ 4 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 9 ,
  11 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 7 ⟶ 10 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 7 ,
  11 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 8 ⟶ 10 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 8 ,
  11 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 2 ⟶ 10 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 2 ,
  11 3 6 2 6 7 1 2 4 0 1 2 6 2 3 4 0 1 2 6 9 ⟶ 10 1 7 5 6 2 4 5 4 1 8 8 8 7 0 1 8 7 5 6 9 ,
  5 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 7 ⟶ 1 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 7 ,
  5 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 8 ⟶ 1 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 8 ,
  5 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 2 ⟶ 1 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 2 ,
  5 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 9 ⟶ 1 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 9 ,
  2 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 7 ⟶ 8 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 7 ,
  2 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 8 ⟶ 8 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 8 ,
  2 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 2 ⟶ 8 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 2 ,
  2 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 9 ⟶ 8 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 9 ,
  3 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 7 ⟶ 6 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 7 ,
  3 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 8 ⟶ 6 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 8 ,
  3 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 2 ⟶ 6 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 2 ,
  3 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 9 ⟶ 6 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 9 ,
  11 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 7 ⟶ 12 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 7 ,
  11 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 8 ⟶ 12 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 8 ,
  11 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 2 ⟶ 12 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 2 ,
  11 6 2 3 3 4 1 2 4 5 3 3 4 5 4 0 0 1 2 6 9 ⟶ 12 7 5 6 8 7 5 3 4 5 3 6 8 2 4 0 0 5 6 8 9 ,
  5 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 7 ⟶ 0 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 7 ,
  5 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 8 ⟶ 0 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 8 ,
  5 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 2 ⟶ 0 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 2 ,
  5 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 9 ⟶ 0 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 9 ,
  2 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 7 ⟶ 7 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 7 ,
  2 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 8 ⟶ 7 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 8 ,
  2 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 2 ⟶ 7 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 2 ,
  2 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 9 ⟶ 7 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 9 ,
  3 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 7 ⟶ 4 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 7 ,
  3 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 8 ⟶ 4 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 8 ,
  3 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 2 ⟶ 4 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 2 ,
  3 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 9 ⟶ 4 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 9 ,
  11 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 7 ⟶ 10 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 7 ,
  11 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 8 ⟶ 10 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 8 ,
  11 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 2 ⟶ 10 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 2 ,
  11 3 3 6 8 2 4 5 4 5 3 3 4 1 7 1 8 2 3 6 9 ⟶ 10 5 6 2 4 5 6 8 7 1 7 0 1 8 7 0 1 8 2 6 9 ,
  5 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 7 ⟶ 1 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 7 ,
  5 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 8 ⟶ 1 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 8 ,
  5 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 2 ⟶ 1 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 2 ,
  5 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 9 ⟶ 1 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 9 ,
  2 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 7 ⟶ 8 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 7 ,
  2 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 8 ⟶ 8 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 8 ,
  2 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 2 ⟶ 8 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 2 ,
  2 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 9 ⟶ 8 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 9 ,
  3 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 7 ⟶ 6 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 7 ,
  3 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 8 ⟶ 6 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 8 ,
  3 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 2 ⟶ 6 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 2 ,
  3 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 9 ⟶ 6 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 9 ,
  11 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 7 ⟶ 12 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 7 ,
  11 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 8 ⟶ 12 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 8 ,
  11 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 2 ⟶ 12 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 2 ,
  11 6 7 0 1 7 1 7 1 7 0 5 3 4 1 2 6 2 3 6 9 ⟶ 12 7 0 5 4 0 5 4 0 5 4 0 5 6 8 2 4 1 7 1 9 ,
  5 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 7 ⟶ 1 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 7 ,
  5 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 8 ⟶ 1 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 8 ,
  5 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 2 ⟶ 1 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 2 ,
  5 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 9 ⟶ 1 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 9 ,
  2 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 7 ⟶ 8 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 7 ,
  2 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 8 ⟶ 8 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 8 ,
  2 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 2 ⟶ 8 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 2 ,
  2 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 9 ⟶ 8 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 9 ,
  3 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 7 ⟶ 6 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 7 ,
  3 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 8 ⟶ 6 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 8 ,
  3 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 2 ⟶ 6 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 2 ,
  3 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 9 ⟶ 6 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 9 ,
  11 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 7 ⟶ 12 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 7 ,
  11 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 8 ⟶ 12 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 8 ,
  11 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 2 ⟶ 12 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 2 ,
  11 4 1 8 8 7 0 0 1 7 1 7 5 3 3 3 6 2 3 6 9 ⟶ 12 2 6 8 8 7 0 0 5 3 4 0 1 7 0 0 5 6 2 6 9 ,
  5 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 7 ⟶ 1 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 7 ,
  5 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 8 ⟶ 1 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 8 ,
  5 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 2 ⟶ 1 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 2 ,
  5 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 9 ⟶ 1 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 9 ,
  2 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 7 ⟶ 8 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 7 ,
  2 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 8 ⟶ 8 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 8 ,
  2 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 2 ⟶ 8 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 2 ,
  2 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 9 ⟶ 8 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 9 ,
  3 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 7 ⟶ 6 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 7 ,
  3 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 8 ⟶ 6 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 8 ,
  3 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 2 ⟶ 6 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 2 ,
  3 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 9 ⟶ 6 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 9 ,
  11 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 7 ⟶ 12 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 7 ,
  11 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 8 ⟶ 12 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 8 ,
  11 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 2 ⟶ 12 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 2 ,
  11 3 6 2 6 7 1 8 2 4 0 1 7 5 4 5 6 2 3 6 9 ⟶ 12 7 1 2 3 3 4 5 6 2 6 7 0 0 1 7 5 6 8 8 9 ,
  1 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 7 ⟶ 0 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 7 ,
  1 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 8 ⟶ 0 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 8 ,
  1 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 2 ⟶ 0 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 2 ,
  1 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 9 ⟶ 0 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 9 ,
  8 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 7 ⟶ 7 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 7 ,
  8 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 8 ⟶ 7 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 8 ,
  8 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 2 ⟶ 7 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 2 ,
  8 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 9 ⟶ 7 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 9 ,
  6 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 7 ⟶ 4 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 7 ,
  6 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 8 ⟶ 4 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 8 ,
  6 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 2 ⟶ 4 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 2 ,
  6 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 9 ⟶ 4 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 9 ,
  12 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 7 ⟶ 10 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 7 ,
  12 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 8 ⟶ 10 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 8 ,
  12 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 2 ⟶ 10 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 2 ,
  12 2 3 4 0 5 4 1 7 0 5 4 5 4 1 7 1 2 3 6 9 ⟶ 10 1 8 7 1 2 4 0 1 7 5 6 2 6 2 3 3 6 7 1 9 ,
  0 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 7 ⟶ 0 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 7 ,
  0 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 8 ⟶ 0 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 8 ,
  0 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 2 ⟶ 0 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 2 ,
  0 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 9 ⟶ 0 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 9 ,
  7 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 7 ⟶ 7 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 7 ,
  7 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 8 ⟶ 7 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 8 ,
  7 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 2 ⟶ 7 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 2 ,
  7 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 9 ⟶ 7 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 9 ,
  4 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 7 ⟶ 4 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 7 ,
  4 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 8 ⟶ 4 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 8 ,
  4 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 2 ⟶ 4 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 2 ,
  4 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 9 ⟶ 4 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 9 ,
  10 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 7 ⟶ 10 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 7 ,
  10 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 8 ⟶ 10 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 8 ,
  10 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 2 ⟶ 10 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 2 ,
  10 1 8 7 1 7 0 0 5 3 3 6 8 2 3 4 1 2 3 6 9 ⟶ 10 5 4 0 1 7 1 8 7 0 0 5 6 2 4 1 2 4 5 6 9 ,
  5 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 7 ⟶ 0 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 7 ,
  5 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 8 ⟶ 0 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 8 ,
  5 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 2 ⟶ 0 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 2 ,
  5 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 9 ⟶ 0 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 9 ,
  2 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 7 ⟶ 7 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 7 ,
  2 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 8 ⟶ 7 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 8 ,
  2 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 2 ⟶ 7 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 2 ,
  2 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 9 ⟶ 7 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 9 ,
  3 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 7 ⟶ 4 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 7 ,
  3 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 8 ⟶ 4 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 8 ,
  3 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 2 ⟶ 4 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 2 ,
  3 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 9 ⟶ 4 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 9 ,
  11 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 7 ⟶ 10 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 7 ,
  11 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 8 ⟶ 10 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 8 ,
  11 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 2 ⟶ 10 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 2 ,
  11 3 3 6 2 6 2 4 5 3 6 2 3 4 5 4 1 2 3 6 9 ⟶ 10 1 2 4 1 8 7 0 1 2 3 6 7 0 5 4 5 3 3 6 9 ,
  1 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 7 ⟶ 0 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 7 ,
  1 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 8 ⟶ 0 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 8 ,
  1 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 2 ⟶ 0 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 2 ,
  1 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 9 ⟶ 0 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 9 ,
  8 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 7 ⟶ 7 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 7 ,
  8 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 8 ⟶ 7 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 8 ,
  8 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 2 ⟶ 7 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 2 ,
  8 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 9 ⟶ 7 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 9 ,
  6 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 7 ⟶ 4 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 7 ,
  6 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 8 ⟶ 4 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 8 ,
  6 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 2 ⟶ 4 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 2 ,
  6 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 9 ⟶ 4 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 9 ,
  12 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 7 ⟶ 10 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 7 ,
  12 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 8 ⟶ 10 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 8 ,
  12 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 2 ⟶ 10 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 2 ,
  12 2 4 5 4 5 4 0 1 7 0 0 5 6 7 0 1 2 3 6 9 ⟶ 10 5 3 4 1 8 8 7 0 0 1 2 4 1 7 1 8 7 1 8 9 ,
  1 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 7 ⟶ 1 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 7 ,
  1 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 8 ⟶ 1 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 8 ,
  1 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 2 ⟶ 1 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 2 ,
  1 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 9 ⟶ 1 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 9 ,
  8 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 7 ⟶ 8 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 7 ,
  8 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 8 ⟶ 8 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 8 ,
  8 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 2 ⟶ 8 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 2 ,
  8 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 9 ⟶ 8 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 9 ,
  6 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 7 ⟶ 6 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 7 ,
  6 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 8 ⟶ 6 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 8 ,
  6 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 2 ⟶ 6 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 2 ,
  6 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 9 ⟶ 6 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 9 ,
  12 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 7 ⟶ 12 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 7 ,
  12 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 8 ⟶ 12 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 8 ,
  12 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 2 ⟶ 12 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 2 ,
  12 2 6 2 4 1 7 0 1 7 1 7 0 5 3 3 3 3 3 6 9 ⟶ 12 7 1 2 6 8 2 6 7 5 3 6 8 7 1 2 3 6 7 1 9 ,
  5 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 7 ⟶ 0 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 7 ,
  5 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 8 ⟶ 0 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 8 ,
  5 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 2 ⟶ 0 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 2 ,
  5 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 9 ⟶ 0 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 9 ,
  2 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 7 ⟶ 7 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 7 ,
  2 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 8 ⟶ 7 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 8 ,
  2 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 2 ⟶ 7 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 2 ,
  2 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 9 ⟶ 7 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 9 ,
  3 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 7 ⟶ 4 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 7 ,
  3 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 8 ⟶ 4 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 8 ,
  3 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 2 ⟶ 4 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 2 ,
  3 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 9 ⟶ 4 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 9 ,
  11 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 7 ⟶ 10 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 7 ,
  11 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 8 ⟶ 10 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 8 ,
  11 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 2 ⟶ 10 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 2 ,
  11 6 7 0 0 1 2 4 0 0 0 1 8 8 7 5 3 3 3 6 9 ⟶ 10 5 4 5 3 3 4 5 4 0 0 5 6 7 5 6 8 8 7 1 9 ,
  1 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 7 ⟶ 5 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 7 ,
  1 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 8 ⟶ 5 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 8 ,
  1 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 2 ⟶ 5 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 2 ,
  1 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 9 ⟶ 5 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 9 ,
  8 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 7 ⟶ 2 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 7 ,
  8 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 8 ⟶ 2 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 8 ,
  8 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 2 ⟶ 2 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 2 ,
  8 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 9 ⟶ 2 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 9 ,
  6 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 7 ⟶ 3 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 7 ,
  6 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 8 ⟶ 3 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 8 ,
  6 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 2 ⟶ 3 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 2 ,
  6 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 9 ⟶ 3 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 9 ,
  12 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 7 ⟶ 11 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 7 ,
  12 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 8 ⟶ 11 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 8 ,
  12 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 2 ⟶ 11 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 2 ,
  12 2 3 4 5 3 3 6 8 2 3 3 4 5 4 0 5 3 3 6 9 ⟶ 11 4 5 4 1 7 0 5 4 1 7 5 3 3 6 7 1 2 6 8 9 ,
  5 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 7 ⟶ 1 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 7 ,
  5 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 8 ⟶ 1 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 8 ,
  5 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 2 ⟶ 1 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 2 ,
  5 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 9 ⟶ 1 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 9 ,
  2 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 7 ⟶ 8 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 7 ,
  2 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 8 ⟶ 8 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 8 ,
  2 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 2 ⟶ 8 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 2 ,
  2 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 9 ⟶ 8 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 9 ,
  3 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 7 ⟶ 6 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 7 ,
  3 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 8 ⟶ 6 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 8 ,
  3 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 2 ⟶ 6 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 2 ,
  3 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 9 ⟶ 6 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 9 ,
  11 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 7 ⟶ 12 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 7 ,
  11 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 8 ⟶ 12 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 8 ,
  11 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 2 ⟶ 12 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 2 ,
  11 6 7 1 8 8 8 2 4 1 7 5 6 8 2 6 7 5 3 6 9 ⟶ 12 7 5 6 2 4 0 1 8 8 2 4 5 4 0 0 5 4 1 8 9 ,
  1 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 7 ⟶ 5 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 7 ,
  1 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 8 ⟶ 5 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 8 ,
  1 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 2 ⟶ 5 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 2 ,
  1 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 9 ⟶ 5 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 9 ,
  8 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 7 ⟶ 2 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 7 ,
  8 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 8 ⟶ 2 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 8 ,
  8 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 2 ⟶ 2 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 2 ,
  8 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 9 ⟶ 2 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 9 ,
  6 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 7 ⟶ 3 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 7 ,
  6 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 8 ⟶ 3 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 8 ,
  6 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 2 ⟶ 3 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 2 ,
  6 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 9 ⟶ 3 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 9 ,
  12 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 7 ⟶ 11 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 7 ,
  12 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 8 ⟶ 11 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 8 ,
  12 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 2 ⟶ 11 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 2 ,
  12 8 2 6 7 0 5 6 7 5 3 4 0 1 7 1 7 5 3 6 9 ⟶ 11 6 2 3 6 7 0 0 0 5 6 7 5 4 1 8 8 7 5 6 9 ,
  1 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 7 ⟶ 0 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 7 ,
  1 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 8 ⟶ 0 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 8 ,
  1 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 2 ⟶ 0 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 2 ,
  1 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 9 ⟶ 0 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 9 ,
  8 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 7 ⟶ 7 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 7 ,
  8 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 8 ⟶ 7 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 8 ,
  8 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 2 ⟶ 7 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 2 ,
  8 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 9 ⟶ 7 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 9 ,
  6 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 7 ⟶ 4 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 7 ,
  6 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 8 ⟶ 4 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 8 ,
  6 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 2 ⟶ 4 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 2 ,
  6 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 9 ⟶ 4 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 9 ,
  12 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 7 ⟶ 10 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 7 ,
  12 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 8 ⟶ 10 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 8 ,
  12 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 2 ⟶ 10 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 2 ,
  12 2 3 6 2 6 2 3 6 8 8 8 2 3 3 3 4 5 3 6 9 ⟶ 10 1 7 0 1 7 0 5 6 7 5 3 3 6 2 6 2 6 8 8 9 ,
  0 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 7 ⟶ 0 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 7 ,
  0 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 8 ⟶ 0 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 8 ,
  0 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 2 ⟶ 0 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 2 ,
  0 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 9 ⟶ 0 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 9 ,
  7 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 7 ⟶ 7 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 7 ,
  7 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 8 ⟶ 7 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 8 ,
  7 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 2 ⟶ 7 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 2 ,
  7 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 9 ⟶ 7 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 9 ,
  4 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 7 ⟶ 4 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 7 ,
  4 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 8 ⟶ 4 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 8 ,
  4 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 2 ⟶ 4 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 2 ,
  4 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 9 ⟶ 4 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 9 ,
  10 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 7 ⟶ 10 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 7 ,
  10 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 8 ⟶ 10 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 8 ,
  10 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 2 ⟶ 10 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 2 ,
  10 0 0 0 5 4 0 5 6 8 7 1 2 4 0 0 0 5 3 6 9 ⟶ 10 1 7 1 2 4 0 5 6 7 5 4 5 6 8 7 1 8 2 6 9 ,
  1 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 7 ⟶ 1 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 7 ,
  1 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 8 ⟶ 1 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 8 ,
  1 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 2 ⟶ 1 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 2 ,
  1 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 9 ⟶ 1 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 9 ,
  8 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 7 ⟶ 8 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 7 ,
  8 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 8 ⟶ 8 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 8 ,
  8 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 2 ⟶ 8 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 2 ,
  8 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 9 ⟶ 8 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 9 ,
  6 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 7 ⟶ 6 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 7 ,
  6 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 8 ⟶ 6 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 8 ,
  6 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 2 ⟶ 6 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 2 ,
  6 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 9 ⟶ 6 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 9 ,
  12 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 7 ⟶ 12 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 7 ,
  12 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 8 ⟶ 12 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 8 ,
  12 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 2 ⟶ 12 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 2 ,
  12 7 5 4 1 8 7 1 2 6 8 7 1 7 5 6 8 7 5 6 9 ⟶ 12 8 8 7 0 1 7 0 5 4 1 8 7 1 8 8 7 5 4 1 9 ,
  1 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 7 ⟶ 5 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 7 ,
  1 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 8 ⟶ 5 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 8 ,
  1 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 2 ⟶ 5 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 2 ,
  1 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 9 ⟶ 5 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 9 ,
  8 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 7 ⟶ 2 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 7 ,
  8 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 8 ⟶ 2 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 8 ,
  8 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 2 ⟶ 2 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 2 ,
  8 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 9 ⟶ 2 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 9 ,
  6 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 7 ⟶ 3 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 7 ,
  6 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 8 ⟶ 3 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 8 ,
  6 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 2 ⟶ 3 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 2 ,
  6 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 9 ⟶ 3 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 9 ,
  12 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 7 ⟶ 11 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 7 ,
  12 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 8 ⟶ 11 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 8 ,
  12 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 2 ⟶ 11 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 2 ,
  12 8 2 3 6 2 3 3 6 2 4 1 2 3 4 1 8 7 5 6 9 ⟶ 11 3 4 1 8 2 4 1 8 7 1 7 0 5 3 6 7 1 8 8 9 ,
  5 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 7 ⟶ 5 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 7 ,
  5 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 8 ⟶ 5 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 8 ,
  5 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 2 ⟶ 5 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 2 ,
  5 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 9 ⟶ 5 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 9 ,
  2 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 7 ⟶ 2 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 7 ,
  2 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 8 ⟶ 2 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 8 ,
  2 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 2 ⟶ 2 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 2 ,
  2 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 9 ⟶ 2 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 9 ,
  3 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 7 ⟶ 3 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 7 ,
  3 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 8 ⟶ 3 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 8 ,
  3 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 2 ⟶ 3 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 2 ,
  3 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 9 ⟶ 3 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 9 ,
  11 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 7 ⟶ 11 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 7 ,
  11 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 8 ⟶ 11 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 8 ,
  11 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 2 ⟶ 11 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 2 ,
  11 4 5 6 7 5 3 3 4 0 5 4 1 7 1 2 6 7 5 6 9 ⟶ 11 4 5 3 4 5 4 1 8 8 8 2 6 8 8 7 0 0 1 8 9 ,
  1 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 7 ⟶ 1 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 7 ,
  1 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 8 ⟶ 1 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 8 ,
  1 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 2 ⟶ 1 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 2 ,
  1 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 9 ⟶ 1 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 9 ,
  8 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 7 ⟶ 8 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 7 ,
  8 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 8 ⟶ 8 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 8 ,
  8 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 2 ⟶ 8 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 2 ,
  8 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 9 ⟶ 8 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 9 ,
  6 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 7 ⟶ 6 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 7 ,
  6 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 8 ⟶ 6 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 8 ,
  6 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 2 ⟶ 6 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 2 ,
  6 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 9 ⟶ 6 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 9 ,
  12 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 7 ⟶ 12 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 7 ,
  12 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 8 ⟶ 12 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 8 ,
  12 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 2 ⟶ 12 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 2 ,
  12 8 8 7 1 8 8 7 0 5 3 3 4 1 8 7 1 7 5 6 9 ⟶ 12 2 6 2 4 5 6 7 0 5 6 2 3 6 2 4 1 8 2 6 9 ,
  5 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 7 ⟶ 1 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 7 ,
  5 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 8 ⟶ 1 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 8 ,
  5 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 2 ⟶ 1 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 2 ,
  5 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 9 ⟶ 1 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 9 ,
  2 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 7 ⟶ 8 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 7 ,
  2 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 8 ⟶ 8 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 8 ,
  2 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 2 ⟶ 8 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 2 ,
  2 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 9 ⟶ 8 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 9 ,
  3 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 7 ⟶ 6 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 7 ,
  3 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 8 ⟶ 6 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 8 ,
  3 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 2 ⟶ 6 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 2 ,
  3 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 9 ⟶ 6 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 9 ,
  11 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 7 ⟶ 12 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 7 ,
  11 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 8 ⟶ 12 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 8 ,
  11 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 2 ⟶ 12 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 2 ,
  11 3 6 2 4 0 5 3 6 8 2 3 4 0 5 6 2 4 5 6 9 ⟶ 12 2 6 8 2 4 0 0 5 4 5 6 7 1 7 1 7 0 0 1 9 ,
  0 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 7 ⟶ 1 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 7 ,
  0 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 8 ⟶ 1 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 8 ,
  0 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 2 ⟶ 1 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 2 ,
  0 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 9 ⟶ 1 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 9 ,
  7 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 7 ⟶ 8 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 7 ,
  7 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 8 ⟶ 8 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 8 ,
  7 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 2 ⟶ 8 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 2 ,
  7 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 9 ⟶ 8 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 9 ,
  4 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 7 ⟶ 6 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 7 ,
  4 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 8 ⟶ 6 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 8 ,
  4 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 2 ⟶ 6 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 2 ,
  4 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 9 ⟶ 6 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 9 ,
  10 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 7 ⟶ 12 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 7 ,
  10 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 8 ⟶ 12 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 8 ,
  10 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 2 ⟶ 12 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 2 ,
  10 5 6 7 0 5 6 7 1 8 2 4 5 3 3 6 7 0 5 6 9 ⟶ 12 8 7 5 6 7 1 2 3 3 6 2 4 0 1 7 1 8 7 1 9 ,
  0 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 7 ⟶ 0 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 7 ,
  0 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 8 ⟶ 0 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 8 ,
  0 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 2 ⟶ 0 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 2 ,
  0 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 9 ⟶ 0 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 9 ,
  7 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 7 ⟶ 7 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 7 ,
  7 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 8 ⟶ 7 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 8 ,
  7 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 2 ⟶ 7 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 2 ,
  7 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 9 ⟶ 7 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 9 ,
  4 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 7 ⟶ 4 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 7 ,
  4 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 8 ⟶ 4 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 8 ,
  4 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 2 ⟶ 4 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 2 ,
  4 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 9 ⟶ 4 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 9 ,
  10 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 7 ⟶ 10 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 7 ,
  10 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 8 ⟶ 10 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 8 ,
  10 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 2 ⟶ 10 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 2 ,
  10 1 8 7 1 8 2 6 2 4 5 6 7 1 8 7 0 0 5 6 9 ⟶ 10 5 6 8 2 6 2 6 8 8 7 0 5 4 1 7 5 6 8 8 9 ,
  5 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 7 ⟶ 5 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 7 ,
  5 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 8 ⟶ 5 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 8 ,
  5 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 2 ⟶ 5 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 2 ,
  5 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 9 ⟶ 5 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 9 ,
  2 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 7 ⟶ 2 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 7 ,
  2 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 8 ⟶ 2 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 8 ,
  2 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 2 ⟶ 2 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 2 ,
  2 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 9 ⟶ 2 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 9 ,
  3 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 7 ⟶ 3 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 7 ,
  3 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 8 ⟶ 3 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 8 ,
  3 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 2 ⟶ 3 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 2 ,
  3 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 9 ⟶ 3 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 9 ,
  11 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 7 ⟶ 11 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 7 ,
  11 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 8 ⟶ 11 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 8 ,
  11 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 2 ⟶ 11 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 2 ,
  11 3 4 5 4 5 3 4 0 1 2 4 0 0 0 0 0 0 5 6 9 ⟶ 11 6 8 8 8 8 7 5 6 8 8 7 5 6 2 4 1 2 4 1 9 ,
  1 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 7 ⟶ 0 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 7 ,
  1 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 8 ⟶ 0 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 8 ,
  1 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 2 ⟶ 0 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 2 ,
  1 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 9 ⟶ 0 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 9 ,
  8 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 7 ⟶ 7 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 7 ,
  8 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 8 ⟶ 7 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 8 ,
  8 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 2 ⟶ 7 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 2 ,
  8 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 9 ⟶ 7 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 9 ,
  6 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 7 ⟶ 4 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 7 ,
  6 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 8 ⟶ 4 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 8 ,
  6 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 2 ⟶ 4 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 2 ,
  6 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 9 ⟶ 4 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 9 ,
  12 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 7 ⟶ 10 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 7 ,
  12 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 8 ⟶ 10 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 8 ,
  12 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 2 ⟶ 10 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 2 ,
  12 8 2 6 8 8 8 2 3 4 0 1 2 3 4 1 8 8 7 1 9 ⟶ 10 5 4 5 4 1 7 1 8 7 0 0 0 1 8 8 2 4 1 8 9 ,
  0 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 7 ⟶ 1 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 7 ,
  0 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 8 ⟶ 1 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 8 ,
  0 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 2 ⟶ 1 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 2 ,
  0 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 9 ⟶ 1 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 9 ,
  7 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 7 ⟶ 8 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 7 ,
  7 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 8 ⟶ 8 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 8 ,
  7 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 2 ⟶ 8 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 2 ,
  7 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 9 ⟶ 8 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 9 ,
  4 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 7 ⟶ 6 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 7 ,
  4 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 8 ⟶ 6 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 8 ,
  4 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 2 ⟶ 6 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 2 ,
  4 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 9 ⟶ 6 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 9 ,
  10 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 7 ⟶ 12 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 7 ,
  10 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 8 ⟶ 12 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 8 ,
  10 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 2 ⟶ 12 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 2 ,
  10 5 3 4 5 4 1 2 6 7 0 1 2 4 1 2 6 8 7 1 9 ⟶ 12 8 8 8 2 6 7 5 6 2 4 5 4 1 2 4 1 2 4 1 9 ,
  1 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 7 ⟶ 0 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 7 ,
  1 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 8 ⟶ 0 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 8 ,
  1 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 2 ⟶ 0 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 2 ,
  1 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 9 ⟶ 0 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 9 ,
  8 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 7 ⟶ 7 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 7 ,
  8 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 8 ⟶ 7 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 8 ,
  8 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 2 ⟶ 7 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 2 ,
  8 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 9 ⟶ 7 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 9 ,
  6 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 7 ⟶ 4 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 7 ,
  6 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 8 ⟶ 4 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 8 ,
  6 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 2 ⟶ 4 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 2 ,
  6 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 9 ⟶ 4 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 9 ,
  12 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 7 ⟶ 10 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 7 ,
  12 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 8 ⟶ 10 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 8 ,
  12 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 2 ⟶ 10 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 2 ,
  12 7 0 0 1 2 4 1 8 2 6 2 3 3 6 2 3 6 7 1 9 ⟶ 10 5 4 5 4 0 5 4 5 6 7 1 8 7 1 8 7 0 0 1 9 ,
  5 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 7 ⟶ 5 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 7 ,
  5 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 8 ⟶ 5 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 8 ,
  5 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 2 ⟶ 5 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 2 ,
  5 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 9 ⟶ 5 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 9 ,
  2 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 7 ⟶ 2 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 7 ,
  2 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 8 ⟶ 2 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 8 ,
  2 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 2 ⟶ 2 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 2 ,
  2 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 9 ⟶ 2 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 9 ,
  3 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 7 ⟶ 3 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 7 ,
  3 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 8 ⟶ 3 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 8 ,
  3 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 2 ⟶ 3 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 2 ,
  3 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 9 ⟶ 3 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 9 ,
  11 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 7 ⟶ 11 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 7 ,
  11 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 8 ⟶ 11 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 8 ,
  11 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 2 ⟶ 11 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 2 ,
  11 6 7 5 4 1 7 1 7 1 7 0 5 6 2 3 3 6 7 1 9 ⟶ 11 4 0 0 1 8 7 5 4 1 2 4 0 0 0 5 6 7 0 1 9 ,
  5 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 7 ⟶ 5 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 7 ,
  5 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 8 ⟶ 5 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 8 ,
  5 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 2 ⟶ 5 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 2 ,
  5 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 9 ⟶ 5 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 9 ,
  2 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 7 ⟶ 2 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 7 ,
  2 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 8 ⟶ 2 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 8 ,
  2 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 2 ⟶ 2 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 2 ,
  2 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 9 ⟶ 2 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 9 ,
  3 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 7 ⟶ 3 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 7 ,
  3 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 8 ⟶ 3 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 8 ,
  3 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 2 ⟶ 3 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 2 ,
  3 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 9 ⟶ 3 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 9 ,
  11 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 7 ⟶ 11 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 7 ,
  11 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 8 ⟶ 11 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 8 ,
  11 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 2 ⟶ 11 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 2 ,
  11 6 7 0 5 6 7 5 4 1 7 5 3 3 3 4 5 6 7 1 9 ⟶ 11 6 8 7 1 8 2 4 1 2 3 6 8 2 4 5 3 3 3 6 9 ,
  1 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 7 ⟶ 1 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 7 ,
  1 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 8 ⟶ 1 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 8 ,
  1 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 2 ⟶ 1 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 2 ,
  1 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 9 ⟶ 1 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 9 ,
  8 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 7 ⟶ 8 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 7 ,
  8 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 8 ⟶ 8 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 8 ,
  8 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 2 ⟶ 8 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 2 ,
  8 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 9 ⟶ 8 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 9 ,
  6 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 7 ⟶ 6 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 7 ,
  6 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 8 ⟶ 6 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 8 ,
  6 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 2 ⟶ 6 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 2 ,
  6 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 9 ⟶ 6 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 9 ,
  12 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 7 ⟶ 12 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 7 ,
  12 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 8 ⟶ 12 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 8 ,
  12 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 2 ⟶ 12 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 2 ,
  12 7 1 7 5 3 3 3 4 1 2 3 4 1 7 1 7 1 7 1 9 ⟶ 12 8 7 0 5 6 8 7 0 0 1 8 2 3 4 5 4 1 2 6 9 ,
  5 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 7 ⟶ 1 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 7 ,
  5 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 8 ⟶ 1 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 8 ,
  5 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 2 ⟶ 1 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 2 ,
  5 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 9 ⟶ 1 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 9 ,
  2 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 7 ⟶ 8 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 7 ,
  2 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 8 ⟶ 8 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 8 ,
  2 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 2 ⟶ 8 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 2 ,
  2 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 9 ⟶ 8 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 9 ,
  3 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 7 ⟶ 6 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 7 ,
  3 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 8 ⟶ 6 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 8 ,
  3 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 2 ⟶ 6 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 2 ,
  3 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 9 ⟶ 6 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 9 ,
  11 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 7 ⟶ 12 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 7 ,
  11 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 8 ⟶ 12 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 8 ,
  11 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 2 ⟶ 12 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 2 ,
  11 6 7 1 2 3 4 5 3 3 6 7 0 5 4 1 7 1 7 1 9 ⟶ 12 2 3 4 0 1 8 8 7 5 3 4 1 2 3 3 6 8 7 1 9 ,
  5 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 7 ⟶ 1 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 7 ,
  5 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 8 ⟶ 1 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 8 ,
  5 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 2 ⟶ 1 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 2 ,
  5 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 9 ⟶ 1 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 9 ,
  2 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 7 ⟶ 8 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 7 ,
  2 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 8 ⟶ 8 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 8 ,
  2 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 2 ⟶ 8 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 2 ,
  2 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 9 ⟶ 8 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 9 ,
  3 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 7 ⟶ 6 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 7 ,
  3 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 8 ⟶ 6 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 8 ,
  3 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 2 ⟶ 6 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 2 ,
  3 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 9 ⟶ 6 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 9 ,
  11 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 7 ⟶ 12 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 7 ,
  11 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 8 ⟶ 12 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 8 ,
  11 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 2 ⟶ 12 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 2 ,
  11 4 0 5 3 3 6 2 6 7 1 7 5 6 8 2 4 1 7 1 9 ⟶ 12 2 6 7 0 0 5 6 8 8 2 4 5 3 6 2 6 2 6 8 9 ,
  1 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 7 ⟶ 0 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 7 ,
  1 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 8 ⟶ 0 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 8 ,
  1 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 2 ⟶ 0 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 2 ,
  1 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 9 ⟶ 0 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 9 ,
  8 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 7 ⟶ 7 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 7 ,
  8 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 8 ⟶ 7 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 8 ,
  8 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 2 ⟶ 7 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 2 ,
  8 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 9 ⟶ 7 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 9 ,
  6 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 7 ⟶ 4 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 7 ,
  6 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 8 ⟶ 4 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 8 ,
  6 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 2 ⟶ 4 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 2 ,
  6 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 9 ⟶ 4 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 9 ,
  12 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 7 ⟶ 10 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 7 ,
  12 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 8 ⟶ 10 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 8 ,
  12 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 2 ⟶ 10 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 2 ,
  12 7 5 6 8 7 5 4 5 4 1 8 8 7 5 3 4 1 7 1 9 ⟶ 10 5 6 8 8 8 2 4 1 8 8 8 2 6 7 5 6 7 0 1 9 ,
  5 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 7 ⟶ 5 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 7 ,
  5 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 8 ⟶ 5 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 8 ,
  5 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 2 ⟶ 5 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 2 ,
  5 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 9 ⟶ 5 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 9 ,
  2 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 7 ⟶ 2 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 7 ,
  2 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 8 ⟶ 2 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 8 ,
  2 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 2 ⟶ 2 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 2 ,
  2 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 9 ⟶ 2 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 9 ,
  3 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 7 ⟶ 3 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 7 ,
  3 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 8 ⟶ 3 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 8 ,
  3 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 2 ⟶ 3 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 2 ,
  3 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 9 ⟶ 3 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 9 ,
  11 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 7 ⟶ 11 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 7 ,
  11 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 8 ⟶ 11 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 8 ,
  11 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 2 ⟶ 11 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 2 ,
  11 3 3 3 3 4 5 3 3 4 1 7 0 5 4 5 4 1 7 1 9 ⟶ 11 6 7 5 3 4 1 8 8 2 4 5 6 2 4 1 2 3 3 6 9 ,
  5 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 7 ⟶ 0 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 7 ,
  5 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 8 ⟶ 0 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 8 ,
  5 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 2 ⟶ 0 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 2 ,
  5 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 9 ⟶ 0 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 9 ,
  2 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 7 ⟶ 7 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 7 ,
  2 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 8 ⟶ 7 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 8 ,
  2 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 2 ⟶ 7 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 2 ,
  2 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 9 ⟶ 7 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 9 ,
  3 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 7 ⟶ 4 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 7 ,
  3 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 8 ⟶ 4 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 8 ,
  3 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 2 ⟶ 4 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 2 ,
  3 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 9 ⟶ 4 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 9 ,
  11 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 7 ⟶ 10 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 7 ,
  11 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 8 ⟶ 10 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 8 ,
  11 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 2 ⟶ 10 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 2 ,
  11 3 4 0 0 0 0 0 1 7 5 6 8 7 0 5 6 2 4 1 9 ⟶ 10 1 2 6 7 0 1 8 8 7 5 6 8 8 7 0 5 6 8 8 9 ,
  5 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 7 ⟶ 5 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 7 ,
  5 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 8 ⟶ 5 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 8 ,
  5 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 2 ⟶ 5 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 2 ,
  5 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 9 ⟶ 5 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 9 ,
  2 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 7 ⟶ 2 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 7 ,
  2 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 8 ⟶ 2 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 8 ,
  2 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 2 ⟶ 2 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 2 ,
  2 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 9 ⟶ 2 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 9 ,
  3 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 7 ⟶ 3 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 7 ,
  3 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 8 ⟶ 3 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 8 ,
  3 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 2 ⟶ 3 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 2 ,
  3 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 9 ⟶ 3 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 9 ,
  11 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 7 ⟶ 11 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 7 ,
  11 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 8 ⟶ 11 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 8 ,
  11 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 2 ⟶ 11 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 2 ,
  11 3 4 0 5 3 3 6 7 0 5 3 3 3 4 1 2 3 4 1 9 ⟶ 11 4 0 1 7 1 8 2 3 6 2 4 0 1 2 6 8 7 1 8 9 ,
  0 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 7 ⟶ 0 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 7 ,
  0 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 8 ⟶ 0 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 8 ,
  0 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 2 ⟶ 0 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 2 ,
  0 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 9 ⟶ 0 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 9 ,
  7 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 7 ⟶ 7 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 7 ,
  7 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 8 ⟶ 7 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 8 ,
  7 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 2 ⟶ 7 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 2 ,
  7 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 9 ⟶ 7 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 9 ,
  4 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 7 ⟶ 4 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 7 ,
  4 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 8 ⟶ 4 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 8 ,
  4 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 2 ⟶ 4 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 2 ,
  4 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 9 ⟶ 4 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 9 ,
  10 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 7 ⟶ 10 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 7 ,
  10 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 8 ⟶ 10 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 8 ,
  10 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 2 ⟶ 10 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 2 ,
  10 5 6 2 4 1 7 5 3 4 5 4 5 6 8 2 3 3 4 1 9 ⟶ 10 0 0 5 6 8 8 7 5 3 3 6 8 8 7 1 2 6 2 6 9 ,
  5 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 7 ⟶ 5 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 7 ,
  5 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 8 ⟶ 5 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 8 ,
  5 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 2 ⟶ 5 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 2 ,
  5 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 9 ⟶ 5 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 9 ,
  2 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 7 ⟶ 2 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 7 ,
  2 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 8 ⟶ 2 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 8 ,
  2 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 2 ⟶ 2 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 2 ,
  2 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 9 ⟶ 2 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 9 ,
  3 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 7 ⟶ 3 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 7 ,
  3 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 8 ⟶ 3 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 8 ,
  3 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 2 ⟶ 3 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 2 ,
  3 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 9 ⟶ 3 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 9 ,
  11 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 7 ⟶ 11 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 7 ,
  11 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 8 ⟶ 11 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 8 ,
  11 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 2 ⟶ 11 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 2 ,
  11 4 1 7 1 8 7 0 1 2 6 2 3 4 1 2 3 3 4 1 9 ⟶ 11 4 1 8 8 8 7 5 4 0 1 2 3 4 0 0 5 6 2 6 9 ,
  5 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 7 ⟶ 5 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 7 ,
  5 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 8 ⟶ 5 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 8 ,
  5 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 2 ⟶ 5 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 2 ,
  5 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 9 ⟶ 5 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 9 ,
  2 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 7 ⟶ 2 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 7 ,
  2 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 8 ⟶ 2 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 8 ,
  2 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 2 ⟶ 2 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 2 ,
  2 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 9 ⟶ 2 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 9 ,
  3 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 7 ⟶ 3 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 7 ,
  3 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 8 ⟶ 3 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 8 ,
  3 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 2 ⟶ 3 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 2 ,
  3 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 9 ⟶ 3 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 9 ,
  11 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 7 ⟶ 11 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 7 ,
  11 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 8 ⟶ 11 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 8 ,
  11 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 2 ⟶ 11 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 2 ,
  11 4 1 2 4 1 8 7 5 4 1 8 8 8 2 3 3 3 4 1 9 ⟶ 11 4 1 2 4 0 0 0 1 8 7 1 7 5 3 6 2 6 8 8 9 ,
  1 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 7 ⟶ 5 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 7 ,
  1 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 8 ⟶ 5 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 8 ,
  1 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 2 ⟶ 5 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 2 ,
  1 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 9 ⟶ 5 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 9 ,
  8 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 7 ⟶ 2 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 7 ,
  8 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 8 ⟶ 2 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 8 ,
  8 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 2 ⟶ 2 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 2 ,
  8 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 9 ⟶ 2 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 9 ,
  6 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 7 ⟶ 3 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 7 ,
  6 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 8 ⟶ 3 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 8 ,
  6 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 2 ⟶ 3 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 2 ,
  6 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 9 ⟶ 3 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 9 ,
  12 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 7 ⟶ 11 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 7 ,
  12 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 8 ⟶ 11 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 8 ,
  12 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 2 ⟶ 11 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 2 ,
  12 7 1 2 4 0 5 6 2 4 1 8 8 7 0 5 3 3 4 1 9 ⟶ 11 4 1 7 5 4 1 8 2 3 4 1 2 6 8 8 2 6 2 6 9 ,
  5 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 7 ⟶ 1 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 7 ,
  5 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 8 ⟶ 1 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 8 ,
  5 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 2 ⟶ 1 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 2 ,
  5 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 9 ⟶ 1 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 9 ,
  2 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 7 ⟶ 8 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 7 ,
  2 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 8 ⟶ 8 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 8 ,
  2 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 2 ⟶ 8 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 2 ,
  2 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 9 ⟶ 8 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 9 ,
  3 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 7 ⟶ 6 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 7 ,
  3 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 8 ⟶ 6 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 8 ,
  3 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 2 ⟶ 6 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 2 ,
  3 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 9 ⟶ 6 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 9 ,
  11 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 7 ⟶ 12 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 7 ,
  11 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 8 ⟶ 12 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 8 ,
  11 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 2 ⟶ 12 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 2 ,
  11 6 8 7 0 1 7 1 7 5 6 7 0 0 1 7 5 3 4 1 9 ⟶ 12 2 3 3 6 2 4 0 0 5 6 7 1 8 8 7 5 4 1 8 9 ,
  1 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 7 ⟶ 1 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 7 ,
  1 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 8 ⟶ 1 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 8 ,
  1 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 2 ⟶ 1 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 2 ,
  1 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 9 ⟶ 1 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 9 ,
  8 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 7 ⟶ 8 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 7 ,
  8 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 8 ⟶ 8 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 8 ,
  8 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 2 ⟶ 8 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 2 ,
  8 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 9 ⟶ 8 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 9 ,
  6 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 7 ⟶ 6 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 7 ,
  6 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 8 ⟶ 6 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 8 ,
  6 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 2 ⟶ 6 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 2 ,
  6 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 9 ⟶ 6 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 9 ,
  12 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 7 ⟶ 12 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 7 ,
  12 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 8 ⟶ 12 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 8 ,
  12 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 2 ⟶ 12 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 2 ,
  12 7 0 5 3 3 4 1 2 6 8 7 0 0 5 4 5 3 4 1 9 ⟶ 12 2 3 6 8 8 7 5 3 3 4 5 4 5 6 2 4 1 8 8 9 ,
  1 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 7 ⟶ 0 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 7 ,
  1 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 8 ⟶ 0 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 8 ,
  1 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 2 ⟶ 0 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 2 ,
  1 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 9 ⟶ 0 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 9 ,
  8 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 7 ⟶ 7 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 7 ,
  8 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 8 ⟶ 7 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 8 ,
  8 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 2 ⟶ 7 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 2 ,
  8 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 9 ⟶ 7 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 9 ,
  6 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 7 ⟶ 4 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 7 ,
  6 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 8 ⟶ 4 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 8 ,
  6 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 2 ⟶ 4 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 2 ,
  6 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 9 ⟶ 4 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 9 ,
  12 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 7 ⟶ 10 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 7 ,
  12 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 8 ⟶ 10 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 8 ,
  12 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 2 ⟶ 10 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 2 ,
  12 7 1 7 1 7 5 4 5 3 6 7 5 3 3 6 7 5 4 1 9 ⟶ 10 0 1 7 0 5 6 2 6 7 5 4 5 3 6 2 3 4 5 6 9 ,
  5 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 7 ⟶ 5 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 7 ,
  5 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 8 ⟶ 5 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 8 ,
  5 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 2 ⟶ 5 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 2 ,
  5 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 9 ⟶ 5 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 9 ,
  2 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 7 ⟶ 2 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 7 ,
  2 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 8 ⟶ 2 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 8 ,
  2 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 2 ⟶ 2 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 2 ,
  2 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 9 ⟶ 2 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 9 ,
  3 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 7 ⟶ 3 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 7 ,
  3 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 8 ⟶ 3 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 8 ,
  3 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 2 ⟶ 3 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 2 ,
  3 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 9 ⟶ 3 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 9 ,
  11 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 7 ⟶ 11 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 7 ,
  11 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 8 ⟶ 11 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 8 ,
  11 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 2 ⟶ 11 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 2 ,
  11 6 8 8 2 4 5 6 2 3 6 7 0 5 3 6 7 5 4 1 9 ⟶ 11 4 1 8 2 6 8 8 2 4 5 6 7 1 7 1 8 2 6 8 9 ,
  1 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 7 ⟶ 5 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 7 ,
  1 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 8 ⟶ 5 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 8 ,
  1 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 2 ⟶ 5 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 2 ,
  1 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 9 ⟶ 5 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 9 ,
  8 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 7 ⟶ 2 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 7 ,
  8 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 8 ⟶ 2 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 8 ,
  8 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 2 ⟶ 2 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 2 ,
  8 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 9 ⟶ 2 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 9 ,
  6 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 7 ⟶ 3 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 7 ,
  6 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 8 ⟶ 3 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 8 ,
  6 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 2 ⟶ 3 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 2 ,
  6 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 9 ⟶ 3 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 9 ,
  12 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 7 ⟶ 11 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 7 ,
  12 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 8 ⟶ 11 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 8 ,
  12 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 2 ⟶ 11 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 2 ,
  12 2 4 0 5 3 6 7 1 7 1 7 1 2 4 1 8 7 0 1 9 ⟶ 11 6 2 6 2 6 7 0 5 6 7 5 6 8 8 8 8 8 7 1 9 ,
  0 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 7 ⟶ 0 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 7 ,
  0 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 8 ⟶ 0 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 8 ,
  0 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 2 ⟶ 0 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 2 ,
  0 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 9 ⟶ 0 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 9 ,
  7 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 7 ⟶ 7 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 7 ,
  7 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 8 ⟶ 7 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 8 ,
  7 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 2 ⟶ 7 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 2 ,
  7 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 9 ⟶ 7 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 9 ,
  4 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 7 ⟶ 4 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 7 ,
  4 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 8 ⟶ 4 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 8 ,
  4 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 2 ⟶ 4 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 2 ,
  4 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 9 ⟶ 4 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 9 ,
  10 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 7 ⟶ 10 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 7 ,
  10 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 8 ⟶ 10 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 8 ,
  10 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 2 ⟶ 10 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 2 ,
  10 5 6 2 4 0 0 5 3 4 5 3 6 7 0 5 6 7 0 1 9 ⟶ 10 0 5 3 4 0 1 2 6 2 3 3 6 7 1 8 8 2 4 1 9 ,
  1 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 7 ⟶ 0 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 7 ,
  1 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 8 ⟶ 0 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 8 ,
  1 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 2 ⟶ 0 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 2 ,
  1 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 9 ⟶ 0 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 9 ,
  8 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 7 ⟶ 7 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 7 ,
  8 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 8 ⟶ 7 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 8 ,
  8 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 2 ⟶ 7 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 2 ,
  8 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 9 ⟶ 7 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 9 ,
  6 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 7 ⟶ 4 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 7 ,
  6 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 8 ⟶ 4 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 8 ,
  6 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 2 ⟶ 4 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 2 ,
  6 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 9 ⟶ 4 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 9 ,
  12 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 7 ⟶ 10 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 7 ,
  12 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 8 ⟶ 10 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 8 ,
  12 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 2 ⟶ 10 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 2 ,
  12 7 5 6 7 1 7 0 1 7 0 0 5 3 6 7 1 7 0 1 9 ⟶ 10 1 8 8 8 2 3 6 2 3 3 6 8 7 1 8 8 2 3 6 9 ,
  1 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 7 ⟶ 5 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 7 ,
  1 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 8 ⟶ 5 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 8 ,
  1 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 2 ⟶ 5 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 2 ,
  1 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 9 ⟶ 5 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 9 ,
  8 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 7 ⟶ 2 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 7 ,
  8 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 8 ⟶ 2 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 8 ,
  8 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 2 ⟶ 2 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 2 ,
  8 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 9 ⟶ 2 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 9 ,
  6 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 7 ⟶ 3 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 7 ,
  6 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 8 ⟶ 3 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 8 ,
  6 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 2 ⟶ 3 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 2 ,
  6 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 9 ⟶ 3 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 9 ,
  12 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 7 ⟶ 11 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 7 ,
  12 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 8 ⟶ 11 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 8 ,
  12 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 2 ⟶ 11 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 2 ,
  12 8 2 4 0 5 3 6 7 0 1 7 5 3 6 8 2 4 0 1 9 ⟶ 11 3 4 5 3 6 2 4 5 6 8 8 8 8 7 0 1 2 4 1 9 ,
  5 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 7 ⟶ 0 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 7 ,
  5 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 8 ⟶ 0 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 8 ,
  5 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 2 ⟶ 0 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 2 ,
  5 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 9 ⟶ 0 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 9 ,
  2 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 7 ⟶ 7 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 7 ,
  2 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 8 ⟶ 7 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 8 ,
  2 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 2 ⟶ 7 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 2 ,
  2 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 9 ⟶ 7 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 9 ,
  3 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 7 ⟶ 4 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 7 ,
  3 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 8 ⟶ 4 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 8 ,
  3 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 2 ⟶ 4 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 2 ,
  3 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 9 ⟶ 4 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 9 ,
  11 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 7 ⟶ 10 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 7 ,
  11 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 8 ⟶ 10 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 8 ,
  11 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 2 ⟶ 10 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 2 ,
  11 4 0 5 3 4 0 1 2 6 2 6 8 2 3 3 3 4 0 1 9 ⟶ 10 1 7 1 8 7 1 7 0 0 0 5 3 4 0 1 7 0 0 1 9 ,
  5 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 7 ⟶ 1 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 7 ,
  5 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 8 ⟶ 1 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 8 ,
  5 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 2 ⟶ 1 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 2 ,
  5 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 9 ⟶ 1 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 9 ,
  2 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 7 ⟶ 8 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 7 ,
  2 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 8 ⟶ 8 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 8 ,
  2 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 2 ⟶ 8 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 2 ,
  2 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 9 ⟶ 8 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 9 ,
  3 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 7 ⟶ 6 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 7 ,
  3 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 8 ⟶ 6 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 8 ,
  3 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 2 ⟶ 6 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 2 ,
  3 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 9 ⟶ 6 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 9 ,
  11 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 7 ⟶ 12 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 7 ,
  11 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 8 ⟶ 12 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 8 ,
  11 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 2 ⟶ 12 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 2 ,
  11 3 4 1 2 6 2 6 7 1 2 6 2 6 7 5 3 4 0 1 9 ⟶ 12 7 1 8 8 7 0 5 3 4 0 1 8 2 3 6 8 2 3 6 9 ,
  1 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 7 ⟶ 5 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 7 ,
  1 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 8 ⟶ 5 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 8 ,
  1 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 2 ⟶ 5 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 2 ,
  1 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 9 ⟶ 5 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 9 ,
  8 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 7 ⟶ 2 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 7 ,
  8 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 8 ⟶ 2 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 8 ,
  8 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 2 ⟶ 2 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 2 ,
  8 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 9 ⟶ 2 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 9 ,
  6 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 7 ⟶ 3 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 7 ,
  6 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 8 ⟶ 3 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 8 ,
  6 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 2 ⟶ 3 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 2 ,
  6 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 9 ⟶ 3 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 9 ,
  12 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 7 ⟶ 11 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 7 ,
  12 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 8 ⟶ 11 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 8 ,
  12 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 2 ⟶ 11 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 2 ,
  12 7 1 7 0 0 5 3 4 5 4 1 2 4 0 5 3 4 0 1 9 ⟶ 11 4 0 5 3 4 5 6 8 8 2 6 8 2 4 0 0 5 4 1 9 ,
  0 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 7 ⟶ 5 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 7 ,
  0 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 8 ⟶ 5 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 8 ,
  0 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 2 ⟶ 5 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 2 ,
  0 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 9 ⟶ 5 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 9 ,
  7 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 7 ⟶ 2 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 7 ,
  7 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 8 ⟶ 2 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 8 ,
  7 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 2 ⟶ 2 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 2 ,
  7 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 9 ⟶ 2 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 9 ,
  4 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 7 ⟶ 3 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 7 ,
  4 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 8 ⟶ 3 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 8 ,
  4 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 2 ⟶ 3 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 2 ,
  4 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 9 ⟶ 3 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 9 ,
  10 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 7 ⟶ 11 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 7 ,
  10 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 8 ⟶ 11 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 8 ,
  10 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 2 ⟶ 11 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 2 ,
  10 0 0 1 2 3 6 7 5 3 6 8 2 3 6 7 5 4 0 1 9 ⟶ 11 3 4 1 8 2 3 4 1 8 7 0 1 8 7 1 7 0 0 1 9 ,
  0 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 7 ⟶ 0 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 7 ,
  0 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 8 ⟶ 0 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 8 ,
  0 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 2 ⟶ 0 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 2 ,
  0 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 9 ⟶ 0 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 9 ,
  7 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 7 ⟶ 7 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 7 ,
  7 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 8 ⟶ 7 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 8 ,
  7 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 2 ⟶ 7 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 2 ,
  7 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 9 ⟶ 7 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 9 ,
  4 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 7 ⟶ 4 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 7 ,
  4 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 8 ⟶ 4 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 8 ,
  4 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 2 ⟶ 4 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 2 ,
  4 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 9 ⟶ 4 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 9 ,
  10 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 7 ⟶ 10 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 7 ,
  10 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 8 ⟶ 10 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 8 ,
  10 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 2 ⟶ 10 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 2 ,
  10 0 5 6 2 3 3 6 2 4 0 1 8 8 2 4 0 0 0 1 9 ⟶ 10 5 3 4 1 8 8 8 7 5 3 6 7 1 7 1 7 0 1 8 9 ,
  5 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 4 ⟶ 0 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 4 ,
  5 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 6 ⟶ 0 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 6 ,
  5 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 3 ⟶ 0 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 3 ,
  5 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 13 ⟶ 0 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 13 ,
  2 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 4 ⟶ 7 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 4 ,
  2 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 6 ⟶ 7 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 6 ,
  2 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 3 ⟶ 7 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 3 ,
  2 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 13 ⟶ 7 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 13 ,
  3 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 4 ⟶ 4 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 4 ,
  3 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 6 ⟶ 4 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 6 ,
  3 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 3 ⟶ 4 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 3 ,
  3 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 13 ⟶ 4 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 13 ,
  11 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 4 ⟶ 10 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 4 ,
  11 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 6 ⟶ 10 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 6 ,
  11 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 3 ⟶ 10 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 3 ,
  11 6 7 1 8 2 6 8 2 4 5 4 5 4 1 7 1 7 0 5 13 ⟶ 10 1 8 2 6 8 2 4 1 8 8 2 6 8 2 6 7 5 6 2 13 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 4 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 2 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

9 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

10 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

11 ↦ ⎛     ⎞
     ⎜ 1 1 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

12 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

13 ↦ ⎛     ⎞
     ⎜ 1 0 ⎟
     ⎜ 0 1 ⎟
     ⎝     ⎠

After renaming modulo the bijection { 5 ↦ 0, 4 ↦ 1, 0 ↦ 2, 1 ↦ 3, 2 ↦ 4, 3 ↦ 5, 6 ↦ 6, 8 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 12 ↦ 11, 11 ↦ 12 },
it remains to prove termination of the 156-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 9 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 9 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 9 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 9 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 155-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 9 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 9 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 154-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 153-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 152-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 151-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 150-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 149-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 148-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 147-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 146-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 9 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 9 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 145-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 144-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 143-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 142-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 141-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 140-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 9 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 9 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 139-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 138-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 9 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 9 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 137-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 136-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 134-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 9 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 9 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  10 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 10 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 9 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 9 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  10 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 10 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  10 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 10 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 9 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 9 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 9 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 9 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 9 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 9 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 9 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 9 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 9 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 9 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 9 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 9 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 9 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 9 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 9 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 9 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 9 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 9 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 9 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 133-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 10 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 10 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 10 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 10 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 10 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 10 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 10 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 10 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 10 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 10 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 10 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 10 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 10 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 10 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 10 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 10 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 10 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 10 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 10 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 10 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 10 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 10 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 10 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 10 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 10 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 10 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 10 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 10 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 10 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 10 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 132-rule system
{ 0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  0 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 3 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 8 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 8 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 7 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 7 ,
  4 1 2 3 4 1 0 5 6 7 4 5 6 8 2 0 1 3 7 7 4 ⟶ 7 4 6 8 3 8 2 3 4 1 0 1 0 6 8 0 5 6 8 3 4 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  2 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 2 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  8 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 8 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  1 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 1 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 8 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 8 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 7 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 7 ,
  9 2 3 4 5 6 8 0 1 3 7 8 2 0 5 1 2 3 7 7 4 ⟶ 9 3 8 0 5 5 1 0 1 0 1 0 1 3 7 4 1 2 2 3 4 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  2 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 2 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  8 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 8 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  1 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 1 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 8 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 8 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 7 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 7 ,
  9 3 4 5 1 2 0 5 1 2 0 5 1 0 5 6 7 4 6 7 4 ⟶ 9 3 8 3 4 5 5 5 5 1 3 8 3 7 8 3 7 4 5 6 4 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  2 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 2 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  8 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 8 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  1 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 1 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 8 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 8 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 7 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 7 ,
  9 0 5 1 3 4 1 2 3 4 5 5 6 8 0 6 8 0 6 7 4 ⟶ 9 0 5 5 6 7 4 1 2 0 6 4 1 2 2 3 8 2 0 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  3 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 10 ⟶ 2 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 10 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 8 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 8 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 7 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 7 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 4 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 4 ,
  7 7 8 0 1 2 2 0 6 4 6 4 6 4 5 5 1 2 3 7 10 ⟶ 8 0 5 5 6 4 1 0 1 3 4 6 4 1 2 3 8 3 4 6 10 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  3 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 10 ⟶ 2 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 10 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 8 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 8 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 7 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 7 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 4 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 4 ,
  7 4 1 2 2 0 6 4 1 0 1 2 0 6 8 2 3 7 4 6 10 ⟶ 8 2 3 7 8 2 3 8 0 1 3 4 1 2 2 3 8 2 3 7 10 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  0 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 10 ⟶ 2 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 10 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 8 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 8 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 7 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 7 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 4 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 4 ,
  4 6 4 6 8 0 5 1 3 4 6 7 7 4 5 6 4 6 4 6 10 ⟶ 8 0 6 8 2 3 4 5 6 4 1 3 8 3 7 4 5 1 3 7 10 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  0 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 3 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 8 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 8 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 7 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 7 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 4 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 4 ,
  4 5 6 4 6 8 3 7 4 1 2 3 8 0 1 0 6 4 5 6 10 ⟶ 7 8 3 4 5 5 1 0 6 4 6 8 2 2 3 8 0 6 7 7 10 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  3 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 10 ⟶ 2 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 10 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 8 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 8 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 7 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 7 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 4 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 4 ,
  7 4 5 1 2 0 1 3 8 2 0 1 0 1 3 8 3 4 5 6 10 ⟶ 8 3 7 8 3 4 1 2 3 8 0 6 4 6 4 5 5 6 8 3 10 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 8 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 8 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 7 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 7 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 4 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 4 ,
  6 7 4 6 8 2 0 6 8 0 5 1 2 3 8 3 8 0 5 6 10 ⟶ 5 6 4 5 6 8 2 2 2 0 6 8 0 1 3 7 7 8 0 6 10 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  3 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 3 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  7 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 7 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 7 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 7 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 4 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 4 ,
  6 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 10 ⟶ 6 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 10 ,
  11 7 7 8 3 7 7 8 2 0 5 5 1 3 7 8 3 8 0 6 8 ⟶ 11 4 6 4 1 0 6 8 2 0 6 4 5 6 4 1 3 7 4 6 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  3 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 10 ⟶ 2 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 10 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 8 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 8 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 7 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 7 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 4 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 4 ,
  7 7 4 6 7 7 7 4 5 1 2 3 4 5 1 3 7 7 8 3 10 ⟶ 8 0 1 0 1 3 8 3 7 8 2 2 2 3 7 7 4 1 3 7 10 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  0 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 0 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  4 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 4 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  5 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 5 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 8 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 8 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 7 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 7 ,
  12 1 3 4 1 3 7 8 0 1 3 7 7 7 4 5 5 5 1 3 4 ⟶ 12 1 3 4 1 2 2 2 3 7 8 3 8 0 5 6 4 6 7 7 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  3 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 10 ⟶ 2 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 10 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 8 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 8 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 7 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 7 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 4 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 4 ,
  7 8 3 8 3 8 0 1 0 5 6 8 0 5 5 6 8 0 1 3 10 ⟶ 8 2 3 8 2 0 6 4 6 8 0 1 0 5 6 4 5 1 0 6 10 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  0 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 3 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 8 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 7 ,
  4 5 1 3 4 6 4 6 8 3 4 6 4 6 8 0 5 1 2 3 4 ⟶ 7 8 3 7 7 8 2 0 5 1 2 3 7 4 5 6 7 4 5 6 4 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 4 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 0 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 129-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 127-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 125-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 123-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 7 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 7 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 0 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 121-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 120-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 0 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 119-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 10 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 10 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 118-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 116-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 114-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 113-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 111-rule system
{ 0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 8 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 8 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 7 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 7 ,
  0 1 2 3 0 1 4 5 6 7 0 5 6 8 2 4 1 3 7 7 0 ⟶ 7 0 6 8 3 8 2 3 0 1 4 1 4 6 8 4 5 6 8 3 0 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  2 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 2 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  8 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 8 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  1 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 1 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 8 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 8 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 7 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 7 ,
  9 2 3 0 5 6 8 4 1 3 7 8 2 4 5 1 2 3 7 7 0 ⟶ 9 3 8 4 5 5 1 4 1 4 1 4 1 3 7 0 1 2 2 3 0 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  2 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 2 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  8 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 8 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  1 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 1 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 8 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 8 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 7 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 7 ,
  9 3 0 5 1 2 4 5 1 2 4 5 1 4 5 6 7 0 6 7 0 ⟶ 9 3 8 3 0 5 5 5 5 1 3 8 3 7 8 3 7 0 5 6 0 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 7 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 7 ,
  2 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 0 ⟶ 2 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 0 ,
  8 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 8 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  1 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 1 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  9 4 5 1 3 0 1 2 3 0 5 5 6 8 4 6 8 4 6 7 8 ⟶ 9 4 5 5 6 7 0 1 2 4 6 0 1 2 2 3 8 2 4 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  3 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 2 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 8 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 8 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 7 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 7 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 0 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 0 ,
  7 7 8 4 1 2 2 4 6 0 6 0 6 0 5 5 1 2 3 7 10 ⟶ 8 4 5 5 6 0 1 4 1 3 0 6 0 1 2 3 8 3 0 6 10 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  3 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 2 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 8 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 8 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 7 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 7 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 0 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 0 ,
  7 0 1 2 2 4 6 0 1 4 1 2 4 6 8 2 3 7 0 6 10 ⟶ 8 2 3 7 8 2 3 8 4 1 3 0 1 2 2 3 8 2 3 7 10 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  4 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 2 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 8 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 8 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 7 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 7 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 0 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 0 ,
  0 6 0 6 8 4 5 1 3 0 6 7 7 0 5 6 0 6 0 6 10 ⟶ 8 4 6 8 2 3 0 5 6 0 1 3 8 3 7 0 5 1 3 7 10 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  4 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 3 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 8 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 8 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 7 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 7 ,
  0 5 6 0 6 8 3 7 0 1 2 3 8 4 1 4 6 0 5 6 0 ⟶ 7 8 3 0 5 5 1 4 6 0 6 8 2 2 3 8 4 6 7 7 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  3 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 2 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 8 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 8 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 7 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 7 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 0 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 0 ,
  7 0 5 1 2 4 1 3 8 2 4 1 4 1 3 8 3 0 5 6 10 ⟶ 8 3 7 8 3 0 1 2 3 8 4 6 0 6 0 5 5 6 8 3 10 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 8 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 8 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 7 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 7 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 0 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 0 ,
  6 7 0 6 8 2 4 6 8 4 5 1 2 3 8 3 8 4 5 6 10 ⟶ 5 6 0 5 6 8 2 2 2 4 6 8 4 1 3 7 7 8 4 6 10 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  3 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 3 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  7 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 7 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 7 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 7 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 0 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 0 ,
  6 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 10 ⟶ 6 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 10 ,
  11 7 7 8 3 7 7 8 2 4 5 5 1 3 7 8 3 8 4 6 8 ⟶ 11 0 6 0 1 4 6 8 2 4 6 0 5 6 0 1 3 7 0 6 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  3 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 2 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 8 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 8 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 7 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 7 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 0 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 0 ,
  7 7 0 6 7 7 7 0 5 1 2 3 0 5 1 3 7 7 8 3 10 ⟶ 8 4 1 4 1 3 8 3 7 8 2 2 2 3 7 7 0 1 3 7 10 ,
  4 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 4 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  0 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 0 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  5 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 5 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  12 1 3 0 1 3 7 8 4 1 3 7 7 7 0 5 5 5 1 3 8 ⟶ 12 1 3 0 1 2 2 2 3 7 8 3 8 4 5 6 0 6 7 7 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  3 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 2 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 8 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 8 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 7 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 7 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 0 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 0 ,
  7 8 3 8 3 8 4 1 4 5 6 8 4 5 5 6 8 4 1 3 10 ⟶ 8 2 3 8 2 4 6 0 6 8 4 1 4 5 6 0 5 1 4 6 10 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  4 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 3 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 8 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 8 ,
  0 5 1 3 0 6 0 6 8 3 0 6 0 6 8 4 5 1 2 3 7 ⟶ 7 8 3 7 7 8 2 4 5 1 2 3 7 0 5 6 7 0 5 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 2 ↦ 0, 3 ↦ 1, 0 ↦ 2, 5 ↦ 3, 6 ↦ 4, 8 ↦ 5, 4 ↦ 6, 1 ↦ 7, 7 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 108-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 106-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 104-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 102-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 101-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 99-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 97-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 8 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 8 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 2 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 2 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 95-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 8 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 8 ,
  0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 2 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 2 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 93-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 91-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

12 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 90-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 8 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 8 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 2 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 2 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 },
it remains to prove termination of the 88-rule system
{ 0 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 0 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  5 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 5 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  7 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 7 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  9 0 1 2 3 4 5 6 7 1 8 5 0 6 3 7 0 1 8 8 5 ⟶ 9 1 5 6 3 3 7 6 7 6 7 6 7 1 8 2 7 0 0 1 5 ,
  0 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 0 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  5 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 5 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  7 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 7 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  9 1 2 3 7 0 6 3 7 0 6 3 7 6 3 4 8 2 4 8 5 ⟶ 9 1 5 1 2 3 3 3 3 7 1 5 1 8 5 1 8 2 3 4 5 ,
  0 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 0 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  5 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 5 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  7 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 7 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  9 6 3 7 1 2 7 0 1 2 3 3 4 5 6 4 5 6 4 8 5 ⟶ 9 6 3 3 4 8 2 7 0 6 4 2 7 0 0 1 5 0 6 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  1 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 0 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 5 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 5 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 8 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 8 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 2 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 2 ,
  8 8 5 6 7 0 0 6 4 2 4 2 4 2 3 3 7 0 1 8 10 ⟶ 5 6 3 3 4 2 7 6 7 1 2 4 2 7 0 1 5 1 2 4 10 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  1 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 0 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 5 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 5 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 8 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 8 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 2 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 2 ,
  8 2 7 0 0 6 4 2 7 6 7 0 6 4 5 0 1 8 2 4 10 ⟶ 5 0 1 8 5 0 1 5 6 7 1 2 7 0 0 1 5 0 1 8 10 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  6 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 0 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 5 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 5 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 8 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 8 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 2 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 2 ,
  2 4 2 4 5 6 3 7 1 2 4 8 8 2 3 4 2 4 2 4 10 ⟶ 5 6 4 5 0 1 2 3 4 2 7 1 5 1 8 2 3 7 1 8 10 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  6 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 1 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 5 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 5 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 8 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 8 ,
  2 3 4 2 4 5 1 8 2 7 0 1 5 6 7 6 4 2 3 4 2 ⟶ 8 5 1 2 3 3 7 6 4 2 4 5 0 0 1 5 6 4 8 8 2 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  1 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 0 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 5 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 5 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 8 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 8 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 2 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 2 ,
  8 2 3 7 0 6 7 1 5 0 6 7 6 7 1 5 1 2 3 4 10 ⟶ 5 1 8 5 1 2 7 0 1 5 6 4 2 4 2 3 3 4 5 1 10 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 5 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 5 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 8 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 8 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 2 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 2 ,
  4 8 2 4 5 0 6 4 5 6 3 7 0 1 5 1 5 6 3 4 10 ⟶ 3 4 2 3 4 5 0 0 0 6 4 5 6 7 1 8 8 5 6 4 10 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  1 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 1 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  8 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 8 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 8 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 8 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 2 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 2 ,
  4 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 10 ⟶ 4 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 10 ,
  11 8 8 5 1 8 8 5 0 6 3 3 7 1 8 5 1 5 6 4 5 ⟶ 11 2 4 2 7 6 4 5 0 6 4 2 3 4 2 7 1 8 2 4 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  1 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 0 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 5 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 5 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 8 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 8 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 2 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 2 ,
  8 8 2 4 8 8 8 2 3 7 0 1 2 3 7 1 8 8 5 1 10 ⟶ 5 6 7 6 7 1 5 1 8 5 0 0 0 1 8 8 2 7 1 8 10 ,
  6 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 6 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  2 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 2 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  3 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 3 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  12 7 1 2 7 1 8 5 6 7 1 8 8 8 2 3 3 3 7 1 5 ⟶ 12 7 1 2 7 0 0 0 1 8 5 1 5 6 3 4 2 4 8 8 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  1 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 0 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 5 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 5 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 8 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 8 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 2 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 2 ,
  8 5 1 5 1 5 6 7 6 3 4 5 6 3 3 4 5 6 7 1 10 ⟶ 5 0 1 5 0 6 4 2 4 5 6 7 6 3 4 2 3 7 6 4 10 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  6 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 1 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 5 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 5 ,
  2 3 7 1 2 4 2 4 5 1 2 4 2 4 5 6 3 7 0 1 8 ⟶ 8 5 1 8 8 5 0 6 3 7 0 1 8 2 3 4 8 2 3 4 8 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

12 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 1 ↦ 0, 8 ↦ 1, 5 ↦ 2, 6 ↦ 3, 7 ↦ 4, 0 ↦ 5, 4 ↦ 6, 2 ↦ 7, 3 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11 },
it remains to prove termination of the 60-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 9 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 9 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 1 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 1 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 7 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 7 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 9 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 9 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 1 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 58-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 9 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 9 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 9 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 9 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 1 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 56-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 1 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 55-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 1 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 53-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 1 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 1 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 52-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 5 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 2 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 2 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 1 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 1 ,
  1 7 8 4 5 3 4 0 2 5 3 4 3 4 0 2 0 7 8 6 7 ⟶ 2 0 1 2 0 7 4 5 0 2 3 6 7 6 7 8 8 6 2 0 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 46-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 45-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 44-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 9 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 9 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 42:

0 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

1 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

2 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

3 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

4 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

5 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

6 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

7 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

8 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

9 ↦ ⎛                                                                                     ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                                                                     ⎠

10 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

11 ↦ ⎛                                                                                     ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                                                                     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 42-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11 },
it remains to prove termination of the 40-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  0 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 5 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 2 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 2 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 1 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 1 ,
  1 7 4 5 5 3 6 7 4 3 4 5 3 6 2 5 0 1 7 6 7 ⟶ 2 5 0 1 2 5 0 2 3 4 0 7 4 5 5 0 2 5 0 1 7 ,
  7 8 6 7 6 2 0 1 7 4 5 0 2 3 4 3 6 7 8 6 2 ⟶ 1 2 0 7 8 8 4 3 6 7 6 2 5 5 0 2 3 6 1 1 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  0 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 0 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  1 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 1 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 1 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 1 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 7 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 7 ,
  6 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 9 ⟶ 6 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 9 ,
  10 1 1 2 0 1 1 2 5 3 8 8 4 0 1 2 0 2 3 6 2 ⟶ 10 7 6 7 4 3 6 2 5 3 6 7 8 6 7 4 0 1 7 6 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  0 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 5 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 2 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 2 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 1 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 1 ,
  1 1 7 6 1 1 1 7 8 4 5 0 7 8 4 0 1 1 2 0 7 ⟶ 2 3 4 3 4 0 2 0 1 2 5 5 5 0 1 1 7 4 0 1 7 ,
  3 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 3 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  7 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 7 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  8 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 8 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  11 4 0 7 4 0 1 2 3 4 0 1 1 1 7 8 8 8 4 0 2 ⟶ 11 4 0 7 4 5 5 5 0 1 2 0 2 3 8 6 7 6 1 1 2 ,
  0 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 5 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 2 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 2 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 1 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 1 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 7 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 7 ,
  1 2 0 2 0 2 3 4 3 8 6 2 3 8 8 6 2 3 4 0 9 ⟶ 2 5 0 2 5 3 6 7 6 2 3 4 3 8 6 7 8 4 3 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 22:

0 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

1 ↦ ⎛                                             ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

2 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

3 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

4 ↦ ⎛                                             ⎞
    ⎜ 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

5 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

6 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

7 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

8 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

9 ↦ ⎛                                             ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                                             ⎠

10 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

11 ↦ ⎛                                             ⎞
     ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
     ⎝                                             ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9 },
it remains to prove termination of the 8-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 ,
  1 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 9 ⟶ 2 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 9 ,
  7 8 4 0 7 6 7 6 2 0 7 6 7 6 2 3 8 4 5 0 2 ⟶ 1 2 0 1 1 2 5 3 8 4 5 0 1 7 8 6 1 7 8 6 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

9 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8 },
it remains to prove termination of the 3-rule system
{ 0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 2 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 2 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 1 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 1 ,
  0 1 2 3 4 5 5 3 6 7 6 7 6 7 8 8 4 5 0 1 7 ⟶ 5 3 8 8 6 7 4 3 4 0 7 6 7 4 5 0 2 0 7 6 7 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

6 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

7 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

8 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection {  },
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.