active
U11
tt
N
mark
N
active
U21
tt
M
N
mark
s
plus
N
M
active
U31
tt
mark
0
active
U41
tt
M
N
mark
plus
x
N
M
N
active
and
tt
X
mark
X
active
isNat
0
mark
tt
active
isNat
plus
V1
V2
mark
and
isNat
V1
isNat
V2
active
isNat
s
V1
mark
isNat
V1
active
isNat
x
V1
V2
mark
and
isNat
V1
isNat
V2
active
plus
N
0
mark
U11
isNat
N
N
active
plus
N
s
M
mark
U21
and
isNat
M
isNat
N
M
N
active
x
N
0
mark
U31
isNat
N
active
x
N
s
M
mark
U41
and
isNat
M
isNat
N
M
N
active
U11
X1
X2
U11
active
X1
X2
active
U21
X1
X2
X3
U21
active
X1
X2
X3
active
s
X
s
active
X
active
plus
X1
X2
plus
active
X1
X2
active
plus
X1
X2
plus
X1
active
X2
active
U31
X
U31
active
X
active
U41
X1
X2
X3
U41
active
X1
X2
X3
active
x
X1
X2
x
active
X1
X2
active
x
X1
X2
x
X1
active
X2
active
and
X1
X2
and
active
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
s
mark
X
mark
s
X
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U31
mark
X
mark
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
x
X1
mark
X2
mark
x
X1
X2
and
mark
X1
X2
mark
and
X1
X2
proper
U11
X1
X2
U11
proper
X1
proper
X2
proper
tt
ok
tt
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
proper
s
X
s
proper
X
proper
plus
X1
X2
plus
proper
X1
proper
X2
proper
U31
X
U31
proper
X
proper
0
ok
0
proper
U41
X1
X2
X3
U41
proper
X1
proper
X2
proper
X3
proper
x
X1
X2
x
proper
X1
proper
X2
proper
and
X1
X2
and
proper
X1
proper
X2
proper
isNat
X
isNat
proper
X
U11
ok
X1
ok
X2
ok
U11
X1
X2
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
s
ok
X
ok
s
X
plus
ok
X1
ok
X2
ok
plus
X1
X2
U31
ok
X
ok
U31
X
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
x
ok
X1
ok
X2
ok
x
X1
X2
and
ok
X1
ok
X2
ok
and
X1
X2
isNat
ok
X
ok
isNat
X
top
mark
X
top
proper
X
top
ok
X
top
active
X
2.2
active
U21
tt
M
N
plus
N
M
active
U21
X1
X2
X3
U21
active
X1
X2
X3
x
mark
X1
X2
x
X1
X2
active
x
N
s
M
isNat
N
active
plus
N
s
M
isNat
M
top
mark
X
top
proper
X
proper
U11
X1
X2
proper
X1
U41
mark
X1
X2
X3
U41
X1
X2
X3
active
x
N
0
isNat
N
active
x
N
0
U31
isNat
N
U11
mark
X1
X2
U11
X1
X2
active
plus
X1
X2
plus
X1
active
X2
active
U31
X
active
X
and
ok
X1
ok
X2
and
X1
X2
active
isNat
plus
V1
V2
isNat
V1
x
X1
mark
X2
x
X1
X2
U31
ok
X
U31
X
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
s
mark
X
s
X
active
plus
N
0
isNat
N
proper
isNat
X
proper
X
active
and
X1
X2
and
active
X1
X2
U31
mark
X
U31
X
and
mark
X1
X2
and
X1
X2
proper
U31
X
U31
proper
X
proper
U11
X1
X2
proper
X2
U11
ok
X1
ok
X2
U11
X1
X2
U41
ok
X1
ok
X2
ok
X3
U41
X1
X2
X3
active
U41
X1
X2
X3
active
X1
proper
U41
X1
X2
X3
proper
X2
proper
x
X1
X2
proper
X1
proper
U41
X1
X2
X3
U41
proper
X1
proper
X2
proper
X3
active
plus
N
0
U11
isNat
N
N
proper
U21
X1
X2
X3
proper
X1
top
ok
X
active
X
active
plus
X1
X2
active
X1
top
ok
X
top
active
X
active
s
X
s
active
X
proper
U21
X1
X2
X3
proper
X3
active
U11
X1
X2
active
X1
active
plus
X1
X2
plus
active
X1
X2
proper
U41
X1
X2
X3
proper
X1
active
isNat
x
V1
V2
isNat
V1
active
x
X1
X2
x
active
X1
X2
proper
U31
X
proper
X
active
U41
tt
M
N
x
N
M
active
s
X
active
X
proper
U41
X1
X2
X3
proper
X3
plus
X1
mark
X2
plus
X1
X2
active
isNat
x
V1
V2
and
isNat
V1
isNat
V2
active
isNat
plus
V1
V2
and
isNat
V1
isNat
V2
U21
mark
X1
X2
X3
U21
X1
X2
X3
x
ok
X1
ok
X2
x
X1
X2
proper
plus
X1
X2
plus
proper
X1
proper
X2
active
U41
tt
M
N
plus
x
N
M
N
U21
ok
X1
ok
X2
ok
X3
U21
X1
X2
X3
active
and
X1
X2
active
X1
proper
x
X1
X2
proper
X2
active
plus
X1
X2
active
X2
active
x
X1
X2
active
X2
active
plus
N
s
M
U21
and
isNat
M
isNat
N
M
N
active
U31
X
U31
active
X
proper
and
X1
X2
proper
X2
active
U11
X1
X2
U11
active
X1
X2
proper
U11
X1
X2
U11
proper
X1
proper
X2
active
x
N
s
M
isNat
M
proper
plus
X1
X2
proper
X2
active
plus
N
s
M
and
isNat
M
isNat
N
top
mark
X
proper
X
active
U21
X1
X2
X3
active
X1
active
x
N
s
M
and
isNat
M
isNat
N
proper
isNat
X
isNat
proper
X
s
ok
X
s
X
active
isNat
x
V1
V2
isNat
V2
plus
ok
X1
ok
X2
plus
X1
X2
active
x
X1
X2
x
X1
active
X2
active
x
N
s
M
U41
and
isNat
M
isNat
N
M
N
active
isNat
s
V1
isNat
V1
plus
mark
X1
X2
plus
X1
X2
active
plus
N
s
M
isNat
N
proper
plus
X1
X2
proper
X1
proper
s
X
proper
X
proper
and
X1
X2
and
proper
X1
proper
X2
proper
U21
X1
X2
X3
proper
X2
active
U21
tt
M
N
s
plus
N
M
active
isNat
plus
V1
V2
isNat
V2
proper
x
X1
X2
x
proper
X1
proper
X2
proper
s
X
s
proper
X
proper
and
X1
X2
proper
X1
active
x
X1
X2
active
X1
active
U41
X1
X2
X3
U41
active
X1
X2
X3
isNat
ok
X
isNat
X
true
top
ok
X
top
active
X
top
mark
X
top
proper
X
true
top
1
1
top
1
1
proper
1
1
ok
1
1
x
2
2
isNat
1
1
active
1
1
U31
1
1
U21
3
5
3
2
1
U11
2
4
2
1
s
1
0
1
isNat
1
0
and
2
4
1
2
plus
2
0
1
2
x
2
7
1
2
0
0
3
s
1
0
mark
1
0
1
proper
1
0
plus
2
5
1
2
U11
2
0
2
1
U31
1
3
1
U41
3
0
1
3
2
active
1
0
U21
3
0
2
1
tt
0
2
U41
3
7
3
2
1
and
2
0
1
2
U21
3
1
0
2
0
3
0
0
U11
2
1
0
2
0
0
s
1
1
0
isNat
1
0
and
2
1
0
2
0
0
plus
2
1
0
2
0
0
x
2
1
0
2
0
0
0
0
0
s
1
0
mark
1
1
0
proper
1
0
plus
2
1
0
2
0
0
U11
2
1
0
2
0
0
U31
1
1
0
U41
3
1
0
2
0
3
0
0
active
1
0
U21
3
1
0
2
0
0
tt
0
0
U41
3
1
0
2
0
3
0
0
and
2
1
0
2
0
0
top
ok
X
top
active
X
active
plus
X1
X2
plus
X1
active
X2
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
active
U41
tt
M
N
mark
plus
x
N
M
N
active
U21
X1
X2
X3
U21
active
X1
X2
X3
active
isNat
s
V1
mark
isNat
V1
active
U11
tt
N
mark
N
active
U31
tt
mark
0
active
s
X
s
active
X
active
x
X1
X2
x
active
X1
X2
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
s
mark
X
mark
s
X
active
U31
X
U31
active
X
x
X1
mark
X2
mark
x
X1
X2
active
plus
X1
X2
plus
active
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
proper
U11
X1
X2
U11
proper
X1
proper
X2
active
x
X1
X2
x
X1
active
X2
plus
X1
mark
X2
mark
plus
X1
X2
proper
isNat
X
isNat
proper
X
active
and
tt
X
mark
X
and
mark
X1
X2
mark
and
X1
X2
active
plus
N
0
mark
U11
isNat
N
N
proper
U31
X
U31
proper
X
active
isNat
plus
V1
V2
mark
and
isNat
V1
isNat
V2
active
U41
X1
X2
X3
U41
active
X1
X2
X3
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
and
ok
X1
ok
X2
ok
and
X1
X2
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
active
U11
X1
X2
U11
active
X1
X2
x
mark
X1
X2
mark
x
X1
X2
active
x
N
0
mark
U31
isNat
N
U11
ok
X1
ok
X2
ok
U11
X1
X2
active
and
X1
X2
and
active
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
active
plus
N
s
M
mark
U21
and
isNat
M
isNat
N
M
N
active
isNat
x
V1
V2
mark
and
isNat
V1
isNat
V2
active
x
N
s
M
mark
U41
and
isNat
M
isNat
N
M
N
x
ok
X1
ok
X2
ok
x
X1
X2
proper
0
ok
0
active
isNat
0
mark
tt
proper
plus
X1
X2
plus
proper
X1
proper
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
proper
s
X
s
proper
X
proper
U41
X1
X2
X3
U41
proper
X1
proper
X2
proper
X3
proper
x
X1
X2
x
proper
X1
proper
X2
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
proper
tt
ok
tt
U31
mark
X
mark
U31
X
proper
and
X1
X2
and
proper
X1
proper
X2
active
U21
tt
M
N
mark
s
plus
N
M
top
ok
X
top
active
X
true
U21
3
1
0
U11
2
1
0
s
1
1
0
isNat
1
0
top
1
0
and
2
1
0
plus
2
0
top
1
1
0
x
2
2
0
proper
1
3
ok
1
1
2
0
0
1
x
2
0
s
1
0
mark
1
0
proper
1
0
isNat
1
1
0
plus
2
1
0
U11
2
0
active
1
1
1
U31
1
1
0
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
2
0
U31
1
0
and
2
0
active
plus
X1
X2
plus
X1
active
X2
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
active
U41
tt
M
N
mark
plus
x
N
M
N
active
U21
X1
X2
X3
U21
active
X1
X2
X3
active
isNat
s
V1
mark
isNat
V1
active
U11
tt
N
mark
N
active
U31
tt
mark
0
active
s
X
s
active
X
active
x
X1
X2
x
active
X1
X2
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
s
mark
X
mark
s
X
active
U31
X
U31
active
X
x
X1
mark
X2
mark
x
X1
X2
active
plus
X1
X2
plus
active
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
proper
U11
X1
X2
U11
proper
X1
proper
X2
active
x
X1
X2
x
X1
active
X2
plus
X1
mark
X2
mark
plus
X1
X2
proper
isNat
X
isNat
proper
X
active
and
tt
X
mark
X
and
mark
X1
X2
mark
and
X1
X2
active
plus
N
0
mark
U11
isNat
N
N
proper
U31
X
U31
proper
X
active
isNat
plus
V1
V2
mark
and
isNat
V1
isNat
V2
active
U41
X1
X2
X3
U41
active
X1
X2
X3
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
and
ok
X1
ok
X2
ok
and
X1
X2
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
active
U11
X1
X2
U11
active
X1
X2
x
mark
X1
X2
mark
x
X1
X2
active
x
N
0
mark
U31
isNat
N
U11
ok
X1
ok
X2
ok
U11
X1
X2
active
and
X1
X2
and
active
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
active
plus
N
s
M
mark
U21
and
isNat
M
isNat
N
M
N
active
isNat
x
V1
V2
mark
and
isNat
V1
isNat
V2
active
x
N
s
M
mark
U41
and
isNat
M
isNat
N
M
N
x
ok
X1
ok
X2
ok
x
X1
X2
proper
0
ok
0
active
isNat
0
mark
tt
proper
plus
X1
X2
plus
proper
X1
proper
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
proper
s
X
s
proper
X
proper
U41
X1
X2
X3
U41
proper
X1
proper
X2
proper
X3
proper
x
X1
X2
x
proper
X1
proper
X2
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
proper
tt
ok
tt
U31
mark
X
mark
U31
X
proper
and
X1
X2
and
proper
X1
proper
X2
active
U21
tt
M
N
mark
s
plus
N
M
top
ok
X
active
X
false
top
mark
X
proper
X
false
proper
and
X1
X2
proper
X1
proper
U41
X1
X2
X3
proper
X3
proper
U31
X
proper
X
proper
U41
X1
X2
X3
proper
X1
proper
U21
X1
X2
X3
proper
X3
proper
U21
X1
X2
X3
proper
X2
proper
s
X
proper
X
proper
plus
X1
X2
proper
X1
proper
U21
X1
X2
X3
proper
X1
proper
x
X1
X2
proper
X1
proper
U41
X1
X2
X3
proper
X2
proper
U11
X1
X2
proper
X2
proper
isNat
X
proper
X
proper
plus
X1
X2
proper
X2
proper
and
X1
X2
proper
X2
proper
x
X1
X2
proper
X2
proper
U11
X1
X2
proper
X1
true
U21
3
1
2
3
1
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
1
2
1
plus
2
0
top
1
0
x
2
1
2
1
proper
1
0
ok
1
17891
0
0
10282
x
2
0
s
1
0
mark
1
1
0
proper
1
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
0
U31
1
1
6617
U41
3
0
active
1
0
U21
3
0
tt
0
9123
U41
3
1
2
3
1
U31
1
0
and
2
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
and
mark
X1
X2
mark
and
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
and
ok
X1
ok
X2
ok
and
X1
X2
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
proper
and
X1
X2
and
proper
X1
proper
X2
false
proper
x
X1
X2
x
proper
X1
proper
X2
false
proper
U41
X1
X2
X3
U41
proper
X1
proper
X2
proper
X3
false
proper
s
X
s
proper
X
false
proper
U31
X
U31
proper
X
false
proper
isNat
X
isNat
proper
X
false
proper
U11
X1
X2
U11
proper
X1
proper
X2
false
proper
U21
X1
X2
X3
U21
proper
X1
proper
X2
proper
X3
false
active
x
X1
X2
active
X1
active
s
X
active
X
active
U11
X1
X2
active
X1
active
plus
X1
X2
active
X1
active
U41
X1
X2
X3
active
X1
active
U21
X1
X2
X3
active
X1
active
U31
X
active
X
active
x
X1
X2
active
X2
active
plus
X1
X2
active
X2
active
and
X1
X2
active
X1
true
U21
3
1
2
3
1
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
1
2
1
plus
2
0
top
1
0
x
2
1
2
1
proper
1
0
ok
1
1
0
0
9133
x
2
0
s
1
0
mark
1
1
0
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
0
U31
1
1
6617
U41
3
0
active
1
1
0
U21
3
0
tt
0
9123
U41
3
1
2
3
1
U31
1
0
and
2
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
and
mark
X1
X2
mark
and
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
and
ok
X1
ok
X2
ok
and
X1
X2
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
active
U21
tt
M
N
s
plus
N
M
false
active
x
N
s
M
U41
and
isNat
M
isNat
N
M
N
false
active
x
N
s
M
and
isNat
M
isNat
N
false
active
x
N
s
M
isNat
M
false
active
isNat
x
V1
V2
and
isNat
V1
isNat
V2
false
active
isNat
x
V1
V2
isNat
V1
false
active
isNat
x
V1
V2
isNat
V2
false
active
plus
N
s
M
U21
and
isNat
M
isNat
N
M
N
false
active
plus
N
s
M
and
isNat
M
isNat
N
false
active
plus
N
s
M
isNat
N
false
active
and
X1
X2
and
active
X1
X2
false
active
x
N
0
U31
isNat
N
false
active
x
N
0
isNat
N
false
active
U11
X1
X2
U11
active
X1
X2
false
active
U41
X1
X2
X3
U41
active
X1
X2
X3
false
U41
ok
X1
ok
X2
ok
X3
U41
X1
X2
X3
U41
mark
X1
X2
X3
U41
X1
X2
X3
true
U21
3
1
3
0
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
1
2
1
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
0
mark
1
1
0
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
0
U31
1
1
1
U41
3
2
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
0
and
2
0
U41
mark
X1
X2
X3
U41
X1
X2
X3
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
and
mark
X1
X2
mark
and
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
and
ok
X1
ok
X2
ok
and
X1
X2
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
U41
mark
X1
X2
X3
U41
X1
X2
X3
true
U21
3
1
3
0
U11
2
1
2
20253
s
1
1
1
isNat
1
0
top
1
0
and
2
2
2
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
1
U31
1
1
2631
U41
3
1
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
0
and
2
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
active
isNat
plus
V1
V2
and
isNat
V1
isNat
V2
false
and
mark
X1
X2
and
X1
X2
and
ok
X1
ok
X2
and
X1
X2
true
U21
3
1
3
0
U11
2
1
2
17979
s
1
1
1
isNat
1
0
top
1
0
and
2
2
2
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
1
U31
1
1
1
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
0
and
2
1
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
active
isNat
plus
V1
V2
isNat
V1
false
active
isNat
plus
V1
V2
isNat
V2
false
active
plus
N
0
U11
isNat
N
N
false
U11
ok
X1
ok
X2
U11
X1
X2
U11
mark
X1
X2
U11
X1
X2
true
U21
3
1
3
0
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
2
21639
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
2
0
active
1
1
U31
1
1
32299
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
0
and
2
0
U11
mark
X1
X2
U11
X1
X2
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
U11
mark
X1
X2
U11
X1
X2
true
U21
3
1
3
0
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
2
21639
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
15530
0
0
1
x
2
0
s
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
1
0
active
1
1
U31
1
1
1
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
0
and
2
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
active
plus
N
0
isNat
N
false
active
x
X1
X2
x
X1
active
X2
false
active
plus
X1
X2
plus
active
X1
X2
false
active
U31
X
U31
active
X
false
U31
mark
X
U31
X
U31
ok
X
U31
X
true
U21
3
1
3
0
U11
2
1
2
1
s
1
1
1
isNat
1
0
top
1
0
and
2
2
21639
plus
2
0
top
1
0
x
2
1
2
0
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
1
2
1
U11
2
0
active
1
1
U31
1
1
7362
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
1
2
3
0
U31
1
1
0
and
2
0
U41
ok
X1
ok
X2
ok
X3
ok
U41
X1
X2
X3
s
mark
X
mark
s
X
x
X1
mark
X2
mark
x
X1
X2
plus
mark
X1
X2
mark
plus
X1
X2
plus
X1
mark
X2
mark
plus
X1
X2
U21
mark
X1
X2
X3
mark
U21
X1
X2
X3
U31
ok
X
ok
U31
X
U41
mark
X1
X2
X3
mark
U41
X1
X2
X3
x
mark
X1
X2
mark
x
X1
X2
U11
ok
X1
ok
X2
ok
U11
X1
X2
U11
mark
X1
X2
mark
U11
X1
X2
x
ok
X1
ok
X2
ok
x
X1
X2
plus
ok
X1
ok
X2
ok
plus
X1
X2
isNat
ok
X
ok
isNat
X
s
ok
X
ok
s
X
U21
ok
X1
ok
X2
ok
X3
ok
U21
X1
X2
X3
U31
mark
X
mark
U31
X
active
x
X1
X2
x
active
X1
X2
false
active
s
X
s
active
X
false
s
ok
X
s
X
s
mark
X
s
X
true
U21
3
3
8703
U11
2
21332
s
1
1
1
isNat
1
0
top
1
0
and
2
28939
plus
2
0
top
1
0
x
2
11404
proper
1
1
ok
1
1
1
0
0
1
x
2
0
s
1
1
0
mark
1
1
1
proper
1
0
isNat
1
1
1
plus
2
8137
U11
2
0
active
1
1
U31
1
1
1
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
27073
U31
1
0
and
2
0
active
isNat
s
V1
isNat
V1
false
active
U41
tt
M
N
x
N
M
false
active
plus
X1
X2
plus
X1
active
X2
false
active
U41
tt
M
N
plus
x
N
M
N
false
active
plus
N
s
M
isNat
M
false
active
x
N
s
M
isNat
N
false
isNat
ok
X
isNat
X
true
U21
3
2
U11
2
2
s
1
2
isNat
1
1
0
top
1
0
and
2
2
plus
2
0
top
1
0
x
2
2
proper
1
1
ok
1
1
1
0
0
17037
x
2
0
s
1
0
mark
1
3
proper
1
0
isNat
1
31607
plus
2
2
2
U11
2
0
active
1
1
U31
1
1
1
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
2
2
U31
1
0
and
2
0
active
U21
X1
X2
X3
U21
active
X1
X2
X3
false
U21
mark
X1
X2
X3
U21
X1
X2
X3
U21
ok
X1
ok
X2
ok
X3
U21
X1
X2
X3
true
U21
3
21541
U11
2
27531
s
1
29829
isNat
1
0
top
1
0
and
2
15093
plus
2
0
top
1
0
x
2
29305
proper
1
1
ok
1
1
1
0
0
17037
x
2
0
s
1
0
mark
1
1
24228
proper
1
0
isNat
1
31607
plus
2
1
2160
U11
2
0
active
1
1
U31
1
2
U41
3
0
active
1
0
U21
3
2
0
tt
0
3288
U41
3
2
2
U31
1
0
and
2
0
U21
mark
X1
X2
X3
U21
X1
X2
X3
U21
mark
X1
X2
X3
U21
X1
X2
X3
true
U21
3
23033
U11
2
23724
s
1
12771
isNat
1
0
top
1
0
and
2
29351
plus
2
0
top
1
0
x
2
21966
proper
1
1
ok
1
1
18418
0
0
17037
x
2
0
s
1
0
mark
1
1
15079
proper
1
0
isNat
1
29007
plus
2
1
7675
U11
2
0
active
1
1
U31
1
2
U41
3
0
active
1
0
U21
3
1
0
tt
0
28472
U41
3
24813
U31
1
0
and
2
0
x
ok
X1
ok
X2
x
X1
X2
x
X1
mark
X2
x
X1
X2
x
mark
X1
X2
x
X1
X2
true
U21
3
2
U11
2
23724
s
1
19079
isNat
1
0
top
1
0
and
2
2992
plus
2
0
top
1
0
x
2
21966
proper
1
1
ok
1
1
9251
0
0
1
x
2
1
2
0
s
1
0
mark
1
1
15079
proper
1
0
isNat
1
2
plus
2
1
879
U11
2
0
active
1
1
U31
1
13421
U41
3
0
active
1
0
U21
3
0
tt
0
6753
U41
3
21796
U31
1
0
and
2
0
active
U21
tt
M
N
plus
N
M
false
proper
plus
X1
X2
plus
proper
X1
proper
X2
false
plus
X1
mark
X2
plus
X1
X2
plus
mark
X1
X2
plus
X1
X2
plus
ok
X1
ok
X2
plus
X1
X2
true
U21
3
1
2
1
U11
2
2
s
1
12783
isNat
1
0
top
1
0
and
2
2
plus
2
1
0
top
1
0
x
2
21966
proper
1
1
ok
1
1
4092
0
0
20540
x
2
0
s
1
0
mark
1
1
4331
proper
1
0
isNat
1
2
plus
2
1
9556
U11
2
0
active
1
1
U31
1
37711
U41
3
0
active
1
0
U21
3
0
tt
0
16542
U41
3
19691
U31
1
0
and
2
0
plus
X1
mark
X2
plus
X1
X2
plus
X1
mark
X2
plus
X1
X2
true
U21
3
1
2
1
U11
2
6559
s
1
2954
isNat
1
0
top
1
0
and
2
2
plus
2
2
0
top
1
0
x
2
21966
proper
1
1
ok
1
1
3
0
0
20540
x
2
0
s
1
0
mark
1
1
4331
proper
1
0
isNat
1
14652
plus
2
1
16161
U11
2
0
active
1
1
U31
1
28085
U41
3
0
active
1
0
U21
3
0
tt
0
1
U41
3
2
U31
1
0
and
2
0
NaTT
certifiable-1.6