active
nats
mark
cons
0
incr
nats
active
pairs
mark
cons
0
incr
odds
active
odds
mark
incr
pairs
active
incr
cons
X
XS
mark
cons
s
X
incr
XS
active
head
cons
X
XS
mark
X
active
tail
cons
X
XS
mark
XS
active
cons
X1
X2
cons
active
X1
X2
active
incr
X
incr
active
X
active
s
X
s
active
X
active
head
X
head
active
X
active
tail
X
tail
active
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
s
mark
X
mark
s
X
head
mark
X
mark
head
X
tail
mark
X
mark
tail
X
proper
nats
ok
nats
proper
cons
X1
X2
cons
proper
X1
proper
X2
proper
0
ok
0
proper
incr
X
incr
proper
X
proper
pairs
ok
pairs
proper
odds
ok
odds
proper
s
X
s
proper
X
proper
head
X
head
proper
X
proper
tail
X
tail
proper
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
incr
ok
X
ok
incr
X
s
ok
X
ok
s
X
head
ok
X
ok
head
X
tail
ok
X
ok
tail
X
top
mark
X
top
proper
X
top
ok
X
top
active
X
2.2
active
pairs
incr
odds
proper
cons
X1
X2
proper
X2
top
ok
X
active
X
active
incr
X
incr
active
X
proper
cons
X1
X2
proper
X1
proper
cons
X1
X2
cons
proper
X1
proper
X2
head
mark
X
head
X
active
incr
cons
X
XS
cons
s
X
incr
XS
active
s
X
active
X
active
incr
cons
X
XS
incr
XS
cons
mark
X1
X2
cons
X1
X2
proper
head
X
head
proper
X
proper
s
X
s
proper
X
active
head
X
head
active
X
active
cons
X1
X2
active
X1
proper
s
X
proper
X
tail
mark
X
tail
X
top
mark
X
top
proper
X
cons
ok
X1
ok
X2
cons
X1
X2
active
head
X
active
X
proper
incr
X
incr
proper
X
active
tail
X
tail
active
X
active
incr
cons
X
XS
s
X
proper
head
X
proper
X
active
nats
cons
0
incr
nats
active
s
X
s
active
X
top
ok
X
top
active
X
active
cons
X1
X2
cons
active
X1
X2
active
nats
incr
nats
incr
ok
X
incr
X
tail
ok
X
tail
X
active
odds
incr
pairs
proper
tail
X
proper
X
s
ok
X
s
X
active
incr
X
active
X
proper
incr
X
proper
X
s
mark
X
s
X
head
ok
X
head
X
active
pairs
cons
0
incr
odds
active
tail
X
active
X
top
mark
X
proper
X
incr
mark
X
incr
X
proper
tail
X
tail
proper
X
true
top
mark
X
top
proper
X
top
ok
X
top
active
X
true
s
1
1
head
1
1
proper
1
1
ok
1
1
proper
1
1
active
1
1
head
1
1
active
1
1
incr
1
2
1
cons
2
0
1
2
top
1
0
pairs
0
8
top
1
0
1
tail
1
7
1
0
0
6
s
1
0
odds
0
9
tail
1
0
mark
1
2
1
incr
1
0
nats
0
5
cons
2
4
1
incr
1
1
0
cons
2
1
2
1
top
1
1
pairs
0
19265
top
1
1
1
tail
1
1
29260
0
0
0
s
1
1
odds
0
19265
tail
1
1
mark
1
1
0
incr
1
1
nats
0
36251
cons
2
1
2
0
top
ok
X
top
active
X
proper
cons
X1
X2
cons
proper
X1
proper
X2
active
incr
cons
X
XS
mark
cons
s
X
incr
XS
head
mark
X
mark
head
X
active
incr
X
incr
active
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
proper
pairs
ok
pairs
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
s
ok
X
ok
s
X
active
head
cons
X
XS
mark
X
active
head
X
head
active
X
active
cons
X1
X2
cons
active
X1
X2
proper
incr
X
incr
proper
X
proper
tail
X
tail
proper
X
tail
ok
X
ok
tail
X
s
mark
X
mark
s
X
cons
mark
X1
X2
mark
cons
X1
X2
proper
s
X
s
proper
X
proper
head
X
head
proper
X
active
tail
X
tail
active
X
active
s
X
s
active
X
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
top
ok
X
top
active
X
true
incr
1
1
0
cons
2
0
s
1
1
0
top
1
0
pairs
0
1
top
1
1
0
head
1
0
tail
1
1
0
proper
1
18589
ok
1
18589
0
0
16908
s
1
0
odds
0
21238
tail
1
0
mark
1
1
incr
1
0
proper
1
0
nats
0
23612
active
1
1
head
1
1
0
cons
2
1
0
active
1
0
proper
cons
X1
X2
cons
proper
X1
proper
X2
active
incr
cons
X
XS
mark
cons
s
X
incr
XS
head
mark
X
mark
head
X
active
incr
X
incr
active
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
proper
pairs
ok
pairs
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
s
ok
X
ok
s
X
active
head
cons
X
XS
mark
X
active
head
X
head
active
X
active
cons
X1
X2
cons
active
X1
X2
proper
incr
X
incr
proper
X
proper
tail
X
tail
proper
X
tail
ok
X
ok
tail
X
s
mark
X
mark
s
X
cons
mark
X1
X2
mark
cons
X1
X2
proper
s
X
s
proper
X
proper
head
X
head
proper
X
active
tail
X
tail
active
X
active
s
X
s
active
X
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
top
mark
X
proper
X
false
top
ok
X
active
X
false
active
head
X
active
X
active
tail
X
active
X
active
cons
X1
X2
active
X1
active
incr
X
active
X
active
s
X
active
X
true
incr
1
1
1
cons
2
0
s
1
1
1
top
1
0
pairs
0
1
top
1
0
head
1
0
tail
1
1
1
proper
1
1
1
ok
1
3
0
0
2
s
1
0
odds
0
21654
tail
1
0
mark
1
1
32742
incr
1
0
proper
1
0
nats
0
2
active
1
1
54399
head
1
1
1
cons
2
1
2
1
active
1
1
0
active
incr
cons
X
XS
mark
cons
s
X
incr
XS
head
mark
X
mark
head
X
active
incr
X
incr
active
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
s
ok
X
ok
s
X
active
head
cons
X
XS
mark
X
active
head
X
head
active
X
active
cons
X1
X2
cons
active
X1
X2
tail
ok
X
ok
tail
X
s
mark
X
mark
s
X
cons
mark
X1
X2
mark
cons
X1
X2
active
tail
X
tail
active
X
active
s
X
s
active
X
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
active
pairs
cons
0
incr
odds
false
active
s
X
s
active
X
false
active
tail
X
tail
active
X
false
active
cons
X1
X2
cons
active
X1
X2
false
active
head
X
head
active
X
false
active
odds
incr
pairs
false
active
nats
cons
0
incr
nats
false
active
nats
incr
nats
false
active
incr
X
incr
active
X
false
active
incr
cons
X
XS
cons
s
X
incr
XS
false
active
incr
cons
X
XS
s
X
false
active
incr
cons
X
XS
incr
XS
false
proper
s
X
proper
X
proper
incr
X
proper
X
proper
tail
X
proper
X
proper
cons
X1
X2
proper
X1
proper
head
X
proper
X
proper
cons
X1
X2
proper
X2
true
incr
1
1
1
cons
2
0
s
1
1
2
top
1
0
pairs
0
1
top
1
0
head
1
0
tail
1
1
29824
proper
1
1
1
ok
1
3
0
0
3154
s
1
0
odds
0
16675
tail
1
0
mark
1
1
1
incr
1
0
proper
1
1
0
nats
0
2
active
1
1
19831
head
1
1
1
cons
2
1
2
1
active
1
0
active
incr
cons
X
XS
mark
cons
s
X
incr
XS
head
mark
X
mark
head
X
active
incr
X
incr
active
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
s
ok
X
ok
s
X
active
head
cons
X
XS
mark
X
active
head
X
head
active
X
active
cons
X1
X2
cons
active
X1
X2
tail
ok
X
ok
tail
X
s
mark
X
mark
s
X
cons
mark
X1
X2
mark
cons
X1
X2
active
tail
X
tail
active
X
active
s
X
s
active
X
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
proper
head
X
head
proper
X
false
head
ok
X
head
X
head
mark
X
head
X
true
incr
1
1
0
cons
2
0
s
1
2090
top
1
0
pairs
0
23638
top
1
0
head
1
1
0
tail
1
1
0
proper
1
54887
ok
1
1
31250
0
0
23637
s
1
0
odds
0
1
tail
1
0
mark
1
1
0
incr
1
0
proper
1
0
nats
0
15620
active
1
1
23638
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
head
X
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
head
mark
X
head
X
true
incr
1
1
0
cons
2
0
s
1
1
2
top
1
0
pairs
0
2
top
1
0
head
1
1
0
tail
1
1
0
proper
1
2
ok
1
1
1
0
0
1
s
1
0
odds
0
1
tail
1
0
mark
1
1
1
incr
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
proper
s
X
s
proper
X
false
s
mark
X
s
X
s
ok
X
s
X
true
incr
1
1
0
cons
2
0
s
1
1
1
top
1
0
pairs
0
2
top
1
0
head
1
0
tail
1
1
0
proper
1
2
ok
1
1
1
0
0
1
s
1
1
0
odds
0
1
tail
1
0
mark
1
1
1
incr
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
proper
tail
X
tail
proper
X
false
tail
mark
X
tail
X
tail
ok
X
tail
X
true
incr
1
1
0
cons
2
0
s
1
1
1
top
1
0
pairs
0
2
top
1
0
head
1
0
tail
1
1
0
proper
1
2
ok
1
1
1
0
0
1
s
1
0
odds
0
1
tail
1
1
0
mark
1
1
1
incr
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
proper
cons
X1
X2
cons
proper
X1
proper
X2
false
cons
ok
X1
ok
X2
cons
X1
X2
cons
mark
X1
X2
cons
X1
X2
true
incr
1
1
0
cons
2
2
0
s
1
1
1
top
1
0
pairs
0
2
top
1
0
head
1
0
tail
1
1
0
proper
1
2
ok
1
1
1
0
0
1
s
1
0
odds
0
1
tail
1
0
mark
1
1
1
incr
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
cons
mark
X1
X2
cons
X1
X2
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
cons
mark
X1
X2
cons
X1
X2
true
incr
1
1
0
cons
2
1
0
s
1
1
1
top
1
0
pairs
0
3
top
1
0
head
1
0
tail
1
1
0
proper
1
20862
ok
1
1
20861
0
0
1
s
1
0
odds
0
1
tail
1
0
mark
1
1
1
incr
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
active
pairs
incr
odds
false
proper
incr
X
incr
proper
X
false
incr
mark
X
incr
X
incr
ok
X
incr
X
true
incr
1
1
0
cons
2
0
s
1
1
1
top
1
0
pairs
0
2
top
1
0
head
1
0
tail
1
1
0
proper
1
2
ok
1
1
1
0
0
1
s
1
0
odds
0
1
tail
1
0
mark
1
1
1
incr
1
1
0
proper
1
0
nats
0
1
active
1
1
3
head
1
1
0
cons
2
1
2
1
active
1
0
head
mark
X
mark
head
X
active
nats
mark
cons
0
incr
nats
active
odds
mark
incr
pairs
tail
mark
X
mark
tail
X
cons
ok
X1
ok
X2
ok
cons
X1
X2
proper
0
ok
0
proper
nats
ok
nats
incr
ok
X
ok
incr
X
proper
odds
ok
odds
active
head
cons
X
XS
mark
X
tail
ok
X
ok
tail
X
cons
mark
X1
X2
mark
cons
X1
X2
incr
mark
X
mark
incr
X
active
tail
cons
X
XS
mark
XS
head
ok
X
ok
head
X
active
pairs
mark
cons
0
incr
odds
NaTT
certifiable-1.6