Identifier
Identifier
Images
[1,0]
=>
[1]

[1,0,1,0]
=>
[1,2]

[1,1,0,0]
=>
[2,1]

[1,0,1,0,1,0]
=>
[1,2,3]

[1,0,1,1,0,0]
=>
[1,3,2]

[1,1,0,0,1,0]
=>
[2,1,3]

[1,1,0,1,0,0]
=>
[2,3,1]

[1,1,1,0,0,0]
=>
[3,2,1]

[1,0,1,0,1,0,1,0]
=>
[1,2,3,4]

[1,0,1,0,1,1,0,0]
=>
[1,2,4,3]

[1,0,1,1,0,0,1,0]
=>
[1,3,2,4]

[1,0,1,1,0,1,0,0]
=>
[1,3,4,2]

[1,0,1,1,1,0,0,0]
=>
[1,4,3,2]

[1,1,0,0,1,0,1,0]
=>
[2,1,3,4]

[1,1,0,0,1,1,0,0]
=>
[2,1,4,3]

[1,1,0,1,0,0,1,0]
=>
[2,3,1,4]

[1,1,0,1,0,1,0,0]
=>
[2,3,4,1]

[1,1,0,1,1,0,0,0]
=>
[2,4,3,1]

[1,1,1,0,0,0,1,0]
=>
[3,2,1,4]

[1,1,1,0,0,1,0,0]
=>
[3,2,4,1]

[1,1,1,0,1,0,0,0]
=>
[4,2,3,1]

[1,1,1,1,0,0,0,0]
=>
[4,3,2,1]

[1,0,1,0,1,0,1,0,1,0]
=>
[1,2,3,4,5]

[1,0,1,0,1,0,1,1,0,0]
=>
[1,2,3,5,4]

[1,0,1,0,1,1,0,0,1,0]
=>
[1,2,4,3,5]

[1,0,1,0,1,1,0,1,0,0]
=>
[1,2,4,5,3]

[1,0,1,0,1,1,1,0,0,0]
=>
[1,2,5,4,3]

[1,0,1,1,0,0,1,0,1,0]
=>
[1,3,2,4,5]

[1,0,1,1,0,0,1,1,0,0]
=>
[1,3,2,5,4]

[1,0,1,1,0,1,0,0,1,0]
=>
[1,3,4,2,5]

[1,0,1,1,0,1,0,1,0,0]
=>
[1,3,4,5,2]

[1,0,1,1,0,1,1,0,0,0]
=>
[1,3,5,4,2]

[1,0,1,1,1,0,0,0,1,0]
=>
[1,4,3,2,5]

[1,0,1,1,1,0,0,1,0,0]
=>
[1,4,3,5,2]

[1,0,1,1,1,0,1,0,0,0]
=>
[1,5,3,4,2]

[1,0,1,1,1,1,0,0,0,0]
=>
[1,5,4,3,2]

[1,1,0,0,1,0,1,0,1,0]
=>
[2,1,3,4,5]

[1,1,0,0,1,0,1,1,0,0]
=>
[2,1,3,5,4]

[1,1,0,0,1,1,0,0,1,0]
=>
[2,1,4,3,5]

[1,1,0,0,1,1,0,1,0,0]
=>
[2,1,4,5,3]

[1,1,0,0,1,1,1,0,0,0]
=>
[2,1,5,4,3]

[1,1,0,1,0,0,1,0,1,0]
=>
[2,3,1,4,5]

[1,1,0,1,0,0,1,1,0,0]
=>
[2,3,1,5,4]

[1,1,0,1,0,1,0,0,1,0]
=>
[2,3,4,1,5]

[1,1,0,1,0,1,0,1,0,0]
=>
[2,3,4,5,1]

[1,1,0,1,0,1,1,0,0,0]
=>
[2,3,5,4,1]

[1,1,0,1,1,0,0,0,1,0]
=>
[2,4,3,1,5]

[1,1,0,1,1,0,0,1,0,0]
=>
[2,4,3,5,1]

[1,1,0,1,1,0,1,0,0,0]
=>
[2,5,3,4,1]

[1,1,0,1,1,1,0,0,0,0]
=>
[2,5,4,3,1]

[1,1,1,0,0,0,1,0,1,0]
=>
[3,2,1,4,5]

[1,1,1,0,0,0,1,1,0,0]
=>
[3,2,1,5,4]

[1,1,1,0,0,1,0,0,1,0]
=>
[3,2,4,1,5]

[1,1,1,0,0,1,0,1,0,0]
=>
[3,2,4,5,1]

[1,1,1,0,0,1,1,0,0,0]
=>
[3,2,5,4,1]

[1,1,1,0,1,0,0,0,1,0]
=>
[4,2,3,1,5]

[1,1,1,0,1,0,0,1,0,0]
=>
[4,2,3,5,1]

[1,1,1,0,1,0,1,0,0,0]
=>
[5,2,3,4,1]

[1,1,1,0,1,1,0,0,0,0]
=>
[5,2,4,3,1]

[1,1,1,1,0,0,0,0,1,0]
=>
[4,3,2,1,5]

[1,1,1,1,0,0,0,1,0,0]
=>
[4,3,2,5,1]

[1,1,1,1,0,0,1,0,0,0]
=>
[5,3,2,4,1]

[1,1,1,1,0,1,0,0,0,0]
=>
[5,3,4,2,1]

[1,1,1,1,1,0,0,0,0,0]
=>
[5,4,3,2,1]

[1,0,1,0,1,0,1,0,1,0,1,0]
=>
[1,2,3,4,5,6]

[1,0,1,0,1,0,1,0,1,1,0,0]
=>
[1,2,3,4,6,5]

[1,0,1,0,1,0,1,1,0,0,1,0]
=>
[1,2,3,5,4,6]

[1,0,1,0,1,0,1,1,0,1,0,0]
=>
[1,2,3,5,6,4]

[1,0,1,0,1,0,1,1,1,0,0,0]
=>
[1,2,3,6,5,4]

[1,0,1,0,1,1,0,0,1,0,1,0]
=>
[1,2,4,3,5,6]

[1,0,1,0,1,1,0,0,1,1,0,0]
=>
[1,2,4,3,6,5]

[1,0,1,0,1,1,0,1,0,0,1,0]
=>
[1,2,4,5,3,6]

[1,0,1,0,1,1,0,1,0,1,0,0]
=>
[1,2,4,5,6,3]

[1,0,1,0,1,1,0,1,1,0,0,0]
=>
[1,2,4,6,5,3]

[1,0,1,0,1,1,1,0,0,0,1,0]
=>
[1,2,5,4,3,6]

[1,0,1,0,1,1,1,0,0,1,0,0]
=>
[1,2,5,4,6,3]

[1,0,1,0,1,1,1,0,1,0,0,0]
=>
[1,2,6,4,5,3]

[1,0,1,0,1,1,1,1,0,0,0,0]
=>
[1,2,6,5,4,3]

[1,0,1,1,0,0,1,0,1,0,1,0]
=>
[1,3,2,4,5,6]

[1,0,1,1,0,0,1,0,1,1,0,0]
=>
[1,3,2,4,6,5]

[1,0,1,1,0,0,1,1,0,0,1,0]
=>
[1,3,2,5,4,6]

[1,0,1,1,0,0,1,1,0,1,0,0]
=>
[1,3,2,5,6,4]

[1,0,1,1,0,0,1,1,1,0,0,0]
=>
[1,3,2,6,5,4]

[1,0,1,1,0,1,0,0,1,0,1,0]
=>
[1,3,4,2,5,6]

[1,0,1,1,0,1,0,0,1,1,0,0]
=>
[1,3,4,2,6,5]

[1,0,1,1,0,1,0,1,0,0,1,0]
=>
[1,3,4,5,2,6]

[1,0,1,1,0,1,0,1,0,1,0,0]
=>
[1,3,4,5,6,2]

[1,0,1,1,0,1,0,1,1,0,0,0]
=>
[1,3,4,6,5,2]

[1,0,1,1,0,1,1,0,0,0,1,0]
=>
[1,3,5,4,2,6]

[1,0,1,1,0,1,1,0,0,1,0,0]
=>
[1,3,5,4,6,2]

[1,0,1,1,0,1,1,0,1,0,0,0]
=>
[1,3,6,4,5,2]

[1,0,1,1,0,1,1,1,0,0,0,0]
=>
[1,3,6,5,4,2]

[1,0,1,1,1,0,0,0,1,0,1,0]
=>
[1,4,3,2,5,6]

[1,0,1,1,1,0,0,0,1,1,0,0]
=>
[1,4,3,2,6,5]

[1,0,1,1,1,0,0,1,0,0,1,0]
=>
[1,4,3,5,2,6]

[1,0,1,1,1,0,0,1,0,1,0,0]
=>
[1,4,3,5,6,2]

[1,0,1,1,1,0,0,1,1,0,0,0]
=>
[1,4,3,6,5,2]

[1,0,1,1,1,0,1,0,0,0,1,0]
=>
[1,5,3,4,2,6]

[1,0,1,1,1,0,1,0,0,1,0,0]
=>
[1,5,3,4,6,2]

[1,0,1,1,1,0,1,0,1,0,0,0]
=>
[1,6,3,4,5,2]

[1,0,1,1,1,0,1,1,0,0,0,0]
=>
[1,6,3,5,4,2]

[1,0,1,1,1,1,0,0,0,0,1,0]
=>
[1,5,4,3,2,6]

[1,0,1,1,1,1,0,0,0,1,0,0]
=>
[1,5,4,3,6,2]

[1,0,1,1,1,1,0,0,1,0,0,0]
=>
[1,6,4,3,5,2]

[1,0,1,1,1,1,0,1,0,0,0,0]
=>
[1,6,4,5,3,2]

[1,0,1,1,1,1,1,0,0,0,0,0]
=>
[1,6,5,4,3,2]

[1,1,0,0,1,0,1,0,1,0,1,0]
=>
[2,1,3,4,5,6]

[1,1,0,0,1,0,1,0,1,1,0,0]
=>
[2,1,3,4,6,5]

[1,1,0,0,1,0,1,1,0,0,1,0]
=>
[2,1,3,5,4,6]

[1,1,0,0,1,0,1,1,0,1,0,0]
=>
[2,1,3,5,6,4]

[1,1,0,0,1,0,1,1,1,0,0,0]
=>
[2,1,3,6,5,4]

[1,1,0,0,1,1,0,0,1,0,1,0]
=>
[2,1,4,3,5,6]

[1,1,0,0,1,1,0,0,1,1,0,0]
=>
[2,1,4,3,6,5]

[1,1,0,0,1,1,0,1,0,0,1,0]
=>
[2,1,4,5,3,6]

[1,1,0,0,1,1,0,1,0,1,0,0]
=>
[2,1,4,5,6,3]

[1,1,0,0,1,1,0,1,1,0,0,0]
=>
[2,1,4,6,5,3]

[1,1,0,0,1,1,1,0,0,0,1,0]
=>
[2,1,5,4,3,6]

[1,1,0,0,1,1,1,0,0,1,0,0]
=>
[2,1,5,4,6,3]

[1,1,0,0,1,1,1,0,1,0,0,0]
=>
[2,1,6,4,5,3]

[1,1,0,0,1,1,1,1,0,0,0,0]
=>
[2,1,6,5,4,3]

[1,1,0,1,0,0,1,0,1,0,1,0]
=>
[2,3,1,4,5,6]

[1,1,0,1,0,0,1,0,1,1,0,0]
=>
[2,3,1,4,6,5]

[1,1,0,1,0,0,1,1,0,0,1,0]
=>
[2,3,1,5,4,6]

[1,1,0,1,0,0,1,1,0,1,0,0]
=>
[2,3,1,5,6,4]

[1,1,0,1,0,0,1,1,1,0,0,0]
=>
[2,3,1,6,5,4]

[1,1,0,1,0,1,0,0,1,0,1,0]
=>
[2,3,4,1,5,6]

[1,1,0,1,0,1,0,0,1,1,0,0]
=>
[2,3,4,1,6,5]

[1,1,0,1,0,1,0,1,0,0,1,0]
=>
[2,3,4,5,1,6]

[1,1,0,1,0,1,0,1,0,1,0,0]
=>
[2,3,4,5,6,1]

[1,1,0,1,0,1,0,1,1,0,0,0]
=>
[2,3,4,6,5,1]

[1,1,0,1,0,1,1,0,0,0,1,0]
=>
[2,3,5,4,1,6]

[1,1,0,1,0,1,1,0,0,1,0,0]
=>
[2,3,5,4,6,1]

[1,1,0,1,0,1,1,0,1,0,0,0]
=>
[2,3,6,4,5,1]

[1,1,0,1,0,1,1,1,0,0,0,0]
=>
[2,3,6,5,4,1]

[1,1,0,1,1,0,0,0,1,0,1,0]
=>
[2,4,3,1,5,6]

[1,1,0,1,1,0,0,0,1,1,0,0]
=>
[2,4,3,1,6,5]

[1,1,0,1,1,0,0,1,0,0,1,0]
=>
[2,4,3,5,1,6]

[1,1,0,1,1,0,0,1,0,1,0,0]
=>
[2,4,3,5,6,1]

[1,1,0,1,1,0,0,1,1,0,0,0]
=>
[2,4,3,6,5,1]

[1,1,0,1,1,0,1,0,0,0,1,0]
=>
[2,5,3,4,1,6]

[1,1,0,1,1,0,1,0,0,1,0,0]
=>
[2,5,3,4,6,1]

[1,1,0,1,1,0,1,0,1,0,0,0]
=>
[2,6,3,4,5,1]

[1,1,0,1,1,0,1,1,0,0,0,0]
=>
[2,6,3,5,4,1]

[1,1,0,1,1,1,0,0,0,0,1,0]
=>
[2,5,4,3,1,6]

[1,1,0,1,1,1,0,0,0,1,0,0]
=>
[2,5,4,3,6,1]

[1,1,0,1,1,1,0,0,1,0,0,0]
=>
[2,6,4,3,5,1]

[1,1,0,1,1,1,0,1,0,0,0,0]
=>
[2,6,4,5,3,1]

[1,1,0,1,1,1,1,0,0,0,0,0]
=>
[2,6,5,4,3,1]

[1,1,1,0,0,0,1,0,1,0,1,0]
=>
[3,2,1,4,5,6]

[1,1,1,0,0,0,1,0,1,1,0,0]
=>
[3,2,1,4,6,5]

[1,1,1,0,0,0,1,1,0,0,1,0]
=>
[3,2,1,5,4,6]

[1,1,1,0,0,0,1,1,0,1,0,0]
=>
[3,2,1,5,6,4]

[1,1,1,0,0,0,1,1,1,0,0,0]
=>
[3,2,1,6,5,4]

[1,1,1,0,0,1,0,0,1,0,1,0]
=>
[3,2,4,1,5,6]

[1,1,1,0,0,1,0,0,1,1,0,0]
=>
[3,2,4,1,6,5]

[1,1,1,0,0,1,0,1,0,0,1,0]
=>
[3,2,4,5,1,6]

[1,1,1,0,0,1,0,1,0,1,0,0]
=>
[3,2,4,5,6,1]

[1,1,1,0,0,1,0,1,1,0,0,0]
=>
[3,2,4,6,5,1]

[1,1,1,0,0,1,1,0,0,0,1,0]
=>
[3,2,5,4,1,6]

[1,1,1,0,0,1,1,0,0,1,0,0]
=>
[3,2,5,4,6,1]

[1,1,1,0,0,1,1,0,1,0,0,0]
=>
[3,2,6,4,5,1]

[1,1,1,0,0,1,1,1,0,0,0,0]
=>
[3,2,6,5,4,1]

[1,1,1,0,1,0,0,0,1,0,1,0]
=>
[4,2,3,1,5,6]

[1,1,1,0,1,0,0,0,1,1,0,0]
=>
[4,2,3,1,6,5]

[1,1,1,0,1,0,0,1,0,0,1,0]
=>
[4,2,3,5,1,6]

[1,1,1,0,1,0,0,1,0,1,0,0]
=>
[4,2,3,5,6,1]

[1,1,1,0,1,0,0,1,1,0,0,0]
=>
[4,2,3,6,5,1]

[1,1,1,0,1,0,1,0,0,0,1,0]
=>
[5,2,3,4,1,6]

[1,1,1,0,1,0,1,0,0,1,0,0]
=>
[5,2,3,4,6,1]

[1,1,1,0,1,0,1,0,1,0,0,0]
=>
[6,2,3,4,5,1]

[1,1,1,0,1,0,1,1,0,0,0,0]
=>
[6,2,3,5,4,1]

[1,1,1,0,1,1,0,0,0,0,1,0]
=>
[5,2,4,3,1,6]

[1,1,1,0,1,1,0,0,0,1,0,0]
=>
[5,2,4,3,6,1]

[1,1,1,0,1,1,0,0,1,0,0,0]
=>
[6,2,4,3,5,1]

[1,1,1,0,1,1,0,1,0,0,0,0]
=>
[6,2,4,5,3,1]

[1,1,1,0,1,1,1,0,0,0,0,0]
=>
[6,2,5,4,3,1]

[1,1,1,1,0,0,0,0,1,0,1,0]
=>
[4,3,2,1,5,6]

[1,1,1,1,0,0,0,0,1,1,0,0]
=>
[4,3,2,1,6,5]

[1,1,1,1,0,0,0,1,0,0,1,0]
=>
[4,3,2,5,1,6]

[1,1,1,1,0,0,0,1,0,1,0,0]
=>
[4,3,2,5,6,1]

[1,1,1,1,0,0,0,1,1,0,0,0]
=>
[4,3,2,6,5,1]

[1,1,1,1,0,0,1,0,0,0,1,0]
=>
[5,3,2,4,1,6]

[1,1,1,1,0,0,1,0,0,1,0,0]
=>
[5,3,2,4,6,1]

[1,1,1,1,0,0,1,0,1,0,0,0]
=>
[6,3,2,4,5,1]

[1,1,1,1,0,0,1,1,0,0,0,0]
=>
[6,3,2,5,4,1]

[1,1,1,1,0,1,0,0,0,0,1,0]
=>
[5,3,4,2,1,6]

[1,1,1,1,0,1,0,0,0,1,0,0]
=>
[5,3,4,2,6,1]

[1,1,1,1,0,1,0,0,1,0,0,0]
=>
[6,3,4,2,5,1]

[1,1,1,1,0,1,0,1,0,0,0,0]
=>
[6,3,4,5,2,1]

[1,1,1,1,0,1,1,0,0,0,0,0]
=>
[6,3,5,4,2,1]

[1,1,1,1,1,0,0,0,0,0,1,0]
=>
[5,4,3,2,1,6]

[1,1,1,1,1,0,0,0,0,1,0,0]
=>
[5,4,3,2,6,1]

[1,1,1,1,1,0,0,0,1,0,0,0]
=>
[6,4,3,2,5,1]

[1,1,1,1,1,0,0,1,0,0,0,0]
=>
[6,4,3,5,2,1]

[1,1,1,1,1,0,1,0,0,0,0,0]
=>
[6,5,3,4,2,1]

[1,1,1,1,1,1,0,0,0,0,0,0]
=>
[6,5,4,3,2,1]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
[1,2,3,4,5,6,7]

[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
[1,2,3,4,5,7,6]

[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
[1,2,3,4,6,5,7]

[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
[1,2,3,4,6,7,5]

[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
[1,2,3,4,7,6,5]

[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
[1,2,3,5,4,6,7]

[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
[1,2,3,5,4,7,6]

[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
[1,2,3,5,6,4,7]

[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
[1,2,3,5,6,7,4]

[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
[1,2,3,5,7,6,4]

[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
[1,2,3,6,5,4,7]

[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
[1,2,3,6,5,7,4]

[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
[1,2,3,7,5,6,4]

[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
[1,2,3,7,6,5,4]

[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
[1,2,4,3,5,6,7]

[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
[1,2,4,3,5,7,6]

[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
[1,2,4,3,6,5,7]

[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
[1,2,4,3,6,7,5]

[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
[1,2,4,3,7,6,5]

[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
[1,2,4,5,3,6,7]

[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
[1,2,4,5,3,7,6]

[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
[1,2,4,5,6,3,7]

[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
[1,2,4,5,6,7,3]

[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
[1,2,4,5,7,6,3]

[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
[1,2,4,6,5,3,7]

[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
[1,2,4,6,5,7,3]

[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
[1,2,4,7,5,6,3]

[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
[1,2,4,7,6,5,3]

[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
[1,2,5,4,3,6,7]

[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
[1,2,5,4,3,7,6]

[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
[1,2,5,4,6,3,7]

[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
[1,2,5,4,6,7,3]

[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
[1,2,5,4,7,6,3]

[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
[1,2,6,4,5,3,7]

[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
[1,2,6,4,5,7,3]

[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
[1,2,7,4,5,6,3]

[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
[1,2,7,4,6,5,3]

[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
[1,2,6,5,4,3,7]

[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
[1,2,6,5,4,7,3]

[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
[1,2,7,5,4,6,3]

[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
[1,2,7,5,6,4,3]

[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
[1,2,7,6,5,4,3]

[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
[1,3,2,4,5,6,7]

[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
[1,3,2,4,5,7,6]

[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
[1,3,2,4,6,5,7]

[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
[1,3,2,4,6,7,5]

[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
[1,3,2,4,7,6,5]

[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
[1,3,2,5,4,6,7]

[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
[1,3,2,5,4,7,6]

[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
[1,3,2,5,6,4,7]

[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
[1,3,2,5,6,7,4]

[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
[1,3,2,5,7,6,4]

[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
[1,3,2,6,5,4,7]

[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
[1,3,2,6,5,7,4]

[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
[1,3,2,7,5,6,4]

[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
[1,3,2,7,6,5,4]

[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
[1,3,4,2,5,6,7]

[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
[1,3,4,2,5,7,6]

[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
[1,3,4,2,6,5,7]

[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
[1,3,4,2,6,7,5]

[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
[1,3,4,2,7,6,5]

[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
[1,3,4,5,2,6,7]

[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
[1,3,4,5,2,7,6]

[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
[1,3,4,5,6,2,7]

[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
[1,3,4,5,6,7,2]

[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
[1,3,4,5,7,6,2]

[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
[1,3,4,6,5,2,7]

[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
[1,3,4,6,5,7,2]

[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
[1,3,4,7,5,6,2]

[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
[1,3,4,7,6,5,2]

[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
[1,3,5,4,2,6,7]

[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
[1,3,5,4,2,7,6]

[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
[1,3,5,4,6,2,7]

[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
[1,3,5,4,6,7,2]

[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
[1,3,5,4,7,6,2]

[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
[1,3,6,4,5,2,7]

[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
[1,3,6,4,5,7,2]

[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
[1,3,7,4,5,6,2]

[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
[1,3,7,4,6,5,2]

[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
[1,3,6,5,4,2,7]

[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
[1,3,6,5,4,7,2]

[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
[1,3,7,5,4,6,2]

[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
[1,3,7,5,6,4,2]

[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
[1,3,7,6,5,4,2]

[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
[1,4,3,2,5,6,7]

[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
[1,4,3,2,5,7,6]

[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
[1,4,3,2,6,5,7]

[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
[1,4,3,2,6,7,5]

[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
[1,4,3,2,7,6,5]

[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
[1,4,3,5,2,6,7]

[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
[1,4,3,5,2,7,6]

[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
[1,4,3,5,6,2,7]

[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
[1,4,3,5,6,7,2]

[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
[1,4,3,5,7,6,2]

[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
[1,4,3,6,5,2,7]

[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
[1,4,3,6,5,7,2]

[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
[1,4,3,7,5,6,2]

[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
[1,4,3,7,6,5,2]

[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
[1,5,3,4,2,6,7]

[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
[1,5,3,4,2,7,6]

[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
[1,5,3,4,6,2,7]

[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
[1,5,3,4,6,7,2]

[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
[1,5,3,4,7,6,2]

[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
[1,6,3,4,5,2,7]

[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
[1,6,3,4,5,7,2]

[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
[1,7,3,4,5,6,2]

[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
[1,7,3,4,6,5,2]

[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
[1,6,3,5,4,2,7]

[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
[1,6,3,5,4,7,2]

[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
[1,7,3,5,4,6,2]

[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
[1,7,3,5,6,4,2]

[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
[1,7,3,6,5,4,2]

[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
[1,5,4,3,2,6,7]

[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
[1,5,4,3,2,7,6]

[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
[1,5,4,3,6,2,7]

[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
[1,5,4,3,6,7,2]

[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
[1,5,4,3,7,6,2]

[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
[1,6,4,3,5,2,7]

[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
[1,6,4,3,5,7,2]

[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
[1,7,4,3,5,6,2]

[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
[1,7,4,3,6,5,2]

[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
[1,6,4,5,3,2,7]

[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
[1,6,4,5,3,7,2]

[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
[1,7,4,5,3,6,2]

[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
[1,7,4,5,6,3,2]

[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
[1,7,4,6,5,3,2]

[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
[1,6,5,4,3,2,7]

[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
[1,6,5,4,3,7,2]

[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
[1,7,5,4,3,6,2]

[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
[1,7,5,4,6,3,2]

[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
[1,7,6,4,5,3,2]

[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
[1,7,6,5,4,3,2]

[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
[2,1,3,4,5,6,7]

[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
[2,1,3,4,5,7,6]

[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
[2,1,3,4,6,5,7]

[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
[2,1,3,4,6,7,5]

[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
[2,1,3,4,7,6,5]

[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
[2,1,3,5,4,6,7]

[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
[2,1,3,5,4,7,6]

[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
[2,1,3,5,6,4,7]

[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
[2,1,3,5,6,7,4]

[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
[2,1,3,5,7,6,4]

[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
[2,1,3,6,5,4,7]

[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
[2,1,3,6,5,7,4]

[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
[2,1,3,7,5,6,4]

[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
[2,1,3,7,6,5,4]

[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=>
[2,1,4,3,5,6,7]

[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=>
[2,1,4,3,5,7,6]

[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=>
[2,1,4,3,6,5,7]

[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=>
[2,1,4,3,6,7,5]

[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=>
[2,1,4,3,7,6,5]

[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=>
[2,1,4,5,3,6,7]

[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=>
[2,1,4,5,3,7,6]

[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=>
[2,1,4,5,6,3,7]

[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=>
[2,1,4,5,6,7,3]

[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=>
[2,1,4,5,7,6,3]

[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=>
[2,1,4,6,5,3,7]

[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=>
[2,1,4,6,5,7,3]

[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=>
[2,1,4,7,5,6,3]

[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=>
[2,1,4,7,6,5,3]

[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=>
[2,1,5,4,3,6,7]

[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=>
[2,1,5,4,3,7,6]

[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
=>
[2,1,5,4,6,3,7]

[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
=>
[2,1,5,4,6,7,3]

[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=>
[2,1,5,4,7,6,3]

[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
=>
[2,1,6,4,5,3,7]

[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
=>
[2,1,6,4,5,7,3]

[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=>
[2,1,7,4,5,6,3]

[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=>
[2,1,7,4,6,5,3]

[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=>
[2,1,6,5,4,3,7]

[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=>
[2,1,6,5,4,7,3]

[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=>
[2,1,7,5,4,6,3]

[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=>
[2,1,7,5,6,4,3]

[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=>
[2,1,7,6,5,4,3]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=>
[2,3,1,4,5,6,7]

[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=>
[2,3,1,4,5,7,6]

[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=>
[2,3,1,4,6,5,7]

[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=>
[2,3,1,4,6,7,5]

[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=>
[2,3,1,4,7,6,5]

[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=>
[2,3,1,5,4,6,7]

[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=>
[2,3,1,5,4,7,6]

[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=>
[2,3,1,5,6,4,7]

[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=>
[2,3,1,5,6,7,4]

[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=>
[2,3,1,5,7,6,4]

[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=>
[2,3,1,6,5,4,7]

[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=>
[2,3,1,6,5,7,4]

[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=>
[2,3,1,7,5,6,4]

[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=>
[2,3,1,7,6,5,4]

[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=>
[2,3,4,1,5,6,7]

[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=>
[2,3,4,1,5,7,6]

[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=>
[2,3,4,1,6,5,7]

[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=>
[2,3,4,1,6,7,5]

[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=>
[2,3,4,1,7,6,5]

[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=>
[2,3,4,5,1,6,7]

[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=>
[2,3,4,5,1,7,6]

[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=>
[2,3,4,5,6,1,7]

[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=>
[2,3,4,5,6,7,1]

[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=>
[2,3,4,5,7,6,1]

[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=>
[2,3,4,6,5,1,7]

[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=>
[2,3,4,6,5,7,1]

[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=>
[2,3,4,7,5,6,1]

[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=>
[2,3,4,7,6,5,1]

[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=>
[2,3,5,4,1,6,7]

[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
=>
[2,3,5,4,1,7,6]

[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=>
[2,3,5,4,6,1,7]

[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=>
[2,3,5,4,6,7,1]

[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=>
[2,3,5,4,7,6,1]

[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=>
[2,3,6,4,5,1,7]

[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=>
[2,3,6,4,5,7,1]

[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=>
[2,3,7,4,5,6,1]

[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=>
[2,3,7,4,6,5,1]

[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
=>
[2,3,6,5,4,1,7]

[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=>
[2,3,6,5,4,7,1]

[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=>
[2,3,7,5,4,6,1]

[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=>
[2,3,7,5,6,4,1]

[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=>
[2,3,7,6,5,4,1]

[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=>
[2,4,3,1,5,6,7]

[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
=>
[2,4,3,1,5,7,6]

[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=>
[2,4,3,1,6,5,7]

[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
=>
[2,4,3,1,6,7,5]

[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
=>
[2,4,3,1,7,6,5]

[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=>
[2,4,3,5,1,6,7]

[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=>
[2,4,3,5,1,7,6]

[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=>
[2,4,3,5,6,1,7]

[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=>
[2,4,3,5,6,7,1]

[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=>
[2,4,3,5,7,6,1]

[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
=>
[2,4,3,6,5,1,7]

[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=>
[2,4,3,6,5,7,1]

[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=>
[2,4,3,7,5,6,1]

[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=>
[2,4,3,7,6,5,1]

[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=>
[2,5,3,4,1,6,7]

[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
=>
[2,5,3,4,1,7,6]

[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=>
[2,5,3,4,6,1,7]

[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=>
[2,5,3,4,6,7,1]

[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=>
[2,5,3,4,7,6,1]

[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=>
[2,6,3,4,5,1,7]

[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=>
[2,6,3,4,5,7,1]

[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=>
[2,7,3,4,5,6,1]

[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=>
[2,7,3,4,6,5,1]

[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=>
[2,6,3,5,4,1,7]

[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=>
[2,6,3,5,4,7,1]

[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=>
[2,7,3,5,4,6,1]

[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=>
[2,7,3,5,6,4,1]

[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=>
[2,7,3,6,5,4,1]

[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=>
[2,5,4,3,1,6,7]

[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=>
[2,5,4,3,1,7,6]

[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
=>
[2,5,4,3,6,1,7]

[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=>
[2,5,4,3,6,7,1]

[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=>
[2,5,4,3,7,6,1]

[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=>
[2,6,4,3,5,1,7]

[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=>
[2,6,4,3,5,7,1]

[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=>
[2,7,4,3,5,6,1]

[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=>
[2,7,4,3,6,5,1]

[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
=>
[2,6,4,5,3,1,7]

[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=>
[2,6,4,5,3,7,1]

[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=>
[2,7,4,5,3,6,1]

[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=>
[2,7,4,5,6,3,1]

[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=>
[2,7,4,6,5,3,1]

[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=>
[2,6,5,4,3,1,7]

[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=>
[2,6,5,4,3,7,1]

[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=>
[2,7,5,4,3,6,1]

[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=>
[2,7,5,4,6,3,1]

[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=>
[2,7,6,4,5,3,1]

[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=>
[2,7,6,5,4,3,1]

[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=>
[3,2,1,4,5,6,7]

[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=>
[3,2,1,4,5,7,6]

[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
=>
[3,2,1,4,6,5,7]

[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
=>
[3,2,1,4,6,7,5]

[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=>
[3,2,1,4,7,6,5]

[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
=>
[3,2,1,5,4,6,7]

[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=>
[3,2,1,5,4,7,6]

[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
=>
[3,2,1,5,6,4,7]

[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
=>
[3,2,1,5,6,7,4]

[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
=>
[3,2,1,5,7,6,4]

[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=>
[3,2,1,6,5,4,7]

[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=>
[3,2,1,6,5,7,4]

[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=>
[3,2,1,7,5,6,4]

[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=>
[3,2,1,7,6,5,4]

[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=>
[3,2,4,1,5,6,7]

[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=>
[3,2,4,1,5,7,6]

[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
=>
[3,2,4,1,6,5,7]

[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
=>
[3,2,4,1,6,7,5]

[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=>
[3,2,4,1,7,6,5]

[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=>
[3,2,4,5,1,6,7]

[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=>
[3,2,4,5,1,7,6]

[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=>
[3,2,4,5,6,1,7]

[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=>
[3,2,4,5,6,7,1]

[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=>
[3,2,4,5,7,6,1]

[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
=>
[3,2,4,6,5,1,7]

[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=>
[3,2,4,6,5,7,1]

[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=>
[3,2,4,7,5,6,1]

[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=>
[3,2,4,7,6,5,1]

[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=>
[3,2,5,4,1,6,7]

[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
=>
[3,2,5,4,1,7,6]

[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
=>
[3,2,5,4,6,1,7]

[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=>
[3,2,5,4,6,7,1]

[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=>
[3,2,5,4,7,6,1]

[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
=>
[3,2,6,4,5,1,7]

[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=>
[3,2,6,4,5,7,1]

[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=>
[3,2,7,4,5,6,1]

[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=>
[3,2,7,4,6,5,1]

[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=>
[3,2,6,5,4,1,7]

[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=>
[3,2,6,5,4,7,1]

[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=>
[3,2,7,5,4,6,1]

[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=>
[3,2,7,5,6,4,1]

[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=>
[3,2,7,6,5,4,1]

[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=>
[4,2,3,1,5,6,7]

[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
=>
[4,2,3,1,5,7,6]

[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
=>
[4,2,3,1,6,5,7]

[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=>
[4,2,3,1,6,7,5]

[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=>
[4,2,3,1,7,6,5]

[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=>
[4,2,3,5,1,6,7]

[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=>
[4,2,3,5,1,7,6]

[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=>
[4,2,3,5,6,1,7]

[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=>
[4,2,3,5,6,7,1]

[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=>
[4,2,3,5,7,6,1]

[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
=>
[4,2,3,6,5,1,7]

[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=>
[4,2,3,6,5,7,1]

[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=>
[4,2,3,7,5,6,1]

[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=>
[4,2,3,7,6,5,1]

[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=>
[5,2,3,4,1,6,7]

[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=>
[5,2,3,4,1,7,6]

[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=>
[5,2,3,4,6,1,7]

[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=>
[5,2,3,4,6,7,1]

[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=>
[5,2,3,4,7,6,1]

[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=>
[6,2,3,4,5,1,7]

[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=>
[6,2,3,4,5,7,1]

[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=>
[7,2,3,4,5,6,1]

[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=>
[7,2,3,4,6,5,1]

[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=>
[6,2,3,5,4,1,7]

[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=>
[6,2,3,5,4,7,1]

[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=>
[7,2,3,5,4,6,1]

[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=>
[7,2,3,5,6,4,1]

[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=>
[7,2,3,6,5,4,1]

[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=>
[5,2,4,3,1,6,7]

[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=>
[5,2,4,3,1,7,6]

[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=>
[5,2,4,3,6,1,7]

[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=>
[5,2,4,3,6,7,1]

[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=>
[5,2,4,3,7,6,1]

[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=>
[6,2,4,3,5,1,7]

[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=>
[6,2,4,3,5,7,1]

[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=>
[7,2,4,3,5,6,1]

[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=>
[7,2,4,3,6,5,1]

[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=>
[6,2,4,5,3,1,7]

[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=>
[6,2,4,5,3,7,1]

[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=>
[7,2,4,5,3,6,1]

[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=>
[7,2,4,5,6,3,1]

[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=>
[7,2,4,6,5,3,1]

[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=>
[6,2,5,4,3,1,7]

[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=>
[6,2,5,4,3,7,1]

[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=>
[7,2,5,4,3,6,1]

[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=>
[7,2,5,4,6,3,1]

[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=>
[7,2,6,4,5,3,1]

[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=>
[7,2,6,5,4,3,1]

[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=>
[4,3,2,1,5,6,7]

[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=>
[4,3,2,1,5,7,6]

[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=>
[4,3,2,1,6,5,7]

[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
=>
[4,3,2,1,6,7,5]

[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=>
[4,3,2,1,7,6,5]

[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=>
[4,3,2,5,1,6,7]

[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
=>
[4,3,2,5,1,7,6]

[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=>
[4,3,2,5,6,1,7]

[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=>
[4,3,2,5,6,7,1]

[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=>
[4,3,2,5,7,6,1]

[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
=>
[4,3,2,6,5,1,7]

[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
=>
[4,3,2,6,5,7,1]

[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
=>
[4,3,2,7,5,6,1]

[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=>
[4,3,2,7,6,5,1]

[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=>
[5,3,2,4,1,6,7]

[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
=>
[5,3,2,4,1,7,6]

[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=>
[5,3,2,4,6,1,7]

[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=>
[5,3,2,4,6,7,1]

[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=>
[5,3,2,4,7,6,1]

[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=>
[6,3,2,4,5,1,7]

[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=>
[6,3,2,4,5,7,1]

[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=>
[7,3,2,4,5,6,1]

[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=>
[7,3,2,4,6,5,1]

[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=>
[6,3,2,5,4,1,7]

[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=>
[6,3,2,5,4,7,1]

[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=>
[7,3,2,5,4,6,1]

[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=>
[7,3,2,5,6,4,1]

[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=>
[7,3,2,6,5,4,1]

[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=>
[5,3,4,2,1,6,7]

[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=>
[5,3,4,2,1,7,6]

[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=>
[5,3,4,2,6,1,7]

[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=>
[5,3,4,2,6,7,1]

[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=>
[5,3,4,2,7,6,1]

[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=>
[6,3,4,2,5,1,7]

[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=>
[6,3,4,2,5,7,1]

[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=>
[7,3,4,2,5,6,1]

[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=>
[7,3,4,2,6,5,1]

[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=>
[6,3,4,5,2,1,7]

[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=>
[6,3,4,5,2,7,1]

[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=>
[7,3,4,5,2,6,1]

[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=>
[7,3,4,5,6,2,1]

[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=>
[7,3,4,6,5,2,1]

[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=>
[6,3,5,4,2,1,7]

[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=>
[6,3,5,4,2,7,1]

[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=>
[7,3,5,4,2,6,1]

[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=>
[7,3,5,4,6,2,1]

[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=>
[7,3,6,4,5,2,1]

[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=>
[7,3,6,5,4,2,1]

[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=>
[5,4,3,2,1,6,7]

[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=>
[5,4,3,2,1,7,6]

[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
=>
[5,4,3,2,6,1,7]

[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=>
[5,4,3,2,6,7,1]

[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=>
[5,4,3,2,7,6,1]

[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
=>
[6,4,3,2,5,1,7]

[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=>
[6,4,3,2,5,7,1]

[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=>
[7,4,3,2,5,6,1]

[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=>
[7,4,3,2,6,5,1]

[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=>
[6,4,3,5,2,1,7]

[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=>
[6,4,3,5,2,7,1]

[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
=>
[7,4,3,5,2,6,1]

[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=>
[7,4,3,5,6,2,1]

[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=>
[7,4,3,6,5,2,1]

[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=>
[6,5,3,4,2,1,7]

[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=>
[6,5,3,4,2,7,1]

[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=>
[7,5,3,4,2,6,1]

[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=>
[7,5,3,4,6,2,1]

[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=>
[7,6,3,4,5,2,1]

[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=>
[7,6,3,5,4,2,1]

[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=>
[6,5,4,3,2,1,7]

[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=>
[6,5,4,3,2,7,1]

[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=>
[7,5,4,3,2,6,1]

[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=>
[7,5,4,3,6,2,1]

[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=>
[7,6,4,3,5,2,1]

[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=>
[7,6,4,5,3,2,1]

[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=>
[7,6,5,4,3,2,1]

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
[1,2,3,4,5,6,7,8]

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
[1,2,3,4,5,6,8,7]

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
[1,2,3,4,5,7,6,8]

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
[1,2,3,4,5,7,8,6]

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
[1,2,3,4,5,8,7,6]

[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
[1,2,3,4,6,5,7,8]

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
[1,2,3,4,6,5,8,7]

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
[1,2,3,4,6,7,5,8]

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
[1,2,3,4,6,7,8,5]

[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
[1,2,3,4,6,8,7,5]

[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
[1,2,3,4,7,6,5,8]

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
[1,2,3,4,7,6,8,5]

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
[1,2,3,4,8,6,7,5]

[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
[1,2,3,4,8,7,6,5]

[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
[1,2,3,5,4,6,7,8]

[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
[1,2,3,5,4,6,8,7]

[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
[1,2,3,5,4,7,6,8]

[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
[1,2,3,5,4,7,8,6]

[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
[1,2,3,5,4,8,7,6]

[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
[1,2,3,5,6,4,7,8]

[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
[1,2,3,5,6,4,8,7]

[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
[1,2,3,5,6,7,4,8]

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
[1,2,3,5,6,7,8,4]

[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
[1,2,3,5,6,8,7,4]

[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
[1,2,3,5,7,6,4,8]

[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
[1,2,3,5,7,6,8,4]

[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
[1,2,3,5,8,6,7,4]

[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
[1,2,3,5,8,7,6,4]

[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
[1,2,3,6,5,4,7,8]

[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
[1,2,3,6,5,4,8,7]

[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
[1,2,3,6,5,7,4,8]

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
[1,2,3,6,5,7,8,4]

[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
[1,2,3,6,5,8,7,4]

[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
[1,2,3,7,5,6,4,8]

[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
[1,2,3,7,5,6,8,4]

[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
[1,2,3,8,5,6,7,4]

[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
[1,2,3,8,5,7,6,4]

[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
[1,2,3,7,6,5,4,8]

[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
[1,2,3,7,6,5,8,4]

[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
[1,2,3,8,6,5,7,4]

[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
[1,2,3,8,6,7,5,4]

[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
[1,2,3,8,7,6,5,4]

[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
[1,2,4,3,5,6,7,8]

[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
[1,2,4,3,5,6,8,7]

[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
[1,2,4,3,5,7,6,8]

[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
[1,2,4,3,5,7,8,6]

[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
[1,2,4,3,5,8,7,6]

[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
[1,2,4,3,6,5,7,8]

[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
[1,2,4,3,6,5,8,7]

[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
[1,2,4,3,6,7,5,8]

[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
[1,2,4,3,6,7,8,5]

[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
[1,2,4,3,6,8,7,5]

[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
[1,2,4,3,7,6,5,8]

[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
[1,2,4,3,7,6,8,5]

[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
[1,2,4,3,8,6,7,5]

[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
[1,2,4,3,8,7,6,5]

[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
[1,2,4,5,3,6,7,8]

[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
[1,2,4,5,3,6,8,7]

[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
[1,2,4,5,3,7,6,8]

[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
[1,2,4,5,3,7,8,6]

[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
[1,2,4,5,3,8,7,6]

[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
[1,2,4,5,6,3,7,8]

[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
[1,2,4,5,6,3,8,7]

[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
[1,2,4,5,6,7,3,8]

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
[1,2,4,5,6,7,8,3]

[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
[1,2,4,5,6,8,7,3]

[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
[1,2,4,5,7,6,3,8]

[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
[1,2,4,5,7,6,8,3]

[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
[1,2,4,5,8,6,7,3]

[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
[1,2,4,5,8,7,6,3]

[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
[1,2,4,6,5,3,7,8]

[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
[1,2,4,6,5,3,8,7]

[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
[1,2,4,6,5,7,3,8]

[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
[1,2,4,6,5,7,8,3]

[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
[1,2,4,6,5,8,7,3]

[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
[1,2,4,7,5,6,3,8]

[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
[1,2,4,7,5,6,8,3]

[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
[1,2,4,8,5,6,7,3]

[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
[1,2,4,8,5,7,6,3]

[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
[1,2,4,7,6,5,3,8]

[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
[1,2,4,7,6,5,8,3]

[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
[1,2,4,8,6,5,7,3]

[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
[1,2,4,8,6,7,5,3]

[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
[1,2,4,8,7,6,5,3]

[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
[1,2,5,4,3,6,7,8]

[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
[1,2,5,4,3,6,8,7]

[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
[1,2,5,4,3,7,6,8]

[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
[1,2,5,4,3,7,8,6]

[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
[1,2,5,4,3,8,7,6]

[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
[1,2,5,4,6,3,7,8]

[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
[1,2,5,4,6,3,8,7]

[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
[1,2,5,4,6,7,3,8]

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
[1,2,5,4,6,7,8,3]

[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
[1,2,5,4,6,8,7,3]

[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
[1,2,5,4,7,6,3,8]

[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
[1,2,5,4,7,6,8,3]

[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
[1,2,5,4,8,6,7,3]

[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
[1,2,5,4,8,7,6,3]

[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
[1,2,6,4,5,3,7,8]

[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
[1,2,6,4,5,3,8,7]

[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
[1,2,6,4,5,7,3,8]

[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
[1,2,6,4,5,7,8,3]

[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
[1,2,6,4,5,8,7,3]

[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
[1,2,7,4,5,6,3,8]

[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
[1,2,7,4,5,6,8,3]

[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
[1,2,8,4,5,6,7,3]

[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
[1,2,8,4,5,7,6,3]

[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
[1,2,7,4,6,5,3,8]

[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
[1,2,7,4,6,5,8,3]

[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
[1,2,8,4,6,5,7,3]

[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
[1,2,8,4,6,7,5,3]

[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
[1,2,8,4,7,6,5,3]

[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
[1,2,6,5,4,3,7,8]

[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
[1,2,6,5,4,3,8,7]

[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
[1,2,6,5,4,7,3,8]

[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
[1,2,6,5,4,7,8,3]

[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
[1,2,6,5,4,8,7,3]

[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
[1,2,7,5,4,6,3,8]

[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
[1,2,7,5,4,6,8,3]

[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
[1,2,8,5,4,6,7,3]

[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
[1,2,8,5,4,7,6,3]

[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
[1,2,7,5,6,4,3,8]

[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
[1,2,7,5,6,4,8,3]

[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
[1,2,8,5,6,4,7,3]

[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
[1,2,8,5,6,7,4,3]

[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
[1,2,8,5,7,6,4,3]

[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
[1,2,7,6,5,4,3,8]

[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
[1,2,7,6,5,4,8,3]

[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
[1,2,8,6,5,4,7,3]

[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
[1,2,8,6,5,7,4,3]

[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
[1,2,8,7,5,6,4,3]

[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
[1,2,8,7,6,5,4,3]

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
[1,3,2,4,5,6,7,8]

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
[1,3,2,4,5,6,8,7]

[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
[1,3,2,4,5,7,6,8]

[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
[1,3,2,4,5,7,8,6]

[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
[1,3,2,4,5,8,7,6]

[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
[1,3,2,4,6,5,7,8]

[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
[1,3,2,4,6,5,8,7]

[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
[1,3,2,4,6,7,5,8]

[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
[1,3,2,4,6,7,8,5]

[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
[1,3,2,4,6,8,7,5]

[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
[1,3,2,4,7,6,5,8]

[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
[1,3,2,4,7,6,8,5]

[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
[1,3,2,4,8,6,7,5]

[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
[1,3,2,4,8,7,6,5]

[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=>
[1,3,2,5,4,6,7,8]

[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=>
[1,3,2,5,4,6,8,7]

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=>
[1,3,2,5,4,7,6,8]

[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=>
[1,3,2,5,4,7,8,6]

[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=>
[1,3,2,5,4,8,7,6]

[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=>
[1,3,2,5,6,4,7,8]

[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=>
[1,3,2,5,6,4,8,7]

[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=>
[1,3,2,5,6,7,4,8]

[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=>
[1,3,2,5,6,7,8,4]

[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=>
[1,3,2,5,6,8,7,4]

[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=>
[1,3,2,5,7,6,4,8]

[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=>
[1,3,2,5,7,6,8,4]

[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=>
[1,3,2,5,8,6,7,4]

[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=>
[1,3,2,5,8,7,6,4]

[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=>
[1,3,2,6,5,4,7,8]

[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=>
[1,3,2,6,5,4,8,7]

[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
=>
[1,3,2,6,5,7,4,8]

[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
=>
[1,3,2,6,5,7,8,4]

[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=>
[1,3,2,6,5,8,7,4]

[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
=>
[1,3,2,7,5,6,4,8]

[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
=>
[1,3,2,7,5,6,8,4]

[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=>
[1,3,2,8,5,6,7,4]

[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=>
[1,3,2,8,5,7,6,4]

[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=>
[1,3,2,7,6,5,4,8]

[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=>
[1,3,2,7,6,5,8,4]

[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=>
[1,3,2,8,6,5,7,4]

[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=>
[1,3,2,8,6,7,5,4]

[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=>
[1,3,2,8,7,6,5,4]

[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=>
[1,3,4,2,5,6,7,8]

[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=>
[1,3,4,2,5,6,8,7]

[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=>
[1,3,4,2,5,7,6,8]

[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=>
[1,3,4,2,5,7,8,6]

[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=>
[1,3,4,2,5,8,7,6]

[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=>
[1,3,4,2,6,5,7,8]

[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=>
[1,3,4,2,6,5,8,7]

[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=>
[1,3,4,2,6,7,5,8]

[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=>
[1,3,4,2,6,7,8,5]

[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=>
[1,3,4,2,6,8,7,5]

[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=>
[1,3,4,2,7,6,5,8]

[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=>
[1,3,4,2,7,6,8,5]

[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=>
[1,3,4,2,8,6,7,5]

[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=>
[1,3,4,2,8,7,6,5]

[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=>
[1,3,4,5,2,6,7,8]

[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=>
[1,3,4,5,2,6,8,7]

[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=>
[1,3,4,5,2,7,6,8]

[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=>
[1,3,4,5,2,7,8,6]

[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=>
[1,3,4,5,2,8,7,6]

[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=>
[1,3,4,5,6,2,7,8]

[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=>
[1,3,4,5,6,2,8,7]

[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=>
[1,3,4,5,6,7,2,8]

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=>
[1,3,4,5,6,7,8,2]

[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=>
[1,3,4,5,6,8,7,2]

[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=>
[1,3,4,5,7,6,2,8]

[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=>
[1,3,4,5,7,6,8,2]

[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=>
[1,3,4,5,8,6,7,2]

[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=>
[1,3,4,5,8,7,6,2]

[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=>
[1,3,4,6,5,2,7,8]

[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
=>
[1,3,4,6,5,2,8,7]

[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=>
[1,3,4,6,5,7,2,8]

[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=>
[1,3,4,6,5,7,8,2]

[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=>
[1,3,4,6,5,8,7,2]

[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=>
[1,3,4,7,5,6,2,8]

[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=>
[1,3,4,7,5,6,8,2]

[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=>
[1,3,4,8,5,6,7,2]

[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=>
[1,3,4,8,5,7,6,2]

[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
=>
[1,3,4,7,6,5,2,8]

[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=>
[1,3,4,7,6,5,8,2]

[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=>
[1,3,4,8,6,5,7,2]

[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=>
[1,3,4,8,6,7,5,2]

[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=>
[1,3,4,8,7,6,5,2]

[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=>
[1,3,5,4,2,6,7,8]

[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
=>
[1,3,5,4,2,6,8,7]

[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=>
[1,3,5,4,2,7,6,8]

[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
=>
[1,3,5,4,2,7,8,6]

[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
=>
[1,3,5,4,2,8,7,6]

[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=>
[1,3,5,4,6,2,7,8]

[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=>
[1,3,5,4,6,2,8,7]

[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=>
[1,3,5,4,6,7,2,8]

[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=>
[1,3,5,4,6,7,8,2]

[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=>
[1,3,5,4,6,8,7,2]

[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
=>
[1,3,5,4,7,6,2,8]

[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=>
[1,3,5,4,7,6,8,2]

[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=>
[1,3,5,4,8,6,7,2]

[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=>
[1,3,5,4,8,7,6,2]

[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=>
[1,3,6,4,5,2,7,8]

[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
=>
[1,3,6,4,5,2,8,7]

[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=>
[1,3,6,4,5,7,2,8]

[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=>
[1,3,6,4,5,7,8,2]

[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=>
[1,3,6,4,5,8,7,2]

[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=>
[1,3,7,4,5,6,2,8]

[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=>
[1,3,7,4,5,6,8,2]

[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=>
[1,3,8,4,5,6,7,2]

[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=>
[1,3,8,4,5,7,6,2]

[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=>
[1,3,7,4,6,5,2,8]

[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=>
[1,3,7,4,6,5,8,2]

[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=>
[1,3,8,4,6,5,7,2]

[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=>
[1,3,8,4,6,7,5,2]

[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=>
[1,3,8,4,7,6,5,2]

[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=>
[1,3,6,5,4,2,7,8]

[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=>
[1,3,6,5,4,2,8,7]

[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
=>
[1,3,6,5,4,7,2,8]

[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=>
[1,3,6,5,4,7,8,2]

[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=>
[1,3,6,5,4,8,7,2]

[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=>
[1,3,7,5,4,6,2,8]

[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=>
[1,3,7,5,4,6,8,2]

[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=>
[1,3,8,5,4,6,7,2]

[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=>
[1,3,8,5,4,7,6,2]

[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
=>
[1,3,7,5,6,4,2,8]

[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=>
[1,3,7,5,6,4,8,2]

[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=>
[1,3,8,5,6,4,7,2]

[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=>
[1,3,8,5,6,7,4,2]

[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=>
[1,3,8,5,7,6,4,2]

[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=>
[1,3,7,6,5,4,2,8]

[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=>
[1,3,7,6,5,4,8,2]

[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=>
[1,3,8,6,5,4,7,2]

[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=>
[1,3,8,6,5,7,4,2]

[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=>
[1,3,8,7,5,6,4,2]

[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=>
[1,3,8,7,6,5,4,2]

[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=>
[1,4,3,2,5,6,7,8]

[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=>
[1,4,3,2,5,6,8,7]

[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
=>
[1,4,3,2,5,7,6,8]

[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
=>
[1,4,3,2,5,7,8,6]

[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=>
[1,4,3,2,5,8,7,6]

[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
=>
[1,4,3,2,6,5,7,8]

[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=>
[1,4,3,2,6,5,8,7]

[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
=>
[1,4,3,2,6,7,5,8]

[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
=>
[1,4,3,2,6,7,8,5]

[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
=>
[1,4,3,2,6,8,7,5]

[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=>
[1,4,3,2,7,6,5,8]

[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=>
[1,4,3,2,7,6,8,5]

[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=>
[1,4,3,2,8,6,7,5]

[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=>
[1,4,3,2,8,7,6,5]

[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=>
[1,4,3,5,2,6,7,8]

[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=>
[1,4,3,5,2,6,8,7]

[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
=>
[1,4,3,5,2,7,6,8]

[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
=>
[1,4,3,5,2,7,8,6]

[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=>
[1,4,3,5,2,8,7,6]

[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=>
[1,4,3,5,6,2,7,8]

[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=>
[1,4,3,5,6,2,8,7]

[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=>
[1,4,3,5,6,7,2,8]

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=>
[1,4,3,5,6,7,8,2]

[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=>
[1,4,3,5,6,8,7,2]

[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
=>
[1,4,3,5,7,6,2,8]

[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=>
[1,4,3,5,7,6,8,2]

[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=>
[1,4,3,5,8,6,7,2]

[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=>
[1,4,3,5,8,7,6,2]

[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=>
[1,4,3,6,5,2,7,8]

[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
=>
[1,4,3,6,5,2,8,7]

[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
=>
[1,4,3,6,5,7,2,8]

[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=>
[1,4,3,6,5,7,8,2]

[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=>
[1,4,3,6,5,8,7,2]

[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
=>
[1,4,3,7,5,6,2,8]

[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=>
[1,4,3,7,5,6,8,2]

[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=>
[1,4,3,8,5,6,7,2]

[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=>
[1,4,3,8,5,7,6,2]

[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=>
[1,4,3,7,6,5,2,8]

[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=>
[1,4,3,7,6,5,8,2]

[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=>
[1,4,3,8,6,5,7,2]

[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=>
[1,4,3,8,6,7,5,2]

[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=>
[1,4,3,8,7,6,5,2]

[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=>
[1,5,3,4,2,6,7,8]

[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
=>
[1,5,3,4,2,6,8,7]

[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
=>
[1,5,3,4,2,7,6,8]

[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=>
[1,5,3,4,2,7,8,6]

[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=>
[1,5,3,4,2,8,7,6]

[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=>
[1,5,3,4,6,2,7,8]

[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=>
[1,5,3,4,6,2,8,7]

[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=>
[1,5,3,4,6,7,2,8]

[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=>
[1,5,3,4,6,7,8,2]

[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=>
[1,5,3,4,6,8,7,2]

[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
=>
[1,5,3,4,7,6,2,8]

[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=>
[1,5,3,4,7,6,8,2]

[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=>
[1,5,3,4,8,6,7,2]

[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=>
[1,5,3,4,8,7,6,2]

[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=>
[1,6,3,4,5,2,7,8]

[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=>
[1,6,3,4,5,2,8,7]

[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=>
[1,6,3,4,5,7,2,8]

[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=>
[1,6,3,4,5,7,8,2]

[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=>
[1,6,3,4,5,8,7,2]

[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=>
[1,7,3,4,5,6,2,8]

[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=>
[1,7,3,4,5,6,8,2]

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=>
[1,8,3,4,5,6,7,2]

[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=>
[1,8,3,4,5,7,6,2]

[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=>
[1,7,3,4,6,5,2,8]

[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=>
[1,7,3,4,6,5,8,2]

[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=>
[1,8,3,4,6,5,7,2]

[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=>
[1,8,3,4,6,7,5,2]

[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=>
[1,8,3,4,7,6,5,2]

[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=>
[1,6,3,5,4,2,7,8]

[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=>
[1,6,3,5,4,2,8,7]

[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=>
[1,6,3,5,4,7,2,8]

[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=>
[1,6,3,5,4,7,8,2]

[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=>
[1,6,3,5,4,8,7,2]

[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=>
[1,7,3,5,4,6,2,8]

[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=>
[1,7,3,5,4,6,8,2]

[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=>
[1,8,3,5,4,6,7,2]

[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=>
[1,8,3,5,4,7,6,2]

[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=>
[1,7,3,5,6,4,2,8]

[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=>
[1,7,3,5,6,4,8,2]

[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=>
[1,8,3,5,6,4,7,2]

[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=>
[1,8,3,5,6,7,4,2]

[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=>
[1,8,3,5,7,6,4,2]

[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=>
[1,7,3,6,5,4,2,8]

[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=>
[1,7,3,6,5,4,8,2]

[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=>
[1,8,3,6,5,4,7,2]

[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=>
[1,8,3,6,5,7,4,2]

[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=>
[1,8,3,7,5,6,4,2]

[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=>
[1,8,3,7,6,5,4,2]

[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=>
[1,5,4,3,2,6,7,8]

[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=>
[1,5,4,3,2,6,8,7]

[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=>
[1,5,4,3,2,7,6,8]

[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
=>
[1,5,4,3,2,7,8,6]

[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=>
[1,5,4,3,2,8,7,6]

[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=>
[1,5,4,3,6,2,7,8]

[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
=>
[1,5,4,3,6,2,8,7]

[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=>
[1,5,4,3,6,7,2,8]

[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=>
[1,5,4,3,6,7,8,2]

[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=>
[1,5,4,3,6,8,7,2]

[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
=>
[1,5,4,3,7,6,2,8]

[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
=>
[1,5,4,3,7,6,8,2]

[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
=>
[1,5,4,3,8,6,7,2]

[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=>
[1,5,4,3,8,7,6,2]

[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=>
[1,6,4,3,5,2,7,8]

[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
=>
[1,6,4,3,5,2,8,7]

[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=>
[1,6,4,3,5,7,2,8]

[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=>
[1,6,4,3,5,7,8,2]

[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=>
[1,6,4,3,5,8,7,2]

[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=>
[1,7,4,3,5,6,2,8]

[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=>
[1,7,4,3,5,6,8,2]

[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=>
[1,8,4,3,5,6,7,2]

[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=>
[1,8,4,3,5,7,6,2]

[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=>
[1,7,4,3,6,5,2,8]

[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=>
[1,7,4,3,6,5,8,2]

[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=>
[1,8,4,3,6,5,7,2]

[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=>
[1,8,4,3,6,7,5,2]

[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=>
[1,8,4,3,7,6,5,2]

[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=>
[1,6,4,5,3,2,7,8]

[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=>
[1,6,4,5,3,2,8,7]

[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=>
[1,6,4,5,3,7,2,8]

[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=>
[1,6,4,5,3,7,8,2]

[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=>
[1,6,4,5,3,8,7,2]

[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=>
[1,7,4,5,3,6,2,8]

[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=>
[1,7,4,5,3,6,8,2]

[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=>
[1,8,4,5,3,6,7,2]

[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=>
[1,8,4,5,3,7,6,2]

[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=>
[1,7,4,5,6,3,2,8]

[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=>
[1,7,4,5,6,3,8,2]

[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=>
[1,8,4,5,6,3,7,2]

[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=>
[1,8,4,5,6,7,3,2]

[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=>
[1,8,4,5,7,6,3,2]

[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=>
[1,7,4,6,5,3,2,8]

[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=>
[1,7,4,6,5,3,8,2]

[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=>
[1,8,4,6,5,3,7,2]

[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=>
[1,8,4,6,5,7,3,2]

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=>
[1,8,4,7,5,6,3,2]

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=>
[1,8,4,7,6,5,3,2]

[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=>
[1,6,5,4,3,2,7,8]

[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=>
[1,6,5,4,3,2,8,7]

[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
=>
[1,6,5,4,3,7,2,8]

[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=>
[1,6,5,4,3,7,8,2]

[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=>
[1,6,5,4,3,8,7,2]

[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
=>
[1,7,5,4,3,6,2,8]

[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=>
[1,7,5,4,3,6,8,2]

[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=>
[1,8,5,4,3,6,7,2]

[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=>
[1,8,5,4,3,7,6,2]

[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=>
[1,7,5,4,6,3,2,8]

[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=>
[1,7,5,4,6,3,8,2]

[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
=>
[1,8,5,4,6,3,7,2]

[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=>
[1,8,5,4,6,7,3,2]

[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=>
[1,8,5,4,7,6,3,2]

[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=>
[1,7,6,4,5,3,2,8]

[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=>
[1,7,6,4,5,3,8,2]

[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=>
[1,8,6,4,5,3,7,2]

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=>
[1,8,6,4,5,7,3,2]

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=>
[1,8,7,4,5,6,3,2]

[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=>
[1,8,7,4,6,5,3,2]

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=>
[1,7,6,5,4,3,2,8]

[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=>
[1,7,6,5,4,3,8,2]

[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=>
[1,8,6,5,4,3,7,2]

[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=>
[1,8,6,5,4,7,3,2]

[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=>
[1,8,7,5,4,6,3,2]

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=>
[1,8,7,5,6,4,3,2]

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=>
[1,8,7,6,5,4,3,2]

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
[2,1,3,4,5,6,7,8]

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
[2,1,3,4,5,6,8,7]

[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
[2,1,3,4,5,7,6,8]

[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
[2,1,3,4,5,7,8,6]

[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
[2,1,3,4,5,8,7,6]

[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
[2,1,3,4,6,5,7,8]

[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
[2,1,3,4,6,5,8,7]

[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
[2,1,3,4,6,7,5,8]

[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
[2,1,3,4,6,7,8,5]

[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
[2,1,3,4,6,8,7,5]

[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
[2,1,3,4,7,6,5,8]

[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
[2,1,3,4,7,6,8,5]

[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
[2,1,3,4,8,6,7,5]

[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
[2,1,3,4,8,7,6,5]

[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
[2,1,3,5,4,6,7,8]

[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
[2,1,3,5,4,6,8,7]

[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
[2,1,3,5,4,7,6,8]

[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
[2,1,3,5,4,7,8,6]

[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
[2,1,3,5,4,8,7,6]

[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
[2,1,3,5,6,4,7,8]

[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
[2,1,3,5,6,4,8,7]

[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
[2,1,3,5,6,7,4,8]

[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
[2,1,3,5,6,7,8,4]

[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
[2,1,3,5,6,8,7,4]

[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
[2,1,3,5,7,6,4,8]

[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
[2,1,3,5,7,6,8,4]

[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
[2,1,3,5,8,6,7,4]

[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
[2,1,3,5,8,7,6,4]

[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
[2,1,3,6,5,4,7,8]

[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
[2,1,3,6,5,4,8,7]

[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
[2,1,3,6,5,7,4,8]

[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
[2,1,3,6,5,7,8,4]

[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
[2,1,3,6,5,8,7,4]

[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
[2,1,3,7,5,6,4,8]

[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
[2,1,3,7,5,6,8,4]

[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
[2,1,3,8,5,6,7,4]

[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
[2,1,3,8,5,7,6,4]

[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
[2,1,3,7,6,5,4,8]

[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
[2,1,3,7,6,5,8,4]

[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
[2,1,3,8,6,5,7,4]

[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
[2,1,3,8,6,7,5,4]

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
[2,1,3,8,7,6,5,4]

[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
[2,1,4,3,5,6,7,8]

[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
[2,1,4,3,5,6,8,7]

[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
[2,1,4,3,5,7,6,8]

[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
[2,1,4,3,5,7,8,6]

[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
[2,1,4,3,5,8,7,6]

[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
[2,1,4,3,6,5,7,8]

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
[2,1,4,3,6,5,8,7]

[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
[2,1,4,3,6,7,5,8]

[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
[2,1,4,3,6,7,8,5]

[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
[2,1,4,3,6,8,7,5]

[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
[2,1,4,3,7,6,5,8]

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
[2,1,4,3,7,6,8,5]

[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
[2,1,4,3,8,6,7,5]

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
[2,1,4,3,8,7,6,5]

[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
[2,1,4,5,3,6,7,8]

[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
[2,1,4,5,3,6,8,7]

[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
[2,1,4,5,3,7,6,8]

[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
[2,1,4,5,3,7,8,6]

[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
[2,1,4,5,3,8,7,6]

[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
[2,1,4,5,6,3,7,8]

[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
[2,1,4,5,6,3,8,7]

[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
[2,1,4,5,6,7,3,8]

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
[2,1,4,5,6,7,8,3]

[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
[2,1,4,5,6,8,7,3]

[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
[2,1,4,5,7,6,3,8]

[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
[2,1,4,5,7,6,8,3]

[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
[2,1,4,5,8,6,7,3]

[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
[2,1,4,5,8,7,6,3]

[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
[2,1,4,6,5,3,7,8]

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
[2,1,4,6,5,3,8,7]

[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
[2,1,4,6,5,7,3,8]

[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
[2,1,4,6,5,7,8,3]

[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
[2,1,4,6,5,8,7,3]

[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
[2,1,4,7,5,6,3,8]

[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
[2,1,4,7,5,6,8,3]

[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
[2,1,4,8,5,6,7,3]

[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
[2,1,4,8,5,7,6,3]

[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
[2,1,4,7,6,5,3,8]

[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
[2,1,4,7,6,5,8,3]

[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
[2,1,4,8,6,5,7,3]

[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
[2,1,4,8,6,7,5,3]

[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
[2,1,4,8,7,6,5,3]

[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
[2,1,5,4,3,6,7,8]

[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
[2,1,5,4,3,6,8,7]

[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
[2,1,5,4,3,7,6,8]

[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
[2,1,5,4,3,7,8,6]

[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
[2,1,5,4,3,8,7,6]

[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
[2,1,5,4,6,3,7,8]

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
[2,1,5,4,6,3,8,7]

[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
[2,1,5,4,6,7,3,8]

[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
[2,1,5,4,6,7,8,3]

[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
[2,1,5,4,6,8,7,3]

[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
[2,1,5,4,7,6,3,8]

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
[2,1,5,4,7,6,8,3]

[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
[2,1,5,4,8,6,7,3]

[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
[2,1,5,4,8,7,6,3]

[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
[2,1,6,4,5,3,7,8]

[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
[2,1,6,4,5,3,8,7]

[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
[2,1,6,4,5,7,3,8]

[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
[2,1,6,4,5,7,8,3]

[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
[2,1,6,4,5,8,7,3]

[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
[2,1,7,4,5,6,3,8]

[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
[2,1,7,4,5,6,8,3]

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
[2,1,8,4,5,6,7,3]

[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
[2,1,8,4,5,7,6,3]

[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
[2,1,7,4,6,5,3,8]

[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
[2,1,7,4,6,5,8,3]

[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
[2,1,8,4,6,5,7,3]

[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
[2,1,8,4,6,7,5,3]

[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
[2,1,8,4,7,6,5,3]

[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
[2,1,6,5,4,3,7,8]

[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
[2,1,6,5,4,3,8,7]

[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
[2,1,6,5,4,7,3,8]

[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
[2,1,6,5,4,7,8,3]

[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
[2,1,6,5,4,8,7,3]

[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
[2,1,7,5,4,6,3,8]

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
[2,1,7,5,4,6,8,3]

[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
[2,1,8,5,4,6,7,3]

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
[2,1,8,5,4,7,6,3]

[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
[2,1,7,5,6,4,3,8]

[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
[2,1,7,5,6,4,8,3]

[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
[2,1,8,5,6,4,7,3]

[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
[2,1,8,5,6,7,4,3]

[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
[2,1,8,5,7,6,4,3]

[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
[2,1,7,6,5,4,3,8]

[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
[2,1,7,6,5,4,8,3]

[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
[2,1,8,6,5,4,7,3]

[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
[2,1,8,6,5,7,4,3]

[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
[2,1,8,7,5,6,4,3]

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
[2,1,8,7,6,5,4,3]

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
[2,3,1,4,5,6,7,8]

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
[2,3,1,4,5,6,8,7]

[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
[2,3,1,4,5,7,6,8]

[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
[2,3,1,4,5,7,8,6]

[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
[2,3,1,4,5,8,7,6]

[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
[2,3,1,4,6,5,7,8]

[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
[2,3,1,4,6,5,8,7]

[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
[2,3,1,4,6,7,5,8]

[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
[2,3,1,4,6,7,8,5]

[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
[2,3,1,4,6,8,7,5]

[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
[2,3,1,4,7,6,5,8]

[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
[2,3,1,4,7,6,8,5]

[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
[2,3,1,4,8,6,7,5]

[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
[2,3,1,4,8,7,6,5]

Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Properties
injectiveA map $\phi: A \rightarrow B$ is injective if $\phi(a) = \phi(b)$ implies $a=b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
References
[1] Stump, C. More bijective Catalan combinatorics on permutations and on signed permutations MathSciNet:3153083 arXiv:0808.2822
Code
def to_noncrossing_permutation(elt): return elt.to_noncrossing_permutation()
Updated
May 08, 2019 at 06:34 by Christian Stump
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