Identifier
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]
[1,0,1,0]=>[2,1]
[1,1,0,0]=>[1,2]
[1,0,1,0,1,0]=>[2,3,1]
[1,0,1,1,0,0]=>[2,1,3]
[1,1,0,0,1,0]=>[1,3,2]
[1,1,0,1,0,0]=>[3,1,2]
[1,1,1,0,0,0]=>[1,2,3]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,6,1,7,8,5]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,4,6,1,7,5,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,6,7,1,8,5]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,8,7]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,8,5,7]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,8,1,5,7]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,4,1,7,5,6,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,1,5,8,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,1,5,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,4,1,5,6,8,7]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,7,8,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,7,4,8,6]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,5,4,6,8,7]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,5,4,8,6,7]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,5,8,4,6,7]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,5,1,6,7,4,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,4,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,5,6,1,7,4,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,7,1,8,4]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,6,1,4,8,7]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,6,1,8,4,7]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,7,8,6]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,7,4,8,6]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,7,8,4,6]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,7,1,4,8,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,7,1,8,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,4,6,8,7]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,4,8,6,7]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,1,4,6,8,5,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,1,4,6,5,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,6,4,7,8,5]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,6,7,4,8,5]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,6,7,4,5,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,8,7]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,7,8,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,6,1,4,7,5,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,6,1,7,4,8,5]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,7,4,5,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,6,7,1,4,8,5]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,6,7,1,8,4,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,1,4,5]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,8,5,7]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,4,7,5,8,6]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,1,4,7,5,6,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,1,7,4,5,6,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,1,4,5,8,6]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,7,1,4,8,5,6]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,7,1,8,4,5,6]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,7,3,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,8,3,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,6,3,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,7,8,3,6]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4,5,3,8,6,7]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,6,3,7,8,5]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,6,3,7,5,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,6,7,3,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,6,3,5,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,4,3,5,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,4,3,7,5,6,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,7,3,5,8,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,4,7,3,8,5,6]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,4,7,3,5,6,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,5,6,3,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,5,3,7,8,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,7,3,8,6]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,7,8,3,6]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,5,1,6,7,3,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,6,8,1,3,7]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,7,1,3,8,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,7,1,8,3,6]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,7,8,1,3,6]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,5,1,3,6,8,7]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,5,1,3,8,6,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,8,1,3,6,7]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,6,7,3,5,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,6,1,3,7,8,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,6,1,7,8,3,5]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,6,1,7,3,5,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,6,7,1,8,3,5]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,6,1,3,5,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,1,3,7,5,6,8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,1,7,3,5,6,8]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,7,1,3,8,5,6]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,3,5,6,8,7]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,3,5,8,6,7]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,5,6,7,4,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,8,4,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,5,6,4,7,8]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,7,4,8,6]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,7,8,4,6]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,5,4,8,6,7]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,5,8,4,6,7]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,1,5,3,6,7,4,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,6,4,7,8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,5,6,3,7,4,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,7,3,8,4]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,5,6,7,3,4,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,1,5,6,3,8,4,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,1,5,6,8,3,4,7]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,1,5,6,3,4,7,8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,7,8,6]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6,8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,5,7,3,4,8,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6,8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,1,5,3,4,8,6,7]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,1,5,8,3,4,6,7]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,5,1,3,6,4,8,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,5,1,6,7,3,4,8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,5,1,6,3,8,4,7]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,1,6,8,3,4,7]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,1,6,3,4,7,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,5,6,1,7,3,8,4]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,5,6,1,7,8,3,4]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,5,6,1,7,3,4,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,7,1,8,3,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,4,8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,8,7]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,5,6,1,3,8,4,7]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,5,6,1,8,3,4,7]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,5,6,1,3,4,7,8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,7,8,6]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,7,3,8,4,6]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,7,8,3,4,6]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,5,7,1,3,8,4,6]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6,8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,5,1,3,4,6,8,7]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,5,1,3,4,8,6,7]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,5,1,8,3,4,6,7]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,5,8,1,3,4,6,7]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,1,3,4,6,7,5,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,1,3,4,6,8,5,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,3,6,4,7,8,5]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,1,3,6,4,7,5,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,1,3,6,7,4,5,8]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,8,7]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,3,6,4,8,5,7]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,1,3,6,8,4,5,7]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,1,3,6,4,5,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,1,6,3,4,7,5,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,1,6,3,7,4,5,8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,1,6,7,3,8,4,5]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,6,7,3,4,5,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,1,6,8,3,4,5,7]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,1,6,3,4,5,7,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,6,1,3,4,7,8,5]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,1,3,7,8,4,5]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,6,1,3,7,4,5,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,5]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,6,1,7,8,3,4,5]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,6,1,7,3,4,5,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,6,7,1,3,8,4,5]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,1,3,4,5,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,8,7]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,8,5,7]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,4,7,5,8,6]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,1,3,4,7,8,5,6]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,1,3,4,7,5,6,8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,7,4,5,8,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,1,3,7,4,8,5,6]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,1,3,7,8,4,5,6]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,1,3,7,4,5,6,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,1,7,3,4,8,5,6]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,7,1,3,4,8,5,6]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,7,1,3,8,4,5,6]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,2,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,5,7,2,8,6]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6,8]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,5,2,6,8,7]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,5,8,2,6,7]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,8,5,7]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,6,5,7,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,6,2,7,8,5]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,6,2,7,5,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,6,7,8,2,5]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,7,2,5,8]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,8,5,7]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,8,2,5,7]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,4,2,7,5,6,8]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,4,7,2,8,5,6]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,4,7,8,2,5,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,5,6,7,4,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,5,6,8,4,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,7,4,8,6]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,5,4,6,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,4]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,5,2,6,4,8,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,6,8,4,7]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,5,2,6,4,7,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,5,6,2,7,8,4]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,7,2,4,8]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,5,6,2,4,8,7]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,5,6,2,8,4,7]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,8,2,4,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,7,8,6]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,7,4,8,6]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,5,2,4,6,8,7]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,5,2,4,8,6,7]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,2,4,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,2,6,4,7,8,5]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,2,6,7,4,8,5]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,7,8,4,5]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,2,6,7,4,5,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,8,7]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,6,8,4,5,7]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,6,2,4,7,8,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,2,4,7,5,8]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,6,2,7,8,4,5]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,7,4,5,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,6,7,2,8,4,5]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,8,7]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,6,8,2,4,5,7]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,4,7,5,6,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,7,4,5,8,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,7,8,4,5,6]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,6,2,7,8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,7,2,8,6]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,7,8,2,6]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6,8]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,2,6,8,7]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4,5,2,8,6,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4,5,8,2,6,7]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,6,5,7,8]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,6,2,7,8,5]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,4,6,2,7,5,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,7,2,8,5]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,4,6,7,8,2,5]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,4,6,7,2,5,8]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,4,6,2,5,7,8]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,2,5,7,6,8]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,7,2,5,8,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,4,7,2,8,5,6]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,4,7,8,2,5,6]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,4,7,2,5,6,8]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,2,5,6,8,7]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,5,6,8,2,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,5,2,7,8,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,5,7,2,8,6]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,5,2,6,8,7]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,2,8,6,7]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,5,8,2,6,7]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,5,2,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,1,6,2,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,5,1,6,8,2,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,1,2,8,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,1,8,2,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,8,1,2,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,5,1,7,2,8,6]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,1,7,8,2,6]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6,8]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,5,7,1,8,2,6]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,5,1,2,6,8,7]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,5,1,2,8,6,7]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,8,7]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,6,2,5,7,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,6,1,2,7,8,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,6,1,7,2,5,8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,6,7,1,2,8,5]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,6,7,1,8,2,5]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,8,7]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,8,5,7]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,8,2,5,7]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,6,1,2,5,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,1,2,7,5,6,8]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,4,1,7,2,5,8,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,7,2,8,5,6]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,1,7,8,2,5,6]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,7,2,5,6,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,4,7,1,2,5,8,6]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,7,1,2,8,5,6]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1,2,5,6,8,7]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,2,5,8,6,7]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,5,6,4,8,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,5,6,8,4,7]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,5,6,4,7,8]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,7,8,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,7,8,4,6]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,5,4,6,8,7]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,5,4,8,6,7]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,5,8,4,6,7]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,5,4,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,5,2,6,7,4,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,4,7,8]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,5,6,2,7,4,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,5,6,7,2,4,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,2,4,8,7]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,5,6,2,4,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,5,2,4,6,8,7]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,4,8,6,7]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,4,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,6,4,8,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,6,4,7,8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,5,1,6,7,2,4,8]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,5,1,6,2,8,4,7]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,1,6,8,2,4,7]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,5,6,1,2,7,4,8]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,7,1,8,2,4]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,7,2,4,8,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,7,1,2,8,4,6]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,5,1,2,8,4,6,7]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,7,5,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,4,6,8,5,7]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,1,2,4,6,5,7,8]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,2,6,4,7,5,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,2,6,7,8,4,5]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,1,2,6,7,4,5,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,8,7]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,1,2,6,4,8,5,7]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,6,4,5,7,8]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,1,6,2,7,8,4,5]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,1,6,2,7,4,5,8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,6,7,2,4,8,5]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,6,7,2,8,4,5]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,6,7,8,2,4,5]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,1,6,2,8,4,5,7]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,6,2,4,5,7,8]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,6,1,2,7,4,5,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,6,1,7,2,4,5,8]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,6,7,1,8,2,4,5]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,6,7,1,2,4,5,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,8,5,7]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,8,4,5,7]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,6,1,2,4,5,7,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,2,4,5,7,8,6]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,2,4,7,8,5,6]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,7,4,5,8,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,2,7,8,4,5,6]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,7,2,4,8,5,6]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,7,1,2,4,8,5,6]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,7,1,2,8,4,5,6]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,7,1,8,2,4,5,6]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,7,3,8]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,6,3,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6,8]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,7,8,3,6]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,8,5,7]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,6,3,7,8,5]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,6,3,7,5,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,6,7,3,8,5]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,6,7,8,3,5]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,6,7,3,5,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,8,7]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,4,7,3,8,5,6]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,3,5,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,5,6,3,8,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,5,6,3,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,5,3,7,8,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,3,6]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,5,3,6,8,7]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,5,8,3,6,7]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,5,2,6,7,3,8]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,5,2,6,3,8,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,6,2,3,8,7]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,6,2,8,3,7]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,7,8,6]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6,8]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6,8]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,5,7,2,8,3,6]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,4,5,2,3,6,8,7]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,2,3,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,6,7,5,8]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,8,5,7]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,6,5,7,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,6,3,7,8,5]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,6,7,3,8,5]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,6,7,3,5,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,8,3,5,7]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,6,2,3,7,5,8]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,6,7,2,3,8,5]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,6,7,8,2,3,5]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,8,7]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,6,2,3,5,7,8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,2,3,5,7,8,6]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,5,6,7,3,8]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,5,7,3,8,6]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,3,6,8,7]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,5,8,3,6,7]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,5,2,6,7,3,8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,6,2,7,8,3]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,5,6,2,7,3,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,5,6,7,2,3,8]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,5,6,2,8,3,7]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6,8]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,5,7,2,3,8,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,5,7,8,2,3,6]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6,8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,5,2,3,6,8,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,5,2,3,8,6,7]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,5,8,2,3,6,7]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,6,3,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,5,1,6,7,2,3,8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,1,6,2,8,3,7]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,6,1,7,2,3,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,1,2,8,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,7,8,6]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,7,8,3,6]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,5,1,7,2,3,8,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6,8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,5,7,1,2,3,8,6]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,5,1,2,3,6,8,7]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,2,3,8,6,7]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,5,1,8,2,3,6,7]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,7,3,8,5]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,6,7,8,3,5]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,8,3,5,7]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,6,3,5,7,8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,6,2,7,8,3,5]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,6,7,2,3,8,5]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,6,7,2,8,3,5]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,2,3,5]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,6,7,2,3,5,8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,8,3,5,7]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,6,1,2,3,7,8,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,6,1,2,7,3,8,5]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,6,1,2,7,3,5,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,6,1,7,2,3,8,5]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,6,7,1,2,3,8,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,6,7,1,2,3,5,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,8,7]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,8,5,7]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[4,1,2,7,3,8,5,6]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,1,2,7,3,5,6,8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6,8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,8,6]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[4,7,1,2,3,8,5,6]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,7,1,2,8,3,5,6]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,2,5,3,6,7,4,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,2,5,3,6,8,4,7]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,2,5,6,7,3,4,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,2,5,6,3,4,8,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,2,5,6,8,3,4,7]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,2,5,7,3,4,8,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,2,5,3,4,6,8,7]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,5,3,4,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,6,7,4,8]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,6,8,4,7]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,5,2,6,7,3,8,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,5,2,6,3,4,8,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,6,2,3,7,4,8]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,5,6,2,7,3,8,4]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,7,3,4,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,8,7]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,5,6,2,3,4,7,8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,7,8,4,6]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,7,8,3,4,6]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6,8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,5,2,3,4,6,8,7]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,6,7,4,8]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,3,6,4,8,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,6,8,4,7]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,6,3,7,4,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,3,4]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,6,7,3,4,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,3,4,8,7]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,6,8,3,4,7]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,1,6,2,3,7,4,8]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,6,2,7,8,3,4]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,1,6,2,7,3,4,8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,1,6,7,2,3,4,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,8,7]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,1,6,8,2,3,4,7]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[5,1,6,2,3,4,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,4,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,1,2,7,3,4,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,6,1,7,2,8,3,4]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,1,7,2,3,4,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,8,7]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,6,1,2,8,3,4,7]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,6,1,8,2,3,4,7]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6,8]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,7,8,4,6]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,7,3,8,4,6]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,7,8,3,4,6]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,7,2,3,4,8,6]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,7,2,3,8,4,6]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,7,8,2,3,4,6]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,7,1,8,2,3,4,6]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,2,6,3,4,7,5,8]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,2,6,3,7,4,5,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,8,5,7]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,7,8,5]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,3,7,8,4,5]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,2,3,7,4,5,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,6,2,7,8,3,4,5]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,6,7,2,3,4,8,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,8,4,5,7]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,7,8,4,5]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,7,4,5,8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,7,3,4,8,5]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,7,2,3,4,8,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,1,7,2,3,8,4,5]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,7,1,2,8,3,4,5]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,8,5,7]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,8,4,5,7]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,1,3,9,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,1,3,4,5,6,7]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8,9]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,9,8]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,9,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,1,3,4,9,5,6,7,8]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7,9]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,1,3,4,5,9,6,7,8]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,1,8,9,3,4,5,6,7]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[2,7,1,9,3,4,5,6,8]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,7,8,1,3,4,5,6,9]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,9,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,9,7,8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,1,8,3,9,4,5,6,7]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,1,3,4,5,7,9]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,8,6,9]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[2,6,1,3,9,4,5,7,8]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[2,7,1,8,3,4,5,6,9]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,1,7,9,3,4,5,6,8]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,8,1,3,4,5,6,9,7]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7,9]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,2,9,4,5,6,7,8]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7,9]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,1,8,3,4,5,6,9,7]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,6,9,8]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1,3,4,9,6,7,8]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,3,4,5,6]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,8,1,3,4,5,9]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,8,9,2,4,5,6,7]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,7,1,9,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,7,9,1,2,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,1,2,7,9]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7,8,9]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,7,8,9,2,6]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,7,1,2,6,8,9]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,9,2,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,6,1,7,8,9,2,5]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,6,1,2,5,7,8,9]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,2,7,8,9,4,6]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,6,1,7,8,9,2,4]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8,9]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,2,6,7,8,9,4,5]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,1,2,7,4,5,6,8,9]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,1,8,2,4,5,6,7,9]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,2,3]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,8,2,3,9]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,6,2,7,8,9,3,5]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,4,9,2,3,5,6,7,8]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,9,2,3]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,9,2,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,6,1,7,8,9,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,7,1,8,9,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,1,9,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,7,1,2,9,3,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,8,9,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,1,2,7,8,9,3,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,6,7,8,9,3,5]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,9,1,2,3,5]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7,9]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,9,3,4]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,9,3,4]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,9,2,3,4]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,9,3,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,6,1,2,7,8,9,3,4]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,7,1,2,8,9,3,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,8,1,2,9,3,4]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,1,2,3,4,6]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[5,1,8,2,3,4,6,7,9]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,9,4,5]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,6,4,5,7,8,9]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,2,6,3,7,8,9,4,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,8,1,9,2,3,4,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[6,1,9,2,3,4,5,7,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,4,7,8,9,5,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,3,7,4,8,9,5,6]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,3,7,4,5,6,8,9]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,7,3,4,5,6,8,9]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,4,8,5,9,6,7]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7,9]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,9,6,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,9,5,6,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[8,1,2,9,3,4,5,6,7]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,9,2,3,4,5,6,7]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,1,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,1,8,9,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,1,7,8,9,5,6]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,9,4,5]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,9,1,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,8,9,1,6,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,6,1,7,8,9,3,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,9,1,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,9,1,4,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,1,3,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,7,8,1,3,4,9]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,6,1,7,9,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,7,6,8,9]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,5]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,6,5,7,8,9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,4]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,7,9,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,2,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,6,7,2,9,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,8,9,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7,9]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,7,8,9,6]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,9,5]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,8,9,4]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,5,3,6,7,8,9]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,9,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,9,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,7,8,9,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,6,1,2,8,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,7,8,1,2,9,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,9,3]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,7,1,2,8,3,9]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,9,2,4,5]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,3,6,7,8,9]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,4,7,8,9]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,5,8,9]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,9,3,4,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,8,2,9,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,7,1,8,2,9]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,9,2,4]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,9,2,4,5,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,6,9,5,7,8]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,4,7,5,8,6,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,5,6,1,7,2,9,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,4,5,1,6,2,8,9,7]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,2,7,8,9,6]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,9,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,8,1,2,3,9,4]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,1,7,9]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,6,7,8,9,3,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,9,3]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,1,2,6,9,3,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,1,9,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,1,9,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,7,3,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,5,6,1,8,2,9,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,6,8,1,2,9,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,1,3,5]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,6,8,9,2,7]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,9,4]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,1,3,4,7,5,6,8,9]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,7,1,2,8,3,9,4]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,8,2,9,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,8,2,9,4]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,6,8,9,2,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,8,2,9,4]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,9,3,5,6]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,9,3,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,7,2,8,9,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,6,7,2,8,9,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,1,7,2,8,9,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,6,2,7,8,9,5]
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,8,9,3,4,5,7]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,1,7,8,3,9,4,5,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,5,6,7,1,8,3,4,9]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,8,1,3,5,9]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[2,1,6,7,8,3,9,4,5]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,9,3,4,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,7,2,8,9,4]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,6,2,9,7,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,8,9,3,7]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,2,8,9,4,5,6,7]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,2,7,8,9,4,5,6]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,7,8,9,4,5]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,6,7,2,8,9,5]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,7,3,8,4,9]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,1,2,6,3,7,9,4,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,5,3,6,8,9,4,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,9,3,6]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,9,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,9,4]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,1,2,5,8,9,3,6,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,9,3,5,6]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,4,2,5,3,6,7,8,9]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,5,3,6,4,7,8,9]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,3,6,4,7,5,8,9]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,7,4,6,8,9]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,8,1,3,9,5]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,4,1,3,5,6,9,7,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,6,1,7,8,2,9,3]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,1,3,10,4,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,1,3,4,10,5,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8,10]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8,9,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,1,3,4,5,10,6,7,8,9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[2,1,9,10,3,4,5,6,7,8]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,9,1,3,4,5,6,7,10]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8,9,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,1,3,4,5,6,10,7,8,9]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8,9,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,7,10,8,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,3,10,2,4,5,6,7,8,9]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,10,2,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,9,10,2,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,9,10,3,4]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,9,10,1,7,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,9,10,2,3]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,1,2,6,7,8,9,10,3,4]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,8,9,10,1,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,6,1,7,8,9,10,2,3]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,9,10,4,5]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,7,8,9,10,3,4]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,7,8,9,10,1,5,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,6,7,1,8,9,10,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,6,7,1,2,8,9,10,3,4]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,9,10,1,4,5]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,7,8,1,9,10,2,3]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,7,8,9,10,5,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,7,8,1,2,9,10,3,4]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,9,10,1,3,4]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,8,9,1,10,2,3]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,7,8,9,1,3,4,10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,8,9,1,2,10,3,4]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,9,10,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,8,9,10,7]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,7,8,9,10,6]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,9,10,5]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,9,10,4]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,2,10]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,9,10,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,9,10,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,10,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,10,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,8,10,2,9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,9,10,1,2,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8,10]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7,9,10]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9,10]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,7,4,5,6,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8,9,10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,9,10,2,4]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,1,9,10,2,8]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,9,10,3]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,6,1,7,8,9,10,5]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,9,1,10,3]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,5,6,1,7,8,9,10,3]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,6,1,7,8,9,10,4]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,8,9,2,10,3]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,10,3,4,5,6]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,9,10,2,4,5]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,10,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,7,8,1,2,10,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[2,9,1,3,4,5,6,7,10,8]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,8,9,10,3,4,5,6,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,8,9,1,3,4,5,10]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,9,10,3,4,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,7,8,2,9,10,3]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,3,2,10,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,9,10,2,8]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,3,9,10,2,4,5,6,7,8]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,3,8,9,10,2,4,5,6,7]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,7,8,9,10,2,4,5,6]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,9,10,1,3,5]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,9,1,10,2,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,1,11,3,4,5,6,7,8,9,10]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,11,1,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,10,11,2,3]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10,11]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,1,11,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,10,11,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,11,10]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9,11]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,11,1,2,3,4,5,6]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,8,9,10,11,3,4,5,6,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,8,9,10,1,3,4,5,11]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,10,11,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,9,1,10,11,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,8,9,10,2,11]
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(only identities of compositions of up to three maps are shown)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
References
[1] Billey, S. C., Jockusch, W., Stanley, R. P. Some combinatorial properties of Schubert polynomials MathSciNet:1241505
[2] Callan, D. Bijections from Dyck paths to 321-avoiding permutations revisited arXiv:0711.2684
[2] Callan, D. Bijections from Dyck paths to 321-avoiding permutations revisited arXiv:0711.2684
Properties
injective, graded
Sage code
def mapping(P): """ sage: sorted([mapping(D) for D in DyckWords(7)]) == sorted(Permutations(7, avoiding=[3,2,1])) True """ n = (len(P)//2) a = P.rise_composition() A = [1+sum(a[:i]) for i in range(1,len(a))] d = P.reverse().rise_composition().reversed() D = [sum(d[:i])-1 for i in range(1,len(a))] pi = [None]*n rest = list(range(1, n+1)) for (e,f) in zip(A, D): pi[f] = e rest.remove(e) i = 0 for e in rest: while pi[i] is not None: i += 1 pi[i] = e return Permutation(pi)
Weight
26
Created
Jan 29, 2020 at 13:27 by FindStatCrew
Updated
Jan 29, 2020 at 13:27 by Martin Rubey
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