Identifier
Images
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]
[1,0,1,0]=>[3,1,2]
[1,1,0,0]=>[2,3,1]
[1,0,1,0,1,0]=>[4,1,2,3]
[1,0,1,1,0,0]=>[3,1,4,2]
[1,1,0,0,1,0]=>[2,4,1,3]
[1,1,0,1,0,0]=>[4,3,1,2]
[1,1,1,0,0,0]=>[2,3,4,1]
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,1,2,3,4,7,5,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,1,2,3,6,4,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,1,2,3,6,4,8,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,2,3,8,7,4,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,1,2,3,6,7,4,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[4,1,2,8,3,7,5,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,1,2,5,3,4,8,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,1,2,6,3,4,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[7,1,2,6,3,4,8,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[8,1,2,5,3,7,4,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[6,1,2,5,3,7,8,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[4,1,2,8,6,3,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[8,1,2,5,7,3,4,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,1,2,8,6,7,3,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,8,2,4,7,5,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,8,2,6,4,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,8,2,7,4,5,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,8,7,4,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[8,1,4,2,3,7,5,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,1,4,2,3,7,8,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,5,2,3,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,1,5,2,3,4,8,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,1,7,2,3,4,5,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[8,1,5,2,3,7,4,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,1,8,2,3,7,4,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[8,1,4,2,7,3,5,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,4,2,6,8,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,1,4,2,8,7,3,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,4,8,2,7,5,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,8,5,2,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,7,5,2,4,8,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,7,6,2,4,8,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,5,2,7,8,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,1,4,5,2,3,8,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,1,4,6,2,3,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,1,4,8,2,3,5,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[7,1,4,6,2,3,8,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,1,6,5,2,3,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,1,8,5,2,3,4,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,1,4,5,2,8,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[8,1,4,5,2,7,3,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[8,1,4,6,2,7,3,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[8,1,6,5,2,7,3,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[6,1,4,5,2,7,8,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,4,8,7,2,5,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,4,7,6,2,8,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,8,5,6,2,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,8,7,6,2,4,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,7,5,6,2,8,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,1,4,5,6,2,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[8,1,7,5,6,2,3,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[7,1,4,5,6,2,8,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,4,5,8,7,2,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,4,8,6,7,2,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,8,1,3,4,7,5,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,8,1,3,6,4,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,7,1,3,6,4,8,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,3,8,7,4,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,8,1,3,6,7,4,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,7,5,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,8,1,5,3,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,7,1,5,3,4,8,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,8,1,6,3,4,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,7,1,6,3,4,8,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,6,1,5,3,8,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,8,1,5,3,7,4,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,8,1,6,3,7,4,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,8,7,3,5,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,1,7,6,3,8,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,8,1,5,6,3,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,8,1,5,7,3,4,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,7,1,5,6,3,8,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,8,7,3,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1,8,6,7,3,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,8,1,5,6,7,3,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[8,3,1,2,4,7,5,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,3,1,2,7,4,8,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[8,3,1,2,7,4,5,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,1,2,6,8,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[8,3,1,2,6,7,4,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,4,1,2,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,4,1,2,3,5,8,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,1,2,3,8,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,4,1,2,3,7,8,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,8,1,2,3,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,8,1,2,3,7,4,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,4,1,2,7,3,8,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,4,1,2,6,3,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,4,1,2,7,3,5,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[5,8,1,2,6,3,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[5,4,1,2,6,8,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,4,1,2,8,7,3,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,3,1,7,2,5,8,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,3,1,6,2,8,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,1,8,2,7,5,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,3,1,5,2,4,8,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,3,1,8,2,4,5,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,1,5,2,8,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8,3,1,6,2,7,4,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,4,1,5,2,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7,4,1,6,2,3,8,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,8,1,5,2,3,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8,7,1,5,2,3,4,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8,4,1,5,2,7,3,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,5,8,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,1,5,7,2,8,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,1,8,6,2,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,1,8,7,2,5,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,1,7,6,2,8,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,1,5,6,2,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8,4,1,5,7,2,3,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8,4,1,7,6,2,3,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,8,1,5,6,2,3,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7,4,1,5,6,2,8,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,3,1,5,8,7,2,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,3,1,8,6,7,2,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8,3,1,5,6,7,2,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8,4,1,5,6,7,2,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,8,1,4,7,5,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,8,1,6,4,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,3,8,1,7,4,5,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,8,1,6,7,4,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,7,4,1,3,5,8,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,8,4,1,3,7,5,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,8,5,1,3,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,7,5,1,3,4,8,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,8,1,3,4,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,8,7,1,3,4,5,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,6,5,1,3,8,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,8,5,1,3,7,4,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,6,8,1,3,7,4,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,5,4,1,8,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,5,4,1,7,3,8,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,8,4,1,6,3,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,8,5,1,6,3,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,7,8,1,6,3,4,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,1,6,8,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,1,8,7,3,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,8,4,1,6,7,3,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,8,5,1,6,7,3,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,3,4,1,2,5,8,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,3,4,1,2,8,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[8,3,4,1,2,7,5,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,3,8,1,2,4,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,3,7,1,2,4,5,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,5,1,2,8,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[6,3,5,1,2,7,8,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,5,4,1,2,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,5,4,1,2,3,8,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,8,4,1,2,3,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,4,1,2,3,5,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,1,2,3,8,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,5,4,1,2,8,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,8,4,1,2,7,3,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,5,4,1,2,7,8,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,3,4,1,8,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,3,4,1,7,2,8,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,3,4,1,6,2,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7,3,4,1,6,2,8,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8,3,5,1,7,2,4,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,5,4,1,6,2,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,1,7,2,3,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,5,4,1,6,2,8,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[5,3,4,1,6,8,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,3,4,1,8,7,2,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8,3,4,1,6,7,2,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8,3,5,1,6,7,2,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,5,4,1,6,7,2,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,8,5,1,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,7,5,1,4,8,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,8,6,1,4,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,7,8,1,4,5,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,8,5,1,7,4,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,8,6,1,7,4,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,8,4,5,1,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,4,5,1,3,8,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,7,4,6,1,3,8,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,7,8,5,1,3,4,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7,8,6,1,3,4,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,6,4,5,1,8,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,8,4,5,1,7,3,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,8,6,5,1,7,3,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,6,4,5,1,7,8,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,3,4,5,1,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,3,4,5,1,2,8,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,3,4,6,1,2,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,3,4,8,1,2,5,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7,3,4,6,1,2,8,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,3,6,5,1,2,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,8,6,1,2,4,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,6,5,1,2,8,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,6,4,5,1,2,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,8,4,5,1,2,3,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,6,4,5,1,2,8,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,4,5,1,8,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8,3,4,5,1,7,2,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8,3,4,6,1,7,2,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8,3,6,5,1,7,2,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,3,8,5,6,1,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,8,7,6,1,4,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,8,4,5,6,1,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,8,4,5,7,1,3,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,7,4,5,6,1,8,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8,3,4,5,7,1,2,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,3,4,7,6,1,2,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,7,4,5,6,1,2,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,8,5,6,7,1,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,1,2,3,4,5,8,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,1,2,3,4,7,5,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,1,2,3,4,8,5,6,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[8,1,2,3,4,7,5,9,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,1,2,3,4,9,8,5,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[9,1,2,3,4,7,8,5,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,9,6,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,1,2,3,9,4,8,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,1,2,3,7,4,8,9,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,1,2,3,6,4,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[8,1,2,3,6,4,5,9,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[9,1,2,3,7,4,5,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,1,2,3,9,4,5,6,7]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[8,1,2,3,7,4,5,9,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,1,2,3,6,4,9,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[9,1,2,3,6,4,8,5,7]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[9,1,2,3,7,4,8,5,6]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[7,1,2,3,6,4,8,9,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[5,1,2,3,6,9,4,7,8]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,1,2,3,6,8,4,9,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[5,1,2,3,9,7,4,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,1,2,3,9,8,4,6,7]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,1,2,3,8,7,4,9,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[9,1,2,3,6,7,4,5,8]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[9,1,2,3,6,8,4,5,7]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[9,1,2,3,8,7,4,5,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[8,1,2,3,6,7,4,9,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,9,4,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,1,2,3,6,9,8,4,7]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,1,2,3,9,7,8,4,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[9,1,2,3,6,7,8,4,5]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,9,3,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,7,3,5,9,6,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,9,3,5,8,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,7,3,5,8,9,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,6,3,9,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,8,5,9,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,9,3,7,5,6,8]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,9,3,8,5,6,7]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,8,3,7,5,9,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,6,3,7,9,5,8]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,6,3,9,8,5,7]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,9,3,7,8,5,6]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,6,3,7,8,9,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,1,2,5,3,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[8,1,2,5,3,4,6,9,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,1,2,5,3,4,9,6,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[9,1,2,5,3,4,8,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[7,1,2,5,3,4,8,9,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,1,2,6,3,4,5,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[8,1,2,6,3,4,5,9,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,1,2,9,3,4,5,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,2,8,3,4,5,6,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[7,1,2,8,3,4,5,9,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,1,2,6,3,4,9,5,8]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[9,1,2,6,3,4,8,5,7]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[7,1,2,9,3,4,8,5,6]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[7,1,2,6,3,4,8,9,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,2,5,3,9,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,1,2,5,3,8,4,9,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[9,1,2,5,3,7,4,6,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[9,1,2,5,3,8,4,6,7]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[8,1,2,5,3,7,4,9,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[9,1,2,6,3,7,4,5,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[9,1,2,6,3,8,4,5,7]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[8,1,2,9,3,7,4,5,6]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[8,1,2,6,3,7,4,9,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,1,2,5,3,7,9,4,8]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,1,2,5,3,9,8,4,7]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[9,1,2,5,3,7,8,4,6]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[9,1,2,6,3,7,8,4,5]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[6,1,2,5,3,7,8,9,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,8,3,6,9,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,7,3,9,6,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,9,3,8,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,7,3,8,9,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,2,9,6,3,5,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,1,2,8,6,3,5,9,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,9,7,3,5,6,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[4,1,2,8,9,3,5,6,7]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,1,2,8,7,3,5,9,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,6,3,9,5,8]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,9,6,3,8,5,7]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,9,7,3,8,5,6]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,6,3,8,9,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[9,1,2,5,6,3,4,7,8]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[8,1,2,5,6,3,4,9,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[9,1,2,5,7,3,4,6,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[8,1,2,5,9,3,4,6,7]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[8,1,2,5,7,3,4,9,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[9,1,2,7,6,3,4,5,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[8,1,2,9,6,3,4,5,7]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[8,1,2,9,7,3,4,5,6]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[8,1,2,7,6,3,4,9,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,1,2,5,6,3,9,4,8]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[9,1,2,5,6,3,8,4,7]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[9,1,2,5,7,3,8,4,6]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[9,1,2,7,6,3,8,4,5]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[7,1,2,5,6,3,8,9,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,5,6,9,3,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,5,6,8,3,9,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,9,7,3,6,8]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,9,8,3,6,7]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,5,8,7,3,9,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,9,6,7,3,5,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,2,9,6,8,3,5,7]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,2,9,8,7,3,5,6]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,2,8,6,7,3,9,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[9,1,2,5,6,7,3,4,8]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[9,1,2,5,6,8,3,4,7]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[9,1,2,5,8,7,3,4,6]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[9,1,2,8,6,7,3,4,5]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[8,1,2,5,6,7,3,9,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,5,6,9,8,3,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,5,9,7,8,3,6]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,1,2,9,6,7,8,3,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[9,1,2,5,6,7,8,3,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,7,2,4,5,9,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,9,2,4,5,8,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,7,2,4,5,8,9,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,9,5,7,8]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,6,2,4,8,5,9,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,9,2,4,7,5,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,9,2,4,8,5,6,7]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,8,2,4,7,5,9,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,6,2,4,7,9,5,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,6,2,4,9,8,5,7]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,9,2,4,7,8,5,6]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,6,2,4,7,8,9,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,9,4,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,5,2,8,4,6,9,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,9,4,8,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,7,4,8,9,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,9,2,6,4,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,8,2,6,4,5,9,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,9,2,7,4,5,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,8,2,9,4,5,6,7]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,8,2,7,4,5,9,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,7,2,6,4,9,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,9,2,6,4,8,5,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,9,2,7,4,8,5,6]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,7,2,6,4,8,9,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,9,4,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,6,8,4,9,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,9,7,4,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,9,8,4,6,7]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,8,7,4,9,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,9,2,6,7,4,5,8]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,9,2,6,8,4,5,7]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,9,2,8,7,4,5,6]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,8,2,6,7,4,9,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,2,6,7,9,4,8]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,6,9,8,4,7]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,9,7,8,4,6]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,9,2,6,7,8,4,5]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,6,7,8,9,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,1,4,2,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,1,4,2,3,5,6,9,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,1,4,2,3,5,9,6,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,1,4,2,3,5,8,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[7,1,4,2,3,5,8,9,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,1,4,2,3,9,5,7,8]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,1,4,2,3,8,5,9,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[9,1,4,2,3,7,5,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[9,1,4,2,3,8,5,6,7]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[8,1,4,2,3,7,5,9,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,1,4,2,3,7,9,5,8]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,1,4,2,3,9,8,5,7]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[9,1,4,2,3,7,8,5,6]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,1,4,2,3,7,8,9,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,1,5,2,3,4,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[8,1,5,2,3,4,6,9,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,1,5,2,3,4,9,6,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[9,1,5,2,3,4,8,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[7,1,5,2,3,4,8,9,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,9,2,3,4,5,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,1,8,2,3,4,5,9,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1,7,2,3,4,5,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,8,2,3,4,5,6,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,1,7,2,3,4,5,9,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,7,2,3,4,9,5,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,1,9,2,3,4,8,5,7]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,1,7,2,3,4,8,5,6]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,7,2,3,4,8,9,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,5,2,3,9,4,7,8]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,1,5,2,3,8,4,9,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[9,1,5,2,3,7,4,6,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[9,1,5,2,3,8,4,6,7]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[8,1,5,2,3,7,4,9,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1,9,2,3,7,4,5,8]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,1,9,2,3,8,4,5,7]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,1,8,2,3,7,4,5,6]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[6,1,8,2,3,7,4,9,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,1,5,2,3,7,9,4,8]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,1,5,2,3,9,8,4,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[9,1,5,2,3,7,8,4,6]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[6,1,9,2,3,7,8,4,5]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[6,1,5,2,3,7,8,9,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,4,2,9,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,4,2,8,3,6,9,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,1,4,2,7,3,9,6,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,1,4,2,9,3,8,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,1,4,2,7,3,8,9,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[9,1,4,2,6,3,5,7,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,1,4,2,6,3,5,9,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[9,1,4,2,7,3,5,6,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,1,4,2,9,3,5,6,7]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[8,1,4,2,7,3,5,9,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1,4,2,6,3,9,5,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[9,1,4,2,6,3,8,5,7]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[9,1,4,2,7,3,8,5,6]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7,1,4,2,6,3,8,9,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[9,1,5,2,6,3,4,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[8,1,5,2,6,3,4,9,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[9,1,5,2,7,3,4,6,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8,1,5,2,9,3,4,6,7]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[8,1,5,2,7,3,4,9,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1,9,2,6,3,4,5,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[9,1,8,2,6,3,4,5,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9,1,8,2,7,3,4,5,6]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,8,2,6,3,4,9,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1,5,2,6,3,9,4,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[9,1,5,2,6,3,8,4,7]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[9,1,5,2,7,3,8,4,6]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7,1,9,2,6,3,8,4,5]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7,1,5,2,6,3,8,9,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,4,2,6,9,3,7,8]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,1,4,2,6,8,3,9,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,4,2,9,7,3,6,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,1,4,2,9,8,3,6,7]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,1,4,2,8,7,3,9,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[9,1,4,2,6,7,3,5,8]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[9,1,4,2,6,8,3,5,7]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9,1,4,2,8,7,3,5,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[8,1,4,2,6,7,3,9,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[9,1,5,2,6,7,3,4,8]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[9,1,5,2,6,8,3,4,7]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,1,5,2,8,7,3,4,6]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[8,1,9,2,6,7,3,4,5]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[8,1,5,2,6,7,3,9,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,4,2,6,7,9,3,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,4,2,6,9,8,3,7]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,4,2,9,7,8,3,6]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[9,1,4,2,6,7,8,3,5]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[9,1,5,2,6,7,8,3,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,4,2,6,7,8,9,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,8,2,5,6,9,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,9,6,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,9,2,5,8,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,7,2,5,8,9,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,6,2,9,5,7,8]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,6,2,8,5,9,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,9,2,7,5,6,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,9,2,8,5,6,7]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,8,2,7,5,9,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,7,9,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,6,2,9,8,5,7]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,9,2,7,8,5,6]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,6,2,7,8,9,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,9,5,2,4,6,7,8]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,8,5,2,4,6,9,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,7,5,2,4,9,6,8]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,9,5,2,4,8,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,7,5,2,4,8,9,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,9,6,2,4,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,8,6,2,4,5,9,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,7,9,2,4,5,6,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,9,8,2,4,5,6,7]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,7,8,2,4,5,9,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,7,6,2,4,9,5,8]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,9,6,2,4,8,5,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,7,9,2,4,8,5,6]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,7,6,2,4,8,9,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,5,2,9,4,7,8]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,6,5,2,8,4,9,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,9,5,2,7,4,6,8]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,9,5,2,8,4,6,7]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,8,5,2,7,4,9,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,9,6,2,7,4,5,8]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,9,6,2,8,4,5,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,8,9,2,7,4,5,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,8,6,2,7,4,9,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,5,2,7,9,4,8]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,5,2,9,8,4,7]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,9,5,2,7,8,4,6]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,9,6,2,7,8,4,5]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,6,5,2,7,8,9,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,1,4,5,2,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[8,1,4,5,2,3,6,9,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,1,4,5,2,3,9,6,8]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[9,1,4,5,2,3,8,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,1,4,5,2,3,8,9,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[9,1,4,6,2,3,5,7,8]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[8,1,4,6,2,3,5,9,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1,4,9,2,3,5,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,1,4,8,2,3,5,6,7]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7,1,4,8,2,3,5,9,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1,4,6,2,3,9,5,8]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[9,1,4,6,2,3,8,5,7]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7,1,4,9,2,3,8,5,6]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7,1,4,6,2,3,8,9,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,1,6,5,2,3,4,7,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[8,1,6,5,2,3,4,9,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1,9,5,2,3,4,6,8]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,1,8,5,2,3,4,6,7]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[7,1,8,5,2,3,4,9,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1,9,6,2,3,4,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,1,8,6,2,3,4,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,9,2,3,4,5,6]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,1,8,6,2,3,4,9,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1,6,5,2,3,9,4,8]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[9,1,6,5,2,3,8,4,7]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,1,9,5,2,3,8,4,6]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,1,9,6,2,3,8,4,5]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,1,6,5,2,3,8,9,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,4,5,2,9,3,7,8]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,1,4,5,2,8,3,9,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[9,1,4,5,2,7,3,6,8]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[9,1,4,5,2,8,3,6,7]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[8,1,4,5,2,7,3,9,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[9,1,4,6,2,7,3,5,8]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[9,1,4,6,2,8,3,5,7]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[8,1,4,9,2,7,3,5,6]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[8,1,4,6,2,7,3,9,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,1,6,5,2,7,3,4,8]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[9,1,6,5,2,8,3,4,7]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[8,1,9,5,2,7,3,4,6]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[8,1,9,6,2,7,3,4,5]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[8,1,6,5,2,7,3,9,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,4,5,2,7,9,3,8]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,1,4,5,2,9,8,3,7]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[9,1,4,5,2,7,8,3,6]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[9,1,4,6,2,7,8,3,5]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[9,1,6,5,2,7,8,3,4]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,1,4,5,2,7,8,9,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,4,5,9,2,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,4,5,8,2,6,9,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,4,5,7,2,9,6,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,4,5,9,2,8,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,1,4,5,7,2,8,9,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,4,9,6,2,5,7,8]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,4,8,6,2,5,9,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,4,9,7,2,5,6,8]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,1,4,8,9,2,5,6,7]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,1,4,8,7,2,5,9,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,4,7,6,2,9,5,8]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,1,4,9,6,2,8,5,7]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,4,9,7,2,8,5,6]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,4,7,6,2,8,9,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,9,5,6,2,4,7,8]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,8,5,6,2,4,9,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,9,5,7,2,4,6,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,1,8,5,9,2,4,6,7]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,1,8,5,7,2,4,9,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,9,7,6,2,4,5,8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,8,9,6,2,4,5,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,7,2,4,5,6]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,8,7,6,2,4,9,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,7,5,6,2,9,4,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,9,5,6,2,8,4,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,1,9,5,7,2,8,4,6]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,9,7,6,2,8,4,5]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,7,5,6,2,8,9,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[9,1,4,5,6,2,3,7,8]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[8,1,4,5,6,2,3,9,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,1,4,5,7,2,3,6,8]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[8,1,4,5,9,2,3,6,7]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[8,1,4,5,7,2,3,9,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,1,4,7,6,2,3,5,8]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8,1,4,9,6,2,3,5,7]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8,1,4,9,7,2,3,5,6]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[8,1,4,7,6,2,3,9,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[9,1,7,5,6,2,3,4,8]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8,1,9,5,6,2,3,4,7]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[8,1,9,5,7,2,3,4,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8,1,9,7,6,2,3,4,5]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[8,1,7,5,6,2,3,9,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1,4,5,6,2,9,3,8]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[9,1,4,5,6,2,8,3,7]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[9,1,4,5,7,2,8,3,6]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[9,1,4,7,6,2,8,3,5]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[9,1,7,5,6,2,8,3,4]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,1,4,5,6,2,8,9,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,4,5,9,7,2,6,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,1,4,5,9,8,2,6,7]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,4,5,8,7,2,9,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,4,9,6,7,2,5,8]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,4,9,6,8,2,5,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,1,4,9,8,7,2,5,6]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,4,8,6,7,2,9,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,9,5,6,7,2,4,8]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,9,5,6,8,2,4,7]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,9,5,8,7,2,4,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,9,8,6,7,2,4,5]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,8,5,6,7,2,9,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,1,4,5,6,7,2,3,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[9,1,4,5,6,8,2,3,7]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[9,1,4,5,8,7,2,3,6]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[9,1,4,8,6,7,2,3,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[9,1,8,5,6,7,2,3,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,1,4,5,6,7,2,9,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,4,5,6,9,8,2,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,4,5,9,7,8,2,6]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,4,9,6,7,8,2,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,9,5,6,7,8,2,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,9,1,3,4,5,8,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,4,8,5,9,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,9,1,3,4,7,5,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,9,1,3,4,8,5,6,7]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,8,1,3,4,7,5,9,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,6,1,3,4,7,9,5,8]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,6,1,3,4,9,8,5,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,9,1,3,4,7,8,5,6]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,6,1,3,4,7,8,9,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,5,1,3,9,4,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,9,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,9,6,8]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,3,9,4,8,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,1,3,7,4,8,9,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,9,1,3,6,4,5,7,8]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,8,1,3,6,4,5,9,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,9,1,3,7,4,5,6,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,8,1,3,9,4,5,6,7]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,8,1,3,7,4,5,9,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,7,1,3,6,4,9,5,8]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,9,1,3,6,4,8,5,7]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,9,1,3,7,4,8,5,6]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,7,1,3,6,4,8,9,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,9,4,7,8]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,9,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,5,1,3,9,7,4,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,3,9,8,4,6,7]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,1,3,8,7,4,9,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,9,1,3,6,7,4,5,8]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,9,1,3,6,8,4,5,7]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,9,1,3,8,7,4,5,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,8,1,3,6,7,4,9,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,6,7,9,4,8]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,9,8,4,7]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,1,3,9,7,8,4,6]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,9,1,3,6,7,8,4,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,9,3,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,8,3,5,6,9,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,7,3,5,9,6,8]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,9,3,5,8,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,7,3,5,8,9,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,6,3,9,5,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,9,3,7,5,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,9,3,8,5,6,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,8,3,7,5,9,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,6,3,7,9,5,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,3,9,8,5,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,9,3,7,8,5,6]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,6,3,7,8,9,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,9,1,5,3,4,6,7,8]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,8,1,5,3,4,6,9,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,7,1,5,3,4,9,6,8]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,9,1,5,3,4,8,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,7,1,5,3,4,8,9,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,9,1,6,3,4,5,7,8]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,8,1,6,3,4,5,9,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,7,1,9,3,4,5,6,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,1,8,3,4,5,6,7]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,7,1,8,3,4,5,9,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,7,1,6,3,4,9,5,8]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,9,1,6,3,4,8,5,7]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,7,1,9,3,4,8,5,6]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,7,1,6,3,4,8,9,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,6,1,5,3,9,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,6,1,5,3,8,4,9,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,9,1,5,3,7,4,6,8]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,9,1,5,3,8,4,6,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,8,1,5,3,7,4,9,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,9,1,6,3,7,4,5,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,9,1,6,3,8,4,5,7]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,8,1,9,3,7,4,5,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,8,1,6,3,7,4,9,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,6,1,5,3,7,9,4,8]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,6,1,5,3,9,8,4,7]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,9,1,5,3,7,8,4,6]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,9,1,6,3,7,8,4,5]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,5,3,7,8,9,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,5,8,3,6,9,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,5,7,3,9,6,8]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,5,9,3,8,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,5,7,3,8,9,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,9,6,3,5,7,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,8,6,3,5,9,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,9,7,3,5,6,8]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,8,9,3,5,6,7]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,8,7,3,5,9,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,7,6,3,9,5,8]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,9,6,3,8,5,7]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,9,7,3,8,5,6]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,6,3,8,9,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,9,1,5,6,3,4,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,8,1,5,6,3,4,9,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,9,1,5,7,3,4,6,8]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,8,1,5,9,3,4,6,7]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,8,1,5,7,3,4,9,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,9,1,7,6,3,4,5,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,8,1,9,6,3,4,5,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,7,3,4,5,6]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,8,1,7,6,3,4,9,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,7,1,5,6,3,9,4,8]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,9,1,5,6,3,8,4,7]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,9,1,5,7,3,8,4,6]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,9,1,7,6,3,8,4,5]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,1,5,6,3,8,9,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,5,6,9,3,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,5,6,8,3,9,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,5,9,7,3,6,8]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,9,8,3,6,7]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,1,5,8,7,3,9,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,9,6,7,3,5,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,9,6,8,3,5,7]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,9,8,7,3,5,6]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,1,8,6,7,3,9,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,9,1,5,6,7,3,4,8]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,9,1,5,6,8,3,4,7]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,9,1,5,8,7,3,4,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,9,1,8,6,7,3,4,5]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,8,1,5,6,7,3,9,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,9,8,3,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,5,9,7,8,3,6]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,9,6,7,8,3,5]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,1,5,6,7,8,3,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,3,1,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,3,1,2,4,5,6,9,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,3,1,2,4,5,9,6,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[9,3,1,2,4,5,8,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[7,3,1,2,4,5,8,9,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,3,1,2,4,9,5,7,8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,3,1,2,4,8,5,9,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[9,3,1,2,4,7,5,6,8]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[9,3,1,2,4,8,5,6,7]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[8,3,1,2,4,7,5,9,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,1,2,4,7,9,5,8]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,3,1,2,4,9,8,5,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[9,3,1,2,4,7,8,5,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[6,3,1,2,4,7,8,9,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[5,3,1,2,9,4,6,7,8]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,3,1,2,8,4,6,9,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,9,6,8]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,3,1,2,9,4,8,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,7,4,8,9,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[9,3,1,2,6,4,5,7,8]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[8,3,1,2,6,4,5,9,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[9,3,1,2,7,4,5,6,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[8,3,1,2,9,4,5,6,7]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[8,3,1,2,7,4,5,9,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,3,1,2,6,4,9,5,8]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[9,3,1,2,6,4,8,5,7]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,3,1,2,7,4,8,5,6]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[7,3,1,2,6,4,8,9,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[5,3,1,2,6,9,4,7,8]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,3,1,2,6,8,4,9,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,9,7,4,6,8]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,3,1,2,9,8,4,6,7]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,3,1,2,8,7,4,9,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[9,3,1,2,6,7,4,5,8]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[9,3,1,2,6,8,4,5,7]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[9,3,1,2,8,7,4,5,6]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[8,3,1,2,6,7,4,9,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,3,1,2,6,7,9,4,8]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,3,1,2,6,9,8,4,7]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,1,2,9,7,8,4,6]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[9,3,1,2,6,7,8,4,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,4,1,2,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,4,1,2,3,5,6,9,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,4,1,2,3,5,9,6,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,4,1,2,3,5,8,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[7,4,1,2,3,5,8,9,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,4,1,2,3,9,5,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,4,1,2,3,8,5,9,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[9,4,1,2,3,7,5,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[9,4,1,2,3,8,5,6,7]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[8,4,1,2,3,7,5,9,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,4,1,2,3,7,9,5,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,1,2,3,9,8,5,7]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[9,4,1,2,3,7,8,5,6]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,4,1,2,3,7,8,9,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,9,1,2,3,4,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,8,1,2,3,4,6,9,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,7,1,2,3,4,9,6,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,9,1,2,3,4,8,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,7,1,2,3,4,8,9,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,6,1,2,3,4,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,6,1,2,3,4,5,9,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,9,1,2,3,4,5,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,7,1,2,3,4,5,9,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,6,1,2,3,4,9,5,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9,6,1,2,3,4,8,5,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,7,1,2,3,4,8,5,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,6,1,2,3,4,8,9,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,6,1,2,3,9,4,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,9,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[5,9,1,2,3,7,4,6,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,9,1,2,3,8,4,6,7]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,8,1,2,3,7,4,9,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[9,6,1,2,3,7,4,5,8]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[9,6,1,2,3,8,4,5,7]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,1,2,3,7,4,5,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8,6,1,2,3,7,4,9,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,9,4,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,6,1,2,3,9,8,4,7]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,9,1,2,3,7,8,4,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[9,6,1,2,3,7,8,4,5]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,1,2,9,3,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,4,1,2,8,3,6,9,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,4,1,2,7,3,9,6,8]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,1,2,9,3,8,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,4,1,2,7,3,8,9,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[9,4,1,2,6,3,5,7,8]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,4,1,2,6,3,5,9,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[9,4,1,2,7,3,5,6,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,4,1,2,9,3,5,6,7]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[8,4,1,2,7,3,5,9,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,1,2,6,3,9,5,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[9,4,1,2,6,3,8,5,7]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[9,4,1,2,7,3,8,5,6]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7,4,1,2,6,3,8,9,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,9,1,2,6,3,4,7,8]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,8,1,2,6,3,4,9,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[5,9,1,2,7,3,4,6,8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,8,1,2,9,3,4,6,7]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,8,1,2,7,3,4,9,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[9,7,1,2,6,3,4,5,8]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[9,8,1,2,6,3,4,5,7]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9,8,1,2,7,3,4,5,6]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[8,7,1,2,6,3,4,9,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[5,7,1,2,6,3,9,4,8]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,9,1,2,6,3,8,4,7]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,9,1,2,7,3,8,4,6]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[9,7,1,2,6,3,8,4,5]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[5,7,1,2,6,3,8,9,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,4,1,2,6,9,3,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,4,1,2,6,8,3,9,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[5,4,1,2,9,7,3,6,8]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,9,8,3,6,7]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,4,1,2,8,7,3,9,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[9,4,1,2,6,7,3,5,8]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[9,4,1,2,6,8,3,5,7]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9,4,1,2,8,7,3,5,6]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[8,4,1,2,6,7,3,9,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[5,9,1,2,6,7,3,4,8]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,9,1,2,6,8,3,4,7]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,9,1,2,8,7,3,4,6]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,2,6,7,3,4,5]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[5,8,1,2,6,7,3,9,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,1,2,6,7,9,3,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,1,2,6,9,8,3,7]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,1,2,9,7,8,3,6]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[9,4,1,2,6,7,8,3,5]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,9,1,2,6,7,8,3,4]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,1,9,2,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,1,8,2,5,6,9,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,1,7,2,5,9,6,8]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,1,9,2,5,8,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,1,7,2,5,8,9,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,1,6,2,9,5,7,8]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,1,6,2,8,5,9,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1,9,2,7,5,6,8]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,1,9,2,8,5,6,7]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,1,8,2,7,5,9,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1,6,2,7,9,5,8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1,6,2,9,8,5,7]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1,9,2,7,8,5,6]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,1,6,2,7,8,9,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[9,3,1,5,2,4,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[8,3,1,5,2,4,6,9,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,3,1,5,2,4,9,6,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[9,3,1,5,2,4,8,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[7,3,1,5,2,4,8,9,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[9,3,1,6,2,4,5,7,8]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[8,3,1,6,2,4,5,9,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,3,1,9,2,4,5,6,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,1,8,2,4,5,6,7]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[7,3,1,8,2,4,5,9,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,3,1,6,2,4,9,5,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[9,3,1,6,2,4,8,5,7]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[7,3,1,9,2,4,8,5,6]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[7,3,1,6,2,4,8,9,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,3,1,5,2,9,4,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,3,1,5,2,8,4,9,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,3,1,5,2,7,4,6,8]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[9,3,1,5,2,8,4,6,7]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,3,1,5,2,7,4,9,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[9,3,1,6,2,7,4,5,8]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[9,3,1,6,2,8,4,5,7]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[8,3,1,9,2,7,4,5,6]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[8,3,1,6,2,7,4,9,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,3,1,5,2,7,9,4,8]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,1,5,2,9,8,4,7]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[9,3,1,5,2,7,8,4,6]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[9,3,1,6,2,7,8,4,5]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[6,3,1,5,2,7,8,9,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,4,1,5,2,3,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[8,4,1,5,2,3,6,9,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,4,1,5,2,3,9,6,8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[9,4,1,5,2,3,8,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,4,1,5,2,3,8,9,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[9,4,1,6,2,3,5,7,8]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[8,4,1,6,2,3,5,9,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,4,1,9,2,3,5,6,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,4,1,8,2,3,5,6,7]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7,4,1,8,2,3,5,9,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,1,6,2,3,9,5,8]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[9,4,1,6,2,3,8,5,7]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7,4,1,9,2,3,8,5,6]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7,4,1,6,2,3,8,9,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,1,5,2,3,4,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,8,1,5,2,3,4,9,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[9,7,1,5,2,3,4,6,8]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,1,5,2,3,4,6,7]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[8,7,1,5,2,3,4,9,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,7,1,6,2,3,4,5,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,8,1,6,2,3,4,5,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,9,2,3,4,5,6]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8,7,1,6,2,3,4,9,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,7,1,5,2,3,9,4,8]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,9,1,5,2,3,8,4,7]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[9,7,1,5,2,3,8,4,6]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[9,7,1,6,2,3,8,4,5]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,1,5,2,3,8,9,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,4,1,5,2,9,3,7,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,4,1,5,2,8,3,9,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[9,4,1,5,2,7,3,6,8]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[9,4,1,5,2,8,3,6,7]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[8,4,1,5,2,7,3,9,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[9,4,1,6,2,7,3,5,8]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[9,4,1,6,2,8,3,5,7]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[8,4,1,9,2,7,3,5,6]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[8,4,1,6,2,7,3,9,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,9,1,5,2,7,3,4,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,9,1,5,2,8,3,4,7]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[9,8,1,5,2,7,3,4,6]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[9,8,1,6,2,7,3,4,5]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,8,1,5,2,7,3,9,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,4,1,5,2,7,9,3,8]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,4,1,5,2,9,8,3,7]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[9,4,1,5,2,7,8,3,6]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[9,4,1,6,2,7,8,3,5]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[6,9,1,5,2,7,8,3,4]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,4,1,5,2,7,8,9,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,1,5,9,2,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,1,5,8,2,6,9,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,1,5,7,2,9,6,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,1,5,9,2,8,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,1,5,7,2,8,9,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,1,9,6,2,5,7,8]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,1,8,6,2,5,9,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,1,9,7,2,5,6,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,1,8,9,2,5,6,7]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,1,8,7,2,5,9,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,1,7,6,2,9,5,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,1,9,6,2,8,5,7]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,1,9,7,2,8,5,6]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,1,7,6,2,8,9,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[9,3,1,5,6,2,4,7,8]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[8,3,1,5,6,2,4,9,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[9,3,1,5,7,2,4,6,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[8,3,1,5,9,2,4,6,7]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[8,3,1,5,7,2,4,9,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[9,3,1,7,6,2,4,5,8]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[8,3,1,9,6,2,4,5,7]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[8,3,1,9,7,2,4,5,6]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[8,3,1,7,6,2,4,9,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,1,5,6,2,9,4,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[9,3,1,5,6,2,8,4,7]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[9,3,1,5,7,2,8,4,6]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[9,3,1,7,6,2,8,4,5]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,1,5,6,2,8,9,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[9,4,1,5,6,2,3,7,8]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[8,4,1,5,6,2,3,9,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,4,1,5,7,2,3,6,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[8,4,1,5,9,2,3,6,7]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[8,4,1,5,7,2,3,9,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,4,1,7,6,2,3,5,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8,4,1,9,6,2,3,5,7]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8,4,1,9,7,2,3,5,6]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[8,4,1,7,6,2,3,9,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,9,1,5,6,2,3,4,8]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,1,5,6,2,3,4,7]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[9,8,1,5,7,2,3,4,6]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[9,8,1,7,6,2,3,4,5]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,1,5,6,2,3,9,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,4,1,5,6,2,9,3,8]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[9,4,1,5,6,2,8,3,7]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[9,4,1,5,7,2,8,3,6]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[9,4,1,7,6,2,8,3,5]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,1,5,6,2,8,3,4]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,4,1,5,6,2,8,9,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,3,1,5,6,9,2,7,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,3,1,5,6,8,2,9,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,3,1,5,9,7,2,6,8]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,3,1,5,9,8,2,6,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,3,1,5,8,7,2,9,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,3,1,9,6,7,2,5,8]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[4,3,1,9,6,8,2,5,7]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3,1,9,8,7,2,5,6]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,3,1,8,6,7,2,9,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[9,3,1,5,6,7,2,4,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[9,3,1,5,6,8,2,4,7]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[9,3,1,5,8,7,2,4,6]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[9,3,1,8,6,7,2,4,5]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,1,5,6,7,2,9,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,4,1,5,6,7,2,3,8]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[9,4,1,5,6,8,2,3,7]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[9,4,1,5,8,7,2,3,6]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[9,4,1,8,6,7,2,3,5]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,1,5,6,7,2,3,4]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,4,1,5,6,7,2,9,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,9,2,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1,5,6,9,8,2,7]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1,5,9,7,8,2,6]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1,9,6,7,8,2,5]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,1,5,6,7,8,2,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,4,1,5,6,7,8,2,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,7,1,4,5,9,6,8]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,9,1,4,5,8,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,7,1,4,5,8,9,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,6,1,4,9,5,7,8]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,6,1,4,8,5,9,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,9,1,4,7,5,6,8]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,9,1,4,8,5,6,7]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,8,1,4,7,5,9,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,6,1,4,7,9,5,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,6,1,4,9,8,5,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,9,1,4,7,8,5,6]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,6,1,4,7,8,9,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,9,4,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,5,1,8,4,6,9,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,9,6,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,9,4,8,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,5,1,7,4,8,9,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,9,1,6,4,5,7,8]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,8,1,6,4,5,9,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,9,1,7,4,5,6,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,8,1,9,4,5,6,7]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,8,1,7,4,5,9,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,7,1,6,4,9,5,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,9,1,6,4,8,5,7]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,9,1,7,4,8,5,6]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,7,1,6,4,8,9,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,6,9,4,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,8,4,9,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,9,7,4,6,8]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,9,8,4,6,7]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,8,7,4,9,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,9,1,6,7,4,5,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,9,1,6,8,4,5,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,9,1,8,7,4,5,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,8,1,6,7,4,9,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,5,1,6,9,8,4,7]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,9,7,8,4,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,9,1,6,7,8,4,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,9,4,1,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,8,4,1,3,5,6,9,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,7,4,1,3,5,9,6,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,9,4,1,3,5,8,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,7,4,1,3,5,8,9,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,6,4,1,3,9,5,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,4,1,3,8,5,9,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,9,4,1,3,7,5,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,9,4,1,3,8,5,6,7]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,8,4,1,3,7,5,9,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,6,4,1,3,7,9,5,8]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,6,4,1,3,9,8,5,7]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,9,4,1,3,7,8,5,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,6,4,1,3,7,8,9,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,9,5,1,3,4,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,8,5,1,3,4,6,9,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,7,5,1,3,4,9,6,8]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,9,5,1,3,4,8,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,7,5,1,3,4,8,9,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,6,9,1,3,4,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,6,8,1,3,4,5,9,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,9,7,1,3,4,5,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,8,1,3,4,5,6,7]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,8,7,1,3,4,5,9,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,6,7,1,3,4,9,5,8]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,6,9,1,3,4,8,5,7]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,9,7,1,3,4,8,5,6]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,6,7,1,3,4,8,9,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,6,5,1,3,9,4,7,8]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,6,5,1,3,8,4,9,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,9,5,1,3,7,4,6,8]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,9,5,1,3,8,4,6,7]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,8,5,1,3,7,4,9,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,6,9,1,3,7,4,5,8]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,6,9,1,3,8,4,5,7]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,9,8,1,3,7,4,5,6]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,8,1,3,7,4,9,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,6,5,1,3,7,9,4,8]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,6,5,1,3,9,8,4,7]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,9,5,1,3,7,8,4,6]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,9,1,3,7,8,4,5]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,1,3,7,8,9,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,5,4,1,9,3,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,4,1,8,3,6,9,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,5,4,1,7,3,9,6,8]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,4,1,9,3,8,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,5,4,1,7,3,8,9,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,9,4,1,6,3,5,7,8]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,8,4,1,6,3,5,9,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,9,4,1,7,3,5,6,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,8,4,1,9,3,5,6,7]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,8,4,1,7,3,5,9,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,7,4,1,6,3,9,5,8]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,9,4,1,6,3,8,5,7]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,9,4,1,7,3,8,5,6]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,7,4,1,6,3,8,9,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,9,5,1,6,3,4,7,8]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,8,5,1,6,3,4,9,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,9,5,1,7,3,4,6,8]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,8,5,1,9,3,4,6,7]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,8,5,1,7,3,4,9,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,7,9,1,6,3,4,5,8]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,9,8,1,6,3,4,5,7]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,9,8,1,7,3,4,5,6]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,8,1,6,3,4,9,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,7,5,1,6,3,9,4,8]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,9,5,1,6,3,8,4,7]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,9,5,1,7,3,8,4,6]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,9,1,6,3,8,4,5]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,5,1,6,3,8,9,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,1,6,9,3,7,8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,1,6,8,3,9,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,1,9,7,3,6,8]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,1,9,8,3,6,7]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,1,8,7,3,9,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,9,4,1,6,7,3,5,8]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,9,4,1,6,8,3,5,7]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,9,4,1,8,7,3,5,6]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,8,4,1,6,7,3,9,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,9,5,1,6,7,3,4,8]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,9,5,1,6,8,3,4,7]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,9,5,1,8,7,3,4,6]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,8,9,1,6,7,3,4,5]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,8,5,1,6,7,3,9,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,4,1,6,7,9,3,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,4,1,6,9,8,3,7]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,4,1,9,7,8,3,6]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,9,4,1,6,7,8,3,5]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,9,5,1,6,7,8,3,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,4,1,6,7,8,9,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,3,4,1,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[8,3,4,1,2,5,6,9,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,3,4,1,2,5,9,6,8]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[9,3,4,1,2,5,8,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[7,3,4,1,2,5,8,9,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,3,4,1,2,9,5,7,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,3,4,1,2,8,5,9,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[9,3,4,1,2,7,5,6,8]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[9,3,4,1,2,8,5,6,7]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[8,3,4,1,2,7,5,9,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,1,2,7,9,5,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,3,4,1,2,9,8,5,7]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[9,3,4,1,2,7,8,5,6]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[6,3,4,1,2,7,8,9,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[9,3,5,1,2,4,6,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[8,3,5,1,2,4,6,9,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,3,5,1,2,4,9,6,8]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[9,3,5,1,2,4,8,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[7,3,5,1,2,4,8,9,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,3,9,1,2,4,5,7,8]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,3,8,1,2,4,5,9,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,3,7,1,2,4,5,6,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,3,8,1,2,4,5,6,7]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[8,3,7,1,2,4,5,9,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,7,1,2,4,9,5,8]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,3,9,1,2,4,8,5,7]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[9,3,7,1,2,4,8,5,6]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[6,3,7,1,2,4,8,9,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,3,5,1,2,9,4,7,8]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,3,5,1,2,8,4,9,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,3,5,1,2,7,4,6,8]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[9,3,5,1,2,8,4,6,7]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,3,5,1,2,7,4,9,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,9,1,2,7,4,5,8]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,3,9,1,2,8,4,5,7]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[9,3,8,1,2,7,4,5,6]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[6,3,8,1,2,7,4,9,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,3,5,1,2,7,9,4,8]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,5,1,2,9,8,4,7]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[9,3,5,1,2,7,8,4,6]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[6,3,9,1,2,7,8,4,5]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[6,3,5,1,2,7,8,9,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,5,4,1,2,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[8,5,4,1,2,3,6,9,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,4,1,2,3,9,6,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[9,5,4,1,2,3,8,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[7,5,4,1,2,3,8,9,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,9,4,1,2,3,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,8,4,1,2,3,5,9,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[9,7,4,1,2,3,5,6,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,4,1,2,3,5,6,7]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[8,7,4,1,2,3,5,9,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,7,4,1,2,3,9,5,8]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,9,4,1,2,3,8,5,7]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[9,7,4,1,2,3,8,5,6]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[6,7,4,1,2,3,8,9,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,9,5,1,2,3,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,8,5,1,2,3,4,9,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[9,7,5,1,2,3,4,6,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,5,1,2,3,4,6,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8,7,5,1,2,3,4,9,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,7,9,1,2,3,4,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,9,8,1,2,3,4,5,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,7,8,1,2,3,4,5,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,9,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,7,5,1,2,3,9,4,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,9,5,1,2,3,8,4,7]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[9,7,5,1,2,3,8,4,6]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,7,9,1,2,3,8,4,5]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,7,5,1,2,3,8,9,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,4,1,2,9,3,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,5,4,1,2,8,3,9,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[9,5,4,1,2,7,3,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[9,5,4,1,2,8,3,6,7]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[8,5,4,1,2,7,3,9,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,9,4,1,2,7,3,5,8]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,9,4,1,2,8,3,5,7]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[9,8,4,1,2,7,3,5,6]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[6,8,4,1,2,7,3,9,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,9,5,1,2,7,3,4,8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,9,5,1,2,8,3,4,7]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[9,8,5,1,2,7,3,4,6]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[6,8,9,1,2,7,3,4,5]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,8,5,1,2,7,3,9,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,5,4,1,2,7,9,3,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,5,4,1,2,9,8,3,7]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[9,5,4,1,2,7,8,3,6]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[6,9,4,1,2,7,8,3,5]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[6,9,5,1,2,7,8,3,4]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,1,2,7,8,9,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,3,4,1,9,2,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,3,4,1,8,2,6,9,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,3,4,1,7,2,9,6,8]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3,4,1,9,2,8,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3,4,1,7,2,8,9,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[9,3,4,1,6,2,5,7,8]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[8,3,4,1,6,2,5,9,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[9,3,4,1,7,2,5,6,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8,3,4,1,9,2,5,6,7]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[8,3,4,1,7,2,5,9,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,3,4,1,6,2,9,5,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[9,3,4,1,6,2,8,5,7]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[9,3,4,1,7,2,8,5,6]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[7,3,4,1,6,2,8,9,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[9,3,5,1,6,2,4,7,8]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[8,3,5,1,6,2,4,9,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[9,3,5,1,7,2,4,6,8]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[8,3,5,1,9,2,4,6,7]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[8,3,5,1,7,2,4,9,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,3,9,1,6,2,4,5,8]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[9,3,8,1,6,2,4,5,7]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[9,3,8,1,7,2,4,5,6]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,8,1,6,2,4,9,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,5,1,6,2,9,4,8]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[9,3,5,1,6,2,8,4,7]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[9,3,5,1,7,2,8,4,6]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,9,1,6,2,8,4,5]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,5,1,6,2,8,9,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[9,5,4,1,6,2,3,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[8,5,4,1,6,2,3,9,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,5,4,1,7,2,3,6,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[8,5,4,1,9,2,3,6,7]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[8,5,4,1,7,2,3,9,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,9,4,1,6,2,3,5,8]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[9,8,4,1,6,2,3,5,7]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[9,8,4,1,7,2,3,5,6]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,4,1,6,2,3,9,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,9,5,1,6,2,3,4,8]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,5,1,6,2,3,4,7]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[9,8,5,1,7,2,3,4,6]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,1,6,2,3,4,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,5,1,6,2,3,9,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,5,4,1,6,2,9,3,8]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[9,5,4,1,6,2,8,3,7]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[9,5,4,1,7,2,8,3,6]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,9,4,1,6,2,8,3,5]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,5,1,6,2,8,3,4]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,5,4,1,6,2,8,9,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,3,4,1,6,9,2,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,3,4,1,6,8,2,9,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,3,4,1,9,7,2,6,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,3,4,1,9,8,2,6,7]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,3,4,1,8,7,2,9,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[9,3,4,1,6,7,2,5,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[9,3,4,1,6,8,2,5,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[9,3,4,1,8,7,2,5,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,1,6,7,2,9,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[9,3,5,1,6,7,2,4,8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[9,3,5,1,6,8,2,4,7]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[9,3,5,1,8,7,2,4,6]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,1,6,7,2,4,5]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,5,1,6,7,2,9,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,5,4,1,6,7,2,3,8]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[9,5,4,1,6,8,2,3,7]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[9,5,4,1,8,7,2,3,6]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,1,6,7,2,3,5]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,5,1,6,7,2,3,4]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8,5,4,1,6,7,2,9,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[5,3,4,1,6,7,9,2,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[5,3,4,1,6,9,8,2,7]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,3,4,1,9,7,8,2,6]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,1,6,7,8,2,5]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,5,1,6,7,8,2,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[9,5,4,1,6,7,8,2,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,8,1,5,6,9,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,7,1,5,9,6,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,9,1,5,8,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,7,1,5,8,9,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,6,1,9,5,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,6,1,8,5,9,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,9,1,7,5,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,9,1,8,5,6,7]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,8,1,7,5,9,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,6,1,7,9,5,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,6,1,9,8,5,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,9,1,7,8,5,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[2,3,9,5,1,4,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[2,3,8,5,1,4,6,9,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[2,3,7,5,1,4,9,6,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[2,3,9,5,1,4,8,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[2,3,7,5,1,4,8,9,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[2,3,9,6,1,4,5,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[2,3,8,6,1,4,5,9,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[2,3,7,9,1,4,5,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,9,8,1,4,5,6,7]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,7,8,1,4,5,9,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[2,3,7,6,1,4,9,5,8]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,9,6,1,4,8,5,7]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,7,9,1,4,8,5,6]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,7,6,1,4,8,9,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[2,3,6,5,1,9,4,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[2,3,6,5,1,8,4,9,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[2,3,9,5,1,7,4,6,8]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,9,5,1,8,4,6,7]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,8,5,1,7,4,9,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[2,3,9,6,1,7,4,5,8]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,9,6,1,8,4,5,7]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,8,9,1,7,4,5,6]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,8,6,1,7,4,9,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,1,7,9,4,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,9,8,4,7]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,9,5,1,7,8,4,6]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,9,6,1,7,8,4,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,5,1,7,8,9,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[2,9,4,5,1,3,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[2,8,4,5,1,3,6,9,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[2,7,4,5,1,3,9,6,8]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,9,4,5,1,3,8,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[2,7,4,5,1,3,8,9,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[2,9,4,6,1,3,5,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,8,4,6,1,3,5,9,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[2,7,4,9,1,3,5,6,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[2,9,4,8,1,3,5,6,7]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[2,7,4,8,1,3,5,9,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[2,7,4,6,1,3,9,5,8]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,9,4,6,1,3,8,5,7]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,7,4,9,1,3,8,5,6]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[2,7,4,6,1,3,8,9,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[2,9,6,5,1,3,4,7,8]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[2,8,6,5,1,3,4,9,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[2,7,9,5,1,3,4,6,8]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[2,9,8,5,1,3,4,6,7]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[2,7,8,5,1,3,4,9,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[2,7,9,6,1,3,4,5,8]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[2,9,8,6,1,3,4,5,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,7,8,9,1,3,4,5,6]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[2,7,8,6,1,3,4,9,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[2,7,6,5,1,3,9,4,8]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[2,9,6,5,1,3,8,4,7]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[2,7,9,5,1,3,8,4,6]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[2,7,9,6,1,3,8,4,5]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[2,7,6,5,1,3,8,9,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[2,6,4,5,1,9,3,7,8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,4,5,1,8,3,9,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[2,9,4,5,1,7,3,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[2,9,4,5,1,8,3,6,7]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[2,8,4,5,1,7,3,9,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[2,9,4,6,1,7,3,5,8]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,9,4,6,1,8,3,5,7]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[2,8,4,9,1,7,3,5,6]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[2,8,4,6,1,7,3,9,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[2,9,6,5,1,7,3,4,8]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,9,6,5,1,8,3,4,7]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[2,8,9,5,1,7,3,4,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[2,8,9,6,1,7,3,4,5]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[2,8,6,5,1,7,3,9,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[2,6,4,5,1,7,9,3,8]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[2,6,4,5,1,9,8,3,7]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[2,9,4,5,1,7,8,3,6]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[2,9,4,6,1,7,8,3,5]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[2,9,6,5,1,7,8,3,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,6,4,5,1,7,8,9,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[9,3,4,5,1,2,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[8,3,4,5,1,2,6,9,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[7,3,4,5,1,2,9,6,8]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[9,3,4,5,1,2,8,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[7,3,4,5,1,2,8,9,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[9,3,4,6,1,2,5,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[8,3,4,6,1,2,5,9,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,3,4,9,1,2,5,6,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9,3,4,8,1,2,5,6,7]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[7,3,4,8,1,2,5,9,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,3,4,6,1,2,9,5,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[9,3,4,6,1,2,8,5,7]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[7,3,4,9,1,2,8,5,6]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[7,3,4,6,1,2,8,9,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[9,3,6,5,1,2,4,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[8,3,6,5,1,2,4,9,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,3,9,5,1,2,4,6,8]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[9,3,8,5,1,2,4,6,7]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[7,3,8,5,1,2,4,9,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,3,9,6,1,2,4,5,8]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[9,3,8,6,1,2,4,5,7]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,8,9,1,2,4,5,6]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,8,6,1,2,4,9,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,6,5,1,2,9,4,8]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[9,3,6,5,1,2,8,4,7]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,9,5,1,2,8,4,6]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,9,6,1,2,8,4,5]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,6,5,1,2,8,9,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[9,6,4,5,1,2,3,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[8,6,4,5,1,2,3,9,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,9,4,5,1,2,3,6,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9,8,4,5,1,2,3,6,7]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[7,8,4,5,1,2,3,9,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,9,4,6,1,2,3,5,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9,8,4,6,1,2,3,5,7]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[7,8,4,9,1,2,3,5,6]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[7,8,4,6,1,2,3,9,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,9,6,5,1,2,3,4,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9,8,6,5,1,2,3,4,7]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,9,5,1,2,3,4,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,6,1,2,3,4,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[7,8,6,5,1,2,3,9,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,6,4,5,1,2,9,3,8]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[9,6,4,5,1,2,8,3,7]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[7,9,4,5,1,2,8,3,6]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[7,9,4,6,1,2,8,3,5]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[7,9,6,5,1,2,8,3,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[7,6,4,5,1,2,8,9,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,3,4,5,1,9,2,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,3,4,5,1,8,2,9,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[9,3,4,5,1,7,2,6,8]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[9,3,4,5,1,8,2,6,7]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[8,3,4,5,1,7,2,9,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[9,3,4,6,1,7,2,5,8]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[9,3,4,6,1,8,2,5,7]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[8,3,4,9,1,7,2,5,6]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,6,1,7,2,9,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[9,3,6,5,1,7,2,4,8]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[9,3,6,5,1,8,2,4,7]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[8,3,9,5,1,7,2,4,6]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,6,1,7,2,4,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8,3,6,5,1,7,2,9,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[9,6,4,5,1,7,2,3,8]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[9,6,4,5,1,8,2,3,7]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[8,9,4,5,1,7,2,3,6]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,6,1,7,2,3,5]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[8,9,6,5,1,7,2,3,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8,6,4,5,1,7,2,9,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[6,3,4,5,1,7,9,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,3,4,5,1,9,8,2,7]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,1,7,8,2,6]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,6,1,7,8,2,5]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[9,3,6,5,1,7,8,2,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[9,6,4,5,1,7,8,2,3]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,5,7,1,9,6,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,9,1,8,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[2,3,4,9,6,1,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[2,3,4,8,6,1,5,9,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[2,3,4,9,7,1,5,6,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,3,4,8,9,1,5,6,7]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[2,3,4,8,7,1,5,9,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[2,3,4,7,6,1,9,5,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,9,6,1,8,5,7]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[2,3,4,9,7,1,8,5,6]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,1,8,9,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[2,3,9,5,6,1,4,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[2,3,8,5,6,1,4,9,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[2,3,9,5,7,1,4,6,8]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[2,3,8,5,9,1,4,6,7]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[2,3,8,5,7,1,4,9,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[2,3,9,7,6,1,4,5,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[2,3,8,9,6,1,4,5,7]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,3,8,9,7,1,4,5,6]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[2,3,8,7,6,1,4,9,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[2,3,7,5,6,1,9,4,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[2,3,9,5,6,1,8,4,7]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[2,3,9,5,7,1,8,4,6]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,3,9,7,6,1,8,4,5]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,3,7,5,6,1,8,9,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[2,9,4,5,6,1,3,7,8]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[2,8,4,5,6,1,3,9,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[2,9,4,5,7,1,3,6,8]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[2,8,4,5,9,1,3,6,7]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[2,8,4,5,7,1,3,9,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[2,9,4,7,6,1,3,5,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,8,4,9,6,1,3,5,7]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,8,4,9,7,1,3,5,6]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[2,8,4,7,6,1,3,9,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[2,9,7,5,6,1,3,4,8]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[2,8,9,5,6,1,3,4,7]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[2,8,9,5,7,1,3,4,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,8,9,7,6,1,3,4,5]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[2,8,7,5,6,1,3,9,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[2,7,4,5,6,1,9,3,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[2,9,4,5,6,1,8,3,7]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[2,9,4,5,7,1,8,3,6]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[2,9,4,7,6,1,8,3,5]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,9,7,5,6,1,8,3,4]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,7,4,5,6,1,8,9,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[9,3,4,5,6,1,2,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[8,3,4,5,6,1,2,9,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[9,3,4,5,7,1,2,6,8]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[8,3,4,5,9,1,2,6,7]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[8,3,4,5,7,1,2,9,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[9,3,4,7,6,1,2,5,8]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8,3,4,9,6,1,2,5,7]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[8,3,4,9,7,1,2,5,6]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8,3,4,7,6,1,2,9,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[9,3,7,5,6,1,2,4,8]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8,3,9,5,6,1,2,4,7]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[8,3,9,5,7,1,2,4,6]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8,3,9,7,6,1,2,4,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8,3,7,5,6,1,2,9,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,7,4,5,6,1,2,3,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8,9,4,5,6,1,2,3,7]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[8,9,4,5,7,1,2,3,6]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[8,9,4,7,6,1,2,3,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,7,5,6,1,2,3,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8,7,4,5,6,1,2,9,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,3,4,5,6,1,9,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,1,8,2,7]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,7,1,8,2,6]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[9,3,4,7,6,1,8,2,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[9,3,7,5,6,1,8,2,4]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[9,7,4,5,6,1,8,2,3]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,9,7,1,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,4,5,9,8,1,6,7]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,4,5,8,7,1,9,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[2,3,4,9,6,7,1,5,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[2,3,4,9,6,8,1,5,7]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[2,3,4,9,8,7,1,5,6]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,6,7,1,9,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[2,3,9,5,6,7,1,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[2,3,9,5,6,8,1,4,7]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,3,9,5,8,7,1,4,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,3,9,8,6,7,1,4,5]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,3,8,5,6,7,1,9,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,9,4,5,6,7,1,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[2,9,4,5,6,8,1,3,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[2,9,4,5,8,7,1,3,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,9,4,8,6,7,1,3,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,9,8,5,6,7,1,3,4]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,8,4,5,6,7,1,9,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[9,3,4,5,6,8,1,2,7]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[9,3,4,5,8,7,1,2,6]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[9,3,4,8,6,7,1,2,5]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[9,3,8,5,6,7,1,2,4]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9,8,4,5,6,7,1,2,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,9,8,1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,9,7,8,1,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,9,6,7,8,1,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,1,2,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10,1,4,5,6,7,8,9,2,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[2,10,4,5,6,7,8,1,3,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,10,2,9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,10,5,6,7,8,9,2,4]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,10,3]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,4,10,6,7,8,9,2,5]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[10,1,9,5,6,7,8,2,3,4]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8,1,4,5,6,7,2,9,10,3]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[2,8,4,5,6,7,1,10,3,9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,3,4,5,1,7,8,10,2,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,1,4,5,10,7,8,9,2,6]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,1,9,5,6,7,8,2,10,4]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,4,5,6,2,8,9,10,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,1,4,5,6,10,8,9,2,7]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,1,10,9,6,7,8,2,4,5]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[10,1,4,8,6,7,2,9,3,5]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[9,1,8,5,6,7,2,3,10,4]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[6,1,4,5,2,7,8,9,10,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[2,3,4,5,6,10,8,1,7,9]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,3,1,5,6,7,8,10,2,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,1,4,5,6,7,10,9,2,8]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[3,1,10,5,9,7,8,2,4,6]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[9,1,7,5,6,2,8,3,10,4]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,4,2,6,7,8,9,10,3]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[9,3,4,5,6,7,1,2,10,8]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[10,1,4,5,7,2,8,9,3,6]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[9,1,4,8,6,7,2,3,10,5]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,1,10,8,6,7,2,9,4,5]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,10,1,5,6,7,8,9,3,4]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[10,1,4,5,6,7,8,2,3,9]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,3,4,5,6,1,9,2,10,8]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,4,1,10,6,7,8,9,3,5]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,9,1,5,6,7,8,3,10,4]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[10,1,2,5,6,7,8,9,3,4]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[3,1,10,5,6,7,8,2,4,9]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1,4,5,6,7,2,10,3,9]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,4,5,2,10,8,9,3,7]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,8,7,2,4,5,6]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8,1,9,7,6,2,3,4,10,5]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,10,1,9,6,7,8,3,4,5]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,2,10,6,7,8,9,3,5]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,1,2,3,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,10,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10,7,1,2,3,4,5,9,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,10,1,2,3,4,5,9,6,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,7,1,2,3,4,5,9,10,6]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9,7,1,2,3,4,8,5,10,6]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7,6,1,2,3,4,8,9,10,5]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,9,1,2,3,10,4,6,7,8]
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[8,6,1,2,3,7,4,9,10,5]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,10,4]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[10,4,1,2,9,3,5,6,7,8]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,10,1,2,9,3,4,6,7,8]
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,7,1,2,6,3,8,9,10,4]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,10,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9,3,1,5,2,10,4,6,7,8]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,10,1,5,2,3,4,6,7,8]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[6,4,1,5,2,7,8,9,10,3]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,1,10,9,2,5,6,7,8]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,3,1,8,6,7,2,9,10,5]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9,3,1,5,6,7,8,2,10,4]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,9,10,1,3,4,5,6,7,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,9,8,1,3,4,5,6,10,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,10,5,1,9,3,4,6,7,8]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,10,5,1,6,7,8,9,3,4]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,5,4,1,6,7,8,9,10,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,3,10,1,2,4,5,6,7,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,10,4,1,2,3,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,10,5,1,2,3,4,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,10,9,1,2,3,4,5,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,7,9,1,2,3,4,5,6,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,9,8,1,2,3,4,5,6,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9,7,8,1,2,3,4,5,10,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,7,10,1,2,3,4,9,5,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,10,5,1,2,3,9,4,7,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[9,5,4,1,2,10,3,6,7,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,1,9,2,5,6,7,8]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10,8,9,1,7,2,3,4,5,6]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9,3,4,1,6,7,8,2,10,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,9,1,4,5,6,7,8]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,10,4,9,1,3,5,6,7,8]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,10,8,9,1,3,4,5,6,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,9,1,2,5,6,7,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10,9,4,5,1,2,3,6,7,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[10,9,6,5,1,2,3,4,7,8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,10,9,6,1,2,3,4,5,8]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,6,1,7,2,3,4,5]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9,3,6,5,1,7,8,2,10,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,10,9,1,5,6,7,8]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,7,6,1,8,9,10,5]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,10,5,9,1,4,6,7,8]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[8,9,10,5,7,1,2,3,4,6]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,7,6,1,2,3,4,5]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[10,3,7,5,6,1,8,9,2,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,9,10,1,6,7,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[2,3,4,9,6,10,1,5,7,8]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,8,6,7,1,9,10,5]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[2,3,8,5,6,7,1,9,10,4]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[10,8,4,5,6,7,1,9,2,3]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[2,3,4,5,6,10,9,1,7,8]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[2,3,4,5,10,7,9,1,6,8]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,10,4]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,10,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[10,3,4,5,6,7,9,1,2,8]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[10,3,4,5,6,9,8,1,2,7]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[10,3,4,5,9,7,8,1,2,6]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[10,3,4,9,6,7,8,1,2,5]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[10,3,9,5,6,7,8,1,2,4]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10,9,4,5,6,7,8,1,2,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,10,9,1,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,10,8,9,1,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,10,7,8,9,1,6]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,10,6,7,8,9,1,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,3]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,1,2,3,4,5,6,9,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,9,6,7,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,1,2,3,4,10,5,6,7,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,9,4,5,6,7,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,9,3,4,5,6,7,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,10,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,1,2,3,4,5,6,9,10,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,1,2,3,4,5,10,9,6,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,1,2,3,4,10,9,5,7,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,9,10,4,6,7,8]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,10,9,3,5,6,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,9,2,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[10,1,2,3,4,5,8,9,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[10,1,2,3,4,9,8,5,6,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10,1,9,5,2,3,4,6,7,8]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[9,1,2,3,10,8,4,5,6,7]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,1,2,9,10,3,4,5,6,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,1,8,9,2,3,4,5,6,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,1,8,9,2,3,4,5,10,6]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,1,2,3,4,5,6,10,7,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,1,2,3,4,5,10,6,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,1,2,3,4,5,8,10,6,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,10,5,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,8,5,9,10,7]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,10,4,6,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,7,4,8,9,10,6]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,6,3,7,8,9,10,5]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,10,3,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,10,2,4,5,6,7,8,9]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,5,2,6,7,8,9,10,4]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,10,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,7,1,3,4,5,10,6,8,9]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,7,1,3,4,5,9,6,10,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,10,5,7,8,9]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,5,1,3,10,4,6,7,8,9]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,1,10,3,5,6,7,8,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,7,8,9,10,5]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,10,1,2,3,4,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,10,1,2,3,4,5,6,7,9]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,1,10,2,5,6,7,8,9]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,1,2,10,3,6,7,8,9]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,6,1,2,3,10,4,7,8,9]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,10,5,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,7,1,2,3,4,5,10,6,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,10,1,3,4,5,6,9,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,8,1,2,3,4,5,6,9]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,4,1,2,5,6,7,8,9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,4,1,3,5,6,7,8,9]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,9,1,2,3,4,5,10,8]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,8,1,9,10,3,4,5,6,7]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,3,1,2,6,7,8,9,10,4]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,3,4,1,2,7,8,9,10,5]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,3,4,5,1,2,8,9,10,6]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[8,3,4,5,6,1,2,9,10,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,8,9,10,2,4,5,6,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,10,8,1,3,4,5,6,7,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,7,1,2,3,4,5,6,10,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,10,1,9,3,4,5,6,7,8]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,9,1,10,8,7,3,4,5,6]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3,4,5,1,8,2,9,10,7]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,10,1,7,8,9,5,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,10,1,9,7,8]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,10,1,8,9,6,7]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,10,1,6,7,8,9,4,5]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[2,3,4,5,9,7,1,6,10,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,1,2,3,4,5,10,7,9]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,7,1,2,3,4,10,6,8,9]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,4,1,2,3,10,5,7,8,9]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,3,1,2,10,4,6,7,8,9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,8,10,6,1,2,3,4,5,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[9,1,2,3,4,5,8,6,10,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,1,9,4,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,4,2,3,5,6,7,8,9]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[10,5,4,1,2,3,8,9,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[10,1,2,3,4,5,8,6,7,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1,8,2,3,4,5,6,7,9]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,8,5,1,2,3,4,9,10,7]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[10,6,1,2,3,4,8,5,7,9]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[10,7,1,2,3,4,8,5,6,9]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,1,8,2,10,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,10,1,3,4,5,9,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,3,1,5,2,4,6,7,8,9]
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[3,1,4,5,8,7,2,9,10,6]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[10,8,6,5,1,2,3,4,7,9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,3,8,1,2,4,5,6,7,9]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,3,1,8,2,4,5,6,7,9]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[10,3,1,2,4,5,9,6,7,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,10,1,8,3,4,5,6,7,9]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,9,2,10,8,4,5,6,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,2,9,4,5,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,3,4,1,7,2,8,9,10,6]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,1,6,2,7,8,9,10,5]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,10,7,1,3,4,5,6,8,9]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,3,7,1,2,4,5,6,8,9]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,10,8,2,4,5,6,7,9]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[5,10,1,2,3,7,4,6,8,9]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[10,4,1,2,6,3,5,7,8,9]
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,7,2,8,4,5,6]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[3,1,9,10,6,8,2,4,5,7]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[9,1,8,6,2,3,4,5,10,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[9,1,8,2,7,3,4,5,10,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,10,9,7,2,4,5,6,8]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,10,9,2,8,4,5,6,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,3,1,10,2,4,5,6,8,9]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,7,1,3,4,5,10,9,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,10,2,4,5,9,6,7,8]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,10,9,7,8,3,5,6]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,4,1,9,10,8,3,5,6,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,10,9,3,5,6,7,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[10,3,1,2,7,4,5,6,8,9]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,9,4,5,1,2,3,6,10,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[10,3,4,6,1,2,5,9,7,8]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,10,5,1,4,9,6,7,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,9,4,1,3,10,5,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,4,1,5,2,3,6,7,8,9]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[10,1,4,5,2,3,6,7,8,9]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[10,3,4,1,2,9,8,5,6,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,9,1,10,8,4,5,6,7]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,6,4,1,3,7,8,9,10,5]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,7,5,1,4,8,9,10,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,8,6,1,5,9,10,7]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,8,1,7,5,9,10,6]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,1,8,2,7,3,4,5,6,9]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,4,2,6,7,10,9,3,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[10,8,5,1,2,3,4,6,7,9]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,1,2,10]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[11,1,4,5,6,7,8,9,10,2,3]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,11,5,6,7,8,9,10,2,4]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10,1,4,5,6,7,8,9,2,11,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3,1,4,11,6,7,8,9,10,2,5]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[9,1,4,5,6,7,8,2,10,11,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[3,1,4,5,11,7,8,9,10,2,6]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,1,10,5,6,7,8,9,2,11,4]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,1,4,5,6,7,2,9,10,11,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[3,1,4,5,6,11,8,9,10,2,7]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,1,11,10,6,7,8,9,2,4,5]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[10,1,9,5,6,7,8,2,3,11,4]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,4,5,6,2,8,9,10,11,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[3,1,4,5,6,7,11,9,10,2,8]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,4,5,2,7,8,9,10,11,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[3,1,4,5,6,7,8,11,10,2,9]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,1,4,2,6,7,8,9,10,11,3]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,11,1,5,6,7,8,9,10,3,4]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,11,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,1,2,3,4,5,6,7,10,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[11,1,2,3,4,5,6,10,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,11,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,4,10,5,6,7,8,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,10,4,5,6,7,8,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,11,3,4,5,6,7,8,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,10,2,3,4,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[9,1,2,3,4,5,6,7,10,11,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,10,11,2,4,5,6,7,8,9]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,11,10,1,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[11,1,2,3,4,5,6,9,10,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[8,1,2,3,4,5,6,9,10,11,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,3,10,1,2,4,5,6,7,8,9]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,10,11,1,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[11,1,2,3,4,5,10,9,6,7,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,4,1,2,3,5,6,7,8,9]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,3,4,11,1,2,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[10,1,2,3,4,11,9,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,11,6]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11,10,5,1,2,3,4,6,7,8,9]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,11,10,1,5,6,7,8,9]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[10,11,4,5,1,2,3,6,7,8,9]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,1,2,3,10,11,4,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,10,11,1,2,3,4,5,7,8,9]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10,11,6,5,1,2,3,4,7,8,9]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,1,2,9,10,3,4,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[10,7,11,1,2,3,4,5,6,8,9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,11,5]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,11,10,1,6,7,8,9]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,11,10,6,1,2,3,4,5,8,9]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,1,10,9,2,3,4,5,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10,11,8,1,2,3,4,5,6,7,9]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10,1,8,9,2,3,4,5,6,11,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,8,11,10,1,2,3,4,5,6,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,1,2,3,4,5,6,7,11,8,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,11,7,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,11,5,7,8,9,10]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,11,4,6,7,8,9,10]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,11,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,11,3,5,6,7,8,9,10]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,11,2,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,11,9]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,4,1,2,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,11,1,2,3,4,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[11,6,1,2,3,4,5,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[11,7,1,2,3,4,5,6,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,11,1,2,3,4,5,6,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,1,2,3,4,5,6,7,8,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10,9,1,2,3,4,5,6,7,11,8]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,11,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,11,4,5,6,7,8,9,10,1,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,11,1,3,4,5,6,7,10,8,9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,11,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,8,11,10,1,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,2]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,11,2]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,9,10,11,2]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,11,2]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,9,10,11,2]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,9,10,11,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8,9,1,2,3,4,5,6,10,11,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[11,8,9,10,1,2,3,4,5,6,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,7,11,9,10,1,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,6,11,8,9,10,1,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,11,7,8,9,10,1,6]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,11,6,7,8,9,10,1,5]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[2,3,11,5,6,7,8,9,10,1,4]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,4,1,2,6,7,8,9,10,11,3]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,6,1,2,3,7,8,9,10,11,4]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7,6,1,2,3,4,8,9,10,11,5]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[8,7,1,2,3,4,5,9,10,11,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[11,10,1,2,3,4,5,9,6,7,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,11,9,1,2,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,11,3]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,11,4]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,10,11,4]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,9,6,7,8,1,10,11,5]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,8,6,7,1,9,10,11,5]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,8,7,1,9,10,11,6]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[8,9,10,11,7,1,2,3,4,5,6]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,10,1,11,3,4,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[11,10,4,5,6,7,8,9,1,2,3]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[11,7,1,2,3,4,5,10,6,8,9]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[9,10,11,8,6,7,1,2,3,4,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,3,4,1,2,5,6,7,8,9,10]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,6,4,5,7,8,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1,11,2,3,4,5,6,7,8,10]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,11,2,3,4,5,7,8,9,10]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[11,1,2,6,3,4,5,7,8,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,9,11,1,3,4,5,6,7,8,10]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,11,8,2,4,5,6,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,11,1,9,10,3,4,5,6,7,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[2,3,4,5,6,7,11,10,1,8,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,10,11,1,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,9,1,2,3,4,5,6,11,7,10]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[11,1,4,5,6,7,8,9,2,3,10]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[3,1,10,11,9,7,8,2,4,5,6]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8,1,9,10,7,2,3,4,5,11,6]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,11,9,10,2,4,5,6,7,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,11,8,1,3,4,5,6,7,9,10]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,4,1,11,6,7,8,9,10,3,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,11,1,3,4,5,6,10,7,8,9]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,11,1,10,6,7,8,9,3,4,5]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,10,1,11,9,7,8,3,4,5,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,9,1,10,11,8,3,4,5,6,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11,1,9,2,10,3,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8,11,1,2,3,4,5,10,6,7,9]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[12,1,4,5,6,7,8,9,10,11,2,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,12,5,6,7,8,9,10,11,2,4]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[11,1,4,5,6,7,8,9,10,2,12,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[12,1,2,3,4,5,6,7,8,11,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[12,1,2,3,4,5,6,7,11,8,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,12,11,1,3,4,5,6,7,8,9,10]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2,12,4,5,6,7,8,9,10,11,1,3]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[12,3,4,5,6,7,8,9,10,11,1,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,12,1]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,12,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[12,10,1,2,3,4,5,6,7,8,9,11]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,12,2,4,5,6,7,8,9,10,11]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,12,2,11]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,11,4,5,6,7,8,9,10,1,12,3]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[9,10,11,12,8,7,1,2,3,4,5,6]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,1,10,11,12,9,8,2,4,5,6,7]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8,1,9,10,11,2,3,4,5,6,12,7]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,1,9,10,11,12,2,4,5,6,7,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[12,9,1,2,3,4,5,6,7,8,10,11]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,11,1,3,4,5,6,7,8,9,12,10]
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Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
References
[1] Ringel, C. M. The finitistic dimension of a Nakayama algebra arXiv:2008.10044
Properties
injective, graded
Sage code
def to_matrix(D): D = DyckWord(D) N = zero_matrix(D.semilength()+1) N[0, 0] = 1 i, j = 0, 0 for p in range(len(D)): if D[p] == 1: i += 1 else: j += 1 N[j, i] = 1 return N def is_projective(N, i, j): return N[i, j] == 1 and (j+1 == N.ncols() or N[i, j+1] == 0) def to_projective(N, i, j): n = N.ncols() while j < n and N[i, j] != 1: j += 1 while j < n and N[i, j] != 0: j += 1 return j-1 def to_injective(N, i, j): while i >= 0 and N[i, j] != 1: i -= 1 while i >= 0 and N[i, j] != 0: i -= 1 return i+1 def to_top(N, i, j): return i def omega(N, i, j): return (j+1, to_projective(N, i, j)) def Ringel_matrix(N, i): S = (i, i) IS = (to_injective(N, *S), i) while True: if is_projective(N, *IS): return to_top(N, *IS) IS = omega(N, *IS) IS = omega(N, *IS) S = omega(N, *S) if is_projective(N, *S): return to_top(N, *S) S = omega(N, *S) def mapping(D): N = to_matrix(D) return Permutation([Ringel_matrix(N, i)+1 for i in range(N.nrows())])
Weight
26
Created
Dec 10, 2020 at 20:42 by Martin Rubey
Updated
Dec 10, 2020 at 20:42 by Martin Rubey
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