Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0] => [2,1,3] => [1,2,3] => [1,2,3] => 0
[1,1,0,1,0,0] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,1,1,0,0,0] => [3,2,1] => [1,3,2] => [2,3,1] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,2,4,3] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,2,4,3] => [2,3,4,1] => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,3,2,4] => [2,3,1,4] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,3,4,2] => [2,4,1,3] => 1
[1,1,1,0,1,0,0,0] => [4,2,3,1] => [1,4,2,3] => [2,1,4,3] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,4,2,3] => [2,1,4,3] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,3,5,4] => [2,3,4,5,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,2,3,5,4] => [2,3,4,5,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,2,4,3,5] => [2,3,4,1,5] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,2,4,5,3] => [2,3,5,1,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => [1,2,5,3,4] => [2,3,1,5,4] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,2,5,3,4] => [2,3,1,5,4] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,2,3,5,4] => [2,3,4,5,1] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,2,3,5,4] => [2,3,4,5,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,2,4,3,5] => [2,3,4,1,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,2,4,5,3] => [2,3,5,1,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => [1,2,5,3,4] => [2,3,1,5,4] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,2,5,3,4] => [2,3,1,5,4] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,3,2,4,5] => [2,3,1,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,3,2,4,5] => [2,3,1,4,5] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,3,4,2,5] => [2,4,1,3,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,3,4,5,2] => [2,5,1,3,4] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,3,5,2,4] => [2,1,4,5,3] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => [1,4,2,3,5] => [2,1,4,3,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => [1,4,5,2,3] => [2,1,5,3,4] => 1
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => [1,5,2,3,4] => [2,1,3,5,4] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => [1,5,2,3,4] => [2,1,3,5,4] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,4,2,3,5] => [2,1,4,3,5] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,4,5,2,3] => [2,1,5,3,4] => 1
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => [1,5,2,3,4] => [2,1,3,5,4] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => [1,5,2,3,4] => [2,1,3,5,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,5,2,4,3] => [3,2,5,4,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
>>> Load all 820 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [2,3,4,1,6,5] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [2,3,1,5,6,4] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [2,3,1,5,4,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [2,3,1,6,4,5] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => [1,2,6,3,4,5] => [2,3,1,4,6,5] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [3,4,2,6,5,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [2,1,4,5,6,3] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [2,1,4,5,3,6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [2,1,4,6,3,5] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [2,1,4,3,6,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [2,1,4,3,5,6] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [2,1,5,3,4,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [2,1,6,3,4,5] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [2,1,3,5,6,4] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [2,1,3,5,4,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => [1,5,6,2,3,4] => [2,1,3,6,4,5] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => [1,6,2,3,4,5] => [2,1,3,4,6,5] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => [1,6,2,3,5,4] => [3,2,4,6,5,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [3,2,5,4,1,6] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [3,2,6,5,1,4] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [3,2,5,1,6,4] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => [1,6,2,4,5,3] => [3,2,6,1,5,4] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [3,2,1,6,5,4] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,2,4,3,5,7,6] => [3,4,5,2,6,7,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [2,3,4,5,6,7,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [2,3,4,5,6,1,7] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => [2,3,4,5,1,6,7] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => [2,3,4,7,1,5,6] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => [1,2,3,7,4,5,6] => [2,3,4,1,5,7,6] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [1,2,4,3,5,6,7] => [2,3,4,1,5,6,7] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [1,2,4,3,5,7,6] => [3,4,5,2,6,7,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => [3,4,2,5,6,7,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [1,3,2,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [1,3,2,4,5,7,6] => [3,4,2,5,6,7,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [1,3,4,2,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [1,3,4,5,2,6,7] => [2,5,1,3,4,6,7] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [1,3,4,5,2,6,7] => [2,5,1,3,4,6,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [1,3,4,5,6,2,7] => [2,6,1,3,4,5,7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [1,3,4,5,6,7,2] => [2,7,1,3,4,5,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => [1,4,5,6,2,3,7] => [2,1,6,3,4,5,7] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => [1,4,5,6,7,2,3] => [2,1,7,3,4,5,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => [1,5,6,7,2,3,4] => [2,1,3,7,4,5,6] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => [1,5,6,7,2,3,4] => [2,1,3,7,4,5,6] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [1,4,5,6,2,3,7] => [2,1,6,3,4,5,7] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [1,4,5,6,7,2,3] => [2,1,7,3,4,5,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => [1,5,6,7,2,3,4] => [2,1,3,7,4,5,6] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => [1,5,6,7,2,3,4] => [2,1,3,7,4,5,6] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,6,7,2,3,4,5] => [2,1,3,4,7,5,6] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,2,3,5,6,8,4,7] => [2,3,4,1,6,7,8,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,5,2,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,5,4,2,6,7,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [1,2,3,5,6,8,4,7] => [2,3,4,1,6,7,8,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [1,2,3,4,5,6,8,7] => [2,3,4,5,6,7,8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,7,1,8] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [1,2,3,4,5,7,8,6] => [2,3,4,5,6,8,1,7] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [1,2,3,4,5,8,6,7] => [2,3,4,5,6,1,8,7] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [1,2,3,4,6,5,7,8] => [2,3,4,5,6,1,7,8] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [1,2,3,5,4,6,7,8] => [2,3,4,5,1,6,7,8] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [1,2,4,3,5,6,8,7] => [3,4,5,2,6,7,8,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,6,4,5,3,8,7,1] => [1,2,6,8,3,4,5,7] => [2,3,1,4,5,7,8,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [1,3,2,4,5,6,8,7] => [3,4,2,5,6,7,8,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [1,3,2,4,5,6,8,7] => [3,4,2,5,6,7,8,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [1,3,2,4,5,6,8,7] => [3,4,2,5,6,7,8,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [1,3,4,5,6,2,7,8] => [2,6,1,3,4,5,7,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [1,3,4,5,6,7,2,8] => [2,7,1,3,4,5,6,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [1,3,4,5,6,7,8,2] => [2,8,1,3,4,5,6,7] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [1,3,5,8,2,4,6,7] => [2,1,4,3,6,5,8,7] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [1,3,7,2,4,6,5,8] => [3,2,5,4,7,6,1,8] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [1,4,2,3,5,8,6,7] => [3,2,5,4,6,1,8,7] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [1,4,2,3,5,8,6,7] => [3,2,5,4,6,1,8,7] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [1,4,5,6,7,8,2,3] => [2,1,8,3,4,5,6,7] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => [1,5,6,7,8,2,3,4] => [2,1,3,8,4,5,6,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8,2,4,5,6,3,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [1,8,2,3,5,7,4,6] => [3,2,4,1,6,8,7,5] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => [1,8,2,3,6,4,5,7] => [3,2,4,1,7,5,8,6] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [1,8,2,3,6,4,5,7] => [3,2,4,1,7,5,8,6] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [1,4,2,3,5,8,6,7] => [3,2,5,4,6,1,8,7] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [1,4,2,3,5,8,6,7] => [3,2,5,4,6,1,8,7] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [1,4,5,6,7,8,2,3] => [2,1,8,3,4,5,6,7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => [1,5,6,7,8,2,3,4] => [2,1,3,8,4,5,6,7] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [1,5,6,7,8,2,3,4] => [2,1,3,8,4,5,6,7] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [1,8,2,3,4,5,6,7] => [2,1,3,4,5,6,8,7] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [1,8,2,3,5,7,4,6] => [3,2,4,1,6,8,7,5] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [1,8,2,3,6,4,5,7] => [3,2,4,1,7,5,8,6] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [1,8,2,3,6,4,5,7] => [3,2,4,1,7,5,8,6] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => [1,6,8,2,4,3,5,7] => [3,2,6,1,4,7,8,5] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [1,8,2,7,3,4,5,6] => [3,2,1,4,5,8,7,6] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [1,8,2,7,3,6,4,5] => [4,3,2,1,8,7,6,5] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [1,8,2,7,3,6,4,5] => [4,3,2,1,8,7,6,5] => 3
[] => [] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,7,9,1,8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [1,3,4,5,6,7,8,9,2] => [2,9,1,3,4,5,6,7,8] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,9,1] => [1,4,5,6,7,8,9,2,3] => [2,1,9,3,4,5,6,7,8] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [1,4,5,6,7,8,9,2,3] => [2,1,9,3,4,5,6,7,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,7,9,1,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [1,3,4,5,6,7,8,9,10,2] => [2,10,1,3,4,5,6,7,8,9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,9,11,10] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,5,7,6,1,8,9] => [1,2,3,4,5,7,6,8,9] => [2,3,4,5,6,7,1,8,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [1,2,3,4,5,6,8,7,9] => [2,3,4,5,6,7,8,1,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [1,3,4,5,6,7,8,2,9] => [2,8,1,3,4,5,6,7,9] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,5,1,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [1,2,3,4,5,6,7,8,9,11,10] => [2,3,4,5,6,7,8,9,10,11,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,6,1,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [1,2,3,4,5,6,8,9,7] => [2,3,4,5,6,7,9,1,8] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,7,9,8,1,10] => [1,2,3,4,5,6,7,9,8,10] => [2,3,4,5,6,7,8,9,1,10] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [1,2,3,4,5,6,7,9,8] => [2,3,4,5,6,7,8,9,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,5,1,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [1,2,3,4,5,6,7,8,10,9] => [2,3,4,5,6,7,8,9,10,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,4,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
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Description
The staircase size of the code of a permutation.
The code $c(\pi)$ of a permutation $\pi$ of length $n$ is given by the sequence $(c_1,\ldots,c_{n})$ with $c_i = |\{j > i : \pi(j) < \pi(i)\}|$. This is a bijection between permutations and all sequences $(c_1,\ldots,c_n)$ with $0 \leq c_i \leq n-i$.
The staircase size of the code is the maximal $k$ such that there exists a subsequence $(c_{i_k},\ldots,c_{i_1})$ of $c(\pi)$ with $c_{i_j} \geq j$.
This statistic is mapped through Mp00062Lehmer-code to major-code bijection to the number of descents, showing that together with the number of inversions St000018The number of inversions of a permutation. it is Euler-Mahonian.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.