Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [1,2] => [1,2] => 1
[1,1,0,0] => [1,2] => [2,1] => [2,1] => 0
[1,0,1,0,1,0] => [3,2,1] => [1,3,2] => [1,3,2] => 1
[1,0,1,1,0,0] => [2,3,1] => [1,2,3] => [1,3,2] => 1
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[1,1,0,1,0,0] => [2,1,3] => [3,2,1] => [3,2,1] => 0
[1,1,1,0,0,0] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,4,3,2] => [1,4,3,2] => 1
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [1,4,2,3] => [1,4,3,2] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,4,2] => [1,4,3,2] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [1,3,2,4] => [1,4,3,2] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => [1,4,3,2] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [4,1,3,2] => [4,1,3,2] => 0
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,1,2,3] => [4,1,3,2] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [4,3,1,2] => [4,3,1,2] => 0
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [4,3,2,1] => [4,3,2,1] => 0
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [4,2,3,1] => [4,2,3,1] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [3,4,1,2] => [3,4,1,2] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [3,4,2,1] => [3,4,2,1] => 0
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,2,4,1] => [3,2,4,1] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => [2,4,3,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,5,4,3,2] => [1,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [1,5,4,2,3] => [1,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,5,3,4,2] => [1,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [1,5,3,2,4] => [1,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [1,5,2,3,4] => [1,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,4,5,3,2] => [1,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [1,4,5,2,3] => [1,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,4,3,5,2] => [1,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [1,4,3,2,5] => [1,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [1,4,2,3,5] => [1,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,3,4,5,2] => [1,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [1,3,4,2,5] => [1,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [1,3,2,4,5] => [1,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [1,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [5,1,4,3,2] => [5,1,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [5,1,4,2,3] => [5,1,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [5,1,3,4,2] => [5,1,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [5,1,3,2,4] => [5,1,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [5,1,2,3,4] => [5,1,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [5,4,1,3,2] => [5,4,1,3,2] => 0
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [5,4,1,2,3] => [5,4,1,3,2] => 0
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [5,4,3,1,2] => [5,4,3,1,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [5,4,2,3,1] => [5,4,2,3,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [5,3,4,1,2] => [5,3,4,1,2] => 0
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [5,3,4,2,1] => [5,3,4,2,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [5,3,2,4,1] => [5,3,2,4,1] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [5,2,3,4,1] => [5,2,4,3,1] => 0
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [4,5,1,3,2] => [4,5,1,3,2] => 0
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,5,1,2,3] => [4,5,1,3,2] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [4,5,3,1,2] => [4,5,3,1,2] => 0
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [4,5,3,2,1] => [4,5,3,2,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,5,2,3,1] => [4,5,2,3,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [4,3,5,1,2] => [4,3,5,1,2] => 0
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [4,3,5,2,1] => [4,3,5,2,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [4,3,2,5,1] => [4,3,2,5,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [4,2,3,5,1] => [4,2,5,3,1] => 0
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => [3,5,4,1,2] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [3,4,5,2,1] => [3,5,4,2,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,4,2,5,1] => [3,5,2,4,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [3,2,4,5,1] => [3,2,5,4,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [2,3,4,5,1] => [2,5,4,3,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [1,6,5,4,2,3] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,6,5,3,4,2] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [1,6,5,3,2,4] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [1,6,5,2,3,4] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,6,4,5,3,2] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [1,6,4,5,2,3] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [1,6,4,3,2,5] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [1,6,4,2,3,5] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [1,6,3,4,2,5] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,6,3,2,4,5] => [1,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,5,6,4,3,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,5,6,3,4,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [1,5,6,3,2,4] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [1,5,6,2,3,4] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,5,4,6,3,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [1,5,4,6,2,3] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,5,4,3,6,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [1,5,4,3,2,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [1,5,4,2,3,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,5,3,4,6,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [1,5,3,4,2,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [1,5,3,2,4,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [1,5,2,3,4,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,4,5,6,3,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [1,4,5,6,2,3] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [1,4,5,3,2,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [1,4,5,2,3,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,4,3,5,6,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [1,4,3,5,2,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [1,4,3,2,5,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [1,4,2,3,5,6] => [1,6,5,4,3,2] => 1
>>> Load all 476 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [1,3,4,5,2,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [1,3,4,2,5,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [1,3,2,4,5,6] => [1,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [6,1,5,4,3,2] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [6,1,5,4,2,3] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [6,1,5,3,4,2] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [6,1,5,3,2,4] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [6,1,5,2,3,4] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [6,1,4,5,3,2] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [6,1,4,5,2,3] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [6,1,4,3,5,2] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [6,1,4,3,2,5] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [6,1,4,2,3,5] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [6,1,3,4,5,2] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [6,1,3,4,2,5] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [6,1,3,2,4,5] => [6,1,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [6,1,2,3,4,5] => [6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [6,5,1,4,2,3] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [6,5,1,3,4,2] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [6,5,1,3,2,4] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [6,5,1,2,3,4] => [6,5,1,4,3,2] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [6,5,4,1,2,3] => [6,5,4,1,3,2] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [6,5,4,2,3,1] => [6,5,4,2,3,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [6,5,3,4,1,2] => [6,5,3,4,1,2] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [6,5,3,2,4,1] => [6,5,3,2,4,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [6,5,2,3,4,1] => [6,5,2,4,3,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [6,4,5,1,3,2] => [6,4,5,1,3,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [6,4,5,1,2,3] => [6,4,5,1,3,2] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [6,4,5,3,1,2] => [6,4,5,3,1,2] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [6,4,5,3,2,1] => [6,4,5,3,2,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [6,4,3,5,1,2] => [6,4,3,5,1,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [6,4,3,5,2,1] => [6,4,3,5,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [6,4,3,2,5,1] => [6,4,3,2,5,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [6,4,2,3,5,1] => [6,4,2,5,3,1] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [6,3,4,5,1,2] => [6,3,5,4,1,2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [6,3,4,5,2,1] => [6,3,5,4,2,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [6,3,4,2,5,1] => [6,3,5,2,4,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [6,3,2,4,5,1] => [6,3,2,5,4,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [6,2,3,4,5,1] => [6,2,5,4,3,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [5,6,1,4,3,2] => [5,6,1,4,3,2] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [5,6,1,4,2,3] => [5,6,1,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [5,6,1,3,4,2] => [5,6,1,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [5,6,1,3,2,4] => [5,6,1,4,3,2] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,6,1,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [5,6,4,1,3,2] => [5,6,4,1,3,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [5,6,4,1,2,3] => [5,6,4,1,3,2] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,6,4,2,3,1] => [5,6,4,2,3,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,6,3,4,2,1] => [5,6,3,4,2,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,6,3,2,4,1] => [5,6,3,2,4,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [5,6,2,3,4,1] => [5,6,2,4,3,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [5,4,6,1,3,2] => [5,4,6,1,3,2] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [5,4,6,1,2,3] => [5,4,6,1,3,2] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [5,4,6,3,1,2] => [5,4,6,3,1,2] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [5,4,6,2,3,1] => [5,4,6,2,3,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [5,4,3,6,1,2] => [5,4,3,6,1,2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [5,4,2,3,6,1] => [5,4,2,6,3,1] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [5,3,4,6,1,2] => [5,3,6,4,1,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [5,3,4,6,2,1] => [5,3,6,4,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [5,3,4,2,6,1] => [5,3,6,2,4,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [5,3,2,4,6,1] => [5,3,2,6,4,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [5,2,3,4,6,1] => [5,2,6,4,3,1] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [4,5,6,1,3,2] => [4,6,5,1,3,2] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => [4,6,5,1,3,2] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,6,3,1,2] => [4,6,5,3,1,2] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [4,5,6,3,2,1] => [4,6,5,3,2,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,5,6,2,3,1] => [4,6,5,2,3,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [4,5,3,6,1,2] => [4,6,3,5,1,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [4,5,3,6,2,1] => [4,6,3,5,2,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [4,5,3,2,6,1] => [4,6,3,2,5,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,5,2,3,6,1] => [4,6,2,5,3,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [4,3,5,6,1,2] => [4,3,6,5,1,2] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [4,3,5,6,2,1] => [4,3,6,5,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [4,3,5,2,6,1] => [4,3,6,2,5,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [4,3,2,5,6,1] => [4,3,2,6,5,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [4,2,3,5,6,1] => [4,2,6,5,3,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => [3,6,5,4,1,2] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [3,4,5,6,2,1] => [3,6,5,4,2,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => [3,2,6,5,4,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [1,7,6,5,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,7,6,5,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [1,7,6,5,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [1,7,6,5,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,7,6,4,5,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [1,7,6,4,5,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,7,6,4,3,5,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [1,7,6,4,3,2,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [1,7,6,4,2,3,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,7,6,3,4,5,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [1,7,6,3,4,2,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [1,7,6,3,2,4,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,7,6,2,3,4,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,7,5,6,4,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [1,7,5,6,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,7,5,6,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [1,7,5,6,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [1,7,5,6,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,7,5,4,6,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [1,7,5,4,6,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,7,5,4,3,6,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [1,7,5,4,3,2,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [1,7,5,4,2,3,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,7,5,3,4,6,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [1,7,5,3,4,2,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,7,5,3,2,4,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [1,7,5,2,3,4,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,7,4,5,6,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [1,7,4,5,6,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,7,4,5,3,6,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [1,7,4,5,3,2,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [1,7,4,5,2,3,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,7,4,3,5,6,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [1,7,4,3,5,2,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,7,4,3,2,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [1,7,4,2,3,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,7,3,4,5,6,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [1,7,3,4,5,2,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [1,7,3,4,2,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [1,7,3,2,4,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,6,7,5,4,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [1,6,7,5,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [1,6,7,5,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [1,6,7,5,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [1,6,7,5,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,6,7,4,5,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [1,6,7,4,5,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,6,7,4,3,5,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [1,6,7,4,3,2,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [1,6,7,4,2,3,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,6,7,3,4,5,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [1,6,7,3,4,2,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [1,6,7,3,2,4,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [1,6,7,2,3,4,5] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,6,5,7,4,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [1,6,5,7,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,6,5,7,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [1,6,5,7,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [1,6,5,7,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,6,5,4,7,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [1,6,5,4,7,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,6,5,4,3,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [1,6,5,4,3,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [1,6,5,4,2,3,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,6,5,3,4,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [1,6,5,3,4,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [1,6,5,3,2,4,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [1,6,5,2,3,4,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,6,4,5,7,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [1,6,4,5,7,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,6,4,5,3,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [1,6,4,5,3,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [1,6,4,5,2,3,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,6,4,3,5,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [1,6,4,3,5,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [1,6,4,3,2,5,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [1,6,4,2,3,5,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,6,3,4,5,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [1,6,3,4,5,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [1,6,3,4,2,5,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [1,6,3,2,4,5,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [1,6,2,3,4,5,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,5,6,7,4,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [1,5,6,7,4,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,5,6,7,3,4,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [1,5,6,7,3,2,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,5,6,4,7,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [1,5,6,4,7,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,5,6,4,3,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [1,5,6,4,3,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [1,5,6,4,2,3,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,5,6,3,4,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [1,5,6,3,4,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [1,5,6,3,2,4,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [1,5,6,2,3,4,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,5,4,6,7,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [1,5,4,6,7,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [1,5,4,6,3,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [1,5,4,6,2,3,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,5,4,3,6,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [1,5,4,3,6,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [1,5,4,3,2,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [1,5,4,2,3,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,5,3,4,6,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [1,5,3,4,6,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [1,5,3,4,2,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [1,5,3,2,4,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [1,5,2,3,4,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,4,5,6,7,3,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [1,4,5,6,7,2,3] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,4,5,6,3,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [1,4,5,6,3,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [1,4,5,6,2,3,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,4,5,3,6,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [1,4,5,3,6,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [1,4,5,3,2,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [1,4,5,2,3,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,4,3,5,6,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [1,4,3,5,6,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [1,4,3,5,2,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [1,4,3,2,5,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [1,4,2,3,5,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,3,4,5,6,7,2] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [1,3,4,5,6,2,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [1,3,4,5,2,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [1,3,4,2,5,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [1,3,2,4,5,6,7] => [1,7,6,5,4,3,2] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,7,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [7,1,6,5,4,3,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [7,1,6,5,4,2,3] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [7,1,6,5,3,4,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [7,1,6,5,3,2,4] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [7,1,6,5,2,3,4] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [7,1,6,4,5,3,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [7,1,6,4,5,2,3] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [7,1,6,4,3,5,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [7,1,6,4,3,2,5] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [7,1,6,4,2,3,5] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [7,1,6,3,4,5,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [7,1,6,3,4,2,5] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [7,1,6,3,2,4,5] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [7,1,6,2,3,4,5] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [7,1,5,6,4,3,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [7,1,5,6,4,2,3] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [7,1,5,6,3,4,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [7,1,5,6,3,2,4] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [7,1,5,6,2,3,4] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [7,1,5,4,6,3,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [7,1,5,4,6,2,3] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [7,1,5,4,3,6,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [7,1,5,4,3,2,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [7,1,5,4,2,3,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [7,1,5,3,4,6,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [7,1,5,3,4,2,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [7,1,5,3,2,4,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [7,1,5,2,3,4,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [7,1,4,5,6,3,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [7,1,4,5,6,2,3] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [7,1,4,5,3,6,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [7,1,4,5,3,2,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [7,1,4,5,2,3,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [7,1,4,3,5,6,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [7,1,4,3,5,2,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [7,1,4,3,2,5,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [7,1,4,2,3,5,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [7,1,3,4,5,6,2] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [7,1,3,4,5,2,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [7,1,3,4,2,5,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [7,1,3,2,4,5,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [7,1,2,3,4,5,6] => [7,1,6,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [7,6,1,5,4,3,2] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [7,6,1,5,4,2,3] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [7,6,1,5,3,4,2] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [7,6,1,5,3,2,4] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [7,6,1,5,2,3,4] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [7,6,1,4,5,3,2] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [7,6,1,4,5,2,3] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [7,6,1,4,3,5,2] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [7,6,1,4,3,2,5] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [7,6,1,4,2,3,5] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [7,6,1,3,4,5,2] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [7,6,1,3,4,2,5] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [7,6,1,3,2,4,5] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [7,6,1,2,3,4,5] => [7,6,1,5,4,3,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [7,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [7,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [7,6,4,5,1,3,2] => [7,6,4,5,1,3,2] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [7,6,4,5,1,2,3] => [7,6,4,5,1,3,2] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [7,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [7,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [7,6,4,5,2,3,1] => [7,6,4,5,2,3,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [7,6,4,3,5,2,1] => [7,6,4,3,5,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [7,6,3,4,5,2,1] => [7,6,3,5,4,2,1] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [7,5,6,4,3,1,2] => [7,5,6,4,3,1,2] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [7,5,6,4,3,2,1] => [7,5,6,4,3,2,1] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [7,5,6,4,2,3,1] => [7,5,6,4,2,3,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [7,5,6,3,4,1,2] => [7,5,6,3,4,1,2] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [7,5,6,3,4,2,1] => [7,5,6,3,4,2,1] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [7,5,4,6,3,2,1] => [7,5,4,6,3,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [7,5,4,3,6,2,1] => [7,5,4,3,6,2,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [7,5,4,3,2,6,1] => [7,5,4,3,2,6,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [7,4,5,6,3,2,1] => [7,4,6,5,3,2,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [7,4,3,5,6,2,1] => [7,4,3,6,5,2,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [7,4,3,2,5,6,1] => [7,4,3,2,6,5,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [7,3,4,5,6,1,2] => [7,3,6,5,4,1,2] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [7,3,4,5,6,2,1] => [7,3,6,5,4,2,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [7,3,2,4,5,6,1] => [7,3,2,6,5,4,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [7,2,3,4,5,6,1] => [7,2,6,5,4,3,1] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [6,7,1,5,4,3,2] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [6,7,1,5,4,2,3] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [6,7,1,5,3,4,2] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [6,7,1,5,3,2,4] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [6,7,1,5,2,3,4] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [6,7,1,4,5,3,2] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [6,7,1,4,5,2,3] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [6,7,1,4,3,5,2] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [6,7,1,4,3,2,5] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [6,7,1,4,2,3,5] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [6,7,1,3,4,5,2] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [6,7,1,3,4,2,5] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [6,7,1,3,2,4,5] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [6,7,1,2,3,4,5] => [6,7,1,5,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [6,7,5,1,4,3,2] => [6,7,5,1,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [6,7,5,1,4,2,3] => [6,7,5,1,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [6,7,5,1,3,4,2] => [6,7,5,1,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [6,7,5,1,3,2,4] => [6,7,5,1,4,3,2] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [6,7,5,1,2,3,4] => [6,7,5,1,4,3,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [6,7,5,4,3,1,2] => [6,7,5,4,3,1,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [6,7,5,4,2,3,1] => [6,7,5,4,2,3,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [6,7,5,3,4,1,2] => [6,7,5,3,4,1,2] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [6,7,5,3,4,2,1] => [6,7,5,3,4,2,1] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [6,7,4,5,1,3,2] => [6,7,4,5,1,3,2] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [6,7,4,5,1,2,3] => [6,7,4,5,1,3,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [6,7,4,5,3,1,2] => [6,7,4,5,3,1,2] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [6,7,4,5,3,2,1] => [6,7,4,5,3,2,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [6,7,4,5,2,3,1] => [6,7,4,5,2,3,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [6,7,4,3,5,2,1] => [6,7,4,3,5,2,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [6,7,4,3,2,5,1] => [6,7,4,3,2,5,1] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [6,7,3,4,5,2,1] => [6,7,3,5,4,2,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [6,7,3,2,4,5,1] => [6,7,3,2,5,4,1] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [6,7,2,3,4,5,1] => [6,7,2,5,4,3,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [6,4,5,7,3,1,2] => [6,4,7,5,3,1,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [6,4,5,7,3,2,1] => [6,4,7,5,3,2,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [6,4,5,7,2,3,1] => [6,4,7,5,2,3,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [6,4,5,3,7,2,1] => [6,4,7,3,5,2,1] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [6,4,5,3,2,7,1] => [6,4,7,3,2,5,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [6,4,2,3,5,7,1] => [6,4,2,7,5,3,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [6,3,4,5,7,2,1] => [6,3,7,5,4,2,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [5,6,7,4,3,2,1] => [5,7,6,4,3,2,1] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [5,6,7,3,4,1,2] => [5,7,6,3,4,1,2] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [5,6,4,7,3,1,2] => [5,7,4,6,3,1,2] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [5,6,4,3,7,2,1] => [5,7,4,3,6,2,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [5,6,3,4,7,2,1] => [5,7,3,6,4,2,1] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [5,6,2,3,4,7,1] => [5,7,2,6,4,3,1] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [5,4,6,7,3,2,1] => [5,4,7,6,3,2,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [5,4,6,3,7,1,2] => [5,4,7,3,6,1,2] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [5,4,6,3,7,2,1] => [5,4,7,3,6,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [5,4,3,6,7,2,1] => [5,4,3,7,6,2,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [5,4,3,2,6,7,1] => [5,4,3,2,7,6,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [5,3,4,6,7,1,2] => [5,3,7,6,4,1,2] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [5,3,4,6,7,2,1] => [5,3,7,6,4,2,1] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [4,5,6,7,3,2,1] => [4,7,6,5,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [4,3,5,6,7,2,1] => [4,3,7,6,5,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [4,3,2,5,6,7,1] => [4,3,2,7,6,5,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [4,2,3,5,6,7,1] => [4,2,7,6,5,3,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [3,4,5,6,7,2,1] => [3,7,6,5,4,2,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [3,2,4,5,6,7,1] => [3,2,7,6,5,4,1] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [2,7,6,5,4,3,1] => 0
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Description
The number of global ascents of a permutation.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].