Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => [1,2] => 0
[1,1,0,0] => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [2,3,1] => [3,2,1] => [1,3,2] => 0
[1,0,1,1,0,0] => [2,1,3] => [2,1,3] => [1,2,3] => 1
[1,1,0,0,1,0] => [1,3,2] => [1,3,2] => [1,2,3] => 1
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => [1,3,2] => 0
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => 1
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [4,2,3,1] => [1,4,2,3] => 1
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [3,2,1,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,1,4,3] => [1,2,3,4] => 2
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [4,2,1,3] => [1,4,3,2] => 0
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [1,2,3,4] => 2
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [1,4,3,2] => [1,2,4,3] => 1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [1,3,2,4] => [1,2,3,4] => 2
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [4,1,3,2] => [1,4,2,3] => 1
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4,3,2,1] => [1,4,2,3] => 1
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,2,4] => [1,3,2,4] => 1
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [1,2,4,3] => [1,2,3,4] => 2
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => [1,2,4,3] => 1
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => [1,4,3,2] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 2
[1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => [5,2,3,4,1] => [1,5,2,3,4] => 2
[1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => 2
[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => 2
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [2,1,5,4,3] => [1,2,3,5,4] => 2
[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 3
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [5,2,1,4,3] => [1,5,3,2,4] => 1
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [5,2,4,3,1] => [1,5,2,3,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => 1
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => 3
[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [2,1,5,3,4] => [1,2,3,5,4] => 2
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => [1,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => [1,5,3,4,2] => [1,2,5,3,4] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => 3
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => 3
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [5,1,3,4,2] => [1,5,2,3,4] => 2
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [4,1,3,2,5] => [1,4,2,3,5] => 2
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [5,3,2,4,1] => [1,5,2,3,4] => 2
[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => 2
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,1,2,5,4] => [1,3,2,4,5] => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [5,1,3,2,4] => [1,5,4,2,3] => 1
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [5,3,2,1,4] => [1,5,4,2,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,3,5,4] => 2
[1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,3,4,5] => 3
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [1,5,2,4,3] => [1,2,5,3,4] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,5,4,3,2] => [1,2,5,3,4] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => [1,2,4,3,5] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [5,1,2,4,3] => [1,5,3,2,4] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [5,1,4,3,2] => [1,5,2,3,4] => 2
[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [5,4,2,3,1] => [1,5,2,4,3] => 1
[1,1,1,0,1,1,0,0,0,0] => [4,1,2,3,5] => [4,1,2,3,5] => [1,4,3,2,5] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,4,5] => 3
[1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => [1,2,3,5,4] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => [1,2,5,4,3] => 1
[1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => [5,1,2,3,4] => [1,5,4,3,2] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [1,6,2,3,4,5] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [1,5,2,3,4,6] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [1,4,2,3,5,6] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => [1,6,5,2,3,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [1,4,2,3,5,6] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [6,2,3,1,5,4] => [1,6,4,2,3,5] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [6,2,3,5,4,1] => [1,6,2,3,4,5] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => [1,5,4,2,3,6] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => [1,3,2,4,6,5] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => [1,6,5,4,2,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [1,2,3,6,4,5] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => [1,2,3,6,5,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [6,2,1,4,5,3] => [1,6,3,2,4,5] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [5,2,1,4,3,6] => [1,5,3,2,4,6] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [6,2,4,3,5,1] => [1,6,2,3,4,5] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [6,2,5,4,3,1] => [1,6,2,3,5,4] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [5,2,4,3,1,6] => [1,5,2,3,4,6] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => [1,4,3,2,5,6] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [6,2,1,4,3,5] => [1,6,5,3,2,4] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [6,2,4,3,1,5] => [1,6,5,2,3,4] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [1,4,3,2,5,6] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [2,1,6,3,5,4] => [1,2,3,6,4,5] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => [1,2,3,5,4,6] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [6,2,1,3,5,4] => [1,6,4,3,2,5] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [6,2,1,5,4,3] => [1,6,3,2,4,5] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [6,2,5,3,4,1] => [1,6,2,3,5,4] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [1,5,4,3,2,6] => 1
>>> Load all 757 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => [1,2,3,4,6,5] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => [1,2,3,6,5,4] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [1,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,2,6,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,2,5,3,4,6] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => [1,2,6,5,3,4] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [1,6,3,2,5,4] => [1,2,6,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [1,6,3,5,4,2] => [1,2,6,3,4,5] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => [1,2,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => [1,2,3,4,6,5] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => [1,2,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [6,1,3,4,5,2] => [1,6,2,3,4,5] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [5,1,3,4,2,6] => [1,5,2,3,4,6] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [4,1,3,2,6,5] => [1,4,2,3,5,6] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [6,1,3,4,2,5] => [1,6,5,2,3,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,1,3,2,5,6] => [1,4,2,3,5,6] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [6,3,2,4,5,1] => [1,6,2,3,4,5] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [5,3,2,4,1,6] => [1,5,2,3,4,6] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [6,4,3,2,5,1] => [1,6,2,4,3,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [6,5,3,4,2,1] => [1,6,2,5,3,4] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [6,3,2,4,1,5] => [1,6,5,2,3,4] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [6,4,3,2,1,5] => [1,6,5,2,4,3] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => [1,3,2,4,6,5] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => [1,3,2,4,5,6] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [6,1,3,2,5,4] => [1,6,4,2,3,5] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [6,1,3,5,4,2] => [1,6,2,3,4,5] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [5,1,3,2,4,6] => [1,5,4,2,3,6] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [6,3,2,1,5,4] => [1,6,4,2,3,5] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [6,3,2,5,4,1] => [1,6,2,3,4,5] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [6,5,3,2,4,1] => [1,6,2,5,4,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [5,3,2,1,4,6] => [1,5,4,2,3,6] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => [1,3,2,4,5,6] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => [1,3,2,4,6,5] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => [6,1,3,2,4,5] => [1,6,5,4,2,3] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => [6,3,2,1,4,5] => [1,6,5,4,2,3] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,3,6,4,5] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => [1,2,3,6,5,4] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => [1,6,2,4,5,3] => [1,2,6,3,4,5] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => [1,5,2,4,3,6] => [1,2,5,3,4,6] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => [1,6,4,3,5,2] => [1,2,6,3,4,5] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => [1,2,4,3,5,6] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => [1,6,2,4,3,5] => [1,2,6,5,3,4] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => [1,6,4,3,2,5] => [1,2,6,5,3,4] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => [1,2,4,3,5,6] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => [6,1,2,4,5,3] => [1,6,3,2,4,5] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => [5,1,2,4,3,6] => [1,5,3,2,4,6] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => [6,1,4,3,5,2] => [1,6,2,3,4,5] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => [6,1,5,4,3,2] => [1,6,2,3,5,4] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => [5,1,4,3,2,6] => [1,5,2,3,4,6] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => [6,4,2,3,5,1] => [1,6,2,4,3,5] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => [6,5,2,4,3,1] => [1,6,2,5,3,4] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,1,2,3,6] => [5,4,2,3,1,6] => [1,5,2,4,3,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => [1,4,3,2,5,6] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => [6,1,2,4,3,5] => [1,6,5,3,2,4] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => [6,1,4,3,2,5] => [1,6,5,2,3,4] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => [6,4,2,3,1,5] => [1,6,5,2,4,3] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [1,4,3,2,5,6] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => [1,2,6,3,5,4] => [1,2,3,6,4,5] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => [1,2,3,5,4,6] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => [1,6,2,3,5,4] => [1,2,6,4,3,5] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => [1,6,2,5,4,3] => [1,2,6,3,4,5] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,6,2,3,4] => [1,6,5,3,4,2] => [1,2,6,3,5,4] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => [1,2,5,4,3,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => [6,1,2,3,5,4] => [1,6,4,3,2,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => [6,1,2,5,4,3] => [1,6,3,2,4,5] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => [6,1,5,3,4,2] => [1,6,2,3,5,4] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [5,6,1,2,3,4] => [6,5,2,3,4,1] => [1,6,2,5,4,3] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [1,5,4,3,2,6] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => [1,2,3,4,6,5] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => [1,2,3,6,5,4] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,2,6,5,4,3] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,6,1] => [1,7,2,3,4,5,6] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,7,5] => [4,2,3,1,7,6,5] => [1,4,2,3,5,7,6] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,7] => [4,2,3,1,6,5,7] => [1,4,2,3,5,6,7] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => [7,2,3,4,6,5,1] => [1,7,2,3,4,5,6] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,1,5,7,6] => [4,2,3,1,5,7,6] => [1,4,2,3,5,6,7] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,5,6] => [4,2,3,1,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,1,5,6,7] => [4,2,3,1,5,6,7] => [1,4,2,3,5,6,7] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,6,7,4] => [3,2,1,7,5,6,4] => [1,3,2,4,7,5,6] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,1,5,6,4,7] => [3,2,1,6,5,4,7] => [1,3,2,4,6,5,7] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6] => [3,2,1,5,4,7,6] => [1,3,2,4,5,6,7] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,3,1,5,7,4,6] => [3,2,1,7,5,4,6] => [1,3,2,4,7,6,5] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [1,3,2,4,5,6,7] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => [7,2,3,5,4,6,1] => [1,7,2,3,4,5,6] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [1,3,2,4,5,7,6] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [1,3,2,4,5,6,7] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,4,7,5] => [3,2,1,7,4,6,5] => [1,3,2,4,7,5,6] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,7,4,5] => [3,2,1,7,6,5,4] => [1,3,2,4,7,5,6] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,4,5,7] => [3,2,1,6,4,5,7] => [1,3,2,4,6,5,7] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [1,3,2,4,5,6,7] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6] => [1,3,2,4,5,7,6] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,4,5,6] => [3,2,1,7,4,5,6] => [1,3,2,4,7,6,5] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [1,3,2,4,5,6,7] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,3] => [2,1,7,4,5,6,3] => [1,2,3,7,4,5,6] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,5,6,3,7] => [2,1,6,4,5,3,7] => [1,2,3,6,4,5,7] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3,7,6] => [2,1,5,4,3,7,6] => [1,2,3,5,4,6,7] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,5,7,3,6] => [2,1,7,4,5,3,6] => [1,2,3,7,6,4,5] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,5,3,6,7] => [2,1,5,4,3,6,7] => [1,2,3,5,4,6,7] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [2,1,7,4,3,6,5] => [1,2,3,7,5,4,6] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,6,7,3,5] => [2,1,7,4,6,5,3] => [1,2,3,7,4,5,6] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5,7] => [2,1,6,4,3,5,7] => [1,2,3,6,5,4,7] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,6] => [2,1,4,3,7,5,6] => [1,2,3,4,5,7,6] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,7,3,5,6] => [2,1,7,4,3,5,6] => [1,2,3,7,6,5,4] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => [7,2,4,3,5,6,1] => [1,7,2,3,4,5,6] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,6,7,5] => [4,2,1,3,7,6,5] => [1,4,3,2,5,7,6] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5,7] => [4,2,1,3,6,5,7] => [1,4,3,2,5,6,7] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,6,1,7,3,5] => [7,2,4,3,6,5,1] => [1,7,2,3,4,5,6] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,4,1,3,5,7,6] => [4,2,1,3,5,7,6] => [1,4,3,2,5,6,7] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,4,1,3,7,5,6] => [4,2,1,3,7,5,6] => [1,4,3,2,5,7,6] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => [1,4,3,2,5,6,7] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,3,5,6,7,4] => [2,1,3,7,5,6,4] => [1,2,3,4,7,5,6] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,3,5,6,4,7] => [2,1,3,6,5,4,7] => [1,2,3,4,6,5,7] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,3,5,7,4,6] => [2,1,3,7,5,4,6] => [1,2,3,4,7,6,5] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [2,1,7,3,5,6,4] => [1,2,3,7,4,5,6] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,7] => [2,1,6,3,5,4,7] => [1,2,3,6,4,5,7] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [2,1,7,5,4,6,3] => [1,2,3,7,4,5,6] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,6,7,3,4] => [2,1,7,6,5,4,3] => [1,2,3,7,4,6,5] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,6,3,4,7] => [2,1,6,5,4,3,7] => [1,2,3,6,4,5,7] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,5,3,4,7,6] => [2,1,5,3,4,7,6] => [1,2,3,5,4,6,7] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,6] => [2,1,7,3,5,4,6] => [1,2,3,7,6,4,5] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,7,3,4,6] => [2,1,7,5,4,3,6] => [1,2,3,7,6,4,5] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7] => [1,2,3,5,4,6,7] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,4,6,7,5] => [2,1,3,4,7,6,5] => [1,2,3,4,5,7,6] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [2,1,3,7,4,6,5] => [1,2,3,4,7,5,6] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,6,7,4,5] => [2,1,3,7,6,5,4] => [1,2,3,4,7,5,6] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7] => [1,2,3,4,6,5,7] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,6,3,4,7,5] => [2,1,7,3,4,6,5] => [1,2,3,7,5,4,6] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,5] => [2,1,7,3,6,5,4] => [1,2,3,7,4,5,6] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,7,3,4,5] => [2,1,7,6,4,5,3] => [1,2,3,7,4,6,5] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => [1,2,3,6,5,4,7] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [1,2,3,4,5,6,7] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => [2,1,3,4,7,5,6] => [1,2,3,4,5,7,6] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => [2,1,3,7,4,5,6] => [1,2,3,4,7,6,5] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => [1,2,3,7,6,5,4] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => [1,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [1,2,3,4,5,6,7] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,2,7,3,4,5,6] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,2,6,3,4,5,7] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,2,5,3,4,6,7] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,4,5,7,2,6] => [1,7,3,4,5,2,6] => [1,2,7,6,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,2,5,3,4,6,7] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,2,4,3,5,7,6] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,2,4,3,5,6,7] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,4,6,2,7,5] => [1,7,3,4,2,6,5] => [1,2,7,5,3,4,6] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,4,6,7,2,5] => [1,7,3,4,6,5,2] => [1,2,7,3,4,5,6] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,4,6,2,5,7] => [1,6,3,4,2,5,7] => [1,2,6,5,3,4,7] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,2,4,3,5,6,7] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,5,6] => [1,4,3,2,7,5,6] => [1,2,4,3,5,7,6] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,7,2,5,6] => [1,7,3,4,2,5,6] => [1,2,7,6,5,3,4] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,2,4,3,5,6,7] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,2,3,4,7,5,6] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,2,3,4,6,5,7] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,2,3,4,5,6,7] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,5,4,6] => [1,2,3,4,7,6,5] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,2,3,4,5,6,7] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,5,2,6,7,4] => [1,7,3,2,5,6,4] => [1,2,7,4,3,5,6] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,5,2,6,4,7] => [1,6,3,2,5,4,7] => [1,2,6,4,3,5,7] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,5,6,2,7,4] => [1,7,3,5,4,6,2] => [1,2,7,3,4,5,6] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5,6,7,2,4] => [1,7,3,6,5,4,2] => [1,2,7,3,4,6,5] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,5,6,2,4,7] => [1,6,3,5,4,2,7] => [1,2,6,3,4,5,7] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,7,6] => [1,5,3,2,4,7,6] => [1,2,5,4,3,6,7] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,7,4,6] => [1,7,3,2,5,4,6] => [1,2,7,6,4,3,5] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,7,2,4,6] => [1,7,3,5,4,2,6] => [1,2,7,6,3,4,5] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,5,2,4,6,7] => [1,5,3,2,4,6,7] => [1,2,5,4,3,6,7] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,2,3,4,5,7,6] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,2,3,4,5,6,7] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5] => [1,3,2,7,4,6,5] => [1,2,3,4,7,5,6] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,7,6,5,4] => [1,2,3,4,7,5,6] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,4,5,7] => [1,2,3,4,6,5,7] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,6,2,4,7,5] => [1,7,3,2,4,6,5] => [1,2,7,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,6,2,7,4,5] => [1,7,3,2,6,5,4] => [1,2,7,4,3,5,6] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,6,7,2,4,5] => [1,7,3,6,4,5,2] => [1,2,7,3,4,6,5] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,6,2,4,5,7] => [1,6,3,2,4,5,7] => [1,2,6,5,4,3,7] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,2,3,4,5,6,7] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,5,6] => [1,2,3,4,5,7,6] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,4,5,6] => [1,2,3,4,7,6,5] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,7,2,4,5,6] => [1,7,3,2,4,5,6] => [1,2,7,6,5,4,3] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,2,3,4,5,6,7] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,2] => [7,1,3,4,5,6,2] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [4,1,3,2,7,6,5] => [1,4,2,3,5,7,6] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,7] => [4,1,3,2,6,5,7] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,4,6,7,2,5] => [7,1,3,4,6,5,2] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,2,5,7,6] => [4,1,3,2,5,7,6] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,6] => [4,1,3,2,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4,2,5,6,7] => [4,1,3,2,5,6,7] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,1,5,6,7,2] => [7,3,2,4,5,6,1] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,4,1,2,6,7,5] => [4,3,2,1,7,6,5] => [1,4,2,3,5,7,6] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5,7] => [4,3,2,1,6,5,7] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,1,6,7,2,5] => [7,3,2,4,6,5,1] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,1,2,5,7,6] => [4,3,2,1,5,7,6] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [3,4,1,2,7,5,6] => [4,3,2,1,7,5,6] => [1,4,2,3,5,7,6] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [4,3,2,1,5,6,7] => [1,4,2,3,5,6,7] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,5,6,7,4] => [3,1,2,7,5,6,4] => [1,3,2,4,7,5,6] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,5,6,4,7] => [3,1,2,6,5,4,7] => [1,3,2,4,6,5,7] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,7,6] => [3,1,2,5,4,7,6] => [1,3,2,4,5,6,7] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,7,4,6] => [3,1,2,7,5,4,6] => [1,3,2,4,7,6,5] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6,7] => [1,3,2,4,5,6,7] => 4
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [7,1,3,5,4,6,2] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1,6,2,7,4] => [7,3,2,5,4,6,1] => [1,7,2,3,4,5,6] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,2,4,6,7,5] => [3,1,2,4,7,6,5] => [1,3,2,4,5,7,6] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5,7] => [1,3,2,4,5,6,7] => 4
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [3,1,2,7,4,6,5] => [1,3,2,4,7,5,6] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,1,2,6,7,4,5] => [3,1,2,7,6,5,4] => [1,3,2,4,7,5,6] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5,7] => [1,3,2,4,6,5,7] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [3,1,2,4,5,7,6] => [1,3,2,4,5,6,7] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [3,1,2,4,7,5,6] => [3,1,2,4,7,5,6] => [1,3,2,4,5,7,6] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [3,1,2,7,4,5,6] => [3,1,2,7,4,5,6] => [1,3,2,4,7,6,5] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,3,7,4,5,6] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,3,6,4,5,7] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,3,5,4,6,7] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,2,4,5,7,3,6] => [1,2,7,4,5,3,6] => [1,2,3,7,6,4,5] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,3,5,4,6,7] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,3,4,5,7,6] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,3,4,5,6,7] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,2,4,6,3,7,5] => [1,2,7,4,3,6,5] => [1,2,3,7,5,4,6] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,4,6,7,3,5] => [1,2,7,4,6,5,3] => [1,2,3,7,4,5,6] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,4,3,5,7] => [1,2,3,6,5,4,7] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,3,4,5,6,7] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,5,6] => [1,2,3,4,5,7,6] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,4,3,5,6] => [1,2,3,7,6,5,4] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,3,4,5,6,7] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,6,7,3] => [1,7,2,4,5,6,3] => [1,2,7,3,4,5,6] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,2,5,6,3,7] => [1,6,2,4,5,3,7] => [1,2,6,3,4,5,7] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6] => [1,5,2,4,3,7,6] => [1,2,5,3,4,6,7] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,2,5,7,3,6] => [1,7,2,4,5,3,6] => [1,2,7,6,3,4,5] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,6,7] => [1,5,2,4,3,6,7] => [1,2,5,3,4,6,7] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,5,2,6,7,3] => [1,7,4,3,5,6,2] => [1,2,7,3,4,5,6] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,4,5,2,6,3,7] => [1,6,4,3,5,2,7] => [1,2,6,3,4,5,7] => 4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,5,6,2,7,3] => [1,7,5,4,3,6,2] => [1,2,7,3,5,4,6] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,5,6,7,2,3] => [1,7,6,4,5,3,2] => [1,2,7,3,6,4,5] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,6,2,3,7] => [1,6,5,4,3,2,7] => [1,2,6,3,5,4,7] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,5,2,3,7,6] => [1,5,4,3,2,7,6] => [1,2,5,3,4,6,7] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,5,2,7,3,6] => [1,7,4,3,5,2,6] => [1,2,7,6,3,4,5] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,7,2,3,6] => [1,7,5,4,3,2,6] => [1,2,7,6,3,5,4] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,2,3,6,7] => [1,5,4,3,2,6,7] => [1,2,5,3,4,6,7] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,3,6,7,5] => [1,4,2,3,7,6,5] => [1,2,4,3,5,7,6] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5,7] => [1,2,4,3,5,6,7] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5] => [1,7,2,4,3,6,5] => [1,2,7,5,3,4,6] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,7,3,5] => [1,7,2,4,6,5,3] => [1,2,7,3,4,5,6] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5,7] => [1,6,2,4,3,5,7] => [1,2,6,5,3,4,7] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,6,2,3,7,5] => [1,7,4,3,2,6,5] => [1,2,7,5,3,4,6] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,6,2,7,3,5] => [1,7,4,3,6,5,2] => [1,2,7,3,4,5,6] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,7,2,3,5] => [1,7,6,4,3,5,2] => [1,2,7,3,6,5,4] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5,7] => [1,6,4,3,2,5,7] => [1,2,6,5,3,4,7] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,3,5,7,6] => [1,4,2,3,5,7,6] => [1,2,4,3,5,6,7] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,2,3,7,5,6] => [1,2,4,3,5,7,6] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,5,6] => [1,7,2,4,3,5,6] => [1,2,7,6,5,3,4] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,7,2,3,5,6] => [1,7,4,3,2,5,6] => [1,2,7,6,5,3,4] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => [1,2,4,3,5,6,7] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [7,1,4,3,5,6,2] => [1,7,2,3,4,5,6] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,6,7,5] => [4,1,2,3,7,6,5] => [1,4,3,2,5,7,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5,7] => [1,4,3,2,5,6,7] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,5] => [7,1,4,3,6,5,2] => [1,7,2,3,4,5,6] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => [1,4,3,2,5,6,7] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [4,1,2,3,7,5,6] => [4,1,2,3,7,5,6] => [1,4,3,2,5,7,6] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => [1,4,3,2,5,6,7] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,4,7,5,6] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,4,6,5,7] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,4,5,6,7] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,5,4,6] => [1,2,3,4,7,6,5] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,4,5,6,7] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,2,5,3,6,7,4] => [1,2,7,3,5,6,4] => [1,2,3,7,4,5,6] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,5,3,6,4,7] => [1,2,6,3,5,4,7] => [1,2,3,6,4,5,7] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,5,6,3,7,4] => [1,2,7,5,4,6,3] => [1,2,3,7,4,5,6] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,2,5,6,7,3,4] => [1,2,7,6,5,4,3] => [1,2,3,7,4,6,5] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,2,3,6,4,5,7] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,2,5,3,4,7,6] => [1,2,5,3,4,7,6] => [1,2,3,5,4,6,7] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,2,5,3,7,4,6] => [1,2,7,3,5,4,6] => [1,2,3,7,6,4,5] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,2,5,7,3,4,6] => [1,2,7,5,4,3,6] => [1,2,3,7,6,4,5] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => [1,2,3,5,4,6,7] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,3,6,7,4] => [1,7,2,3,5,6,4] => [1,2,7,4,3,5,6] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2,3,6,4,7] => [1,6,2,3,5,4,7] => [1,2,6,4,3,5,7] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4] => [1,7,2,5,4,6,3] => [1,2,7,3,4,5,6] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,7,3,4] => [1,7,2,6,5,4,3] => [1,2,7,3,4,6,5] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,4,7] => [1,6,2,5,4,3,7] => [1,2,6,3,4,5,7] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,6,2,3,7,4] => [1,7,5,3,4,6,2] => [1,2,7,3,5,4,6] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,6,2,7,3,4] => [1,7,6,3,5,4,2] => [1,2,7,3,6,4,5] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,6,7,2,3,4] => [1,7,6,5,4,3,2] => [1,2,7,3,6,4,5] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,6,2,3,4,7] => [1,6,5,3,4,2,7] => [1,2,6,3,5,4,7] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => [1,5,2,3,4,7,6] => [1,2,5,4,3,6,7] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,7,2,3,5,4,6] => [1,2,7,6,4,3,5] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,4,6] => [1,7,2,5,4,3,6] => [1,2,7,6,3,4,5] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,7,2,3,4,6] => [1,7,5,3,4,2,6] => [1,2,7,6,3,5,4] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6,7] => [1,2,5,4,3,6,7] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,5,7,6] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,5,6,7] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => [1,2,3,7,4,6,5] => [1,2,3,4,7,5,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,2,3,4,7,5,6] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5,7] => [1,2,3,4,6,5,7] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => [1,2,7,3,4,6,5] => [1,2,3,7,5,4,6] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,2,6,3,7,4,5] => [1,2,7,3,6,5,4] => [1,2,3,7,4,5,6] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,6,4,5,3] => [1,2,3,7,4,6,5] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => [1,2,3,6,5,4,7] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => [1,7,2,3,4,6,5] => [1,2,7,5,4,3,6] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,7,2,3,6,5,4] => [1,2,7,4,3,5,6] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,4,5] => [1,7,2,6,4,5,3] => [1,2,7,3,4,6,5] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,7,2,3,4,5] => [1,7,6,3,4,5,2] => [1,2,7,3,6,5,4] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5,7] => [1,2,6,5,4,3,7] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6,7] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => [1,2,3,4,5,7,6] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => [1,2,3,4,7,6,5] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => [1,2,3,7,6,5,4] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => [1,2,7,6,5,4,3] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => [1,7,2,3,4,5,6,8] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => [1,6,2,3,4,5,7,8] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,5,7,8,1,6] => [8,2,3,4,5,7,6,1] => [1,8,2,3,4,5,6,7] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => [1,5,2,3,4,6,7,8] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => [1,5,2,3,4,6,7,8] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => [1,4,2,3,5,8,6,7] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => [1,4,2,3,5,7,6,8] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => [1,4,2,3,5,6,7,8] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => [1,4,2,3,5,6,7,8] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,4,6,7,1,5,8] => [7,2,3,4,6,5,1,8] => [1,7,2,3,4,5,6,8] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => [1,4,2,3,5,6,7,8] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,3,4,1,7,5,8,6] => [4,2,3,1,8,5,7,6] => [1,4,2,3,5,8,6,7] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,4,1,7,8,5,6] => [4,2,3,1,8,7,6,5] => [1,4,2,3,5,8,6,7] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => [1,4,2,3,5,6,7,8] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => [1,3,2,4,5,6,7,8] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => [1,3,2,4,5,6,7,8] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,5,6,1,7,8,4] => [8,2,3,5,4,6,7,1] => [1,8,2,3,4,5,6,7] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,5,6,1,7,4,8] => [7,2,3,5,4,6,1,8] => [1,7,2,3,4,5,6,8] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,5,6,7,1,8,4] => [8,2,3,6,5,4,7,1] => [1,8,2,3,4,6,5,7] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,8,1,4] => [8,2,3,7,5,6,4,1] => [1,8,2,3,4,7,5,6] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,6,7,1,4,8] => [7,2,3,6,5,4,1,8] => [1,7,2,3,4,6,5,8] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,6,1,4,8,7] => [6,2,3,5,4,1,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [6,2,3,5,4,1,7,8] => [1,6,2,3,4,5,7,8] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,7,1,8,4,6] => [8,2,3,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => [1,3,2,4,5,8,6,7] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => [1,3,2,4,5,7,6,8] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,6,7,8,1,4,5] => [8,2,3,7,6,5,4,1] => [1,8,2,3,4,7,5,6] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => [1,3,2,4,5,6,7,8] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,4,7,8,5,6] => [3,2,1,4,8,7,6,5] => [1,3,2,4,5,8,6,7] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => [1,3,2,4,5,6,7,8] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,8,1,4,5,6,7] => [8,2,3,1,4,5,6,7] => [1,8,7,6,5,4,2,3] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => [1,2,3,6,4,5,7,8] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4,5,7,8,3,6] => [2,1,8,4,5,7,6,3] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => [1,2,3,5,4,6,7,8] => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => [1,2,3,5,4,6,7,8] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,6,7,3,8,5] => [2,1,8,4,6,5,7,3] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,3,7,5,8,6] => [2,1,4,3,8,5,7,6] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,3,5,8,6,7] => [2,1,4,3,5,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,4,5,1,6,3,8,7] => [6,2,4,3,5,1,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,4,5,1,3,7,6,8] => [5,2,4,3,1,7,6,8] => [1,5,2,3,4,6,7,8] => 5
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,1,3,6,7,8] => [5,2,4,3,1,6,7,8] => [1,5,2,3,4,6,7,8] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,6,1,7,3,8,5] => [8,2,4,3,6,5,7,1] => [1,8,2,3,4,5,6,7] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,7,8,4] => [2,1,8,3,5,6,7,4] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,1,5,3,6,4,8,7] => [2,1,6,3,5,4,8,7] => [1,2,3,6,4,5,7,8] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,5,6,3,7,8,4] => [2,1,8,5,4,6,7,3] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,5,6,7,3,8,4] => [2,1,8,6,5,4,7,3] => [1,2,3,8,4,6,5,7] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,5,6,7,8,3,4] => [2,1,8,7,5,6,4,3] => [1,2,3,8,4,7,5,6] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,5,6,7,3,4,8] => [2,1,7,6,5,4,3,8] => [1,2,3,7,4,6,5,8] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => [1,2,3,6,4,5,7,8] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,5,3,7,8,4,6] => [2,1,8,3,5,7,6,4] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,5,7,3,8,4,6] => [2,1,8,5,4,7,6,3] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,1,5,3,4,6,8,7] => [2,1,5,3,4,6,8,7] => [1,2,3,5,4,6,7,8] => 5
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,5,3,4,6,7,8] => [2,1,5,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,1,6,3,7,4,8,5] => [2,1,8,3,6,5,7,4] => [1,2,3,8,4,5,6,7] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,6,7,3,4,8,5] => [2,1,8,6,4,5,7,3] => [1,2,3,8,4,6,5,7] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,1,6,7,3,8,4,5] => [2,1,8,7,4,6,5,3] => [1,2,3,8,4,7,5,6] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => [1,2,3,8,4,7,5,6] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,1,3,4,7,8,5] => [8,2,1,3,4,6,7,5] => [1,8,5,4,3,2,6,7] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,4,7,5,8,6] => [2,1,3,4,8,5,7,6] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,1,3,4,7,8,5,6] => [2,1,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,3,4,7,5,6,8] => [2,1,3,4,7,5,6,8] => [1,2,3,4,5,7,6,8] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,3,4,5,8,6,7] => [2,1,3,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,3,4,5,2,6,7] => [1,2,8,7,6,3,4,5] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,2,4,6,7,5,8] => [1,3,2,4,7,6,5,8] => [1,2,3,4,5,7,6,8] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,4,6,5,8,7] => [1,3,2,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,8,5,7,6] => [1,2,3,4,5,8,6,7] => 5
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,4,7,8,5,6] => [1,3,2,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,2] => [8,1,3,4,5,6,7,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,4,5,6,7,2,8] => [7,1,3,4,5,6,2,8] => [1,7,2,3,4,5,6,8] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6,8] => [5,1,3,4,2,7,6,8] => [1,5,2,3,4,6,7,8] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4,5,7,8,2,6] => [8,1,3,4,5,7,6,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,2,6,7,8] => [5,1,3,4,2,6,7,8] => [1,5,2,3,4,6,7,8] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,6,7,8,5] => [4,1,3,2,8,6,7,5] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,7,5,8,6] => [4,1,3,2,8,5,7,6] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,1,4,2,7,8,5,6] => [4,1,3,2,8,7,6,5] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,2] => [8,3,2,4,5,6,7,1] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,5,2,7,6,8] => [5,3,2,4,1,7,6,8] => [1,5,2,3,4,6,7,8] => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4,1,5,2,6,7,8] => [5,3,2,4,1,6,7,8] => [1,5,2,3,4,6,7,8] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,4,5,1,6,7,8,2] => [8,4,3,2,5,6,7,1] => [1,8,2,4,3,5,6,7] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,4,5,1,6,2,8,7] => [6,4,3,2,5,1,8,7] => [1,6,2,4,3,5,7,8] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,4,5,1,6,2,7,8] => [6,4,3,2,5,1,7,8] => [1,6,2,4,3,5,7,8] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,4,5,6,1,7,8,2] => [8,5,3,4,2,6,7,1] => [1,8,2,5,3,4,6,7] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,4,5,6,1,7,2,8] => [7,5,3,4,2,6,1,8] => [1,7,2,5,3,4,6,8] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,6,7,1,8,2] => [8,6,3,4,5,2,7,1] => [1,8,2,6,3,4,5,7] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,7,8,1,2] => [8,7,3,4,5,6,2,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,6,7,1,2,8] => [7,6,3,4,5,2,1,8] => [1,7,2,6,3,4,5,8] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,4,5,6,1,2,8,7] => [6,5,3,4,2,1,8,7] => [1,6,2,5,3,4,7,8] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,5,3,4,2,1,7,8] => [1,6,2,5,3,4,7,8] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,4,5,1,7,8,2,6] => [8,4,3,2,5,7,6,1] => [1,8,2,4,3,5,6,7] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [3,4,5,7,1,8,2,6] => [8,5,3,4,2,7,6,1] => [1,8,2,5,3,4,6,7] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,4,5,1,2,6,8,7] => [5,4,3,2,1,6,8,7] => [1,5,2,4,3,6,7,8] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [5,4,3,2,1,6,7,8] => [1,5,2,4,3,6,7,8] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,6,7,8,5] => [4,3,2,1,8,6,7,5] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,4,1,2,6,7,5,8] => [4,3,2,1,7,6,5,8] => [1,4,2,3,5,7,6,8] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,4,1,2,6,5,8,7] => [4,3,2,1,6,5,8,7] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,4,1,2,6,5,7,8] => [4,3,2,1,6,5,7,8] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,4,1,6,7,2,8,5] => [8,3,2,4,6,5,7,1] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,4,6,1,7,2,8,5] => [8,4,3,2,6,5,7,1] => [1,8,2,4,3,5,6,7] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,4,6,7,8,1,2,5] => [8,7,3,4,6,5,2,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,7,6,8] => [4,3,2,1,5,7,6,8] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,4,1,2,7,5,8,6] => [4,3,2,1,8,5,7,6] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => [1,4,2,3,5,8,6,7] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [3,4,1,2,7,5,6,8] => [4,3,2,1,7,5,6,8] => [1,4,2,3,5,7,6,8] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1,2,5,6,8,7] => [4,3,2,1,5,6,8,7] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [4,3,2,1,5,6,7,8] => [1,4,2,3,5,6,7,8] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [1,3,2,4,5,6,7,8] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,2,5,4,6,8,7] => [3,1,2,5,4,6,8,7] => [1,3,2,4,5,6,7,8] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,5,6,7,8,2,4] => [8,1,3,7,5,6,4,2] => [1,8,2,3,4,7,5,6] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,5,6,2,4,8,7] => [6,1,3,5,4,2,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,5,6,2,4,7,8] => [6,1,3,5,4,2,7,8] => [1,6,2,3,4,5,7,8] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,5,7,2,8,4,6] => [8,1,3,5,4,7,6,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,5,1,6,2,7,4,8] => [7,3,2,5,4,6,1,8] => [1,7,2,3,4,5,6,8] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,5,1,6,7,8,2,4] => [8,3,2,7,5,6,4,1] => [1,8,2,3,4,7,5,6] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,5,1,6,2,4,8,7] => [6,3,2,5,4,1,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,5,1,6,2,4,7,8] => [6,3,2,5,4,1,7,8] => [1,6,2,3,4,5,7,8] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,5,6,7,1,2,8,4] => [8,6,3,5,4,2,7,1] => [1,8,2,6,3,4,5,7] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,5,6,7,1,8,2,4] => [8,7,3,5,4,6,2,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,5,6,7,1,2,4,8] => [7,6,3,5,4,2,1,8] => [1,7,2,6,3,4,5,8] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,1,7,2,8,4,6] => [8,3,2,5,4,7,6,1] => [1,8,2,3,4,5,6,7] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,4,6,7,8,5] => [3,1,2,4,8,6,7,5] => [1,3,2,4,5,8,6,7] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [3,1,2,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [1,3,2,4,5,6,7,8] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,6,7,2,8,4,5] => [8,1,3,7,4,6,5,2] => [1,8,2,3,4,7,5,6] => 4
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,1,6,7,2,4,5,8] => [7,1,3,6,4,5,2,8] => [1,7,2,3,4,6,5,8] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,6,1,7,2,8,4,5] => [8,3,2,7,4,6,5,1] => [1,8,2,3,4,7,5,6] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [3,6,1,7,8,2,4,5] => [8,3,2,7,6,5,4,1] => [1,8,2,3,4,7,5,6] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,2,4,5,7,6,8] => [3,1,2,4,5,7,6,8] => [1,3,2,4,5,6,7,8] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,4,7,5,8,6] => [3,1,2,4,8,5,7,6] => [1,3,2,4,5,8,6,7] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,2,4,7,8,5,6] => [3,1,2,4,8,7,6,5] => [1,3,2,4,5,8,6,7] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [3,1,2,4,7,5,6,8] => [3,1,2,4,7,5,6,8] => [1,3,2,4,5,7,6,8] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [3,1,2,4,5,6,8,7] => [1,3,2,4,5,6,7,8] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,8,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => [1,8,7,6,5,4,2,3] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,8,1,2,4,5,6,7] => [8,3,2,1,4,5,6,7] => [1,8,7,6,5,4,2,3] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,7,8,3] => [1,2,8,4,5,6,7,3] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,4,5,6,3,7,8] => [1,2,6,4,5,3,7,8] => [1,2,3,6,4,5,7,8] => 5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,4,3,6,7,8] => [1,2,3,5,4,6,7,8] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,6,7,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,8,5,7,6] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,8,7,6,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,4,3,7,5,6,8] => [1,2,4,3,7,5,6,8] => [1,2,3,4,5,7,6,8] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,6,7,8,3] => [8,1,4,3,5,6,7,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,2,6,3,8,7] => [6,1,4,3,5,2,8,7] => [1,6,2,3,4,5,7,8] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,5,2,7,8,3,6] => [8,1,4,3,5,7,6,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,5,2,3,6,7,8] => [5,1,4,3,2,6,7,8] => [1,5,2,3,4,6,7,8] => 5
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,5,1,2,6,7,8,3] => [8,4,2,3,5,6,7,1] => [1,8,2,4,3,5,6,7] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,7,3,8] => [7,4,2,3,5,6,1,8] => [1,7,2,4,3,5,6,8] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [4,5,1,2,6,3,8,7] => [6,4,2,3,5,1,8,7] => [1,6,2,4,3,5,7,8] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,5,1,6,7,2,8,3] => [8,6,2,4,5,3,7,1] => [1,8,2,6,3,4,5,7] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,5,1,6,7,8,2,3] => [8,7,2,4,5,6,3,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [4,5,1,6,7,2,3,8] => [7,6,2,4,5,3,1,8] => [1,7,2,6,3,4,5,8] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,5,6,1,2,7,8,3] => [8,5,4,3,2,6,7,1] => [1,8,2,5,3,4,6,7] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,5,6,1,2,7,3,8] => [7,5,4,3,2,6,1,8] => [1,7,2,5,3,4,6,8] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,5,6,1,7,2,8,3] => [8,6,4,3,5,2,7,1] => [1,8,2,6,3,4,5,7] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,5,6,1,7,8,2,3] => [8,7,4,3,5,6,2,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,5,6,1,7,2,3,8] => [7,6,4,3,5,2,1,8] => [1,7,2,6,3,4,5,8] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,5,6,7,1,2,8,3] => [8,6,5,4,3,2,7,1] => [1,8,2,6,3,5,4,7] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,5,6,7,1,8,2,3] => [8,7,5,4,3,6,2,1] => [1,8,2,7,3,5,4,6] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,5,6,7,8,1,2,3] => [8,7,6,4,5,3,2,1] => [1,8,2,7,3,6,4,5] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,3,8] => [7,6,5,4,3,2,1,8] => [1,7,2,6,3,5,4,8] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => [1,6,2,5,3,4,7,8] => 4
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [6,5,4,3,2,1,7,8] => [1,6,2,5,3,4,7,8] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [4,5,1,2,7,8,3,6] => [8,4,2,3,5,7,6,1] => [1,8,2,4,3,5,6,7] => 4
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [4,5,7,1,2,8,3,6] => [8,5,4,3,2,7,6,1] => [1,8,2,5,3,4,6,7] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [5,4,2,3,1,6,7,8] => [1,5,2,4,3,6,7,8] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,6,2,7,3,8,5] => [8,1,4,3,6,5,7,2] => [1,8,2,3,4,5,6,7] => 5
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [4,6,1,2,7,3,5,8] => [7,4,2,3,6,5,1,8] => [1,7,2,4,3,5,6,8] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [4,6,1,7,8,2,3,5] => [8,7,2,4,6,5,3,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [8,7,4,3,6,5,2,1] => [1,8,2,7,3,4,5,6] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,2,5,3,6,7,8,4] => [1,2,8,3,5,6,7,4] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,2,5,3,6,4,7,8] => [1,2,6,3,5,4,7,8] => [1,2,3,6,4,5,7,8] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,2,5,6,3,7,8,4] => [1,2,8,5,4,6,7,3] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,2,5,6,3,7,4,8] => [1,2,7,5,4,6,3,8] => [1,2,3,7,4,5,6,8] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,2,5,6,7,3,8,4] => [1,2,8,6,5,4,7,3] => [1,2,3,8,4,6,5,7] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,6,7,8,3,4] => [1,2,8,7,5,6,4,3] => [1,2,3,8,4,7,5,6] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,6,5,4,3,7,8] => [1,2,3,6,4,5,7,8] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,2,5,3,4,7,6,8] => [1,2,5,3,4,7,6,8] => [1,2,3,5,4,6,7,8] => 5
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,2,5,3,7,8,4,6] => [1,2,8,3,5,7,6,4] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,2,5,7,3,8,4,6] => [1,2,8,5,4,7,6,3] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,2,5,3,4,6,8,7] => [1,2,5,3,4,6,8,7] => [1,2,3,5,4,6,7,8] => 5
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [5,6,1,7,2,3,8,4] => [8,6,2,5,4,3,7,1] => [1,8,2,6,3,4,5,7] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,1,7,2,3,4,8] => [7,6,2,5,4,3,1,8] => [1,7,2,6,3,4,5,8] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,6,7,1,2,3,8,4] => [8,6,5,3,4,2,7,1] => [1,8,2,6,3,5,4,7] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [5,6,7,1,2,8,3,4] => [8,7,5,3,4,6,2,1] => [1,8,2,7,3,5,4,6] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [8,7,6,3,5,4,2,1] => [1,8,2,7,3,6,4,5] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => [1,8,2,7,3,6,4,5] => 3
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,7,1,2,3,4,8] => [7,6,5,3,4,2,1,8] => [1,7,2,6,3,5,4,8] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,6,7,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,6,5,8] => [1,2,3,4,5,7,6,8] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,2,6,3,7,4,8,5] => [1,2,8,3,6,5,7,4] => [1,2,3,8,4,5,6,7] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,2,6,7,3,4,8,5] => [1,2,8,6,4,5,7,3] => [1,2,3,8,4,6,5,7] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,2,6,7,3,8,4,5] => [1,2,8,7,4,6,5,3] => [1,2,3,8,4,7,5,6] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,8,7,6,5,4,3] => [1,2,3,8,4,7,5,6] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,7,8,5] => [8,1,2,3,4,6,7,5] => [1,8,5,4,3,2,6,7] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,8,5,7,6] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,8,7,6,5] => [1,2,3,4,5,8,6,7] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,5,6,8] => [1,2,3,4,5,7,6,8] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,1,2,3,4,8,5,6] => [8,1,2,3,4,7,6,5] => [1,8,5,4,3,2,6,7] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,8,7] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,11,1,3,4,5,6,7,8,9,10] => [11,2,1,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,9,7,8] => [2,1,3,4,5,6,9,7,8] => [1,2,3,4,5,6,7,9,8] => 6
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,1,3,4,5,6,7,10,8,9] => [2,1,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 7
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[] => [] => [] => [] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,7,9,8] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => [1,9,2,3,4,5,6,7,8] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => [1,10,2,3,4,5,6,7,8,9] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => [1,11,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => [1,2,3,4,5,6,7,8,9] => 7
[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] => [1,3,2,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => [1,2,3,4,5,6,7,9,8] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => [1,2,3,4,5,6,7,8,10,9] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,2] => [9,1,3,4,5,6,7,8,2] => [1,9,2,3,4,5,6,7,8] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,2] => [9,3,2,4,5,6,7,8,1] => [1,9,2,3,4,5,6,7,8] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,2] => [10,1,3,4,5,6,7,8,9,2] => [1,10,2,3,4,5,6,7,8,9] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,5,6,7,8,9,10,2] => [10,3,2,4,5,6,7,8,9,1] => [1,10,2,3,4,5,6,7,8,9] => 7
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,5,6,7,8,9,10,11,2] => [11,1,3,4,5,6,7,8,9,10,2] => [1,11,2,3,4,5,6,7,8,9,10] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,9,11,10] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,7,8] => [2,1,4,3,6,5,9,7,8] => [1,2,3,4,5,6,7,9,8] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,10,8,9] => [1,2,3,4,5,6,7,8,10,9] => 7
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Description
The number of occurrences of the vincular pattern |12-3 in a permutation.
This is the number of occurrences of the pattern $123$, where the first matched entry is the first entry of the permutation and the other two matched entries are consecutive.
In other words, this is the number of ascents whose bottom value is strictly larger than the first entry of the permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.