Identifier
Values
[1,0] => [1] => [1] => [] => 0
[1,0,1,0] => [2,1] => [2,1] => [1] => 0
[1,1,0,0] => [1,2] => [1,2] => [1] => 0
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [2,1] => 1
[1,0,1,1,0,0] => [2,3,1] => [3,1,2] => [1,2] => 0
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => [1,2] => 0
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [2,1] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [4,3,1,2] => [3,1,2] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [4,1,3,2] => [1,3,2] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [4,2,1,3] => [2,1,3] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,4,3,2] => [1,3,2] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [1,4,2,3] => [1,2,3] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,1,4,2] => [3,1,2] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [3,2,1] => 2
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,1,2,4] => [3,1,2] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,2,4,3] => [1,2,3] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,3,2,4] => [1,3,2] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [5,4,3,1,2] => [4,3,1,2] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [5,4,1,3,2] => [4,1,3,2] => 2
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [5,4,2,1,3] => [4,2,1,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [5,4,1,2,3] => [4,1,2,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [5,1,4,3,2] => [1,4,3,2] => 2
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [5,1,4,2,3] => [1,4,2,3] => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [5,3,1,4,2] => [3,1,4,2] => 2
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [5,3,2,1,4] => [3,2,1,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [5,3,1,2,4] => [3,1,2,4] => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [5,1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [5,1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [5,2,1,3,4] => [2,1,3,4] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,5,4,3,2] => [1,4,3,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [1,5,4,2,3] => [1,4,2,3] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,5,2,4,3] => [1,2,4,3] => 1
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [1,5,3,2,4] => [1,3,2,4] => 1
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [4,1,5,3,2] => [4,1,3,2] => 2
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [4,1,5,2,3] => [4,1,2,3] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,3,1,5,2] => [4,3,1,2] => 2
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1] => 3
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [4,3,1,2,5] => [4,3,1,2] => 2
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [4,1,2,5,3] => [4,1,2,3] => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [4,1,3,2,5] => [4,1,3,2] => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [4,2,1,3,5] => [4,2,1,3] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => [1,2,4,3] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,4,2,5,3] => [1,4,2,3] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,4,3,2,5] => [1,4,3,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [1,4,2,3,5] => [1,4,2,3] => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,1,2,5,4] => [3,1,2,4] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,1,4,2,5] => [3,1,4,2] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4] => 2
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,2,3,5,4] => [1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,4,3,5] => [1,2,4,3] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [1,3,2,4,5] => [1,3,2,4] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => [5,4,3,1,2] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [6,5,4,1,3,2] => [5,4,1,3,2] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => [5,4,2,1,3] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => [5,4,1,2,3] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [6,5,1,4,3,2] => [5,1,4,3,2] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [6,5,1,4,2,3] => [5,1,4,2,3] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [6,5,3,1,4,2] => [5,3,1,4,2] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => [5,3,2,1,4] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => [5,3,1,2,4] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [6,5,1,2,4,3] => [5,1,2,4,3] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [6,5,1,3,2,4] => [5,1,3,2,4] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => [5,2,1,3,4] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => [5,1,2,3,4] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [6,1,5,4,3,2] => [1,5,4,3,2] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [6,1,5,4,2,3] => [1,5,4,2,3] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [6,1,5,2,4,3] => [1,5,2,4,3] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [6,1,5,3,2,4] => [1,5,3,2,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [6,1,5,2,3,4] => [1,5,2,3,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [6,4,1,5,3,2] => [4,1,5,3,2] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [6,4,1,5,2,3] => [4,1,5,2,3] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [6,4,3,1,5,2] => [4,3,1,5,2] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => [4,3,2,1,5] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => [4,3,1,2,5] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [6,4,1,2,5,3] => [4,1,2,5,3] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [6,4,1,3,2,5] => [4,1,3,2,5] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => [4,2,1,3,5] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => [4,1,2,3,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [6,1,2,5,4,3] => [1,2,5,4,3] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [6,1,2,5,3,4] => [1,2,5,3,4] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [6,1,4,2,5,3] => [1,4,2,5,3] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [6,1,4,3,2,5] => [1,4,3,2,5] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [6,1,4,2,3,5] => [1,4,2,3,5] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [6,3,1,2,5,4] => [3,1,2,5,4] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [6,3,1,4,2,5] => [3,1,4,2,5] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => [3,2,1,4,5] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => [3,1,2,4,5] => 1
>>> Load all 819 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [6,1,2,3,5,4] => [1,2,3,5,4] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [6,1,2,4,3,5] => [1,2,4,3,5] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [6,1,3,2,4,5] => [1,3,2,4,5] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => [2,1,3,4,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [1,6,5,4,2,3] => [1,5,4,2,3] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,6,5,2,4,3] => [1,5,2,4,3] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [1,6,5,3,2,4] => [1,5,3,2,4] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [1,6,5,2,3,4] => [1,5,2,3,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,6,2,5,4,3] => [1,2,5,4,3] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [1,6,2,5,3,4] => [1,2,5,3,4] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,6,4,2,5,3] => [1,4,2,5,3] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [1,6,4,3,2,5] => [1,4,3,2,5] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [1,6,4,2,3,5] => [1,4,2,3,5] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,6,2,3,5,4] => [1,2,3,5,4] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [1,6,2,4,3,5] => [1,2,4,3,5] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [1,6,3,2,4,5] => [1,3,2,4,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [1,6,2,3,4,5] => [1,2,3,4,5] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [5,1,6,4,3,2] => [5,1,4,3,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [5,1,6,4,2,3] => [5,1,4,2,3] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [5,1,6,2,4,3] => [5,1,2,4,3] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [5,1,6,3,2,4] => [5,1,3,2,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [5,1,6,2,3,4] => [5,1,2,3,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [5,4,1,6,3,2] => [5,4,1,3,2] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [5,4,1,6,2,3] => [5,4,1,2,3] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,4,3,1,6,2] => [5,4,3,1,2] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => [5,4,3,1,2] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [5,4,1,2,6,3] => [5,4,1,2,3] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [5,4,1,3,2,6] => [5,4,1,3,2] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => [5,4,2,1,3] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => [5,4,1,2,3] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [5,1,2,6,4,3] => [5,1,2,4,3] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [5,1,2,6,3,4] => [5,1,2,3,4] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [5,1,4,2,6,3] => [5,1,4,2,3] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [5,1,4,3,2,6] => [5,1,4,3,2] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [5,1,4,2,3,6] => [5,1,4,2,3] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [5,3,1,2,6,4] => [5,3,1,2,4] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [5,3,1,4,2,6] => [5,3,1,4,2] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => [5,3,2,1,4] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => [5,3,1,2,4] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [5,1,2,3,6,4] => [5,1,2,3,4] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [5,1,2,4,3,6] => [5,1,2,4,3] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [5,1,3,2,4,6] => [5,1,3,2,4] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => [5,2,1,3,4] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [5,1,2,3,4] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => [1,2,5,4,3] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [1,2,6,5,3,4] => [1,2,5,3,4] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,2,6,3,5,4] => [1,2,3,5,4] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [1,2,6,4,3,5] => [1,2,4,3,5] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [1,2,6,3,4,5] => [1,2,3,4,5] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,5,2,6,4,3] => [1,5,2,4,3] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [1,5,2,6,3,4] => [1,5,2,3,4] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,5,4,2,6,3] => [1,5,4,2,3] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [1,5,4,2,3,6] => [1,5,4,2,3] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,5,2,3,6,4] => [1,5,2,3,4] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [1,5,2,4,3,6] => [1,5,2,4,3] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [1,5,3,2,4,6] => [1,5,3,2,4] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [1,5,2,3,4,6] => [1,5,2,3,4] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,1,2,6,5,3] => [4,1,2,5,3] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [4,1,2,6,3,5] => [4,1,2,3,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [4,1,5,2,6,3] => [4,1,5,2,3] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [4,1,5,3,2,6] => [4,1,5,3,2] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [4,1,5,2,3,6] => [4,1,5,2,3] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [4,3,1,2,6,5] => [4,3,1,2,5] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [4,3,1,5,2,6] => [4,3,1,5,2] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => [4,3,1,2,5] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [4,1,2,3,6,5] => [4,1,2,3,5] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [4,1,2,5,3,6] => [4,1,2,5,3] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [4,1,3,2,5,6] => [4,1,3,2,5] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => [4,2,1,3,5] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => [1,2,3,5,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [1,2,3,6,4,5] => [1,2,3,4,5] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,2,5,3,6,4] => [1,2,5,3,4] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [1,2,5,3,4,6] => [1,2,5,3,4] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,4,2,3,6,5] => [1,4,2,3,5] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [1,4,2,5,3,6] => [1,4,2,5,3] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [3,1,2,4,6,5] => [3,1,2,4,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [3,1,2,5,4,6] => [3,1,2,5,4] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,1,4,2,5,6] => [3,1,4,2,5] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [3,1,2,4,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => [1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => [6,5,4,3,1,2] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [7,6,5,4,1,3,2] => [6,5,4,1,3,2] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [7,6,5,4,2,1,3] => [6,5,4,2,1,3] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => [6,5,4,1,2,3] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [7,6,5,1,4,3,2] => [6,5,1,4,3,2] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [7,6,5,1,4,2,3] => [6,5,1,4,2,3] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [7,6,5,3,1,4,2] => [6,5,3,1,4,2] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [7,6,5,3,2,1,4] => [6,5,3,2,1,4] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [6,5,3,1,2,4] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [7,6,5,1,2,4,3] => [6,5,1,2,4,3] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [7,6,5,1,3,2,4] => [6,5,1,3,2,4] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [6,5,2,1,3,4] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => [6,5,1,2,3,4] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [7,6,1,5,4,3,2] => [6,1,5,4,3,2] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [7,6,1,5,4,2,3] => [6,1,5,4,2,3] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [7,6,1,5,2,4,3] => [6,1,5,2,4,3] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [7,6,1,5,3,2,4] => [6,1,5,3,2,4] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [7,6,1,5,2,3,4] => [6,1,5,2,3,4] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [7,6,4,1,5,3,2] => [6,4,1,5,3,2] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [7,6,4,1,5,2,3] => [6,4,1,5,2,3] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [7,6,4,3,1,5,2] => [6,4,3,1,5,2] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [7,6,4,3,2,1,5] => [6,4,3,2,1,5] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [7,6,4,3,1,2,5] => [6,4,3,1,2,5] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [7,6,4,1,2,5,3] => [6,4,1,2,5,3] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [7,6,4,1,3,2,5] => [6,4,1,3,2,5] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [7,6,4,2,1,3,5] => [6,4,2,1,3,5] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [7,6,4,1,2,3,5] => [6,4,1,2,3,5] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [7,6,1,2,5,4,3] => [6,1,2,5,4,3] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [7,6,1,2,5,3,4] => [6,1,2,5,3,4] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [7,6,1,4,2,5,3] => [6,1,4,2,5,3] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [7,6,1,4,3,2,5] => [6,1,4,3,2,5] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [7,6,1,4,2,3,5] => [6,1,4,2,3,5] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [7,6,3,1,2,5,4] => [6,3,1,2,5,4] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [7,6,3,1,4,2,5] => [6,3,1,4,2,5] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [7,6,3,2,1,4,5] => [6,3,2,1,4,5] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [7,6,3,1,2,4,5] => [6,3,1,2,4,5] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [7,6,1,2,3,5,4] => [6,1,2,3,5,4] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [7,6,1,2,4,3,5] => [6,1,2,4,3,5] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [7,6,1,3,2,4,5] => [6,1,3,2,4,5] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [7,6,2,1,3,4,5] => [6,2,1,3,4,5] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => [6,1,2,3,4,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [7,1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [7,1,6,5,4,2,3] => [1,6,5,4,2,3] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [7,1,6,5,2,4,3] => [1,6,5,2,4,3] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [7,1,6,5,3,2,4] => [1,6,5,3,2,4] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [7,1,6,5,2,3,4] => [1,6,5,2,3,4] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [7,1,6,2,5,4,3] => [1,6,2,5,4,3] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [7,1,6,2,5,3,4] => [1,6,2,5,3,4] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [7,1,6,4,2,5,3] => [1,6,4,2,5,3] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [7,1,6,4,3,2,5] => [1,6,4,3,2,5] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [7,1,6,4,2,3,5] => [1,6,4,2,3,5] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [7,1,6,2,3,5,4] => [1,6,2,3,5,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [7,1,6,2,4,3,5] => [1,6,2,4,3,5] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [7,1,6,3,2,4,5] => [1,6,3,2,4,5] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [7,1,6,2,3,4,5] => [1,6,2,3,4,5] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [7,5,1,6,4,3,2] => [5,1,6,4,3,2] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [7,5,1,6,4,2,3] => [5,1,6,4,2,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [7,5,1,6,2,4,3] => [5,1,6,2,4,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [7,5,1,6,3,2,4] => [5,1,6,3,2,4] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [7,5,1,6,2,3,4] => [5,1,6,2,3,4] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [7,5,4,1,6,3,2] => [5,4,1,6,3,2] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [7,5,4,1,6,2,3] => [5,4,1,6,2,3] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [7,5,4,3,1,6,2] => [5,4,3,1,6,2] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [7,5,4,1,2,6,3] => [5,4,1,2,6,3] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [7,5,4,1,3,2,6] => [5,4,1,3,2,6] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [7,5,1,2,6,4,3] => [5,1,2,6,4,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [7,5,1,2,6,3,4] => [5,1,2,6,3,4] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [7,5,1,4,2,6,3] => [5,1,4,2,6,3] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [7,5,1,4,3,2,6] => [5,1,4,3,2,6] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [7,5,1,4,2,3,6] => [5,1,4,2,3,6] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [7,5,3,1,2,6,4] => [5,3,1,2,6,4] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [7,5,3,1,4,2,6] => [5,3,1,4,2,6] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [7,5,1,2,3,6,4] => [5,1,2,3,6,4] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [7,5,1,2,4,3,6] => [5,1,2,4,3,6] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [7,5,1,3,2,4,6] => [5,1,3,2,4,6] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [7,1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [7,1,2,6,5,3,4] => [1,2,6,5,3,4] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [7,1,2,6,3,5,4] => [1,2,6,3,5,4] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [7,1,2,6,4,3,5] => [1,2,6,4,3,5] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [7,1,2,6,3,4,5] => [1,2,6,3,4,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [7,1,5,2,6,4,3] => [1,5,2,6,4,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [7,1,5,2,6,3,4] => [1,5,2,6,3,4] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [7,1,5,4,2,6,3] => [1,5,4,2,6,3] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [7,1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [7,1,5,4,2,3,6] => [1,5,4,2,3,6] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [7,1,5,2,3,6,4] => [1,5,2,3,6,4] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [7,1,5,2,4,3,6] => [1,5,2,4,3,6] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [7,1,5,3,2,4,6] => [1,5,3,2,4,6] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [7,1,5,2,3,4,6] => [1,5,2,3,4,6] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [7,4,1,2,6,5,3] => [4,1,2,6,5,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [7,4,1,2,6,3,5] => [4,1,2,6,3,5] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [7,4,1,5,2,6,3] => [4,1,5,2,6,3] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [7,4,1,5,3,2,6] => [4,1,5,3,2,6] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [7,4,1,5,2,3,6] => [4,1,5,2,3,6] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [7,4,3,1,2,6,5] => [4,3,1,2,6,5] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [7,4,3,1,5,2,6] => [4,3,1,5,2,6] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [7,4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [7,4,1,2,5,3,6] => [4,1,2,5,3,6] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [7,4,1,3,2,5,6] => [4,1,3,2,5,6] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [7,1,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [7,1,2,3,6,4,5] => [1,2,3,6,4,5] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [7,1,2,5,3,6,4] => [1,2,5,3,6,4] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [7,1,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [7,1,2,5,3,4,6] => [1,2,5,3,4,6] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [7,1,4,2,3,6,5] => [1,4,2,3,6,5] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [7,1,4,2,5,3,6] => [1,4,2,5,3,6] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [7,1,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [7,1,4,2,3,5,6] => [1,4,2,3,5,6] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [7,3,1,2,4,6,5] => [3,1,2,4,6,5] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [7,3,1,2,5,4,6] => [3,1,2,5,4,6] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [7,3,1,4,2,5,6] => [3,1,4,2,5,6] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [7,1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [7,1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [7,1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [7,1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [1,7,6,5,4,2,3] => [1,6,5,4,2,3] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [1,7,6,5,2,4,3] => [1,6,5,2,4,3] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [1,7,6,5,3,2,4] => [1,6,5,3,2,4] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [1,7,6,5,2,3,4] => [1,6,5,2,3,4] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,7,6,2,5,4,3] => [1,6,2,5,4,3] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [1,7,6,2,5,3,4] => [1,6,2,5,3,4] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,7,6,4,2,5,3] => [1,6,4,2,5,3] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [1,7,6,4,3,2,5] => [1,6,4,3,2,5] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [1,7,6,4,2,3,5] => [1,6,4,2,3,5] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,7,6,2,3,5,4] => [1,6,2,3,5,4] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [1,7,6,2,4,3,5] => [1,6,2,4,3,5] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [1,7,6,3,2,4,5] => [1,6,3,2,4,5] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [1,7,6,2,3,4,5] => [1,6,2,3,4,5] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,7,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [1,7,2,6,5,3,4] => [1,2,6,5,3,4] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,7,2,6,3,5,4] => [1,2,6,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [1,7,2,6,4,3,5] => [1,2,6,4,3,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [1,7,2,6,3,4,5] => [1,2,6,3,4,5] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,7,5,2,6,4,3] => [1,5,2,6,4,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [1,7,5,2,6,3,4] => [1,5,2,6,3,4] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,7,5,4,2,6,3] => [1,5,4,2,6,3] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [1,7,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [1,7,5,4,2,3,6] => [1,5,4,2,3,6] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,7,5,2,3,6,4] => [1,5,2,3,6,4] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [1,7,5,2,4,3,6] => [1,5,2,4,3,6] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [1,7,5,3,2,4,6] => [1,5,3,2,4,6] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [1,7,5,2,3,4,6] => [1,5,2,3,4,6] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,7,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [1,7,2,3,6,4,5] => [1,2,3,6,4,5] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,7,2,5,3,6,4] => [1,2,5,3,6,4] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [1,7,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [1,7,2,5,3,4,6] => [1,2,5,3,4,6] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,7,4,2,3,6,5] => [1,4,2,3,6,5] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [1,7,4,2,5,3,6] => [1,4,2,5,3,6] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [1,7,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [1,7,4,2,3,5,6] => [1,4,2,3,5,6] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,7,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [1,7,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [1,7,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [1,7,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [1,7,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [6,1,7,5,4,3,2] => [6,1,5,4,3,2] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [6,1,7,5,4,2,3] => [6,1,5,4,2,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [6,1,7,5,2,4,3] => [6,1,5,2,4,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [6,1,7,5,3,2,4] => [6,1,5,3,2,4] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [6,1,7,5,2,3,4] => [6,1,5,2,3,4] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [6,1,7,2,5,4,3] => [6,1,2,5,4,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [6,1,7,2,5,3,4] => [6,1,2,5,3,4] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [6,1,7,4,2,5,3] => [6,1,4,2,5,3] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [6,1,7,4,3,2,5] => [6,1,4,3,2,5] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [6,1,7,4,2,3,5] => [6,1,4,2,3,5] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [6,1,7,2,3,5,4] => [6,1,2,3,5,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [6,1,7,2,4,3,5] => [6,1,2,4,3,5] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [6,1,7,3,2,4,5] => [6,1,3,2,4,5] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [6,1,7,2,3,4,5] => [6,1,2,3,4,5] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [6,5,1,7,4,3,2] => [6,5,1,4,3,2] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [6,5,1,7,4,2,3] => [6,5,1,4,2,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [6,5,1,7,2,4,3] => [6,5,1,2,4,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [6,5,1,7,3,2,4] => [6,5,1,3,2,4] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [6,5,1,7,2,3,4] => [6,5,1,2,3,4] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [6,5,4,1,7,3,2] => [6,5,4,1,3,2] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [6,5,4,1,7,2,3] => [6,5,4,1,2,3] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [6,5,4,3,1,7,2] => [6,5,4,3,1,2] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [6,5,4,1,2,7,3] => [6,5,4,1,2,3] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [6,5,4,1,3,2,7] => [6,5,4,1,3,2] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [6,5,1,2,7,4,3] => [6,5,1,2,4,3] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [6,5,1,2,7,3,4] => [6,5,1,2,3,4] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [6,5,1,4,2,7,3] => [6,5,1,4,2,3] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [6,5,1,4,3,2,7] => [6,5,1,4,3,2] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [6,5,1,4,2,3,7] => [6,5,1,4,2,3] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [6,5,3,1,2,7,4] => [6,5,3,1,2,4] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [6,5,3,1,4,2,7] => [6,5,3,1,4,2] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [6,5,3,2,1,4,7] => [6,5,3,2,1,4] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [6,5,3,1,2,4,7] => [6,5,3,1,2,4] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [6,5,1,2,3,7,4] => [6,5,1,2,3,4] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [6,5,1,2,4,3,7] => [6,5,1,2,4,3] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [6,5,1,3,2,4,7] => [6,5,1,3,2,4] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [6,5,2,1,3,4,7] => [6,5,2,1,3,4] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [6,5,1,2,3,4,7] => [6,5,1,2,3,4] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [6,1,2,7,5,4,3] => [6,1,2,5,4,3] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [6,1,2,7,5,3,4] => [6,1,2,5,3,4] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [6,1,2,7,3,5,4] => [6,1,2,3,5,4] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [6,1,2,7,4,3,5] => [6,1,2,4,3,5] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [6,1,2,7,3,4,5] => [6,1,2,3,4,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [6,1,5,2,7,4,3] => [6,1,5,2,4,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [6,1,5,2,7,3,4] => [6,1,5,2,3,4] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [6,1,5,4,2,7,3] => [6,1,5,4,2,3] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [6,1,5,4,3,2,7] => [6,1,5,4,3,2] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [6,1,5,4,2,3,7] => [6,1,5,4,2,3] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [6,1,5,2,3,7,4] => [6,1,5,2,3,4] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [6,1,5,2,4,3,7] => [6,1,5,2,4,3] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [6,1,5,3,2,4,7] => [6,1,5,3,2,4] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [6,1,5,2,3,4,7] => [6,1,5,2,3,4] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [6,4,1,2,7,5,3] => [6,4,1,2,5,3] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [6,4,1,2,7,3,5] => [6,4,1,2,3,5] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [6,4,1,5,2,7,3] => [6,4,1,5,2,3] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [6,4,1,5,3,2,7] => [6,4,1,5,3,2] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [6,4,1,5,2,3,7] => [6,4,1,5,2,3] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [6,4,3,1,2,7,5] => [6,4,3,1,2,5] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [6,4,3,1,5,2,7] => [6,4,3,1,5,2] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [6,4,1,2,3,7,5] => [6,4,1,2,3,5] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [6,4,1,2,5,3,7] => [6,4,1,2,5,3] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [6,4,1,3,2,5,7] => [6,4,1,3,2,5] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [6,1,2,3,7,5,4] => [6,1,2,3,5,4] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [6,1,2,3,7,4,5] => [6,1,2,3,4,5] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [6,1,2,5,3,7,4] => [6,1,2,5,3,4] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [6,1,2,5,4,3,7] => [6,1,2,5,4,3] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [6,1,2,5,3,4,7] => [6,1,2,5,3,4] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [6,1,4,2,3,7,5] => [6,1,4,2,3,5] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [6,1,4,2,5,3,7] => [6,1,4,2,5,3] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [6,1,4,3,2,5,7] => [6,1,4,3,2,5] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [6,1,4,2,3,5,7] => [6,1,4,2,3,5] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [6,3,1,2,4,7,5] => [6,3,1,2,4,5] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [6,3,1,2,5,4,7] => [6,3,1,2,5,4] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [6,3,1,4,2,5,7] => [6,3,1,4,2,5] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [6,1,2,3,4,7,5] => [6,1,2,3,4,5] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [6,1,2,3,5,4,7] => [6,1,2,3,5,4] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [6,1,2,4,3,5,7] => [6,1,2,4,3,5] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [6,1,3,2,4,5,7] => [6,1,3,2,4,5] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [1,2,7,6,5,3,4] => [1,2,6,5,3,4] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,2,7,6,3,5,4] => [1,2,6,3,5,4] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [1,2,7,6,4,3,5] => [1,2,6,4,3,5] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [1,2,7,6,3,4,5] => [1,2,6,3,4,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,7,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [1,2,7,3,6,4,5] => [1,2,3,6,4,5] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,2,7,5,3,6,4] => [1,2,5,3,6,4] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [1,2,7,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [1,2,7,5,3,4,6] => [1,2,5,3,4,6] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,2,7,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [1,2,7,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [1,2,7,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [1,2,7,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,6,2,7,5,4,3] => [1,6,2,5,4,3] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [1,6,2,7,5,3,4] => [1,6,2,5,3,4] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,6,2,7,3,5,4] => [1,6,2,3,5,4] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [1,6,2,7,4,3,5] => [1,6,2,4,3,5] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [1,6,2,7,3,4,5] => [1,6,2,3,4,5] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,6,5,2,7,4,3] => [1,6,5,2,4,3] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [1,6,5,2,7,3,4] => [1,6,5,2,3,4] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,6,5,4,2,7,3] => [1,6,5,4,2,3] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7] => [1,6,5,4,3,2] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [1,6,5,4,2,3,7] => [1,6,5,4,2,3] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,6,5,2,3,7,4] => [1,6,5,2,3,4] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [1,6,5,2,4,3,7] => [1,6,5,2,4,3] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [1,6,5,3,2,4,7] => [1,6,5,3,2,4] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [1,6,5,2,3,4,7] => [1,6,5,2,3,4] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,6,2,3,7,5,4] => [1,6,2,3,5,4] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [1,6,2,3,7,4,5] => [1,6,2,3,4,5] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,6,2,5,3,7,4] => [1,6,2,5,3,4] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [1,6,2,5,4,3,7] => [1,6,2,5,4,3] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [1,6,2,5,3,4,7] => [1,6,2,5,3,4] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,6,4,2,3,7,5] => [1,6,4,2,3,5] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [1,6,4,2,5,3,7] => [1,6,4,2,5,3] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [1,6,4,3,2,5,7] => [1,6,4,3,2,5] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [1,6,4,2,3,5,7] => [1,6,4,2,3,5] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,6,2,3,4,7,5] => [1,6,2,3,4,5] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [1,6,2,3,5,4,7] => [1,6,2,3,5,4] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [1,6,2,4,3,5,7] => [1,6,2,4,3,5] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [1,6,3,2,4,5,7] => [1,6,3,2,4,5] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [1,6,2,3,4,5,7] => [1,6,2,3,4,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [5,1,2,7,6,4,3] => [5,1,2,6,4,3] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [5,1,2,7,6,3,4] => [5,1,2,6,3,4] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [5,1,2,7,3,6,4] => [5,1,2,3,6,4] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [5,1,2,7,4,3,6] => [5,1,2,4,3,6] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [5,1,2,7,3,4,6] => [5,1,2,3,4,6] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [5,1,6,2,7,4,3] => [5,1,6,2,4,3] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [5,1,6,2,7,3,4] => [5,1,6,2,3,4] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [5,1,6,4,2,7,3] => [5,1,6,4,2,3] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [5,1,6,4,3,2,7] => [5,1,6,4,3,2] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [5,1,6,4,2,3,7] => [5,1,6,4,2,3] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [5,1,6,2,3,7,4] => [5,1,6,2,3,4] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [5,1,6,2,4,3,7] => [5,1,6,2,4,3] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [5,1,6,3,2,4,7] => [5,1,6,3,2,4] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [5,1,6,2,3,4,7] => [5,1,6,2,3,4] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [5,4,1,2,7,6,3] => [5,4,1,2,6,3] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [5,4,1,2,7,3,6] => [5,4,1,2,3,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [5,4,1,6,2,7,3] => [5,4,1,6,2,3] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [5,4,1,6,3,2,7] => [5,4,1,6,3,2] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [5,4,1,6,2,3,7] => [5,4,1,6,2,3] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [5,4,3,1,2,7,6] => [5,4,3,1,2,6] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [5,4,3,1,6,2,7] => [5,4,3,1,6,2] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [5,4,1,2,3,7,6] => [5,4,1,2,3,6] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [5,4,1,2,6,3,7] => [5,4,1,2,6,3] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [5,4,1,3,2,6,7] => [5,4,1,3,2,6] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [5,1,2,3,7,6,4] => [5,1,2,3,6,4] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [5,1,2,3,7,4,6] => [5,1,2,3,4,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [5,1,2,6,3,7,4] => [5,1,2,6,3,4] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [5,1,2,6,4,3,7] => [5,1,2,6,4,3] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [5,1,2,6,3,4,7] => [5,1,2,6,3,4] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [5,1,4,2,3,7,6] => [5,1,4,2,3,6] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [5,1,4,2,6,3,7] => [5,1,4,2,6,3] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [5,1,4,3,2,6,7] => [5,1,4,3,2,6] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [5,1,4,2,3,6,7] => [5,1,4,2,3,6] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [5,3,1,2,4,7,6] => [5,3,1,2,4,6] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [5,3,1,2,6,4,7] => [5,3,1,2,6,4] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [5,3,1,4,2,6,7] => [5,3,1,4,2,6] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [5,1,2,3,4,7,6] => [5,1,2,3,4,6] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [5,1,2,3,6,4,7] => [5,1,2,3,6,4] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [5,1,2,4,3,6,7] => [5,1,2,4,3,6] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [5,1,3,2,4,6,7] => [5,1,3,2,4,6] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => [1,2,3,6,5,4] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [1,2,3,7,6,4,5] => [1,2,3,6,4,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,2,3,7,4,6,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [1,2,3,7,5,4,6] => [1,2,3,5,4,6] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [1,2,3,7,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,6,3,7,5,4] => [1,2,6,3,5,4] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [1,2,6,3,7,4,5] => [1,2,6,3,4,5] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,2,6,5,3,7,4] => [1,2,6,5,3,4] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [1,2,6,5,3,4,7] => [1,2,6,5,3,4] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,2,6,3,4,7,5] => [1,2,6,3,4,5] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [1,2,6,3,5,4,7] => [1,2,6,3,5,4] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [1,2,6,4,3,5,7] => [1,2,6,4,3,5] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,5,2,3,7,6,4] => [1,5,2,3,6,4] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [1,5,2,3,7,4,6] => [1,5,2,3,4,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,5,2,6,3,7,4] => [1,5,2,6,3,4] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [1,5,2,6,4,3,7] => [1,5,2,6,4,3] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [1,5,2,6,3,4,7] => [1,5,2,6,3,4] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,5,4,2,3,7,6] => [1,5,4,2,3,6] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [1,5,4,2,6,3,7] => [1,5,4,2,6,3] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [1,5,4,3,2,6,7] => [1,5,4,3,2,6] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [1,5,4,2,3,6,7] => [1,5,4,2,3,6] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,5,2,3,4,7,6] => [1,5,2,3,4,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [1,5,2,3,6,4,7] => [1,5,2,3,6,4] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [1,5,2,4,3,6,7] => [1,5,2,4,3,6] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [1,5,3,2,4,6,7] => [1,5,3,2,4,6] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [1,5,2,3,4,6,7] => [1,5,2,3,4,6] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [4,1,2,3,7,6,5] => [4,1,2,3,6,5] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [4,1,2,3,7,5,6] => [4,1,2,3,5,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [4,1,2,6,3,7,5] => [4,1,2,6,3,5] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [4,1,2,6,5,3,7] => [4,1,2,6,5,3] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [4,1,2,6,3,5,7] => [4,1,2,6,3,5] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [4,1,5,2,3,7,6] => [4,1,5,2,3,6] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [4,1,5,2,6,3,7] => [4,1,5,2,6,3] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [4,1,5,3,2,6,7] => [4,1,5,3,2,6] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,1,5,2,3,6,7] => [4,1,5,2,3,6] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [4,3,1,2,5,7,6] => [4,3,1,2,5,6] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [4,3,1,2,6,5,7] => [4,3,1,2,6,5] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [4,3,1,5,2,6,7] => [4,3,1,5,2,6] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [4,1,2,3,5,7,6] => [4,1,2,3,5,6] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [4,1,2,5,3,6,7] => [4,1,2,5,3,6] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,1,3,2,5,6,7] => [4,1,3,2,5,6] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [1,2,3,4,7,5,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,2,3,6,4,7,5] => [1,2,3,6,4,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [1,2,3,6,4,5,7] => [1,2,3,6,4,5] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,2,5,3,4,7,6] => [1,2,5,3,4,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [1,2,5,3,6,4,7] => [1,2,5,3,6,4] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [1,2,5,3,4,6,7] => [1,2,5,3,4,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,4,2,3,5,7,6] => [1,4,2,3,5,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,4,2,3,6,5,7] => [1,4,2,3,6,5] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [1,4,2,5,3,6,7] => [1,4,2,5,3,6] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [3,1,2,4,5,7,6] => [3,1,2,4,5,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [3,1,4,2,5,6,7] => [3,1,4,2,5,6] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [8,7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [8,7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [8,7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [8,7,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [8,7,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [8,7,4,1,2,3,5,6] => [7,4,1,2,3,5,6] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [8,7,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [8,1,7,2,3,4,5,6] => [1,7,2,3,4,5,6] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [8,1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [8,1,2,7,3,4,6,5] => [1,2,7,3,4,6,5] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [8,1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [8,1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [8,1,2,3,7,4,5,6] => [1,2,3,7,4,5,6] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [8,1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [8,4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [8,1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [8,1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [8,1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [8,1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [8,3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [8,1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,8,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [1,8,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [1,8,2,7,3,5,4,6] => [1,2,7,3,5,4,6] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [1,8,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [1,8,2,6,3,7,4,5] => [1,2,6,3,7,4,5] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [1,8,2,6,3,5,4,7] => [1,2,6,3,5,4,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [1,8,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [1,8,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [1,8,2,5,3,6,4,7] => [1,2,5,3,6,4,7] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [1,8,2,5,3,4,6,7] => [1,2,5,3,4,6,7] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [1,8,4,2,5,3,6,7] => [1,4,2,5,3,6,7] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,8,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [1,8,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [1,8,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [1,8,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [1,8,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [7,1,8,2,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [7,6,1,8,2,3,4,5] => [7,6,1,2,3,4,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2] => 5
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [7,6,1,2,3,4,8,5] => [7,6,1,2,3,4,5] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [7,1,2,8,3,4,5,6] => [7,1,2,3,4,5,6] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [7,5,1,2,8,3,4,6] => [7,5,1,2,3,4,6] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [7,5,1,2,3,4,6,8] => [7,5,1,2,3,4,6] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [7,1,2,3,4,8,5,6] => [7,1,2,3,4,5,6] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [7,3,1,2,4,5,8,6] => [7,3,1,2,4,5,6] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [7,3,1,2,4,5,6,8] => [7,3,1,2,4,5,6] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [7,1,2,3,4,5,8,6] => [7,1,2,3,4,5,6] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [1,2,8,7,6,3,4,5] => [1,2,7,6,3,4,5] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [1,2,8,7,5,3,6,4] => [1,2,7,5,3,6,4] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [1,2,8,7,3,4,5,6] => [1,2,7,3,4,5,6] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [1,2,8,3,7,4,5,6] => [1,2,3,7,4,5,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [1,2,8,6,3,7,5,4] => [1,2,6,3,7,5,4] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [1,2,8,5,4,3,6,7] => [1,2,5,4,3,6,7] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [1,2,8,4,3,5,6,7] => [1,2,4,3,5,6,7] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [1,7,2,8,3,4,5,6] => [1,7,2,3,4,5,6] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [1,7,2,3,8,4,5,6] => [1,7,2,3,4,5,6] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [1,7,2,3,4,8,5,6] => [1,7,2,3,4,5,6] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,7,2,3,4,5,8,6] => [1,7,2,3,4,5,6] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [1,7,2,3,4,5,6,8] => [1,7,2,3,4,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [6,1,2,8,3,4,5,7] => [6,1,2,3,4,5,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [6,1,2,3,8,7,4,5] => [6,1,2,3,7,4,5] => 2
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [6,1,2,7,3,4,5,8] => [6,1,2,7,3,4,5] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [6,1,2,3,4,5,8,7] => [6,1,2,3,4,5,7] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,8,7,6,5,4] => [1,2,3,7,6,5,4] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [1,2,3,8,4,7,5,6] => [1,2,3,4,7,5,6] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [1,2,3,8,4,6,5,7] => [1,2,3,4,6,5,7] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,7,3,8,6,5,4] => [1,2,7,3,6,5,4] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [1,2,7,6,3,8,5,4] => [1,2,7,6,3,5,4] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [1,2,7,6,5,3,8,4] => [1,2,7,6,5,3,4] => 3
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [1,2,7,6,3,4,5,8] => [1,2,7,6,3,4,5] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [1,2,7,3,4,5,8,6] => [1,2,7,3,4,5,6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [1,6,2,7,3,8,4,5] => [1,6,2,7,3,4,5] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [1,6,2,7,3,4,5,8] => [1,6,2,7,3,4,5] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [5,1,2,3,8,7,4,6] => [5,1,2,3,7,4,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [5,1,2,3,8,4,7,6] => [5,1,2,3,4,7,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [5,1,2,3,8,4,6,7] => [5,1,2,3,4,6,7] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [5,1,6,2,3,8,4,7] => [5,1,6,2,3,4,7] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [5,1,6,2,3,4,7,8] => [5,1,6,2,3,4,7] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [5,1,2,3,4,6,8,7] => [5,1,2,3,4,6,7] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,5] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [1,2,3,7,4,8,5,6] => [1,2,3,7,4,5,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,2,3,7,4,5,8,6] => [1,2,3,7,4,5,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [1,2,3,7,4,6,5,8] => [1,2,3,7,4,6,5] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,6,3,4,8,7,5] => [1,2,6,3,4,7,5] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [1,2,6,3,4,8,5,7] => [1,2,6,3,4,5,7] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [1,5,2,3,4,7,6,8] => [1,5,2,3,4,7,6] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [4,1,2,3,5,8,7,6] => [4,1,2,3,5,7,6] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [4,1,2,3,5,8,6,7] => [4,1,2,3,5,6,7] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [4,1,2,3,5,6,8,7] => [4,1,2,3,5,6,7] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [4,1,2,3,5,7,6,8] => [4,1,2,3,5,7,6] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,2,3,4,7,5,8,6] => [1,2,3,4,7,5,6] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [1,2,3,6,4,7,5,8] => [1,2,3,6,4,7,5] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [1,2,5,3,6,4,7,8] => [1,2,5,3,6,4,7] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [1,4,2,3,5,7,6,8] => [1,4,2,3,5,7,6] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [1,4,2,5,3,6,7,8] => [1,4,2,5,3,6,7] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => 1
[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] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [9,2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,1,7,8] => [7,1,2,3,4,5,6,9,8] => [7,1,2,3,4,5,6,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,8,6,7] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [8,1,2,3,4,5,6,9,7] => [8,1,2,3,4,5,6,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [1,9,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [9,1,2,3,4,5,6,7,10,8] => [9,1,2,3,4,5,6,7,8] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [1,10,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [8,7,6,5,4,3,1,2,9] => [8,7,6,5,4,3,1,2] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [7,1,2,3,4,5,6,8] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8] => 1
[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] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1,2] => [8,7,6,5,4,3,1,2] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,1,2] => [9,8,7,6,5,4,3,1,2] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [9,8,7,6,5,4,1,2,3] => [8,7,6,5,4,1,2,3] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,1,2,3] => [9,8,7,6,5,4,1,2,3] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [9,8,7,6,5,1,2,3,4] => [8,7,6,5,1,2,3,4] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [10,9,8,7,6,5,1,2,3,4] => [9,8,7,6,5,1,2,3,4] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [9,8,7,6,1,2,3,4,5] => [8,7,6,1,2,3,4,5] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [10,9,8,7,6,1,2,3,4,5] => [9,8,7,6,1,2,3,4,5] => 4
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [9,8,7,1,2,3,4,5,6] => [8,7,1,2,3,4,5,6] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [10,9,8,7,1,2,3,4,5,6] => [9,8,7,1,2,3,4,5,6] => 3
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [9,1,8,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [9,1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,6,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [1,9,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => 6
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [10,9,8,1,2,3,4,5,6,7] => [9,8,1,2,3,4,5,6,7] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [1,10,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => 7
[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] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [1,11,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => 8
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9] => 7
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [1,11,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,1,2,3,4,5,6,7,8,9,11] => [10,1,2,3,4,5,6,7,8,9] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9] => 5
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [11,2,3,4,5,6,7,8,9,1,10] => [10,1,2,3,4,5,6,7,8,11,9] => [10,1,2,3,4,5,6,7,8,9] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [1,8,2,3,4,5,6,9,7] => [1,8,2,3,4,5,6,7] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,1,5] => [8,1,2,3,9,4,5,6,7] => [8,1,2,3,4,5,6,7] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [11,10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => 1
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Description
The staircase size of the code of a permutation.
The code $c(\pi)$ of a permutation $\pi$ of length $n$ is given by the sequence $(c_1,\ldots,c_{n})$ with $c_i = |\{j > i : \pi(j) < \pi(i)\}|$. This is a bijection between permutations and all sequences $(c_1,\ldots,c_n)$ with $0 \leq c_i \leq n-i$.
The staircase size of the code is the maximal $k$ such that there exists a subsequence $(c_{i_k},\ldots,c_{i_1})$ of $c(\pi)$ with $c_{i_j} \geq j$.
This statistic is mapped through Mp00062Lehmer-code to major-code bijection to the number of descents, showing that together with the number of inversions St000018The number of inversions of a permutation. it is Euler-Mahonian.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.