Identifier
Values
[1,0] => [1] => 0
[1,0,1,0] => [1,2] => 0
[1,1,0,0] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => 2
[1,1,1,0,0,0] => [3,1,2] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => 3
[1,1,0,1,1,0,0,0] => [2,4,1,3] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => 0
[1,1,1,0,0,1,0,0] => [3,1,4,2] => 1
[1,1,1,0,1,0,0,0] => [3,4,1,2] => 0
[1,1,1,1,0,0,0,0] => [4,1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => 0
>>> Load all 510 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,4,7,5] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,3,4,7,5] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,2,4,5,6] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,2,3,5] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,2,3,5,6] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,2,7,3,4,6] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,2,7,3,4] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,2,3,4] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,2,3,4,6] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,2,3,7,4,5] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,2,7,3,4,5] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,2,3,4,5] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,5,6] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,3,4,5,7] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,3,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,1,5] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,3,5,6,7] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,1,3,4,6,7] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,1,3,4,6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,1,7,3,4,5] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,1,3,4,5] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,2,4,5,7,6] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,1,2,4,7] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,1,2,4,5,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,2,3,5,6,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2,3,5,7,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,6,2,3,5,7] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,1,6,2,3,7] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,1,2,3,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,1,2,3,5,7] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,1,2,3,7,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,2,3,4,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,1,2,3,4,7,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,3,6,4,7] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,2,3,6,7,4] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,1,2,3,7,4,6] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,6,3,4,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,6,2,3,4,7] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,6,2,3,7,4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,1,2,3,4,7] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,1,2,3,7,4] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,1,2,3,4] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,7,5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1,2,3,7,4,5] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1,2,7,3,4,5] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,1,2,3,4,5] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,6,7] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,6,7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,4,5,7,8] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5,8] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,4,8,5,7] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,4,5,6,8] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,4,8,5,6] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,4,5,6,7] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,3,4,7,8] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,3,4,5,8,6] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,6,7] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,6,7] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,4,5,7,8] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,4,7,5,8] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,4,8,5,7] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,4,5,6,8] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,4,8,5,6] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,4,5,6,7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,2,7,4,8] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,2,4,6,7] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7,8] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,2,3,5,7,6,8] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,2,3,5,8,6,7] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,2,3,7,5,6,8] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,2,5,3,6,7,8] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,5,3,7,6,8] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,2,5,3,8,6,7] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,2,6,3,5,7,8] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,2,6,3,7,5,8] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,8,5,7] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,2,6,7,8,3,5] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,2,7,3,5,6,8] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,2,7,3,8,5,6] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,2,8,3,5,6,7] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,2,3,8] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,2,3,4,6,7,8] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,3,4,7,6,8] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,2,3,4,8,6,7] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,2,6,3,4,7,8] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,2,6,3,7,4,8] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,2,6,3,8,4,7] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,7,3,4,6,8] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,5,2,7,3,8,4,6] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,5,2,8,3,4,6,7] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,2,3,4,6,7] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,2,3,4,5,7,8] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,2,3,4,7,5,8] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,2,3,4,8,5,7] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,7,3,4,5,8] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,6,2,7,3,8,4,5] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,2,8,3,4,5,7] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,2,3,4,5,8] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,2,3,4,5] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,2,3,4,5,7] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,2,3,4,5,6,8] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,2,3,4,8,5,6] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,2,3,8,4,5,6] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,2,8,3,4,5,6] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,2,3,4,5,6] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,2,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,4,5,6,7] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,5,8,6] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,5,6,7] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,3,6,4,8,7] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,3,7,4,8,6] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,3,4,8,7] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,3,8,4,6] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,3,4,5,8,7] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,3,4,7,8,5] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,3,7,4,8,5] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,3,4,5] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,1,7] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,1,6] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,1,7,8,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,1,3,7,5,8,6] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,1,8,3] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,1,7,3,8,5] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,1,3,5,7] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,1,3,5,6] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,1,7,3,4,8,6] => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,5,6,8,1,3,4,7] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,5,7,8,1,3,4,6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,6,1,3,4,5,7,8] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,6,7,1,3,4,8,5] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,1,3,4,5] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,1,3,4,5,6,8] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,2,4,5,8,6,7] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,4,2,6,5,8,7] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,4,2,6,8,5,7] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,4,2,7,5,8,6] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,5,2,6,4,8,7] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,7,4,8,6] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,1,5,6,2,8,4,7] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,6,2,7,4,8,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,1,2,7,8,5,6] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,1,2] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,6,8,1,2,5,7] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,4,7,8,1,2,5,6] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,1,6,2,4,8,7] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,1,7,2,8,4,6] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,1,2,4,7] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,1,2,4,6] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,6,1,7,8,2,4,5] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,6,7,1,2,8,4,5] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,6,7,8,1,2,4,5] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,3,6,5,8,7] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,2,3,8,5,6,7] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,5,2,6,3,8,7] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,5,2,7,3,8,6] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,5,2,7,8,3,6] => 0
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,5,6,8,2,3,7] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,1,7,8,2,3,6] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,1,2,3,7,8] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,1,2,3,8,7] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,1,2,3,7] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,5,7,1,2,8,3,6] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,1,2,3,6] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,1,8,2,3,5] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,1,2,3,5] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,1,2,3,5,6,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,2,3,4,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2,3,4,6,8,7] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,1,2,8,3,4,6,7] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,6,2,7,3,8,4] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,1,2,3,4,8] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,1,2,3,4,6,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,2,3,4,5,7,8] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2,3,4,5,8,7] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,2,7,3,4,5,8] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,7,2,3,4,5,8] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,1,8,2,3,4,5,7] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,1,2,3,4,5,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,1,2,3,4,8,5] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,1,2,3,4,5] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,8,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,8,5,6] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => [8,1,2,3,4,5,6,7,9] => 0
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,1,2,3,4,5,6,9] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,2,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,2,3,4,5,6,7,8,9] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9,11] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,1,2,3,4,5,6,7,10] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,8,2,3,4,5,6,9] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,1,2,3,4,5,7,9] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,2,9,3,4,5,6,7] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,2,3,4,5,6,8] => 0
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,8,1,2,3,4,9] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,1,3,4,5,6,7,9] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2,3,4,5,6,9,8] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,2,3,4,5,6,8,9] => 0
[] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,1,8] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,9,7] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => [1,2,3,4,5,6,7,8,9] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 5
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,1,2,3,4,5,6,7,8,9] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,1,2,3,4,9] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,1,2,5,6,7,8,9,10] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,7,8,9,10,1,2,3,5,6] => 0
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,6,7,9,10,1,2,3,4,8] => 0
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,6,8,9,10,1,2,3,4,7] => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,7,8,9,10,1,2,3,4,6] => 0
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,5,7,9,10,1,2,4,6,8] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9,10] => 0
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,4,6,9,10,1,3,5,7,8] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,4,6,8,10,12,1,3,5,7,9,11] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,6,1,2,3,7,8,9] => 0
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,5,6,9,10,1,2,3,7,8] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,5,8,9,10,1,2,3,6,7] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,6,7,8,10,1,2,3,5,9] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,8,9,10,12,1,2,3,4,5,11] => 0
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Description
The number of small exceedances.
This is the number of indices $i$ such that $\pi_i=i+1$.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.