Identifier
Values
[1,0] => [1] => 0
[1,0,1,0] => [2,1] => 0
[1,1,0,0] => [1,2] => 0
[1,0,1,0,1,0] => [3,2,1] => 1
[1,0,1,1,0,0] => [2,3,1] => 0
[1,1,0,0,1,0] => [3,1,2] => 0
[1,1,0,1,0,0] => [2,1,3] => 0
[1,1,1,0,0,0] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => 0
[1,0,1,1,0,1,0,0] => [3,2,4,1] => 0
[1,0,1,1,1,0,0,0] => [2,3,4,1] => 0
[1,1,0,0,1,0,1,0] => [4,3,1,2] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => 0
[1,1,0,1,0,0,1,0] => [4,2,1,3] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => 0
[1,1,1,0,0,0,1,0] => [4,1,2,3] => 0
[1,1,1,0,0,1,0,0] => [3,1,2,4] => 0
[1,1,1,0,1,0,0,0] => [2,1,3,4] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 0
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => 0
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 0
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => 0
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 0
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => 0
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => 2
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => 2
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => 0
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => 0
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => 0
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => 1
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => 0
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => 0
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => 0
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => 0
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => 0
>>> Load all 490 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 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] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 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] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => 0
[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
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => 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] => 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] => 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] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 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] => 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] => 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] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => 1
[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] => 0
[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] => 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] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => 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] => 0
[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] => 0
[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] => 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
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => 1
[] => [] => 0
[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] => 6
[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] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => 4
[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] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => 0
[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] => 5
[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] => 0
[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] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => 0
[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] => 3
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => 0
[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] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => 0
[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] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => 0
[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] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 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] => 7
[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] => 8
[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] => 7
[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] => 8
[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] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => 0
[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] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => 0
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 0
[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] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => 6
[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] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => 0
[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] => 0
[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] => 0
[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] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => 5
[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] => 6
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => 0
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => 0
[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] => 4
[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] => 1
[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] => 3
[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] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => 0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => 0
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Description
The number of double descents of a permutation.
A double descent of a permutation $\pi$ is a position $i$ such that $\pi(i) > \pi(i+1) > \pi(i+2)$.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].