Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [2,3,1] => 2
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [3,2,1] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => [1,3,4,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [2,3,1,4] => 3
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [2,3,4,1] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [4,3,1,2] => [3,4,2,1] => 5
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 5
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [4,1,3,2] => [2,4,3,1] => 4
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [4,2,1,3] => [3,2,4,1] => 5
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 6
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [1,2,4,5,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => [1,3,4,2,5] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [1,3,4,5,2] => 3
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,4,2,3] => [1,4,5,3,2] => 5
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,2,4,3] => [1,3,5,4,2] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,3,2,4] => [1,4,3,5,2] => 5
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 6
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => [2,1,4,5,3] => 6
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 7
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => [2,3,1,5,4] => 5
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [2,3,4,1,5] => 4
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [2,3,4,5,1] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [5,4,1,2,3] => [3,4,5,2,1] => 7
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [4,3,1,2,5] => [3,4,2,1,5] => 7
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [5,1,2,4,3] => [2,3,5,4,1] => 5
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [5,3,1,2,4] => [3,4,2,5,1] => 7
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [5,4,3,1,2] => [4,5,3,2,1] => 9
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 7
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 8
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [4,1,3,2,5] => [2,4,3,1,5] => 6
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [5,1,3,2,4] => [2,4,3,5,1] => 6
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [5,4,1,3,2] => [3,5,4,2,1] => 8
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [4,2,1,3,5] => [3,2,4,1,5] => 7
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [5,1,4,2,3] => [2,4,5,3,1] => 6
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [5,2,1,3,4] => [3,2,4,5,1] => 7
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [5,4,2,1,3] => [4,3,5,2,1] => 9
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 9
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [5,1,4,3,2] => [2,5,4,3,1] => 7
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [5,2,1,4,3] => [3,2,5,4,1] => 8
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [5,3,2,1,4] => [4,3,2,5,1] => 9
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [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] => [1,2,3,4,6,5] => [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] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,6,5,3,4] => [1,2,5,6,4,3] => 5
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,6,4,3,5] => [1,2,5,4,6,3] => 5
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,5,2,3,4] => [1,4,5,6,3,2] => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,5,4,2,3,6] => [1,4,5,3,2,6] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,4,2,3,5] => [1,4,5,3,6,2] => 7
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,5,4,2,3] => [1,5,6,4,3,2] => 9
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 8
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => 8
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,5,3,2,4,6] => [1,4,3,5,2,6] => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,3,2,4,5] => [1,4,3,5,6,2] => 7
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,6,5,3,2,4] => [1,5,4,6,3,2] => 9
>>> Load all 305 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 9
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,3,2,5,4] => [1,4,3,6,5,2] => 8
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,6,4,3,2,5] => [1,5,4,3,6,2] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => 7
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 8
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 8
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => 8
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => 8
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,5,3,4] => [2,1,5,6,4,3] => 10
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,3,5,4] => [2,1,4,6,5,3] => 9
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,4,3,5] => [2,1,5,4,6,3] => 10
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 11
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 7
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => 7
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [2,3,1,6,5,4] => 8
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => 9
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => 9
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 12
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 9
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => 10
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [5,1,2,4,3,6] => [2,3,5,4,1,6] => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [6,1,2,4,3,5] => [2,3,5,4,6,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => 10
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => 9
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => 12
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => 12
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [6,3,1,2,5,4] => [3,4,2,6,5,1] => 10
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => 12
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => 14
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 11
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,6,4,5] => [3,2,1,5,6,4] => 11
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [4,1,3,2,5,6] => [2,4,3,1,5,6] => 8
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [4,1,3,2,6,5] => [2,4,3,1,6,5] => 9
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [5,1,3,2,4,6] => [2,4,3,5,1,6] => 8
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [6,1,3,2,4,5] => [2,4,3,5,6,1] => 8
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [6,5,1,3,2,4] => [3,5,4,6,2,1] => 11
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [5,4,1,3,2,6] => [3,5,4,2,1,6] => 11
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [6,1,3,2,5,4] => [2,4,3,6,5,1] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [6,4,1,3,2,5] => [3,5,4,2,6,1] => 11
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [6,5,4,1,3,2] => [4,6,5,3,2,1] => 13
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [4,2,1,3,6,5] => [3,2,4,1,6,5] => 10
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [5,1,4,2,3,6] => [2,4,5,3,1,6] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [6,5,1,4,2,3] => [3,5,6,4,2,1] => 11
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => 8
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => 9
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => 12
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => 12
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [6,1,5,4,2,3] => [2,5,6,4,3,1] => 10
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [6,2,1,3,5,4] => [3,2,4,6,5,1] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => 12
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => 14
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 12
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 13
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [5,1,4,3,2,6] => [2,5,4,3,1,6] => 10
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [6,1,4,3,2,5] => [2,5,4,3,6,1] => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => 12
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [5,2,1,4,3,6] => [3,2,5,4,1,6] => 11
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [6,2,1,4,3,5] => [3,2,5,4,6,1] => 11
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [6,5,2,1,4,3] => [4,3,6,5,2,1] => 13
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => 12
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [6,1,5,3,2,4] => [2,5,4,6,3,1] => 10
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [6,2,1,5,3,4] => [3,2,5,6,4,1] => 11
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => 14
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 14
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => 11
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [6,2,1,5,4,3] => [3,2,6,5,4,1] => 12
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [6,3,2,1,5,4] => [4,3,2,6,5,1] => 13
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => 14
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [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] => [1,2,3,4,5,7,6] => [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] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,2,3,7,6,4,5] => [1,2,3,6,7,5,4] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,2,3,7,5,4,6] => [1,2,3,6,5,7,4] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => 6
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,2,4,5,6,3,7] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5] => [1,2,5,6,7,4,3] => 7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,2,6,5,3,4,7] => [1,2,5,6,4,3,7] => 7
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,2,7,5,3,4,6] => [1,2,5,6,4,7,3] => 7
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,2,7,6,5,3,4] => [1,2,6,7,5,4,3] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,2,6,3,5,4,7] => [1,2,4,6,5,3,7] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,2,7,3,5,4,6] => [1,2,4,6,5,7,3] => 6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,2,7,6,3,5,4] => [1,2,5,7,6,4,3] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,2,6,4,3,5,7] => [1,2,5,4,6,3,7] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,2,7,4,3,5,6] => [1,2,5,4,6,7,3] => 7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,2,7,6,4,3,5] => [1,2,6,5,7,4,3] => 9
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,2,7,3,6,5,4] => [1,2,4,7,6,5,3] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,2,7,4,3,6,5] => [1,2,5,4,7,6,3] => 8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,2,7,5,4,3,6] => [1,2,6,5,4,7,3] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,3,2,4,6,7,5] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => [1,3,2,4,7,6,5] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,3,2,5,6,4,7] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,3,2,5,6,7,4] => 8
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,3,2,7,6,4,5] => [1,3,2,6,7,5,4] => 10
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => [1,3,2,6,5,4,7] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,3,2,7,4,6,5] => [1,3,2,5,7,6,4] => 9
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,3,2,7,5,4,6] => [1,3,2,6,5,7,4] => 10
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => [1,3,2,7,6,5,4] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,3,4,2,5,6,7] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,3,4,2,5,7,6] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,3,4,2,6,5,7] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,3,4,2,6,7,5] => 7
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,4,2,3,7,6,5] => [1,3,4,2,7,6,5] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,3,4,5,2,6,7] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,3,4,5,2,7,6] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,3,4,5,6,2,7] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,7,6,2,3,4,5] => [1,4,5,6,7,3,2] => 9
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,6,5,2,3,4,7] => [1,4,5,6,3,2,7] => 9
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,7,5,2,3,4,6] => [1,4,5,6,3,7,2] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,5,4,2,3,6,7] => [1,4,5,3,2,6,7] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,5,4,2,3,7,6] => [1,4,5,3,2,7,6] => 10
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,6,2,3,5,4,7] => [1,3,4,6,5,2,7] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,2,3,5,4,6] => [1,3,4,6,5,7,2] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,7,6,2,3,5,4] => [1,4,5,7,6,3,2] => 10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,6,4,2,3,5,7] => [1,4,5,3,6,2,7] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,7,4,2,3,5,6] => [1,4,5,3,6,7,2] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,2,3,6,5,4] => [1,3,4,7,6,5,2] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,7,4,2,3,6,5] => [1,4,5,3,7,6,2] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => [1,4,3,2,5,6,7] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => [1,4,3,2,5,7,6] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => [1,4,3,2,6,5,7] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,4,3,2,7,5,6] => [1,4,3,2,6,7,5] => 11
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => [1,4,3,2,7,6,5] => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,5,2,4,3,6,7] => [1,3,5,4,2,6,7] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,5,2,4,3,7,6] => [1,3,5,4,2,7,6] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,6,2,4,3,5,7] => [1,3,5,4,6,2,7] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,2,4,3,5,6] => [1,3,5,4,6,7,2] => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,6,5,2,4,3,7] => [1,4,6,5,3,2,7] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,2,4,3,6,5] => [1,3,5,4,7,6,2] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,7,5,2,4,3,6] => [1,4,6,5,3,7,2] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,5,3,2,4,6,7] => [1,4,3,5,2,6,7] => 9
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,5,3,2,4,7,6] => [1,4,3,5,2,7,6] => 10
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,6,2,5,3,4,7] => [1,3,5,6,4,2,7] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,2,5,3,4,6] => [1,3,5,6,4,7,2] => 8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,6,3,2,4,5,7] => [1,4,3,5,6,2,7] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,7,3,2,4,5,6] => [1,4,3,5,6,7,2] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,2,6,5,3,4] => [1,3,6,7,5,4,2] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,7,3,2,4,6,5] => [1,4,3,5,7,6,2] => 10
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,6,2,5,4,3,7] => [1,3,6,5,4,2,7] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,2,5,4,3,6] => [1,3,6,5,4,7,2] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,6,3,2,5,4,7] => [1,4,3,6,5,2,7] => 11
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,2,6,3,5,4] => [1,3,5,7,6,4,2] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,7,3,2,5,4,6] => [1,4,3,6,5,7,2] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,2,6,4,3,5] => [1,3,6,5,7,4,2] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,7,3,2,6,4,5] => [1,4,3,6,7,5,2] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,2,6,5,4,3] => [1,3,7,6,5,4,2] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,7,3,2,6,5,4] => [1,4,3,7,6,5,2] => 12
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Description
The disorder of a permutation.
Consider a permutation $\pi = [\pi_1,\ldots,\pi_n]$ and cyclically scanning $\pi$ from left to right and remove the elements $1$ through $n$ on this order one after the other. The disorder of $\pi$ is defined to be the number of times a position was not removed in this process.
For example, the disorder of $[3,5,2,1,4]$ is $8$ since on the first scan, 3,5,2 and 4 are not removed, on the second, 3,5 and 4, and on the third and last scan, 5 is once again not removed.
Map
inverse
Description
Sends a permutation to its inverse.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.