Identifier
Values
[1] => [1,0] => [1] => 0
[1,2] => [1,0,1,0] => [1,2] => 0
[2,1] => [1,1,0,0] => [2,1] => 0
[1,2,3] => [1,0,1,0,1,0] => [1,2,3] => 1
[1,3,2] => [1,0,1,1,0,0] => [1,3,2] => 0
[2,1,3] => [1,1,0,0,1,0] => [2,1,3] => 0
[2,3,1] => [1,1,0,1,0,0] => [2,3,1] => 0
[3,1,2] => [1,1,1,0,0,0] => [3,2,1] => 0
[3,2,1] => [1,1,1,0,0,0] => [3,2,1] => 0
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 3
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 2
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 1
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 1
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 0
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 0
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => 0
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => 0
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 0
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 0
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => 0
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [3,4,2,1] => 0
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [3,4,2,1] => 0
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 6
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 5
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 4
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 4
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 3
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 3
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 3
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 3
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 3
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 2
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 0
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 3
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 1
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 3
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 3
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 3
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 2
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 2
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 1
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 1
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 1
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 0
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 1
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 1
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 1
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 1
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 1
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 1
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 0
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 1
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 1
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 1
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 1
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 1
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 1
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
>>> Load all 1197 entries. <<<
[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 0
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 0
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 0
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 0
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 10
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 9
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 8
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 8
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 7
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 7
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 7
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 6
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 7
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 7
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 6
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 6
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 5
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 5
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 5
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 5
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 5
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 6
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 5
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 4
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 3
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 6
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 5
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 6
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 6
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 5
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 5
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 4
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 4
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 4
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 4
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 4
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 4
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 3
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 2
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 3
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 3
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 2
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 2
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 3
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 2
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 2
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 3
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => 3
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 3
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => 3
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => 3
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => 3
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 1
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 0
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 6
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 5
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 4
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 3
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 3
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 2
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => 1
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 6
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 5
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 3
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 5
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 6
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 6
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 5
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 5
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 4
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 4
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 4
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => 4
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 3
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 3
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 2
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 3
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 3
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 2
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 2
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 2
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 2
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => 3
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => 3
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => 3
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => 3
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 1
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 0
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 3
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 2
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 1
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 1
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 0
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 0
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 3
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 2
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 3
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 3
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 2
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 2
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 1
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 1
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 1
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 0
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 0
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 2
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 2
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 1
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 1
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => 3
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => 2
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => 3
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => 3
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 2
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 2
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 2
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => 3
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => 3
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => 3
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => 3
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 1
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 0
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 0
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 0
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 0
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 0
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 0
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 0
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 15
[1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 14
[1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 13
[1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => 13
[1,2,3,4,7,5,6] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 12
[1,2,3,4,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => 12
[1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => 12
[1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => 11
[1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => 12
[1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => 12
[1,2,3,5,7,4,6] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 11
[1,2,3,5,7,6,4] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => 11
[1,2,3,6,4,5,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 10
[1,2,3,6,4,7,5] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 10
[1,2,3,6,5,4,7] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => 10
[1,2,3,6,5,7,4] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => 10
[1,2,3,6,7,4,5] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => 10
[1,2,3,6,7,5,4] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => 10
[1,2,3,7,4,5,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,3,7,4,6,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,3,7,5,4,6] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,3,7,5,6,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,3,7,6,4,5] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,3,7,6,5,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => 9
[1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => 11
[1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => 10
[1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => 9
[1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => 9
[1,2,4,3,7,5,6] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 8
[1,2,4,3,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => 8
[1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => 11
[1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => 10
[1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => 11
[1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => 11
[1,2,4,5,7,3,6] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 10
[1,2,4,5,7,6,3] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => 10
[1,2,4,6,3,5,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 9
[1,2,4,6,3,7,5] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 9
[1,2,4,6,5,3,7] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => 9
[1,2,4,6,5,7,3] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => 9
[1,2,4,6,7,3,5] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => 9
[1,2,4,6,7,5,3] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => 9
[1,2,4,7,3,5,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,4,7,3,6,5] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,4,7,5,3,6] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,4,7,5,6,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,4,7,6,3,5] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,4,7,6,5,3] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => 8
[1,2,5,3,4,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 8
[1,2,5,3,4,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 7
[1,2,5,3,6,4,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 8
[1,2,5,3,6,7,4] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 8
[1,2,5,3,7,4,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 7
[1,2,5,3,7,6,4] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 7
[1,2,5,4,3,6,7] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => 8
[1,2,5,4,3,7,6] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => 7
[1,2,5,4,6,3,7] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => 8
[1,2,5,4,6,7,3] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => 8
[1,2,5,4,7,3,6] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 7
[1,2,5,4,7,6,3] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => 7
[1,2,5,6,3,4,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => 8
[1,2,5,6,3,7,4] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => 8
[1,2,5,6,4,3,7] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => 8
[1,2,5,6,4,7,3] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => 8
[1,2,5,6,7,3,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => 8
[1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => 8
[1,2,5,7,3,4,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,5,7,3,6,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,5,7,4,3,6] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,5,7,4,6,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,5,7,6,3,4] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,5,7,6,4,3] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => 7
[1,2,6,3,4,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,3,4,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,3,5,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,3,5,7,4] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,3,7,4,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,3,7,5,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,4,3,5,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,4,3,7,5] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,4,5,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,4,5,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,4,7,3,5] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,4,7,5,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,5,3,4,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,5,3,7,4] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,5,4,3,7] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => 6
[1,2,6,5,4,7,3] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => 6
[1,2,6,5,7,3,4] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,5,7,4,3] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => 6
[1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,6,7,3,5,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,6,7,4,3,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,6,7,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,6,7,5,3,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,6,7,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => 6
[1,2,7,3,4,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,3,4,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,3,5,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,3,5,6,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,3,6,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,3,6,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,3,5,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,3,6,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,5,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,5,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,6,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,4,6,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,3,4,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,3,6,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,4,3,6] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,4,6,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,6,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,5,6,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,3,4,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,3,5,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,4,3,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,4,5,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,5,3,4] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,2,7,6,5,4,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => 5
[1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 10
[1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => 9
[1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => 8
[1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => 8
[1,3,2,4,7,5,6] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 7
[1,3,2,4,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => 7
[1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => 7
[1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => 6
[1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => 7
[1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => 7
[1,3,2,5,7,4,6] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 6
[1,3,2,5,7,6,4] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => 6
[1,3,2,6,4,5,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 5
[1,3,2,6,4,7,5] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 5
[1,3,2,6,5,4,7] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => 5
[1,3,2,6,5,7,4] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => 5
[1,3,2,6,7,4,5] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => 5
[1,3,2,6,7,5,4] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => 5
[1,3,2,7,4,5,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,2,7,4,6,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,2,7,5,4,6] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,2,7,5,6,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,2,7,6,4,5] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,2,7,6,5,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => 10
[1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => 9
[1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => 8
[1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => 8
[1,3,4,2,7,5,6] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 7
[1,3,4,2,7,6,5] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => 7
[1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => 10
[1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => 9
[1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => 10
[1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => 10
[1,3,4,5,7,2,6] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 9
[1,3,4,5,7,6,2] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => 9
[1,3,4,6,2,5,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 8
[1,3,4,6,2,7,5] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 8
[1,3,4,6,5,2,7] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => 8
[1,3,4,6,5,7,2] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => 8
[1,3,4,6,7,2,5] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => 8
[1,3,4,6,7,5,2] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => 8
[1,3,4,7,2,5,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,4,7,2,6,5] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,4,7,5,2,6] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,4,7,5,6,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,4,7,6,2,5] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,4,7,6,5,2] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => 7
[1,3,5,2,4,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 7
[1,3,5,2,4,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 6
[1,3,5,2,6,4,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 7
[1,3,5,2,6,7,4] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 7
[1,3,5,2,7,4,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 6
[1,3,5,2,7,6,4] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 6
[1,3,5,4,2,6,7] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => 7
[1,3,5,4,2,7,6] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => 7
[1,3,5,4,6,7,2] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => 7
[1,3,5,4,7,2,6] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 6
[1,3,5,4,7,6,2] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => 6
[1,3,5,6,2,4,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => 7
[1,3,5,6,2,7,4] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => 7
[1,3,5,6,4,2,7] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => 7
[1,3,5,6,4,7,2] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => 7
[1,3,5,6,7,2,4] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => 7
[1,3,5,6,7,4,2] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => 7
[1,3,5,7,2,4,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,5,7,2,6,4] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,5,7,4,2,6] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,5,7,4,6,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,5,7,6,2,4] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,5,7,6,4,2] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => 6
[1,3,6,2,4,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,2,4,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,2,5,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,2,5,7,4] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,2,7,4,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,2,7,5,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,4,2,5,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,4,2,7,5] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,4,5,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,4,5,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,4,7,2,5] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,4,7,5,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,5,2,4,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,5,2,7,4] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,5,4,2,7] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => 5
[1,3,6,5,4,7,2] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => 5
[1,3,6,5,7,2,4] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,5,7,4,2] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => 5
[1,3,6,7,2,4,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,6,7,2,5,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,6,7,4,2,5] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,6,7,4,5,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,6,7,5,2,4] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,6,7,5,4,2] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => 5
[1,3,7,2,4,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,2,4,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,2,5,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,2,5,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,2,6,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,2,6,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,2,5,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,2,6,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,5,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,5,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,6,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,4,6,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,2,4,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,2,6,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,4,2,6] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,4,6,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,6,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,5,6,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,2,4,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,2,5,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,4,2,5] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,4,5,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,5,2,4] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,3,7,6,5,4,2] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 6
[1,4,2,3,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 5
[1,4,2,3,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 4
[1,4,2,3,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 4
[1,4,2,3,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 3
[1,4,2,3,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 3
[1,4,2,5,3,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 6
[1,4,2,5,3,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 5
[1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 6
[1,4,2,5,6,7,3] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 6
[1,4,2,5,7,3,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 5
[1,4,2,5,7,6,3] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 5
[1,4,2,6,3,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 4
[1,4,2,6,3,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 4
[1,4,2,6,5,3,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 4
[1,4,2,6,5,7,3] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 4
[1,4,2,6,7,3,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => 4
[1,4,2,6,7,5,3] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => 4
[1,4,2,7,3,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,2,7,3,6,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,2,7,5,3,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,2,7,5,6,3] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,2,7,6,3,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,2,7,6,5,3] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,2,5,6,7] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => 6
[1,4,3,2,5,7,6] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => 5
[1,4,3,2,6,5,7] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => 4
[1,4,3,2,6,7,5] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 3
[1,4,3,2,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => 3
[1,4,3,5,2,6,7] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => 5
[1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => 6
[1,4,3,5,6,7,2] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => 6
[1,4,3,5,7,2,6] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 5
[1,4,3,5,7,6,2] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => 5
[1,4,3,6,2,5,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 4
[1,4,3,6,2,7,5] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 4
[1,4,3,6,5,2,7] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => 4
[1,4,3,6,7,2,5] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => 4
[1,4,3,6,7,5,2] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,7,2,6,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,7,5,2,6] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,7,5,6,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,7,6,2,5] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,3,7,6,5,2] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => 3
[1,4,5,2,3,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => 6
[1,4,5,2,3,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => 5
[1,4,5,2,6,3,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => 6
[1,4,5,2,6,7,3] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => 6
[1,4,5,2,7,3,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => 5
[1,4,5,2,7,6,3] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => 5
[1,4,5,3,2,6,7] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => 6
[1,4,5,3,2,7,6] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => 5
[1,4,5,3,6,2,7] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => 6
[1,4,5,3,6,7,2] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => 6
[1,4,5,3,7,2,6] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => 5
[1,4,5,3,7,6,2] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => 5
[1,4,5,6,2,3,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => 6
[1,4,5,6,2,7,3] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => 6
[1,4,5,6,3,2,7] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => 6
[1,4,5,6,7,2,3] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => 6
[1,4,5,6,7,3,2] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => 6
[1,4,5,7,2,3,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,5,7,2,6,3] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,5,7,3,2,6] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,5,7,3,6,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,5,7,6,2,3] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,5,7,6,3,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => 5
[1,4,6,2,3,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,2,3,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
[1,4,6,2,5,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,2,5,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
[1,4,6,3,2,5,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,3,2,7,5] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
[1,4,6,3,5,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,3,5,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
[1,4,6,5,2,3,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,5,2,7,3] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
[1,4,6,5,3,2,7] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => 4
[1,4,6,5,3,7,2] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => 4
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of occurrences of the pattern 12-3.
See Permutations/#Pattern-avoiding_permutations for the definition of the pattern $12\!\!-\!\!3$.
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
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.