Identifier
Values
[1,1,0,0] => [2,3,1] => [1,1,0,1,0,0] => [1] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => [2] => 0
[1,1,0,0,1,0] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,1] => 0
[1,1,1,0,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [2,1] => 0
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [2,2] => 0
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [3,2] => 1
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 0
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 0
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [3] => 0
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 1
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 0
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 2
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 4
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 5
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 4
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 3
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 0
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,1,2,3,6,4,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,1,2,5,3,4,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [7,1,2,6,3,4,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [7,1,2,5,6,3,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,1,4,2,3,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,1,5,2,3,4,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,1,4,5,2,3,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
>>> Load all 330 entries. <<<
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [7,1,6,5,2,3,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [7,1,4,5,6,2,8,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,8,1,3,4,7,5,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,8,1,3,6,4,5,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,8,1,3,7,4,5,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,8,1,3,6,7,4,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,8,1,5,3,4,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,8,1,6,3,4,5,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,8,1,5,3,7,4,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,8,1,5,6,3,4,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,8,1,7,6,3,4,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,8,1,5,6,7,3,4] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,3,1,2,4,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [7,3,1,2,6,4,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,4,1,2,3,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,3,1,5,2,4,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7,3,1,5,6,2,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,8,4,1,3,5,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,8,4,1,3,7,5,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,8,5,1,3,4,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,8,4,1,6,7,3,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,3,4,1,2,5,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7,3,4,1,6,2,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,8,4,5,1,3,6,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,3,4,5,1,2,8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,8,4,5,6,1,3,7] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,3,4,5,6,1,8,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,1,2,3,4,7,5,9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,1,2,3,9,4,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [8,1,2,9,6,3,4,5,7] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,1,4,2,3,5,6,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,1,7,2,3,4,5,9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1,4,9,2,3,5,6,8] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1,9,6,2,3,4,5,8] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [8,1,4,5,6,2,3,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8,1,4,9,7,2,3,5,6] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8,1,9,5,6,2,3,4,7] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,7,6,2,3,4,5] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,9,1,3,4,5,8,6,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,9,1,3,4,8,5,6,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,9,1,3,8,7,4,5,6] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,9,1,3,6,7,8,4,5] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,9,1,8,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,9,1,8,6,7,3,4,5] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,9,1,5,6,7,8,3,4] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [8,3,1,2,4,5,6,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,9,1,2,3,4,6,7,8] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,6,1,2,3,4,5,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,7,1,2,3,4,5,9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,9,1,2,3,8,4,6,7] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8,6,1,2,3,7,4,9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,4,1,2,9,3,5,6,7] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,9,1,2,6,3,4,7,8] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,9,1,5,2,3,4,7,8] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,1,9,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8,7,1,6,2,3,4,9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,9,1,5,6,7,2,3,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,9,4,1,3,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [2,9,5,1,3,4,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,9,7,1,3,4,5,6,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,8,1,3,4,5,6,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,9,4,1,6,3,5,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,9,4,1,6,3,8,5,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [2,9,8,1,7,3,4,5,6] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [2,9,5,1,6,7,8,3,4] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [8,5,4,1,2,3,6,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,9,4,1,2,3,5,7,8] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,9,5,1,2,3,4,7,8] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,7,5,1,2,3,4,9,6] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [6,7,9,1,2,3,4,5,8] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [6,9,8,1,2,3,4,5,7] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,1,6,2,3,4,5] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [7,8,5,1,6,2,3,9,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,3,4,1,6,7,2,9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,5,4,1,6,7,2,9,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [2,9,4,5,1,3,6,7,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [2,9,8,6,1,3,4,5,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [2,8,9,6,1,7,3,4,5] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [2,9,6,5,1,7,8,3,4] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,3,8,9,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [7,8,4,6,1,2,3,9,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,6,5,1,2,3,9,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,9,6,1,7,2,4,5] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,6,5,1,7,2,9,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,6,4,5,1,7,2,9,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,8,9,5,7,1,3,4,6] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,8,9,7,6,1,3,4,5] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,9,7,5,6,1,8,3,4] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [8,3,4,5,6,1,2,9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,3,4,7,6,1,2,9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,3,9,7,6,1,2,4,5] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,3,7,5,6,1,2,9,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8,9,4,5,6,1,2,3,7] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,7,5,6,1,2,3,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,4,5,6,1,2,9,3] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [2,9,4,5,6,7,1,3,8] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [2,9,4,5,6,8,1,3,7] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,9,4,5,8,7,1,3,6] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [2,9,4,8,6,7,1,3,5] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,9,8,5,6,7,1,3,4] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,10,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9,1,10,8,6,7,2,3,4,5] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [9,3,4,5,6,7,1,2,10,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10,1,11,9,6,7,8,2,3,4,5] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 0
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,10,1,5,6,7,8,9,3,4] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,10,1,2,3,4,8,5,6,7] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9,7,1,2,3,4,8,5,10,6] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,7,2,3,4,5,6] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [8,9,4,5,10,1,2,3,6,7] => [1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,7,4,5,6,1,8,2,10,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [2,10,8,5,6,7,1,9,3,4] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,3,8,5,6,7,1,2,10,4] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,10,3] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [2,10,4,5,6,7,9,1,3,8] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [2,10,4,9,6,7,8,1,3,5] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [2,10,9,5,6,7,8,1,3,4] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,1,10,9,2,3,4,5,6,8] => [1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,10,7,2,3,4,5,6] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,11,8,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,11,1,2,3,4,5,6,7,9,10] => [1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,10,1,3,4,5,6,9,7,8] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,3,1,2,4,5,6,7,10,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,7,10,1,2,3,4,5,8,9] => [1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,10,5,1,2,3,4,7,8,9] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,7,1,10,2,3,4,5,6,9] => [1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,11,1,9,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,10,1,5,3,4,6,7,8,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,10,8,1,3,4,5,6,7,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,1,8,2,3,4,5,6,10,7] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,7,1,2,3,4,5,6,10,8] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,10,1,9,3,4,5,6,7,8] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8,11,1,2,3,4,5,9,10,6,7] => [1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,4,8,9,5,6,7] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,9,8,4,5,6,7] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,10,4,1,6,3,8,5,7,9] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 0
search for individual values
searching the database for the individual values of this statistic
Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight.
Given $\lambda$ count how many integer partitions $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.