Identifier
Values
[1,0] => [1,1,0,0] => [1,2] => [1,1] => 2
[1,0,1,0] => [1,1,0,1,0,0] => [1,3,2] => [2,1] => 1
[1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => [1,1,1] => 3
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => [2,1,1] => 2
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,3,4,2] => [3,1] => 1
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => [3,1] => 1
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => [2,1,1] => 2
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,1,1,1] => 4
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [2,2,1] => 1
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [4,1] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [2,1,1,1] => 3
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [3,1,1] => 2
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [4,1] => 1
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [4,1] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [2,2,1] => 1
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [3,1,1] => 2
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [2,1,1,1] => 3
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [3,1,1] => 2
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [4,1] => 1
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [3,1,1] => 2
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [2,1,1,1] => 3
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [2,2,1,1] => 2
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [4,1,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [5,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [3,2,1] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [3,2,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [5,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [2,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [3,2,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [5,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [2,1,1,1,1] => 4
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [3,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [4,1,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [5,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [4,1,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [2,2,1,1] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [5,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [5,1] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [5,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [3,2,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [3,2,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [2,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [4,1,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [3,1,1,1] => 3
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [2,1,1,1,1] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [3,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [4,1,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [5,1] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [5,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [4,1,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [2,2,1,1] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [4,1,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [3,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [2,1,1,1,1] => 4
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [3,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [5,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [4,1,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [3,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [2,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [4,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [4,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [6,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [3,3,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [2,2,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [4,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [3,2,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [5,1,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [3,2,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [4,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [6,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [3,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [6,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [4,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [6,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [4,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [6,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [3,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [5,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [2,2,1,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [3,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [5,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [3,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [3,3,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [6,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [4,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [4,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [6,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [3,2,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [3,3,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [6,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [2,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [3,2,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [4,2,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [6,1] => 1
>>> Load all 739 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [2,1,1,1,1,1] => 5
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [3,1,1,1,1] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [4,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [5,1,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [6,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [4,2,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [2,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [6,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [4,2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [6,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [4,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [2,2,1,1,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [5,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [3,2,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [5,1,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [6,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [4,2,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [6,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [3,3,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [6,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [4,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [4,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [4,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [5,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [3,2,1,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [3,2,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [2,2,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [4,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [3,3,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [3,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [5,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [3,2,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [6,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [4,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [3,3,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [3,2,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [5,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [3,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [2,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [3,2,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [5,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [3,1,1,1,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [2,1,1,1,1,1] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [3,1,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [4,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [5,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [3,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [6,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [6,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [4,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [2,2,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [3,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [5,1,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [5,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [4,1,1,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [2,2,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [6,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [5,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [3,2,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [5,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [3,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [6,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [6,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [5,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [3,2,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [4,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [3,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [2,2,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [4,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [3,1,1,1,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [2,1,1,1,1,1] => 5
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [3,1,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [4,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [6,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [3,3,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [4,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [3,2,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [5,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [6,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [5,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [4,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [2,2,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [5,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [4,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [3,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [2,1,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [3,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [6,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [5,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [4,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [3,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [2,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [2,2,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,8] => [4,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,8] => [4,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,8] => [6,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,8] => [3,3,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [3,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [7,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,2,4,8,6] => [4,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,7,8,4,6] => [3,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [5,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [3,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [5,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [3,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [4,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [5,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [7,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [4,3,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,8,7] => [4,2,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,8,7] => [3,2,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,8,7] => [5,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,8,7] => [3,2,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => [7,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => [4,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => [7,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [2,2,1,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [4,1,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7,8] => [3,2,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [3,2,1,1,1] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4,8] => [4,2,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [6,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [3,3,1,1] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4,8] => [6,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,5,6,7,8,4] => [5,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [4,3,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [4,3,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => [4,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5,8] => [6,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => [2,2,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5,8] => [4,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => [7,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [3,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,6,2,7,4,8,5] => [4,3,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,6,7,2,4,8,5] => [7,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => [5,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [7,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => [3,2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,8,5,7] => [5,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,8,5,7] => [7,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,8,4,5,7] => [3,2,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,8,7] => [5,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,8,7] => [2,2,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7] => [3,2,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => [5,2,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,8,5,7] => [4,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,8,2,5,7] => [4,3,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7,8] => [3,2,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7,8] => [5,1,1,1] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7,8] => [5,1,1,1] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [3,3,1,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5,8] => [6,1,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5,8] => [4,2,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,6,7,8,5] => [4,2,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => [4,3,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,4,6,7,2,8,5] => [4,3,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [3,2,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,3,7,2,4,8,5,6] => [5,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [7,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [4,3,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [7,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [4,2,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => [4,3,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,4,7,2,5,8,6] => [7,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,3,2,4,7,8,5,6] => [2,2,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,3,4,2,7,8,5,6] => [3,2,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,3,4,7,8,2,5,6] => [7,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6,8] => [4,2,1,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [6,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6,8] => [6,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6,8] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,8] => [4,2,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [3,2,1,1,1] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [3,3,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [4,3,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [5,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => [5,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [7,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => [4,2,1,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [4,3,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [7,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [3,2,1,1,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,3,4,2,5,8,6,7] => [3,3,1,1] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [4,3,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [7,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [2,2,1,1,1,1] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,8,7] => [3,2,1,1,1] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,8,7] => [5,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,3,4,5,6,8,2,7] => [7,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [2,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [3,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [4,1,1,1,1] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [5,1,1,1] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [6,1,1] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [7,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => [4,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [2,2,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6,8] => [6,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => [4,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6,8] => [6,1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => [3,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [7,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,7,3,8,6] => [5,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,4,5,7,2,3,8,6] => [7,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,7,8,3,6] => [5,2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [3,2,2,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,7,8,2,3,6] => [7,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [4,3,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [3,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [5,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,8,7] => [4,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,8,7] => [3,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [5,2,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [4,3,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7,8] => [4,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [2,2,1,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [3,2,1,1,1] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7,8] => [5,1,1,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3,8] => [6,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [4,2,1,1] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [6,1,1] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [3,3,1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [7,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [5,2,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [4,3,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [7,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [6,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5,8] => [4,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [2,2,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [4,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [5,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [3,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [7,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,6,2,7,8,3,5] => [5,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,6,7,2,8,3,5] => [7,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,6,7,8,2,3,5] => [5,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [7,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [5,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,8,3,5,7] => [4,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,8,3,5,7] => [3,2,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [5,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => [5,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,8,7] => [3,2,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7] => [3,2,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [2,2,2,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,8,7] => [4,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [4,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,8,5,7] => [6,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [3,3,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [5,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7,8] => [3,2,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7,8] => [3,2,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [2,2,1,1,1,1] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [4,1,1,1,1] => 4
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5,8] => [3,3,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5,8] => [3,2,1,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,6,7,8,5] => [4,3,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => [4,2,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [6,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => [5,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => [3,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [7,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,7,2,8,3,5,6] => [5,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [5,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [4,3,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,4,7,3,5,8,6] => [6,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [3,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [2,2,2,1,1] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => [4,2,1,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => [6,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [6,1,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6,8] => [4,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [3,3,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6,8] => [3,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6,8] => [5,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6,8] => [3,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [2,2,1,1,1,1] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6,8] => [3,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,8] => [5,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => [3,3,1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [3,2,1,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,7,8,6] => [3,3,1,1] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => [4,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => [5,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => [4,3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [4,2,1,1] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [6,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [3,3,1,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [3,2,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [3,3,1,1] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [6,1,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,8,7] => [3,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [2,2,1,1,1,1] => 4
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7] => [4,2,1,1] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [6,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [3,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [2,1,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => [4,1,1,1,1] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => [5,1,1,1] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [6,1,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [3,3,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4,8] => [6,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [2,2,2,1,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [4,3,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [7,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [1,5,2,6,7,8,3,4] => [4,3,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [7,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [5,2,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [7,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [4,3,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [7,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => [7,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,5,6,2,8,3,4,7] => [5,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [3,2,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,8,7] => [3,2,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,8,7] => [5,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,8,7] => [5,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,8,7] => [4,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [4,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [6,1,1] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7,8] => [3,2,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7,8] => [5,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7,8] => [5,1,1,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7,8] => [4,1,1,1,1] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [2,2,1,1,1,1] => 4
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4,8] => [6,1,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => [5,1,1,1] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [3,2,1,1,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [6,1,1] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [4,2,1,1] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [6,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [3,3,1,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [3,2,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [5,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,7,8,3,4,6] => [5,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [7,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [5,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => [4,3,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [7,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,7,4,8,6] => [7,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [6,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => [4,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => [5,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,7,8,4,6] => [4,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [2,2,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [4,2,1,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [3,3,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6,8] => [6,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6,8] => [5,1,1,1] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [3,2,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6,8] => [4,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6,8] => [3,2,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [2,2,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [4,1,1,1,1] => 4
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,7,8,6] => [4,3,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [3,3,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [3,2,1,1,1] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [5,1,1,1] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [3,2,1,1,1] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [4,3,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [6,1,1] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [4,2,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [4,3,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => [3,3,1,1] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [3,2,1,1,1] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [5,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,8,7] => [4,2,1,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,8,7] => [3,2,1,1,1] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [2,2,1,1,1,1] => 4
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [3,2,1,1,1] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [5,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7,8] => [4,1,1,1,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [3,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [2,1,1,1,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [3,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [4,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [5,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,5] => [5,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [7,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => [3,2,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [5,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [7,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => [7,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,6,2,3,7,4,8,5] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => [3,3,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [6,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,6,2,3,7,8,4,5] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [6,1,1] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [4,2,1,1] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [2,2,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5,8] => [6,1,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [3,3,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5,8] => [4,2,1,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5,8] => [3,2,1,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [5,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [6,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,8] => [5,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [2,2,1,1,1,1] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,8,5] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [6,1,1] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [5,1,1,1] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [3,2,1,1,1] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [5,1,1,1] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,6,2,8,3,4,5,7] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [4,3,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => [4,3,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,8,4,5,7] => [3,3,1,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [6,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => [6,1,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [5,1,1,1] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [3,2,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => [5,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,8,7] => [4,2,1,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [3,2,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [2,2,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [4,1,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [5,1,1,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => [4,1,1,1,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7,8] => [3,1,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [3,1,1,1,1,1] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [4,3,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [6,1,1] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [3,3,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,7,2,3,4,8,5,6] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [4,2,1,1] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [3,2,1,1,1] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [5,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [6,1,1] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [5,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [2,2,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [6,1,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => [5,1,1,1] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [4,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [3,1,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [3,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [6,1,1] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [5,1,1,1] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [4,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [3,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [2,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,1,1,1,1,1,1,1] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => [2,2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8] => [4,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6,9,8] => [4,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6,9,8] => [6,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,9,8] => [3,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8] => [3,3,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,9,6] => [3,3,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,9,8] => [3,3,2,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8,9] => [4,1,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,9,8] => [4,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6,7,8,9,2,4,5] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,9] => [3,2,2,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,9,8] => [4,2,2,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,8,9,2,7] => [6,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => [8,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => [2,2,1,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,9,8] => [6,2,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,9,2,8] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [3,1,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8,9] => [6,1,1,1] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2,9] => [7,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [8,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => [4,2,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,9,8] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [8,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,9,3] => [8,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,2,3] => [4,4,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,9,8] => [6,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,9] => [3,2,2,1,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,9] => [2,2,2,1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,9,8] => [5,2,1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,4,9,3,5,6,7,8] => [7,1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => [3,1,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => [2,1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8,9] => [3,1,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8,9] => [4,1,1,1,1,1] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => [7,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,5,2,6,7,8,9,3,4] => [8,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,5,6,7,8,9,2,3,4] => [8,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,9,8] => [3,2,2,1,1] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,9,4] => [7,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,7,8,9,2,3,4,6] => [4,2,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,9,8] => [3,2,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => [2,2,2,1,1,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,9,8] => [4,2,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,5,9,4,6,7,8] => [6,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4,9] => [5,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => [6,1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [1,6,2,7,3,8,4,9,5] => [6,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,6,7,8,2,9,3,4,5] => [4,2,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [2,2,2,2,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5,9,8] => [5,2,1,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,9,8] => [4,2,1,1,1] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,9] => [4,1,1,1,1,1] => 5
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,9,5,7,8] => [5,1,1,1,1] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,9,5,8] => [5,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,7,8,9,2,3,4,5,6] => [8,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,9,6] => [3,3,1,1,1] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6,9] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,9] => [4,1,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6,9] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => [5,1,1,1,1] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,9,6] => [3,2,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => [8,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,9,5,6,8] => [3,2,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => [6,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,9,8] => [3,2,1,1,1,1] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,9,6,8] => [4,1,1,1,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8,9] => [6,1,1,1] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6,9] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => [4,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => [4,4,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [1,8,2,3,4,5,9,6,7] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,8,5,9,6,7] => [3,2,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,8,9,5,6,7] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,9,7] => [7,1,1] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,9,7] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => [4,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => [2,2,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7,9] => [7,1,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => [8,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [7,1,1] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [6,1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [5,1,1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [4,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [3,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [2,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => [9,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => [9,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [10,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => [8,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2,10] => [8,1,1] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [10,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,10,2,9] => [9,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,12,2] => [11,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [9,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,10,2,3] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,9,2,10,3,4,5,6,7,8] => [5,4,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[] => [1,0] => [1] => [1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,8,7,10,9] => [4,2,2,1,1] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => [8,1,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8,10] => [2,2,2,1,1,1,1] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,9,8,10] => [4,2,1,1,1,1] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4,9,10] => [5,1,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => [7,1,1,1] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,9,8,10] => [4,2,1,1,1,1] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,10,9] => [4,2,1,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => [6,1,1,1,1] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,10,9] => [4,2,1,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6,10] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7,10] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,10,7,9] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7,10] => [3,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,10,8] => [8,1,1] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,10,8] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,10,8] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [2,2,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => [3,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [8,1,1] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [7,1,1,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [6,1,1,1,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [5,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [4,1,1,1,1,1,1] => 6
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [3,1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [2,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,1,1,1,1,1,1,1,1,1] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [2,2,2,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6,9,8,10] => [4,2,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,10,9] => [3,2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [2,2,2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6,9,8,10] => [3,3,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,6,8,10] => [3,3,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,9,4,10,6,8] => [3,2,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,9,6,10] => [3,3,2,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,9,8,10] => [3,3,2,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,9,8,10] => [4,2,2,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [3,2,2,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8,10] => [4,2,2,1,1] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,5,6,7,8,9,10,2,3,4] => [3,3,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5,10] => [2,2,2,2,1,1] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,6,7,8,9,10,2,3,4,5] => [9,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,7,8,9,10,2,3,4,5,6] => [9,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [3,3,3,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7,8,9,10,11,2,3,4,5,6] => [2,2,2,2,2,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,10,7,9] => [9,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,8,7,10,9] => [3,2,2,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7,10,9,11] => [4,2,1,1,1,1,1] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,10,9,11] => [4,2,1,1,1,1,1] => 5
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [3,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [3,1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [2,1,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [2,1,1,1,1,1,1,1,1,1] => 9
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Description
The multiplicity of the smallest part of a partition.
This counts the number of occurrences of the smallest part $spt(\lambda)$ of a partition $\lambda$.
The sum $spt(n) = \sum_{\lambda \vdash n} spt(\lambda)$ satisfies the congruences
\begin{align*}
spt(5n+4) &\equiv 0\quad \pmod{5}\\
spt(7n+5) &\equiv 0\quad \pmod{7}\\
spt(13n+6) &\equiv 0\quad \pmod{13},
\end{align*}
analogous to those of the counting function of partitions, see [1] and [2].
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.