Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00153: Standard tableaux —inverse promotion⟶ Standard tableaux
St001803: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [[1]] => [[1]] => 0
[1,0,1,0] => [1,2] => [[1,2]] => [[1,2]] => 0
[1,1,0,0] => [2,1] => [[1],[2]] => [[1],[2]] => 1
[1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => [[1,2,3]] => 0
[1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => [[1,3],[2]] => 0
[1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => [[1,2],[3]] => 1
[1,1,0,1,0,0] => [2,3,1] => [[1,2],[3]] => [[1,3],[2]] => 0
[1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => [[1],[2],[3]] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => [[1,2,3,4]] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => [[1,2,4],[3]] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => [[1,3,4],[2]] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,3],[4]] => [[1,2,4],[3]] => 0
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => [[1,2,3],[4]] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => [[1,2],[3,4]] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,2,4],[3]] => [[1,3,4],[2]] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,2,3],[4]] => [[1,2,4],[3]] => 0
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 0
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => [[1,3],[2],[4]] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => [[1,2],[3],[4]] => 1
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => [[1,4],[2],[3]] => 0
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => [[1,2,4,5],[3]] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => [[1,3,4,5],[2]] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => [[1,3,5],[2,4]] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,3,5],[4]] => [[1,2,4,5],[3]] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => [[1,4,5],[2],[3]] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => [[1,2,3,4],[5]] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => [[1,2,3],[4,5]] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => [[1,2,4],[3,5]] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,4],[2,5]] => [[1,2,3],[4,5]] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => [[1,2],[3,5],[4]] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => [[1,3,4,5],[2]] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,2,4],[3,5]] => [[1,3,5],[2,4]] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => [[1,2,4,5],[3]] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => [[1,2,3,5],[4]] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,2,5],[3],[4]] => [[1,4,5],[2],[3]] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => [[1,3,4],[2],[5]] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => [[1,3],[2,4],[5]] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => [[1,2,3],[4],[5]] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => [[1,2],[3,5],[4]] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => [[1,4,5],[2],[3]] => 0
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => [[1,2,5],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 0
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => [[1,4],[2],[3],[5]] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => [[1,3],[2],[4],[5]] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => [[1,2],[3],[4],[5]] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 0
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => [[1,2,3,5,6],[4]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => [[1,2,4,5,6],[3]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => [[1,2,4,6],[3,5]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => [[1,2,3,5,6],[4]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => [[1,3,4,5,6],[2]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => [[1,3,5,6],[2,4]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => [[1,3,6],[2,4],[5]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => [[1,2,4,5,6],[3]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => [[1,2,4,6],[3,5]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => [[1,2,3,5,6],[4]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => [[1,4,5,6],[2],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => [[1,4,6],[2,5],[3]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => [[1,3,5,6],[2],[4]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => [[1,3,6],[2,4],[5]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
>>> Load all 1647 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => [[1,5,6],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => [[1,4,6],[2],[3],[5]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [[1,2,4],[3],[5],[6]] => [[1,3,6],[2],[4],[5]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [[1,2,3,4,5],[6]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => [[1,2,3,4],[5,6]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => [[1,2,3,5],[4,6]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => [[1,2,3,4],[5,6]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => [[1,2,3],[4,6],[5]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => [[1,2,4,5],[3,6]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => [[1,2,4],[3,5,6]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => [[1,2,3,5],[4,6]] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => [[1,2,3,4],[5,6]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => [[1,2,3],[4,6],[5]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => [[1,2,4],[3,6],[5]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => [[1,2,3],[4,6],[5]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => [[1,2],[3,6],[4],[5]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => [[1,3,4,5,6],[2]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => [[1,3,5,6],[2,4]] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => [[1,3,6],[2,4],[5]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => [[1,2,4,5,6],[3]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => [[1,2,4,6],[3,5]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => [[1,2,3,5,6],[4]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => [[1,2,3,4,6],[5]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => [[1,4,5,6],[2],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => [[1,4,6],[2,5],[3]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => [[1,3,5,6],[2],[4]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => [[1,3,6],[2,4],[5]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => [[1,5,6],[2],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => [[1,4,6],[2],[3],[5]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[1,2,4],[3],[5],[6]] => [[1,3,6],[2],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [[1,3,4,5],[2],[6]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => [[1,3,4],[2,5],[6]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => [[1,3,5],[2,4],[6]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => [[1,3,4],[2,5],[6]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => [[1,3],[2,4],[5,6]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => [[1,2,4,5],[3],[6]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => [[1,2,4],[3,5],[6]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => [[1,2,3,5],[4],[6]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => [[1,2,3,4],[5],[6]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => [[1,2,3],[4,6],[5]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => [[1,2,4],[3,6],[5]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[1,3,4],[2,5],[6]] => [[1,2,3],[4,6],[5]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => [[1,2],[3,6],[4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => [[1,4,5,6],[2],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => [[1,4,6],[2,5],[3]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => [[1,3,5,6],[2],[4]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[1,2,4],[3,5],[6]] => [[1,3,6],[2,4],[5]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => [[1,2,4,6],[3],[5]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => [[1,2,3,6],[4],[5]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[1,2,6],[3],[4],[5]] => [[1,5,6],[2],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[1,2,5],[3],[4],[6]] => [[1,4,6],[2],[3],[5]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[1,2,4],[3],[5],[6]] => [[1,3,6],[2],[4],[5]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [[1,4,5],[2],[3],[6]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => [[1,4],[2,5],[3],[6]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => [[1,3,5],[2],[4],[6]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => [[1,3,4],[2],[5],[6]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => [[1,2,5],[3],[4],[6]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => [[1,2,4],[3],[5],[6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => [[1,2,3],[4],[5],[6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => [[1,2],[3,6],[4],[5]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => [[1,5,6],[2],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => [[1,4,6],[2],[3],[5]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => [[1,3,6],[2],[4],[5]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => [[1,2,6],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [[1,5],[2],[3],[4],[6]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => [[1,4],[2],[3],[5],[6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => [[1,3],[2],[4],[5],[6]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,6,7],[5]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,5,7],[4,6]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,6,7],[5]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,4,5,6,7],[3]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,4,6,7],[3,5]] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,5,7],[4,6]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,6,7],[5]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [[1,3,4,5,6,7],[2]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [[1,3,4,6,7],[2,5]] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [[1,3,5,6,7],[2,4]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [[1,3,5,7],[2,4,6]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]] => [[1,3,4,6,7],[2,5]] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => [[1,3,6,7],[2,4],[5]] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,4],[6]] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,4,5,6,7],[3]] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,4,6,7],[3,5]] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,5,7],[4,6]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,6,7],[5]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => [[1,4,5,6,7],[2],[3]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => [[1,4,6,7],[2,5],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => [[1,4,7],[2,5],[3,6]] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,3,5,6,7],[2],[4]] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,6],[4]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]] => [[1,3,4,6,7],[2],[5]] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]] => [[1,3,4,5,7],[2],[6]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [[1,2,4,7],[3,5],[6]] => [[1,3,6,7],[2,4],[5]] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,4],[6]] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,5,6,7],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,5,7],[2,6],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [[1,2,5,7],[3],[4],[6]] => [[1,4,6,7],[2],[3],[5]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [[1,2,5,6],[3],[4],[7]] => [[1,4,5,7],[2],[3],[6]] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [[1,2,5],[3,6],[4],[7]] => [[1,4,7],[2,5],[3],[6]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [[1,2,4,7],[3],[5],[6]] => [[1,3,6,7],[2],[4],[5]] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [[1,2,4,5],[3],[6],[7]] => [[1,3,4,7],[2],[5],[6]] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [[1,2,6],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [[1,2,4],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => [[1,2,3,4,6],[5,7]] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => [[1,2,3,5,6],[4,7]] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => [[1,2,3,5],[4,6,7]] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]] => [[1,2,3,4,6],[5,7]] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,3,6],[4,7],[5]] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => [[1,2,4,5,6],[3,7]] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => [[1,2,4,5],[3,6,7]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]] => [[1,2,4,5],[3,6,7]] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => [[1,2,4],[3,5,7],[6]] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => [[1,2,3,5,6],[4,7]] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => [[1,2,3,5],[4,6,7]] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => [[1,2,3,4,6],[5,7]] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => [[1,2,3,4,5],[6,7]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,3,6],[4,7],[5]] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => [[1,2,5,6],[3,7],[4]] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => [[1,2,5],[3,6,7],[4]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,7],[5]] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,5],[3,7],[6]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[1,3,5],[2,4,6],[7]] => [[1,2,4],[3,5,7],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,3,6],[4,7],[5]] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => [[1,2,6],[3,7],[4],[5]] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[1,3,6],[2,4],[5],[7]] => [[1,2,5],[3,7],[4],[6]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4],[3,7],[5],[6]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => [[1,2],[3,7],[4],[5],[6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [[1,3,4,5,6,7],[2]] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => [[1,3,4,6,7],[2,5]] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => [[1,3,5,6,7],[2,4]] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => [[1,3,5,7],[2,4,6]] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => [[1,3,4,6,7],[2,5]] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => [[1,3,6,7],[2,4],[5]] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,4],[6]] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => [[1,2,4,5,6,7],[3]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => [[1,2,4,6,7],[3,5]] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => [[1,2,4,5,7],[3,6]] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => [[1,2,3,5,7],[4,6]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => [[1,2,3,4,6,7],[5]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => [[1,2,3,4,5,7],[6]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => [[1,4,5,6,7],[2],[3]] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => [[1,4,6,7],[2,5],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => [[1,4,7],[2,5],[3,6]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,3,5,6,7],[2],[4]] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,6],[4]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => [[1,3,4,6,7],[2],[5]] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => [[1,3,4,5,7],[2],[6]] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => [[1,3,6,7],[2,4],[5]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,4],[6]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,5,6,7],[2],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,5,7],[2,6],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[1,2,5,7],[3],[4],[6]] => [[1,4,6,7],[2],[3],[5]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[1,2,5,6],[3],[4],[7]] => [[1,4,5,7],[2],[3],[6]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[1,2,5],[3,6],[4],[7]] => [[1,4,7],[2,5],[3],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[1,2,4,7],[3],[5],[6]] => [[1,3,6,7],[2],[4],[5]] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[1,2,4,5],[3],[6],[7]] => [[1,3,4,7],[2],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => [[1,3,4,5,6],[2],[7]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => [[1,3,4,5],[2,6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => [[1,3,4,6],[2,5],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[1,4,5,6],[2,7],[3]] => [[1,3,4,5],[2,6],[7]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => [[1,3,5,6],[2,4],[7]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => [[1,3,5],[2,4,6],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[1,4,5,7],[2,6],[3]] => [[1,3,4,6],[2,5],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[1,4,5,6],[2,7],[3]] => [[1,3,4,5],[2,6],[7]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[1,4,5],[2,6],[3,7]] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => [[1,3,6],[2,4],[5,7]] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[1,4,6],[2,5],[3,7]] => [[1,3,5],[2,4],[6,7]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[1,4,5],[2,6],[3,7]] => [[1,3,4],[2,5],[6,7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => [[1,3],[2,4],[5,7],[6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [[1,2,4,5,6],[3],[7]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,5],[3,6],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,5],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => [[1,2,4,5],[3,6],[7]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => [[1,2,4],[3,5],[6,7]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => [[1,2,3,5,6],[4],[7]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => [[1,2,3,5],[4,6],[7]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => [[1,2,3,4,6],[5],[7]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => [[1,2,3,4,5],[6],[7]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,3,6],[4,7],[5]] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[1,3,6,7],[2,4],[5]] => [[1,2,5,6],[3,7],[4]] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[1,3,6],[2,4,7],[5]] => [[1,2,5],[3,6,7],[4]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,7],[5]] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]] => [[1,2,4,5],[3,7],[6]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[1,3,5],[2,4,6],[7]] => [[1,2,4],[3,5,7],[6]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[1,3,4,7],[2,5],[6]] => [[1,2,3,6],[4,7],[5]] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => [[1,2,3,5],[4,7],[6]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[1,3,4,5],[2,6],[7]] => [[1,2,3,4],[5,7],[6]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[1,3,7],[2,4],[5],[6]] => [[1,2,6],[3,7],[4],[5]] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[1,3,6],[2,4],[5],[7]] => [[1,2,5],[3,7],[4],[6]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4],[3,7],[5],[6]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => [[1,2],[3,7],[4],[5],[6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => [[1,4,5,6,7],[2],[3]] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => [[1,4,6,7],[2,5],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => [[1,4,5,7],[2,6],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => [[1,4,7],[2,5],[3,6]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => [[1,3,5,6,7],[2],[4]] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,6],[4]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => [[1,3,4,6,7],[2],[5]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => [[1,3,4,5,7],[2],[6]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => [[1,3,6,7],[2,4],[5]] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,4],[6]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => [[1,3,4,7],[2,5],[6]] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => [[1,2,5,6,7],[3],[4]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [[1,2,3,6],[4,7],[5]] => [[1,2,5,7],[3,6],[4]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => [[1,2,4,5,7],[3],[6]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[1,2,3,5],[4,6],[7]] => [[1,2,4,7],[3,5],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => [[1,2,3,6,7],[4],[5]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => [[1,2,3,5,7],[4],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => [[1,2,3,4,7],[5],[6]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,5,6,7],[2],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,5,7],[2,6],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => [[1,4,6,7],[2],[3],[5]] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => [[1,4,5,7],[2],[3],[6]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => [[1,4,7],[2,5],[3],[6]] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => [[1,3,6,7],[2],[4],[5]] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => [[1,3,4,7],[2],[5],[6]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => [[1,4,5,6],[2],[3],[7]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => [[1,4,5],[2,6],[3],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => [[1,4,6],[2,5],[3],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[1,5,6],[2,7],[3],[4]] => [[1,4,5],[2,6],[3],[7]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => [[1,4],[2,5],[3,6],[7]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [[1,3,5,6],[2],[4],[7]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[1,4,6],[2,7],[3],[5]] => [[1,3,5],[2,6],[4],[7]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [[1,3,4,6],[2],[5],[7]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [[1,3,4,5],[2],[6],[7]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[1,4,5],[2,6],[3],[7]] => [[1,3,4],[2,5],[6],[7]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[1,4,7],[2,5],[3],[6]] => [[1,3,6],[2,4],[5],[7]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[1,4,6],[2,5],[3],[7]] => [[1,3,5],[2,4],[6],[7]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[1,4,5],[2,6],[3],[7]] => [[1,3,4],[2,5],[6],[7]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => [[1,3],[2,4],[5,7],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [[1,2,5,6],[3],[4],[7]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[1,3,6],[2,7],[4],[5]] => [[1,2,5],[3,6],[4],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => [[1,2,4,5],[3],[6],[7]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[1,3,5],[2,6],[4],[7]] => [[1,2,4],[3,5],[6],[7]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => [[1,2,3,6],[4],[5],[7]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => [[1,2,3,5],[4],[6],[7]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => [[1,2,3,4],[5],[6],[7]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[1,3,7],[2,4],[5],[6]] => [[1,2,6],[3,7],[4],[5]] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[1,3,6],[2,4],[5],[7]] => [[1,2,5],[3,7],[4],[6]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[1,3,5],[2,4],[6],[7]] => [[1,2,4],[3,7],[5],[6]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[1,3,4],[2,5],[6],[7]] => [[1,2,3],[4,7],[5],[6]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => [[1,2],[3,7],[4],[5],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => [[1,5,6,7],[2],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => [[1,5,7],[2,6],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => [[1,4,6,7],[2],[3],[5]] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => [[1,4,5,7],[2],[3],[6]] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => [[1,4,7],[2,5],[3],[6]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => [[1,3,6,7],[2],[4],[5]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => [[1,3,4,7],[2],[5],[6]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => [[1,3,7],[2,4],[5],[6]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => [[1,5,6],[2],[3],[4],[7]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => [[1,5],[2,6],[3],[4],[7]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => [[1,4,6],[2],[3],[5],[7]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => [[1,4,5],[2],[3],[6],[7]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => [[1,4],[2,5],[3],[6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [[1,3,6],[2],[4],[5],[7]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [[1,3,5],[2],[4],[6],[7]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => [[1,3,4],[2],[5],[6],[7]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[1,4],[2,5],[3],[6],[7]] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => [[1,2,6],[3],[4],[5],[7]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => [[1,2,5],[3],[4],[6],[7]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => [[1,2,4],[3],[5],[6],[7]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => [[1,2],[3,7],[4],[5],[6]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [[1,4],[2],[3],[5],[6],[7]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [[1,3],[2],[4],[5],[6],[7]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,6,8],[5,7]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,5,6,7,8],[4]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,5,7,8],[4,6]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,6,8],[5,7]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,2,3,6,8],[4,7],[5]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,4,5,6,7,8],[3]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [[1,2,4,6,7,8],[3,5]] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,5,7,8],[4,6]] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,6,8],[5,7]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,5,6,7,8],[3],[4]] => 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,5,8],[3,6],[4,7]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,4,5,7,8],[3],[6]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,4,5,6,8],[3],[7]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [[1,3,4,5,6,7,8],[2]] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [[1,3,4,5,7,8],[2,6]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,3,4,6,7,8],[2,5]] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,3,4,6,8],[2,5,7]] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [[1,3,5,6,7,8],[2,4]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [[1,3,5,7,8],[2,4,6]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]] => [[1,3,5,6,8],[2,4,7]] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => [[1,3,5,8],[2,4,6],[7]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,3,4,6,7,8],[2,5]] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,3,4,6,8],[2,5,7]] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => [[1,3,4,5,7,8],[2,6]] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,3,6,7,8],[2,4],[5]] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,3,5,7,8],[2,4],[6]] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,5,6,8],[2,4],[7]] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => [[1,3,5,8],[2,4,6],[7]] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,3,7,8],[2,4],[5],[6]] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,4,5,6,7,8],[3]] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,5,6,7,8],[4]] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,5,7,8],[4,6]] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,6,8],[5,7]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,5,7,8],[3,6],[4]] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [[1,2,3,5,8],[4,6],[7]] => [[1,2,4,7,8],[3,5],[6]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,5,7,8],[3],[4],[6]] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [[1,4,5,6,7,8],[2],[3]] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => [[1,4,5,6,8],[2,7],[3]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => [[1,4,5,7,8],[2,6],[3]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => [[1,4,5,6,8],[2,7],[3]] => 0
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => [[1,4,5,7,8],[2,6],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => [[1,4,5,6,8],[2,7],[3]] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => [[1,4,7,8],[2,5],[3,6]] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => [[1,4,6,8],[2,5],[3,7]] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [[1,4,8],[2,5],[3,6],[7]] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [[1,3,5,7,8],[2,6],[4]] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => [[1,3,4,6,7,8],[2],[5]] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => [[1,3,4,5,6,8],[2],[7]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,3,6,7,8],[2,4],[5]] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,3,5,7,8],[2,4],[6]] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,5,6,8],[2,4],[7]] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]] => [[1,3,5,8],[2,4,6],[7]] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,5,6,7,8],[3],[4]] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,5,7,8],[3,6],[4]] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,5,8],[3,6],[4,7]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,4,6,7,8],[3],[5]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,4,5,7,8],[3],[6]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,4,5,6,8],[3],[7]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,5,6,7,8],[2],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,5,7,8],[2,6],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,5,8],[2,6],[3,7],[4]] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [[1,4,6,7,8],[2],[3],[5]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [[1,2,5,6,8],[3],[4],[7]] => [[1,4,5,7,8],[2],[3],[6]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [[1,2,5,6,7],[3],[4],[8]] => [[1,4,5,6,8],[2],[3],[7]] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => [[1,4,5,8],[2,6],[3],[7]] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]] => [[1,4,8],[2,5],[3,6],[7]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => [[1,3,6,7,8],[2],[4],[5]] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => [[1,3,6,8],[2,7],[4],[5]] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7,8],[2],[4],[6]] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [[1,2,4,6,7],[3],[5],[8]] => [[1,3,5,6,8],[2],[4],[7]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [[1,2,4,5,8],[3],[6],[7]] => [[1,3,4,7,8],[2],[5],[6]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [[1,2,4,5,6],[3],[7],[8]] => [[1,3,4,5,8],[2],[6],[7]] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [[1,6,7,8],[2],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,6,8],[2,7],[3],[4],[5]] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,3,7,8],[2],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,7,8],[2],[3],[4],[5],[6]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => [[1,2,3,4,5,7],[6,8]] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => [[1,2,3,4,6,7],[5,8]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,3,4,6],[5,7,8]] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => [[1,2,3,5,6],[4,7,8]] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,7],[2,5,8]] => [[1,2,3,5,6],[4,7,8]] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,3,4,6],[5,7,8]] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,3,4,7],[5,8],[6]] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => [[1,2,4,5,6,7],[3,8]] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,5,6],[3,7,8]] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,5,6],[3,7,8]] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => [[1,2,4,6,7],[3,5,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => [[1,2,4,6],[3,5,7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[1,3,5,6,7],[2,4,8]] => [[1,2,4,5,6],[3,7,8]] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4],[3,5,8],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => [[1,2,3,5,6,7],[4,8]] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[1,3,4,6,7],[2,5,8]] => [[1,2,3,5,6],[4,7,8]] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => [[1,2,3,4,6],[5,7,8]] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => [[1,2,3,4,5,7],[6,8]] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => [[1,2,3,4,5,6],[7,8]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => [[1,2,3,6,7],[4,8],[5]] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,2,3,6],[4,7,8],[5]] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => [[1,2,5,6,7],[3,8],[4]] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => [[1,2,5,7],[3,6,8],[4]] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => [[1,2,5],[3,6,8],[4,7]] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6],[3,7,8],[5]] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,5,6],[3,8],[7]] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4],[3,5,8],[6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => [[1,2,3,6,7],[4,8],[5]] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,2,3,6],[4,7,8],[5]] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,3,4,7],[5,8],[6]] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,3,5],[4,8],[6],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [[1,2,6],[3,7,8],[4],[5]] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,5],[3,6,8],[4],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6],[3,8],[5],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,5],[3,8],[6],[7]] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4],[3,5,8],[6],[7]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [[1,3,4,8],[2,5],[6],[7]] => [[1,2,3,7],[4,8],[5],[6]] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,3,5],[4,8],[6],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,6],[3,8],[4],[5],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,5],[3,8],[4],[6],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4],[3,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2],[3,8],[4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [[1,3,4,5,6,7,8],[2]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => [[1,3,4,5,7,8],[2,6]] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => [[1,3,4,6,8],[2,5,7]] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => [[1,3,4,5,7,8],[2,6]] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => [[1,3,5,6,7,8],[2,4]] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => [[1,3,5,7,8],[2,4,6]] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => [[1,3,4,6,7,8],[2,5]] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => [[1,3,4,5,7,8],[2,6]] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,3,6,7,8],[2,4],[5]] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,3,5,7,8],[2,4],[6]] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => [[1,3,5,8],[2,4,6],[7]] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [[1,2,4,5,6,7,8],[3]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => [[1,2,4,6,7,8],[3,5]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => [[1,2,4,6,8],[3,5,7]] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => [[1,2,4,5,6,8],[3,7]] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[1,2,3,5,8],[4,6],[7]] => [[1,2,4,7,8],[3,5],[6]] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [[1,2,3,5,6,7,8],[4]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[1,2,3,4,6,8],[5,7]] => [[1,2,3,5,7,8],[4,6]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[1,2,3,4,6,7],[5,8]] => [[1,2,3,5,6,8],[4,7]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,6,7,8],[5]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]] => [[1,2,3,4,6,8],[5,7]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,7,8],[6]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => [[1,2,3,4,5,6,8],[7]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,5,6,7,8],[3],[4]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,5,7,8],[3,6],[4]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,5,8],[3,6],[4,7]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,4,6,7,8],[3],[5]] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,4,5,7,8],[3],[6]] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,4,5,6,8],[3],[7]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,2,3,6,8],[4,7],[5]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [[1,4,5,6,7,8],[2],[3]] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[1,2,5,7,8],[3,6],[4]] => [[1,4,6,7,8],[2,5],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => [[1,4,6,8],[2,5,7],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => [[1,4,5,6,8],[2,7],[3]] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => [[1,4,6,8],[2,5],[3,7]] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [[1,4,8],[2,5],[3,6],[7]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [[1,3,5,6,7,8],[2],[4]] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => [[1,3,5,6,8],[2,7],[4]] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [[1,3,5,7,8],[2,6],[4]] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => [[1,3,5,6,8],[2,7],[4]] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,3,5,8],[2,6],[4,7]] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,3,4,6,8],[2,7],[5]] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,3,4,5,6,8],[2],[7]] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[1,2,4,7,8],[3,5],[6]] => [[1,3,6,7,8],[2,4],[5]] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,3,5,7,8],[2,4],[6]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,5,6,8],[2,4],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[1,2,4,6],[3,5,7],[8]] => [[1,3,5,8],[2,4,6],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,5,6,7,8],[3],[4]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,5,7,8],[3,6],[4]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,5,8],[3,6],[4,7]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,2,4,6,8],[3,7],[5]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,4,5,6,8],[3],[7]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,5,6,7,8],[2],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,5,7,8],[2,6],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,5,8],[2,6],[3,7],[4]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => [[1,4,6,8],[2,7],[3],[5]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => [[1,4,5,7,8],[2],[3],[6]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,4,5,6,8],[2],[3],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,4,5,8],[2,6],[3],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,4,6,8],[2,5],[3],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,4,5,8],[2,6],[3],[7]] => 0
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[1,2,5],[3,6],[4,7],[8]] => [[1,4,8],[2,5],[3,6],[7]] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7,8],[2],[4],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => [[1,3,4,7,8],[2],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [[1,2,4,5,6],[3],[7],[8]] => [[1,3,4,5,8],[2],[6],[7]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,3,7,8],[2,4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,6,8],[2,7],[3],[4],[5]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,7,8],[2],[3],[4],[5],[6]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [[1,3,4,5,6,7],[2],[8]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => [[1,3,4,5,6],[2,7],[8]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => [[1,3,4,5,6],[2,7],[8]] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => [[1,3,4,5,6],[2,7],[8]] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => [[1,3,4,7],[2,5],[6,8]] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => [[1,3,5,6,7],[2,4],[8]] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => [[1,3,5,7],[2,4,6],[8]] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[1,4,5,7,8],[2,6],[3]] => [[1,3,4,6,7],[2,5],[8]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => [[1,3,4,5,6],[2,7],[8]] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]] => [[1,3,4,7],[2,5],[6,8]] => 0
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]] => [[1,3,6,7],[2,4],[5,8]] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]] => [[1,3,6],[2,4,7],[5,8]] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[1,4,6,7],[2,5],[3,8]] => [[1,3,5,6],[2,4],[7,8]] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => [[1,3,5],[2,4,6],[7,8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [[1,4,5,7],[2,6],[3,8]] => [[1,3,4,6],[2,5],[7,8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [[1,4,5,6],[2,7],[3,8]] => [[1,3,4,5],[2,6],[7,8]] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]] => [[1,3,7],[2,4],[5,8],[6]] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[1,4,7],[2,5],[3,6],[8]] => [[1,3,6],[2,4],[5,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [[1,4,6],[2,5],[3,7],[8]] => [[1,3,5],[2,4],[6,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [[1,2,4,5,6,7],[3],[8]] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,5],[3,6],[7,8]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => [[1,2,4,6,7],[3,5],[8]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => [[1,2,4,6],[3,5,7],[8]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[1,3,5,6,8],[2,7],[4]] => [[1,2,4,5,7],[3,6],[8]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => [[1,2,4,5,6],[3,7],[8]] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,5],[3,6],[7,8]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[1,3,5,8],[2,6],[4,7]] => [[1,2,4,7],[3,5],[6,8]] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => [[1,2,4,6],[3,5],[7,8]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => [[1,2,4,5],[3,6],[7,8]] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => [[1,2,4],[3,5],[6,8],[7]] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [[1,2,3,5,6,7],[4],[8]] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => [[1,2,3,5],[4,6],[7,8]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [[1,2,3,4,6,7],[5],[8]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [[1,2,3,4,5,7],[6],[8]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [[1,2,3,4,5,6],[7],[8]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => [[1,2,3,5],[4,6,8],[7]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,3,4,7],[5,8],[6]] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => [[1,2,5,6,7],[3,8],[4]] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[1,3,6,7],[2,4,8],[5]] => [[1,2,5,6],[3,7,8],[4]] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => [[1,2,5,7],[3,6,8],[4]] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => [[1,2,5,6],[3,7,8],[4]] => 0
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => [[1,2,5],[3,6,8],[4,7]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => [[1,2,4,6],[3,7,8],[5]] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => [[1,2,4,5,6],[3,8],[7]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]] => [[1,2,4,7],[3,5,8],[6]] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => [[1,2,4,6],[3,5,8],[7]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [[1,3,5,6],[2,4,7],[8]] => [[1,2,4,5],[3,6,8],[7]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [[1,3,4,7],[2,5,8],[6]] => [[1,2,3,6],[4,7,8],[5]] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [[1,3,4,6,7],[2,5],[8]] => [[1,2,3,5,6],[4,8],[7]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [[1,3,4,5,8],[2,6],[7]] => [[1,2,3,4,7],[5,8],[6]] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [[1,3,4,5,7],[2,6],[8]] => [[1,2,3,4,6],[5,8],[7]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [[1,3,4,5,6],[2,7],[8]] => [[1,2,3,4,5],[6,8],[7]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => [[1,2,3,7],[4,8],[5],[6]] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,3,5],[4,8],[6],[7]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [[1,2,6],[3,7,8],[4],[5]] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[1,3,6,8],[2,4],[5],[7]] => [[1,2,5,7],[3,8],[4],[6]] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,5],[3,6,8],[4],[7]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,7],[3,8],[5],[6]] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6],[3,8],[5],[7]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => [[1,2,3,7],[4,8],[5],[6]] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,6],[3,8],[4],[5],[7]] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2],[3,8],[4],[5],[6],[7]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [[1,4,5,6,7,8],[2],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => [[1,4,6,8],[2,5,7],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => [[1,4,5,6,8],[2,7],[3]] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => [[1,4,6,8],[2,5],[3,7]] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 0
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => [[1,4,8],[2,5],[3,6],[7]] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [[1,3,5,6,7,8],[2],[4]] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => [[1,3,5,7,8],[2,6],[4]] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => [[1,3,5,6,8],[2,7],[4]] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => [[1,3,5,8],[2,6],[4,7]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => [[1,3,4,6,7,8],[2],[5]] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => [[1,3,4,6,8],[2,7],[5]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => [[1,3,4,5,7,8],[2],[6]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [[1,3,4,5,6,8],[2],[7]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [[1,2,4,5,6],[3,7],[8]] => [[1,3,4,5,8],[2,6],[7]] => 0
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => [[1,3,5,7,8],[2,4],[6]] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => [[1,3,5,6,8],[2,4],[7]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [[1,2,4,5,8],[3,6],[7]] => [[1,3,4,7,8],[2,5],[6]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => [[1,3,4,6,8],[2,5],[7]] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,3,7,8],[2,4],[5],[6]] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [[1,2,5,6,7,8],[3],[4]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => [[1,2,5,6,8],[3,7],[4]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => [[1,2,5,7,8],[3,6],[4]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => [[1,2,5,8],[3,6],[4,7]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => [[1,2,4,6,7,8],[3],[5]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => [[1,2,4,6,8],[3,7],[5]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => [[1,2,4,5,7,8],[3],[6]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [[1,2,4,5,6,8],[3],[7]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [[1,2,3,5,8],[4,6],[7]] => [[1,2,4,7,8],[3,5],[6]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => [[1,2,4,6,8],[3,5],[7]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => [[1,2,4,5,8],[3,6],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => [[1,2,3,6,8],[4,7],[5]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => [[1,2,3,5,7,8],[4],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [[1,2,3,5,6,8],[4],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => [[1,2,3,5,8],[4,6],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,7,8],[5],[6]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[1,2,3,4,5,7],[6],[8]] => [[1,2,3,4,6,8],[5],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => [[1,2,3,4,5,8],[6],[7]] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,5,7,8],[3],[4],[6]] => 0
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,5,6,7,8],[2],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,5,7,8],[2,6],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,5,8],[2,6],[3,7],[4]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [[1,4,6,7,8],[2],[3],[5]] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => [[1,4,6,8],[2,7],[3],[5]] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => [[1,4,5,7,8],[2],[3],[6]] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,4,5,6,8],[2],[3],[7]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => [[1,4,7,8],[2,5],[3],[6]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => [[1,4,6,8],[2,5],[3],[7]] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => [[1,4,5,8],[2,6],[3],[7]] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7,8],[2],[4],[6]] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => [[1,3,5,6,8],[2],[4],[7]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [[1,2,4,5,6],[3],[7],[8]] => [[1,3,4,5,8],[2],[6],[7]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,3,7,8],[2,4],[5],[6]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => [[1,2,5,7,8],[3],[4],[6]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [[1,2,3,5,8],[4],[6],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => [[1,2,4,5,8],[3],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [[1,6,7,8],[2],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,6,8],[2,7],[3],[4],[5]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => [[1,5,7,8],[2],[3],[4],[6]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => [[1,4,7,8],[2],[3],[5],[6]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [[1,4,5,6,7],[2],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => [[1,4,5,6],[2,7],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => [[1,4,5,7],[2,6],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => [[1,4,5,6],[2,7],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => [[1,4,5],[2,6],[3,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => [[1,4,6,7],[2,5],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => [[1,4,6],[2,5,7],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => [[1,4,5,7],[2,6],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => [[1,4,5,6],[2,7],[3],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => [[1,4,5],[2,6],[3,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => [[1,4,7],[2,5],[3,6],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[1,5,7],[2,6],[3,8],[4]] => [[1,4,6],[2,5],[3,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [[1,5,6],[2,7],[3,8],[4]] => [[1,4,5],[2,6],[3,7],[8]] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => [[1,4],[2,5],[3,6],[7,8]] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [[1,3,5,6,7],[2],[4],[8]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]] => [[1,3,5,6],[2,7],[4],[8]] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => [[1,3,5],[2,6],[4,7],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [[1,3,4,6,7],[2],[5],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => [[1,3,4,6],[2,7],[5],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [[1,3,4,5,7],[2],[6],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [[1,3,4,5,6],[2],[7],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[1,4,5,6],[2,7],[3],[8]] => [[1,3,4,5],[2,6],[7],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => [[1,3,4,7],[2,5],[6],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]] => [[1,3,4,6],[2,5],[7],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [[1,4,5,6],[2,7],[3],[8]] => [[1,3,4,5],[2,6],[7],[8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => [[1,3,6,7],[2,4],[5],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => [[1,3,6],[2,4,7],[5],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => [[1,3,5,7],[2,4],[6],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => [[1,3,5,6],[2,4],[7],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => [[1,3,5],[2,4,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [[1,4,5,8],[2,6],[3],[7]] => [[1,3,4,7],[2,5],[6],[8]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [[1,4,5,7],[2,6],[3],[8]] => [[1,3,4,6],[2,5],[7],[8]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]] => [[1,3,6],[2,4],[5,8],[7]] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [[1,4,5],[2,6],[3,7],[8]] => [[1,3,4],[2,5],[6,8],[7]] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [[1,2,5,6,7],[3],[4],[8]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => [[1,2,5,6],[3,7],[4],[8]] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => [[1,2,5],[3,6],[4,7],[8]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6,7],[3],[5],[8]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => [[1,2,4,6],[3,7],[5],[8]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => [[1,2,4,5,6],[3],[7],[8]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,7],[3,5],[6],[8]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => [[1,2,4,6],[3,5],[7],[8]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => [[1,2,3,6],[4,7],[5],[8]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [[1,2,3,5,6],[4],[7],[8]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => [[1,2,3,4,6],[5],[7],[8]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [[1,2,3,4,5],[6],[7],[8]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [[1,3,4,8],[2,5],[6],[7]] => [[1,2,3,7],[4,8],[5],[6]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [[1,3,4,6],[2,5],[7],[8]] => [[1,2,3,5],[4,8],[6],[7]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => [[1,2,6,7],[3,8],[4],[5]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => [[1,2,6],[3,7,8],[4],[5]] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => [[1,2,5],[3,6,8],[4],[7]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,7],[3,8],[5],[6]] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => [[1,2,4,6],[3,8],[5],[7]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => [[1,2,4,5],[3,8],[6],[7]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [[1,3,5],[2,4,6],[7],[8]] => [[1,2,4],[3,5,8],[6],[7]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [[1,3,4,7],[2,5],[6],[8]] => [[1,2,3,6],[4,8],[5],[7]] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [[1,3,4,5],[2,6],[7],[8]] => [[1,2,3,4],[5,8],[6],[7]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => [[1,2,6],[3,8],[4],[5],[7]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,5],[3,8],[4],[6],[7]] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2],[3,8],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [[1,5,6,7,8],[2],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => [[1,5,6,8],[2,7],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => [[1,5,7,8],[2,6],[3],[4]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => [[1,5,8],[2,6],[3,7],[4]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [[1,4,6,7,8],[2],[3],[5]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => [[1,4,6,8],[2,7],[3],[5]] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [[1,4,5,6,8],[2],[3],[7]] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => [[1,4,7,8],[2,5],[3],[6]] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => [[1,3,6,8],[2,7],[4],[5]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7,8],[2],[4],[6]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => [[1,3,5,8],[2,6],[4],[7]] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => 0
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [[1,2,4,5],[3,6],[7],[8]] => [[1,3,4,8],[2,5],[6],[7]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => [[1,3,7,8],[2,4],[5],[6]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,8],[2,4],[6],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [[1,2,6,7,8],[3],[4],[5]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => [[1,2,6,8],[3,7],[4],[5]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [[1,2,5,6,8],[3],[4],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [[1,2,3,5],[4,6],[7],[8]] => [[1,2,4,8],[3,5],[6],[7]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,7,8],[4],[5],[6]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [[1,2,3,6,8],[4],[5],[7]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => [[1,2,3,5,8],[4],[6],[7]] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [[1,2,3,4,8],[5],[6],[7]] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,6,8],[2,7],[3],[4],[5]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,3,7,8],[2],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,7,8],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [[1,5,6,7],[2],[3],[4],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => [[1,5,6],[2,7],[3],[4],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => [[1,5,7],[2,6],[3],[4],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[1,6,7],[2,8],[3],[4],[5]] => [[1,5,6],[2,7],[3],[4],[8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => [[1,5],[2,6],[3,7],[4],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => [[1,4,6,7],[2],[3],[5],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => [[1,4,6],[2,7],[3],[5],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [[1,4,5,7],[2],[3],[6],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [[1,4,5,6],[2],[3],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => [[1,4,5],[2,6],[3],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => [[1,4,7],[2,5],[3],[6],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => [[1,4,6],[2,5],[3],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [[1,5,6],[2,7],[3],[4],[8]] => [[1,4,5],[2,6],[3],[7],[8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => [[1,3,6,7],[2],[4],[5],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => [[1,3,6],[2,7],[4],[5],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [[1,3,5,6],[2],[4],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [[1,4,6],[2,7],[3],[5],[8]] => [[1,3,5],[2,6],[4],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => [[1,3,4,7],[2],[5],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [[1,3,4,6],[2],[5],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [[1,3,4,5],[2],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => [[1,3,4],[2,5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => [[1,3,7],[2,4],[5],[6],[8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => [[1,3,6],[2,4],[5],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => [[1,3,4],[2,5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => [[1,2,6],[3,7],[4],[5],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => [[1,2,5,6],[3],[4],[7],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => [[1,2,5],[3,6],[4],[7],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6],[3],[5],[7],[8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => [[1,2,3,5],[4],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => [[1,2,5],[3,8],[4],[6],[7]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => [[1,2,4],[3,8],[5],[6],[7]] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => [[1,2,3],[4,8],[5],[6],[7]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [[1,6,7,8],[2],[3],[4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => [[1,6,8],[2,7],[3],[4],[5]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => [[1,5,7,8],[2],[3],[4],[6]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => [[1,4,7,8],[2],[3],[5],[6]] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => [[1,3,7,8],[2],[4],[5],[6]] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [[1,2,6,8],[3],[4],[5],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => [[1,2,5,8],[3],[4],[6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => [[1,2,4,8],[3],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [[1,2,3,8],[4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,7,8],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [[1,6,7],[2],[3],[4],[5],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => [[1,6],[2,7],[3],[4],[5],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [[1,5,7],[2],[3],[4],[6],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [[1,5,6],[2],[3],[4],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => [[1,5],[2,6],[3],[4],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [[1,4,6],[2],[3],[5],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [[1,4,5],[2],[3],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => [[1,4],[2,5],[3],[6],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [[1,3,7],[2],[4],[5],[6],[8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [[1,3,6],[2],[4],[5],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [[1,3,5],[2],[4],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [[1,3,4],[2],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [[1,2,6],[3],[4],[5],[7],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [[1,2,5],[3],[4],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [[1,2,4],[3],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => [[1,2],[3,8],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [[1,7,8],[2],[3],[4],[5],[6]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 7
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,1,1 9,4,0,1 29,10,2,0,1 96,31,4,0,0,1 323,97,8,0,0,0,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 3 + q + q^{2}$
$F_{4} = 9 + 4\ q + q^{3}$
$F_{5} = 29 + 10\ q + 2\ q^{2} + q^{4}$
$F_{6} = 96 + 31\ q + 4\ q^{2} + q^{5}$
$F_{7} = 323 + 97\ q + 8\ q^{2} + q^{6}$
Description
The maximal overlap of the cylindrical tableau associated with a tableau.
A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
In particular, the statistic equals $0$, if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.
A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
In particular, the statistic equals $0$, if and only if the last entry of the first row is larger than or equal to the first entry of the last row. Moreover, the statistic attains its maximal value, the number of rows of the tableau minus 1, if and only if the tableau consists of a single column.
Map
to 312-avoiding permutation
Description
Map
inverse promotion
Description
The inverse promotion of a standard Young tableau.
This map replaces the entry $1$ of the tableau with $n+1$, uses the jeu de taquin to move it to the outer rim, and finally decreases all entries by one.
This map replaces the entry $1$ of the tableau with $n+1$, uses the jeu de taquin to move it to the outer rim, and finally decreases all entries by one.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
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