Identifier
-
Mp00227:
Dyck paths
—Delest-Viennot-inverse⟶
Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St001712: Standard tableaux ⟶ ℤ
Values
[1,0] => [1,0] => [1] => [[1]] => 0
[1,0,1,0] => [1,1,0,0] => [2,1] => [[1],[2]] => 0
[1,1,0,0] => [1,0,1,0] => [1,2] => [[1,2]] => 0
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => 0
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => 0
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => 0
[1,1,1,0,0,0] => [1,1,0,1,0,0] => [2,3,1] => [[1,2],[3]] => 0
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => 0
[1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => 1
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => 1
[1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => 0
[1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => 1
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => 0
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,3],[4]] => 0
[1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,2],[3],[4]] => 0
[1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,2,4],[3]] => 1
[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => 0
[1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,2,3],[4]] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,4],[2,5]] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,4],[3],[5]] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,4],[5]] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,3,5],[4]] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [[1,2,3],[4],[5]] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,3,4],[5]] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,2,5],[3],[4]] => 1
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,2,4],[3,5]] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,2,4],[3],[5]] => 1
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[1,2,3],[4],[5]] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => 2
>>> Load all 1647 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,0,1,1,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,1,0,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,1,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,1,1,0,0,0,0,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,1,1,0,0,0] => [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
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [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
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [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
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [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
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [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
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [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
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [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
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [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
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [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
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [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
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [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
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [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
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [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
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [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
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [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
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [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
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [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
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [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
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [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
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [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
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [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
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [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
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [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
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [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
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [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
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [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
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [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
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [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
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [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
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [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
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [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
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [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
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [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]] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [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
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [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
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [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
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [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
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [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
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [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]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [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
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [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
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [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
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [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
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [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
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [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
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [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
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [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
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [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
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [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
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [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]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [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
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [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]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [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]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [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
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [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
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [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
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [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]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [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]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [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
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [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
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [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
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [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
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [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
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [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
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [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
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [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
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [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
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [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
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [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
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [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
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [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
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [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
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [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
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [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
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [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
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [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
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [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
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [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
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [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
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [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
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [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
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [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
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [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
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [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
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [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
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [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
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [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
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [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
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [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
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [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
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [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
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [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
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [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
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [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
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [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
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [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
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [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
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [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
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [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]] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [[1,2,3,4,5,6],[7],[8]] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [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
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [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
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [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
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [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
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [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
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [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
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [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
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [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]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [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]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [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
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [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
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [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]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [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]] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [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
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [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
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [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
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [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
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [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
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [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
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [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
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [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
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [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
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [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
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [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
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [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]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [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]] => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [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]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [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
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [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
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [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
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [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
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [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]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [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]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [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
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [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
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [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
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [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
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [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
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [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
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [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
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [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
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [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
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [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
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [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
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [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
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [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
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [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
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [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
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [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
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [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
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [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
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [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
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [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
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [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
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [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]] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [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
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [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
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [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
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [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
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [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
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [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
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [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
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [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
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [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
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [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
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [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
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [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
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [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
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [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
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [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
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [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
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [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
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [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
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [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]] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [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
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [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]] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [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
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [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
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [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
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [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]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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]] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [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
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [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]] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [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
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [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]] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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]] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,24,2 32,80,20 64,240,120,5
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 8 + 6\ q$
$F_{5} = 16 + 24\ q + 2\ q^{2}$
$F_{6} = 32 + 80\ q + 20\ q^{2}$
$F_{7} = 64 + 240\ q + 120\ q^{2} + 5\ q^{3}$
Description
The number of natural descents of a standard Young tableau.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation.
Map
to 312-avoiding permutation
Description
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.
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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!