Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000507: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [1] => [[1]] => 1
[1,0,1,0] => [1,2] => [1,2] => [[1,2]] => 2
[1,1,0,0] => [2,1] => [2,1] => [[1],[2]] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,3,2] => [[1,2],[3]] => 2
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [[1,2],[3]] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [[1,3],[2]] => 2
[1,1,0,1,0,0] => [2,3,1] => [2,3,1] => [[1,2],[3]] => 2
[1,1,1,0,0,0] => [3,2,1] => [3,2,1] => [[1],[2],[3]] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,4,3,2] => [[1,2],[3],[4]] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,4,3] => [[1,3],[2,4]] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [2,4,1,3] => [[1,2],[3,4]] => 3
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [2,4,3,1] => [[1,2],[3],[4]] => 2
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [2,4,3,1] => [[1,2],[3],[4]] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [3,2,1,4] => [[1,4],[2],[3]] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [[1,3],[2],[4]] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [3,4,2,1] => [[1,2],[3],[4]] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [4,3,2,1] => [[1],[2],[3],[4]] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [2,5,1,4,3] => [[1,2],[3,4],[5]] => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [2,5,1,4,3] => [[1,2],[3,4],[5]] => 3
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [2,5,4,1,3] => [[1,2],[3,5],[4]] => 3
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [2,5,4,1,3] => [[1,2],[3,5],[4]] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [3,2,5,1,4] => [[1,3],[2,5],[4]] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [3,5,2,1,4] => [[1,2],[3,5],[4]] => 3
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [3,5,2,4,1] => [[1,2],[3,4],[5]] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [3,5,4,2,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [3,5,4,2,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
>>> Load all 2027 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [3,2,6,1,5,4] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [3,2,6,1,5,4] => [[1,3],[2,5],[4,6]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [3,2,6,5,1,4] => [[1,3],[2,4],[5,6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [3,2,6,5,1,4] => [[1,3],[2,4],[5,6]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [3,6,2,1,5,4] => [[1,2],[3,5],[4,6]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [3,6,2,1,5,4] => [[1,2],[3,5],[4,6]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [3,6,2,5,1,4] => [[1,2],[3,4],[5,6]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [3,6,2,5,4,1] => [[1,2],[3,4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [3,6,2,5,4,1] => [[1,2],[3,4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [3,6,5,2,1,4] => [[1,2],[3,6],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [3,6,5,2,4,1] => [[1,2],[3,5],[4],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [3,6,5,2,1,4] => [[1,2],[3,6],[4],[5]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [3,6,5,2,4,1] => [[1,2],[3,5],[4],[6]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [4,3,2,6,1,5] => [[1,4],[2,6],[3],[5]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [4,3,6,2,1,5] => [[1,3],[2,6],[4],[5]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [4,3,6,2,5,1] => [[1,3],[2,5],[4],[6]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [4,6,3,2,1,5] => [[1,2],[3,6],[4],[5]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [4,6,3,2,5,1] => [[1,2],[3,5],[4],[6]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [4,6,3,5,2,1] => [[1,2],[3,4],[5],[6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [3,2,7,6,1,5,4] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [3,2,7,6,1,5,4] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [3,2,7,6,1,5,4] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [3,2,7,6,1,5,4] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [3,7,2,6,1,5,4] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [3,7,2,6,1,5,4] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [3,7,2,6,5,1,4] => [[1,2],[3,4],[5,7],[6]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [3,7,2,6,5,1,4] => [[1,2],[3,4],[5,7],[6]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [3,7,6,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [3,7,6,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [3,7,6,2,5,1,4] => [[1,2],[3,5],[4,7],[6]] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [3,7,6,2,5,4,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [3,7,6,2,5,4,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [3,7,6,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [3,7,6,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [3,7,6,2,5,1,4] => [[1,2],[3,5],[4,7],[6]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [3,7,6,2,5,4,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [3,7,6,2,5,4,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [4,3,2,7,1,6,5] => [[1,4],[2,6],[3,7],[5]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [4,3,2,7,1,6,5] => [[1,4],[2,6],[3,7],[5]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [4,3,2,7,6,1,5] => [[1,4],[2,5],[3,7],[6]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [4,3,2,7,6,1,5] => [[1,4],[2,5],[3,7],[6]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [4,3,7,2,1,6,5] => [[1,3],[2,6],[4,7],[5]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [4,3,7,2,1,6,5] => [[1,3],[2,6],[4,7],[5]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [4,3,7,2,6,1,5] => [[1,3],[2,5],[4,7],[6]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [4,3,7,2,6,5,1] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [4,3,7,2,6,5,1] => [[1,3],[2,5],[4,6],[7]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [4,3,7,6,2,1,5] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [4,3,7,6,2,5,1] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [4,3,7,6,2,1,5] => [[1,3],[2,4],[5,7],[6]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [4,3,7,6,2,5,1] => [[1,3],[2,4],[5,6],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [4,7,3,2,1,6,5] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [4,7,3,2,1,6,5] => [[1,2],[3,6],[4,7],[5]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [4,7,3,2,6,1,5] => [[1,2],[3,5],[4,7],[6]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [4,7,3,2,6,5,1] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [4,7,3,2,6,5,1] => [[1,2],[3,5],[4,6],[7]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [4,7,3,6,2,1,5] => [[1,2],[3,4],[5,7],[6]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [4,7,3,6,2,5,1] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [4,7,3,6,5,2,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [4,7,3,6,5,2,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [4,7,6,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [4,7,6,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [4,7,6,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [4,7,6,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [4,7,6,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [4,7,6,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [5,4,3,2,7,1,6] => [[1,5],[2,7],[3],[4],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [5,4,3,7,2,1,6] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [5,4,3,7,2,6,1] => [[1,4],[2,6],[3],[5],[7]] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,7,6,2,1] => [[1,4],[2,5],[3],[6],[7]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [5,4,3,7,6,2,1] => [[1,4],[2,5],[3],[6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [5,4,7,3,2,1,6] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [5,4,7,3,2,6,1] => [[1,3],[2,6],[4],[5],[7]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [5,4,7,3,6,2,1] => [[1,3],[2,5],[4],[6],[7]] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [5,4,7,6,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [5,4,7,6,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [5,7,4,3,2,1,6] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [5,7,4,3,2,6,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [5,7,4,3,6,2,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [5,7,4,6,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [5,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [5,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,4,6,5,7,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,2,4,6,7,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,6,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,5,4,6,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,4,7,8,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,5,7,6,4,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,7,6,8,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,3,7,6,5,4,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,3,6,7,5,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,4,5,6,3,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,4,5,7,8,6,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,5,4,6,8,7,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,4,7,6,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,6,5,4,8,7,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,4,6,7,5,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,4,6,7,5,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,7,6,8,5,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,4,3,5,8,7,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,4,5,3,6,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,5,4,6,3,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,6,5,7,8,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,6,7,5,4,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,6,7,5,4,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [3,2,8,7,6,1,5,4] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [3,2,8,7,6,1,5,4] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [3,2,8,7,6,1,5,4] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [3,2,8,7,6,1,5,4] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,6,5,8,7,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,4,2,1,5,6,8,7] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,4,2,1,5,8,7,6] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [3,8,2,7,1,6,5,4] => [[1,2],[3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [3,8,2,7,1,6,5,4] => [[1,2],[3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [3,8,2,7,1,6,5,4] => [[1,2],[3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [3,8,2,7,1,6,5,4] => [[1,2],[3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [3,8,2,7,6,1,5,4] => [[1,2],[3,4],[5,7],[6],[8]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [3,8,2,7,6,1,5,4] => [[1,2],[3,4],[5,7],[6],[8]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,5,2,1,7,8,6] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [3,8,7,2,6,1,5,4] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [3,8,7,2,6,1,5,4] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [3,8,7,2,6,5,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [3,8,7,2,6,5,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [3,8,7,2,6,1,5,4] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [3,8,7,2,6,1,5,4] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [3,8,7,2,6,5,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [3,8,7,2,6,5,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,5,4,6,2,8,7,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,6,7,5,8,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [4,3,2,8,1,7,6,5] => [[1,4],[2,6],[3,7],[5,8]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [4,3,2,8,1,7,6,5] => [[1,4],[2,6],[3,7],[5,8]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [4,3,2,8,1,7,6,5] => [[1,4],[2,6],[3,7],[5,8]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [4,3,2,8,7,1,6,5] => [[1,4],[2,5],[3,7],[6,8]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [4,3,2,8,7,1,6,5] => [[1,4],[2,5],[3,7],[6,8]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [4,3,2,8,7,6,1,5] => [[1,4],[2,5],[3,6],[7,8]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [4,3,2,8,7,6,1,5] => [[1,4],[2,5],[3,6],[7,8]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [4,3,2,8,7,1,6,5] => [[1,4],[2,5],[3,7],[6,8]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [4,3,2,8,7,1,6,5] => [[1,4],[2,5],[3,7],[6,8]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [4,3,2,8,7,6,1,5] => [[1,4],[2,5],[3,6],[7,8]] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [4,3,2,8,7,6,1,5] => [[1,4],[2,5],[3,6],[7,8]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [4,3,8,2,7,1,6,5] => [[1,3],[2,5],[4,7],[6,8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [4,3,8,2,7,1,6,5] => [[1,3],[2,5],[4,7],[6,8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [4,3,8,2,7,6,5,1] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [4,3,8,2,7,6,1,5] => [[1,3],[2,5],[4,6],[7,8]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [4,3,8,2,7,6,5,1] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [4,3,8,2,7,6,5,1] => [[1,3],[2,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [4,3,8,7,2,1,6,5] => [[1,3],[2,4],[5,7],[6,8]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [4,3,8,7,2,6,1,5] => [[1,3],[2,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [4,3,8,7,2,6,5,1] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [4,3,8,7,6,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [4,3,8,7,6,2,1,5] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [4,3,8,7,2,1,6,5] => [[1,3],[2,4],[5,7],[6,8]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [4,3,8,7,2,1,6,5] => [[1,3],[2,4],[5,7],[6,8]] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [4,3,8,7,2,6,5,1] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [4,3,8,7,6,2,1,5] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [4,3,8,7,6,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [4,3,8,7,6,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [4,3,8,7,6,2,1,5] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [4,3,8,7,6,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [4,8,3,2,1,7,6,5] => [[1,2],[3,6],[4,7],[5,8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [4,8,3,2,1,7,6,5] => [[1,2],[3,6],[4,7],[5,8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [4,8,3,2,1,7,6,5] => [[1,2],[3,6],[4,7],[5,8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [4,8,3,2,1,7,6,5] => [[1,2],[3,6],[4,7],[5,8]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [4,8,3,2,7,6,5,1] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,5,3,2,6,8,7,1] => [4,8,3,2,7,6,5,1] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [4,8,3,2,7,6,1,5] => [[1,2],[3,5],[4,6],[7,8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [4,8,3,2,7,6,5,1] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [4,8,3,7,2,1,6,5] => [[1,2],[3,4],[5,7],[6,8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [4,8,3,7,2,6,1,5] => [[1,2],[3,4],[5,6],[7,8]] => 5
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [4,8,3,7,6,2,5,1] => [[1,2],[3,4],[5,7],[6],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [4,8,3,7,6,5,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,5,3,7,6,2,8,1] => [4,8,3,7,6,2,5,1] => [[1,2],[3,4],[5,7],[6],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [4,8,3,7,6,5,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [4,8,3,7,6,5,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [4,8,7,3,2,1,6,5] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [4,8,7,3,2,1,6,5] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [4,8,7,3,2,6,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [4,8,7,3,2,6,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [4,8,7,3,6,2,5,1] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,5,6,3,7,8,2,1] => [4,8,7,3,6,5,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [4,8,7,3,6,5,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [4,8,7,6,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [4,8,7,6,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [4,8,7,3,2,1,6,5] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [4,8,7,3,2,6,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [4,8,7,3,6,2,5,1] => [[1,2],[3,5],[4,7],[6],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [4,8,7,6,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [4,8,7,6,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [4,8,7,6,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [4,8,7,6,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,8,1,7,6] => [[1,5],[2,7],[3,8],[4],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [5,4,3,2,8,1,7,6] => [[1,5],[2,7],[3,8],[4],[6]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [5,4,3,2,8,7,1,6] => [[1,5],[2,6],[3,8],[4],[7]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [5,4,3,2,8,7,1,6] => [[1,5],[2,6],[3,8],[4],[7]] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [5,4,3,8,2,1,7,6] => [[1,4],[2,7],[3,8],[5],[6]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [5,4,3,8,2,1,7,6] => [[1,4],[2,7],[3,8],[5],[6]] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [5,4,3,8,2,7,1,6] => [[1,4],[2,6],[3,8],[5],[7]] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [5,4,3,8,2,7,6,1] => [[1,4],[2,6],[3,7],[5],[8]] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [5,4,3,8,2,7,6,1] => [[1,4],[2,6],[3,7],[5],[8]] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [5,4,8,3,2,1,7,6] => [[1,3],[2,7],[4,8],[5],[6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [5,4,8,3,2,1,7,6] => [[1,3],[2,7],[4,8],[5],[6]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [5,4,8,3,2,7,1,6] => [[1,3],[2,6],[4,8],[5],[7]] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [5,4,8,3,2,7,6,1] => [[1,3],[2,6],[4,7],[5],[8]] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [5,4,8,3,2,7,6,1] => [[1,3],[2,6],[4,7],[5],[8]] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [5,4,8,3,7,2,1,6] => [[1,3],[2,5],[4,8],[6],[7]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [5,4,8,3,7,2,6,1] => [[1,3],[2,5],[4,7],[6],[8]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [5,4,8,7,3,6,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [5,4,8,7,3,2,1,6] => [[1,3],[2,4],[5,8],[6],[7]] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [5,4,8,7,3,6,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [5,8,4,3,2,1,7,6] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [5,8,4,3,2,1,7,6] => [[1,2],[3,7],[4,8],[5],[6]] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [5,8,4,3,7,2,1,6] => [[1,2],[3,5],[4,8],[6],[7]] => 4
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [5,8,4,3,7,6,2,1] => [[1,2],[3,5],[4,6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [5,8,4,7,3,2,1,6] => [[1,2],[3,4],[5,8],[6],[7]] => 4
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [5,8,4,7,6,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [5,8,4,7,6,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [5,8,7,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [5,8,7,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [5,8,7,4,6,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [5,8,7,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [5,8,7,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [5,8,7,4,6,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [6,5,4,3,2,8,1,7] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [6,5,4,3,8,2,1,7] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [6,5,4,3,8,2,7,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [6,5,4,3,8,7,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [6,5,4,3,8,7,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [6,5,4,8,3,2,1,7] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [6,5,4,8,3,2,7,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [6,5,4,8,3,7,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [6,5,8,4,3,2,1,7] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [6,5,8,4,3,2,7,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [6,5,8,4,3,7,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [6,5,8,4,7,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,8,7,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [6,5,8,7,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [6,8,5,4,3,2,1,7] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [6,8,5,4,3,2,7,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [6,8,5,4,3,7,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [6,8,5,4,7,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [6,8,5,7,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [6,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [6,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,6,9,8,7,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,8,10,9,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,7,6,9,8,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,7,10,9,8,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,6,8,9,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,9,8,7,6,5,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [7,6,5,4,3,2,1,9,8] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,5,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,10,9,8,7,6,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,9,8] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,8,9,7,6,5,4,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,10,9,8,7,6,5,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,8,6,5,4,3,2,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,6,5,7,8,9,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[] => [] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,5,7,8,6,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,6,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,7,9,8,6,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,5,8,7,6,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,8,7,9,6,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,8,9,7,6,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,4,6,7,5,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,6,5,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,4,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,6,5,7,8,9,4,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,5,4,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,4,3,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8,7,9,6,5,4,3,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,7,6,5,4,3,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [3,2,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [3,9,2,8,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,4,2,1] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,7,9,8,4,2,1] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,8,7,6,5,4,9,2,1] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,8,3,2,1] => [4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,8,7,6,5,9,3,2,1] => [4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,9,8,7,6,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [5,4,3,2,9,8,7,6,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,8,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,7,9,8,6,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,8,7,6,9,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,5,4,9,8,7,3,2,1] => [6,5,4,9,8,7,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,8,7,9,5,4,3,2,1] => [6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [7,6,9,8,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [7,6,9,8,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [7,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [7,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,7,4,8,9,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,4,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,10,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [2,10,1,9,8,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,9,3,2,1] => [4,10,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,8,9,7] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [8,10,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,8,10,9,6,5,4,3,2,1] => [7,10,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [8,7,10,9,6,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,6,7,9,10,8] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,10,9,8,6,5,4,3,2,1] => [7,10,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [6,10,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => [4,10,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,10,9,8,7,6,5,4,2,1] => [3,10,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,9,4,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,5,6,3,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,5,6,4,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,4,6,5,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,9,3,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,9,10,8,7,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,8,9,10,7,6,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,10,6,5,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,9,5,4,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,10,5,4,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,10,4,3,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [4,10,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,4,9,8,7,6,5,3] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,2,1,6,9,8,7,5,4] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,2,1,8,9,7,6,5] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,3,2,1,8,9,7,6] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,1,8,9,7,6,5,4] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,3,5,7,8,9,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,4,5,7,6,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [2,10,1,9,8,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,7,9,10,8,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,6,8,9,10,7,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,9,10,5,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,9,10,4,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [3,10,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,5,6,9,8,10,7,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,7,10,9,6,5,4,3,2,1] => [8,7,10,9,6,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,6,5,10,9,8,4,3,2,1] => [7,6,5,10,9,8,4,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => [6,5,4,3,10,9,8,7,2,1] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,4] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,5] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [5,10,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [8,10,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [6,10,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [7,10,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,9,4] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,6,8,9,7,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,9,8,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,6] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,6,8,7,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,8,3,9] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,4,3,7,6,9,8,10,5] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,9,8,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,5] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,8,6,4,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,4,5,7,8,9,10,6] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,1,6,5,7,4,8,3,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,4,3,7,6,8,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,7,6,8,3,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,3,8,7,9,6,10,5] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,5,4,8,7,9,6,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,5,4,8,7,9,6,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,8,7,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,8,7,9,4,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,2,7,6,8,5,9,4,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,1,6,5,7,4,9,8,10,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,2,6,5,7,4,9,8,10,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,7,8,10,9,1] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,6,5,4,3,2,1,9,10,8] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,3,2,1,8,9,10,7] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,7,8,9,10,6] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,9,10,5] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,9,10,4] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,6,9,8,7,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [2,6,5,8,9,7,10,4,3,1] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,6,5,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,7,4,8,3,9,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,9,10,5] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,5,8,9,10,7] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,1,7,8,9,10,6,5,4,3] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,5,7,9,10,8,6] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,3,5,6,8,9,7,4] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,5,9,8,7,6,4,2] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5,10,9,8,7,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,5,7,10,9,8,6,4,2] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4 1,12,1 1,34,7 1,98,32,1 1,294,124,10
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 4\ q^{2}$
$F_{4} = q + 12\ q^{2} + q^{3}$
$F_{5} = q + 34\ q^{2} + 7\ q^{3}$
$F_{6} = q + 98\ q^{2} + 32\ q^{3} + q^{4}$
$F_{7} = q + 294\ q^{2} + 124\ q^{3} + 10\ q^{4}$
Description
The number of ascents of a standard tableau.
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
to 312-avoiding permutation
Description
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
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