Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000016: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [[1]] => 0
[1,0,1,0] => [2,1] => [[1],[2]] => 0
[1,1,0,0] => [1,2] => [[1,2]] => 1
[1,0,1,0,1,0] => [3,2,1] => [[1],[2],[3]] => 0
[1,0,1,1,0,0] => [2,3,1] => [[1,2],[3]] => 1
[1,1,0,0,1,0] => [3,1,2] => [[1,3],[2]] => 1
[1,1,0,1,0,0] => [2,1,3] => [[1,3],[2]] => 1
[1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => 3
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1],[2],[3],[4]] => 0
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[1,3],[2],[4]] => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,2,3],[4]] => 3
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[1,4],[2],[3]] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => 3
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[1,4],[2],[3]] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[1,4],[2],[3]] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[1,2,4],[3]] => 3
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,3,4],[2]] => 3
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[1,3,4],[2]] => 3
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[1,3,4],[2]] => 3
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => 6
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 0
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[1,3],[2],[4],[5]] => 1
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => 1
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[1,4],[2],[3],[5]] => 1
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[1,2],[3,4],[5]] => 3
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[1,4],[2],[3],[5]] => 1
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => 1
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => 3
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => 3
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[1,3,4],[2],[5]] => 3
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => 3
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => 6
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[1,5],[2],[3],[4]] => 1
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => 3
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[1,3],[2,5],[4]] => 3
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[1,3],[2,5],[4]] => 3
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[1,2,3],[4,5]] => 5
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[1,5],[2],[3],[4]] => 1
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[1,2],[3,5],[4]] => 3
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[1,5],[2],[3],[4]] => 1
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => 1
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => 3
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[1,3,5],[2],[4]] => 3
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => 3
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => 6
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[1,2,5],[3,4]] => 5
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => 5
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => 3
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => 6
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[1,3,4,5],[2]] => 6
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[1,3,4,5],[2]] => 6
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[1,3,4,5],[2]] => 6
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 6
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => 6
>>> Load all 1611 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => 5
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 5
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 9
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => 5
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => 8
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => 10
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => 8
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => 10
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 10
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[1,2,3],[4,5],[6],[7]] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[1,2,5],[3,4],[6],[7]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[1,2,5],[3,4],[6],[7]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[1,2,3],[4,6],[5],[7]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[1,2,4],[3,6],[5],[7]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[1,2,3,4],[5,6],[7]] => 8
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[1,2,3],[4,6],[5],[7]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[1,2,6],[3,4],[5],[7]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[1,2,6],[3,4],[5],[7]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7]] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[1,2,6],[3,5],[4],[7]] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[1,2,6],[3,5],[4],[7]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[1,3,6],[2,5],[4],[7]] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => 5
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[1,2,3,6],[4,5],[7]] => 8
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[1,2,6],[3,5],[4],[7]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[1,2,6],[3,5],[4],[7]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]] => 6
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => 10
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[1,2,5,6],[3,4],[7]] => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[1,2,5,6],[3,4],[7]] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[1,2,5,6],[3,4],[7]] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[1,2,3],[4,7],[5],[6]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[1,2],[3,4],[5,7],[6]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[1,2,4],[3,7],[5],[6]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[1,2,3,4],[5,7],[6]] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[1,5],[2,7],[3],[4],[6]] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[1,2,3],[4,5],[6,7]] => 7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[1,5],[2,7],[3],[4],[6]] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[1,5],[2,7],[3],[4],[6]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[1,5],[2,7],[3],[4],[6]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[1,2,5],[3,7],[4],[6]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[1,3,5],[2,7],[4],[6]] => 5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[1,2,3,5],[4,7],[6]] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[1,2,5],[3,4],[6,7]] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[1,3,4,5],[2,7],[6]] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[1,3,4,5],[2,7],[6]] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => 12
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[1,2,3],[4,7],[5],[6]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[1,2],[3,4],[5,7],[6]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[1,2,4],[3,7],[5],[6]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[1,2,3,4],[5,7],[6]] => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[1,2,3],[4,7],[5],[6]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[1,3,7],[2],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[1,2,7],[3,4],[5],[6]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[1,2,7],[3,4],[5],[6]] => 5
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[1,3,4,7],[2],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => 10
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[1,2,7],[3,5],[4],[6]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => 5
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[1,2,3],[4,5,7],[6]] => 9
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[1,2,7],[3,5],[4],[6]] => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[1,2,7],[3,5],[4],[6]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[1,3,7],[2,5],[4],[6]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[1,2,3,7],[4,5],[6]] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[1,2,7],[3,5],[4],[6]] => 5
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[1,2,7],[3,5],[4],[6]] => 5
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[1,3,5,7],[2],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => 10
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[1,2,5,7],[3,4],[6]] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[1,2,5,7],[3,4],[6]] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[1,2,5,7],[3,4],[6]] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 10
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[1,3,4,5,7],[2],[6]] => 10
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 10
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => 10
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 10
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => 15
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => 9
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[1,2,7],[3,4],[5,6]] => 7
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => 9
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5]] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 9
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => 12
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[1,2,3],[4,6,7],[5]] => 9
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[1,2,3,7],[4,6],[5]] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[1,2,7],[3,4],[5,6]] => 7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[1,3,4,7],[2,6],[5]] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[1,3,4,7],[2,6],[5]] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => 12
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[1,2,3],[4,6,7],[5]] => 9
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[1,2,3,7],[4,6],[5]] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[1,2,7],[3,6],[4],[5]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[1,3,6,7],[2],[4],[5]] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[1,3,6,7],[2],[4],[5]] => 6
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => 10
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[1,2,6,7],[3,4],[5]] => 8
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[1,2,6,7],[3,4],[5]] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[1,2,6,7],[3,4],[5]] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[1,3,4,6,7],[2],[5]] => 10
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[1,3,4,6,7],[2],[5]] => 10
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => 15
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => 12
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => 12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => 12
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[1,2,6,7],[3,5],[4]] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => 15
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => 12
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => 12
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => 12
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 12
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 15
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 8
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 10
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 9
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 8
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[1,2,4],[3,7],[5],[6],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 5
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => 7
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[1,3,4,5],[2,7],[6],[8]] => 8
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[1,2,3,4,5],[6,7],[8]] => 12
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => 5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[1,2,7],[3,4],[5],[6],[8]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 6
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 10
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[1,2,3],[4,5,7],[6],[8]] => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 10
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [[1,3,4,5,7],[2],[6],[8]] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 10
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 10
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 10
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[1,2,3,4,5,7],[6],[8]] => 15
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[1,2,3],[4,6,7],[5],[8]] => 9
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[1,2,7],[3,4],[5,6],[8]] => 7
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[1,2,4],[3,6,7],[5],[8]] => 9
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => 9
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => 9
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[1,2,3,4],[5,6,7],[8]] => 12
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 8
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[1,2,7],[3,4],[5,6],[8]] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 5
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 8
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 8
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[1,2,3,4,7],[5,6],[8]] => 12
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 9
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[1,2,7],[3,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => 6
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 6
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[1,2,6,7],[3,4],[5],[8]] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 6
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 10
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 15
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[1,2,6,7],[3,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[1,2,3,7],[4,5,6],[8]] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[1,2,3,7],[4,5,6],[8]] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 8
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => 12
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => 8
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 6
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 10
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[1,3,5,6,7],[2],[4],[8]] => 10
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 10
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 10
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 15
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[1,2,5,6,7],[3,4],[8]] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[1,2,5,6,7],[3,4],[8]] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[1,2,5,6,7],[3,4],[8]] => 12
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 10
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 15
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 7
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 5
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 5
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[1,2,4,5],[3,8],[6],[7]] => 8
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 8
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[1,2,3,4,5],[6,8],[7]] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 7
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6],[7,8]] => 10
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[1,3,6],[2,8],[4],[5],[7]] => 5
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 8
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 7
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 5
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 8
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[1,2,3,4,6],[5,8],[7]] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 7
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 5
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 8
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 8
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[1,2,3,5,6],[4,8],[7]] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [[1,2,5,6],[3,4],[7,8]] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 8
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[1,2,4,5,6],[3,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[1,3,4,5,6],[2,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 12
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => 17
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 5
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 8
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[1,4,5],[2,8],[3],[6],[7]] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 8
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 8
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[1,2,3,4,5],[6,8],[7]] => 12
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[1,4,8],[2],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [[1,4,8],[2],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[1,3,4,8],[2],[5],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 10
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 9
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[1,3,5,8],[2],[4],[6],[7]] => 6
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[1,4,5,8],[2],[3],[6],[7]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[1,2,5,8],[3,4],[6],[7]] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[1,3,4,5,8],[2],[6],[7]] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 10
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[1,2,3,4,5,8],[6],[7]] => 15
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[1,2,8],[3,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[1,2,3],[4,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[1,2,8],[3,4],[5,6],[7]] => 7
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[1,2,4],[3,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[1,2,3,4],[5,6,8],[7]] => 12
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 7
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 5
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[1,3,4,8],[2,6],[5],[7]] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[1,3,4,8],[2,6],[5],[7]] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[1,2,3,4,8],[5,6],[7]] => 12
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 9
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => 6
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 6
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[1,4,6,8],[2],[3],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[1,4,6,8],[2],[3],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 10
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 10
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 10
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 10
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 15
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[1,2,3,8],[4,5,6],[7]] => 12
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[1,2,6,8],[3,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[1,2,3,8],[4,5,6],[7]] => 12
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [[1,3,5,6,8],[2],[4],[7]] => 10
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => 15
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[1,2,5,6,8],[3,4],[7]] => 12
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[1,2,5,6,8],[3,4],[7]] => 12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[1,2,5,6,8],[3,4],[7]] => 12
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 10
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 15
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => 21
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 9
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => 7
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [[1,2,4],[3,7,8],[5],[6]] => 9
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [[1,2,3,4],[5,7,8],[6]] => 12
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [[1,3,8],[2,5],[4,7],[6]] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 11
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [[1,2,8],[3,5],[4,7],[6]] => 7
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 9
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 9
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 9
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [[1,2,3,5],[4,7,8],[6]] => 12
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 9
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 11
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 11
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 9
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 12
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 12
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 12
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[1,2,3,4,5],[6,7,8]] => 16
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => 7
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 9
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => 12
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[1,3,4,8],[2,7],[5],[6]] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[1,2,3,4,8],[5,7],[6]] => 12
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[1,2,8],[3,5],[4,7],[6]] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [[1,3,8],[2,5],[4,7],[6]] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[1,2,3],[4,5,8],[6,7]] => 11
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [[1,3,5,8],[2,7],[4],[6]] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [[1,3,5,8],[2,7],[4],[6]] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[1,4,5,8],[2,7],[3],[6]] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [[1,2,5,8],[3,4],[6,7]] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[1,3,4,5,8],[2,7],[6]] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => 12
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => 12
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[1,2,3,4,5,8],[6,7]] => 17
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[1,2,3],[4,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => 7
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[1,2,3,4],[5,7,8],[6]] => 12
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[1,2,3],[4,7,8],[5],[6]] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[1,3,4,8],[2,7],[5],[6]] => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[1,3,4,8],[2,7],[5],[6]] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[1,2,3,4,8],[5,7],[6]] => 12
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[1,2,3],[4,7,8],[5],[6]] => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[1,3,8],[2,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[1,2,8],[3,7],[4],[5],[6]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[1,3,7,8],[2],[4],[5],[6]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[1,3,7,8],[2],[4],[5],[6]] => 6
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => 6
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[1,2,7,8],[3,4],[5],[6]] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[1,3,4,7,8],[2],[5],[6]] => 10
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 15
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[1,2,3,8],[4,5,7],[6]] => 12
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[1,2,3,8],[4,5,7],[6]] => 12
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 8
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[1,2,7,8],[3,5],[4],[6]] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 6
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 10
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => 10
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[1,2,5,7,8],[3,4],[6]] => 12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[1,2,5,7,8],[3,4],[6]] => 12
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[1,2,5,7,8],[3,4],[6]] => 12
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 10
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => 21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [[1,2,7,8],[3,4],[5,6]] => 10
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 12
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 18
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [[1,2,7,8],[3,4],[5,6]] => 10
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => 12
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[1,2,3,4,8],[5,6,7]] => 16
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [[1,2,7,8],[3,4],[5,6]] => 10
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [[1,2,7,8],[3,4],[5,6]] => 10
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [[1,2,7,8],[3,4],[5,6]] => 10
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[1,3,4,7,8],[2,6],[5]] => 12
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[1,3,4,7,8],[2,6],[5]] => 12
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[1,2,3,4,7,8],[5,6]] => 17
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[1,2,3,8],[4,6,7],[5]] => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 12
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[1,3,6,7,8],[2],[4],[5]] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 10
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 10
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 10
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 15
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[1,2,6,7,8],[3,4],[5]] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 12
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 10
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[1,3,4,6,7,8],[2],[5]] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[1,3,4,6,7,8],[2],[5]] => 15
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 15
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 15
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 15
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 21
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,7,8],[4,5,6]] => 16
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [[1,2,3,7,8],[4,5,6]] => 16
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => 16
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 12
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[1,2,6,7,8],[3,5],[4]] => 12
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 10
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 21
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => 17
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => 17
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 17
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 17
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 28
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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 1,3,0,1 1,6,0,6,0,0,1 1,10,0,20,0,3,7,0,0,0,1 1,15,0,50,0,22,28,0,5,1,9,0,0,0,0,1 1,21,0,105,0,91,84,6,45,9,45,0,10,0,0,11,0,0,0,0,0,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{3}$
$F_{4} = 1 + 6\ q + 6\ q^{3} + q^{6}$
$F_{5} = 1 + 10\ q + 20\ q^{3} + 3\ q^{5} + 7\ q^{6} + q^{10}$
$F_{6} = 1 + 15\ q + 50\ q^{3} + 22\ q^{5} + 28\ q^{6} + 5\ q^{8} + q^{9} + 9\ q^{10} + q^{15}$
$F_{7} = 1 + 21\ q + 105\ q^{3} + 91\ q^{5} + 84\ q^{6} + 6\ q^{7} + 45\ q^{8} + 9\ q^{9} + 45\ q^{10} + 10\ q^{12} + 11\ q^{15} + q^{21}$
Description
The number of attacking pairs of a standard tableau.
Note that this is actually a statistic on the underlying partition.
A pair of cells $(c, d)$ of a Young diagram (in English notation) is said to be attacking if one of the following conditions holds:
1. $c$ and $d$ lie in the same row with $c$ strictly to the west of $d$.
2. $c$ is in the row immediately to the south of $d$, and $c$ lies strictly east of $d$.
Note that this is actually a statistic on the underlying partition.
A pair of cells $(c, d)$ of a Young diagram (in English notation) is said to be attacking if one of the following conditions holds:
1. $c$ and $d$ lie in the same row with $c$ strictly to the west of $d$.
2. $c$ is in the row immediately to the south of $d$, and $c$ lies strictly east of $d$.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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