Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000169: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [[1]] => 0
[1,0,1,0] => [1,2] => [[1,2]] => 0
[1,1,0,0] => [2,1] => [[1],[2]] => 1
[1,0,1,0,1,0] => [1,2,3] => [[1,2,3]] => 0
[1,0,1,1,0,0] => [1,3,2] => [[1,2],[3]] => 1
[1,1,0,0,1,0] => [2,1,3] => [[1,3],[2]] => 2
[1,1,0,1,0,0] => [2,3,1] => [[1,2],[3]] => 1
[1,1,1,0,0,0] => [3,2,1] => [[1],[2],[3]] => 3
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [[1,2,3,4]] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [[1,2,3],[4]] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [[1,2,4],[3]] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [[1,2,3],[4]] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [[1,2],[3],[4]] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[1,3],[2,4]] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[1,2,4],[3]] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[1,2,3],[4]] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[1,2],[3],[4]] => 3
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[1,4],[2],[3]] => 5
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => 4
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => 3
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[1],[2],[3],[4]] => 6
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [[1,2,3,4],[5]] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 3
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [[1,2,4],[3,5]] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [[1,2,3,5],[4]] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [[1,2,3,4],[5]] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [[1,2,5],[3],[4]] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [[1,2,4],[3],[5]] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [[1,2],[3],[4],[5]] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => 6
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[1,3,4],[2,5]] => 5
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[1,3],[2,4],[5]] => 7
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => 3
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[1,2,4],[3,5]] => 4
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[1,2,3],[4],[5]] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[1,2,5],[3],[4]] => 5
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[1,2,4],[3],[5]] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[1,2,3],[4],[5]] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[1,2],[3],[4],[5]] => 6
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => 7
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[1,4],[2,5],[3]] => 8
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => 6
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => 5
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[1,3],[2,4],[5]] => 7
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => 5
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => 4
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[1,2],[3],[4],[5]] => 6
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => 9
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => 8
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => 7
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => 6
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => 8
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [[1,2,3,6],[4],[5]] => 5
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => 6
>>> Load all 1926 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => 9
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [[1,2,4],[3],[5],[6]] => 7
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 7
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => 8
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 8
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => 8
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => 9
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => 8
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 11
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => 8
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[1,2,3,6],[4],[5]] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => 9
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[1,2,4],[3],[5],[6]] => 7
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => 11
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => 8
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => 9
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => 7
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => 10
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[1,3,4],[2,5],[6]] => 8
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 11
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => 7
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => 5
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[1,2,4],[3,5],[6]] => 7
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => 5
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[1,2,6],[3],[4],[5]] => 9
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[1,2,5],[3],[4],[6]] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[1,2,4],[3],[5],[6]] => 7
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 10
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => 12
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => 13
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => 11
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => 10
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => 12
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => 10
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => 8
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => 11
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => 8
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => 7
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => 10
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 14
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => 13
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => 12
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 10
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 4
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [[1,2,3,5],[4,6],[7]] => 7
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => [[1,2,3,6],[4],[5],[7]] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [[1,2,3,5],[4],[6],[7]] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 6
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 8
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 10
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 9
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => 8
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => 5
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [[1,2,3,5],[4,6],[7]] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [[1,2,3,5],[4,6],[7]] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [[1,2,3,6],[4],[5],[7]] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [[1,2,3,5],[4],[6],[7]] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => 9
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => 10
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => 11
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => [[1,2,5,6],[3,7],[4]] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]] => 9
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [[1,2,4,5],[3,6],[7]] => 8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [[1,2,4,7],[3,5],[6]] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => 9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [[1,2,4,5],[3,6],[7]] => 8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [[1,2,4],[3,5],[6],[7]] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,5,3,2,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,4,5,3,6,2,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [[1,2,3,5,6],[4],[7]] => 5
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [[1,2,3,5],[4,6],[7]] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [[1,2,3,4,6],[5],[7]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [[1,2,3,6],[4],[5],[7]] => 8
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [[1,2,3,5],[4],[6],[7]] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => 13
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => [[1,2,5,7],[3],[4],[6]] => 11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [[1,2,5,6],[3],[4],[7]] => 10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [[1,2,5],[3,6],[4],[7]] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [[1,2,4,7],[3],[5],[6]] => 10
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [[1,2,4,6],[3],[5],[7]] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [[1,2,4,5],[3],[6],[7]] => 8
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [[1,2,4],[3,5],[6],[7]] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [[1,2,3,6],[4],[5],[7]] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [[1,2,3,5],[4],[6],[7]] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [[1,2,3,4],[5],[6],[7]] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => 14
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => [[1,2,6],[3],[4],[5],[7]] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [[1,2,5],[3],[4],[6],[7]] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [[1,2,4],[3],[5],[6],[7]] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 8
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]] => 7
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 9
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 10
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => 7
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 10
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 11
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => 13
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => 9
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => 7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => 10
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => 14
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]] => 11
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[1,3,5],[2,4,6],[7]] => 13
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[1,3,4,7],[2,5],[6]] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => 15
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => [[1,3,6],[2,4],[5],[7]] => 14
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[1,3,5],[2,4],[6],[7]] => 13
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 6
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 7
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 7
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => 5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[1,2,3,5],[4,6],[7]] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[1,2,3,5],[4,6],[7]] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => 9
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => 11
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => 12
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 8
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 9
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => 10
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[1,2,3,5],[4,6],[7]] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 13
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 11
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 12
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[1,2,4,7],[3],[5],[6]] => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[1,2,4,6],[3],[5],[7]] => 9
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[1,2,4,5],[3],[6],[7]] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[1,2,7],[3],[4],[5],[6]] => 14
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[1,2,6],[3],[4],[5],[7]] => 13
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[1,2,5],[3],[4],[6],[7]] => 12
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[1,2,4],[3],[5],[6],[7]] => 11
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => 11
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => 13
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => [[1,4,5,6],[2,7],[3]] => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 14
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => 14
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => 15
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => [[1,4,5,7],[2,6],[3]] => 13
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => [[1,4,5,6],[2,7],[3]] => 12
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[1,4,5],[2,6],[3,7]] => 14
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 16
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => [[1,4,6],[2,5],[3,7]] => 15
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[1,4,5],[2,6],[3,7]] => 14
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 17
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 10
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 11
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => 11
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 13
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 9
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => 10
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => 10
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[1,3,6,7],[2,4],[5]] => 13
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => [[1,3,6],[2,4,7],[5]] => 14
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]] => 12
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]] => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[1,3,5],[2,4,6],[7]] => 13
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[1,3,4,7],[2,5],[6]] => 11
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => 10
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[1,3,4,5],[2,6],[7]] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[1,3,7],[2,4],[5],[6]] => 15
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[1,3,6],[2,4],[5],[7]] => 14
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[1,3,5],[2,4],[6],[7]] => 13
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 16
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => 9
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => 10
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => 12
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 8
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 6
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => 10
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,2,1,7,6] => [[1,2,3,6],[4,7],[5]] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[1,2,3,5],[4,6],[7]] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 12
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 13
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 11
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 12
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 14
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 12
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[1,2,4],[3],[5],[6],[7]] => 11
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => 15
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => 16
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => 17
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => [[1,5,6],[2,7],[3],[4]] => 16
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 18
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 14
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[1,4,6],[2,7],[3],[5]] => 15
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 13
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 12
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[1,4,5],[2,6],[3],[7]] => 14
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[1,4,7],[2,5],[3],[6]] => 16
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[1,4,6],[2,5],[3],[7]] => 15
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[1,4,5],[2,6],[3],[7]] => 14
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 17
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 13
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[1,3,6],[2,7],[4],[5]] => 14
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 12
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 11
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[1,3,5],[2,6],[4],[7]] => 13
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 11
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[1,3,7],[2,4],[5],[6]] => 15
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[1,3,6],[2,4],[5],[7]] => 14
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[1,3,5],[2,4],[6],[7]] => 13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[1,3,4],[2,5],[6],[7]] => 12
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 16
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 12
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 13
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 11
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 10
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 9
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => 11
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 14
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 13
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 12
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 11
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => 18
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 19
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => 17
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => 16
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => 18
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 16
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 15
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[1,4],[2,5],[3],[6],[7]] => 17
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 15
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 13
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 12
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => 16
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 13
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 12
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 11
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => 20
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => 19
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 18
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 17
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 16
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 15
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [[1,2,3,4,5,7],[6,8]] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => 8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 9
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [[1,2,3,4,5,7],[6,8]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 12
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [[1,2,3,5,6,8],[4],[7]] => 7
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,2,5,6,4,7,3,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 8
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => 9
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 10
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 12
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]] => 11
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 13
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => 9
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => 8
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => 7
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 13
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => 14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 12
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 13
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => 15
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 9
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 6
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 6
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [[1,2,3,4,5,7],[6,8]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 11
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [[1,2,3,5,8],[4,6],[7]] => 10
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [[1,2,3,6,8],[4],[5],[7]] => 11
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 11
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 13
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 12
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => 16
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 15
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 17
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 12
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => 13
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 12
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]] => 13
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 11
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 12
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [[1,2,3,5,7,8],[4],[6]] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [[1,2,3,5,6,8],[4],[7]] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 17
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 18
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 14
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [[1,2,5,6,8],[3],[4],[7]] => 13
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [[1,2,5,6,7],[3],[4],[8]] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => 14
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]] => 17
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 14
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [[1,2,4,6,8],[3],[5],[7]] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [[1,2,4,6,7],[3],[5],[8]] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [[1,2,4,5,8],[3],[6],[7]] => 11
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 10
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [[1,2,4,5,6],[3],[7],[8]] => 9
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 19
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [[1,2,6],[3,7],[4],[5],[8]] => 18
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 14
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 15
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [[1,2,4,7],[3],[5],[6],[8]] => 14
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 12
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 20
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 19
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 17
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 9
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 10
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 11
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 8
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 11
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[1,3,4,6,7],[2,5,8]] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[1,3,4,5,7],[2,6,8]] => 11
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => 8
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [[1,3,4,5,8],[2,6],[7]] => 12
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 12
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => 13
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[1,3,5,6,7],[2,4,8]] => 13
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 15
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 16
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 13
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => 16
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => 18
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => 11
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[1,3,4,6,7],[2,5,8]] => 12
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => 9
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => 8
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => 14
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 15
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [[1,3,4,5,7],[2,6],[8]] => 11
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 16
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 19
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 16
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 13
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => 16
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]] => 18
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => 14
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,5,6,4,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 15
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [[1,3,4,6,7],[2,5],[8]] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [[1,3,4,5,8],[2,6],[7]] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [[1,3,4,5,7],[2,6],[8]] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 14
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 20
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[1,3,6],[2,4,7],[5],[8]] => 19
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 16
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [[1,3,5,6],[2,4],[7],[8]] => 15
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 18
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [[1,3,4,8],[2,5],[6],[7]] => 16
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 14
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => 21
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [[1,3,7],[2,4],[5],[6],[8]] => 20
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 19
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 18
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 22
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => 8
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 7
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 10
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 12
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => 9
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => 7
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 13
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => 14
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 12
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 13
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 9
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 7
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 6
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[1,2,3,5,8],[4,6],[7]] => 10
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 11
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 12
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 11
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[1,2,5,7,8],[3,6],[4]] => 14
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => 15
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 15
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 17
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 10
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 12
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 13
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 7
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[1,2,4,7,8],[3,5],[6]] => 13
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 14
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 11
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[1,2,4,6],[3,5,7],[8]] => 13
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 9
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 12
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,4,7,6,5,8,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 15
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 17
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 18
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 15
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 13
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 12
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => 14
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 15
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 14
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[1,2,5],[3,6],[4,7],[8]] => 17
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 12
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => 11
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [[1,2,4,5,6],[3],[7],[8]] => 9
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 15
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 19
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 16
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 18
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => 14
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 17
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 20
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 19
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 13
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 14
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => 14
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 14
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 18
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => 17
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => 17
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 19
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[1,4,5,7,8],[2,6],[3]] => 16
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => 14
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]] => 18
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => 17
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]] => 20
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]] => 21
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[1,4,6,7],[2,5],[3,8]] => 18
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => 20
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [[1,4,5,7],[2,6],[3,8]] => 17
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [[1,4,5,6],[2,7],[3,8]] => 16
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]] => 22
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [[1,4,7],[2,5],[3,6],[8]] => 21
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 20
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 23
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 12
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => 13
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 14
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 13
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => 15
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => 15
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 16
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[1,3,5,6,8],[2,7],[4]] => 14
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 13
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 15
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[1,3,5,8],[2,6],[4,7]] => 17
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => 16
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => 15
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 18
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 11
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 14
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 9
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[1,3,4,5,7],[2,6],[8]] => 11
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => 14
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [[1,3,4,5,8],[2,6],[7]] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 16
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[1,3,6,7],[2,4,8],[5]] => 17
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 18
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => 17
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 19
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 16
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => 13
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]] => 17
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => 16
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [[1,3,5,6],[2,4,7],[8]] => 15
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [[1,3,4,7],[2,5,8],[6]] => 15
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [[1,3,4,6,7],[2,5],[8]] => 12
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [[1,3,4,5,8],[2,6],[7]] => 12
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [[1,3,4,5,7],[2,6],[8]] => 11
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [[1,3,4,5,6],[2,7],[8]] => 10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 16
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 14
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 20
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 18
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => 19
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 17
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 16
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 16
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 21
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 20
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 22
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 11
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => 15
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 15
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 14
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 17
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 11
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 13
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 7
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [[1,2,4,5,6],[3,7],[8]] => 9
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 14
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 12
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [[1,2,4,5,8],[3,6],[7]] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 15
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 11
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => 7
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [[1,2,3,5,8],[4,6],[7]] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,4,5,6,2,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,6,2,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 6
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[1,2,3,4,5,8],[6],[7]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[1,2,3,4,5,7],[6],[8]] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,8,7,6,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,8,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 15
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 17
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 18
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 14
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,5,4,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 15
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,5,4,2,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 13
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 12
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 16
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 15
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 14
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 12
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => 11
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 10
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [[1,2,4,5,6],[3],[7],[8]] => 9
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 15
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 14
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 18
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 19
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => 17
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 16
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 18
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 16
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 15
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 14
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 17
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 17
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 18
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 19
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => 20
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 19
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 21
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 21
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 22
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 20
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 19
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => 21
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => 23
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [[1,5,7],[2,6],[3,8],[4]] => 22
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [[1,5,6],[2,7],[3,8],[4]] => 21
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 24
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 17
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]] => 18
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 20
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 16
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 17
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 15
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 14
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[1,4,5,6],[2,7],[3],[8]] => 16
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 18
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 17
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [[1,4,5,6],[2,7],[3],[8]] => 16
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 20
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 21
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 19
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 18
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 20
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 18
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 17
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 21
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [[1,4,5],[2,6],[3,7],[8]] => 19
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 23
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 16
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 17
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 19
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => 15
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 16
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 13
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 17
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 16
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 15
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 13
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 12
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 11
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,3,5,7,6,2,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 16
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [[1,3,4,6],[2,5],[7],[8]] => 14
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 19
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 20
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => 19
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 17
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 16
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 15
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [[1,3,5],[2,4,6],[7],[8]] => 18
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 15
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 13
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 21
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 20
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 19
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 22
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 15
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,5,3,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 16
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,5,3,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 17
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 18
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,5,3,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 14
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 15
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 12
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 16
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 14
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 12
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => 13
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 10
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 12
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,5,3,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 15
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 12
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 13
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 12
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 9
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 11
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 7
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 6
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,5,7,8,6,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 19
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 18
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 14
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 12
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,6,7,8,5,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 20
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 19
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 17
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 22
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 23
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => 24
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [[1,6,7],[2,8],[3],[4],[5]] => 23
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 25
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 21
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 22
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 20
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 19
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => 21
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 23
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 22
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [[1,5,6],[2,7],[3],[4],[8]] => 21
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 24
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 20
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 21
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 19
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 18
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [[1,4,6],[2,7],[3],[5],[8]] => 20
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 18
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 17
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 16
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 19
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 22
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => 21
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 19
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 23
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => 19
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 20
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 18
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 17
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => 19
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 17
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 16
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 16
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 14
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 13
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 21
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 19
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 18
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 18
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 19
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => 17
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 16
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 17
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 15
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 12
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 16
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 14
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 13
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 12
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 11
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 10
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 20
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 19
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 17
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 25
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => 26
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 24
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 23
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 25
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 23
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 22
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 21
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 24
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 22
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 21
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 20
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 19
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 21
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 20
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 19
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 18
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 17
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 22
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 20
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 19
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 18
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 17
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 16
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 15
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 27
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 26
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 25
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 24
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 23
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 22
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 28
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 35
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 44
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,6,5,4,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 27
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,9,7,6,5,4,3,2,1,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 35
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,8,7,5,4,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 27
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 28
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,6,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,8,7,6,5,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 27
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,7,6,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 21
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,9,8,7,6,4,3,2,1,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 35
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 27
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 34
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,5,4,3,2] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 29
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 33
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 27
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,10,6,5,4,3,2] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 15
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 43
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 25
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 37
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,10,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 28
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 42
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 35
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 28
[] => [] => [] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,5,7,8,9,6,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,5,7,9,8,6,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,8,9,7,6,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,6,5,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,5,4,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,3,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,4,3,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,7,6,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => 21
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 29
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,9,4,2,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,7,9,8,4,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,7,3,9,8,2,1] => [[1,2,3,4,6],[5,7],[8],[9]] => 11
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,9,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => 31
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,9,8,3,2,1] => [[1,3,5],[2,4,6],[7],[8],[9]] => 24
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,9,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,7,9,8,6,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,5,4,9,8,7,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 30
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,7,5,9,8,4,3,2,1] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 22
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,7,9,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 29
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 21
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 28
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 36
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,4,3,2] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 15
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,10,3,2] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,9,10,4,3,2] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,4,6,5,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 9
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,3,5,4,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => 11
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,6,5,4,9,8,7] => [[1,2,3,4,7],[5,8],[6,9]] => 12
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,4,3,9,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8],[9]] => 16
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 16
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,2,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 22
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 13
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9]] => 24
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4]] => 14
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 20
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,6,5,9,8,7] => [[1,3,5,7],[2,4,6,8],[9]] => 21
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9]] => 24
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => 15
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [[1,4,6,7,8,9],[2,5],[3]] => 20
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [[1,4,6,8],[2,5,7,9],[3]] => 24
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,6,5,4,7,8,9] => [[1,4,7,8,9],[2,5],[3,6]] => 24
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4,9,8,7] => [[1,4,7],[2,5,8],[3,6,9]] => 27
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 30
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => 21
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [[1,5,7,8,9],[2,6],[3],[4]] => 25
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [[1,5,7,9],[2,6,8],[3],[4]] => 27
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,2,1,7,6,5,8,9] => [[1,5,8,9],[2,6],[3,7],[4]] => 28
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2,1,7,6,5,9,8] => [[1,5,8],[2,6,9],[3,7],[4]] => 29
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,8,7,6,5,9] => [[1,5,9],[2,6],[3,7],[4,8]] => 30
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 31
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 26
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [[1,6,8,9],[2,7],[3],[4],[5]] => 29
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,4,3,2,1,8,7,6,9] => [[1,6,9],[2,7],[3,8],[4],[5]] => 31
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 30
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 32
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 33
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => 4
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 12
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 21
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3,10,9,8,7] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 24
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 20
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [[1,2,4,6,8],[3,5,7,9],[10]] => 21
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,2,10,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 29
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]] => 16
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 25
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10]] => 28
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [[1,3,7],[2,4,8],[5,9],[6,10]] => 33
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => 17
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9,10] => [[1,4,6,7,8,9,10],[2,5],[3]] => 23
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [[1,4,6,8,10],[2,5,7,9],[3]] => 29
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7,10,9] => [[1,4,7,9],[2,5,8,10],[3,6]] => 32
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,6,5,4,10,9,8,7] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 34
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 38
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 24
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 33
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5,10,9,8] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 36
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,8,7,6,5,9,10] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 36
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 37
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 39
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 30
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 36
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,3,2,1,9,8,7,6,10] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 39
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 40
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 35
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,5,4,3,2,1,9,8,7,10] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 40
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 41
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 39
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 41
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 42
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 45
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 13
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,7,8,10,9,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 15
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,7,8,10,9,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,8,10,9,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 28
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 13
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,10,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,10,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 36
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,9,10,3,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 22
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,2,1,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9]] => 23
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,5,3,2,1,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9]] => 24
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,9,10,5,4,3,2] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => 11
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,5,6,9,10,8,7,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,8,9,10,7,6,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,7,8,9,10,6,5,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,9,10,5,4,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,9,10,4,3,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 16
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [[1,2,4,6,8],[3,5,7,9],[10]] => 21
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 20
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,7,10,9,6,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 37
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,6,5,10,9,8,4,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 38
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 39
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 10
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 10
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [[1,2,7,8,9],[3],[4],[5],[6]] => 22
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [[1,2,6,7,8,9],[3],[4],[5]] => 18
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 28
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,7,9,8,4] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 15
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 21
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 37
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,6,8,9,7,5] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3],[4]] => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => 26
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [[1,2,8,9,10],[3],[4],[5],[6],[7]] => 30
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,6,8,10,9,7] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,7,10,9,8,5] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,8,10,9,2] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3],[4]] => 15
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,5,7,9,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8],[9]] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,9,8,5] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,9,8,3] => [[1,2,3,5,7],[4,6,8],[9]] => 13
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,10,9,2] => [[1,2,4,6,8],[3,5,7,9],[10]] => 21
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 36
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,7,1,9,8,10] => [[1,2,3,4,5,6,8,10],[7,9]] => 6
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,10,9,2,1] => [[1,3,5,7],[2,4,6,8],[9],[10]] => 27
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 16
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,10,9,8,1] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 34
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,3,4,6,7,8,10,9,5] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,4,5,7,8,10,9,6] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 12
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 9
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 9
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 12
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,5,7,9,10,8,6] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,3,5,6,8,9,7,4] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,10,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 21
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 9
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 16
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,5,9,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 15
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5,10,9,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 21
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,5,7,10,9,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 15
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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 1,2,1,1 1,3,2,4,2,1,1 1,4,3,8,6,6,6,4,2,1,1 1,5,4,13,11,14,19,15,15,10,11,6,4,2,1,1 1,6,5,19,17,24,39,37,41,40,45,35,35,24,20,16,11,6,4,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 2\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 3\ q^{2} + 8\ q^{3} + 6\ q^{4} + 6\ q^{5} + 6\ q^{6} + 4\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 4\ q^{2} + 13\ q^{3} + 11\ q^{4} + 14\ q^{5} + 19\ q^{6} + 15\ q^{7} + 15\ q^{8} + 10\ q^{9} + 11\ q^{10} + 6\ q^{11} + 4\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
$F_{7} = 1 + 6\ q + 5\ q^{2} + 19\ q^{3} + 17\ q^{4} + 24\ q^{5} + 39\ q^{6} + 37\ q^{7} + 41\ q^{8} + 40\ q^{9} + 45\ q^{10} + 35\ q^{11} + 35\ q^{12} + 24\ q^{13} + 20\ q^{14} + 16\ q^{15} + 11\ q^{16} + 6\ q^{17} + 4\ q^{18} + 2\ q^{19} + q^{20} + q^{21}$
Description
The cocharge of a standard tableau.
The cocharge of a standard tableau $T$, denoted $\mathrm{cc}(T)$, is defined to be the cocharge of the reading word of the tableau. The cocharge of a permutation $w_1 w_2\cdots w_n$ can be computed by the following algorithm:
1) Starting from $w_n$, scan the entries right-to-left until finding the entry $1$ with a superscript $0$.
2) Continue scanning until the $2$ is found, and label this with a superscript $1$. Then scan until the $3$ is found, labeling with a $2$, and so on, incrementing the label each time, until the beginning of the word is reached. Then go back to the end and scan again from right to left, and *do not* increment the superscript label for the first number found in the next scan. Then continue scanning and labeling, each time incrementing the superscript only if we have not cycled around the word since the last labeling.
3) The cocharge is defined as the sum of the superscript labels on the letters.
The cocharge of a standard tableau $T$, denoted $\mathrm{cc}(T)$, is defined to be the cocharge of the reading word of the tableau. The cocharge of a permutation $w_1 w_2\cdots w_n$ can be computed by the following algorithm:
1) Starting from $w_n$, scan the entries right-to-left until finding the entry $1$ with a superscript $0$.
2) Continue scanning until the $2$ is found, and label this with a superscript $1$. Then scan until the $3$ is found, labeling with a $2$, and so on, incrementing the label each time, until the beginning of the word is reached. Then go back to the end and scan again from right to left, and *do not* increment the superscript label for the first number found in the next scan. Then continue scanning and labeling, each time incrementing the superscript only if we have not cycled around the word since the last labeling.
3) The cocharge is defined as the sum of the superscript labels on the letters.
Map
to 312-avoiding permutation
Description
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
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