Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [1] => [[1]] => 1
[1,0,1,0] => [1,1] => [1,1] => [[1],[2]] => 2
[1,1,0,0] => [2] => [2] => [[1,2]] => 1
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 3
[1,0,1,1,0,0] => [1,2] => [2,1] => [[1,2],[3]] => 2
[1,1,0,0,1,0] => [2,1] => [2,1] => [[1,2],[3]] => 2
[1,1,0,1,0,0] => [3] => [3] => [[1,2,3]] => 1
[1,1,1,0,0,0] => [3] => [3] => [[1,2,3]] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 4
[1,0,1,0,1,1,0,0] => [1,1,2] => [2,1,1] => [[1,2],[3],[4]] => 3
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => [[1,2],[3],[4]] => 3
[1,0,1,1,0,1,0,0] => [1,3] => [3,1] => [[1,2,3],[4]] => 2
[1,0,1,1,1,0,0,0] => [1,3] => [3,1] => [[1,2,3],[4]] => 2
[1,1,0,0,1,0,1,0] => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 3
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [[1,2],[3,4]] => 2
[1,1,0,1,0,0,1,0] => [3,1] => [3,1] => [[1,2,3],[4]] => 2
[1,1,0,1,0,1,0,0] => [4] => [4] => [[1,2,3,4]] => 1
[1,1,0,1,1,0,0,0] => [4] => [4] => [[1,2,3,4]] => 1
[1,1,1,0,0,0,1,0] => [3,1] => [3,1] => [[1,2,3],[4]] => 2
[1,1,1,0,0,1,0,0] => [4] => [4] => [[1,2,3,4]] => 1
[1,1,1,0,1,0,0,0] => [4] => [4] => [[1,2,3,4]] => 1
[1,1,1,1,0,0,0,0] => [4] => [4] => [[1,2,3,4]] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,3] => [3,2] => [[1,2,3],[4,5]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [3,2] => [[1,2,3],[4,5]] => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,0,1,0,0,1,1,0,0] => [3,2] => [3,2] => [[1,2,3],[4,5]] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,0,1,0,1,0,1,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,0,1,0,1,1,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,0,1,1,0,0,1,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,0,1,1,0,1,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,0,1,1,1,0,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [3,2] => [[1,2,3],[4,5]] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,1,0,0,1,0,1,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,0,0,1,1,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,1,0,1,0,0,1,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,0,1,0,1,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,0,1,1,0,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 2
[1,1,1,1,0,0,0,1,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,1,0,0,1,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,1,0,1,0,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
>>> Load all 4746 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[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] => [1,1,6] => [6,1,1] => [[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] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[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] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[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] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[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] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [[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] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[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] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => [9] => [[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] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[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] => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[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] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,2,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 4
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,4,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,6,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,6,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 5
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,4,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,4] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,6,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [5,1,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,2,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,5,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,4,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,5,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,5,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,4,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,2,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,5,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 5
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 5
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,5,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,2,1,4] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,4,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,1,5] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,3,5] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,4] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,3,5] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,5,4] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,4] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,3,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,5,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,3,5] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,5,2,3,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 6
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,5,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,3,2,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 5
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,5] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,2,5] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,2,4,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,2,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,2,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,4,3] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,2,4,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,2,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 3
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 1
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,3,1 14,14,9,4,1 42,42,28,14,5,1 132,132,90,48,20,6,1 429,429,297,165,75,27,7,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 3\ q^{3} + q^{4}$
$F_{5} = 14\ q + 14\ q^{2} + 9\ q^{3} + 4\ q^{4} + q^{5}$
$F_{6} = 42\ q + 42\ q^{2} + 28\ q^{3} + 14\ q^{4} + 5\ q^{5} + q^{6}$
$F_{7} = 132\ q + 132\ q^{2} + 90\ q^{3} + 48\ q^{4} + 20\ q^{5} + 6\ q^{6} + q^{7}$
$F_{8} = 429\ q + 429\ q^{2} + 297\ q^{3} + 165\ q^{4} + 75\ q^{5} + 27\ q^{6} + 7\ q^{7} + q^{8}$
Description
The row containing the largest entry of a standard tableau.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
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