Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000734: Standard tableaux ⟶ ℤ
Values
[1,0] => [1] => [1] => [[1]] => 1
[1,0,1,0] => [1,1] => [1,1] => [[1],[2]] => 1
[1,1,0,0] => [2] => [2] => [[1,2]] => 2
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
[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] => [2,1] => [2,1] => [[1,2],[3]] => 2
[1,1,1,0,0,0] => [3] => [3] => [[1,2,3]] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
[1,0,1,0,1,1,0,0] => [1,1,2] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,0,1,1,0,1,0,0] => [1,2,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,0,1,1,1,0,0,0] => [1,3] => [3,1] => [[1,2,3],[4]] => 3
[1,1,0,0,1,0,1,0] => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[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] => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,0,1,0,1,0,0] => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
[1,1,0,1,1,0,0,0] => [2,2] => [2,2] => [[1,2],[3,4]] => 2
[1,1,1,0,0,0,1,0] => [3,1] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,0,0,1,0,0] => [3,1] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,0,1,0,0,0] => [3,1] => [3,1] => [[1,2,3],[4]] => 3
[1,1,1,1,0,0,0,0] => [4] => [4] => [[1,2,3,4]] => 4
[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]] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[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]] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => [2,2,1] => [[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] => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [2,2,1] => [[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]] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
[1,1,0,1,1,1,0,0,0,0] => [2,3] => [3,2] => [[1,2,3],[4,5]] => 3
[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]] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [3,2] => [[1,2,3],[4,5]] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [[1,2,3,4,5]] => 5
[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]] => 1
[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]] => 2
[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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[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]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [3,1,1,1] => [[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]] => 4
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[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] => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[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]] => 3
[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] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
>>> Load all 4870 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]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [2,2,2] => [[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] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 4
[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]] => 3
[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] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => [[1,2,3,4,5,6]] => 6
[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]] => 1
[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]] => 2
[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]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[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]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[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]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => [3,2,1,1] => [[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]] => 3
[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]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [3,2,1,1] => [[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] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[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]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [3,2,1,1] => [[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]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[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]] => 3
[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]] => 3
[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]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => [[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] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[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]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[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]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[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]] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [3,2,1,1] => [[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]] => 4
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[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] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[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]] => 3
[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] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[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]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[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]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[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]] => 3
[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]] => 3
[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]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[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]] => 3
[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] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[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] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[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]] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[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]] => 4
[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]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[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]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
[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]] => 5
[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]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
[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]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => [[1,2,3,4,5,6,7]] => 7
[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]] => 1
[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]] => 2
[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]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 3
[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]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => [4,1,1,1,1] => [[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] => [1,1,1,4,1] => [4,1,1,1,1] => [[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] => [1,1,1,4,1] => [4,1,1,1,1] => [[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]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 2
[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]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[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]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => [3,2,1,1,1] => [[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] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => [3,2,1,1,1] => [[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] => [1,1,2,3,1] => [3,2,1,1,1] => [[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] => [1,1,2,3,1] => [3,2,1,1,1] => [[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] => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[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]] => 3
[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]] => 3
[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]] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,1,3,1,2] => [3,2,1,1,1] => [[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] => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => [3,2,1,1,1] => [[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] => [1,1,3,2,1] => [3,2,1,1,1] => [[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] => [1,1,3,3] => [3,3,1,1] => [[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] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,1,3,1,2] => [3,2,1,1,1] => [[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] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,1,3,1,2] => [3,2,1,1,1] => [[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] => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => [3,2,1,1,1] => [[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] => [1,1,3,2,1] => [3,2,1,1,1] => [[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] => [1,1,3,2,1] => [3,2,1,1,1] => [[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] => [1,1,3,3] => [3,3,1,1] => [[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]] => 4
[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] => [1,1,4,1,1] => [4,1,1,1,1] => [[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] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[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] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[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] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[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]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 2
[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]] => 2
[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]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => [3,2,2,1] => [[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]] => 3
[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]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,2] => [3,2,2,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,2] => [3,2,2,1] => [[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] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[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] => [1,2,1,3,1] => [3,2,1,1,1] => [[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] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => [3,2,1,1,1] => [[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] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[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] => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[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] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[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] => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[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] => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,1,2,2] => [2,2,2,1,1] => [[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] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,1,2,2] => [2,2,2,1,1] => [[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] => [1,2,1,3,1] => [3,2,1,1,1] => [[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] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => [3,2,2,1] => [[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] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,2,1,2] => [2,2,2,1,1] => [[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] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[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] => [1,2,2,2,1] => [2,2,2,1,1] => [[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] => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,2,1,2] => [2,2,2,1,1] => [[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] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [1,2,2,1,2] => [2,2,2,1,1] => [[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] => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => [2,2,2,1,1] => [[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] => [1,2,2,2,1] => [2,2,2,1,1] => [[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] => [1,2,2,2,1] => [2,2,2,1,1] => [[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] => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => [3,2,2,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[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] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[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]] => 3
[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]] => 3
[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]] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,2] => [3,2,2,1] => [[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]] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => [3,3,1,1] => [[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] => [1,3,3,1] => [3,3,1,1] => [[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]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[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] => [1,3,1,3] => [3,3,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[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] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[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] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[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] => [1,3,1,3] => [3,3,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[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] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[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] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[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] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => [3,2,2,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[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] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => [3,3,1,1] => [[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] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[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]] => 4
[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] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[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] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[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] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[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] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[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]] => 5
[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]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[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]] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[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]] => 7
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[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]] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[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]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => [3,2,2,1] => [[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]] => 3
[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]] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[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] => [2,1,3,2] => [3,2,2,1] => [[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] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[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] => [2,1,3,1,1] => [3,2,1,1,1] => [[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] => [2,1,3,2] => [3,2,2,1] => [[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] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[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]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [3,2,2,1] => [[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] => [2,2,3,1] => [3,2,2,1] => [[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]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,2,1,1,2] => [2,2,2,1,1] => [[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] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,2] => [2,2,2,2] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,2] => [2,2,2,2] => [[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] => [2,2,3,1] => [3,2,2,1] => [[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] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[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]] => 3
[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]] => 3
[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]] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [3,2,2,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[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] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[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] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [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]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[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]] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[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]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[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] => [2,1,1,3,1] => [3,2,1,1,1] => [[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] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,2,1,2] => [2,2,2,1,1] => [[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] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[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] => [2,1,2,2,1] => [2,2,2,1,1] => [[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] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[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] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[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] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,1,2,2] => [2,2,2,1,1] => [[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] => [2,1,1,3,1] => [3,2,1,1,1] => [[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] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[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] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[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] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[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] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[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] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[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] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[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] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[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] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,2] => [2,2,2,2] => [[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] => [2,2,3,1] => [3,2,2,1] => [[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] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[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] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[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] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[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] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[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] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[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]] => 3
[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]] => 3
[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]] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,2] => [3,2,2,1] => [[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]] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[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] => [3,1,3,1] => [3,3,1,1] => [[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]] => 4
[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]] => 3
[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]] => 3
[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]] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[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] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => [[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] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[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] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[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] => [3,3,1,1] => [3,3,1,1] => [[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] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[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] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[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]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[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] => [3,1,1,3] => [3,3,1,1] => [[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] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => [[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] => [3,2,2,1] => [3,2,2,1] => [[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] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[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] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[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] => [3,1,1,3] => [3,3,1,1] => [[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] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[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] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [3,2,2,1] => [[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] => [3,2,2,1] => [3,2,2,1] => [[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] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[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] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[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] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[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]] => 4
[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] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[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]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[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]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[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]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
[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]] => 5
[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]] => 5
[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]] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[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]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
[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]] => 6
[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]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
[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]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
[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]] => 8
[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]] => 8
[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]] => 8
[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]] => 9
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[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]] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[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]] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[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]] => 7
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[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]] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[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]] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,5,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[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]] => 7
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[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]] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,5,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[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]] => 8
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[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]] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[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]] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[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]] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [2,3,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,6] => [6,3] => [[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] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [3,2,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[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] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
[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]] => 9
[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]] => 1
[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]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 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]] => 1
[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]] => 2
[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]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[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] => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[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]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[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] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[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] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[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]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [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]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[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] => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[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] => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[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] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[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] => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[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] => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[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] => [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]] => 3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [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]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[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] => [1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[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]] => 5
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[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] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [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]] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[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] => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[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] => [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]] => 3
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[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]] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [[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] => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [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]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 4
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 4
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 4
[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]] => 5
[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]] => 3
[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]] => 4
[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]] => 5
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 5
[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]] => 6
[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]] => 3
[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]] => 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]] => 4
[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]] => 4
[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]] => 4
[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]] => 5
[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]] => 6
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 4
[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]] => 2
[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]] => 3
[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]] => 4
[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]] => 5
[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]] => 2
[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]] => 5
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 5
[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]] => 3
[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]] => 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]] => 4
[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]] => 4
[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]] => 5
[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]] => 5
[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]] => 6
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 5
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 4
[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]] => 5
[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]] => 6
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 4
[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]] => 2
[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]] => 3
[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]] => 5
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 4
[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]] => 6
[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]] => 7
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[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]] => 5
[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]] => 6
[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]] => 7
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 3
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 4
[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]] => 7
[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]] => 3
[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]] => 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]] => 4
[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]] => 5
[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]] => 5
[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]] => 6
[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]] => 7
[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]] => 7
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 2
[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]] => 3
[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]] => 4
[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]] => 2
[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]] => 4
[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]] => 6
[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]] => 7
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 2
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 4
[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]] => 6
[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]] => 6
[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]] => 7
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 5
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 3
[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]] => 4
[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]] => 4
[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]] => 6
[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]] => 7
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 4
[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]] => 5
[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]] => 6
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 5
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 6
[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]] => 7
[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]] => 7
[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]] => 7
[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]] => 7
[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]] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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]] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => [4,4,1] => [[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] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[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] => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[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] => [2,2,2,1,2] => [2,2,2,2,1] => [[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] => [2,2,1,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => [3,2,2,1,1] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[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] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[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] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,1,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[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] => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[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] => [2,3,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,2,4] => [4,2,1,1,1] => [[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] => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[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] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [2,1,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[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] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[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] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => [[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] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [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]] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,2,4,1] => [4,2,1,1,1] => [[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] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [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]] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [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]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [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]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[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] => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[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] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[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] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,1,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,4,1] => [4,2,1,1,1] => [[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] => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2,2] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => [3,2,2,1,1] => [[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] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[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] => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[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] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[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] => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,4,2] => [4,2,1,1,1] => [[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] => [4,2,1,1,1] => [4,2,1,1,1] => [[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] => [2,4,1,1,1] => [4,2,1,1,1] => [[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] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[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] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[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] => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [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]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[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] => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [[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] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [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]] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => [[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] => [3,2,2,2] => [3,2,2,2] => [[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] => [3,1,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[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] => [3,2,1,2,2] => [3,2,2,2,1] => [[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] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[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] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,1,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,6,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [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]] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[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] => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,2,1] => [3,3,2,1] => [[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] => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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]] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,3,2,1] => [3,2,2,1,1] => [[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] => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => [3,2,2,1,1] => [[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] => [2,2,3,2,1] => [3,2,2,2,1] => [[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] => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[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] => [2,2,2,2,1] => [2,2,2,2,1] => [[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] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [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]] => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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]] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [2,2,1,2,2] => [2,2,2,2,1] => [[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] => [2,1,2,2,2] => [2,2,2,2,1] => [[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] => [1,2,2,2,2] => [2,2,2,2,1] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,4,1,2] => [4,2,1,1,1] => [[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] => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,4,1,2] => [4,2,1,1,1] => [[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] => [1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,3,1,3] => [3,3,2,1] => [[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] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,3,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,4,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,3,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,3,1,2] => [3,3,2,1,1] => [[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] => [4,1,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,3,2,1,2] => [3,2,2,2,1] => [[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] => [2,2,4,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [3,4,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,3,1] => [3,3,2,1,1] => [[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] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,3,1] => [3,3,2,1,1] => [[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] => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [3,3,1,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,1,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[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] => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,2,3,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[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] => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[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] => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[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] => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[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] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[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] => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[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] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[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] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[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] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[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] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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]] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[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] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[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] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,2,1,2,2] => [2,2,2,2,1] => [[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] => [4,1,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,2,1] => [2,2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11]] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,1,4,1] => [4,2,1,1,1] => [[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] => [4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,4,1,2,1] => [4,2,1,1,1] => [[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] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[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] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[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] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[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] => [1,2,1,4,1,1] => [4,2,1,1,1,1] => [[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] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[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] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[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] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[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] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[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] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[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] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[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] => [1,2,1,4,1,1] => [4,2,1,1,1,1] => [[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] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[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] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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]] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[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] => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[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] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,6,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,6,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,1,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0] => [3,4,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[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] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [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]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [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]] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[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] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,3,1,2] => [3,3,2,1] => [[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] => [1,3,2,1,2] => [3,2,2,1,1] => [[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] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[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] => [2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [[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] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1,2,1] => [3,2,2,1,1,1] => [[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] => [2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [[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] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[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] => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[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] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [2,3,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[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] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[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] => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[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] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[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] => [1,1,4,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[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] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[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] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [2,2,3,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,4,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [2,3,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2,1,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0] => [2,5,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => [2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [3,1,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,1,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,1,4,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,1,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [4,3,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [5,2,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,2,4,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,2,2,3] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [2,3,4,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [2,3,5,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,3,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [2,4,2,3,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0] => [2,2,5,2,1] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0] => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [4,2,2,3,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0] => [4,5,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0] => [5,4,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0] => [3,5,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,1,2,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,5,1] => [5,4,1] => [[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] => [2,3,2,1,1] => [3,2,2,1,1] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[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] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 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] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 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] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 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] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 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] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,2,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[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] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [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]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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]] => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[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] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[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] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[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] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [[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] => [1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[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] => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[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] => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,3,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [2,1,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [[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] => [2,3,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,5] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,2,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [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]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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]] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,3,3,1] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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]] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => [3,2,2,1,1] => [[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] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,1,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [5,1,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [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]] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,4,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,2,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => [3,2,2,1,1] => [[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] => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[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] => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[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] => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,4,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,3,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,3,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,3,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [1,5,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,4,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [3,3,1,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,1,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,3,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [2,4,3,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,3,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [3,3,2,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [5,1,2,3,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0] => [5,3,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,3,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [3,1,4,3,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [3,3,2,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,3,4,1,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,4,3,2,2] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,2,3,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [2,3,2,3,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[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] => [2,1,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,1,4,1] => [4,3,1,1,1] => [[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] => [2,2,1,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,3,1] => [3,3,2,1,1] => [[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] => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,1,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,1,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [3,1,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [3,1,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,1,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,1,2,2,3] => [3,3,2,2,1,1] => [[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] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,1,2,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[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] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [2,2,4,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[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] => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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]] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,2,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [6,1,1,1,1] => [6,1,1,1,1] => [[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] => [5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[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] => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => [3,2,2,2] => [[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] => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,3,2] => [3,3,2,1] => [[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] => [3,4,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,3,1] => [3,3,3,1] => [[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] => [6,1,3] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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]] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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]] => 2
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[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] => [1,2,3,2,1] => [3,2,2,1,1] => [[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] => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [[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] => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [[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] => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [[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] => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[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] => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [[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] => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[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] => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[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] => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [[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] => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[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] => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [[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] => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[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] => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [[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] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,4,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [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]] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [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]] => 3
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [5,2,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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]] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[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] => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[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] => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[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] => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[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] => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [[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] => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1 1,8,4,1 1,20,15,5,1 1,50,53,21,6,1 1,126,182,84,28,7,1 1,322,616,326,120,36,8,1
F1=q
F2=q+q2
F3=q+3 q2+q3
F4=q+8 q2+4 q3+q4
F5=q+20 q2+15 q3+5 q4+q5
F6=q+50 q2+53 q3+21 q4+6 q5+q6
F7=q+126 q2+182 q3+84 q4+28 q5+7 q6+q7
F8=q+322 q2+616 q3+326 q4+120 q5+36 q6+8 q7+q8
Description
The last entry in the first row of a standard tableau.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers 1 through n row by row.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!