Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000621: Integer partitions ⟶ ℤ
Values
[1,1,0,0,1,0,1,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,0,1,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,1,0,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,1,0,0,1,0,0] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,1,0,1,0,0,0] => [3,1] => [[3,3],[2]] => [2] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [[4,3],[2]] => [2] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [[4,3],[2]] => [2] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [[4,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [[4,4],[3]] => [3] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [[4,4],[3]] => [3] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [[4,4],[3]] => [3] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [[4,4],[3]] => [3] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [[4,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [[4,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [[4,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [[4,4,1],[3]] => [3] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
>>> Load all 1846 entries. <<<[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [[5,4],[3]] => [3] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => [[5,4],[3]] => [3] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => [[5,4],[3]] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => [[5,4],[3]] => [3] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [[5,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [[5,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [[5,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [[5,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [[6,4],[3]] => [3] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => [[6,4],[3]] => [3] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => [[6,4],[3]] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => [[6,4],[3]] => [3] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => [[6,6],[5]] => [5] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [2,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [3,2] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => 3
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 5
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 6
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => 8
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 8
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 16
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [3,2] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [[6,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => [[6,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [[6,4,1],[3]] => [3] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 16
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 6
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [[6,4,1],[3]] => [3] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 4
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 9
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => 12
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 20
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 14
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 25
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => 61
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 6
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [4,2,1] => 14
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 77
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [3,3,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 28
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [4,4,1] => 34
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => 30
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 91
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [3,2,2] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 22
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => 168
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 16
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [4,3,2] => 66
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 100
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [[7,4],[3]] => [3] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => [[7,4],[3]] => [3] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => [[7,4],[3]] => [3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => 168
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [3,3,3] => 16
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 82
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [4,4,3] => 182
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => [[6,6,4],[5,3]] => [5,3] => 12
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => [[7,4],[3]] => [3] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [4,4,4] => 182
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 18
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [[9,9],[8]] => [8] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1] => [[7,7,7],[6,6]] => [6,6] => 57
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => [[8,8],[7]] => [7] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[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] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,1] => [[9,9],[8]] => [8] => 1
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
[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] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => 42
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Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even.
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even.
This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1].
The case of an odd minimum is St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd..
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is even.
This notion was used in [1, Proposition 2.3], see also [2, Theorem 1.1].
The case of an odd minimum is St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd..
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
Map
inner shape
Description
The inner shape of a skew partition.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
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