Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001097: Integer partitions ⟶ ℤ
Values
[1,1,0,0,1,0,1,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,0,1,0,0,1,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,0,1,0,1,0,0] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,1,0,0,0,1,0] => [3,1] => [[3,3],[2]] => [2] => 0
[1,1,1,0,0,1,0,0] => [3,1] => [[3,3],[2]] => [2] => 0
[1,1,1,0,1,0,0,0] => [3,1] => [[3,3],[2]] => [2] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [[3,3,1],[2]] => [2] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 6
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[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] => 6
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 6
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 6
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[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] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [[4,3],[2]] => [2] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [[4,3],[2]] => [2] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [[4,3],[2]] => [2] => 0
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 0
[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] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[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] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[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] => 6
[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] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [[4,3,1],[2]] => [2] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[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] => 12
[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] => 12
[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] => 12
[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] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[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] => 24
[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] => 6
[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] => 24
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[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] => 12
[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] => 12
[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] => 12
[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] => 12
>>> 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] => 12
[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] => 12
[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] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 0
[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] => 30
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 0
[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] => 30
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[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] => 30
[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] => 30
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 0
[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] => 30
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[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] => 30
[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] => 30
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[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] => 30
[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] => 30
[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] => 30
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => [[5,3],[2]] => [2] => 0
[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] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [[5,5],[4]] => [4] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [[5,5],[4]] => [4] => 0
[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] => 2
[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] => 2
[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] => 2
[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] => 0
[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] => 0
[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] => 0
[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] => 6
[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] => 2
[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] => 6
[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] => 2
[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] => 6
[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] => 6
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 0
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 0
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 2
[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] => 12
[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] => 12
[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] => 12
[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] => 0
[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] => 0
[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] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 2
[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] => 24
[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] => 6
[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] => 24
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 6
[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] => 2
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 30
[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] => 2
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 0
[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] => 30
[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] => 2
[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] => 30
[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] => 30
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 0
[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] => 30
[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] => 2
[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] => 30
[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] => 30
[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] => 2
[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] => 30
[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] => 30
[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] => 30
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [[5,3,1],[2]] => [2] => 0
[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] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [[5,5,1],[4]] => [4] => 0
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 6
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 2
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 18
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[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] => 18
[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] => 18
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[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] => 18
[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] => 18
[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] => 18
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 6
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 2
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 6
[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] => 120
[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] => 24
[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] => 120
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 36
[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] => 6
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 84
[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] => 6
[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] => 2
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 10
[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] => 18
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[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] => 18
[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] => 18
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[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] => 18
[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] => 18
[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] => 18
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[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] => 18
[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] => 18
[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] => 18
[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] => 18
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 0
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 74
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 0
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 864
[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] => 30
[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] => 864
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 74
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[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] => 74
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 0
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 864
[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] => 30
[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] => 864
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 864
[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] => 30
[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] => 864
[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] => 864
[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] => 30
[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] => 864
[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] => 864
[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] => 864
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[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] => 38
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 2
[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] => 74
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[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] => 74
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[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] => 74
[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] => 74
[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] => 74
[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] => 74
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => [[6,3],[2]] => [2] => 0
[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] => 174
[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] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[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] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [[6,5],[4]] => [4] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => [[6,5],[4]] => [4] => 0
[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] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => 2
[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] => 6
[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] => 2
[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] => 6
[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] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 6
[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] => 6
[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] => 2
[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] => 0
[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] => 0
[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] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 12
[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] => 12
[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] => 12
[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] => 0
[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] => 0
[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] => 0
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 24
[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] => 6
[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] => 24
[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] => 24
[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] => 6
[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] => 6
[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] => 6
[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] => 6
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 12
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2
[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] => 1
[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] => 1
[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] => 0
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 0
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 0
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 18
[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] => 0
[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] => 18
[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] => 18
[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] => 0
[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] => 18
[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] => 18
[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] => 18
[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] => 0
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 120
[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] => 24
[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] => 120
[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] => 120
[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] => 24
[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] => 36
[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] => 36
[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] => 36
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 6
[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] => 84
[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] => 84
[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] => 84
[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] => 6
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 12
[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] => 246
[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] => 246
[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] => 246
[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] => 12
[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] => 10
[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] => 10
[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] => 10
[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] => 10
[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] => 18
[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] => 0
[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] => 18
[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] => 18
[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] => 0
[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] => 18
[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] => 18
[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] => 18
[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] => 0
[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] => 18
[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] => 18
[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] => 18
[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] => 18
[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] => 0
[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] => 30
[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] => 38
[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] => 38
[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] => 2
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 30
[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] => 38
[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] => 38
[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] => 2
[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] => 30
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[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] => 2
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 74
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 30
[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] => 38
[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] => 38
[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] => 2
[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] => 30
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[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] => 2
[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] => 30
[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] => 30
[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] => 30
[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] => 38
[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] => 38
[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] => 38
[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] => 38
[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] => 2
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 74
[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] => 1
[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] => 74
[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] => 74
[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] => 74
[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] => 74
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 174
[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] => 1
[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] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[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] => 1
[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] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 174
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 720
[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] => 120
[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] => 240
[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] => 240
[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] => 660
[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] => 36
[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] => 660
[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] => 660
[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] => 36
[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] => 24
[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] => 24
[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] => 24
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 6
[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] => 2220
[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] => 84
[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] => 2220
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 96
[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] => 6
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 12
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 10
[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] => 3
[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] => 3
[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] => 3
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 12
[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] => 8760
[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] => 246
[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] => 8760
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 384
[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] => 12
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 836
[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] => 10
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 0
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 14
[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] => 0
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 14
[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] => 14
[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] => 0
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 0
[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] => 720
[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] => 120
[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] => 240
[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] => 240
[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] => 660
[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] => 36
[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] => 660
[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] => 660
[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] => 36
[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] => 24
[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] => 24
[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] => 24
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 6
[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] => 2220
[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] => 84
[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] => 2220
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 96
[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] => 6
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 720
[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] => 120
[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] => 240
[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] => 240
[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] => 660
[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] => 36
[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] => 660
[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] => 660
[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] => 36
[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] => 24
[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] => 24
[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] => 24
[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] => 720
[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] => 120
[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] => 240
[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] => 240
[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] => 720
[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] => 120
[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] => 720
[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] => 720
[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] => 120
[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] => 240
[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] => 240
[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] => 240
[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] => 660
[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] => 36
[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] => 660
[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] => 660
[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] => 36
[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] => 660
[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] => 660
[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] => 660
[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] => 36
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 6
[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] => 2220
[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] => 84
[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] => 2220
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 96
[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] => 6
[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] => 2220
[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] => 84
[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] => 2220
[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] => 2220
[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] => 84
[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] => 2220
[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] => 2220
[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] => 2220
[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] => 84
[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] => 96
[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] => 96
[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] => 96
[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] => 96
[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] => 6
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 184
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 12
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 10
[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] => 3
[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] => 3
[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] => 3
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 12
[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] => 8760
[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] => 246
[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] => 8760
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 384
[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] => 12
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 836
[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] => 10
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 12
[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] => 8760
[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] => 246
[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] => 8760
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 384
[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] => 12
[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] => 8760
[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] => 246
[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] => 8760
[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] => 8760
[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] => 246
[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] => 8760
[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] => 8760
[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] => 8760
[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] => 246
[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] => 384
[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] => 384
[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] => 384
[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] => 384
[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] => 12
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 836
[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] => 10
[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] => 836
[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] => 836
[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] => 836
[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] => 836
[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] => 10
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 3
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 0
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 14
[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] => 0
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 14
[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] => 14
[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] => 0
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 2184
[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] => 18
[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] => 2184
[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] => 2184
[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] => 2184
[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] => 2184
[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] => 18
[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] => 14
[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] => 14
[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] => 14
[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] => 14
[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] => 14
[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] => 0
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 0
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 0
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 30
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 1686
[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] => 30
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 39480
[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] => 1686
[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] => 1686
[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] => 1686
[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] => 1686
[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] => 30
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 4204
[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] => 38
[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] => 4204
[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] => 4204
[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] => 4204
[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] => 4204
[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] => 38
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 24
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 12336
[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] => 74
[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] => 12336
[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] => 12336
[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] => 12336
[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] => 12336
[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] => 74
[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] => 79
[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] => 79
[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] => 79
[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] => 79
[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] => 79
[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] => 1
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 138
[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] => 138
[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] => 138
[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] => 138
[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] => 138
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 248
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 248
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 41304
[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] => 174
[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] => 41304
[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] => 41304
[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] => 41304
[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] => 41304
[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] => 174
[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] => 248
[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] => 248
[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] => 248
[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] => 248
[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] => 248
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 480
[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] => 480
[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] => 480
[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] => 480
[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] => 480
[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] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 1092
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => [[7,7],[6]] => [6] => 0
[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] => 0
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 5040
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 40320
[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] => 5040
[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] => 2631600
[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] => 40320
[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] => 5040
[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] => 5040
[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] => 5040
[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] => 5040
[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] => 5040
[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] => 5040
[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] => 40320
[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] => 40320
[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] => 40320
[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] => 40320
[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] => 40320
[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] => 40320
[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] => 40320
[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] => 0
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 0
[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] => 2631600
[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] => 0
[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] => 2631600
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
[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] => 2631600
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Description
The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders.
For a generating function $f$ the associated formal group law is the symmetric function $f(f^{(-1)}(x_1) + f^{(-1)}(x_2), \dots)$, see [1].
This statistic records the coefficient of the monomial symmetric function $m_\lambda$ in the formal group law for linear orders, with generating function $f(x) = x/(1-x)$, see [1, sec. 3.4].
This statistic gives the number of Smirnov arrangements of a set of letters with $\lambda_i$ of the $i$th letter, where a Smirnov word is a word with no repeated adjacent letters. e.g., [3,2,1] = > 10 since there are 10 Smirnov rearrangements of the word 'aaabbc': 'ababac', 'ababca', 'abacab', 'abacba', 'abcaba', 'acabab', 'acbaba', 'babaca', 'bacaba', 'cababa'.
For a generating function $f$ the associated formal group law is the symmetric function $f(f^{(-1)}(x_1) + f^{(-1)}(x_2), \dots)$, see [1].
This statistic records the coefficient of the monomial symmetric function $m_\lambda$ in the formal group law for linear orders, with generating function $f(x) = x/(1-x)$, see [1, sec. 3.4].
This statistic gives the number of Smirnov arrangements of a set of letters with $\lambda_i$ of the $i$th letter, where a Smirnov word is a word with no repeated adjacent letters. e.g., [3,2,1] = > 10 since there are 10 Smirnov rearrangements of the word 'aaabbc': 'ababac', 'ababca', 'abacab', 'abacba', 'abcaba', 'acabab', 'acbaba', 'babaca', 'bacaba', 'cababa'.
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.
Map
inner shape
Description
The inner shape of a skew partition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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