Identifier
Values
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [2,1] => [1] => 1
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [2,2] => [2] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [2,1] => [1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [3,1] => [1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [2,1] => [1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [3,3] => [3] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [3,1] => [1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [3,1] => [1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [2,1] => [1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [2,2] => [2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [2,1] => [1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [2,2] => [2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [2,1] => [1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [2,2] => [2] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [3,1] => [1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [2,2] => [2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [3,2] => [2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [3,3] => [3] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [3,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [2,1] => [1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [3,1] => [1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [4,1] => [1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [2,2,2] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [4,2] => [2] => 2
>>> Load all 314 entries. <<<
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [3,3,3] => [3,3] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [3,3] => [3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [4,3] => [3] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [4,4] => [4] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5],[4,3]] => [4,3] => [3] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]] => [3,3] => [3] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5],[4,2]] => [4,2] => [2] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]] => [2,2] => [2] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => [3,1] => [1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => [3,1] => [1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4,1]] => [4,1] => [1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]] => [3,1] => [1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]] => [2,1] => [1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]] => [3,1,1] => [1,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]] => [1,1] => [1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => [2,2] => [2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => [2,1] => [1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => [2,1] => [1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]] => [2,2] => [2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => [2,1] => [1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => [3,1] => [1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => [2,1] => [1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3]] => [3,3] => [3] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]] => [3,2] => [2] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]] => [2,2] => [2] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]] => [3,1] => [1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]] => [2,1] => [1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1]] => [1,1] => [1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2]] => [2,2] => [2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]] => [2,1] => [1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1,1],[1,1]] => [1,1] => [1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1,1],[3,1]] => [3,1] => [1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1,1],[2,2]] => [2,2] => [2] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1,1],[3,2]] => [3,2] => [2] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => [1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,1],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,1],[2,1]] => [2,1] => [1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,1],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,1],[3,1]] => [3,1] => [1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]] => [2,2] => [2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,1],[3,2]] => [3,2] => [2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,1],[4,2]] => [4,2] => [2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => [3,3] => 8
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,1],[3,3]] => [3,3] => [3] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,1],[4,3]] => [4,3] => [3] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [1,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [2,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [2,2,1,1] => 5
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [2,1,1] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,2],[2,1,1]] => [2,1,1] => [1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [3,1,1] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,2],[3,1,1]] => [3,1,1] => [1,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => [2,2,2,1] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [2,2,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [2,2,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,2],[2,2,1]] => [2,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [3,2,1] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,2],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,2],[4,2,1]] => [4,2,1] => [2,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => [3,3,1] => 10
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,2],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,2],[4,3,1]] => [4,3,1] => [3,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,2],[3,1]] => [3,1] => [1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,2],[4,4,1]] => [4,4,1] => [4,1] => 5
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,2],[4,1]] => [4,1] => [1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => [2,2,2,2] => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => [2,2,2] => 8
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]] => [2,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => [3,2,2] => 10
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[5,4,3,3],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[5,5,3,3],[4,2,2]] => [4,2,2] => [2,2] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => [3,3,2] => 15
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[5,4,4,3],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[5,5,4,3],[4,3,2]] => [4,3,2] => [3,2] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[6,4,3],[3,2]] => [3,2] => [2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[5,5,5,3],[4,4,2]] => [4,4,2] => [4,2] => 5
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[6,5,3],[4,2]] => [4,2] => [2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[6,6,3],[5,2]] => [5,2] => [2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => [3,3,3] => 15
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[5,4,4,4],[3,3,3]] => [3,3,3] => [3,3] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[5,5,4,4],[4,3,3]] => [4,3,3] => [3,3] => 8
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[6,4,4],[3,3]] => [3,3] => [3] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[5,5,5,4],[4,4,3]] => [4,4,3] => [4,3] => 10
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[6,5,4],[4,3]] => [4,3] => [3] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[6,6,4],[5,3]] => [5,3] => [3] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[5,5,5,5],[4,4,4]] => [4,4,4] => [4,4] => 15
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[6,6,6],[5,5]] => [5,5] => [5] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[6,6,6],[5,4]] => [5,4] => [4] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[6,6,6],[4,4]] => [4,4] => [4] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,3]] => [4,4,3] => [4,3] => 10
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,3]] => [4,3,3] => [3,3] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,3]] => [3,3,3] => [3,3] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[6,6,6],[5,3]] => [5,3] => [3] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2] => [3,3,2] => 15
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2] => [3,2,2] => 10
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2] => [2,2,2] => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,2]] => [4,4,2] => [4,2] => 5
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,2]] => [4,3,2] => [3,2] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[6,6,6],[4,2]] => [4,2] => [2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[5,5,5,5],[4,2,2]] => [4,2,2] => [2,2] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[5,5,5,5],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => [2,2,2,1] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1] => [2,2,1,1] => 5
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1] => [3,3,1] => 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => [3,2,1] => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => [2,2,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[5,5,5,5],[4,4,1]] => [4,4,1] => [4,1] => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[5,5,5,5],[4,3,1]] => [4,3,1] => [3,1] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[5,5,5,5],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[5,5,5,5],[4,2,1]] => [4,2,1] => [2,1] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[5,5,5,5],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => [3,1,1] => 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => [2,1,1] => 4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [2,2,2] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [2,1,1] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[4,4,4,4,4],[3,3,3]] => [3,3,3] => [3,3] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,2]] => [3,3,2] => [3,2] => 4
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,2]] => [3,2,2] => [2,2] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[4,4,4,4,4],[3,3,1]] => [3,3,1] => [3,1] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[4,4,4,4,4],[3,2,1]] => [3,2,1] => [2,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4,1]] => [4,1] => [1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3,1]] => [3,1] => [1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4,1]] => [4,1] => [1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[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] => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => [2,2,2,2,2] => 24
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => [3,3,3,3] => 48
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => [4,4,4] => 48
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[6,6,6,6],[5,5,5]] => [5,5,5] => [5,5] => 24
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[7,7,7],[6,6]] => [6,6] => [6] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 35
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => [2,2,2,2,1] => 18
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2] => [3,3,3,2] => 24
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3] => [4,4,3] => 24
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[6,6,6,6],[5,5,4]] => [5,5,4] => [5,4] => 18
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[7,7,7,7],[6,6,6]] => [6,6,6] => [6,6] => 35
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[7,7,7],[6,5]] => [6,5] => [5] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[8,8,8],[7,7]] => [7,7] => [7] => 7
search for individual values
searching the database for the individual values of this statistic
Description
The product of the hook lengths of the diagonal cells in an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the product of the hook lengths of the diagonal cells $(i,i)$ of a partition.
Map
inner shape
Description
The inner shape of a skew partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.