Identifier
Values
[1,1,0,0,1,0] => [[2,2],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [1] => [1,0] => 1
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => [1] => [1,0] => 1
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [1] => [1,0] => 1
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [1] => [1,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => [1] => [1,0] => 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] => [1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [1] => [1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 2
>>> Load all 485 entries. <<<
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [1] => [1,0] => 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] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [2] => [1,0,1,0] => 2
[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] => [1,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [3] => [1,0,1,0,1,0] => 3
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [1] => [1,0] => 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] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1],[2]] => [2] => [1,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1],[1]] => [1] => [1,0] => 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] => [1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [1] => [1,0] => 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] => [1,1,0,1,0,0] => 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] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6],[3]] => [3] => [1,0,1,0,1,0] => 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] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6],[2]] => [2] => [1,0,1,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,0] => 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] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6],[1]] => [1] => [1,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2],[1]] => [1] => [1,0] => 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] => [1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,2],[1]] => [1] => [1,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,2],[1]] => [1] => [1,0] => 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] => [1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]] => [2] => [1,0,1,0] => 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] => [1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[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] => [1,0,1,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => 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] => [1,1,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1]] => [1] => [1,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[4,4,4,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[3,3,3,3,3],[1]] => [1] => [1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4],[1]] => [1] => [1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1,1],[1]] => [1] => [1,0] => 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] => [1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]] => [1] => [1,0] => 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] => [1,1,0,1,0,0] => 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] => [1,1,0,0] => 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] => [1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1,1],[2]] => [2] => [1,0,1,0] => 2
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,0] => 3
[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] => [1,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,0,0] => 2
[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] => [1,0,1,0,1,1,0,0] => 3
[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] => [1,1,1,0,0,0] => 1
[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] => [1,0,1,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1,1],[2]] => [2] => [1,0,1,0] => 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] => [1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,0,1,1,0,1,0,1,0,0] => 4
[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] => [1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,0] => 4
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[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] => [1,1,1,1,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 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] => [1,0,1,0,1,1,1,0,0,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,1],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5,1],[1]] => [1] => [1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1]] => [1] => [1,0] => 1
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,1,0,0] => 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] => [1,1,1,0,0,1,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,1,0,0] => 4
[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] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,0,1,0,0] => 3
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,0,1,0,0] => 4
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[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] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[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] => [1,1,1,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => [1,1,1,1,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,0] => 2
[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] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[6,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => 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] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[6,5,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[6,6,3],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
[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] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[6,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[6,5,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[6,6,4],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[7,4],[3]] => [3] => [1,0,1,0,1,0] => 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] => [1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[6,6,6],[5,5]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[7,7],[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[7,7],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[6,6,6],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[6,6,6],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[7,7],[4]] => [4] => [1,0,1,0,1,0,1,0] => 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] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[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] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[6,6,6],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
[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] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[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] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[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] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
[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] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[6,6,6],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[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] => [1,0,1,0,1,1,1,1,0,0,0,0] => 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] => [1,0,1,1,1,1,0,0,0,0] => 2
[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] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,0,1,0,0] => 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] => [1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,0,1,1,1,0,0,1,0,0] => 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] => [1,0,1,1,1,0,0,1,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,1,0,0] => 3
[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] => [1,1,0,1,0,1,0,0] => 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] => [1,1,1,1,0,1,0,0,0,0] => 2
[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] => [1,1,1,0,0,1,0,1,0,0] => 3
[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] => [1,1,1,1,1,0,0,0,0,0] => 1
[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] => [1,1,1,0,1,1,0,0,0,0] => 2
[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] => [1,0,1,1,1,1,0,0,0,0] => 2
[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] => [1,1,1,0,1,0,0,1,0,0] => 3
[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] => [1,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3,3],[2]] => [2] => [1,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4,3],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[5,5,5,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,1,0,0] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[5,5,5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[4,4,4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[6,6,6,6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[5,5,5,5,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => 4
[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] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[5,5,5,5,1],[1]] => [1] => [1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[8,8],[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[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] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[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] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[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] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[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] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[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] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[8,8],[7]] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[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] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[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] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 2
[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] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[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] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 3
[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] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[9,9],[8]] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
search for individual values
searching the database for the individual values of this statistic
Description
The global dimension of the LNakayama algebra associated to a Dyck path.
An n-LNakayama algebra is a quiver algebra with a directed line as a connected quiver with $n$ points for $n \geq 2$. Number those points from the left to the right by $0,1,\ldots,n-1$.
The algebra is then uniquely determined by the dimension $c_i$ of the projective indecomposable modules at point $i$. Such algebras are then uniquely determined by lists of the form $[c_0,c_1,...,c_{n-1}]$ with the conditions: $c_{n-1}=1$ and $c_i -1 \leq c_{i+1}$ for all $i$. The number of such algebras is then the $n-1$-st Catalan number $C_{n-1}$.
One can get also an interpretation with Dyck paths by associating the top boundary of the Auslander-Reiten quiver (which is a Dyck path) to those algebras. Example: [3,4,3,3,2,1] corresponds to the Dyck path [1,1,0,1,1,0,0,1,0,0].
Conjecture: that there is an explicit bijection between $n$-LNakayama algebras with global dimension bounded by $m$ and Dyck paths with height at most $m$.
Examples:
  • For $m=2$, the number of Dyck paths with global dimension at most $m$ starts for $n \geq 2$ with 1,2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192.
  • For $m=3$, the number of Dyck paths with global dimension at most $m$ starts for $n \geq 2$ with 1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181, 10946, 28657, 75025, 196418.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
inner shape
Description
The inner shape of a skew 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 $\gamma(D)$.