Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001568: Integer partitions ⟶ ℤ
Values
[1,1,1,2] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,1,1,2] => [4,1] => [[4,4],[3]] => [3] => 1
[1,1,1,2,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,3] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,3,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,1,1,1,2] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,2,1] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3] => [4,1] => [[4,4],[3]] => [3] => 1
[1,1,1,2,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,2,2] => [3,2] => [[4,3],[2]] => [2] => 1
[1,1,1,3,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,4] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[1,1,2,1,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,2,1] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,2,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,3,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,4,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,1,1,1,2] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,1,1,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,2,1,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,2,1] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,1,1,1,1,2] => [6,1] => [[6,6],[5]] => [5] => 1
[1,1,1,1,1,2,1] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,3] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,2,1,1] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,2,2] => [4,2] => [[5,4],[3]] => [3] => 1
[1,1,1,1,3,1] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,4] => [4,1] => [[4,4],[3]] => [3] => 1
[1,1,1,2,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,2,1,2] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,2,1] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,3] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,2] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,5] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[1,1,2,1,1,2] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,2,1,2,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,2,1,1] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,2,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,4] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,4,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,5,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,2,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,2,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,2,1,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,2,1] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,1,1,1,1,2] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[2,1,1,1,2,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,3] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,1,1,2,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,3,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,2,1,1,2] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[2,2,1,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,2,1,1] => [3,2] => [[4,3],[2]] => [2] => 1
[2,2,3,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,1,1,1,2] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[3,1,1,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,1,1,1,1,1,1,2] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,2,1] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 1
[1,1,1,1,1,1,3] => [6,1] => [[6,6],[5]] => [5] => 1
[1,1,1,1,1,2,2] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,3,1] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,4] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,2,1,1,1] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,2,1,2] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,2,1] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,2,3] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3,1,1] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3,2] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,4,1] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,5] => [4,1] => [[4,4],[3]] => [3] => 1
[1,1,1,2,1,1,2] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,2,1,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,3] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,2,1,1] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,2,2] => [3,3] => [[5,3],[2]] => [2] => 1
[1,1,1,2,3,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,4] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,1,2] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,2,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,3] => [3,2] => [[4,3],[2]] => [2] => 1
[1,1,1,4,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,2] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,5,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,6] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1,1,1,2] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,2,1,1,2,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,3] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
>>> Load all 1017 entries. <<<[1,1,2,1,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,2,2] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,1,3,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,4] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,2,1,1,1] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[1,1,2,2,1,2] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,2,1] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,2,2,3] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,2,3,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,3,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,4,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,5] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,1,2] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,3,1,2,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,2] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,3,3,1] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,3,4] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,4,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[1,1,4,1,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,5,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,5,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,6,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,2,1,1,1,1,2] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,3] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,2,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,3,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,2,1,1,2] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,2,2,1,2,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,3] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,2,1,1] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[1,2,2,3,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,3,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,3,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,1,1,1,1,2] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[2,1,1,1,1,2,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,1,1,1,1,3] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[2,1,1,1,2,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,2,2] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[2,1,1,1,3,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,4] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,1,1,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,2,1,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,2,2,1] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[2,1,1,2,3] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,3,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,3,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,4,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,2,1,1,1,2] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[2,2,1,1,2,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[2,2,1,1,3] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[2,2,1,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,2,2] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[2,2,1,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,4] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,2,1,1,1] => [3,3] => [[5,3],[2]] => [2] => 1
[2,2,2,1,2] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[2,2,2,2,1] => [4,1] => [[4,4],[3]] => [3] => 1
[2,2,2,3] => [3,1] => [[3,3],[2]] => [2] => 1
[2,2,3,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[2,2,3,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,4,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,1,1,1,1,2] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[3,1,1,1,2,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[3,1,1,1,3] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[3,1,1,2,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,3,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,3,1,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,3,2,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[4,1,1,1,2] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[4,1,1,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,1,1,1,1,1,1,1,2] => [8,1] => [[8,8],[7]] => [7] => 1
[1,1,1,1,1,1,1,3] => [7,1] => [[7,7],[6]] => [6] => 1
[1,1,1,1,1,1,3,1] => [6,1,1] => [[6,6,6],[5,5]] => [5,5] => 1
[1,1,1,1,1,1,4] => [6,1] => [[6,6],[5]] => [5] => 1
[1,1,1,1,1,2,3] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,3,2] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,4,1] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,5] => [5,1] => [[5,5],[4]] => [4] => 1
[1,1,1,1,2,1,1,2] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 1
[1,1,1,1,2,1,3] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,2,1,1] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,2,2,2] => [4,3] => [[6,4],[3]] => [3] => 1
[1,1,1,1,2,3,1] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,4] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3,1,1,1] => [4,1,3] => [[6,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3,1,2] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,3,2,1] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,3,3] => [4,2] => [[5,4],[3]] => [3] => 1
[1,1,1,1,4,1,1] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,4,2] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,5,1] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,6] => [4,1] => [[4,4],[3]] => [3] => 1
[1,1,1,2,1,1,1,2] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [4,2,2] => 1
[1,1,1,2,1,1,2,1] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => 1
[1,1,1,2,1,1,3] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,2,1,2,2] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,1,3,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,4] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,2,1,1,1] => [3,2,3] => [[6,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,2,1,2] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,1,2,2,2,1] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 1
[1,1,1,2,2,3] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,3,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,3,2] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,4,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,5] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,1,1,2] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,3,1,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,1,3] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,2,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,2,2] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,3,3,1] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,3,4] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,1,2] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,4,2,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,4,3] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,5,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,5,2] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,6,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,7] => [3,1] => [[3,3],[2]] => [2] => 1
[1,1,2,1,1,1,2,1] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 2
[1,1,2,1,1,1,3] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,2,1,1,2,1,1] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,2,2] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,2,1,1,3,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,4] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,2,2,1] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,1,2,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,3,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,3,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,4,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,5] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,2,1,1,2] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 1
[1,1,2,2,1,2,1] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,2,2,1,3] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,2,1,1] => [2,3,2] => [[5,4,2],[3,1]] => [3,1] => 1
[1,1,2,2,3,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,4] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,2,3,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,3,1,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,3,2,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,3,3] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,2,4,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,4,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,5,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,6] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,3,1,1,1,2] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,3,1,1,2,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,3,1,1,3] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,3,1,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,2,2] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,1,3,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,4] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,1,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,2,2,1] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,3,2,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,3,1,1] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,3,3,2] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[1,1,3,4,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,3,5] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,4,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[1,1,4,1,1,2] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,4,1,2,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,4,1,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,2,2] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,4,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,5,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[1,1,5,1,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,5,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,5,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,6,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,6,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,7,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,2,1,1,1,1,3] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,2,1,1,1,2,1,1] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,2,2] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,4] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,2,1,1,2,3] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,3,2] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,4,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,2,1,1,1,2] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[1,2,2,1,1,3] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,2,2,1,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,2,2] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,1,3,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,4] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,2,1,1,1] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[1,2,2,2,1,2] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,2,2,2,2,1] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[1,2,2,2,3] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,2,2,3,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,3,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,4,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,3,1,1,1,1,2] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,3,1,1,1,3] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,3,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,3,1,1,3,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,3,3,1,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,3,3,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,4,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,4,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,1,1,1,1,3] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[2,1,1,1,1,2,1,1] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 1
[2,1,1,1,1,2,2] => [1,4,2] => [[5,4,1],[3]] => [3] => 1
[2,1,1,1,1,3,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,1,1,1,1,4] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[2,1,1,1,2,1,1,1] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,2,1,2] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[2,1,1,1,2,2,1] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
[2,1,1,1,2,3] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,3,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,3,2] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,4,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,5] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,1,1,2,1,1,2] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[2,1,1,2,1,3] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,2,2,1,1] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[2,1,1,2,3,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,2,4] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,3,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,3,1,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,3,2,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,4,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,4,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,5,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,2,1,1,1,2] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,1,2,2,1,2] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,2,2,2,1] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[2,2,1,1,1,1,2] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 1
[2,2,1,1,1,2,1] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[2,2,1,1,1,3] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[2,2,1,1,2,1,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[2,2,1,1,2,2] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[2,2,1,1,3,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[2,2,1,1,4] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[2,2,1,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,2,1,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,1,2,2,1] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,2,1,2,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,3,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,3,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,4,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,5] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,2,1,1,1,1] => [3,4] => [[6,3],[2]] => [2] => 1
[2,2,2,1,1,2] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[2,2,2,1,2,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[2,2,2,1,3] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[2,2,2,2,1,1] => [4,2] => [[5,4],[3]] => [3] => 1
[2,2,2,3,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[2,2,2,4] => [3,1] => [[3,3],[2]] => [2] => 1
[2,2,3,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[2,2,3,1,2] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,3,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,4,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[2,2,4,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,5,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,3,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[2,3,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[3,1,1,1,1,1,2] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[3,1,1,1,1,2,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[3,1,1,1,1,3] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[3,1,1,1,2,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[3,1,1,1,2,2] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[3,1,1,1,3,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[3,1,1,1,4] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[3,1,1,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,2,1,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[3,1,1,2,2,1] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[3,1,1,2,3] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,3,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,3,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,4,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,2,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[3,2,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[3,2,2,1,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,2,2,2,1] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[3,3,1,1,2] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[3,3,1,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,3,1,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,3,2,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[3,3,3,1] => [3,1] => [[3,3],[2]] => [2] => 1
[4,1,1,1,1,2] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[4,1,1,1,2,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[4,1,1,1,3] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[4,1,1,2,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[4,1,1,3,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[5,1,1,1,2] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[5,1,1,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,1,8,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,1,1,1,2,2,2,2] => [4,4] => [[7,4],[3]] => [3] => 1
[1,1,1,1,3,3,1,1] => [4,2,2] => [[6,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,3,1,1,3] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [4,3,3] => 1
[1,1,1,1,4,4] => [4,2] => [[5,4],[3]] => [3] => 1
[1,1,2,2,1,1,2,2] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 1
[1,1,2,2,2,2,1,1] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 1
[1,1,2,2,2,1,1,2] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 1
[1,1,2,2,3,3] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,2,1,1,2,2,2] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,2,1,1,1,2,3] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => 2
[1,1,2,1,2,3,1,1] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,2,2,1,2] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 3
[1,1,2,1,2,1,1,3] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => 2
[1,1,2,1,3,4] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,3,2,2] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,3,2,1,2,1,1] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,2,1,1,1,2] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 2
[1,1,3,2,2,3] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,3,1,1,3,1,1] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,3,1,1,2,1,2] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => 3
[1,1,3,1,2,4] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,4,4,1,1] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[1,1,4,3,1,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,4,2,1,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,4,1,1,4] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,2,1,1,1,1,2,2] => [2,4,2] => [[6,5,2],[4,1]] => [4,1] => 1
[2,2,1,1,2,2,1,1] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [3,2,1] => 1
[2,2,1,1,2,1,1,2] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 1
[2,2,1,1,3,3] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[2,2,2,2,1,1,1,1] => [4,4] => [[7,4],[3]] => [3] => 1
[2,2,2,1,1,2,1,1] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 1
[2,2,2,1,1,1,1,2] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 1
[2,2,2,1,2,3] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[2,2,3,3,1,1] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[2,2,3,2,1,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,3,1,1,3] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,1,1,2,1,1,2,2] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[2,1,1,2,2,2,1,1] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[2,1,1,2,2,1,1,2] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 1
[2,1,1,2,3,3] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,1,1,2,2,2] => [1,4,3] => [[6,4,1],[3]] => [3] => 1
[2,1,1,1,2,3,1,1] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[2,1,1,1,2,2,1,2] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 1
[2,1,1,1,2,1,1,3] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 1
[2,1,1,1,3,4] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,2,2,1,2,1,1] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[2,1,2,2,1,1,1,2] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[2,1,2,2,2,3] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[2,1,2,1,1,3,1,1] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,1,2,1,1,2,1,2] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 2
[2,1,3,3,1,2] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[3,3,1,1,2,2] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[3,3,2,2,1,1] => [2,2,2] => [[4,3,2],[2,1]] => [2,1] => 1
[3,3,2,1,1,2] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[3,2,1,1,1,2,1,1] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [2,2] => 1
[3,2,1,1,2,3] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[3,2,2,3,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[3,2,2,2,1,2] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[3,2,2,1,1,3] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[3,1,1,3,2,2] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[3,1,1,2,1,2,1,1] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[3,1,1,2,1,1,1,2] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[3,1,1,2,2,3] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[3,1,1,1,1,3,1,1] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [3,3] => 1
[3,1,1,1,1,2,1,2] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 1
[3,1,1,1,2,4] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[3,1,2,2,1,3] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[4,3,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[4,2,1,1,1,3] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[4,1,1,4,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[4,1,1,3,1,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[4,1,1,2,1,3] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[4,1,1,1,1,4] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[1,2,2,2,2,2,1] => [1,5,1] => [[5,5,1],[4]] => [4] => 1
[1,2,2,2,3,2] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,2,2,3,3,1] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,2,2,3,2,2] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,4,3] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,2,3,3,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,3,3,2,2,1] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,3,3,3,2] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,3,2,2,3,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,3,3,4,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,3,3,2,3] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,4,4,2,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,3,2,2,2,1] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[2,3,3,3,1] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[2,2,3,2,2,1] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,2,3,3,2] => [2,2,1] => [[3,3,2],[2,1]] => [2,1] => 1
[2,2,4,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,4,2,2] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[2,2,5,3] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,2,2,3,2,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[2,2,2,4,2] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[2,2,2,2,3,1] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[2,2,2,3,3] => [3,2] => [[4,3],[2]] => [2] => 1
[2,2,3,4,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,3,2,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,3,3,2,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[3,3,4,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,3,2,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,2,2,4,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,2,2,3,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[3,2,2,2,3] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[3,3,5,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[3,3,2,4] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[4,4,3,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,5,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,4,1,1,1,1,2] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,1,1,1,1,1,1,1,1,2] => [9,1] => [[9,9],[8]] => [8] => 1
[1,6,1,1,1,2] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,5,1,1,1,1,2] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,2,2,2,1,3] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[1,2,2,1,3,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,2,3] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,1,4] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[1,2,1,1,4,2] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,2,4] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,1,5] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[1,1,3,2,2,2] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[1,1,3,2,1,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,3,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,2,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,1,4] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,2,3,2,2] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,3,1,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,2,3,2] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,2,3] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,2,2,1,4] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,1,4,2] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,3,3] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,1,2,4] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,1,5] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,1,4,2,2] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,1,3] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,3,2] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,3,2,3] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,1,4] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,4,2] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,3,3] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[1,1,1,2,2,4] => [3,2,1] => [[4,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,1,5] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,1,5,2] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,4,3] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,3,4] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,2,5] => [4,1,1] => [[4,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,1,6] => [5,1] => [[5,5],[4]] => [4] => 1
[1,2,2,2,2,1,3] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,2,2,2,1,1,4] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[1,2,2,1,1,3,3] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[1,2,2,1,1,1,5] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,1,6] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[1,1,3,2,2,2,2] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[1,1,3,2,2,1,3] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,2,1,1,4] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,3,1,3,2,2] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,1,2,2,3] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,3,1,1,4,2] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,3,1,1,3,3] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,3,1,1,2,4] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,3,1,1,1,5] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,2,3,2,2,2] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,3,1,1,4] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,2,3,2,2] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,3,1,3] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,2,2,2,3,2] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,2,2,2,2,3] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 1
[1,1,2,2,2,1,4] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,2,2,1,4,2] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,2,2,1,3,3] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,1,2,4] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,2,2,1,1,5] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 1
[1,1,2,1,4,2,2] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,3,3,2] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,2,3,3] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,2,2,4] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,1,5,2] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,4,3] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,3,4] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,2,5] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[1,1,2,1,1,1,6] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[1,1,1,4,2,2,2] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,2,1,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,4,1,3,2] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,4,1,2,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,4,1,1,4] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,3,3,2,2] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,3,3,1,3] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,1,3,2,3,2] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,2,2,3] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,3,2,1,4] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,1,4,2] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,1,3,3] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,3,1,2,4] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,1,1,5] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,2,4,2,2] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,1,1,2,4,1,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,3,3,2] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,2,3,2,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,3,1,4] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,2,4,2] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,1,2,2,3,3] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[1,1,1,2,2,2,4] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 1
[1,1,1,2,2,1,5] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,1,2,1,5,2] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,4,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,3,4] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,2,5] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,1,6] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,1,1,5,2,2] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 1
[1,1,1,1,5,1,3] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,4,3,2] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,4,2,3] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,4,1,4] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,3,4,2] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,3,3,3] => [4,3] => [[6,4],[3]] => [3] => 1
[1,1,1,1,3,2,4] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,3,1,5] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,5,2] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,4,3] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,3,4] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,2,2,5] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,1,1,2,1,6] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[1,1,1,1,1,6,2] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,5,3] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,4,4] => [5,2] => [[6,5],[4]] => [4] => 1
[1,1,1,1,1,3,5] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,2,6] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,1,1,1,7] => [6,1] => [[6,6],[5]] => [5] => 1
[1,1,2,1,7] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,2,2,2,5] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,1,2,3,5] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,1,5] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,1,2,1,1,5] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,2,1,2,2,3] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,5,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,3,3] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,1,2,1,3,3] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[3,3,2,1,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,2,2,2,1,3] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,6,1,3] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,1,2,3,1,3] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[3,1,1,2,1,1,3] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,1,4,1,1,3] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[5,2,2,2,1] => [1,3,1] => [[3,3,1],[2]] => [2] => 1
[1,1,2,3,2,2,1] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,2,2,6,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,1,2,7,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,4,5,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,1,2,1,5,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,2,2,3,1] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[1,1,6,3,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,1,2,3,3,1] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,1,4,1,3,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[3,2,2,1,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,2,2,3,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,1,2,4,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[3,1,2,2,2,1,1] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,3,2,2,2,1,1] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[1,1,4,2,2,1,1] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,2,2,1,4,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[3,3,4,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,2,2,4,1,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,8,1,1] => [2,1,2] => [[3,2,2],[1,1]] => [1,1] => 2
[1,1,1,2,5,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[3,1,1,2,3,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,1,4,3,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[5,1,1,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[3,3,1,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,3,3,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[1,1,5,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,1,1,4,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[1,1,3,4,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,1,6,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[2,2,2,2,1,2,1] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [3,3,3] => 1
[2,2,2,1,2,1,2] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[2,2,2,1,2,2,1] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [3,2,2] => 1
[2,2,2,1,1,2,2] => [3,2,2] => [[5,4,3],[3,2]] => [3,2] => 1
[2,2,1,2,1,2,2] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,1,2,1,1,2,1] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => 3
[2,2,1,2,2,1,2] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[2,2,1,2,2,2,1] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [3,1,1] => 2
[2,2,1,1,2,2,2] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[2,2,1,1,2,1,2,1] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 1
[2,2,1,1,1,2,2,1] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [4,3,1] => 1
[2,1,2,1,1,2,2,1] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[2,1,2,1,1,1,2,2] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
[2,1,2,2,1,2,2] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,2,2,1,1,2,1] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 1
[2,1,2,2,2,1,2] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[2,1,2,2,2,2,1] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[2,1,1,2,2,1,2,1] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 1
[2,1,1,2,1,2,1,2] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[2,1,1,2,1,2,2,1] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 2
[2,1,1,1,2,2,2,1] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 1
[2,1,1,1,2,1,2,2] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,2,1,2,2,1,2,1] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,2,1,2,2] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,2,2,1,2] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => 1
[1,2,1,1,2,2,2,1] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [3,1] => 1
[1,2,1,1,1,2,2,2] => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
[1,2,2,1,2,2,2] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[1,2,2,1,2,1,2,1] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,2,2,1,1,2,1,2] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => 1
[1,2,2,1,1,2,2,1] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [3,2,1] => 1
[1,2,2,1,1,1,2,2] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [3,1] => 1
[1,2,2,2,1,2,2] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,2,2,2,1,1,2,1] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [3,3,2] => 1
[1,2,2,2,2,1,2] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[1,1,2,2,2,1,2,1] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 1
[1,1,2,2,1,2,1,2] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => 1
[1,1,2,2,1,2,2,1] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => 1
[1,1,2,1,2,1,2,2] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,1,2,1,2,2,2,1] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 2
[1,1,1,2,2,1,2,2] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [3,3,2] => 1
[1,1,1,2,2,2,1,2] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 1
[1,1,1,2,2,2,2,1] => [3,4,1] => [[6,6,3],[5,2]] => [5,2] => 1
[1,1,1,2,1,2,2,2] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 1
[3,3,3,2] => [3,1] => [[3,3],[2]] => [2] => 1
[3,2,2,2,2,1] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[4,2,2,3,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,6,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,1,5,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,1,1,4,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,2,6,1] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[2,1,1,7,1] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,1,1,1,6,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,1,1,2,4,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,1,1,1,1,5,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,1,1,1,2,3,1] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[2,1,1,1,1,2,2,1] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [4,3] => 1
[2,2,2,2,2,1] => [5,1] => [[5,5],[4]] => [4] => 1
[3,1,2,2,2,1] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[4,1,1,2,2,1] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [2,1] => 1
[2,2,3,1,2,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[3,2,2,1,2,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,4,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[3,3,1,1,2,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[4,2,1,1,2,1] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [1,1] => 2
[5,1,1,1,2,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,2,2,3,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [2,2] => 1
[4,1,1,3,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,2,3,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,2,2,2,1,1] => [1,3,2] => [[4,3,1],[2]] => [2] => 1
[3,3,1,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[5,1,1,2,1,1] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [1,1] => 2
[2,2,4,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[3,3,2,1,1,1] => [2,1,3] => [[4,2,2],[1,1]] => [1,1] => 2
[2,2,2,2,2,2,1] => [6,1] => [[6,6],[5]] => [5] => 1
[3,1,2,2,2,2,1] => [1,1,4,1] => [[4,4,1,1],[3]] => [3] => 1
[2,3,1,2,2,2,1] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[3,2,1,2,2,2,1] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[4,1,1,2,2,2,1] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[2,2,3,1,2,2,1] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[3,2,2,1,2,2,1] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[2,4,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[3,3,1,1,2,2,1] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [3,2,1] => 1
[4,2,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[5,1,1,1,2,2,1] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
[2,2,2,3,1,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[3,2,2,2,1,2,1] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,4,1,1,2,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,3,3,1,1,2,1] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[3,3,2,1,1,2,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[4,2,2,1,1,2,1] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,5,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[3,4,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[4,3,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[5,2,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[6,1,1,1,1,2,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,2,2,2,3,1,1] => [4,1,2] => [[5,4,4],[3,3]] => [3,3] => 1
[3,1,2,2,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[4,1,1,2,3,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,2,3,1,3,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[3,2,2,1,3,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,4,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[3,3,1,1,3,1,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[4,2,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[5,1,1,1,3,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[2,2,2,3,2,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[4,1,1,3,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,2,3,2,2,1,1] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,3,2,2,2,1,1] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[3,2,2,2,2,1,1] => [1,4,2] => [[5,4,1],[3]] => [3] => 1
[4,1,2,2,2,1,1] => [1,1,3,2] => [[4,3,1,1],[2]] => [2] => 1
[3,3,1,2,2,1,1] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[5,1,1,2,2,1,1] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[2,2,4,1,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,3,3,1,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[3,3,2,1,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[4,2,2,1,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,5,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[3,4,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[4,3,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[5,2,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[6,1,1,1,2,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[2,2,2,4,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[4,1,1,4,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[2,2,3,3,1,1,1] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[3,2,2,3,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[3,3,1,3,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[5,1,1,3,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[2,2,4,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,3,3,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[3,3,2,2,1,1,1] => [2,2,3] => [[5,3,2],[2,1]] => [2,1] => 1
[4,2,2,2,1,1,1] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[6,1,1,2,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[2,2,5,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[3,3,3,1,1,1,1] => [3,4] => [[6,3],[2]] => [2] => 1
[2,2,1,2,1,2,1,1] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[1,2,2,2,1,2,1,1] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [2,2,2] => 1
[1,2,2,1,2,1,1,2] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => 2
[1,2,2,1,2,2,1,1] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[1,2,1,2,2,1,1,2] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [2,1] => 1
[1,2,1,2,2,2,1,1] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [2] => 1
[2,1,1,1,1,2,1,2] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [3,3,3] => 1
[2,1,1,1,2,1,1,2] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [3,2,2] => 1
[2,1,1,2,1,1,1,2] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [3,1,1] => 2
[1,2,2,4,2,1] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,4,2,2,2,1] => [1,1,3,1] => [[3,3,1,1],[2]] => [2] => 1
[2,2,5,2,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,2,2,2,1,1] => [5,2] => [[6,5],[4]] => [4] => 1
[2,2,2,1,2,1,1,1] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [2,2,2] => 1
[2,2,1,2,2,1,1,1] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [2,1,1] => 2
[2,1,2,2,2,1,1,1] => [1,1,3,3] => [[5,3,1,1],[2]] => [2] => 1
[1,2,2,2,2,1,1,1] => [1,4,3] => [[6,4,1],[3]] => [3] => 1
[1,2,2,2,3,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,2,4,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [2] => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,2,2,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,2,1,2,3,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => 2
[2,2,1,3,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,1,4,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[3,1,1,2,2,2,1] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [3,1] => 1
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[3,1,1,3,2,1,1] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [1,1,1] => 2
[2,2,2,1,3,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [2,2,2] => 1
[2,3,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[2,3,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[3,2,1,1,2,2,1] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [2,1] => 1
[3,2,1,1,3,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[4,1,1,1,2,2,1] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [3,2] => 1
[4,1,1,1,3,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[2,2,3,1,1,2,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => 3
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[2,4,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[3,2,2,1,1,2,1] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [2,2,1] => 1
[3,3,1,1,1,2,1] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [3,3,1] => 1
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[4,2,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[5,1,1,1,1,2,1] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [3,3] => 1
[2,2,2,3,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[2,2,3,1,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,3,2,1,1,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,4,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[2,4,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[4,1,1,2,2,1,1] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [2,1] => 1
[4,1,1,3,1,1,1] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [1,1] => 2
[3,3,1,1,2,1,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[4,2,1,1,2,1,1] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [1,1] => 2
[5,1,1,1,2,1,1] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [2,2] => 1
[3,2,2,2,1,1,1] => [1,3,3] => [[5,3,1],[2]] => [2] => 1
[3,3,2,1,1,1,1] => [2,1,4] => [[5,2,2],[1,1]] => [1,1] => 2
[1,1,2,2,4,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => 2
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,4,3,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,4,1,4,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,3,1,5,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,5,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,3,4,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,6,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,1,1,7,1] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,2,3,2,3] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[2,2,2,2,4] => [4,1] => [[4,4],[3]] => [3] => 1
[1,2,2,2,2,3] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[1,2,2,3,4] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[2,2,3,5] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[5,1,1,1,1,2] => [1,4,1] => [[4,4,1],[3]] => [3] => 1
[1,1,1,1,1,5,1] => [5,1,1] => [[5,5,5],[4,4]] => [4,4] => 1
[1,1,1,3,1,3,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,5,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,7,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,4,1,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,1,4,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,1,1,2,3,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,3,1,1,1,3,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,4,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,2,1,2,2,1] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [2,1,1] => 2
[1,1,1,7,1,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [2,2] => 1
[1,1,1,9,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,1,1,6,1,2,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => 1
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,6,1,1,1,2,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [2,2] => 1
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => 2
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [1,1] => 2
[1,1,1,1,1,1,1,1,3] => [8,1] => [[8,8],[7]] => [7] => 1
[2,2,2,2,1,1,2] => [4,2,1] => [[5,5,4],[4,3]] => [4,3] => 1
[1,1,2,2,1,2,3] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,1,2,2,2,3] => [3,3,1] => [[5,5,3],[4,2]] => [4,2] => 1
[2,2,2,6] => [3,1] => [[3,3],[2]] => [2] => 1
[2,2,6,2] => [2,1,1] => [[2,2,2],[1,1]] => [1,1] => 2
[1,2,2,2,4,1] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [2,2] => 1
[2,2,2,5,1] => [3,1,1] => [[3,3,3],[2,2]] => [2,2] => 1
[1,2,2,5,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [1,1] => 2
[1,1,2,2,2,2,1] => [2,4,1] => [[5,5,2],[4,1]] => [4,1] => 1
[1,1,2,2,2,1,1,1] => [2,3,3] => [[6,4,2],[3,1]] => [3,1] => 1
[1,1,2,2,3,1,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [2,2,1] => 1
[1,1,2,2,1,2,1,1] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => 1
[1,1,2,3,2,1,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => 2
[1,1,2,1,2,2,1,1] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => 2
[1,1,3,2,2,1,1] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [2,1,1] => 2
[1,1,1,2,2,2,1,1] => [3,3,2] => [[6,5,3],[4,2]] => [4,2] => 1
[1,2,2,2,2,1,1] => [1,4,2] => [[5,4,1],[3]] => [3] => 1
[1,1,2,2,2,4] => [2,3,1] => [[4,4,2],[3,1]] => [3,1] => 1
[1,1,2,5,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[1,1,5,2,1,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [1,1,1] => 2
[2,2,1,1,1,2,1,2] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => 1
[1,2,2,2,1,1,1,2] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [4,2] => 1
[2,2,1,2,1,1,1,2] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => 2
[2,2,2,1,1,1,2,1] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [4,4,2] => 1
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Description
The smallest positive integer that does not appear twice in the partition.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
inner shape
Description
The inner shape of a skew partition.
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