Identifier
-
Mp00128:
Set partitions
—to composition⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001597: Skew partitions ⟶ ℤ
Values
{{1}} => [1] => [[1],[]] => 1
{{1,2}} => [2] => [[2],[]] => 1
{{1},{2}} => [1,1] => [[1,1],[]] => 1
{{1,2,3}} => [3] => [[3],[]] => 1
{{1,2},{3}} => [2,1] => [[2,2],[1]] => 1
{{1,3},{2}} => [2,1] => [[2,2],[1]] => 1
{{1},{2,3}} => [1,2] => [[2,1],[]] => 1
{{1},{2},{3}} => [1,1,1] => [[1,1,1],[]] => 1
{{1,2,3,4}} => [4] => [[4],[]] => 1
{{1,2,3},{4}} => [3,1] => [[3,3],[2]] => 1
{{1,2,4},{3}} => [3,1] => [[3,3],[2]] => 1
{{1,2},{3,4}} => [2,2] => [[3,2],[1]] => 1
{{1,2},{3},{4}} => [2,1,1] => [[2,2,2],[1,1]] => 1
{{1,3,4},{2}} => [3,1] => [[3,3],[2]] => 1
{{1,3},{2,4}} => [2,2] => [[3,2],[1]] => 1
{{1,3},{2},{4}} => [2,1,1] => [[2,2,2],[1,1]] => 1
{{1,4},{2,3}} => [2,2] => [[3,2],[1]] => 1
{{1},{2,3,4}} => [1,3] => [[3,1],[]] => 1
{{1},{2,3},{4}} => [1,2,1] => [[2,2,1],[1]] => 1
{{1,4},{2},{3}} => [2,1,1] => [[2,2,2],[1,1]] => 1
{{1},{2,4},{3}} => [1,2,1] => [[2,2,1],[1]] => 1
{{1},{2},{3,4}} => [1,1,2] => [[2,1,1],[]] => 1
{{1},{2},{3},{4}} => [1,1,1,1] => [[1,1,1,1],[]] => 1
{{1,2,3,4,5}} => [5] => [[5],[]] => 1
{{1,2,3,4},{5}} => [4,1] => [[4,4],[3]] => 1
{{1,2,3,5},{4}} => [4,1] => [[4,4],[3]] => 1
{{1,2,3},{4,5}} => [3,2] => [[4,3],[2]] => 1
{{1,2,3},{4},{5}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,2,4,5},{3}} => [4,1] => [[4,4],[3]] => 1
{{1,2,4},{3,5}} => [3,2] => [[4,3],[2]] => 1
{{1,2,4},{3},{5}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,2,5},{3,4}} => [3,2] => [[4,3],[2]] => 1
{{1,2},{3,4,5}} => [2,3] => [[4,2],[1]] => 1
{{1,2},{3,4},{5}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,2,5},{3},{4}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,2},{3,5},{4}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,2},{3},{4,5}} => [2,1,2] => [[3,2,2],[1,1]] => 1
{{1,2},{3},{4},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 1
{{1,3,4,5},{2}} => [4,1] => [[4,4],[3]] => 1
{{1,3,4},{2,5}} => [3,2] => [[4,3],[2]] => 1
{{1,3,4},{2},{5}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,3,5},{2,4}} => [3,2] => [[4,3],[2]] => 1
{{1,3},{2,4,5}} => [2,3] => [[4,2],[1]] => 1
{{1,3},{2,4},{5}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,3,5},{2},{4}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,3},{2,5},{4}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,3},{2},{4,5}} => [2,1,2] => [[3,2,2],[1,1]] => 1
{{1,3},{2},{4},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 1
{{1,4,5},{2,3}} => [3,2] => [[4,3],[2]] => 1
{{1,4},{2,3,5}} => [2,3] => [[4,2],[1]] => 1
{{1,4},{2,3},{5}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,5},{2,3,4}} => [2,3] => [[4,2],[1]] => 1
{{1},{2,3,4,5}} => [1,4] => [[4,1],[]] => 1
{{1},{2,3,4},{5}} => [1,3,1] => [[3,3,1],[2]] => 1
{{1,5},{2,3},{4}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1},{2,3,5},{4}} => [1,3,1] => [[3,3,1],[2]] => 1
{{1},{2,3},{4,5}} => [1,2,2] => [[3,2,1],[1]] => 1
{{1},{2,3},{4},{5}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => 1
{{1,4,5},{2},{3}} => [3,1,1] => [[3,3,3],[2,2]] => 1
{{1,4},{2,5},{3}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1,4},{2},{3,5}} => [2,1,2] => [[3,2,2],[1,1]] => 1
{{1,4},{2},{3},{5}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 1
{{1,5},{2,4},{3}} => [2,2,1] => [[3,3,2],[2,1]] => 1
{{1},{2,4,5},{3}} => [1,3,1] => [[3,3,1],[2]] => 1
{{1},{2,4},{3,5}} => [1,2,2] => [[3,2,1],[1]] => 1
{{1},{2,4},{3},{5}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => 1
{{1,5},{2},{3,4}} => [2,1,2] => [[3,2,2],[1,1]] => 1
{{1},{2,5},{3,4}} => [1,2,2] => [[3,2,1],[1]] => 1
{{1},{2},{3,4,5}} => [1,1,3] => [[3,1,1],[]] => 1
{{1},{2},{3,4},{5}} => [1,1,2,1] => [[2,2,1,1],[1]] => 1
{{1,5},{2},{3},{4}} => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => 1
{{1},{2,5},{3},{4}} => [1,2,1,1] => [[2,2,2,1],[1,1]] => 1
{{1},{2},{3,5},{4}} => [1,1,2,1] => [[2,2,1,1],[1]] => 1
{{1},{2},{3},{4,5}} => [1,1,1,2] => [[2,1,1,1],[]] => 1
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
{{1,2,3,4,5,6}} => [6] => [[6],[]] => 1
{{1,2,3,4,5},{6}} => [5,1] => [[5,5],[4]] => 1
{{1,2,3,4,6},{5}} => [5,1] => [[5,5],[4]] => 1
{{1,2,3,4},{5,6}} => [4,2] => [[5,4],[3]] => 1
{{1,2,3,4},{5},{6}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,3,5,6},{4}} => [5,1] => [[5,5],[4]] => 1
{{1,2,3,5},{4,6}} => [4,2] => [[5,4],[3]] => 1
{{1,2,3,5},{4},{6}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,3,6},{4,5}} => [4,2] => [[5,4],[3]] => 1
{{1,2,3},{4,5,6}} => [3,3] => [[5,3],[2]] => 1
{{1,2,3},{4,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,3,6},{4},{5}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,3},{4,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,3},{4},{5,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,2,4,5,6},{3}} => [5,1] => [[5,5],[4]] => 1
{{1,2,4,5},{3,6}} => [4,2] => [[5,4],[3]] => 1
{{1,2,4,5},{3},{6}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,4,6},{3,5}} => [4,2] => [[5,4],[3]] => 1
{{1,2,4},{3,5,6}} => [3,3] => [[5,3],[2]] => 1
{{1,2,4},{3,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,4,6},{3},{5}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,4},{3,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,4},{3},{5,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,2,5,6},{3,4}} => [4,2] => [[5,4],[3]] => 1
>>> Load all 1155 entries. <<<{{1,2,5},{3,4,6}} => [3,3] => [[5,3],[2]] => 1
{{1,2,5},{3,4},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,6},{3,4,5}} => [3,3] => [[5,3],[2]] => 1
{{1,2},{3,4,5,6}} => [2,4] => [[5,2],[1]] => 1
{{1,2},{3,4,5},{6}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,2,6},{3,4},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2},{3,4,6},{5}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,2},{3,4},{5,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,2,5,6},{3},{4}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,2,5},{3,6},{4}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2,5},{3},{4,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,2,6},{3,5},{4}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,2},{3,5,6},{4}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,2},{3,5},{4,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,2,6},{3},{4,5}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,2},{3,6},{4,5}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,2},{3},{4,5,6}} => [2,1,3] => [[4,2,2],[1,1]] => 1
{{1,2},{3},{4,5},{6}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,2},{3},{4,6},{5}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,2},{3},{4},{5,6}} => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 1
{{1,3,4,5,6},{2}} => [5,1] => [[5,5],[4]] => 1
{{1,3,4,5},{2,6}} => [4,2] => [[5,4],[3]] => 1
{{1,3,4,5},{2},{6}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,3,4,6},{2,5}} => [4,2] => [[5,4],[3]] => 1
{{1,3,4},{2,5,6}} => [3,3] => [[5,3],[2]] => 1
{{1,3,4},{2,5},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3,4,6},{2},{5}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,3,4},{2,6},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3,4},{2},{5,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,3,5,6},{2,4}} => [4,2] => [[5,4],[3]] => 1
{{1,3,5},{2,4,6}} => [3,3] => [[5,3],[2]] => 1
{{1,3,5},{2,4},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3,6},{2,4,5}} => [3,3] => [[5,3],[2]] => 1
{{1,3},{2,4,5,6}} => [2,4] => [[5,2],[1]] => 1
{{1,3},{2,4,5},{6}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,3,6},{2,4},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3},{2,4,6},{5}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,3},{2,4},{5,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,3,5,6},{2},{4}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,3,5},{2,6},{4}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3,5},{2},{4,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,3,6},{2,5},{4}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,3},{2,5,6},{4}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,3},{2,5},{4,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,3,6},{2},{4,5}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,3},{2,6},{4,5}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,3},{2},{4,5,6}} => [2,1,3] => [[4,2,2],[1,1]] => 1
{{1,3},{2},{4,5},{6}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,3},{2},{4,6},{5}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,3},{2},{4},{5,6}} => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => 1
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 1
{{1,4,5,6},{2,3}} => [4,2] => [[5,4],[3]] => 1
{{1,4,5},{2,3,6}} => [3,3] => [[5,3],[2]] => 1
{{1,4,5},{2,3},{6}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,4,6},{2,3,5}} => [3,3] => [[5,3],[2]] => 1
{{1,4},{2,3,5,6}} => [2,4] => [[5,2],[1]] => 1
{{1,4},{2,3,5},{6}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,4,6},{2,3},{5}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,4},{2,3,6},{5}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,4},{2,3},{5,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,5,6},{2,3,4}} => [3,3] => [[5,3],[2]] => 1
{{1,5},{2,3,4,6}} => [2,4] => [[5,2],[1]] => 1
{{1,5},{2,3,4},{6}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,6},{2,3,4,5}} => [2,4] => [[5,2],[1]] => 1
{{1},{2,3,4,5,6}} => [1,5] => [[5,1],[]] => 1
{{1},{2,3,4,5},{6}} => [1,4,1] => [[4,4,1],[3]] => 1
{{1,6},{2,3,4},{5}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1},{2,3,4,6},{5}} => [1,4,1] => [[4,4,1],[3]] => 1
{{1},{2,3,4},{5,6}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,3,4},{5},{6}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1,5,6},{2,3},{4}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,5},{2,3,6},{4}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,5},{2,3},{4,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,6},{2,3,5},{4}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1},{2,3,5,6},{4}} => [1,4,1] => [[4,4,1],[3]] => 1
{{1},{2,3,5},{4,6}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,3,5},{4},{6}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1,6},{2,3},{4,5}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1},{2,3,6},{4,5}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,3},{4,5,6}} => [1,2,3] => [[4,2,1],[1]] => 1
{{1},{2,3},{4,5},{6}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1},{2,3,6},{4},{5}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1},{2,3},{4,6},{5}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [[3,2,2,1],[1,1]] => 1
{{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => 1
{{1,4,5,6},{2},{3}} => [4,1,1] => [[4,4,4],[3,3]] => 1
{{1,4,5},{2,6},{3}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,4,5},{2},{3,6}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,4,6},{2,5},{3}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,4},{2,5,6},{3}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,4},{2,5},{3,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,4,6},{2},{3,5}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,4},{2,6},{3,5}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,4},{2},{3,5,6}} => [2,1,3] => [[4,2,2],[1,1]] => 1
{{1,4},{2},{3,5},{6}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,4},{2},{3,6},{5}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,4},{2},{3},{5,6}} => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => 1
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 1
{{1,5,6},{2,4},{3}} => [3,2,1] => [[4,4,3],[3,2]] => 1
{{1,5},{2,4,6},{3}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1,5},{2,4},{3,6}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,6},{2,4,5},{3}} => [2,3,1] => [[4,4,2],[3,1]] => 1
{{1},{2,4,5,6},{3}} => [1,4,1] => [[4,4,1],[3]] => 1
{{1},{2,4,5},{3,6}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,4,5},{3},{6}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1,6},{2,4},{3,5}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1},{2,4,6},{3,5}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,4},{3,5,6}} => [1,2,3] => [[4,2,1],[1]] => 1
{{1},{2,4},{3,5},{6}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1},{2,4,6},{3},{5}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1},{2,4},{3,6},{5}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [[3,2,2,1],[1,1]] => 1
{{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => 1
{{1,5,6},{2},{3,4}} => [3,1,2] => [[4,3,3],[2,2]] => 1
{{1,5},{2,6},{3,4}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1,5},{2},{3,4,6}} => [2,1,3] => [[4,2,2],[1,1]] => 1
{{1,5},{2},{3,4},{6}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,6},{2,5},{3,4}} => [2,2,2] => [[4,3,2],[2,1]] => 1
{{1},{2,5,6},{3,4}} => [1,3,2] => [[4,3,1],[2]] => 1
{{1},{2,5},{3,4,6}} => [1,2,3] => [[4,2,1],[1]] => 1
{{1},{2,5},{3,4},{6}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1,6},{2},{3,4,5}} => [2,1,3] => [[4,2,2],[1,1]] => 1
{{1},{2,6},{3,4,5}} => [1,2,3] => [[4,2,1],[1]] => 1
{{1},{2},{3,4,5,6}} => [1,1,4] => [[4,1,1],[]] => 1
{{1},{2},{3,4,5},{6}} => [1,1,3,1] => [[3,3,1,1],[2]] => 1
{{1,6},{2},{3,4},{5}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1},{2,6},{3,4},{5}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1},{2},{3,4,6},{5}} => [1,1,3,1] => [[3,3,1,1],[2]] => 1
{{1},{2},{3,4},{5,6}} => [1,1,2,2] => [[3,2,1,1],[1]] => 1
{{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => 1
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => 1
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1,5},{2},{3,6},{4}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1,5},{2},{3},{4,6}} => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => 1
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 1
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => 1
{{1},{2,5,6},{3},{4}} => [1,3,1,1] => [[3,3,3,1],[2,2]] => 1
{{1},{2,5},{3,6},{4}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [[3,2,2,1],[1,1]] => 1
{{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => 1
{{1,6},{2},{3,5},{4}} => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => 1
{{1},{2,6},{3,5},{4}} => [1,2,2,1] => [[3,3,2,1],[2,1]] => 1
{{1},{2},{3,5,6},{4}} => [1,1,3,1] => [[3,3,1,1],[2]] => 1
{{1},{2},{3,5},{4,6}} => [1,1,2,2] => [[3,2,1,1],[1]] => 1
{{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => 1
{{1,6},{2},{3},{4,5}} => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => 1
{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [[3,2,2,1],[1,1]] => 1
{{1},{2},{3,6},{4,5}} => [1,1,2,2] => [[3,2,1,1],[1]] => 1
{{1},{2},{3},{4,5,6}} => [1,1,1,3] => [[3,1,1,1],[]] => 1
{{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => 1
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 1
{{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => 1
{{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => 1
{{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => 1
{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [[2,1,1,1,1],[]] => 1
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => 1
{{1,2,3,4,5,6,7}} => [7] => [[7],[]] => 1
{{1,2,3,4,5,6},{7}} => [6,1] => [[6,6],[5]] => 1
{{1,2,3,4,5,7},{6}} => [6,1] => [[6,6],[5]] => 1
{{1,2,3,4,5},{6,7}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,4,6,7},{5}} => [6,1] => [[6,6],[5]] => 1
{{1,2,3,4,6},{5,7}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,4,7},{5,6}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,4},{5,6,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,4},{5},{6,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,3,5,6,7},{4}} => [6,1] => [[6,6],[5]] => 1
{{1,2,3,5,6},{4,7}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,5,7},{4,6}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,5},{4,6,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,5},{4},{6,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,3,6,7},{4,5}} => [5,2] => [[6,5],[4]] => 1
{{1,2,3,6},{4,5,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,7},{4,5,6}} => [4,3] => [[6,4],[3]] => 1
{{1,2,3},{4,5,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,3},{4,5},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3,6},{4},{5,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,3},{4,6},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,3,7},{4},{5,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,3},{4,7},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,3},{4},{5,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,2,4,5,6,7},{3}} => [6,1] => [[6,6],[5]] => 1
{{1,2,4,5,6},{3,7}} => [5,2] => [[6,5],[4]] => 1
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,4,5,7},{3,6}} => [5,2] => [[6,5],[4]] => 1
{{1,2,4,5},{3,6,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4,5},{3},{6,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,4,6,7},{3,5}} => [5,2] => [[6,5],[4]] => 1
{{1,2,4,6},{3,5,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4,7},{3,5,6}} => [4,3] => [[6,4],[3]] => 1
{{1,2,4},{3,5,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,4},{3,5},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4,6},{3},{5,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,4},{3,6},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,4,7},{3},{5,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,4},{3,7},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,4},{3},{5,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,2,5,6,7},{3,4}} => [5,2] => [[6,5],[4]] => 1
{{1,2,5,6},{3,4,7}} => [4,3] => [[6,4],[3]] => 1
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,5,7},{3,4,6}} => [4,3] => [[6,4],[3]] => 1
{{1,2,5},{3,4,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,5},{3,4},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,6,7},{3,4,5}} => [4,3] => [[6,4],[3]] => 1
{{1,2,6},{3,4,5,7}} => [3,4] => [[6,3],[2]] => 1
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,7},{3,4,5,6}} => [3,4] => [[6,3],[2]] => 1
{{1,2},{3,4,5,6,7}} => [2,5] => [[6,2],[1]] => 1
{{1,2},{3,4,5,6},{7}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2},{3,4,5,7},{6}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,2},{3,4,5},{6,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,4,5},{6},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,6},{3,4},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2},{3,4,6,7},{5}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,2},{3,4,6},{5,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2,7},{3,4},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2},{3,4,7},{5,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,4},{5,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,5,6},{3},{4,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,5},{3,6},{4,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,5,7},{3},{4,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,5},{3,7},{4,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,5},{3},{4,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2,6},{3,5},{4,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,2},{3,5,6,7},{4}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,2},{3,5,6},{4,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2,7},{3,5},{4,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2},{3,5,7},{4,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,5},{4,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,2,6,7},{3},{4,5}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,2,6},{3,7},{4,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2,6},{3},{4,5,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,7},{3,6},{4,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,2},{3,6,7},{4,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,2},{3,6},{4,5,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2,7},{3},{4,5,6}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,2},{3,7},{4,5,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,2},{3},{4,5,6,7}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1,3,4,5,6,7},{2}} => [6,1] => [[6,6],[5]] => 1
{{1,3,4,5,6},{2,7}} => [5,2] => [[6,5],[4]] => 1
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,3,4,5,7},{2,6}} => [5,2] => [[6,5],[4]] => 1
{{1,3,4,5},{2,6,7}} => [4,3] => [[6,4],[3]] => 1
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4,5},{2},{6,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,4,6,7},{2,5}} => [5,2] => [[6,5],[4]] => 1
{{1,3,4,6},{2,5,7}} => [4,3] => [[6,4],[3]] => 1
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4,7},{2,5,6}} => [4,3] => [[6,4],[3]] => 1
{{1,3,4},{2,5,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,4},{2,5},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4,6},{2},{5,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,4},{2,6},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,4,7},{2},{5,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,4},{2,7},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,4},{2},{5,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,3,5,6,7},{2,4}} => [5,2] => [[6,5],[4]] => 1
{{1,3,5,6},{2,4,7}} => [4,3] => [[6,4],[3]] => 1
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,5,7},{2,4,6}} => [4,3] => [[6,4],[3]] => 1
{{1,3,5},{2,4,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,5},{2,4},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,6,7},{2,4,5}} => [4,3] => [[6,4],[3]] => 1
{{1,3,6},{2,4,5,7}} => [3,4] => [[6,3],[2]] => 1
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,7},{2,4,5,6}} => [3,4] => [[6,3],[2]] => 1
{{1,3},{2,4,5,6,7}} => [2,5] => [[6,2],[1]] => 1
{{1,3},{2,4,5,6},{7}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3},{2,4,5,7},{6}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,3},{2,4,5},{6,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,4,5},{6},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,6},{2,4},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3},{2,4,6,7},{5}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,3},{2,4,6},{5,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3,7},{2,4},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3},{2,4,7},{5,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,4},{5,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,5,6},{2},{4,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,5},{2,6},{4,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,5,7},{2},{4,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,5},{2,7},{4,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,5},{2},{4,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3,6},{2,5},{4,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,3},{2,5,6,7},{4}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,3},{2,5,6},{4,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3,7},{2,5},{4,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3},{2,5,7},{4,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,5},{4,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,3,6,7},{2},{4,5}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,3,6},{2,7},{4,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3,6},{2},{4,5,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,7},{2,6},{4,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,3},{2,6,7},{4,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,3},{2,6},{4,5,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3,7},{2},{4,5,6}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,3},{2,7},{4,5,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,3},{2},{4,5,6,7}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1,4,5,6,7},{2,3}} => [5,2] => [[6,5],[4]] => 1
{{1,4,5,6},{2,3,7}} => [4,3] => [[6,4],[3]] => 1
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,5,7},{2,3,6}} => [4,3] => [[6,4],[3]] => 1
{{1,4,5},{2,3,6,7}} => [3,4] => [[6,3],[2]] => 1
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,5},{2,3},{6,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,6,7},{2,3,5}} => [4,3] => [[6,4],[3]] => 1
{{1,4,6},{2,3,5,7}} => [3,4] => [[6,3],[2]] => 1
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,7},{2,3,5,6}} => [3,4] => [[6,3],[2]] => 1
{{1,4},{2,3,5,6,7}} => [2,5] => [[6,2],[1]] => 1
{{1,4},{2,3,5,6},{7}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4},{2,3,5,7},{6}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,4},{2,3,5},{6,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,3,5},{6},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,6},{2,3},{5,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4},{2,3,6,7},{5}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,4},{2,3,6},{5,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4,7},{2,3},{5,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4},{2,3,7},{5,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,3},{5,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,5,6,7},{2,3,4}} => [4,3] => [[6,4],[3]] => 1
{{1,5,6},{2,3,4,7}} => [3,4] => [[6,3],[2]] => 1
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5,7},{2,3,4,6}} => [3,4] => [[6,3],[2]] => 1
{{1,5},{2,3,4,6,7}} => [2,5] => [[6,2],[1]] => 1
{{1,5},{2,3,4,6},{7}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5},{2,3,4,7},{6}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,5},{2,3,4},{6,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,6,7},{2,3,4,5}} => [3,4] => [[6,3],[2]] => 1
{{1,6},{2,3,4,5,7}} => [2,5] => [[6,2],[1]] => 1
{{1,6},{2,3,4,5},{7}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,7},{2,3,4,5,6}} => [2,5] => [[6,2],[1]] => 1
{{1},{2,3,4,5,6,7}} => [1,6] => [[6,1],[]] => 1
{{1},{2,3,4,5,6},{7}} => [1,5,1] => [[5,5,1],[4]] => 1
{{1,7},{2,3,4,5},{6}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1},{2,3,4,5,7},{6}} => [1,5,1] => [[5,5,1],[4]] => 1
{{1},{2,3,4,5},{6,7}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,4,5},{6},{7}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,6},{2,3,4,7},{5}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,6},{2,3,4},{5,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,7},{2,3,4,6},{5}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1},{2,3,4,6,7},{5}} => [1,5,1] => [[5,5,1],[4]] => 1
{{1},{2,3,4,6},{5,7}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1,7},{2,3,4},{5,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,3,4,7},{5,6}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,4},{5,6,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,3,4},{5},{6},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5,6},{2,3},{4,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5},{2,3,6,7},{4}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,5},{2,3,6},{4,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,5,7},{2,3},{4,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5},{2,3,7},{4,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,3},{4,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,6},{2,3,5,7},{4}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,6},{2,3,5},{4,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,7},{2,3,5,6},{4}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1},{2,3,5,6,7},{4}} => [1,5,1] => [[5,5,1],[4]] => 1
{{1},{2,3,5,6},{4,7}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1,7},{2,3,5},{4,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,3,5,7},{4,6}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,5},{4,6,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,6,7},{2,3},{4,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,6},{2,3,7},{4,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,3},{4,5,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,7},{2,3,6},{4,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,3,6,7},{4,5}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,3,6},{4,5,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,3},{4,5,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1},{2,3,7},{4,5,6}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,3},{4,5,6,7}} => [1,2,4] => [[5,2,1],[1]] => 1
{{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,3},{4,5},{6,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,3},{4,5},{6},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,3},{4,6},{5,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [[4,2,2,1],[1,1]] => 1
{{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 1
{{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [[5,5,5],[4,4]] => 1
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,5,6},{2},{3,7}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,5},{2,6},{3,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,5,7},{2},{3,6}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,4,5},{2,7},{3,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,5},{2},{3,6,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4,6},{2,5},{3,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,4},{2,5,6,7},{3}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,4},{2,5,6},{3,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4,7},{2,5},{3,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4},{2,5,7},{3,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,5},{3,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,4,6,7},{2},{3,5}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,4,6},{2,7},{3,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4,6},{2},{3,5,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4,7},{2,6},{3,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,4},{2,6,7},{3,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,4},{2,6},{3,5,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4,7},{2},{3,5,6}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,4},{2,7},{3,5,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,4},{2},{3,5,6,7}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [[5,5,4],[4,3]] => 1
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5,6},{2,4},{3,7}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,5},{2,4,6,7},{3}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,5},{2,4,6},{3,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,5,7},{2,4},{3,6}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5},{2,4,7},{3,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,4},{3,6,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [[5,5,3],[4,2]] => 1
{{1,6},{2,4,5,7},{3}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1,6},{2,4,5},{3,7}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,7},{2,4,5,6},{3}} => [2,4,1] => [[5,5,2],[4,1]] => 1
{{1},{2,4,5,6,7},{3}} => [1,5,1] => [[5,5,1],[4]] => 1
{{1},{2,4,5,6},{3,7}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1,7},{2,4,5},{3,6}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,4,5,7},{3,6}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,4,5},{3,6,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,6,7},{2,4},{3,5}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,6},{2,4,7},{3,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,4},{3,5,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,7},{2,4,6},{3,5}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,4,6,7},{3,5}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,4,6},{3,5,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,4},{3,5,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1},{2,4,7},{3,5,6}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,4},{3,5,6,7}} => [1,2,4] => [[5,2,1],[1]] => 1
{{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [[4,2,2,1],[1,1]] => 1
{{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 1
{{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
{{1,5,6,7},{2},{3,4}} => [4,1,2] => [[5,4,4],[3,3]] => 1
{{1,5,6},{2,7},{3,4}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5,6},{2},{3,4,7}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,5,7},{2,6},{3,4}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,5},{2,6,7},{3,4}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,5},{2,6},{3,4,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5,7},{2},{3,4,6}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,5},{2,7},{3,4,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,5},{2},{3,4,6,7}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,6,7},{2,5},{3,4}} => [3,2,2] => [[5,4,3],[3,2]] => 1
{{1,6},{2,5,7},{3,4}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1,6},{2,5},{3,4,7}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,7},{2,5,6},{3,4}} => [2,3,2] => [[5,4,2],[3,1]] => 1
{{1},{2,5,6,7},{3,4}} => [1,4,2] => [[5,4,1],[3]] => 1
{{1},{2,5,6},{3,4,7}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1,7},{2,5},{3,4,6}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1},{2,5,7},{3,4,6}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,5},{3,4,6,7}} => [1,2,4] => [[5,2,1],[1]] => 1
{{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,6,7},{2},{3,4,5}} => [3,1,3] => [[5,3,3],[2,2]] => 1
{{1,6},{2,7},{3,4,5}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1,6},{2},{3,4,5,7}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,7},{2,6},{3,4,5}} => [2,2,3] => [[5,3,2],[2,1]] => 1
{{1},{2,6,7},{3,4,5}} => [1,3,3] => [[5,3,1],[2]] => 1
{{1},{2,6},{3,4,5,7}} => [1,2,4] => [[5,2,1],[1]] => 1
{{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1,7},{2},{3,4,5,6}} => [2,1,4] => [[5,2,2],[1,1]] => 1
{{1},{2,7},{3,4,5,6}} => [1,2,4] => [[5,2,1],[1]] => 1
{{1},{2},{3,4,5,6,7}} => [1,1,5] => [[5,1,1],[]] => 1
{{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => [[4,4,1,1],[3]] => 1
{{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => [[4,4,1,1],[3]] => 1
{{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => [[4,4,1,1],[3]] => 1
{{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => [[4,2,1,1],[1]] => 1
{{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => 1
{{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => 1
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => 1
{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => 1
{{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => 1
{{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => [[4,4,4,1],[3,3]] => 1
{{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [[4,2,2,1],[1,1]] => 1
{{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 1
{{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
{{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => 1
{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => 1
{{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [[4,4,3,1],[3,2]] => 1
{{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => 1
{{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [[4,4,2,1],[3,1]] => 1
{{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => [[4,4,1,1],[3]] => 1
{{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => [[4,2,1,1],[1]] => 1
{{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => 1
{{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => 1
{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => 1
{{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => 1
{{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [[4,3,3,1],[2,2]] => 1
{{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [[4,2,2,1],[1,1]] => 1
{{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => 1
{{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => [[4,3,2,1],[2,1]] => 1
{{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => [[4,3,1,1],[2]] => 1
{{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => [[4,2,1,1],[1]] => 1
{{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => 1
{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [[4,2,2,1],[1,1]] => 1
{{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => [[4,2,1,1],[1]] => 1
{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [[4,1,1,1],[]] => 1
{{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => 1
{{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => 1
{{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => 1
{{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => 1
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 1
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 1
{{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 1
{{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 1
{{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
{{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 1
{{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 1
{{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 1
{{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => 1
{{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => 1
{{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 1
{{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 1
{{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 1
{{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => 1
{{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => 1
{{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => 1
{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 1
{{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 1
{{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => 1
{{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => 1
{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [[3,1,1,1,1],[]] => 1
{{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => 1
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
{{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
{{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => 1
{{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => 1
{{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => 1
{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [[2,1,1,1,1,1],[]] => 1
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => 1
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Generating function
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 5\ q$
$F_{4} = 15\ q$
$F_{5} = 52\ q$
$F_{6} = 203\ q$
$F_{7} = 877\ q$
Description
The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
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Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
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Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
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