Identifier
Mp00258:
Set partitions
—Standard tableau associated to a set partition⟶
Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
{{1}} => [[1]] => [1] => [1]
{{1,2}} => [[1,2]] => [1,2] => [2]
{{1},{2}} => [[1],[2]] => [2,1] => [1,1]
{{1,2,3}} => [[1,2,3]] => [1,2,3] => [3]
{{1,2},{3}} => [[1,2],[3]] => [3,1,2] => [1,2]
{{1,3},{2}} => [[1,3],[2]] => [2,1,3] => [1,2]
{{1},{2,3}} => [[1,3],[2]] => [2,1,3] => [1,2]
{{1},{2},{3}} => [[1],[2],[3]] => [3,2,1] => [1,1,1]
{{1,2,3,4}} => [[1,2,3,4]] => [1,2,3,4] => [4]
{{1,2,3},{4}} => [[1,2,3],[4]] => [4,1,2,3] => [1,3]
{{1,2,4},{3}} => [[1,2,4],[3]] => [3,1,2,4] => [1,3]
{{1,2},{3,4}} => [[1,2],[3,4]] => [3,4,1,2] => [2,2]
{{1,2},{3},{4}} => [[1,2],[3],[4]] => [4,3,1,2] => [1,1,2]
{{1,3,4},{2}} => [[1,3,4],[2]] => [2,1,3,4] => [1,3]
{{1,3},{2,4}} => [[1,3],[2,4]] => [2,4,1,3] => [2,2]
{{1,3},{2},{4}} => [[1,3],[2],[4]] => [4,2,1,3] => [1,1,2]
{{1,4},{2,3}} => [[1,3],[2,4]] => [2,4,1,3] => [2,2]
{{1},{2,3,4}} => [[1,3,4],[2]] => [2,1,3,4] => [1,3]
{{1},{2,3},{4}} => [[1,3],[2],[4]] => [4,2,1,3] => [1,1,2]
{{1,4},{2},{3}} => [[1,4],[2],[3]] => [3,2,1,4] => [1,1,2]
{{1},{2,4},{3}} => [[1,4],[2],[3]] => [3,2,1,4] => [1,1,2]
{{1},{2},{3,4}} => [[1,4],[2],[3]] => [3,2,1,4] => [1,1,2]
{{1},{2},{3},{4}} => [[1],[2],[3],[4]] => [4,3,2,1] => [1,1,1,1]
{{1,2,3,4,5}} => [[1,2,3,4,5]] => [1,2,3,4,5] => [5]
{{1,2,3,4},{5}} => [[1,2,3,4],[5]] => [5,1,2,3,4] => [1,4]
{{1,2,3,5},{4}} => [[1,2,3,5],[4]] => [4,1,2,3,5] => [1,4]
{{1,2,3},{4,5}} => [[1,2,3],[4,5]] => [4,5,1,2,3] => [2,3]
{{1,2,3},{4},{5}} => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [1,1,3]
{{1,2,4,5},{3}} => [[1,2,4,5],[3]] => [3,1,2,4,5] => [1,4]
{{1,2,4},{3,5}} => [[1,2,4],[3,5]] => [3,5,1,2,4] => [2,3]
{{1,2,4},{3},{5}} => [[1,2,4],[3],[5]] => [5,3,1,2,4] => [1,1,3]
{{1,2,5},{3,4}} => [[1,2,5],[3,4]] => [3,4,1,2,5] => [2,3]
{{1,2},{3,4,5}} => [[1,2,5],[3,4]] => [3,4,1,2,5] => [2,3]
{{1,2},{3,4},{5}} => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [1,2,2]
{{1,2,5},{3},{4}} => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,1,3]
{{1,2},{3,5},{4}} => [[1,2],[3,5],[4]] => [4,3,5,1,2] => [1,2,2]
{{1,2},{3},{4,5}} => [[1,2],[3,5],[4]] => [4,3,5,1,2] => [1,2,2]
{{1,2},{3},{4},{5}} => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [1,1,1,2]
{{1,3,4,5},{2}} => [[1,3,4,5],[2]] => [2,1,3,4,5] => [1,4]
{{1,3,4},{2,5}} => [[1,3,4],[2,5]] => [2,5,1,3,4] => [2,3]
{{1,3,4},{2},{5}} => [[1,3,4],[2],[5]] => [5,2,1,3,4] => [1,1,3]
{{1,3,5},{2,4}} => [[1,3,5],[2,4]] => [2,4,1,3,5] => [2,3]
{{1,3},{2,4,5}} => [[1,3,5],[2,4]] => [2,4,1,3,5] => [2,3]
{{1,3},{2,4},{5}} => [[1,3],[2,4],[5]] => [5,2,4,1,3] => [1,2,2]
{{1,3,5},{2},{4}} => [[1,3,5],[2],[4]] => [4,2,1,3,5] => [1,1,3]
{{1,3},{2,5},{4}} => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,2,2]
{{1,3},{2},{4,5}} => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,2,2]
{{1,3},{2},{4},{5}} => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => [1,1,1,2]
{{1,4,5},{2,3}} => [[1,3,5],[2,4]] => [2,4,1,3,5] => [2,3]
{{1,4},{2,3,5}} => [[1,3,5],[2,4]] => [2,4,1,3,5] => [2,3]
{{1,4},{2,3},{5}} => [[1,3],[2,4],[5]] => [5,2,4,1,3] => [1,2,2]
{{1,5},{2,3,4}} => [[1,3,4],[2,5]] => [2,5,1,3,4] => [2,3]
{{1},{2,3,4,5}} => [[1,3,4,5],[2]] => [2,1,3,4,5] => [1,4]
{{1},{2,3,4},{5}} => [[1,3,4],[2],[5]] => [5,2,1,3,4] => [1,1,3]
{{1,5},{2,3},{4}} => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,2,2]
{{1},{2,3,5},{4}} => [[1,3,5],[2],[4]] => [4,2,1,3,5] => [1,1,3]
{{1},{2,3},{4,5}} => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [1,2,2]
{{1},{2,3},{4},{5}} => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => [1,1,1,2]
{{1,4,5},{2},{3}} => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,1,3]
{{1,4},{2,5},{3}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1,4},{2},{3,5}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1,4},{2},{3},{5}} => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => [1,1,1,2]
{{1,5},{2,4},{3}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1},{2,4,5},{3}} => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,1,3]
{{1},{2,4},{3,5}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1},{2,4},{3},{5}} => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => [1,1,1,2]
{{1,5},{2},{3,4}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1},{2,5},{3,4}} => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [1,2,2]
{{1},{2},{3,4,5}} => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,1,3]
{{1},{2},{3,4},{5}} => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => [1,1,1,2]
{{1,5},{2},{3},{4}} => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,2]
{{1},{2,5},{3},{4}} => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,2]
{{1},{2},{3,5},{4}} => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,2]
{{1},{2},{3},{4,5}} => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,1,1,2]
{{1},{2},{3},{4},{5}} => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [1,1,1,1,1]
{{1,2,3,4,5,6}} => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6]
{{1,2,3,4,5},{6}} => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [1,5]
{{1,2,3,4,6},{5}} => [[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [1,5]
{{1,2,3,4},{5,6}} => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [2,4]
{{1,2,3,4},{5},{6}} => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [1,1,4]
{{1,2,3,5,6},{4}} => [[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [1,5]
{{1,2,3,5},{4,6}} => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [2,4]
{{1,2,3,5},{4},{6}} => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [1,1,4]
{{1,2,3,6},{4,5}} => [[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [2,4]
{{1,2,3},{4,5,6}} => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,3]
{{1,2,3},{4,5},{6}} => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [1,2,3]
{{1,2,3,6},{4},{5}} => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [1,1,4]
{{1,2,3},{4,6},{5}} => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [1,2,3]
{{1,2,3},{4},{5,6}} => [[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [1,2,3]
{{1,2,3},{4},{5},{6}} => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [1,1,1,3]
{{1,2,4,5,6},{3}} => [[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [1,5]
{{1,2,4,5},{3,6}} => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [2,4]
{{1,2,4,5},{3},{6}} => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [1,1,4]
{{1,2,4,6},{3,5}} => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [2,4]
{{1,2,4},{3,5,6}} => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [3,3]
{{1,2,4},{3,5},{6}} => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [1,2,3]
{{1,2,4,6},{3},{5}} => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [1,1,4]
{{1,2,4},{3,6},{5}} => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [1,2,3]
{{1,2,4},{3},{5,6}} => [[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [1,2,3]
{{1,2,4},{3},{5},{6}} => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [1,1,1,3]
{{1,2,5,6},{3,4}} => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [2,4]
>>> Load all 1624 entries. <<<
{{1,2,5},{3,4,6}} => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [3,3]
{{1,2,5},{3,4},{6}} => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [1,2,3]
{{1,2,6},{3,4,5}} => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [3,3]
{{1,2},{3,4,5,6}} => [[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [2,4]
{{1,2},{3,4,5},{6}} => [[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [1,2,3]
{{1,2,6},{3,4},{5}} => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [1,2,3]
{{1,2},{3,4,6},{5}} => [[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [1,2,3]
{{1,2},{3,4},{5,6}} => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [2,2,2]
{{1,2},{3,4},{5},{6}} => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [1,1,2,2]
{{1,2,5,6},{3},{4}} => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [1,1,4]
{{1,2,5},{3,6},{4}} => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,2,3]
{{1,2,5},{3},{4,6}} => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [1,2,3]
{{1,2,5},{3},{4},{6}} => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [1,1,1,3]
{{1,2,6},{3,5},{4}} => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,2,3]
{{1,2},{3,5,6},{4}} => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,2,3]
{{1,2},{3,5},{4,6}} => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [2,2,2]
{{1,2},{3,5},{4},{6}} => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [1,1,2,2]
{{1,2,6},{3},{4,5}} => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,2,3]
{{1,2},{3,6},{4,5}} => [[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [2,2,2]
{{1,2},{3},{4,5,6}} => [[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [1,2,3]
{{1,2},{3},{4,5},{6}} => [[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [1,1,2,2]
{{1,2,6},{3},{4},{5}} => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [1,1,1,3]
{{1,2},{3,6},{4},{5}} => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [1,1,2,2]
{{1,2},{3},{4,6},{5}} => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [1,1,2,2]
{{1,2},{3},{4},{5,6}} => [[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [1,1,2,2]
{{1,2},{3},{4},{5},{6}} => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [1,1,1,1,2]
{{1,3,4,5,6},{2}} => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [1,5]
{{1,3,4,5},{2,6}} => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [2,4]
{{1,3,4,5},{2},{6}} => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [1,1,4]
{{1,3,4,6},{2,5}} => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [2,4]
{{1,3,4},{2,5,6}} => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [3,3]
{{1,3,4},{2,5},{6}} => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [1,2,3]
{{1,3,4,6},{2},{5}} => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [1,1,4]
{{1,3,4},{2,6},{5}} => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [1,2,3]
{{1,3,4},{2},{5,6}} => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [1,2,3]
{{1,3,4},{2},{5},{6}} => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [1,1,1,3]
{{1,3,5,6},{2,4}} => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,4]
{{1,3,5},{2,4,6}} => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [3,3]
{{1,3,5},{2,4},{6}} => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [1,2,3]
{{1,3,6},{2,4,5}} => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [3,3]
{{1,3},{2,4,5,6}} => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,4]
{{1,3},{2,4,5},{6}} => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [1,2,3]
{{1,3,6},{2,4},{5}} => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [1,2,3]
{{1,3},{2,4,6},{5}} => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [1,2,3]
{{1,3},{2,4},{5,6}} => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [2,2,2]
{{1,3},{2,4},{5},{6}} => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [1,1,2,2]
{{1,3,5,6},{2},{4}} => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [1,1,4]
{{1,3,5},{2,6},{4}} => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [1,2,3]
{{1,3,5},{2},{4,6}} => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [1,2,3]
{{1,3,5},{2},{4},{6}} => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [1,1,1,3]
{{1,3,6},{2,5},{4}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,3},{2,5,6},{4}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,3},{2,5},{4,6}} => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [2,2,2]
{{1,3},{2,5},{4},{6}} => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [1,1,2,2]
{{1,3,6},{2},{4,5}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,3},{2,6},{4,5}} => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [2,2,2]
{{1,3},{2},{4,5,6}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,3},{2},{4,5},{6}} => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [1,1,2,2]
{{1,3,6},{2},{4},{5}} => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [1,1,1,3]
{{1,3},{2,6},{4},{5}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1,3},{2},{4,6},{5}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1,3},{2},{4},{5,6}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1,3},{2},{4},{5},{6}} => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [1,1,1,1,2]
{{1,4,5,6},{2,3}} => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,4]
{{1,4,5},{2,3,6}} => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [3,3]
{{1,4,5},{2,3},{6}} => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [1,2,3]
{{1,4,6},{2,3,5}} => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [3,3]
{{1,4},{2,3,5,6}} => [[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [2,4]
{{1,4},{2,3,5},{6}} => [[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [1,2,3]
{{1,4,6},{2,3},{5}} => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [1,2,3]
{{1,4},{2,3,6},{5}} => [[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [1,2,3]
{{1,4},{2,3},{5,6}} => [[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [2,2,2]
{{1,4},{2,3},{5},{6}} => [[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [1,1,2,2]
{{1,5,6},{2,3,4}} => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [3,3]
{{1,5},{2,3,4,6}} => [[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [2,4]
{{1,5},{2,3,4},{6}} => [[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [1,2,3]
{{1,6},{2,3,4,5}} => [[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [2,4]
{{1},{2,3,4,5,6}} => [[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [1,5]
{{1},{2,3,4,5},{6}} => [[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [1,1,4]
{{1,6},{2,3,4},{5}} => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [1,2,3]
{{1},{2,3,4,6},{5}} => [[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [1,1,4]
{{1},{2,3,4},{5,6}} => [[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [1,2,3]
{{1},{2,3,4},{5},{6}} => [[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [1,1,1,3]
{{1,5,6},{2,3},{4}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,5},{2,3,6},{4}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1,5},{2,3},{4,6}} => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [2,2,2]
{{1,5},{2,3},{4},{6}} => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [1,1,2,2]
{{1,6},{2,3,5},{4}} => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [1,2,3]
{{1},{2,3,5,6},{4}} => [[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [1,1,4]
{{1},{2,3,5},{4,6}} => [[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [1,2,3]
{{1},{2,3,5},{4},{6}} => [[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [1,1,1,3]
{{1,6},{2,3},{4,5}} => [[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [2,2,2]
{{1},{2,3,6},{4,5}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1},{2,3},{4,5,6}} => [[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [1,2,3]
{{1},{2,3},{4,5},{6}} => [[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [1,1,2,2]
{{1,6},{2,3},{4},{5}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1},{2,3,6},{4},{5}} => [[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [1,1,1,3]
{{1},{2,3},{4,6},{5}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1},{2,3},{4},{5,6}} => [[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [1,1,2,2]
{{1},{2,3},{4},{5},{6}} => [[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [1,1,1,1,2]
{{1,4,5,6},{2},{3}} => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [1,1,4]
{{1,4,5},{2,6},{3}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1,4,5},{2},{3,6}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1,4,5},{2},{3},{6}} => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [1,1,1,3]
{{1,4,6},{2,5},{3}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,4},{2,5,6},{3}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,4},{2,5},{3,6}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1,4},{2,5},{3},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,4,6},{2},{3,5}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,4},{2,6},{3,5}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1,4},{2},{3,5,6}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,4},{2},{3,5},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,4,6},{2},{3},{5}} => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [1,1,1,3]
{{1,4},{2,6},{3},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1,4},{2},{3,6},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1,4},{2},{3},{5,6}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1,4},{2},{3},{5},{6}} => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [1,1,1,1,2]
{{1,5,6},{2,4},{3}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,5},{2,4,6},{3}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,5},{2,4},{3,6}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1,5},{2,4},{3},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,6},{2,4,5},{3}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1},{2,4,5,6},{3}} => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [1,1,4]
{{1},{2,4,5},{3,6}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1},{2,4,5},{3},{6}} => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [1,1,1,3]
{{1,6},{2,4},{3,5}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1},{2,4,6},{3,5}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1},{2,4},{3,5,6}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1},{2,4},{3,5},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,6},{2,4},{3},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2,4,6},{3},{5}} => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [1,1,1,3]
{{1},{2,4},{3,6},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2,4},{3},{5,6}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2,4},{3},{5},{6}} => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [1,1,1,1,2]
{{1,5,6},{2},{3,4}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,5},{2,6},{3,4}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1,5},{2},{3,4,6}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1,5},{2},{3,4},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,6},{2,5},{3,4}} => [[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [2,2,2]
{{1},{2,5,6},{3,4}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1},{2,5},{3,4,6}} => [[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [1,2,3]
{{1},{2,5},{3,4},{6}} => [[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [1,1,2,2]
{{1,6},{2},{3,4,5}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1},{2,6},{3,4,5}} => [[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [1,2,3]
{{1},{2},{3,4,5,6}} => [[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [1,1,4]
{{1},{2},{3,4,5},{6}} => [[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [1,1,1,3]
{{1,6},{2},{3,4},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2,6},{3,4},{5}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2},{3,4,6},{5}} => [[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [1,1,1,3]
{{1},{2},{3,4},{5,6}} => [[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [1,1,2,2]
{{1},{2},{3,4},{5},{6}} => [[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [1,1,1,1,2]
{{1,5,6},{2},{3},{4}} => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,3]
{{1,5},{2,6},{3},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1,5},{2},{3,6},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1,5},{2},{3},{4,6}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1,5},{2},{3},{4},{6}} => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [1,1,1,1,2]
{{1,6},{2,5},{3},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2,5,6},{3},{4}} => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,3]
{{1},{2,5},{3,6},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2,5},{3},{4,6}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2,5},{3},{4},{6}} => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [1,1,1,1,2]
{{1,6},{2},{3,5},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2,6},{3,5},{4}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2},{3,5,6},{4}} => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,3]
{{1},{2},{3,5},{4,6}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2},{3,5},{4},{6}} => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [1,1,1,1,2]
{{1,6},{2},{3},{4,5}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2,6},{3},{4,5}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2},{3,6},{4,5}} => [[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [1,1,2,2]
{{1},{2},{3},{4,5,6}} => [[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [1,1,1,3]
{{1},{2},{3},{4,5},{6}} => [[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [1,1,1,1,2]
{{1,6},{2},{3},{4},{5}} => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
{{1},{2,6},{3},{4},{5}} => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
{{1},{2},{3,6},{4},{5}} => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
{{1},{2},{3},{4,6},{5}} => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
{{1},{2},{3},{4},{5,6}} => [[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [1,1,1,1,2]
{{1},{2},{3},{4},{5},{6}} => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [1,1,1,1,1,1]
{{1,2,3,4,5,6,7}} => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => [7]
{{1,2,3,4,5,6},{7}} => [[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [1,6]
{{1,2,3,4,5,7},{6}} => [[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [1,6]
{{1,2,3,4,5},{6,7}} => [[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [2,5]
{{1,2,3,4,5},{6},{7}} => [[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [1,1,5]
{{1,2,3,4,6,7},{5}} => [[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [1,6]
{{1,2,3,4,6},{5,7}} => [[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [2,5]
{{1,2,3,4,6},{5},{7}} => [[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [1,1,5]
{{1,2,3,4,7},{5,6}} => [[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [2,5]
{{1,2,3,4},{5,6,7}} => [[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [3,4]
{{1,2,3,4},{5,6},{7}} => [[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [1,2,4]
{{1,2,3,4,7},{5},{6}} => [[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [1,1,5]
{{1,2,3,4},{5,7},{6}} => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4]
{{1,2,3,4},{5},{6,7}} => [[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [1,2,4]
{{1,2,3,4},{5},{6},{7}} => [[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [1,1,1,4]
{{1,2,3,5,6,7},{4}} => [[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [1,6]
{{1,2,3,5,6},{4,7}} => [[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [2,5]
{{1,2,3,5,6},{4},{7}} => [[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [1,1,5]
{{1,2,3,5,7},{4,6}} => [[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [2,5]
{{1,2,3,5},{4,6,7}} => [[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => [3,4]
{{1,2,3,5},{4,6},{7}} => [[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [1,2,4]
{{1,2,3,5,7},{4},{6}} => [[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [1,1,5]
{{1,2,3,5},{4,7},{6}} => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4]
{{1,2,3,5},{4},{6,7}} => [[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [1,2,4]
{{1,2,3,5},{4},{6},{7}} => [[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [1,1,1,4]
{{1,2,3,6,7},{4,5}} => [[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => [2,5]
{{1,2,3,6},{4,5,7}} => [[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => [3,4]
{{1,2,3,6},{4,5},{7}} => [[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => [1,2,4]
{{1,2,3,7},{4,5,6}} => [[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [3,4]
{{1,2,3},{4,5,6,7}} => [[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [3,4]
{{1,2,3},{4,5,6},{7}} => [[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [1,3,3]
{{1,2,3,7},{4,5},{6}} => [[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => [1,2,4]
{{1,2,3},{4,5,7},{6}} => [[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [1,3,3]
{{1,2,3},{4,5},{6,7}} => [[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [2,2,3]
{{1,2,3},{4,5},{6},{7}} => [[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [1,1,2,3]
{{1,2,3,6,7},{4},{5}} => [[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [1,1,5]
{{1,2,3,6},{4,7},{5}} => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4]
{{1,2,3,6},{4},{5,7}} => [[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [1,2,4]
{{1,2,3,6},{4},{5},{7}} => [[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [1,1,1,4]
{{1,2,3,7},{4,6},{5}} => [[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [1,2,4]
{{1,2,3},{4,6,7},{5}} => [[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [1,3,3]
{{1,2,3},{4,6},{5,7}} => [[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [2,2,3]
{{1,2,3},{4,6},{5},{7}} => [[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [1,1,2,3]
{{1,2,3,7},{4},{5,6}} => [[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [1,2,4]
{{1,2,3},{4,7},{5,6}} => [[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [2,2,3]
{{1,2,3},{4},{5,6,7}} => [[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [1,3,3]
{{1,2,3},{4},{5,6},{7}} => [[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [1,1,2,3]
{{1,2,3,7},{4},{5},{6}} => [[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [1,1,1,4]
{{1,2,3},{4,7},{5},{6}} => [[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [1,1,2,3]
{{1,2,3},{4},{5,7},{6}} => [[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [1,1,2,3]
{{1,2,3},{4},{5},{6,7}} => [[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [1,1,2,3]
{{1,2,3},{4},{5},{6},{7}} => [[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [1,1,1,1,3]
{{1,2,4,5,6,7},{3}} => [[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [1,6]
{{1,2,4,5,6},{3,7}} => [[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [2,5]
{{1,2,4,5,6},{3},{7}} => [[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [1,1,5]
{{1,2,4,5,7},{3,6}} => [[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [2,5]
{{1,2,4,5},{3,6,7}} => [[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => [3,4]
{{1,2,4,5},{3,6},{7}} => [[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [1,2,4]
{{1,2,4,5,7},{3},{6}} => [[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [1,1,5]
{{1,2,4,5},{3,7},{6}} => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4]
{{1,2,4,5},{3},{6,7}} => [[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [1,2,4]
{{1,2,4,5},{3},{6},{7}} => [[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [1,1,1,4]
{{1,2,4,6,7},{3,5}} => [[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [2,5]
{{1,2,4,6},{3,5,7}} => [[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [3,4]
{{1,2,4,6},{3,5},{7}} => [[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [1,2,4]
{{1,2,4,7},{3,5,6}} => [[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [3,4]
{{1,2,4},{3,5,6,7}} => [[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [3,4]
{{1,2,4},{3,5,6},{7}} => [[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [1,3,3]
{{1,2,4,7},{3,5},{6}} => [[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [1,2,4]
{{1,2,4},{3,5,7},{6}} => [[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [1,3,3]
{{1,2,4},{3,5},{6,7}} => [[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [2,2,3]
{{1,2,4},{3,5},{6},{7}} => [[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [1,1,2,3]
{{1,2,4,6,7},{3},{5}} => [[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [1,1,5]
{{1,2,4,6},{3,7},{5}} => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4]
{{1,2,4,6},{3},{5,7}} => [[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [1,2,4]
{{1,2,4,6},{3},{5},{7}} => [[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [1,1,1,4]
{{1,2,4,7},{3,6},{5}} => [[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [1,2,4]
{{1,2,4},{3,6,7},{5}} => [[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [1,3,3]
{{1,2,4},{3,6},{5,7}} => [[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [2,2,3]
{{1,2,4},{3,6},{5},{7}} => [[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [1,1,2,3]
{{1,2,4,7},{3},{5,6}} => [[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [1,2,4]
{{1,2,4},{3,7},{5,6}} => [[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [2,2,3]
{{1,2,4},{3},{5,6,7}} => [[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [1,3,3]
{{1,2,4},{3},{5,6},{7}} => [[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [1,1,2,3]
{{1,2,4,7},{3},{5},{6}} => [[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [1,1,1,4]
{{1,2,4},{3,7},{5},{6}} => [[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [1,1,2,3]
{{1,2,4},{3},{5,7},{6}} => [[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [1,1,2,3]
{{1,2,4},{3},{5},{6,7}} => [[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [1,1,2,3]
{{1,2,4},{3},{5},{6},{7}} => [[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [1,1,1,1,3]
{{1,2,5,6,7},{3,4}} => [[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [2,5]
{{1,2,5,6},{3,4,7}} => [[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [3,4]
{{1,2,5,6},{3,4},{7}} => [[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [1,2,4]
{{1,2,5,7},{3,4,6}} => [[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [3,4]
{{1,2,5},{3,4,6,7}} => [[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [3,4]
{{1,2,5},{3,4,6},{7}} => [[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [1,3,3]
{{1,2,5,7},{3,4},{6}} => [[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [1,2,4]
{{1,2,5},{3,4,7},{6}} => [[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [1,3,3]
{{1,2,5},{3,4},{6,7}} => [[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [2,2,3]
{{1,2,5},{3,4},{6},{7}} => [[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [1,1,2,3]
{{1,2,6,7},{3,4,5}} => [[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [3,4]
{{1,2,6},{3,4,5,7}} => [[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [3,4]
{{1,2,6},{3,4,5},{7}} => [[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [1,3,3]
{{1,2,7},{3,4,5,6}} => [[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [3,4]
{{1,2},{3,4,5,6,7}} => [[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [2,5]
{{1,2},{3,4,5,6},{7}} => [[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [1,2,4]
{{1,2,7},{3,4,5},{6}} => [[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [1,3,3]
{{1,2},{3,4,5,7},{6}} => [[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [1,2,4]
{{1,2},{3,4,5},{6,7}} => [[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [2,2,3]
{{1,2},{3,4,5},{6},{7}} => [[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [1,1,2,3]
{{1,2,6,7},{3,4},{5}} => [[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [1,2,4]
{{1,2,6},{3,4,7},{5}} => [[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [1,3,3]
{{1,2,6},{3,4},{5,7}} => [[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [2,2,3]
{{1,2,6},{3,4},{5},{7}} => [[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [1,1,2,3]
{{1,2,7},{3,4,6},{5}} => [[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [1,3,3]
{{1,2},{3,4,6,7},{5}} => [[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [1,2,4]
{{1,2},{3,4,6},{5,7}} => [[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [2,2,3]
{{1,2},{3,4,6},{5},{7}} => [[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [1,1,2,3]
{{1,2,7},{3,4},{5,6}} => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [2,2,3]
{{1,2},{3,4,7},{5,6}} => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [2,2,3]
{{1,2},{3,4},{5,6,7}} => [[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [2,2,3]
{{1,2},{3,4},{5,6},{7}} => [[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [1,2,2,2]
{{1,2,7},{3,4},{5},{6}} => [[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [1,1,2,3]
{{1,2},{3,4,7},{5},{6}} => [[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [1,1,2,3]
{{1,2},{3,4},{5,7},{6}} => [[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [1,2,2,2]
{{1,2},{3,4},{5},{6,7}} => [[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [1,2,2,2]
{{1,2},{3,4},{5},{6},{7}} => [[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [1,1,1,2,2]
{{1,2,5,6,7},{3},{4}} => [[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [1,1,5]
{{1,2,5,6},{3,7},{4}} => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4]
{{1,2,5,6},{3},{4,7}} => [[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [1,2,4]
{{1,2,5,6},{3},{4},{7}} => [[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [1,1,1,4]
{{1,2,5,7},{3,6},{4}} => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4]
{{1,2,5},{3,6,7},{4}} => [[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [1,3,3]
{{1,2,5},{3,6},{4,7}} => [[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [2,2,3]
{{1,2,5},{3,6},{4},{7}} => [[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,1,2,3]
{{1,2,5,7},{3},{4,6}} => [[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [1,2,4]
{{1,2,5},{3,7},{4,6}} => [[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [2,2,3]
{{1,2,5},{3},{4,6,7}} => [[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [1,3,3]
{{1,2,5},{3},{4,6},{7}} => [[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [1,1,2,3]
{{1,2,5,7},{3},{4},{6}} => [[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [1,1,1,4]
{{1,2,5},{3,7},{4},{6}} => [[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [1,1,2,3]
{{1,2,5},{3},{4,7},{6}} => [[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [1,1,2,3]
{{1,2,5},{3},{4},{6,7}} => [[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [1,1,2,3]
{{1,2,5},{3},{4},{6},{7}} => [[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [1,1,1,1,3]
{{1,2,6,7},{3,5},{4}} => [[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,2,4]
{{1,2,6},{3,5,7},{4}} => [[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,3,3]
{{1,2,6},{3,5},{4,7}} => [[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [2,2,3]
{{1,2,6},{3,5},{4},{7}} => [[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,1,2,3]
{{1,2,7},{3,5,6},{4}} => [[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,3,3]
{{1,2},{3,5,6,7},{4}} => [[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,2,4]
{{1,2},{3,5,6},{4,7}} => [[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [2,2,3]
{{1,2},{3,5,6},{4},{7}} => [[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,1,2,3]
{{1,2,7},{3,5},{4,6}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,5,7},{4,6}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,5},{4,6,7}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,5},{4,6},{7}} => [[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [1,2,2,2]
{{1,2,7},{3,5},{4},{6}} => [[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,1,2,3]
{{1,2},{3,5,7},{4},{6}} => [[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,1,2,3]
{{1,2},{3,5},{4,7},{6}} => [[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,2,2,2]
{{1,2},{3,5},{4},{6,7}} => [[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,2,2,2]
{{1,2},{3,5},{4},{6},{7}} => [[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [1,1,1,2,2]
{{1,2,6,7},{3},{4,5}} => [[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,2,4]
{{1,2,6},{3,7},{4,5}} => [[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [2,2,3]
{{1,2,6},{3},{4,5,7}} => [[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,3,3]
{{1,2,6},{3},{4,5},{7}} => [[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,1,2,3]
{{1,2,7},{3,6},{4,5}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,6,7},{4,5}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,6},{4,5,7}} => [[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [2,2,3]
{{1,2},{3,6},{4,5},{7}} => [[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [1,2,2,2]
{{1,2,7},{3},{4,5,6}} => [[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [1,3,3]
{{1,2},{3,7},{4,5,6}} => [[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [2,2,3]
{{1,2},{3},{4,5,6,7}} => [[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [1,2,4]
{{1,2},{3},{4,5,6},{7}} => [[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [1,1,2,3]
{{1,2,7},{3},{4,5},{6}} => [[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,1,2,3]
{{1,2},{3,7},{4,5},{6}} => [[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,2,2,2]
{{1,2},{3},{4,5,7},{6}} => [[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [1,1,2,3]
{{1,2},{3},{4,5},{6,7}} => [[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [1,2,2,2]
{{1,2},{3},{4,5},{6},{7}} => [[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [1,1,1,2,2]
{{1,2,6,7},{3},{4},{5}} => [[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [1,1,1,4]
{{1,2,6},{3,7},{4},{5}} => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3]
{{1,2,6},{3},{4,7},{5}} => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3]
{{1,2,6},{3},{4},{5,7}} => [[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [1,1,2,3]
{{1,2,6},{3},{4},{5},{7}} => [[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [1,1,1,1,3]
{{1,2,7},{3,6},{4},{5}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3,6,7},{4},{5}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3,6},{4,7},{5}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3,6},{4},{5,7}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3,6},{4},{5},{7}} => [[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [1,1,1,2,2]
{{1,2,7},{3},{4,6},{5}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3,7},{4,6},{5}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3},{4,6,7},{5}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3},{4,6},{5,7}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3},{4,6},{5},{7}} => [[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [1,1,1,2,2]
{{1,2,7},{3},{4},{5,6}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3,7},{4},{5,6}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3},{4,7},{5,6}} => [[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [1,2,2,2]
{{1,2},{3},{4},{5,6,7}} => [[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [1,1,2,3]
{{1,2},{3},{4},{5,6},{7}} => [[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [1,1,1,2,2]
{{1,2,7},{3},{4},{5},{6}} => [[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [1,1,1,1,3]
{{1,2},{3,7},{4},{5},{6}} => [[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,1,1,2,2]
{{1,2},{3},{4,7},{5},{6}} => [[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,1,1,2,2]
{{1,2},{3},{4},{5,7},{6}} => [[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,1,1,2,2]
{{1,2},{3},{4},{5},{6,7}} => [[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [1,1,1,2,2]
{{1,2},{3},{4},{5},{6},{7}} => [[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [1,1,1,1,1,2]
{{1,3,4,5,6,7},{2}} => [[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [1,6]
{{1,3,4,5,6},{2,7}} => [[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [2,5]
{{1,3,4,5,6},{2},{7}} => [[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [1,1,5]
{{1,3,4,5,7},{2,6}} => [[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [2,5]
{{1,3,4,5},{2,6,7}} => [[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [3,4]
{{1,3,4,5},{2,6},{7}} => [[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [1,2,4]
{{1,3,4,5,7},{2},{6}} => [[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [1,1,5]
{{1,3,4,5},{2,7},{6}} => [[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [1,2,4]
{{1,3,4,5},{2},{6,7}} => [[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [1,2,4]
{{1,3,4,5},{2},{6},{7}} => [[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [1,1,1,4]
{{1,3,4,6,7},{2,5}} => [[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [2,5]
{{1,3,4,6},{2,5,7}} => [[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [3,4]
{{1,3,4,6},{2,5},{7}} => [[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [1,2,4]
{{1,3,4,7},{2,5,6}} => [[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [3,4]
{{1,3,4},{2,5,6,7}} => [[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [3,4]
{{1,3,4},{2,5,6},{7}} => [[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [1,3,3]
{{1,3,4,7},{2,5},{6}} => [[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [1,2,4]
{{1,3,4},{2,5,7},{6}} => [[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [1,3,3]
{{1,3,4},{2,5},{6,7}} => [[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [2,2,3]
{{1,3,4},{2,5},{6},{7}} => [[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [1,1,2,3]
{{1,3,4,6,7},{2},{5}} => [[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [1,1,5]
{{1,3,4,6},{2,7},{5}} => [[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [1,2,4]
{{1,3,4,6},{2},{5,7}} => [[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [1,2,4]
{{1,3,4,6},{2},{5},{7}} => [[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [1,1,1,4]
{{1,3,4,7},{2,6},{5}} => [[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [1,2,4]
{{1,3,4},{2,6,7},{5}} => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,3,3]
{{1,3,4},{2,6},{5,7}} => [[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [2,2,3]
{{1,3,4},{2,6},{5},{7}} => [[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [1,1,2,3]
{{1,3,4,7},{2},{5,6}} => [[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [1,2,4]
{{1,3,4},{2,7},{5,6}} => [[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [2,2,3]
{{1,3,4},{2},{5,6,7}} => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,3,3]
{{1,3,4},{2},{5,6},{7}} => [[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [1,1,2,3]
{{1,3,4,7},{2},{5},{6}} => [[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [1,1,1,4]
{{1,3,4},{2,7},{5},{6}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1,3,4},{2},{5,7},{6}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1,3,4},{2},{5},{6,7}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1,3,4},{2},{5},{6},{7}} => [[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [1,1,1,1,3]
{{1,3,5,6,7},{2,4}} => [[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [2,5]
{{1,3,5,6},{2,4,7}} => [[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [3,4]
{{1,3,5,6},{2,4},{7}} => [[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [1,2,4]
{{1,3,5,7},{2,4,6}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,3,5},{2,4,6,7}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,3,5},{2,4,6},{7}} => [[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [1,3,3]
{{1,3,5,7},{2,4},{6}} => [[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [1,2,4]
{{1,3,5},{2,4,7},{6}} => [[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [1,3,3]
{{1,3,5},{2,4},{6,7}} => [[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [2,2,3]
{{1,3,5},{2,4},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [1,1,2,3]
{{1,3,6,7},{2,4,5}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,3,6},{2,4,5,7}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,3,6},{2,4,5},{7}} => [[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [1,3,3]
{{1,3,7},{2,4,5,6}} => [[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [3,4]
{{1,3},{2,4,5,6,7}} => [[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [2,5]
{{1,3},{2,4,5,6},{7}} => [[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [1,2,4]
{{1,3,7},{2,4,5},{6}} => [[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [1,3,3]
{{1,3},{2,4,5,7},{6}} => [[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [1,2,4]
{{1,3},{2,4,5},{6,7}} => [[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [2,2,3]
{{1,3},{2,4,5},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [1,1,2,3]
{{1,3,6,7},{2,4},{5}} => [[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [1,2,4]
{{1,3,6},{2,4,7},{5}} => [[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [1,3,3]
{{1,3,6},{2,4},{5,7}} => [[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [2,2,3]
{{1,3,6},{2,4},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [1,1,2,3]
{{1,3,7},{2,4,6},{5}} => [[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [1,3,3]
{{1,3},{2,4,6,7},{5}} => [[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [1,2,4]
{{1,3},{2,4,6},{5,7}} => [[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [2,2,3]
{{1,3},{2,4,6},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [1,1,2,3]
{{1,3,7},{2,4},{5,6}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,3},{2,4,7},{5,6}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,3},{2,4},{5,6,7}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,3},{2,4},{5,6},{7}} => [[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [1,2,2,2]
{{1,3,7},{2,4},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [1,1,2,3]
{{1,3},{2,4,7},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [1,1,2,3]
{{1,3},{2,4},{5,7},{6}} => [[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [1,2,2,2]
{{1,3},{2,4},{5},{6,7}} => [[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [1,2,2,2]
{{1,3},{2,4},{5},{6},{7}} => [[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [1,1,1,2,2]
{{1,3,5,6,7},{2},{4}} => [[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [1,1,5]
{{1,3,5,6},{2,7},{4}} => [[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [1,2,4]
{{1,3,5,6},{2},{4,7}} => [[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [1,2,4]
{{1,3,5,6},{2},{4},{7}} => [[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [1,1,1,4]
{{1,3,5,7},{2,6},{4}} => [[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [1,2,4]
{{1,3,5},{2,6,7},{4}} => [[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [1,3,3]
{{1,3,5},{2,6},{4,7}} => [[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [2,2,3]
{{1,3,5},{2,6},{4},{7}} => [[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [1,1,2,3]
{{1,3,5,7},{2},{4,6}} => [[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [1,2,4]
{{1,3,5},{2,7},{4,6}} => [[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [2,2,3]
{{1,3,5},{2},{4,6,7}} => [[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [1,3,3]
{{1,3,5},{2},{4,6},{7}} => [[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [1,1,2,3]
{{1,3,5,7},{2},{4},{6}} => [[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [1,1,1,4]
{{1,3,5},{2,7},{4},{6}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1,3,5},{2},{4,7},{6}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1,3,5},{2},{4},{6,7}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1,3,5},{2},{4},{6},{7}} => [[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [1,1,1,1,3]
{{1,3,6,7},{2,5},{4}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,3,6},{2,5,7},{4}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,3,6},{2,5},{4,7}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,3,6},{2,5},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,3,7},{2,5,6},{4}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,3},{2,5,6,7},{4}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,3},{2,5,6},{4,7}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,3},{2,5,6},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,3,7},{2,5},{4,6}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,5,7},{4,6}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,5},{4,6,7}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,5},{4,6},{7}} => [[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [1,2,2,2]
{{1,3,7},{2,5},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,3},{2,5,7},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,3},{2,5},{4,7},{6}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,3},{2,5},{4},{6,7}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,3},{2,5},{4},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [1,1,1,2,2]
{{1,3,6,7},{2},{4,5}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,3,6},{2,7},{4,5}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,3,6},{2},{4,5,7}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,3,6},{2},{4,5},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,3,7},{2,6},{4,5}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,6,7},{4,5}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,6},{4,5,7}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,3},{2,6},{4,5},{7}} => [[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [1,2,2,2]
{{1,3,7},{2},{4,5,6}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,3},{2,7},{4,5,6}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,3},{2},{4,5,6,7}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,3},{2},{4,5,6},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,3,7},{2},{4,5},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,3},{2,7},{4,5},{6}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,3},{2},{4,5,7},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,3},{2},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,3},{2},{4,5},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [1,1,1,2,2]
{{1,3,6,7},{2},{4},{5}} => [[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [1,1,1,4]
{{1,3,6},{2,7},{4},{5}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1,3,6},{2},{4,7},{5}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1,3,6},{2},{4},{5,7}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1,3,6},{2},{4},{5},{7}} => [[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [1,1,1,1,3]
{{1,3,7},{2,6},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2,6,7},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2,6},{4,7},{5}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2,6},{4},{5,7}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2,6},{4},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,3,7},{2},{4,6},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2,7},{4,6},{5}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2},{4,6,7},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2},{4,6},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,3,7},{2},{4},{5,6}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2,7},{4},{5,6}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,3},{2},{4},{5,6,7}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,3},{2},{4},{5,6},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,3,7},{2},{4},{5},{6}} => [[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [1,1,1,1,3]
{{1,3},{2,7},{4},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1,3},{2},{4,7},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1,3},{2},{4},{5,7},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1,3},{2},{4},{5},{6,7}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1,3},{2},{4},{5},{6},{7}} => [[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2]
{{1,4,5,6,7},{2,3}} => [[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [2,5]
{{1,4,5,6},{2,3,7}} => [[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [3,4]
{{1,4,5,6},{2,3},{7}} => [[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [1,2,4]
{{1,4,5,7},{2,3,6}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,4,5},{2,3,6,7}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,4,5},{2,3,6},{7}} => [[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [1,3,3]
{{1,4,5,7},{2,3},{6}} => [[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [1,2,4]
{{1,4,5},{2,3,7},{6}} => [[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [1,3,3]
{{1,4,5},{2,3},{6,7}} => [[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [2,2,3]
{{1,4,5},{2,3},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [1,1,2,3]
{{1,4,6,7},{2,3,5}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,4,6},{2,3,5,7}} => [[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [3,4]
{{1,4,6},{2,3,5},{7}} => [[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [1,3,3]
{{1,4,7},{2,3,5,6}} => [[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [3,4]
{{1,4},{2,3,5,6,7}} => [[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [2,5]
{{1,4},{2,3,5,6},{7}} => [[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [1,2,4]
{{1,4,7},{2,3,5},{6}} => [[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [1,3,3]
{{1,4},{2,3,5,7},{6}} => [[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [1,2,4]
{{1,4},{2,3,5},{6,7}} => [[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [2,2,3]
{{1,4},{2,3,5},{6},{7}} => [[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [1,1,2,3]
{{1,4,6,7},{2,3},{5}} => [[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [1,2,4]
{{1,4,6},{2,3,7},{5}} => [[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [1,3,3]
{{1,4,6},{2,3},{5,7}} => [[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [2,2,3]
{{1,4,6},{2,3},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [1,1,2,3]
{{1,4,7},{2,3,6},{5}} => [[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [1,3,3]
{{1,4},{2,3,6,7},{5}} => [[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [1,2,4]
{{1,4},{2,3,6},{5,7}} => [[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [2,2,3]
{{1,4},{2,3,6},{5},{7}} => [[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [1,1,2,3]
{{1,4,7},{2,3},{5,6}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,4},{2,3,7},{5,6}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,4},{2,3},{5,6,7}} => [[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [2,2,3]
{{1,4},{2,3},{5,6},{7}} => [[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [1,2,2,2]
{{1,4,7},{2,3},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [1,1,2,3]
{{1,4},{2,3,7},{5},{6}} => [[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [1,1,2,3]
{{1,4},{2,3},{5,7},{6}} => [[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [1,2,2,2]
{{1,4},{2,3},{5},{6,7}} => [[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [1,2,2,2]
{{1,4},{2,3},{5},{6},{7}} => [[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [1,1,1,2,2]
{{1,5,6,7},{2,3,4}} => [[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [3,4]
{{1,5,6},{2,3,4,7}} => [[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [3,4]
{{1,5,6},{2,3,4},{7}} => [[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [1,3,3]
{{1,5,7},{2,3,4,6}} => [[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [3,4]
{{1,5},{2,3,4,6,7}} => [[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [2,5]
{{1,5},{2,3,4,6},{7}} => [[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [1,2,4]
{{1,5,7},{2,3,4},{6}} => [[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [1,3,3]
{{1,5},{2,3,4,7},{6}} => [[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [1,2,4]
{{1,5},{2,3,4},{6,7}} => [[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [2,2,3]
{{1,5},{2,3,4},{6},{7}} => [[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [1,1,2,3]
{{1,6,7},{2,3,4,5}} => [[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [3,4]
{{1,6},{2,3,4,5,7}} => [[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [2,5]
{{1,6},{2,3,4,5},{7}} => [[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [1,2,4]
{{1,7},{2,3,4,5,6}} => [[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [2,5]
{{1},{2,3,4,5,6,7}} => [[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => [1,6]
{{1},{2,3,4,5,6},{7}} => [[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [1,1,5]
{{1,7},{2,3,4,5},{6}} => [[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [1,2,4]
{{1},{2,3,4,5,7},{6}} => [[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [1,1,5]
{{1},{2,3,4,5},{6,7}} => [[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [1,2,4]
{{1},{2,3,4,5},{6},{7}} => [[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [1,1,1,4]
{{1,6,7},{2,3,4},{5}} => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,3,3]
{{1,6},{2,3,4,7},{5}} => [[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [1,2,4]
{{1,6},{2,3,4},{5,7}} => [[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [2,2,3]
{{1,6},{2,3,4},{5},{7}} => [[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [1,1,2,3]
{{1,7},{2,3,4,6},{5}} => [[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [1,2,4]
{{1},{2,3,4,6,7},{5}} => [[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [1,1,5]
{{1},{2,3,4,6},{5,7}} => [[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [1,2,4]
{{1},{2,3,4,6},{5},{7}} => [[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [1,1,1,4]
{{1,7},{2,3,4},{5,6}} => [[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [2,2,3]
{{1},{2,3,4,7},{5,6}} => [[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [1,2,4]
{{1},{2,3,4},{5,6,7}} => [[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [1,3,3]
{{1},{2,3,4},{5,6},{7}} => [[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [1,1,2,3]
{{1,7},{2,3,4},{5},{6}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1},{2,3,4,7},{5},{6}} => [[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [1,1,1,4]
{{1},{2,3,4},{5,7},{6}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1},{2,3,4},{5},{6,7}} => [[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [1,1,2,3]
{{1},{2,3,4},{5},{6},{7}} => [[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [1,1,1,1,3]
{{1,5,6,7},{2,3},{4}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,5,6},{2,3,7},{4}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,5,6},{2,3},{4,7}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,5,6},{2,3},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,5,7},{2,3,6},{4}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1,5},{2,3,6,7},{4}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1,5},{2,3,6},{4,7}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1,5},{2,3,6},{4},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,5,7},{2,3},{4,6}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,5},{2,3,7},{4,6}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,5},{2,3},{4,6,7}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,5},{2,3},{4,6},{7}} => [[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [1,2,2,2]
{{1,5,7},{2,3},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,5},{2,3,7},{4},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1,5},{2,3},{4,7},{6}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,5},{2,3},{4},{6,7}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1,5},{2,3},{4},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [1,1,1,2,2]
{{1,6,7},{2,3,5},{4}} => [[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [1,3,3]
{{1,6},{2,3,5,7},{4}} => [[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [1,2,4]
{{1,6},{2,3,5},{4,7}} => [[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [2,2,3]
{{1,6},{2,3,5},{4},{7}} => [[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [1,1,2,3]
{{1,7},{2,3,5,6},{4}} => [[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [1,2,4]
{{1},{2,3,5,6,7},{4}} => [[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [1,1,5]
{{1},{2,3,5,6},{4,7}} => [[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [1,2,4]
{{1},{2,3,5,6},{4},{7}} => [[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [1,1,1,4]
{{1,7},{2,3,5},{4,6}} => [[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [2,2,3]
{{1},{2,3,5,7},{4,6}} => [[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [1,2,4]
{{1},{2,3,5},{4,6,7}} => [[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [1,3,3]
{{1},{2,3,5},{4,6},{7}} => [[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [1,1,2,3]
{{1,7},{2,3,5},{4},{6}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1},{2,3,5,7},{4},{6}} => [[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [1,1,1,4]
{{1},{2,3,5},{4,7},{6}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1},{2,3,5},{4},{6,7}} => [[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [1,1,2,3]
{{1},{2,3,5},{4},{6},{7}} => [[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [1,1,1,1,3]
{{1,6,7},{2,3},{4,5}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,6},{2,3,7},{4,5}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,6},{2,3},{4,5,7}} => [[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [2,2,3]
{{1,6},{2,3},{4,5},{7}} => [[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [1,2,2,2]
{{1,7},{2,3,6},{4,5}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1},{2,3,6,7},{4,5}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1},{2,3,6},{4,5,7}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1},{2,3,6},{4,5},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,7},{2,3},{4,5,6}} => [[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,2,3]
{{1},{2,3,7},{4,5,6}} => [[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [1,3,3]
{{1},{2,3},{4,5,6,7}} => [[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [1,2,4]
{{1},{2,3},{4,5,6},{7}} => [[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [1,1,2,3]
{{1,7},{2,3},{4,5},{6}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1},{2,3,7},{4,5},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1},{2,3},{4,5,7},{6}} => [[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [1,1,2,3]
{{1},{2,3},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [1,2,2,2]
{{1},{2,3},{4,5},{6},{7}} => [[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [1,1,1,2,2]
{{1,6,7},{2,3},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,6},{2,3,7},{4},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1,6},{2,3},{4,7},{5}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,6},{2,3},{4},{5,7}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1,6},{2,3},{4},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,7},{2,3,6},{4},{5}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1},{2,3,6,7},{4},{5}} => [[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [1,1,1,4]
{{1},{2,3,6},{4,7},{5}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1},{2,3,6},{4},{5,7}} => [[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [1,1,2,3]
{{1},{2,3,6},{4},{5},{7}} => [[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [1,1,1,1,3]
{{1,7},{2,3},{4,6},{5}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1},{2,3,7},{4,6},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1},{2,3},{4,6,7},{5}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1},{2,3},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1},{2,3},{4,6},{5},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,7},{2,3},{4},{5,6}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1},{2,3,7},{4},{5,6}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1},{2,3},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [1,2,2,2]
{{1},{2,3},{4},{5,6,7}} => [[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [1,1,2,3]
{{1},{2,3},{4},{5,6},{7}} => [[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [1,1,1,2,2]
{{1,7},{2,3},{4},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1},{2,3,7},{4},{5},{6}} => [[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [1,1,1,1,3]
{{1},{2,3},{4,7},{5},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1},{2,3},{4},{5,7},{6}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1},{2,3},{4},{5},{6,7}} => [[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [1,1,1,2,2]
{{1},{2,3},{4},{5},{6},{7}} => [[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [1,1,1,1,1,2]
{{1,4,5,6,7},{2},{3}} => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [1,1,5]
{{1,4,5,6},{2,7},{3}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1,4,5,6},{2},{3,7}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1,4,5,6},{2},{3},{7}} => [[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [1,1,1,4]
{{1,4,5,7},{2,6},{3}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1,4,5},{2,6,7},{3}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1,4,5},{2,6},{3,7}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1,4,5},{2,6},{3},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,4,5,7},{2},{3,6}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1,4,5},{2,7},{3,6}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1,4,5},{2},{3,6,7}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1,4,5},{2},{3,6},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,4,5,7},{2},{3},{6}} => [[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [1,1,1,4]
{{1,4,5},{2,7},{3},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1,4,5},{2},{3,7},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1,4,5},{2},{3},{6,7}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1,4,5},{2},{3},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [1,1,1,1,3]
{{1,4,6,7},{2,5},{3}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,4,6},{2,5,7},{3}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,4,6},{2,5},{3,7}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,4,6},{2,5},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,4,7},{2,5,6},{3}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,4},{2,5,6,7},{3}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,4},{2,5,6},{3,7}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,4},{2,5,6},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,4,7},{2,5},{3,6}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,5,7},{3,6}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,5},{3,6,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,5},{3,6},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,4,7},{2,5},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,4},{2,5,7},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,4},{2,5},{3,7},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,4},{2,5},{3},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,4},{2,5},{3},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,4,6,7},{2},{3,5}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,4,6},{2,7},{3,5}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,4,6},{2},{3,5,7}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,4,6},{2},{3,5},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,4,7},{2,6},{3,5}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,6,7},{3,5}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,6},{3,5,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,4},{2,6},{3,5},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,4,7},{2},{3,5,6}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,4},{2,7},{3,5,6}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,4},{2},{3,5,6,7}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,4},{2},{3,5,6},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,4,7},{2},{3,5},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,4},{2,7},{3,5},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,4},{2},{3,5,7},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,4},{2},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,4},{2},{3,5},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,4,6,7},{2},{3},{5}} => [[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [1,1,1,4]
{{1,4,6},{2,7},{3},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1,4,6},{2},{3,7},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1,4,6},{2},{3},{5,7}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1,4,6},{2},{3},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [1,1,1,1,3]
{{1,4,7},{2,6},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2,6,7},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2,6},{3,7},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2,6},{3},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2,6},{3},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,4,7},{2},{3,6},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2,7},{3,6},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2},{3,6,7},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2},{3,6},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,4,7},{2},{3},{5,6}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2,7},{3},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,4},{2},{3},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,4},{2},{3},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,4,7},{2},{3},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [1,1,1,1,3]
{{1,4},{2,7},{3},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1,4},{2},{3,7},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1,4},{2},{3},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1,4},{2},{3},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1,4},{2},{3},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2]
{{1,5,6,7},{2,4},{3}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,5,6},{2,4,7},{3}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,5,6},{2,4},{3,7}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,5,6},{2,4},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,5,7},{2,4,6},{3}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,5},{2,4,6,7},{3}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,5},{2,4,6},{3,7}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,5},{2,4,6},{3},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,5,7},{2,4},{3,6}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,4,7},{3,6}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,4},{3,6,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,4},{3,6},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,5,7},{2,4},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,5},{2,4,7},{3},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,5},{2,4},{3,7},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,5},{2,4},{3},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,5},{2,4},{3},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,6,7},{2,4,5},{3}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1,6},{2,4,5,7},{3}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1,6},{2,4,5},{3,7}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1,6},{2,4,5},{3},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,7},{2,4,5,6},{3}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1},{2,4,5,6,7},{3}} => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [1,1,5]
{{1},{2,4,5,6},{3,7}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1},{2,4,5,6},{3},{7}} => [[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [1,1,1,4]
{{1,7},{2,4,5},{3,6}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1},{2,4,5,7},{3,6}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1},{2,4,5},{3,6,7}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1},{2,4,5},{3,6},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,7},{2,4,5},{3},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2,4,5,7},{3},{6}} => [[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [1,1,1,4]
{{1},{2,4,5},{3,7},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2,4,5},{3},{6,7}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2,4,5},{3},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [1,1,1,1,3]
{{1,6,7},{2,4},{3,5}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,4,7},{3,5}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,4},{3,5,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,4},{3,5},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,7},{2,4,6},{3,5}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1},{2,4,6,7},{3,5}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1},{2,4,6},{3,5,7}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1},{2,4,6},{3,5},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,7},{2,4},{3,5,6}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1},{2,4,7},{3,5,6}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1},{2,4},{3,5,6,7}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1},{2,4},{3,5,6},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,7},{2,4},{3,5},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1},{2,4,7},{3,5},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1},{2,4},{3,5,7},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1},{2,4},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1},{2,4},{3,5},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,6,7},{2,4},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,6},{2,4,7},{3},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,6},{2,4},{3,7},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,6},{2,4},{3},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,6},{2,4},{3},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2,4,6},{3},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2,4,6,7},{3},{5}} => [[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [1,1,1,4]
{{1},{2,4,6},{3,7},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2,4,6},{3},{5,7}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2,4,6},{3},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [1,1,1,1,3]
{{1,7},{2,4},{3,6},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,4,7},{3,6},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,4},{3,6,7},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,4},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,4},{3,6},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2,4},{3},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,4,7},{3},{5,6}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,4},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,4},{3},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,4},{3},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2,4},{3},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2,4,7},{3},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [1,1,1,1,3]
{{1},{2,4},{3,7},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2,4},{3},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2,4},{3},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2,4},{3},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2]
{{1,5,6,7},{2},{3,4}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,5,6},{2,7},{3,4}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,5,6},{2},{3,4,7}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,5,6},{2},{3,4},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,5,7},{2,6},{3,4}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,6,7},{3,4}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,6},{3,4,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,5},{2,6},{3,4},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,5,7},{2},{3,4,6}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1,5},{2,7},{3,4,6}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1,5},{2},{3,4,6,7}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1,5},{2},{3,4,6},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,5,7},{2},{3,4},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,5},{2,7},{3,4},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,5},{2},{3,4,7},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1,5},{2},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1,5},{2},{3,4},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,6,7},{2,5},{3,4}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,5,7},{3,4}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,5},{3,4,7}} => [[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [2,2,3]
{{1,6},{2,5},{3,4},{7}} => [[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [1,2,2,2]
{{1,7},{2,5,6},{3,4}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1},{2,5,6,7},{3,4}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1},{2,5,6},{3,4,7}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1},{2,5,6},{3,4},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,7},{2,5},{3,4,6}} => [[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [2,2,3]
{{1},{2,5,7},{3,4,6}} => [[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [1,3,3]
{{1},{2,5},{3,4,6,7}} => [[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [1,2,4]
{{1},{2,5},{3,4,6},{7}} => [[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [1,1,2,3]
{{1,7},{2,5},{3,4},{6}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1},{2,5,7},{3,4},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1},{2,5},{3,4,7},{6}} => [[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [1,1,2,3]
{{1},{2,5},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [1,2,2,2]
{{1},{2,5},{3,4},{6},{7}} => [[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [1,1,1,2,2]
{{1,6,7},{2},{3,4,5}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1,6},{2,7},{3,4,5}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1,6},{2},{3,4,5,7}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1,6},{2},{3,4,5},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,7},{2,6},{3,4,5}} => [[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [2,2,3]
{{1},{2,6,7},{3,4,5}} => [[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [1,3,3]
{{1},{2,6},{3,4,5,7}} => [[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [1,2,4]
{{1},{2,6},{3,4,5},{7}} => [[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [1,1,2,3]
{{1,7},{2},{3,4,5,6}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1},{2,7},{3,4,5,6}} => [[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [1,2,4]
{{1},{2},{3,4,5,6,7}} => [[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [1,1,5]
{{1},{2},{3,4,5,6},{7}} => [[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [1,1,1,4]
{{1,7},{2},{3,4,5},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2,7},{3,4,5},{6}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2},{3,4,5,7},{6}} => [[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [1,1,1,4]
{{1},{2},{3,4,5},{6,7}} => [[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [1,1,2,3]
{{1},{2},{3,4,5},{6},{7}} => [[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [1,1,1,1,3]
{{1,6,7},{2},{3,4},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,6},{2,7},{3,4},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,6},{2},{3,4,7},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1,6},{2},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1,6},{2},{3,4},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2,6},{3,4},{5}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,6,7},{3,4},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,6},{3,4,7},{5}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2,6},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,6},{3,4},{5},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2},{3,4,6},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2,7},{3,4,6},{5}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2},{3,4,6,7},{5}} => [[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [1,1,1,4]
{{1},{2},{3,4,6},{5,7}} => [[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [1,1,2,3]
{{1},{2},{3,4,6},{5},{7}} => [[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [1,1,1,1,3]
{{1,7},{2},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2,7},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [1,2,2,2]
{{1},{2},{3,4,7},{5,6}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2},{3,4},{5,6,7}} => [[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [1,1,2,3]
{{1},{2},{3,4},{5,6},{7}} => [[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [1,1,1,2,2]
{{1,7},{2},{3,4},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2,7},{3,4},{5},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2},{3,4,7},{5},{6}} => [[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [1,1,1,1,3]
{{1},{2},{3,4},{5,7},{6}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2},{3,4},{5},{6,7}} => [[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [1,1,1,2,2]
{{1},{2},{3,4},{5},{6},{7}} => [[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [1,1,1,1,1,2]
{{1,5,6,7},{2},{3},{4}} => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,4]
{{1,5,6},{2,7},{3},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1,5,6},{2},{3,7},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1,5,6},{2},{3},{4,7}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1,5,6},{2},{3},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [1,1,1,1,3]
{{1,5,7},{2,6},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2,6,7},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2,6},{3,7},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2,6},{3},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2,6},{3},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,5,7},{2},{3,6},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2,7},{3,6},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2},{3,6,7},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2},{3,6},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,5,7},{2},{3},{4,6}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2,7},{3},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,5},{2},{3},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,5},{2},{3},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,5,7},{2},{3},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [1,1,1,1,3]
{{1,5},{2,7},{3},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1,5},{2},{3,7},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1,5},{2},{3},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1,5},{2},{3},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1,5},{2},{3},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2]
{{1,6,7},{2,5},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2,5,7},{3},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2,5},{3,7},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2,5},{3},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2,5},{3},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2,5,6},{3},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2,5,6,7},{3},{4}} => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,4]
{{1},{2,5,6},{3,7},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2,5,6},{3},{4,7}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2,5,6},{3},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [1,1,1,1,3]
{{1,7},{2,5},{3,6},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,5,7},{3,6},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,5},{3,6,7},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,5},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,5},{3,6},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2,5},{3},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,5,7},{3},{4,6}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,5},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,5},{3},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,5},{3},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2,5},{3},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,5,7},{3},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [1,1,1,1,3]
{{1},{2,5},{3,7},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,5},{3},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,5},{3},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,5},{3},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2]
{{1,6,7},{2},{3,5},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2,7},{3,5},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2},{3,5,7},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2},{3,5},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2,6},{3,5},{4}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,6,7},{3,5},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,6},{3,5,7},{4}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,6},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,6},{3,5},{4},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2},{3,5,6},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2,7},{3,5,6},{4}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2},{3,5,6,7},{4}} => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,4]
{{1},{2},{3,5,6},{4,7}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2},{3,5,6},{4},{7}} => [[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [1,1,1,1,3]
{{1,7},{2},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,7},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2},{3,5,7},{4,6}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2},{3,5},{4,6,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2},{3,5},{4,6},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2},{3,5},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,7},{3,5},{4},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3,5,7},{4},{6}} => [[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [1,1,1,1,3]
{{1},{2},{3,5},{4,7},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3,5},{4},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3,5},{4},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2]
{{1,6,7},{2},{3},{4,5}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2,7},{3},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1,6},{2},{3},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1,6},{2},{3},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2,6},{3},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,6,7},{3},{4,5}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,6},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,6},{3},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2,6},{3},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2,7},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [1,2,2,2]
{{1},{2},{3,6,7},{4,5}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2},{3,6},{4,5,7}} => [[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [1,1,2,3]
{{1},{2},{3,6},{4,5},{7}} => [[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [1,1,1,2,2]
{{1,7},{2},{3},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2,7},{3},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2},{3,7},{4,5,6}} => [[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [1,1,2,3]
{{1},{2},{3},{4,5,6,7}} => [[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [1,1,1,4]
{{1},{2},{3},{4,5,6},{7}} => [[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [1,1,1,1,3]
{{1,7},{2},{3},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2,7},{3},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3,7},{4,5},{6}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3},{4,5,7},{6}} => [[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [1,1,1,1,3]
{{1},{2},{3},{4,5},{6,7}} => [[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [1,1,1,2,2]
{{1},{2},{3},{4,5},{6},{7}} => [[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [1,1,1,1,1,2]
{{1,6,7},{2},{3},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
{{1,6},{2,7},{3},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1,6},{2},{3,7},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1,6},{2},{3},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1,6},{2},{3},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1,6},{2},{3},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
{{1,7},{2,6},{3},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,6,7},{3},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
{{1},{2,6},{3,7},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,6},{3},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,6},{3},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,6},{3},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
{{1,7},{2},{3,6},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,7},{3,6},{4},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3,6,7},{4},{5}} => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
{{1},{2},{3,6},{4,7},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3,6},{4},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3,6},{4},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
{{1,7},{2},{3},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,7},{3},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3,7},{4,6},{5}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3},{4,6,7},{5}} => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
{{1},{2},{3},{4,6},{5,7}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3},{4,6},{5},{7}} => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2,7},{3},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3,7},{4},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3},{4,7},{5,6}} => [[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [1,1,1,2,2]
{{1},{2},{3},{4},{5,6,7}} => [[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [1,1,1,1,3]
{{1},{2},{3},{4},{5,6},{7}} => [[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [1,1,1,1,1,2]
{{1,7},{2},{3},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2,7},{3},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2},{3,7},{4},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2},{3},{4,7},{5},{6}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2},{3},{4},{5,7},{6}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6,7}} => [[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [1,1,1,1,1,2]
{{1},{2},{3},{4},{5},{6},{7}} => [[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1]
{{1,2},{3,4},{5,6},{7,8}} => [[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [2,2,2,2]
{{1,3},{2,4},{5,6},{7,8}} => [[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [2,2,2,2]
{{1,4},{2,3},{5,6},{7,8}} => [[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [2,2,2,2]
{{1,5},{2,3},{4,6},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => [2,2,2,2]
{{1,6},{2,3},{4,5},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => [2,2,2,2]
{{1,7},{2,3},{4,5},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,8},{2,3},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,8},{2,4},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,7},{2,4},{3,5},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,6},{2,4},{3,5},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,5},{2,4},{3,6},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,4},{2,5},{3,6},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,3},{2,5},{4,6},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => [2,2,2,2]
{{1,2},{3,5},{4,6},{7,8}} => [[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [2,2,2,2]
{{1,2},{3,6},{4,5},{7,8}} => [[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [2,2,2,2]
{{1,3},{2,6},{4,5},{7,8}} => [[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => [2,2,2,2]
{{1,4},{2,6},{3,5},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,5},{2,6},{3,4},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,6},{2,5},{3,4},{7,8}} => [[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [2,2,2,2]
{{1,7},{2,5},{3,4},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,8},{2,5},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,8},{2,6},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,7},{2,6},{3,4},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,6},{2,7},{3,4},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,5},{2,7},{3,4},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,4},{2,7},{3,5},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,3},{2,7},{4,5},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,2},{3,7},{4,5},{6,8}} => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [2,2,2,2]
{{1,2},{3,8},{4,5},{6,7}} => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [2,2,2,2]
{{1,3},{2,8},{4,5},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,4},{2,8},{3,5},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,5},{2,8},{3,4},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,6},{2,8},{3,4},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,7},{2,8},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,8},{2,7},{3,4},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,8},{2,7},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,8},{3,5},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,8},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,5},{2,8},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,4},{2,8},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,3},{2,8},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,2},{3,8},{4,6},{5,7}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,2},{3,7},{4,6},{5,8}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,3},{2,7},{4,6},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,4},{2,7},{3,6},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,5},{2,7},{3,6},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,7},{3,5},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,6},{3,5},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,8},{2,6},{3,5},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,8},{2,5},{3,6},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,5},{3,6},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,5},{3,7},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,5},{2,6},{3,7},{4,8}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,4},{2,6},{3,7},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,3},{2,6},{4,7},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,2},{3,6},{4,7},{5,8}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,2},{3,5},{4,7},{6,8}} => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [2,2,2,2]
{{1,3},{2,5},{4,7},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,4},{2,5},{3,7},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,5},{2,4},{3,7},{6,8}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,6},{2,4},{3,7},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,7},{2,4},{3,6},{5,8}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,8},{2,4},{3,6},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,8},{2,3},{4,6},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,7},{2,3},{4,6},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,6},{2,3},{4,7},{5,8}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,5},{2,3},{4,7},{6,8}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,4},{2,3},{5,7},{6,8}} => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [2,2,2,2]
{{1,3},{2,4},{5,7},{6,8}} => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [2,2,2,2]
{{1,2},{3,4},{5,7},{6,8}} => [[1,2],[3,4],[5,7],[6,8]] => [6,8,5,7,3,4,1,2] => [2,2,2,2]
{{1,2},{3,4},{5,8},{6,7}} => [[1,2],[3,4],[5,7],[6,8]] => [6,8,5,7,3,4,1,2] => [2,2,2,2]
{{1,3},{2,4},{5,8},{6,7}} => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [2,2,2,2]
{{1,4},{2,3},{5,8},{6,7}} => [[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [2,2,2,2]
{{1,5},{2,3},{4,8},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,6},{2,3},{4,8},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,7},{2,3},{4,8},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,8},{2,3},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,8},{2,4},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,7},{2,4},{3,8},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,6},{2,4},{3,8},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,5},{2,4},{3,8},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,4},{2,5},{3,8},{6,7}} => [[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [2,2,2,2]
{{1,3},{2,5},{4,8},{6,7}} => [[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => [2,2,2,2]
{{1,2},{3,5},{4,8},{6,7}} => [[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [2,2,2,2]
{{1,2},{3,6},{4,8},{5,7}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,3},{2,6},{4,8},{5,7}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,4},{2,6},{3,8},{5,7}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,5},{2,6},{3,8},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,5},{3,8},{4,7}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,5},{3,8},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,8},{2,5},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,8},{2,6},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,6},{3,8},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,7},{3,8},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,5},{2,7},{3,8},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,4},{2,7},{3,8},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,3},{2,7},{4,8},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,2},{3,7},{4,8},{5,6}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,2},{3,8},{4,7},{5,6}} => [[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [2,2,2,2]
{{1,3},{2,8},{4,7},{5,6}} => [[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [2,2,2,2]
{{1,4},{2,8},{3,7},{5,6}} => [[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [2,2,2,2]
{{1,5},{2,8},{3,7},{4,6}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,6},{2,8},{3,7},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,7},{2,8},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1,8},{2,7},{3,6},{4,5}} => [[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [2,2,2,2]
{{1},{2,3},{4,5,6,8},{7}} => [[1,3,6,8],[2,5],[4],[7]] => [7,4,2,5,1,3,6,8] => [1,1,2,4]
{{1},{2,4,6,8},{3},{5},{7}} => [[1,4,6,8],[2],[3],[5],[7]] => [7,5,3,2,1,4,6,8] => [1,1,1,1,4]
{{1},{2,4,8},{3},{5,7},{6}} => [[1,4,8],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4,8] => [1,1,1,2,3]
{{1},{2,8},{3,4},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1},{2,3,5},{4},{6,7,8}} => [[1,3,5],[2,7,8],[4],[6]] => [6,4,2,7,8,1,3,5] => [1,1,3,3]
{{1},{2,8},{3,7},{4,6},{5}} => [[1,6],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6] => [1,1,2,2,2]
{{1,2},{3,4},{5,6,8},{7}} => [[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => [1,2,2,3]
{{1,2},{3,6,7,8},{4},{5}} => [[1,2,7,8],[3,6],[4],[5]] => [5,4,3,6,1,2,7,8] => [1,1,2,4]
{{1,2},{3,5,6},{4},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,2,2,3]
{{1,2},{3,7,8},{4},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,2},{3,5,8},{4},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,2},{3,5,6,8},{4},{7}} => [[1,2,6,8],[3,5],[4],[7]] => [7,4,3,5,1,2,6,8] => [1,1,2,4]
{{1,2},{3,6,8},{4,5},{7}} => [[1,2,8],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2,8] => [1,2,2,3]
{{1,2},{3,4,6},{5},{7,8}} => [[1,2,6],[3,4],[5,8],[7]] => [7,5,8,3,4,1,2,6] => [1,2,2,3]
{{1,2},{3,7,8},{4,6},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,2},{3,8},{4,6,7},{5}} => [[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,2,2,3]
{{1,2},{3,4,6,8},{5},{7}} => [[1,2,6,8],[3,4],[5],[7]] => [7,5,3,4,1,2,6,8] => [1,1,2,4]
{{1,2},{3,8},{4,5,7},{6}} => [[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [1,2,2,3]
{{1,3},{2},{4,6,8},{5},{7}} => [[1,3,8],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3,8] => [1,1,1,2,3]
{{1,3},{2},{4,8},{5,7},{6}} => [[1,3],[2,7],[4,8],[5],[6]] => [6,5,4,8,2,7,1,3] => [1,1,2,2,2]
{{1,3},{2},{4,5,6,8},{7}} => [[1,3,6,8],[2,5],[4],[7]] => [7,4,2,5,1,3,6,8] => [1,1,2,4]
{{1,5,6,7,8},{2},{3},{4}} => [[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => [1,1,1,5]
{{1,6,7,8},{2},{3},{4,5}} => [[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
{{1,4,5,6},{2},{3},{7,8}} => [[1,4,5,6],[2,8],[3],[7]] => [7,3,2,8,1,4,5,6] => [1,1,2,4]
{{1,4,7,8},{2},{3},{5,6}} => [[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => [1,1,2,4]
{{1,4,5,8},{2},{3},{6,7}} => [[1,4,5,8],[2,7],[3],[6]] => [6,3,2,7,1,4,5,8] => [1,1,2,4]
{{1,3,4},{2},{5,6},{7,8}} => [[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [1,2,2,3]
{{1,3,4},{2},{5,7,8},{6}} => [[1,3,4],[2,7,8],[5],[6]] => [6,5,2,7,8,1,3,4] => [1,1,3,3]
{{1,3,4},{2},{5,8},{6,7}} => [[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [1,2,2,3]
{{1,5,6},{2},{3,4},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,2,2,3]
{{1,7,8},{2},{3,4},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,5,8},{2},{3,4},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,3,5},{2},{4},{6,7,8}} => [[1,3,5],[2,7,8],[4],[6]] => [6,4,2,7,8,1,3,5] => [1,1,3,3]
{{1,6,7,8},{2},{3,5},{4}} => [[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
{{1,7,8},{2},{3,5,6},{4}} => [[1,5,6],[2,7,8],[3],[4]] => [4,3,2,7,8,1,5,6] => [1,1,3,3]
{{1,3,5,7},{2},{4},{6},{8}} => [[1,3,5,7],[2],[4],[6],[8]] => [8,6,4,2,1,3,5,7] => [1,1,1,1,4]
{{1,3,6},{2},{4,5},{7,8}} => [[1,3,6],[2,5],[4,8],[7]] => [7,4,8,2,5,1,3,6] => [1,2,2,3]
{{1,7,8},{2},{3,6},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,3,8},{2},{4,5},{6,7}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,3,7},{2},{4,6},{5},{8}} => [[1,3,7],[2,6],[4],[5],[8]] => [8,5,4,2,6,1,3,7] => [1,1,1,2,3]
{{1,3,8},{2},{4,6,7},{5}} => [[1,3,7],[2,6,8],[4],[5]] => [5,4,2,6,8,1,3,7] => [1,1,3,3]
{{1,3,8},{2},{4,7},{5,6}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,4},{2,3},{5,7,8},{6}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1,4},{2,3},{5,6,8},{7}} => [[1,3,8],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3,8] => [1,2,2,3]
{{1,8},{2,3},{4},{5,6,7}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,6,8},{2,3},{4,5},{7}} => [[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [1,2,2,3]
{{1,4,6},{2,3},{5},{7,8}} => [[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [1,2,2,3]
{{1,8},{2,3},{4,6,7},{5}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,4,8},{2,3},{5},{6,7}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1,4,6,8},{2,3},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [1,1,2,4]
{{1,8},{2,3},{4,5,7},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,4,8},{2,3},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1,2,4},{3},{5,6},{7,8}} => [[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [1,2,2,3]
{{1,2,4},{3},{5,8},{6,7}} => [[1,2,4],[3,7],[5,8],[6]] => [6,5,8,3,7,1,2,4] => [1,2,2,3]
{{1,2,4},{3},{5,6,8},{7}} => [[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [1,1,3,3]
{{1,5},{2,4},{3},{6,8},{7}} => [[1,4],[2,5],[3,8],[6],[7]] => [7,6,3,8,2,5,1,4] => [1,1,2,2,2]
{{1,5,6},{2,4},{3},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,2,2,3]
{{1,7,8},{2,4},{3},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,5,8},{2,4},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,6,7,8},{2,5},{3},{4}} => [[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
{{1,7,8},{2,5,6},{3},{4}} => [[1,5,6],[2,7,8],[3],[4]] => [4,3,2,7,8,1,5,6] => [1,1,3,3]
{{1,8},{2,5,6,7},{3},{4}} => [[1,5,6,7],[2,8],[3],[4]] => [4,3,2,8,1,5,6,7] => [1,1,2,4]
{{1,6},{2,4,5},{3},{7,8}} => [[1,4,5],[2,6],[3,8],[7]] => [7,3,8,2,6,1,4,5] => [1,2,2,3]
{{1,8},{2,4,5},{3},{6,7}} => [[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [1,2,2,3]
{{1,2,6},{3},{4,5},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,2,2,3]
{{1,7,8},{2,6},{3},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,8},{2,6,7},{3},{4,5}} => [[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [1,2,2,3]
{{1,2,8},{3},{4,5},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,2,6,8},{3},{4,5},{7}} => [[1,2,6,8],[3,5],[4],[7]] => [7,4,3,5,1,2,6,8] => [1,1,2,4]
{{1,2,4,6},{3},{5},{7,8}} => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4]
{{1,7},{2,4,6},{3},{5},{8}} => [[1,4,6],[2,7],[3],[5],[8]] => [8,5,3,2,7,1,4,6] => [1,1,1,2,3]
{{1,2,4,8},{3},{5},{6,7}} => [[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [1,1,2,4]
{{1,2,4,6,8},{3},{5},{7}} => [[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [1,1,1,5]
{{1,8},{2,4,7},{3},{5,6}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,2,8},{3},{4,7},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,2,8},{3},{4,5,7},{6}} => [[1,2,7],[3,5,8],[4],[6]] => [6,4,3,5,8,1,2,7] => [1,1,3,3]
{{1,2,4,8},{3},{5,7},{6}} => [[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [1,1,2,4]
{{1,6,8},{2,5},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,8},{2,5,7},{3,4},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,6},{2,3,5},{4},{7,8}} => [[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [1,2,2,3]
{{1,8},{2,3,5},{4},{6,7}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,6,8},{2,3,5},{4},{7}} => [[1,3,5],[2,6,8],[4],[7]] => [7,4,2,6,8,1,3,5] => [1,1,3,3]
{{1,2,6},{3,5},{4},{7,8}} => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,2,2,3]
{{1,7},{2,6},{3,5},{4},{8}} => [[1,5],[2,6],[3,7],[4],[8]] => [8,4,3,7,2,6,1,5] => [1,1,2,2,2]
{{1,7,8},{2,6},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,8},{2,6,7},{3,5},{4}} => [[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [1,2,2,3]
{{1,2,8},{3,5},{4},{6,7}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,2,6,8},{3,5},{4},{7}} => [[1,2,6,8],[3,5],[4],[7]] => [7,4,3,5,1,2,6,8] => [1,1,2,4]
{{1,8},{2,7},{3,5,6},{4}} => [[1,5,6],[2,7],[3,8],[4]] => [4,3,8,2,7,1,5,6] => [1,2,2,3]
{{1,8},{2,3,7},{4},{5,6}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,2,8},{3,7},{4},{5,6}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,8},{2,3,5,7},{4},{6}} => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,2,4]
{{1,2,8},{3,5,7},{4},{6}} => [[1,2,7],[3,5,8],[4],[6]] => [6,4,3,5,8,1,2,7] => [1,1,3,3]
{{1,8},{2,3,7},{4,5},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,8},{2,7},{3,4,6},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,8},{2,3,7},{4,6},{5}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,2,8},{3,7},{4,6},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,5,7,8},{2,6},{3},{4}} => [[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
{{1,5,6,8},{2,7},{3},{4}} => [[1,5,6,8],[2,7],[3],[4]] => [4,3,2,7,1,5,6,8] => [1,1,2,4]
{{1,2,4,8},{3,7},{5},{6}} => [[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [1,1,2,4]
{{1,3,6,8},{2,4},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [1,1,2,4]
{{1,2,5,8},{3,6},{4},{7}} => [[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => [1,1,2,4]
{{1,3,4,8},{2,6},{5},{7}} => [[1,3,4,8],[2,6],[5],[7]] => [7,5,2,6,1,3,4,8] => [1,1,2,4]
{{1,2,4,8},{3,6},{5},{7}} => [[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [1,1,2,4]
{{1,4,6,7},{2,8},{3},{5}} => [[1,4,6,7],[2,8],[3],[5]] => [5,3,2,8,1,4,6,7] => [1,1,2,4]
{{1,3,5,7},{2,8},{4},{6}} => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,2,4]
{{1,3,4,7},{2,8},{5},{6}} => [[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => [1,1,2,4]
{{1,2,4,7},{3,8},{5},{6}} => [[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [1,1,2,4]
{{1,2,5,6},{3,8},{4},{7}} => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4]
{{1,3,5,7},{2,6},{4},{8}} => [[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => [1,1,2,4]
{{1,3,5,7},{2,4},{6},{8}} => [[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => [1,1,2,4]
{{1,4,7},{2,6,8},{3},{5}} => [[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => [1,1,3,3]
{{1,3,7},{2,4,8},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [1,1,3,3]
{{1,3,6},{2,7,8},{4},{5}} => [[1,3,6],[2,7,8],[4],[5]] => [5,4,2,7,8,1,3,6] => [1,1,3,3]
{{1,2,4},{3,7,8},{5},{6}} => [[1,2,4],[3,7,8],[5],[6]] => [6,5,3,7,8,1,2,4] => [1,1,3,3]
{{1,2,6},{3,5,8},{4},{7}} => [[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => [1,1,3,3]
{{1,3,6},{2,4,8},{5},{7}} => [[1,3,6],[2,4,8],[5],[7]] => [7,5,2,4,8,1,3,6] => [1,1,3,3]
{{1,3,5},{2,6,8},{4},{7}} => [[1,3,5],[2,6,8],[4],[7]] => [7,4,2,6,8,1,3,5] => [1,1,3,3]
{{1,3,4},{2,6,8},{5},{7}} => [[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => [1,1,3,3]
{{1,2,4},{3,6,8},{5},{7}} => [[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [1,1,3,3]
{{1,4,8},{2,6},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,3,8},{2,6},{4,7},{5}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,2,8},{3,6},{4,7},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,4,8},{2,5},{3,7},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,3,8},{2,5},{4,7},{6}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,2,8},{3,5},{4,7},{6}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,4,8},{2,5},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,4,7},{2,6},{3,8},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,3,7},{2,6},{4,8},{5}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,2,7},{3,6},{4,8},{5}} => [[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,2,2,3]
{{1,4,7},{2,5},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,3,7},{2,5},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,2,7},{3,5},{4,8},{6}} => [[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [1,2,2,3]
{{1,4,6},{2,7},{3,8},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,3,6},{2,7},{4,8},{5}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,2,6},{3,7},{4,8},{5}} => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,2,2,3]
{{1,3,5},{2,7},{4,8},{6}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,2,5},{3,7},{4,8},{6}} => [[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [1,2,2,3]
{{1,3,6},{2,5},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => [7,4,8,2,5,1,3,6] => [1,2,2,3]
{{1,2,6},{3,5},{4,8},{7}} => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,2,2,3]
{{1,3,5},{2,6},{4,8},{7}} => [[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [1,2,2,3]
{{1,2,5},{3,6},{4,8},{7}} => [[1,2,5],[3,6],[4,8],[7]] => [7,4,8,3,6,1,2,5] => [1,2,2,3]
{{1,3,4},{2,6},{5,8},{7}} => [[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [1,2,2,3]
{{1,2,4},{3,6},{5,8},{7}} => [[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [1,2,2,3]
{{1,3,5},{2,4},{6,8},{7}} => [[1,3,5],[2,4],[6,8],[7]] => [7,6,8,2,4,1,3,5] => [1,2,2,3]
{{1,4,7},{2,5},{3,6},{8}} => [[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [1,2,2,3]
{{1,3,7},{2,5},{4,6},{8}} => [[1,3,7],[2,5],[4,6],[8]] => [8,4,6,2,5,1,3,7] => [1,2,2,3]
{{1,3,5,8},{2},{4,6},{7}} => [[1,3,5,8],[2,6],[4],[7]] => [7,4,2,6,1,3,5,8] => [1,1,2,4]
{{1,3,5,7},{2},{4},{6,8}} => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,2,4]
{{1,5,7},{2,4},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,5},{2,4,8},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,5,8},{2,4},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,6,8},{2,4},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1},{2,3,5,8},{4,6},{7}} => [[1,3,5,8],[2,6],[4],[7]] => [7,4,2,6,1,3,5,8] => [1,1,2,4]
{{1,5,8},{2,6},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,4,8},{2,6},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,4},{2,5,8},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,4,7},{2,5},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,4},{2},{3,6,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,4},{2},{3,6},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,4},{2},{3,7},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,4},{2},{3,5,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,5},{2},{3,4,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,2,5},{3},{4,7,8},{6}} => [[1,2,5],[3,7,8],[4],[6]] => [6,4,3,7,8,1,2,5] => [1,1,3,3]
{{1,2,5,7},{3},{4,8},{6}} => [[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [1,1,2,4]
{{1},{2,3,5,7},{4},{6,8}} => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,2,4]
{{1,5,7},{2},{3,4},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,4,7},{2},{3,5},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,4},{2},{3,8},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,4,6},{2},{3,8},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,4,6},{2},{3,7},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1},{2,6},{3,4,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,6},{2,3,7},{4},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,2},{3,6,7},{4,8},{5}} => [[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,2,2,3]
{{1,2},{3,6},{4,7,8},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,6},{2,3},{4},{5,7,8}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1},{2,6},{3,4},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1},{2,7},{3,4},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,7},{2,3},{4},{5,6,8}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,2},{3,7},{4,6,8},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,2},{3,5,8},{4,7},{6}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,7},{2,3,8},{4,5},{6}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1},{2,5},{3,4,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1},{2,4},{3,5,8},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1},{2,4},{3,7},{5,6,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1},{2,4},{3,6},{5,7,8}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1},{2,4},{3,6,7},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,3},{2,6,7},{4},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,3},{2,6},{4},{5,7,8}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,3},{2,7},{4},{5,6,8}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,3},{2,7,8},{4,5},{6}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,3,8},{2,4,7},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [1,1,3,3]
{{1,4,8},{2,3,7},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [1,1,3,3]
{{1,4,7},{2,3,8},{5},{6}} => [[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [1,1,3,3]
{{1,3,7},{2,8},{4,5},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,3},{2,8},{4},{5,6,7}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,3,6},{2,8},{4},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,3,6},{2,7},{4},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1},{2,4,6},{3,7},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1},{2,4,6},{3,8},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1},{2,4},{3,8},{5,6,7}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1},{2,4,7},{3,5},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1},{2,5,7},{3,4},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1},{2,8},{3,4,6},{5,7}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,8},{2,3,6},{4},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,2,6},{3,8},{4,7},{5}} => [[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [1,2,2,3]
{{1,7},{2,3,6},{4},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1},{2,7},{3,4,6},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,2},{3,6,8},{4,7},{5}} => [[1,2,8],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2,8] => [1,2,2,3]
{{1,2},{3,5,7},{4,8},{6}} => [[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [1,2,2,3]
{{1,2},{3,7},{4,5,8},{6}} => [[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => [1,2,2,3]
{{1,4,8},{2,7},{3},{5,6}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,3,7},{2,8},{4},{5,6}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,3,7},{2,8},{4,6},{5}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,3,7},{2},{4,5,8},{6}} => [[1,3,7],[2,5,8],[4],[6]] => [6,4,2,5,8,1,3,7] => [1,1,3,3]
{{1,7},{2,3},{4,5,8},{6}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,7},{2,3,8},{4,6},{5}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,7},{2,3,8},{4},{5,6}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,7,8},{2,5},{3,6},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,7},{2,4,6,8},{3},{5}} => [[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [1,1,2,4]
{{1,7},{2,4,5},{3,8},{6}} => [[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [1,2,2,3]
{{1,4,6},{2,5},{3},{7,8}} => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,2,2,3]
{{1,5,7,8},{2},{3,6},{4}} => [[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [1,1,2,4]
{{1,5,8},{2,7},{3,6},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,8},{2,5,7},{3,6},{4}} => [[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [1,2,2,3]
{{1,5,8},{2,6,7},{3},{4}} => [[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [1,1,3,3]
{{1,4,5,7},{2},{3,8},{6}} => [[1,4,5,7],[2,8],[3],[6]] => [6,3,2,8,1,4,5,7] => [1,1,2,4]
{{1,3,5},{2,6},{4},{7,8}} => [[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [1,2,2,3]
{{1,3,6},{2,8},{4,7},{5}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,4,6,8},{2},{3,7},{5}} => [[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [1,1,2,4]
{{1,8},{2,4,6},{3,7},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,4,8},{2,5},{3},{6,7}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,3,5},{2,8},{4},{6,7}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,5},{2,3,8},{4},{6,7}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,8},{2,6},{3,4,7},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,6,8},{2},{3,4,7},{5}} => [[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => [1,1,3,3]
{{1,6,8},{2,4},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,6},{2,3,8},{4,7},{5}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,6},{2,3,7,8},{4},{5}} => [[1,3,7,8],[2,6],[4],[5]] => [5,4,2,6,1,3,7,8] => [1,1,2,4]
{{1,5},{2,3,7},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,5},{2,3,6},{4},{7,8}} => [[1,3,6],[2,5],[4,8],[7]] => [7,4,8,2,5,1,3,6] => [1,2,2,3]
{{1,5,7},{2,4},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,6,7},{2,4,8},{3},{5}} => [[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => [1,1,3,3]
{{1,6,8},{2,5,7},{3},{4}} => [[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [1,1,3,3]
{{1,6,8},{2,7},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,6,8},{2,7},{3},{4,5}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,6,7},{2,8},{3,4},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,5,7},{2},{3,4,8},{6}} => [[1,4,7],[2,5,8],[3],[6]] => [6,3,2,5,8,1,4,7] => [1,1,3,3]
{{1,7},{2,5},{3,4,8},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,7},{2,6,8},{3,4},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,4,8},{2,3,6},{5},{7}} => [[1,3,6],[2,4,8],[5],[7]] => [7,5,2,4,8,1,3,6] => [1,1,3,3]
{{1,5},{2,4,8},{3,7},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,5},{2,4,7},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,5},{2,4,8},{3,6},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,6},{2,4,8},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,6},{2,5},{3,4,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,6},{2,3,5},{4,8},{7}} => [[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [1,2,2,3]
{{1,5},{2,3,6},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => [7,4,8,2,5,1,3,6] => [1,2,2,3]
{{1,5},{2,6},{3,4,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,4,8},{2,7},{3,6},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,4,7},{2,8},{3,6},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,4,6},{2,8},{3,7},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,4,7},{2,8},{3,5},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,5},{2,8},{3,4,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,5},{2,3,8},{4,7},{6}} => [[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [1,2,2,3]
{{1,2,5},{3,8},{4,7},{6}} => [[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [1,2,2,3]
{{1,5},{2,7},{3,4,8},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,4,8},{2,7},{3,5},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,7},{2,6},{3,4,8},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,7},{2,3,6},{4,8},{5}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,8},{2,3,6},{4,7},{5}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,8},{2,3,5},{4,7},{6}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,8},{2,5},{3,4,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,8},{2,4,7},{3,5},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,8},{2,4,7},{3,6},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,7},{2,4,8},{3,6},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,3,5},{2,8},{4,7},{6}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,3,8},{2,7},{4,6},{5}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,6},{2,4,8},{3,7},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,6},{2,4,7},{3,8},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,7},{2,4,6},{3,8},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,7},{2,4,8},{3,5},{6}} => [[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [1,2,2,3]
{{1,7},{2,3,5},{4,8},{6}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,2,7},{3,8},{4,6},{5}} => [[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => [1,2,2,3]
{{1,7},{2,8},{3,4,6},{5}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,6},{2,8},{3,4,7},{5}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,6},{2,3,7},{4,8},{5}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,6},{2,7},{3,4,8},{5}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,3,5},{2},{4,6,8},{7}} => [[1,3,5],[2,6,8],[4],[7]] => [7,4,2,6,8,1,3,5] => [1,1,3,3]
{{1,3},{2,4,6,8},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [1,1,2,4]
{{1},{2,4,6,8},{3},{5,7}} => [[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [1,1,2,4]
{{1,3},{2},{4,6,8},{5,7}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,3,6},{2},{4,8},{5,7}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,3,6},{2},{4,7},{5,8}} => [[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => [1,2,2,3]
{{1,3,5},{2},{4,7},{6,8}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,3,5,7},{2},{4,6},{8}} => [[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => [1,1,2,4]
{{1,3,7},{2},{4,6,8},{5}} => [[1,3,7],[2,6,8],[4],[5]] => [5,4,2,6,8,1,3,7] => [1,1,3,3]
{{1,3,7},{2},{4,6},{5,8}} => [[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => [1,2,2,3]
{{1,3,5,7},{2},{4,8},{6}} => [[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [1,1,2,4]
{{1,3},{2,4,8},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1},{2,4,8},{3,5,7},{6}} => [[1,4,7],[2,5,8],[3],[6]] => [6,3,2,5,8,1,4,7] => [1,1,3,3]
{{1,4},{2,8},{3,5,7},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,4},{2,5,7},{3,8},{6}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,3},{2,5,7},{4,8},{6}} => [[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [1,2,2,3]
{{1,3},{2,7},{4,6,8},{5}} => [[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => [1,2,2,3]
{{1,3,7},{2,4,6},{5},{8}} => [[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => [1,1,3,3]
{{1,7},{2,4,6},{3},{5,8}} => [[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => [1,2,2,3]
{{1,5,7},{2,4,8},{3},{6}} => [[1,4,7],[2,5,8],[3],[6]] => [6,3,2,5,8,1,4,7] => [1,1,3,3]
{{1},{2,8},{3,5,7},{4,6}} => [[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [1,2,2,3]
{{1,7},{2,4,6},{3,5},{8}} => [[1,4,6],[2,5],[3,7],[8]] => [8,3,7,2,5,1,4,6] => [1,2,2,3]
{{1,4,7},{2,6},{3,5},{8}} => [[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [1,2,2,3]
{{1},{2,5,8},{3,7},{4,6}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1},{2,5,8},{3,6},{4,7}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1},{2,4,8},{3,6},{5,7}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1},{2,4,6,8},{3,5},{7}} => [[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [1,1,2,4]
{{1,4},{2,6,8},{3,5},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,4},{2,5},{3,6,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,3},{2,5},{4,6,8},{7}} => [[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [1,2,2,3]
{{1,5},{2,4,6,8},{3},{7}} => [[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [1,1,2,4]
{{1,5},{2,4},{3,6,8},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1},{2,6,8},{3,5,7},{4}} => [[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [1,1,3,3]
{{1,6},{2,8},{3,5,7},{4}} => [[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => [1,2,2,3]
{{1,6},{2,4,8},{3},{5,7}} => [[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [1,2,2,3]
{{1,6},{2,4,7},{3},{5,8}} => [[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => [1,2,2,3]
{{1,5},{2,4,7},{3},{6,8}} => [[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [1,2,2,3]
{{1,5,7},{2,4,6},{3},{8}} => [[1,4,6],[2,5,7],[3],[8]] => [8,3,2,5,7,1,4,6] => [1,1,3,3]
{{1,5,7},{2,4},{3,6},{8}} => [[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [1,2,2,3]
{{1},{2,6,8},{3,5},{4,7}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1},{2,4,6,8},{3,7},{5}} => [[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [1,1,2,4]
{{1,6},{2,7},{3,5,8},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,3,5},{2,7},{4},{6,8}} => [[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [1,2,2,3]
{{1,7},{2,6,8},{3,5},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,7},{2,6},{3,5,8},{4}} => [[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => [1,2,2,3]
{{1,2},{3,4,6},{5,8},{7}} => [[1,2,6],[3,4],[5,8],[7]] => [7,5,8,3,4,1,2,6] => [1,2,2,3]
{{1,2},{3,6},{4,5,8},{7}} => [[1,2,8],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2,8] => [1,2,2,3]
{{1,2},{3,5,6},{4,8},{7}} => [[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => [1,2,2,3]
{{1,2,5,6},{3},{4,8},{7}} => [[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [1,1,2,4]
{{1,2,6},{3},{4,5,8},{7}} => [[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => [1,1,3,3]
{{1,6},{2,3},{4,5,8},{7}} => [[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [1,2,2,3]
{{1,5,6},{2,3},{4,8},{7}} => [[1,3,6],[2,5],[4,8],[7]] => [7,4,8,2,5,1,3,6] => [1,2,2,3]
{{1,5,6},{2,3,8},{4},{7}} => [[1,3,6],[2,5,8],[4],[7]] => [7,4,2,5,8,1,3,6] => [1,1,3,3]
{{1,5,6},{2,8},{3,4},{7}} => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,2,2,3]
{{1,5},{2,8},{3,4,6},{7}} => [[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [1,2,2,3]
{{1,5},{2,3,8},{4,6},{7}} => [[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [1,2,2,3]
{{1,6},{2,3,5,8},{4},{7}} => [[1,3,5,8],[2,6],[4],[7]] => [7,4,2,6,1,3,5,8] => [1,1,2,4]
{{1,2,5},{3,8},{4,6},{7}} => [[1,2,5],[3,6],[4,8],[7]] => [7,4,8,3,6,1,2,5] => [1,2,2,3]
{{1,2,4},{3,6},{5},{7,8}} => [[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [1,2,2,3]
{{1,2,4,6},{3},{5,8},{7}} => [[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [1,1,2,4]
{{1,2,4},{3,8},{5,7},{6}} => [[1,2,4],[3,7],[5,8],[6]] => [6,5,8,3,7,1,2,4] => [1,2,2,3]
{{1,2,4},{3,8},{5},{6,7}} => [[1,2,4],[3,7],[5,8],[6]] => [6,5,8,3,7,1,2,4] => [1,2,2,3]
{{1,4},{2,3,8},{5},{6,7}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1,3,4},{2,8},{5},{6,7}} => [[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [1,2,2,3]
{{1,3,4},{2,8},{5,7},{6}} => [[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [1,2,2,3]
{{1,4},{2,3,8},{5,7},{6}} => [[1,3,8],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3,8] => [1,2,2,3]
{{1,4,6},{2,3},{5,8},{7}} => [[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [1,2,2,3]
{{1,4},{2,3,6},{5},{7,8}} => [[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [1,2,2,3]
{{1,4},{2,3,6,8},{5},{7}} => [[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [1,1,2,4]
{{1,4},{2,3,6},{5,8},{7}} => [[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [1,2,2,3]
{{1,8},{2,4,5},{3,7},{6}} => [[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [1,2,2,3]
{{1,3,8},{2,6},{4,5},{7}} => [[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [1,2,2,3]
{{1,3,4},{2,6},{5},{7,8}} => [[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [1,2,2,3]
{{1,6},{2,5,8},{3,4},{7}} => [[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [1,2,2,3]
{{1,6},{2,4,5},{3,8},{7}} => [[1,4,5],[2,6],[3,8],[7]] => [7,3,8,2,6,1,4,5] => [1,2,2,3]
{{1,4,5},{2,8},{3,6},{7}} => [[1,4,5],[2,6],[3,8],[7]] => [7,3,8,2,6,1,4,5] => [1,2,2,3]
Map
Standard tableau associated to a set partition
Description
Sends a set partition to the associated standard tableau.
The jth column of the standard tableau associated to a set partition is the set of jth smallest elements of its blocks arranged in increassing order.
The jth column of the standard tableau associated to a set partition is the set of jth smallest elements of its blocks arranged in increassing order.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
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