Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000157: Standard tableaux ⟶ ℤ
Values
{{1}} => [1] => [1] => [[1]] => 0
{{1,2}} => [2,1] => [2,1] => [[1],[2]] => 1
{{1},{2}} => [1,2] => [1,2] => [[1,2]] => 0
{{1,2,3}} => [2,3,1] => [3,1,2] => [[1,3],[2]] => 1
{{1,2},{3}} => [2,1,3] => [2,1,3] => [[1,3],[2]] => 1
{{1,3},{2}} => [3,2,1] => [2,3,1] => [[1,2],[3]] => 1
{{1},{2,3}} => [1,3,2] => [1,3,2] => [[1,2],[3]] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [[1,2,3]] => 0
{{1,2,3,4}} => [2,3,4,1] => [4,1,2,3] => [[1,3,4],[2]] => 1
{{1,2,3},{4}} => [2,3,1,4] => [3,1,2,4] => [[1,3,4],[2]] => 1
{{1,2,4},{3}} => [2,4,3,1] => [3,4,1,2] => [[1,2],[3,4]] => 1
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [[1,3],[2,4]] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [[1,3,4],[2]] => 1
{{1,3,4},{2}} => [3,2,4,1] => [2,4,1,3] => [[1,2],[3,4]] => 1
{{1,3},{2,4}} => [3,4,1,2] => [3,1,4,2] => [[1,3],[2,4]] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [2,3,1,4] => [[1,2,4],[3]] => 1
{{1,4},{2,3}} => [4,3,2,1] => [3,2,4,1] => [[1,3],[2],[4]] => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,4,2,3] => [[1,2,4],[3]] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [[1,2,4],[3]] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,4,1] => [[1,2,3],[4]] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [1,3,4,2] => [[1,2,3],[4]] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [[1,2,3],[4]] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [5,1,2,3,4] => [[1,3,4,5],[2]] => 1
{{1,2,3,4},{5}} => [2,3,4,1,5] => [4,1,2,3,5] => [[1,3,4,5],[2]] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => [4,5,1,2,3] => [[1,2,5],[3,4]] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,1,2,5,4] => [[1,3,4],[2,5]] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,1,2,4,5] => [[1,3,4,5],[2]] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [3,5,1,2,4] => [[1,2,5],[3,4]] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [4,1,2,5,3] => [[1,3,4],[2,5]] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [3,4,1,2,5] => [[1,2,5],[3,4]] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [4,3,5,1,2] => [[1,3],[2,5],[4]] => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [2,1,5,3,4] => [[1,3,5],[2,4]] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [2,1,4,3,5] => [[1,3,5],[2,4]] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [3,4,5,1,2] => [[1,2,3],[4,5]] => 1
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [2,1,4,5,3] => [[1,3,4],[2,5]] => 2
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [2,1,3,5,4] => [[1,3,4],[2,5]] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [2,5,1,3,4] => [[1,2,5],[3,4]] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => [4,1,3,5,2] => [[1,3,4],[2],[5]] => 2
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [2,4,1,3,5] => [[1,2,5],[3,4]] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [4,2,5,1,3] => [[1,3],[2,5],[4]] => 2
{{1,3},{2,4,5}} => [3,4,1,5,2] => [3,1,5,2,4] => [[1,3,5],[2,4]] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [3,1,4,2,5] => [[1,3,5],[2,4]] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [2,4,5,1,3] => [[1,2,3],[4,5]] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [3,1,4,5,2] => [[1,3,4],[2,5]] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [2,3,1,5,4] => [[1,2,4],[3,5]] => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [2,3,1,4,5] => [[1,2,4,5],[3]] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [3,2,5,1,4] => [[1,3],[2,5],[4]] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [4,1,5,2,3] => [[1,3,5],[2,4]] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => 2
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,2,3,5,1] => [[1,3,4],[2],[5]] => 2
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,5,2,3,4] => [[1,2,4,5],[3]] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,4,2,3,5] => [[1,2,4,5],[3]] => 1
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,4,5,2,3] => [[1,2,3],[4,5]] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [[1,2,4],[3,5]] => 2
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [2,3,5,1,4] => [[1,2,3],[4,5]] => 1
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [3,4,1,5,2] => [[1,2,4],[3,5]] => 2
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [2,4,1,5,3] => [[1,2,4],[3,5]] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [2,3,4,1,5] => [[1,2,3,5],[4]] => 1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => 2
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,3,5,2,4] => [[1,2,3],[4,5]] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,2,5,3] => [[1,2,4],[3,5]] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,3,4,2,5] => [[1,2,3,5],[4]] => 1
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,4,3,5,1] => [[1,2,4],[3],[5]] => 2
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,4,3,5,2] => [[1,2,4],[3],[5]] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,5,3,4] => [[1,2,3,5],[4]] => 1
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [[1,2,3,5],[4]] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [2,3,4,5,1] => [[1,2,3,4],[5]] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,3,4,5,2] => [[1,2,3,4],[5]] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,4,5,3] => [[1,2,3,4],[5]] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [[1,2,3,4],[5]] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => 1
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => 1
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => 1
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [[1,3,4,5],[2,6]] => 2
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => 1
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [4,6,1,2,3,5] => [[1,2,5,6],[3,4]] => 1
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [[1,3,4,5],[2,6]] => 2
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => 2
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [[1,3,4,6],[2,5]] => 2
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [[1,3,4,6],[2,5]] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 1
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,1,2,5,6,4] => [[1,3,4,5],[2,6]] => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [[1,3,4,5],[2,6]] => 2
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => 1
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [3,6,1,2,4,5] => [[1,2,5,6],[3,4]] => 1
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [5,1,2,4,6,3] => [[1,3,4,5],[2],[6]] => 2
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [3,5,1,2,4,6] => [[1,2,5,6],[3,4]] => 1
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [5,3,6,1,2,4] => [[1,3,6],[2,5],[4]] => 2
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [4,1,2,6,3,5] => [[1,3,4,6],[2,5]] => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [[1,3,4,6],[2,5]] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [3,5,6,1,2,4] => [[1,2,3],[4,5,6]] => 1
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [4,1,2,5,6,3] => [[1,3,4,5],[2,6]] => 2
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => 1
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [4,3,6,1,2,5] => [[1,3,6],[2,5],[4]] => 2
>>> Load all 2876 entries. <<<{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [5,1,2,6,3,4] => [[1,3,4,6],[2,5]] => 2
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => 2
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => 2
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [[1,3,5,6],[2,4]] => 2
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [[1,3,5,6],[2,4]] => 2
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => 2
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => 2
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 3
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 2
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [3,4,6,1,2,5] => [[1,2,3],[4,5,6]] => 1
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [4,5,1,2,6,3] => [[1,2,5],[3,4,6]] => 2
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [3,5,1,2,6,4] => [[1,2,5],[3,4,6]] => 2
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => 1
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => 2
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [2,1,4,6,3,5] => [[1,3,4],[2,5,6]] => 2
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [[1,3,5],[2,4,6]] => 3
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => 2
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [3,5,4,6,1,2] => [[1,2,4],[3,6],[5]] => 2
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => 3
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [[1,3,4,6],[2,5]] => 2
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 2
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => 1
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => 2
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => 2
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => 2
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 1
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [2,6,1,3,4,5] => [[1,2,5,6],[3,4]] => 1
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [5,1,3,4,6,2] => [[1,3,4,5],[2],[6]] => 2
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [2,5,1,3,4,6] => [[1,2,5,6],[3,4]] => 1
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [5,2,6,1,3,4] => [[1,3,6],[2,5],[4]] => 2
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [4,1,3,6,2,5] => [[1,3,4],[2,6],[5]] => 2
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [4,1,3,5,2,6] => [[1,3,4,6],[2],[5]] => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [2,5,6,1,3,4] => [[1,2,3],[4,5,6]] => 1
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [4,1,3,5,6,2] => [[1,3,4,5],[2],[6]] => 2
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [2,4,1,3,6,5] => [[1,2,5],[3,4,6]] => 2
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [2,4,1,3,5,6] => [[1,2,5,6],[3,4]] => 1
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [4,2,6,1,3,5] => [[1,3,6],[2,5],[4]] => 2
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [5,1,3,6,2,4] => [[1,3,4],[2,6],[5]] => 2
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => 2
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [5,2,4,6,1,3] => [[1,3,4],[2,6],[5]] => 2
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [3,1,6,2,4,5] => [[1,3,5,6],[2,4]] => 2
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [3,1,5,2,4,6] => [[1,3,5,6],[2,4]] => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [4,2,5,6,1,3] => [[1,3,4],[2,6],[5]] => 2
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [3,1,5,6,2,4] => [[1,3,4],[2,5,6]] => 2
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [[1,3,5],[2,4,6]] => 3
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [[1,3,5,6],[2,4]] => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [2,4,6,1,3,5] => [[1,2,3],[4,5,6]] => 1
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [4,5,1,3,6,2] => [[1,2,5],[3,4],[6]] => 2
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [2,5,1,3,6,4] => [[1,2,5],[3,4,6]] => 2
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [2,4,5,1,3,6] => [[1,2,3,6],[4,5]] => 1
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [4,5,2,6,1,3] => [[1,2,4],[3,6],[5]] => 2
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [3,1,4,6,2,5] => [[1,3,4],[2,5,6]] => 2
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [[1,3,5],[2,4,6]] => 3
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [3,1,4,5,2,6] => [[1,3,4,6],[2,5]] => 2
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [2,5,4,6,1,3] => [[1,2,4],[3,6],[5]] => 2
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [3,1,5,4,6,2] => [[1,3,5],[2,4],[6]] => 3
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [2,3,1,6,4,5] => [[1,2,4,6],[3,5]] => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => 2
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [2,4,5,6,1,3] => [[1,2,3,4],[5,6]] => 1
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [3,1,4,5,6,2] => [[1,3,4,5],[2,6]] => 2
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => 2
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [3,2,6,1,4,5] => [[1,3,6],[2,5],[4]] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [5,1,4,6,2,3] => [[1,3,4],[2,6],[5]] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [3,2,5,1,4,6] => [[1,3,6],[2,5],[4]] => 2
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => 2
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [4,1,6,2,3,5] => [[1,3,5,6],[2,4]] => 2
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [4,1,5,2,3,6] => [[1,3,5,6],[2,4]] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [3,2,5,6,1,4] => [[1,3,4],[2,6],[5]] => 2
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [4,1,5,6,2,3] => [[1,3,4],[2,5,6]] => 2
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => 3
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => 2
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [4,2,3,6,1,5] => [[1,3,4],[2,6],[5]] => 2
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [5,1,6,2,3,4] => [[1,3,5,6],[2,4]] => 2
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => 2
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => 2
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 1
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 1
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => 2
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 1
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [[1,2,4,5],[3,6]] => 2
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 1
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [3,2,4,6,1,5] => [[1,3,4],[2,6],[5]] => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [4,5,1,6,2,3] => [[1,2,4],[3,5,6]] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [[1,3,5],[2,6],[4]] => 3
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => 2
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => 2
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => 1
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [[1,2,4,5],[3,6]] => 2
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => 1
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => 3
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,5,4,6,2,3] => [[1,2,4],[3,6],[5]] => 2
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [[1,2,4,6],[3,5]] => 2
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => 2
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => 2
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => 1
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => 2
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => 2
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [2,3,6,1,4,5] => [[1,2,3,6],[4,5]] => 1
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [3,5,1,4,6,2] => [[1,2,5],[3,4],[6]] => 2
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [2,5,1,4,6,3] => [[1,2,5],[3,4],[6]] => 2
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [2,3,5,1,4,6] => [[1,2,3,6],[4,5]] => 1
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [3,5,2,6,1,4] => [[1,2,4],[3,6],[5]] => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [3,4,1,6,2,5] => [[1,2,4],[3,5,6]] => 2
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [[1,3,5],[2,4,6]] => 3
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [3,4,1,5,2,6] => [[1,2,4,6],[3,5]] => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [2,5,3,6,1,4] => [[1,2,4],[3,6],[5]] => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [4,1,5,3,6,2] => [[1,3,5],[2,4],[6]] => 3
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [2,4,1,6,3,5] => [[1,2,4],[3,5,6]] => 2
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [[1,2,4,6],[3,5]] => 2
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [2,3,5,6,1,4] => [[1,2,3,4],[5,6]] => 1
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [3,4,1,5,6,2] => [[1,2,4,5],[3,6]] => 2
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [2,4,1,5,6,3] => [[1,2,4,5],[3,6]] => 2
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => 2
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => 1
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [3,4,2,6,1,5] => [[1,2,4],[3,6],[5]] => 2
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => 2
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [4,2,5,1,6,3] => [[1,3,5],[2,6],[4]] => 3
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => 2
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [3,5,2,4,6,1] => [[1,2,5],[3,4],[6]] => 2
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => 1
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,5,2,4,6,3] => [[1,2,4,5],[3],[6]] => 2
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => 1
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [4,2,5,3,6,1] => [[1,3,5],[2,4],[6]] => 3
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => 2
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [[1,2,4,6],[3,5]] => 2
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [[1,2,4,6],[3,5]] => 2
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => 2
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => 1
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,4,2,5,6,3] => [[1,2,4,5],[3,6]] => 2
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => 2
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => 1
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [2,4,3,6,1,5] => [[1,2,4],[3,6],[5]] => 2
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [4,3,5,1,6,2] => [[1,3,5],[2,6],[4]] => 3
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [2,5,1,6,3,4] => [[1,2,4],[3,5,6]] => 2
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => 2
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => 3
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,4,3,6,2,5] => [[1,2,4],[3,6],[5]] => 2
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,5,2,6,3,4] => [[1,2,4,6],[3,5]] => 2
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => 2
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [2,5,3,4,6,1] => [[1,2,4,5],[3],[6]] => 2
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,5,3,4,6,2] => [[1,2,4,5],[3],[6]] => 2
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 1
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 1
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => 2
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => 2
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 1
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => 2
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 1
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [2,3,4,6,1,5] => [[1,2,3,4],[5,6]] => 1
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [3,4,5,1,6,2] => [[1,2,3,5],[4,6]] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [2,4,5,1,6,3] => [[1,2,3,5],[4,6]] => 2
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [2,3,5,1,6,4] => [[1,2,3,5],[4,6]] => 2
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => 1
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => 2
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => 1
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,4,5,2,6,3] => [[1,2,3,5],[4,6]] => 2
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,3,5,2,6,4] => [[1,2,3,5],[4,6]] => 2
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => 1
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => 2
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => 2
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => 1
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [[1,2,3,5],[4,6]] => 2
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => 1
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => 2
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => 2
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => 2
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 1
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 1
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 1
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => 1
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 1
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 1
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 1
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => 1
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => 1
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => 1
{{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => [5,7,1,2,3,4,6] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [6,1,2,3,4,7,5] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [6,5,7,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [4,1,2,3,6,7,5] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
{{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => [4,7,1,2,3,5,6] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [6,1,2,3,5,7,4] => [[1,3,4,5,6],[2],[7]] => 2
{{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => [4,6,1,2,3,5,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [6,4,7,1,2,3,5] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [5,1,2,3,7,4,6] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [5,1,2,3,6,4,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => [4,6,7,1,2,3,5] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [5,1,2,3,6,7,4] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [4,5,1,2,3,7,6] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [5,4,7,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [6,1,2,3,7,4,5] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [5,4,6,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [6,4,5,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [5,4,6,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [3,1,2,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 2
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [4,5,7,1,2,3,6] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [5,6,1,2,3,7,4] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [4,6,1,2,3,7,5] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [5,6,4,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,3},{4,6,7},{5}} => [2,3,1,6,5,7,4] => [3,1,2,5,7,4,6] => [[1,3,4,5],[2,6,7]] => 2
{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [3,1,2,6,4,7,5] => [[1,3,4,6],[2,5,7]] => 3
{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [3,1,2,5,6,4,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [4,6,5,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => [3,1,2,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => 1
{{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => [3,1,2,5,6,7,4] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [3,1,2,4,6,7,5] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
{{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => [3,7,1,2,4,5,6] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => [6,1,2,4,5,7,3] => [[1,3,4,5,6],[2],[7]] => 2
{{1,2,4,5,6},{3},{7}} => [2,4,3,5,6,1,7] => [3,6,1,2,4,5,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [6,3,7,1,2,4,5] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => [5,1,2,4,7,3,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2,4,5},{3,6},{7}} => [2,4,6,5,1,3,7] => [5,1,2,4,6,3,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,2,4,5,7},{3},{6}} => [2,4,3,5,7,6,1] => [3,6,7,1,2,4,5] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,4,5},{3,7},{6}} => [2,4,7,5,1,6,3] => [5,1,2,4,6,7,3] => [[1,3,4,5,6],[2],[7]] => 2
{{1,2,4,5},{3},{6,7}} => [2,4,3,5,1,7,6] => [3,5,1,2,4,7,6] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,4,5},{3},{6},{7}} => [2,4,3,5,1,6,7] => [3,5,1,2,4,6,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [5,3,7,1,2,4,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [6,1,2,4,7,3,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [5,3,6,1,2,4,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [6,3,5,7,1,2,4] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [4,1,2,7,3,5,6] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [4,1,2,6,3,5,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => [5,3,6,7,1,2,4] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => [4,1,2,6,7,3,5] => [[1,3,4,5],[2,6,7]] => 2
{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [4,1,2,5,3,7,6] => [[1,3,4,6],[2,5,7]] => 3
{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [4,1,2,5,3,6,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => [3,5,7,1,2,4,6] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,4,6},{3,7},{5}} => [2,4,7,6,5,1,3] => [5,6,1,2,4,7,3] => [[1,2,5,6],[3,4],[7]] => 2
{{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => [3,6,1,2,4,7,5] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => [3,5,6,1,2,4,7] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [5,6,3,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => [4,1,2,5,7,3,6] => [[1,3,4,5],[2,6,7]] => 2
{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [4,1,2,6,3,7,5] => [[1,3,4,6],[2,5,7]] => 3
{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [4,1,2,5,6,3,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,4,7},{3},{5,6}} => [2,4,3,7,6,5,1] => [3,6,5,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,4},{3,7},{5,6}} => [2,4,7,1,6,5,3] => [4,1,2,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [3,4,1,2,7,5,6] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => [3,5,6,7,1,2,4] => [[1,2,3,4],[5,6,7]] => 1
{{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => [4,1,2,5,6,7,3] => [[1,3,4,5,6],[2,7]] => 2
{{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => [3,4,1,2,6,7,5] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => [4,3,7,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [6,1,2,5,7,3,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [4,3,6,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [6,3,4,7,1,2,5] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => [5,1,2,7,3,4,6] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [5,1,2,6,3,4,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [4,3,6,7,1,2,5] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => [5,1,2,6,7,3,4] => [[1,3,4,5],[2,6,7]] => 2
{{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => [4,3,5,1,2,7,6] => [[1,3,6],[2,5,7],[4]] => 3
{{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => [4,3,5,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => [5,3,4,7,1,2,6] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [6,1,2,7,3,4,5] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [5,3,4,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [6,3,4,5,7,1,2] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [[1,3,5,6,7],[2,4]] => 2
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => [5,3,4,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [2,1,6,7,3,4,5] => [[1,3,4,7],[2,5,6]] => 2
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [[1,3,5,6],[2,4,7]] => 3
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => [4,3,5,7,1,2,6] => [[1,3,4],[2,6,7],[5]] => 2
{{1,2,6},{3,4,7},{5}} => [2,6,4,7,5,1,3] => [5,6,1,2,7,3,4] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [4,3,6,1,2,7,5] => [[1,3,6],[2,5,7],[4]] => 3
{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [4,3,5,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [5,6,3,4,7,1,2] => [[1,2,5],[3,4],[6,7]] => 2
{{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => [2,1,5,7,3,4,6] => [[1,3,4,7],[2,5,6]] => 2
{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [2,1,6,3,4,7,5] => [[1,3,5,6],[2,4,7]] => 3
{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => 2
{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [4,3,6,5,7,1,2] => [[1,3,5],[2,4],[6,7]] => 3
{{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => [2,1,6,5,7,3,4] => [[1,3,5],[2,4,7],[6]] => 3
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [[1,3,5,7],[2,4,6]] => 3
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 3
{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [4,3,5,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 2
{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [2,1,5,6,7,3,4] => [[1,3,4,5],[2,6,7]] => 2
{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]] => 3
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 3
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,2,5,6,7},{3},{4}} => [2,5,3,4,6,7,1] => [3,4,7,1,2,5,6] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => [4,6,1,2,5,7,3] => [[1,2,5,6],[3,4],[7]] => 2
{{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => [3,6,1,2,5,7,4] => [[1,2,5,6],[3,4],[7]] => 2
{{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => [3,4,6,1,2,5,7] => [[1,2,3,7],[4,5,6]] => 1
{{1,2,5,7},{3,6},{4}} => [2,5,6,4,7,3,1] => [4,6,3,7,1,2,5] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,5},{3,6,7},{4}} => [2,5,6,4,1,7,3] => [4,5,1,2,7,3,6] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,5},{3,6},{4,7}} => [2,5,6,7,1,3,4] => [5,1,2,6,3,7,4] => [[1,3,4,6],[2,5,7]] => 3
{{1,2,5},{3,6},{4},{7}} => [2,5,6,4,1,3,7] => [4,5,1,2,6,3,7] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [3,6,4,7,1,2,5] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => [5,1,2,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2,5},{3},{4,6,7}} => [2,5,3,6,1,7,4] => [3,5,1,2,7,4,6] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [3,5,1,2,6,4,7] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => [3,4,6,7,1,2,5] => [[1,2,3,4],[5,6,7]] => 1
{{1,2,5},{3,7},{4},{6}} => [2,5,7,4,1,6,3] => [4,5,1,2,6,7,3] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [3,5,1,2,6,7,4] => [[1,2,5,6],[3,4,7]] => 2
{{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => [3,4,5,1,2,7,6] => [[1,2,3,6],[4,5,7]] => 2
{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,2,6,7},{3,5},{4}} => [2,6,5,4,3,7,1] => [4,5,3,7,1,2,6] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,6},{3,5,7},{4}} => [2,6,5,4,7,1,3] => [4,6,1,2,7,3,5] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => [5,3,6,1,2,7,4] => [[1,3,6],[2,5,7],[4]] => 3
{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [4,5,3,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => [4,6,3,5,7,1,2] => [[1,2,5],[3,4],[6,7]] => 2
{{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => [2,1,4,7,3,5,6] => [[1,3,4,7],[2,5,6]] => 2
{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [2,1,6,3,5,7,4] => [[1,3,5,6],[2,4],[7]] => 3
{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [2,1,4,6,3,5,7] => [[1,3,4,7],[2,5,6]] => 2
{{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => [5,3,6,4,7,1,2] => [[1,3,5],[2,4],[6,7]] => 3
{{1,2},{3,5,7},{4,6}} => [2,1,5,6,7,4,3] => [2,1,6,4,7,3,5] => [[1,3,5],[2,4,7],[6]] => 3
{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [2,1,5,3,7,4,6] => [[1,3,5,7],[2,4,6]] => 3
{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [2,1,5,3,6,4,7] => [[1,3,5,7],[2,4,6]] => 3
{{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => [4,5,3,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => 2
{{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => [2,1,4,6,7,3,5] => [[1,3,4,5],[2,6,7]] => 2
{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [2,1,5,3,6,7,4] => [[1,3,5,6],[2,4,7]] => 3
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => 3
{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => [3,5,4,7,1,2,6] => [[1,2,4],[3,6,7],[5]] => 2
{{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => [5,4,6,1,2,7,3] => [[1,3,6],[2,5,7],[4]] => 3
{{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => [3,6,1,2,7,4,5] => [[1,2,5,7],[3,4,6]] => 2
{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [3,5,4,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [5,4,6,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 3
{{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => [2,1,5,4,7,3,6] => [[1,3,5],[2,4,7],[6]] => 3
{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [2,1,6,3,7,4,5] => [[1,3,5,7],[2,4,6]] => 3
{{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => [2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]] => 3
{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [3,6,4,5,7,1,2] => [[1,2,4,5],[3,7],[6]] => 2
{{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => [2,1,6,4,5,7,3] => [[1,3,5,6],[2,4],[7]] => 3
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [[1,3,4,6,7],[2,5]] => 2
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => [3,5,4,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => 2
{{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => [2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]] => 3
{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 2
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [3,4,5,7,1,2,6] => [[1,2,3,4],[5,6,7]] => 1
{{1,2,6},{3,7},{4},{5}} => [2,6,7,4,5,1,3] => [4,5,6,1,2,7,3] => [[1,2,3,6],[4,5,7]] => 2
{{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => [3,5,6,1,2,7,4] => [[1,2,3,6],[4,5,7]] => 2
{{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => [3,4,6,1,2,7,5] => [[1,2,3,6],[4,5,7]] => 2
{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [4,5,6,3,7,1,2] => [[1,2,3,5],[4,7],[6]] => 2
{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [2,1,4,5,7,3,6] => [[1,3,4,5],[2,6,7]] => 2
{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [2,1,5,6,3,7,4] => [[1,3,4,6],[2,5,7]] => 3
{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [2,1,4,6,3,7,5] => [[1,3,4,6],[2,5,7]] => 3
{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [3,5,6,4,7,1,2] => [[1,2,3,5],[4,7],[6]] => 2
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => [2,1,3,5,7,4,6] => [[1,3,4,5],[2,6,7]] => 2
{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [2,1,3,6,4,7,5] => [[1,3,4,6],[2,5,7]] => 3
{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => [3,4,6,5,7,1,2] => [[1,2,3,5],[4,7],[6]] => 2
{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => 3
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [2,1,3,4,7,5,6] => [[1,3,4,5,7],[2,6]] => 2
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => 1
{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => 2
{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => 2
{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]] => 2
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => [[1,2,5,6,7],[3,4]] => 1
{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [6,1,3,4,5,7,2] => [[1,3,4,5,6],[2],[7]] => 2
{{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [6,2,7,1,3,4,5] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => [5,1,3,4,7,2,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => [5,1,3,4,6,2,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [2,6,7,1,3,4,5] => [[1,2,3,7],[4,5,6]] => 1
{{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => [5,1,3,4,6,7,2] => [[1,3,4,5,6],[2],[7]] => 2
{{1,3,4,5},{2},{6,7}} => [3,2,4,5,1,7,6] => [2,5,1,3,4,7,6] => [[1,2,5,6],[3,4,7]] => 2
{{1,3,4,5},{2},{6},{7}} => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => [5,2,7,1,3,4,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,4,6},{2,5,7}} => [3,5,4,6,7,1,2] => [6,1,3,4,7,2,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => [5,2,6,1,3,4,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [6,2,5,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => [4,1,3,7,2,5,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => [4,1,3,6,2,5,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [5,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,4},{2,5,7},{6}} => [3,5,4,1,7,6,2] => [4,1,3,6,7,2,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => [4,1,3,5,2,7,6] => [[1,3,4,6],[2,7],[5]] => 3
{{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => [4,1,3,5,2,6,7] => [[1,3,4,6,7],[2],[5]] => 2
{{1,3,4,6,7},{2},{5}} => [3,2,4,6,5,7,1] => [2,5,7,1,3,4,6] => [[1,2,3,7],[4,5,6]] => 1
{{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => [5,6,1,3,4,7,2] => [[1,2,5,6],[3,4],[7]] => 2
{{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => [2,6,1,3,4,7,5] => [[1,2,5,6],[3,4,7]] => 2
{{1,3,4,6},{2},{5},{7}} => [3,2,4,6,5,1,7] => [2,5,6,1,3,4,7] => [[1,2,3,7],[4,5,6]] => 1
{{1,3,4,7},{2,6},{5}} => [3,6,4,7,5,2,1] => [5,6,2,7,1,3,4] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,4},{2,6,7},{5}} => [3,6,4,1,5,7,2] => [4,1,3,5,7,2,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => [4,1,3,6,2,7,5] => [[1,3,4,6],[2,7],[5]] => 3
{{1,3,4},{2,6},{5},{7}} => [3,6,4,1,5,2,7] => [4,1,3,5,6,2,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [2,6,5,7,1,3,4] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,4},{2,7},{5,6}} => [3,7,4,1,6,5,2] => [4,1,3,6,5,7,2] => [[1,3,4,6],[2,5],[7]] => 3
{{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => [2,4,1,3,7,5,6] => [[1,2,5,7],[3,4,6]] => 2
{{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => [2,4,1,3,6,5,7] => [[1,2,5,7],[3,4,6]] => 2
{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [2,5,6,7,1,3,4] => [[1,2,3,4],[5,6,7]] => 1
{{1,3,4},{2,7},{5},{6}} => [3,7,4,1,5,6,2] => [4,1,3,5,6,7,2] => [[1,3,4,5,6],[2],[7]] => 2
{{1,3,4},{2},{5,7},{6}} => [3,2,4,1,7,6,5] => [2,4,1,3,6,7,5] => [[1,2,5,6],[3,4,7]] => 2
{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [2,4,1,3,5,7,6] => [[1,2,5,6],[3,4,7]] => 2
{{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => [[1,2,5,6,7],[3,4]] => 1
{{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => [4,2,7,1,3,5,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => [6,1,3,5,7,2,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => [4,2,6,1,3,5,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [6,2,4,7,1,3,5] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,5},{2,4,6,7}} => [3,4,5,6,1,7,2] => [5,1,3,7,2,4,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,5},{2,4,6},{7}} => [3,4,5,6,1,2,7] => [5,1,3,6,2,4,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => [4,2,6,7,1,3,5] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,5},{2,4,7},{6}} => [3,4,5,7,1,6,2] => [5,1,3,6,7,2,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => [4,2,5,1,3,7,6] => [[1,3,6],[2,5,7],[4]] => 3
{{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => [5,2,4,7,1,3,6] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,6},{2,4,5,7}} => [3,4,6,5,7,1,2] => [6,1,3,7,2,4,5] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,6},{2,4,5},{7}} => [3,4,6,5,2,1,7] => [5,2,4,6,1,3,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => [6,2,4,5,7,1,3] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [3,1,7,2,4,5,6] => [[1,3,5,6,7],[2,4]] => 2
{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [3,1,6,2,4,5,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,3,7},{2,4,5},{6}} => [3,4,7,5,2,6,1] => [5,2,4,6,7,1,3] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [3,1,6,7,2,4,5] => [[1,3,4,7],[2,5,6]] => 2
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [3,1,5,2,4,7,6] => [[1,3,5,6],[2,4,7]] => 3
{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [3,1,5,2,4,6,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => [4,2,5,7,1,3,6] => [[1,3,4],[2,6,7],[5]] => 2
{{1,3,6},{2,4,7},{5}} => [3,4,6,7,5,1,2] => [5,6,1,3,7,2,4] => [[1,2,5],[3,4,7],[6]] => 2
{{1,3,6},{2,4},{5,7}} => [3,4,6,2,7,1,5] => [4,2,6,1,3,7,5] => [[1,3,6],[2,5,7],[4]] => 3
{{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => [4,2,5,6,1,3,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => [5,6,2,4,7,1,3] => [[1,2,5],[3,4],[6,7]] => 2
{{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => [3,1,5,7,2,4,6] => [[1,3,4,7],[2,5,6]] => 2
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [3,1,6,2,4,7,5] => [[1,3,5,6],[2,4,7]] => 3
{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [3,1,5,6,2,4,7] => [[1,3,4,7],[2,5,6]] => 2
{{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => [4,2,6,5,7,1,3] => [[1,3,5],[2,4],[6,7]] => 3
{{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => [3,1,6,5,7,2,4] => [[1,3,5],[2,4,7],[6]] => 3
{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [3,1,4,2,7,5,6] => [[1,3,5,7],[2,4,6]] => 3
{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [3,1,4,2,6,5,7] => [[1,3,5,7],[2,4,6]] => 3
{{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => [4,2,5,6,7,1,3] => [[1,3,4,5],[2,7],[6]] => 2
{{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => [3,1,5,6,7,2,4] => [[1,3,4,5],[2,6,7]] => 2
{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [3,1,4,2,6,7,5] => [[1,3,5,6],[2,4,7]] => 3
{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [3,1,4,2,5,7,6] => [[1,3,5,6],[2,4,7]] => 3
{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => [2,4,7,1,3,5,6] => [[1,2,3,7],[4,5,6]] => 1
{{1,3,5,6},{2,7},{4}} => [3,7,5,4,6,1,2] => [4,6,1,3,5,7,2] => [[1,2,5,6],[3,4],[7]] => 2
{{1,3,5,6},{2},{4,7}} => [3,2,5,7,6,1,4] => [2,6,1,3,5,7,4] => [[1,2,5,6],[3,4],[7]] => 2
{{1,3,5,6},{2},{4},{7}} => [3,2,5,4,6,1,7] => [2,4,6,1,3,5,7] => [[1,2,3,7],[4,5,6]] => 1
{{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => [4,6,2,7,1,3,5] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,5},{2,6,7},{4}} => [3,6,5,4,1,7,2] => [4,5,1,3,7,2,6] => [[1,2,5],[3,4,7],[6]] => 2
{{1,3,5},{2,6},{4,7}} => [3,6,5,7,1,2,4] => [5,1,3,6,2,7,4] => [[1,3,4,6],[2,7],[5]] => 3
{{1,3,5},{2,6},{4},{7}} => [3,6,5,4,1,2,7] => [4,5,1,3,6,2,7] => [[1,2,5,7],[3,4],[6]] => 2
{{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => [2,6,4,7,1,3,5] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,5},{2,7},{4,6}} => [3,7,5,6,1,4,2] => [5,1,3,6,4,7,2] => [[1,3,4,6],[2,5],[7]] => 3
{{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => [2,5,1,3,7,4,6] => [[1,2,5,7],[3,4,6]] => 2
{{1,3,5},{2},{4,6},{7}} => [3,2,5,6,1,4,7] => [2,5,1,3,6,4,7] => [[1,2,5,7],[3,4,6]] => 2
{{1,3,5,7},{2},{4},{6}} => [3,2,5,4,7,6,1] => [2,4,6,7,1,3,5] => [[1,2,3,4],[5,6,7]] => 1
{{1,3,5},{2,7},{4},{6}} => [3,7,5,4,1,6,2] => [4,5,1,3,6,7,2] => [[1,2,5,6],[3,4],[7]] => 2
{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [2,5,1,3,6,7,4] => [[1,2,5,6],[3,4,7]] => 2
{{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => [2,4,5,1,3,7,6] => [[1,2,3,6],[4,5,7]] => 2
{{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => [2,4,5,1,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => [4,5,2,7,1,3,6] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => [4,6,1,3,7,2,5] => [[1,2,5],[3,4,7],[6]] => 2
{{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => [5,2,6,1,3,7,4] => [[1,3,6],[2,5,7],[4]] => 3
{{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => [4,5,2,6,1,3,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,3,7},{2,5,6},{4}} => [3,5,7,4,6,2,1] => [4,6,2,5,7,1,3] => [[1,2,5],[3,4],[6,7]] => 2
{{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => [3,1,4,7,2,5,6] => [[1,3,4,7],[2,5,6]] => 2
{{1,3},{2,5,6},{4,7}} => [3,5,1,7,6,2,4] => [3,1,6,2,5,7,4] => [[1,3,5,6],[2,4],[7]] => 3
{{1,3},{2,5,6},{4},{7}} => [3,5,1,4,6,2,7] => [3,1,4,6,2,5,7] => [[1,3,4,7],[2,5,6]] => 2
{{1,3,7},{2,5},{4,6}} => [3,5,7,6,2,4,1] => [5,2,6,4,7,1,3] => [[1,3,5],[2,4],[6,7]] => 3
{{1,3},{2,5,7},{4,6}} => [3,5,1,6,7,4,2] => [3,1,6,4,7,2,5] => [[1,3,5],[2,4,7],[6]] => 3
{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [3,1,5,2,7,4,6] => [[1,3,5,7],[2,4,6]] => 3
{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [3,1,5,2,6,4,7] => [[1,3,5,7],[2,4,6]] => 3
{{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => [4,5,2,6,7,1,3] => [[1,2,4,5],[3,7],[6]] => 2
{{1,3},{2,5,7},{4},{6}} => [3,5,1,4,7,6,2] => [3,1,4,6,7,2,5] => [[1,3,4,5],[2,6,7]] => 2
{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [3,1,5,2,6,7,4] => [[1,3,5,6],[2,4,7]] => 3
{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [3,1,4,5,2,7,6] => [[1,3,4,6],[2,5,7]] => 3
{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [3,1,4,5,2,6,7] => [[1,3,4,6,7],[2,5]] => 2
{{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => [2,5,4,7,1,3,6] => [[1,2,4],[3,6,7],[5]] => 2
{{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => [5,4,6,1,3,7,2] => [[1,3,6],[2,5],[4],[7]] => 3
{{1,3,6},{2},{4,5,7}} => [3,2,6,5,7,1,4] => [2,6,1,3,7,4,5] => [[1,2,5,7],[3,4,6]] => 2
{{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => [2,5,4,6,1,3,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => [5,4,6,2,7,1,3] => [[1,3,5],[2,7],[4],[6]] => 3
{{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => [3,1,5,4,7,2,6] => [[1,3,5],[2,4,7],[6]] => 3
{{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => [3,1,6,2,7,4,5] => [[1,3,5,7],[2,4,6]] => 3
{{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => [3,1,5,4,6,2,7] => [[1,3,5,7],[2,4],[6]] => 3
{{1,3,7},{2},{4,5,6}} => [3,2,7,5,6,4,1] => [2,6,4,5,7,1,3] => [[1,2,4,5],[3,7],[6]] => 2
{{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => [3,1,6,4,5,7,2] => [[1,3,5,6],[2,4],[7]] => 3
{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [2,3,1,7,4,5,6] => [[1,2,4,6,7],[3,5]] => 2
{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [2,3,1,6,4,5,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => [2,5,4,6,7,1,3] => [[1,2,4,5],[3,7],[6]] => 2
{{1,3},{2,7},{4,5},{6}} => [3,7,1,5,4,6,2] => [3,1,5,4,6,7,2] => [[1,3,5,6],[2,4],[7]] => 3
{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [2,3,1,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 2
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 3
{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => [2,4,5,7,1,3,6] => [[1,2,3,4],[5,6,7]] => 1
{{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => [4,5,6,1,3,7,2] => [[1,2,3,6],[4,5],[7]] => 2
{{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => [2,5,6,1,3,7,4] => [[1,2,3,6],[4,5,7]] => 2
{{1,3,6},{2},{4},{5,7}} => [3,2,6,4,7,1,5] => [2,4,6,1,3,7,5] => [[1,2,3,6],[4,5,7]] => 2
{{1,3,6},{2},{4},{5},{7}} => [3,2,6,4,5,1,7] => [2,4,5,6,1,3,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => [4,5,6,2,7,1,3] => [[1,2,3,5],[4,7],[6]] => 2
{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [3,1,4,5,7,2,6] => [[1,3,4,5],[2,6,7]] => 2
{{1,3},{2,6},{4,7},{5}} => [3,6,1,7,5,2,4] => [3,1,5,6,2,7,4] => [[1,3,4,6],[2,5,7]] => 3
{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [3,1,4,6,2,7,5] => [[1,3,4,6],[2,5,7]] => 3
{{1,3},{2,6},{4},{5},{7}} => [3,6,1,4,5,2,7] => [3,1,4,5,6,2,7] => [[1,3,4,5,7],[2,6]] => 2
{{1,3,7},{2},{4,6},{5}} => [3,2,7,6,5,4,1] => [2,5,6,4,7,1,3] => [[1,2,3,5],[4,7],[6]] => 2
{{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => [3,1,5,6,4,7,2] => [[1,3,4,6],[2,5],[7]] => 3
{{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => [2,3,1,5,7,4,6] => [[1,2,4,5],[3,6,7]] => 2
{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [2,3,1,6,4,7,5] => [[1,2,4,6],[3,5,7]] => 3
{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,3,7},{2},{4},{5,6}} => [3,2,7,4,6,5,1] => [2,4,6,5,7,1,3] => [[1,2,3,5],[4,7],[6]] => 2
{{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => [3,1,4,6,5,7,2] => [[1,3,4,6],[2,5],[7]] => 3
{{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => [2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 3
{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [2,3,1,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 2
{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => [2,4,5,6,7,1,3] => [[1,2,3,4,5],[6,7]] => 1
{{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => [3,1,4,5,6,7,2] => [[1,3,4,5,6],[2,7]] => 2
{{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => [2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 2
{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 2
{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [3,2,7,1,4,5,6] => [[1,3,6,7],[2,5],[4]] => 2
{{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => [6,1,4,5,7,2,3] => [[1,3,4,5],[2,7],[6]] => 2
{{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => [3,2,6,1,4,5,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,4,5,7},{2,3,6}} => [4,3,6,5,7,2,1] => [6,2,3,7,1,4,5] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [5,1,4,7,2,3,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [5,1,4,6,2,3,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => [3,2,6,7,1,4,5] => [[1,3,4],[2,6,7],[5]] => 2
{{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => [5,1,4,6,7,2,3] => [[1,3,4,5],[2,7],[6]] => 2
{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [3,2,5,1,4,7,6] => [[1,3,6],[2,5,7],[4]] => 3
{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [3,2,5,1,4,6,7] => [[1,3,6,7],[2,5],[4]] => 2
{{1,4,6,7},{2,3,5}} => [4,3,5,6,2,7,1] => [5,2,3,7,1,4,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,6},{2,3,5,7}} => [4,3,5,6,7,1,2] => [6,1,4,7,2,3,5] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,6},{2,3,5},{7}} => [4,3,5,6,2,1,7] => [5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => [6,2,3,5,7,1,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => [4,1,7,2,3,5,6] => [[1,3,5,6,7],[2,4]] => 2
{{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => [4,1,6,2,3,5,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => [5,2,3,6,7,1,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => [4,1,6,7,2,3,5] => [[1,3,4,7],[2,5,6]] => 2
{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [4,1,5,2,3,7,6] => [[1,3,5,6],[2,4,7]] => 3
{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [4,1,5,2,3,6,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => [3,2,5,7,1,4,6] => [[1,3,4],[2,6,7],[5]] => 2
{{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => [5,6,1,4,7,2,3] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => [3,2,6,1,4,7,5] => [[1,3,6],[2,5,7],[4]] => 3
{{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => [3,2,5,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,4,7},{2,3,6},{5}} => [4,3,6,7,5,2,1] => [5,6,2,3,7,1,4] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => [4,1,5,7,2,3,6] => [[1,3,4,7],[2,5,6]] => 2
{{1,4},{2,3,6},{5,7}} => [4,3,6,1,7,2,5] => [4,1,6,2,3,7,5] => [[1,3,5,6],[2,4,7]] => 3
{{1,4},{2,3,6},{5},{7}} => [4,3,6,1,5,2,7] => [4,1,5,6,2,3,7] => [[1,3,4,7],[2,5,6]] => 2
{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [3,2,6,5,7,1,4] => [[1,3,5],[2,4],[6,7]] => 3
{{1,4},{2,3,7},{5,6}} => [4,3,7,1,6,5,2] => [4,1,6,5,7,2,3] => [[1,3,5],[2,4,7],[6]] => 3
{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [3,2,4,1,7,5,6] => [[1,3,5,7],[2,6],[4]] => 3
{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 3
{{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => [3,2,5,6,7,1,4] => [[1,3,4,5],[2,7],[6]] => 2
{{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => [4,1,5,6,7,2,3] => [[1,3,4,5],[2,6,7]] => 2
{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => 3
{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 3
{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 2
{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [4,2,3,7,1,5,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => [6,1,5,7,2,3,4] => [[1,3,4,7],[2,6],[5]] => 2
{{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => [4,2,3,6,1,5,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => [6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,5},{2,3,4,6,7}} => [5,3,4,6,1,7,2] => [5,1,7,2,3,4,6] => [[1,3,5,6,7],[2,4]] => 2
{{1,5},{2,3,4,6},{7}} => [5,3,4,6,1,2,7] => [5,1,6,2,3,4,7] => [[1,3,5,6,7],[2,4]] => 2
{{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => [4,2,3,6,7,1,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [5,1,6,7,2,3,4] => [[1,3,4,7],[2,5,6]] => 2
{{1,5},{2,3,4},{6,7}} => [5,3,4,2,1,7,6] => [4,2,3,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => 3
{{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 2
{{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => [5,2,3,4,7,1,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [6,1,7,2,3,4,5] => [[1,3,5,6,7],[2,4]] => 2
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => 2
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 1
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 1
{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => 2
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 1
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 1
{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [4,2,3,5,7,1,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => [5,6,1,7,2,3,4] => [[1,2,4,7],[3,5,6]] => 2
{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [4,2,3,6,1,7,5] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => [5,6,2,3,4,7,1] => [[1,2,5,6],[3,4],[7]] => 2
{{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => [1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 1
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [1,6,2,3,4,7,5] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [4,2,3,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => 3
{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [1,6,5,7,2,3,4] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [[1,2,4,5,7],[3,6]] => 2
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 2
{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 1
{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [1,4,2,3,6,7,5] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [3,2,4,7,1,5,6] => [[1,3,4,7],[2,6],[5]] => 2
{{1,5,6},{2,3,7},{4}} => [5,3,7,4,6,1,2] => [4,6,1,5,7,2,3] => [[1,2,5],[3,4,7],[6]] => 2
{{1,5,6},{2,3},{4,7}} => [5,3,2,7,6,1,4] => [3,2,6,1,5,7,4] => [[1,3,6],[2,5],[4,7]] => 3
{{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => [3,2,4,6,1,5,7] => [[1,3,4,7],[2,6],[5]] => 2
{{1,5,7},{2,3,6},{4}} => [5,3,6,4,7,2,1] => [4,6,2,3,7,1,5] => [[1,2,5],[3,4,7],[6]] => 2
{{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => [4,5,1,7,2,3,6] => [[1,2,4,7],[3,5,6]] => 2
{{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => [5,1,6,2,3,7,4] => [[1,3,5,6],[2,4,7]] => 3
{{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => [4,5,1,6,2,3,7] => [[1,2,4,7],[3,5,6]] => 2
{{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => [3,2,6,4,7,1,5] => [[1,3,5],[2,4,7],[6]] => 3
{{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => [5,1,6,4,7,2,3] => [[1,3,5],[2,4,7],[6]] => 3
{{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => [3,2,5,1,7,4,6] => [[1,3,5],[2,6,7],[4]] => 3
{{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => [3,2,5,1,6,4,7] => [[1,3,5,7],[2,6],[4]] => 3
{{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => [3,2,4,6,7,1,5] => [[1,3,4,5],[2,7],[6]] => 2
{{1,5},{2,3,7},{4},{6}} => [5,3,7,4,1,6,2] => [4,5,1,6,7,2,3] => [[1,2,4,5],[3,6,7]] => 2
{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [3,2,5,1,6,7,4] => [[1,3,5,6],[2,7],[4]] => 3
{{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => [3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => 3
{{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 2
{{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => [4,5,2,3,7,1,6] => [[1,2,5],[3,4,7],[6]] => 2
{{1,6},{2,3,5,7},{4}} => [6,3,5,4,7,1,2] => [4,6,1,7,2,3,5] => [[1,2,4,7],[3,5,6]] => 2
{{1,6},{2,3,5},{4,7}} => [6,3,5,7,2,1,4] => [5,2,3,6,1,7,4] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [4,5,2,3,6,1,7] => [[1,2,5,7],[3,4],[6]] => 2
{{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => [4,6,2,3,5,7,1] => [[1,2,5,6],[3,4],[7]] => 2
{{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => [1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 1
{{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => [1,6,2,3,5,7,4] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [1,4,6,2,3,5,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => [5,2,3,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => 3
{{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => [1,6,4,7,2,3,5] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [1,5,2,3,7,4,6] => [[1,2,4,5,7],[3,6]] => 2
{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [1,5,2,3,6,4,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => [4,5,2,3,6,7,1] => [[1,2,5,6],[3,4],[7]] => 2
{{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => [1,4,6,7,2,3,5] => [[1,2,3,4],[5,6,7]] => 1
{{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => [1,5,2,3,6,7,4] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => 2
{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => [3,2,5,4,7,1,6] => [[1,3,5],[2,4,7],[6]] => 3
{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [5,4,6,1,7,2,3] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [3,2,6,1,7,4,5] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]] => 3
{{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => [5,4,6,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => 3
{{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => [1,5,4,7,2,3,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => [1,6,2,3,7,4,5] => [[1,2,4,5,7],[3,6]] => 2
{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [1,5,4,6,2,3,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [3,2,6,4,5,7,1] => [[1,3,5,6],[2,4],[7]] => 3
{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [1,6,4,5,7,2,3] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [[1,2,4,6,7],[3,5]] => 2
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]] => 3
{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [1,5,4,6,7,2,3] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 2
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 3
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => [3,2,4,5,7,1,6] => [[1,3,4,5],[2,7],[6]] => 2
{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [4,5,6,1,7,2,3] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => [3,2,5,6,1,7,4] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [3,2,4,6,1,7,5] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 2
{{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => [4,5,6,2,3,7,1] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => [1,4,5,7,2,3,6] => [[1,2,3,4],[5,6,7]] => 1
{{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => [1,5,6,2,3,7,4] => [[1,2,3,6],[4,5,7]] => 2
{{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => [1,4,6,2,3,7,5] => [[1,2,3,6],[4,5,7]] => 2
{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [1,4,5,6,2,3,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => [3,2,5,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => 3
{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [1,5,6,4,7,2,3] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => [1,3,2,5,7,4,6] => [[1,2,4,5],[3,6,7]] => 2
{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [1,3,2,6,4,7,5] => [[1,2,4,6],[3,5,7]] => 3
{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => 3
{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [1,4,6,5,7,2,3] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 2
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 2
{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [1,4,5,6,7,2,3] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [2,3,7,1,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
{{1,4,5,6},{2,7},{3}} => [4,7,3,5,6,1,2] => [3,6,1,4,5,7,2] => [[1,2,5,6],[3,4],[7]] => 2
{{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => [2,6,1,4,5,7,3] => [[1,2,5,6],[3,4],[7]] => 2
{{1,4,5,6},{2},{3},{7}} => [4,2,3,5,6,1,7] => [2,3,6,1,4,5,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,4,5,7},{2,6},{3}} => [4,6,3,5,7,2,1] => [3,6,2,7,1,4,5] => [[1,2,4],[3,6,7],[5]] => 2
{{1,4,5},{2,6,7},{3}} => [4,6,3,5,1,7,2] => [3,5,1,4,7,2,6] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4,5},{2,6},{3,7}} => [4,6,7,5,1,2,3] => [5,1,4,6,2,7,3] => [[1,3,4,6],[2,7],[5]] => 3
{{1,4,5},{2,6},{3},{7}} => [4,6,3,5,1,2,7] => [3,5,1,4,6,2,7] => [[1,2,5,7],[3,4],[6]] => 2
{{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => [2,6,3,7,1,4,5] => [[1,2,4,7],[3,6],[5]] => 2
{{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => [5,1,4,6,3,7,2] => [[1,3,4,6],[2],[5],[7]] => 3
{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [2,5,1,4,7,3,6] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [2,5,1,4,6,3,7] => [[1,2,5,7],[3,4],[6]] => 2
{{1,4,5,7},{2},{3},{6}} => [4,2,3,5,7,6,1] => [2,3,6,7,1,4,5] => [[1,2,3,4],[5,6,7]] => 1
{{1,4,5},{2,7},{3},{6}} => [4,7,3,5,1,6,2] => [3,5,1,4,6,7,2] => [[1,2,5,6],[3,4],[7]] => 2
{{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => [2,5,1,4,6,7,3] => [[1,2,5,6],[3,4],[7]] => 2
{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [2,3,5,1,4,7,6] => [[1,2,3,6],[4,5,7]] => 2
{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [2,3,5,1,4,6,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => [3,5,2,7,1,4,6] => [[1,2,4],[3,6,7],[5]] => 2
{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [3,6,1,4,7,2,5] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [5,2,6,1,4,7,3] => [[1,3,6],[2,5],[4,7]] => 3
{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [3,5,2,6,1,4,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [3,6,2,5,7,1,4] => [[1,2,5],[3,4],[6,7]] => 2
{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [3,4,1,7,2,5,6] => [[1,2,4,7],[3,5,6]] => 2
{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [4,1,6,2,5,7,3] => [[1,3,5,6],[2,4],[7]] => 3
{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [3,4,1,6,2,5,7] => [[1,2,4,7],[3,5,6]] => 2
{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [5,2,6,3,7,1,4] => [[1,3,5],[2,4,7],[6]] => 3
{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [4,1,6,3,7,2,5] => [[1,3,5],[2,4,7],[6]] => 3
{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [4,1,5,2,7,3,6] => [[1,3,5,7],[2,4,6]] => 3
{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [[1,3,5,7],[2,4,6]] => 3
{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [3,5,2,6,7,1,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [3,4,1,6,7,2,5] => [[1,2,4,5],[3,6,7]] => 2
{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [4,1,5,2,6,7,3] => [[1,3,5,6],[2,4,7]] => 3
{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [3,4,1,5,2,7,6] => [[1,2,4,6],[3,5,7]] => 3
{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [3,4,1,5,2,6,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [2,5,3,7,1,4,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [5,3,6,1,4,7,2] => [[1,3,6],[2,5],[4,7]] => 3
{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [2,6,1,4,7,3,5] => [[1,2,5],[3,4,7],[6]] => 2
{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [2,5,3,6,1,4,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [5,3,6,2,7,1,4] => [[1,3,5],[2,7],[4],[6]] => 3
{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [4,1,5,3,7,2,6] => [[1,3,5],[2,4,7],[6]] => 3
{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [4,1,6,2,7,3,5] => [[1,3,5,7],[2,4,6]] => 3
{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [4,1,5,3,6,2,7] => [[1,3,5,7],[2,4],[6]] => 3
{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [2,6,3,5,7,1,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [4,1,6,3,5,7,2] => [[1,3,5,6],[2,4],[7]] => 3
{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [2,4,1,7,3,5,6] => [[1,2,4,7],[3,5,6]] => 2
{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [2,4,1,6,3,5,7] => [[1,2,4,7],[3,5,6]] => 2
{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [2,5,3,6,7,1,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [4,1,5,3,6,7,2] => [[1,3,5,6],[2,4],[7]] => 3
{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [2,4,1,6,7,3,5] => [[1,2,4,5],[3,6,7]] => 2
{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [2,4,1,5,3,7,6] => [[1,2,4,6],[3,5,7]] => 3
{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [2,4,1,5,3,6,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [2,3,5,7,1,4,6] => [[1,2,3,4],[5,6,7]] => 1
{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [3,5,6,1,4,7,2] => [[1,2,3,6],[4,5],[7]] => 2
{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [2,5,6,1,4,7,3] => [[1,2,3,6],[4,5],[7]] => 2
{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [2,3,6,1,4,7,5] => [[1,2,3,6],[4,5,7]] => 2
{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [2,3,5,6,1,4,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [3,5,6,2,7,1,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [3,4,1,5,7,2,6] => [[1,2,4,5],[3,6,7]] => 2
{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [4,1,5,6,2,7,3] => [[1,3,4,6],[2,5,7]] => 3
{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [3,4,1,6,2,7,5] => [[1,2,4,6],[3,5,7]] => 3
{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [3,4,1,5,6,2,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [2,5,6,3,7,1,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [4,1,5,6,3,7,2] => [[1,3,4,6],[2,5],[7]] => 3
{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [2,4,1,5,7,3,6] => [[1,2,4,5],[3,6,7]] => 2
{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [2,4,1,6,3,7,5] => [[1,2,4,6],[3,5,7]] => 3
{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [2,4,1,5,6,3,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [2,3,6,5,7,1,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [3,4,1,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => 3
{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [2,4,1,6,5,7,3] => [[1,2,4,6],[3,5],[7]] => 3
{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [2,3,4,1,7,5,6] => [[1,2,3,5,7],[4,6]] => 2
{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [2,3,5,6,7,1,4] => [[1,2,3,4,5],[6,7]] => 1
{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [3,4,1,5,6,7,2] => [[1,2,4,5,6],[3,7]] => 2
{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [2,4,1,5,6,7,3] => [[1,2,4,5,6],[3,7]] => 2
{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => 2
{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [3,4,2,7,1,5,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [3,6,1,5,7,2,4] => [[1,2,5],[3,4,7],[6]] => 2
{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [4,2,6,1,5,7,3] => [[1,3,6],[2,5],[4,7]] => 3
{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [3,4,2,6,1,5,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [3,6,2,4,7,1,5] => [[1,2,5],[3,4,7],[6]] => 2
{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [3,5,1,7,2,4,6] => [[1,2,4,7],[3,5,6]] => 2
{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [5,1,6,2,4,7,3] => [[1,3,5,6],[2,4],[7]] => 3
{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => 2
{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [4,2,6,3,7,1,5] => [[1,3,5],[2,4,7],[6]] => 3
{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [5,1,6,3,7,2,4] => [[1,3,5],[2,4,7],[6]] => 3
{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [4,2,5,1,7,3,6] => [[1,3,5],[2,6,7],[4]] => 3
{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [4,2,5,1,6,3,7] => [[1,3,5,7],[2,6],[4]] => 3
{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [3,4,2,6,7,1,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [3,5,1,6,7,2,4] => [[1,2,4,5],[3,6,7]] => 2
{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [4,2,5,1,6,7,3] => [[1,3,5,6],[2,7],[4]] => 3
{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 3
{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 2
{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [3,5,2,4,7,1,6] => [[1,2,5],[3,4,7],[6]] => 2
{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [3,6,1,7,2,4,5] => [[1,2,4,7],[3,5,6]] => 2
{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [5,2,4,6,1,7,3] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [3,5,2,4,6,1,7] => [[1,2,5,7],[3,4],[6]] => 2
{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [3,6,2,4,5,7,1] => [[1,2,5,6],[3,4],[7]] => 2
{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 1
{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [1,6,2,4,5,7,3] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [1,3,6,2,4,5,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [5,2,4,6,3,7,1] => [[1,3,4,6],[2],[5],[7]] => 3
{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [1,6,3,7,2,4,5] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [1,5,2,4,7,3,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [1,5,2,4,6,3,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [3,5,2,4,6,7,1] => [[1,2,5,6],[3,4],[7]] => 2
{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [1,3,6,7,2,4,5] => [[1,2,3,4],[5,6,7]] => 1
{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [1,5,2,4,6,7,3] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [1,3,5,2,4,7,6] => [[1,2,3,6],[4,5,7]] => 2
{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [1,3,5,2,4,6,7] => [[1,2,3,6,7],[4,5]] => 1
{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [4,2,5,3,7,1,6] => [[1,3,5],[2,4,7],[6]] => 3
{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [5,3,6,1,7,2,4] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [4,2,6,1,7,3,5] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [4,2,5,3,6,1,7] => [[1,3,5,7],[2,4],[6]] => 3
{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [5,3,6,2,4,7,1] => [[1,3,6],[2,5],[4],[7]] => 3
{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,5,3,7,2,4,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [1,6,2,4,7,3,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [1,5,3,6,2,4,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [4,2,6,3,5,7,1] => [[1,3,5,6],[2,4],[7]] => 3
{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [1,6,3,5,7,2,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [1,4,2,7,3,5,6] => [[1,2,4,6,7],[3,5]] => 2
{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [1,4,2,6,3,5,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [4,2,5,3,6,7,1] => [[1,3,5,6],[2,4],[7]] => 3
{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [1,5,3,6,7,2,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [1,4,2,6,7,3,5] => [[1,2,4,5],[3,6,7]] => 2
{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [1,4,2,5,3,7,6] => [[1,2,4,6],[3,5,7]] => 3
{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [1,4,2,5,3,6,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [3,4,2,5,7,1,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [3,5,6,1,7,2,4] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [4,2,5,6,1,7,3] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [3,4,2,6,1,7,5] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [3,5,6,2,4,7,1] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [1,3,5,7,2,4,6] => [[1,2,3,4],[5,6,7]] => 1
{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [1,5,6,2,4,7,3] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [1,3,6,2,4,7,5] => [[1,2,3,6],[4,5,7]] => 2
{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [1,3,5,6,2,4,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [4,2,5,6,3,7,1] => [[1,3,4,6],[2,5],[7]] => 3
{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [1,5,6,3,7,2,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [1,4,2,5,7,3,6] => [[1,2,4,5],[3,6,7]] => 2
{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [1,4,2,6,3,7,5] => [[1,2,4,6],[3,5,7]] => 3
{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [1,4,2,5,6,3,7] => [[1,2,4,5,7],[3,6]] => 2
{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [3,4,2,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [1,3,6,5,7,2,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [1,4,2,6,5,7,3] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [1,3,4,2,7,5,6] => [[1,2,3,5,7],[4,6]] => 2
{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [1,3,5,6,7,2,4] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [1,4,2,5,6,7,3] => [[1,2,4,5,6],[3,7]] => 2
{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [2,4,3,7,1,5,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [4,3,6,1,5,7,2] => [[1,3,6],[2,5],[4,7]] => 3
{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [2,6,1,5,7,3,4] => [[1,2,5],[3,4,7],[6]] => 2
{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [2,4,3,6,1,5,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [4,3,6,2,7,1,5] => [[1,3,5],[2,7],[4],[6]] => 3
{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [4,3,5,1,7,2,6] => [[1,3,5],[2,6,7],[4]] => 3
{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [5,1,6,2,7,3,4] => [[1,3,5,7],[2,4,6]] => 3
{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [4,3,5,1,6,2,7] => [[1,3,5,7],[2,6],[4]] => 3
{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [2,6,3,4,7,1,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [5,1,6,3,4,7,2] => [[1,3,5,6],[2,4],[7]] => 3
{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [2,5,1,7,3,4,6] => [[1,2,4,7],[3,5,6]] => 2
{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [2,5,1,6,3,4,7] => [[1,2,4,7],[3,5,6]] => 2
{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [2,4,3,6,7,1,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [4,3,5,1,6,7,2] => [[1,3,5,6],[2,7],[4]] => 3
{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [2,5,1,6,7,3,4] => [[1,2,4,5],[3,6,7]] => 2
{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 3
{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 2
{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [4,3,5,2,7,1,6] => [[1,3,5],[2,7],[4],[6]] => 3
{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [4,3,6,1,7,2,5] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [5,2,6,1,7,3,4] => [[1,3,5],[2,6,7],[4]] => 3
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 3
{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [4,3,6,2,5,7,1] => [[1,3,6],[2,5],[4],[7]] => 3
{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [1,4,3,7,2,5,6] => [[1,2,4,7],[3,6],[5]] => 2
{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [1,6,2,5,7,3,4] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [1,4,3,6,2,5,7] => [[1,2,4,7],[3,6],[5]] => 2
{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [5,2,6,3,4,7,1] => [[1,3,5,6],[2,4],[7]] => 3
{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [1,5,2,7,3,4,6] => [[1,2,4,6,7],[3,5]] => 2
{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [1,5,2,6,3,4,7] => [[1,2,4,6,7],[3,5]] => 2
{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 3
{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [1,4,3,6,7,2,5] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [1,5,2,6,7,3,4] => [[1,2,4,5],[3,6,7]] => 2
{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]] => 3
{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]] => 2
{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [2,5,3,4,7,1,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [5,3,4,6,1,7,2] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [2,6,1,7,3,4,5] => [[1,2,4,7],[3,5,6]] => 2
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [2,5,3,4,6,1,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [5,3,4,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 3
{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [1,5,3,4,7,2,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [1,6,2,7,3,4,5] => [[1,2,4,6,7],[3,5]] => 2
{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [1,5,3,4,6,2,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [2,6,3,4,5,7,1] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,6,3,4,5,7,2] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 1
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 1
{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [2,5,3,4,6,7,1] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,5,3,4,6,7,2] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 1
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 1
{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [2,4,3,5,7,1,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [4,3,5,6,1,7,2] => [[1,3,4,6],[2,7],[5]] => 3
{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [2,5,6,1,7,3,4] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [2,4,3,6,1,7,5] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 3
{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [1,4,3,5,7,2,6] => [[1,2,4,5],[3,7],[6]] => 2
{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [1,5,6,2,7,3,4] => [[1,2,3,5],[4,6,7]] => 2
{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [1,4,3,6,2,7,5] => [[1,2,4,6],[3,7],[5]] => 3
{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]] => 2
{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [2,5,6,3,4,7,1] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,5,6,3,4,7,2] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 1
{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [1,2,6,3,4,7,5] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [1,2,6,5,7,3,4] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [[1,2,3,5,7],[4,6]] => 2
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]] => 2
{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [2,3,4,7,1,5,6] => [[1,2,3,4,7],[5,6]] => 1
{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [3,4,6,1,5,7,2] => [[1,2,3,6],[4,5],[7]] => 2
{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [2,4,6,1,5,7,3] => [[1,2,3,6],[4,5],[7]] => 2
{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [2,3,6,1,5,7,4] => [[1,2,3,6],[4,5],[7]] => 2
{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [2,3,4,6,1,5,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [3,4,6,2,7,1,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [3,4,5,1,7,2,6] => [[1,2,3,5],[4,6,7]] => 2
{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [4,5,1,6,2,7,3] => [[1,2,4,6],[3,5,7]] => 3
{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [3,5,1,6,2,7,4] => [[1,2,4,6],[3,5,7]] => 3
{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [3,4,5,1,6,2,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [2,4,6,3,7,1,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [4,5,1,6,3,7,2] => [[1,2,4,6],[3,5],[7]] => 3
{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [2,4,5,1,7,3,6] => [[1,2,3,5],[4,6,7]] => 2
{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [2,5,1,6,3,7,4] => [[1,2,4,6],[3,5,7]] => 3
{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [2,4,5,1,6,3,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [2,3,6,4,7,1,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [3,5,1,6,4,7,2] => [[1,2,4,6],[3,5],[7]] => 3
{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [2,5,1,6,4,7,3] => [[1,2,4,6],[3,5],[7]] => 3
{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [2,3,5,1,7,4,6] => [[1,2,3,5],[4,6,7]] => 2
{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [2,3,5,1,6,4,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [2,3,4,6,7,1,5] => [[1,2,3,4,5],[6,7]] => 1
{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [3,4,5,1,6,7,2] => [[1,2,3,5,6],[4,7]] => 2
{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [2,4,5,1,6,7,3] => [[1,2,3,5,6],[4,7]] => 2
{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [2,3,5,1,6,7,4] => [[1,2,3,5,6],[4,7]] => 2
{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => 2
{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => 1
{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [3,4,5,2,7,1,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [3,4,6,1,7,2,5] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [4,5,2,6,1,7,3] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [3,5,2,6,1,7,4] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [3,4,6,2,5,7,1] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [1,3,4,7,2,5,6] => [[1,2,3,4,7],[5,6]] => 1
{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [1,4,6,2,5,7,3] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [1,3,6,2,5,7,4] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [1,3,4,6,2,5,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [4,5,2,6,3,7,1] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [1,4,6,3,7,2,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [1,4,5,2,7,3,6] => [[1,2,3,5],[4,6,7]] => 2
{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [1,5,2,6,3,7,4] => [[1,2,4,6],[3,5,7]] => 3
{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [1,4,5,2,6,3,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [3,5,2,6,4,7,1] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,3,6,4,7,2,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [1,5,2,6,4,7,3] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [1,3,5,2,7,4,6] => [[1,2,3,5],[4,6,7]] => 2
{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [1,3,5,2,6,4,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [1,3,4,6,7,2,5] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [1,4,5,2,6,7,3] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [1,3,5,2,6,7,4] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => 1
{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [2,4,5,3,7,1,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [4,5,3,6,1,7,2] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [2,4,6,1,7,3,5] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [2,5,3,6,1,7,4] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 3
{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [1,4,5,3,7,2,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => 2
{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [1,5,3,6,2,7,4] => [[1,2,4,6],[3,7],[5]] => 3
{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [1,4,5,3,6,2,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [2,4,6,3,5,7,1] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [1,4,6,3,5,7,2] => [[1,2,3,6],[4,5],[7]] => 2
{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 1
{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [1,2,6,3,5,7,4] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [1,2,4,6,3,5,7] => [[1,2,3,4,7],[5,6]] => 1
{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [2,5,3,6,4,7,1] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [1,5,3,6,4,7,2] => [[1,2,4,6],[3,5],[7]] => 3
{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [1,2,6,4,7,3,5] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [1,2,5,3,7,4,6] => [[1,2,3,5,7],[4,6]] => 2
{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [1,2,5,3,6,4,7] => [[1,2,3,5,7],[4,6]] => 2
{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [2,4,5,3,6,7,1] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [1,2,4,6,7,3,5] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [1,2,5,3,6,7,4] => [[1,2,3,5,6],[4,7]] => 2
{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 1
{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [2,3,5,4,7,1,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [3,5,4,6,1,7,2] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [2,5,4,6,1,7,3] => [[1,2,4,6],[3,7],[5]] => 3
{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [2,3,6,1,7,4,5] => [[1,2,3,5],[4,6,7]] => 2
{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [3,5,4,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 3
{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [1,3,5,4,7,2,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [1,5,4,6,2,7,3] => [[1,2,4,6],[3,7],[5]] => 3
{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [1,3,6,2,7,4,5] => [[1,2,3,5],[4,6,7]] => 2
{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [2,5,4,6,3,7,1] => [[1,2,4,6],[3],[5],[7]] => 3
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => [[1,2,4,6],[3],[5],[7]] => 3
{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [1,2,5,4,7,3,6] => [[1,2,3,5],[4,7],[6]] => 2
{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [1,2,6,3,7,4,5] => [[1,2,3,5,7],[4,6]] => 2
{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]] => 2
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [2,3,6,4,5,7,1] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,3,6,4,5,7,2] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [1,2,6,4,5,7,3] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 1
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 1
{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]] => 2
{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [2,3,4,5,7,1,6] => [[1,2,3,4,5],[6,7]] => 1
{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [3,4,5,6,1,7,2] => [[1,2,3,4,6],[5,7]] => 2
{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [2,4,5,6,1,7,3] => [[1,2,3,4,6],[5,7]] => 2
{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [2,3,5,6,1,7,4] => [[1,2,3,4,6],[5,7]] => 2
{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [2,3,4,6,1,7,5] => [[1,2,3,4,6],[5,7]] => 2
{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => 1
{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [1,3,4,5,7,2,6] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [1,4,5,6,2,7,3] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [1,3,5,6,2,7,4] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [1,3,4,6,2,7,5] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => 1
{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [2,4,5,6,3,7,1] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [1,2,4,5,7,3,6] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [1,2,5,6,3,7,4] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [1,2,4,6,3,7,5] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => 1
{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [2,3,5,6,4,7,1] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [1,2,5,6,4,7,3] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 1
{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [1,2,3,6,4,7,5] => [[1,2,3,4,6],[5,7]] => 2
{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 1
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]] => 2
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 1
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 1
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 1
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 0
{{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,3},{2,4},{5,6},{7,8}} => [3,4,1,2,6,5,8,7] => [3,1,4,2,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,5},{2,3},{4,6},{7,8}} => [5,3,2,6,1,4,8,7] => [3,2,5,1,6,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,6},{2,3},{4,5},{7,8}} => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,7},{2,3},{4,5},{6,8}} => [7,3,2,5,4,8,1,6] => [3,2,5,4,7,1,8,6] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,8},{2,4},{3,5},{6,7}} => [8,4,5,2,3,7,6,1] => [4,2,5,3,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,7},{2,4},{3,5},{6,8}} => [7,4,5,2,3,8,1,6] => [4,2,5,3,7,1,8,6] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,6},{2,4},{3,5},{7,8}} => [6,4,5,2,3,1,8,7] => [4,2,5,3,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,5},{2,4},{3,6},{7,8}} => [5,4,6,2,1,3,8,7] => [4,2,5,1,6,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,4},{2,5},{3,6},{7,8}} => [4,5,6,1,2,3,8,7] => [4,1,5,2,6,3,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,3},{2,5},{4,6},{7,8}} => [3,5,1,6,2,4,8,7] => [3,1,5,2,6,4,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7] => [2,1,5,3,6,4,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,3},{2,6},{4,5},{7,8}} => [3,6,1,5,4,2,8,7] => [3,1,5,4,6,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,4},{2,6},{3,5},{7,8}} => [4,6,5,1,3,2,8,7] => [4,1,5,3,6,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,5},{2,6},{3,4},{7,8}} => [5,6,4,3,1,2,8,7] => [4,3,5,1,6,2,8,7] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,7},{2,5},{3,4},{6,8}} => [7,5,4,3,2,8,1,6] => [4,3,5,2,7,1,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,8},{2,5},{3,4},{6,7}} => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 4
{{1,8},{2,6},{3,4},{5,7}} => [8,6,4,3,7,2,5,1] => [4,3,6,2,7,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 4
{{1,7},{2,6},{3,4},{5,8}} => [7,6,4,3,8,2,1,5] => [4,3,6,2,7,1,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,6},{2,7},{3,4},{5,8}} => [6,7,4,3,8,1,2,5] => [4,3,6,1,7,2,8,5] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,5},{2,7},{3,4},{6,8}} => [5,7,4,3,1,8,2,6] => [4,3,5,1,7,2,8,6] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,4},{2,7},{3,5},{6,8}} => [4,7,5,1,3,8,2,6] => [4,1,5,3,7,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,3},{2,7},{4,5},{6,8}} => [3,7,1,5,4,8,2,6] => [3,1,5,4,7,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,2},{3,7},{4,5},{6,8}} => [2,1,7,5,4,8,3,6] => [2,1,5,4,7,3,8,6] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,3},{2,8},{4,5},{6,7}} => [3,8,1,5,4,7,6,2] => [3,1,5,4,7,6,8,2] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,4},{2,8},{3,5},{6,7}} => [4,8,5,1,3,7,6,2] => [4,1,5,3,7,6,8,2] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,5},{2,8},{3,4},{6,7}} => [5,8,4,3,1,7,6,2] => [4,3,5,1,7,6,8,2] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,6},{2,8},{3,4},{5,7}} => [6,8,4,3,7,1,5,2] => [4,3,6,1,7,5,8,2] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,7},{2,8},{3,4},{5,6}} => [7,8,4,3,6,5,1,2] => [4,3,6,5,7,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 4
{{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,8},{2,7},{3,5},{4,6}} => [8,7,5,6,3,4,2,1] => [5,3,6,4,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,7},{2,8},{3,5},{4,6}} => [7,8,5,6,3,4,1,2] => [5,3,6,4,7,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 4
{{1,6},{2,8},{3,5},{4,7}} => [6,8,5,7,3,1,4,2] => [5,3,6,1,7,4,8,2] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,5},{2,8},{3,6},{4,7}} => [5,8,6,7,1,3,4,2] => [5,1,6,3,7,4,8,2] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,4},{2,8},{3,6},{5,7}} => [4,8,6,1,7,3,5,2] => [4,1,6,3,7,5,8,2] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,3},{2,8},{4,6},{5,7}} => [3,8,1,6,7,4,5,2] => [3,1,6,4,7,5,8,2] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,2},{3,8},{4,6},{5,7}} => [2,1,8,6,7,4,5,3] => [2,1,6,4,7,5,8,3] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,2},{3,7},{4,6},{5,8}} => [2,1,7,6,8,4,3,5] => [2,1,6,4,7,3,8,5] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,3},{2,7},{4,6},{5,8}} => [3,7,1,6,8,4,2,5] => [3,1,6,4,7,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,4},{2,7},{3,6},{5,8}} => [4,7,6,1,8,3,2,5] => [4,1,6,3,7,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,5},{2,7},{3,6},{4,8}} => [5,7,6,8,1,3,2,4] => [5,1,6,3,7,2,8,4] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,6},{2,7},{3,5},{4,8}} => [6,7,5,8,3,1,2,4] => [5,3,6,1,7,2,8,4] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,7},{2,6},{3,5},{4,8}} => [7,6,5,8,3,2,1,4] => [5,3,6,2,7,1,8,4] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,8},{2,6},{3,5},{4,7}} => [8,6,5,7,3,2,4,1] => [5,3,6,2,7,4,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 4
{{1,8},{2,5},{3,6},{4,7}} => [8,5,6,7,2,3,4,1] => [5,2,6,3,7,4,8,1] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,7},{2,5},{3,6},{4,8}} => [7,5,6,8,2,3,1,4] => [5,2,6,3,7,1,8,4] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,6},{2,5},{3,7},{4,8}} => [6,5,7,8,2,1,3,4] => [5,2,6,1,7,3,8,4] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,5},{2,6},{3,7},{4,8}} => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,4},{2,6},{3,7},{5,8}} => [4,6,7,1,8,2,3,5] => [4,1,6,2,7,3,8,5] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,3},{2,6},{4,7},{5,8}} => [3,6,1,7,8,2,4,5] => [3,1,6,2,7,4,8,5] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,6},{4,7},{5,8}} => [2,1,6,7,8,3,4,5] => [2,1,6,3,7,4,8,5] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => [2,1,5,3,7,4,8,6] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,3},{2,5},{4,7},{6,8}} => [3,5,1,7,2,8,4,6] => [3,1,5,2,7,4,8,6] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,4},{2,5},{3,7},{6,8}} => [4,5,7,1,2,8,3,6] => [4,1,5,2,7,3,8,6] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,5},{2,4},{3,7},{6,8}} => [5,4,7,2,1,8,3,6] => [4,2,5,1,7,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,6},{2,4},{3,7},{5,8}} => [6,4,7,2,8,1,3,5] => [4,2,6,1,7,3,8,5] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,7},{2,4},{3,6},{5,8}} => [7,4,6,2,8,3,1,5] => [4,2,6,3,7,1,8,5] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,8},{2,4},{3,6},{5,7}} => [8,4,6,2,7,3,5,1] => [4,2,6,3,7,5,8,1] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,8},{2,3},{4,6},{5,7}} => [8,3,2,6,7,4,5,1] => [3,2,6,4,7,5,8,1] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,7},{2,3},{4,6},{5,8}} => [7,3,2,6,8,4,1,5] => [3,2,6,4,7,1,8,5] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,6},{2,3},{4,7},{5,8}} => [6,3,2,7,8,1,4,5] => [3,2,6,1,7,4,8,5] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,5},{2,3},{4,7},{6,8}} => [5,3,2,7,1,8,4,6] => [3,2,5,1,7,4,8,6] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,4},{2,3},{5,7},{6,8}} => [4,3,2,1,7,8,5,6] => [3,2,4,1,7,5,8,6] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6] => [3,1,4,2,7,5,8,6] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,5,8,6] => [[1,3,5,7],[2,4,6,8]] => 4
{{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,3},{2,4},{5,8},{6,7}} => [3,4,1,2,8,7,6,5] => [3,1,4,2,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,4},{2,3},{5,8},{6,7}} => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,5},{2,3},{4,8},{6,7}} => [5,3,2,8,1,7,6,4] => [3,2,5,1,7,6,8,4] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,6},{2,3},{4,8},{5,7}} => [6,3,2,8,7,1,5,4] => [3,2,6,1,7,5,8,4] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,7},{2,3},{4,8},{5,6}} => [7,3,2,8,6,5,1,4] => [3,2,6,5,7,1,8,4] => [[1,3,5,7],[2,4],[6,8]] => 4
{{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,8},{2,4},{3,7},{5,6}} => [8,4,7,2,6,5,3,1] => [4,2,6,5,7,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,7},{2,4},{3,8},{5,6}} => [7,4,8,2,6,5,1,3] => [4,2,6,5,7,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 4
{{1,6},{2,4},{3,8},{5,7}} => [6,4,8,2,7,1,5,3] => [4,2,6,1,7,5,8,3] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,5},{2,4},{3,8},{6,7}} => [5,4,8,2,1,7,6,3] => [4,2,5,1,7,6,8,3] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,4},{2,5},{3,8},{6,7}} => [4,5,8,1,2,7,6,3] => [4,1,5,2,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,3},{2,5},{4,8},{6,7}} => [3,5,1,8,2,7,6,4] => [3,1,5,2,7,6,8,4] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,2},{3,5},{4,8},{6,7}} => [2,1,5,8,3,7,6,4] => [2,1,5,3,7,6,8,4] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,2},{3,6},{4,8},{5,7}} => [2,1,6,8,7,3,5,4] => [2,1,6,3,7,5,8,4] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,3},{2,6},{4,8},{5,7}} => [3,6,1,8,7,2,5,4] => [3,1,6,2,7,5,8,4] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,4},{2,6},{3,8},{5,7}} => [4,6,8,1,7,2,5,3] => [4,1,6,2,7,5,8,3] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,5},{2,6},{3,8},{4,7}} => [5,6,8,7,1,2,4,3] => [5,1,6,2,7,4,8,3] => [[1,3,5,7],[2,4,6],[8]] => 4
{{1,6},{2,5},{3,8},{4,7}} => [6,5,8,7,2,1,4,3] => [5,2,6,1,7,4,8,3] => [[1,3,5,7],[2,6],[4,8]] => 4
{{1,7},{2,5},{3,8},{4,6}} => [7,5,8,6,2,4,1,3] => [5,2,6,4,7,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 4
{{1,8},{2,5},{3,7},{4,6}} => [8,5,7,6,2,4,3,1] => [5,2,6,4,7,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,8},{2,6},{3,7},{4,5}} => [8,6,7,5,4,2,3,1] => [5,4,6,2,7,3,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 4
{{1,7},{2,6},{3,8},{4,5}} => [7,6,8,5,4,2,1,3] => [5,4,6,2,7,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,6},{2,7},{3,8},{4,5}} => [6,7,8,5,4,1,2,3] => [5,4,6,1,7,2,8,3] => [[1,3,5,7],[2,6,8],[4]] => 4
{{1,5},{2,7},{3,8},{4,6}} => [5,7,8,6,1,4,2,3] => [5,1,6,4,7,2,8,3] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,4},{2,7},{3,8},{5,6}} => [4,7,8,1,6,5,2,3] => [4,1,6,5,7,2,8,3] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,3},{2,7},{4,8},{5,6}} => [3,7,1,8,6,5,2,4] => [3,1,6,5,7,2,8,4] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,2},{3,7},{4,8},{5,6}} => [2,1,7,8,6,5,3,4] => [2,1,6,5,7,3,8,4] => [[1,3,5,7],[2,4,8],[6]] => 4
{{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,3},{2,8},{4,7},{5,6}} => [3,8,1,7,6,5,4,2] => [3,1,6,5,7,4,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,4},{2,8},{3,7},{5,6}} => [4,8,7,1,6,5,3,2] => [4,1,6,5,7,3,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,5},{2,8},{3,7},{4,6}} => [5,8,7,6,1,4,3,2] => [5,1,6,4,7,3,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 4
{{1,6},{2,8},{3,7},{4,5}} => [6,8,7,5,4,1,3,2] => [5,4,6,1,7,3,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 4
{{1,7},{2,8},{3,6},{4,5}} => [7,8,6,5,4,3,1,2] => [5,4,6,3,7,1,8,2] => [[1,3,5,7],[2,8],[4],[6]] => 4
{{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 4
{{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
{{1,6},{2,7},{3,8},{4,9},{5,10}} => [6,7,8,9,10,1,2,3,4,5] => [6,1,7,2,8,3,9,4,10,5] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2},{3},{4},{5},{6,8},{7}} => [1,2,3,4,5,8,7,6] => [1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2},{3},{4},{5},{6,7,8}} => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 1
{{1},{2},{3},{4},{5,8},{6},{7}} => [1,2,3,4,8,6,7,5] => [1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2},{3},{4},{5,7,8},{6}} => [1,2,3,4,7,6,8,5] => [1,2,3,4,6,8,5,7] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3},{4},{5,8},{6,7}} => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]] => 2
{{1},{2},{3},{4},{5,6,8},{7}} => [1,2,3,4,6,8,7,5] => [1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3},{4},{5,6,7,8}} => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 1
{{1},{2},{3},{4,8},{5},{6},{7}} => [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2},{3},{4,6,8},{5},{7}} => [1,2,3,6,5,8,7,4] => [1,2,3,5,7,8,4,6] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3},{4,6,7,8},{5}} => [1,2,3,6,5,7,8,4] => [1,2,3,5,8,4,6,7] => [[1,2,3,4,5,8],[6,7]] => 1
{{1},{2},{3},{4,7,8},{5,6}} => [1,2,3,7,6,5,8,4] => [1,2,3,6,5,8,4,7] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1},{2},{3},{4,5,8},{6},{7}} => [1,2,3,5,8,6,7,4] => [1,2,3,6,7,8,4,5] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3},{4,8},{5,6,7}} => [1,2,3,8,6,7,5,4] => [1,2,3,7,5,6,8,4] => [[1,2,3,4,6,7],[5],[8]] => 2
{{1},{2},{3},{4,5,6,8},{7}} => [1,2,3,5,6,8,7,4] => [1,2,3,7,8,4,5,6] => [[1,2,3,4,5,8],[6,7]] => 1
{{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 1
{{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2},{3,4},{5,8},{6,7}} => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1},{2},{3,4},{5,6,7,8}} => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2},{3,5},{4},{6,7,8}} => [1,2,5,4,3,7,8,6] => [1,2,4,5,3,8,6,7] => [[1,2,3,4,6,8],[5,7]] => 2
{{1},{2},{3,8},{4},{5},{6},{7}} => [1,2,8,4,5,6,7,3] => [1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2},{3,7,8},{4},{5,6}} => [1,2,7,4,6,5,8,3] => [1,2,4,6,5,8,3,7] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1},{2},{3,5,8},{4},{6},{7}} => [1,2,5,4,8,6,7,3] => [1,2,4,6,7,8,3,5] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3,5,7,8},{4},{6}} => [1,2,5,4,7,6,8,3] => [1,2,4,6,8,3,5,7] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2},{3,8},{4},{5,6,7}} => [1,2,8,4,6,7,5,3] => [1,2,4,7,5,6,8,3] => [[1,2,3,4,6,7],[5],[8]] => 2
{{1},{2},{3,5,6,7,8},{4}} => [1,2,5,4,6,7,8,3] => [1,2,4,8,3,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
{{1},{2},{3,4,5},{6,7,8}} => [1,2,4,5,3,7,8,6] => [1,2,5,3,4,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 2
{{1},{2},{3,6,7,8},{4,5}} => [1,2,6,5,4,7,8,3] => [1,2,5,4,8,3,6,7] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,4,8},{5},{6},{7}} => [1,2,4,8,5,6,7,3] => [1,2,5,6,7,8,3,4] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2},{3,8},{4,6,7},{5}} => [1,2,8,6,5,7,4,3] => [1,2,5,7,4,6,8,3] => [[1,2,3,4,7],[5,6],[8]] => 2
{{1},{2},{3,4,5,6},{7,8}} => [1,2,4,5,6,3,8,7] => [1,2,6,3,4,5,8,7] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2},{3,7,8},{4,5,6}} => [1,2,7,5,6,4,8,3] => [1,2,6,4,5,8,3,7] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2},{3,4,7,8},{5,6}} => [1,2,4,7,6,5,8,3] => [1,2,6,5,8,3,4,7] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,4,5,8},{6},{7}} => [1,2,4,5,8,6,7,3] => [1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2},{3,4,5,6,7},{8}} => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => 1
{{1},{2},{3,8},{4,5,6,7}} => [1,2,8,5,6,7,4,3] => [1,2,7,4,5,6,8,3] => [[1,2,3,5,6,7],[4],[8]] => 2
{{1},{2},{3,4,8},{5,6,7}} => [1,2,4,8,6,7,5,3] => [1,2,7,5,6,8,3,4] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2},{3,4,5,8},{6,7}} => [1,2,4,5,8,7,6,3] => [1,2,7,6,8,3,4,5] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,4,5,6,8},{7}} => [1,2,4,5,6,8,7,3] => [1,2,7,8,3,4,5,6] => [[1,2,3,4,7,8],[5,6]] => 1
{{1},{2},{3,4,5,6,7,8}} => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 1
{{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 2
{{1},{2,3},{4},{5,8},{6,7}} => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2,3},{4},{5,6,7,8}} => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => 2
{{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,3},{4,5},{6,8},{7}} => [1,3,2,5,4,8,7,6] => [1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]] => 3
{{1},{2,3},{4,5},{6,7,8}} => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,3},{4,6,7},{5},{8}} => [1,3,2,6,5,7,4,8] => [1,3,2,5,7,4,6,8] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,3},{4,6,8},{5},{7}} => [1,3,2,6,5,8,7,4] => [1,3,2,5,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,3},{4,6,7,8},{5}} => [1,3,2,6,5,7,8,4] => [1,3,2,5,8,4,6,7] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,3},{4,7},{5,6},{8}} => [1,3,2,7,6,5,4,8] => [1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1},{2,3},{4,8},{5,6},{7}} => [1,3,2,8,6,5,7,4] => [1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,3},{4,7,8},{5,6}} => [1,3,2,7,6,5,8,4] => [1,3,2,6,5,8,4,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,3},{4,8},{5,7},{6}} => [1,3,2,8,7,6,5,4] => [1,3,2,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2,3},{4,5,8},{6},{7}} => [1,3,2,5,8,6,7,4] => [1,3,2,6,7,8,4,5] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,3},{4,8},{5,6,7}} => [1,3,2,8,6,7,5,4] => [1,3,2,7,5,6,8,4] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,3},{4,5,8},{6,7}} => [1,3,2,5,8,7,6,4] => [1,3,2,7,6,8,4,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,3},{4,5,6,7,8}} => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 2
{{1},{2,4},{3},{5},{6},{7,8}} => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2,4},{3},{5},{6,8},{7}} => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2,4},{3},{5},{6,7,8}} => [1,4,3,2,5,7,8,6] => [1,3,4,2,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 2
{{1},{2,4},{3},{5,6},{7,8}} => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
{{1},{2,4},{3},{5,7},{6},{8}} => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 2
{{1},{2,4},{3},{5,8},{6,7}} => [1,4,3,2,8,7,6,5] => [1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1},{2,4},{3},{5,6,7,8}} => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2,5},{3},{4},{6,8},{7}} => [1,5,3,4,2,8,7,6] => [1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 2
{{1},{2,8},{3},{4},{5},{6},{7}} => [1,8,3,4,5,6,7,2] => [1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => 1
{{1},{2,5,6,7,8},{3},{4}} => [1,5,3,4,6,7,8,2] => [1,3,4,8,2,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
{{1},{2,4,5},{3},{6,7},{8}} => [1,4,3,5,2,7,6,8] => [1,3,5,2,4,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,4,5},{3},{6,7,8}} => [1,4,3,5,2,7,8,6] => [1,3,5,2,4,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,6,8},{3},{4,5},{7}} => [1,6,3,5,4,8,7,2] => [1,3,5,4,7,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,4,8},{3},{5},{6},{7}} => [1,4,3,8,5,6,7,2] => [1,3,5,6,7,8,2,4] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2,4,6,7},{3},{5},{8}} => [1,4,3,6,5,7,2,8] => [1,3,5,7,2,4,6,8] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,8},{3},{4,6,7},{5}} => [1,8,3,6,5,7,4,2] => [1,3,5,7,4,6,8,2] => [[1,2,3,4,7],[5,6],[8]] => 2
{{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,2,4,6] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2,4,6,7,8},{3},{5}} => [1,4,3,6,5,7,8,2] => [1,3,5,8,2,4,6,7] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,7,8},{3},{4,5,6}} => [1,7,3,5,6,4,8,2] => [1,3,6,4,5,8,2,7] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,4,7},{3},{5,6},{8}} => [1,4,3,7,6,5,2,8] => [1,3,6,5,7,2,4,8] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2,8},{3},{4,7},{5,6}} => [1,8,3,7,6,5,4,2] => [1,3,6,5,7,4,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 3
{{1},{2,4,8},{3},{5,6},{7}} => [1,4,3,8,6,5,7,2] => [1,3,6,5,7,8,2,4] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => [1,3,6,7,5,8,2,4] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1},{2,4,8},{3},{5,6,7}} => [1,4,3,8,6,7,5,2] => [1,3,7,5,6,8,2,4] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,4,5,6,8},{3},{7}} => [1,4,3,5,6,8,7,2] => [1,3,7,8,2,4,5,6] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,4,5,6,7,8},{3}} => [1,4,3,5,6,7,8,2] => [1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,3,4},{5},{6,7,8}} => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 2
{{1},{2,3,4},{5,6},{7,8}} => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 3
{{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [[1,2,4,5,7,8],[3,6]] => 2
{{1},{2,3,4},{5,8},{6,7}} => [1,3,4,2,8,7,6,5] => [1,4,2,3,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2,3,4},{5,6,8},{7}} => [1,3,4,2,6,8,7,5] => [1,4,2,3,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,5},{3,4},{6,7},{8}} => [1,5,4,3,2,7,6,8] => [1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 3
{{1},{2,6,8},{3,4},{5},{7}} => [1,6,4,3,5,8,7,2] => [1,4,3,5,7,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,7},{3,4},{5,6},{8}} => [1,7,4,3,6,5,2,8] => [1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1},{2,8},{3,4},{5,6},{7}} => [1,8,4,3,6,5,7,2] => [1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,7,8},{3,4},{5,6}} => [1,7,4,3,6,5,8,2] => [1,4,3,6,5,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,5,8},{3,4},{6,7}} => [1,5,4,3,8,7,6,2] => [1,4,3,7,6,8,2,5] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1},{2,5,6,7,8},{3,4}} => [1,5,4,3,6,7,8,2] => [1,4,3,8,2,5,6,7] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1},{2,3,5},{4},{6,7,8}} => [1,3,5,4,2,7,8,6] => [1,4,5,2,3,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => [1,4,5,3,7,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,6,7,8},{3,5},{4}} => [1,6,5,4,3,7,8,2] => [1,4,5,3,8,2,6,7] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,8,4,5,6,7,2] => [1,4,5,6,7,8,2,3] => [[1,2,3,4,5,6],[7,8]] => 1
{{1},{2,3,7,8},{4},{5},{6}} => [1,3,7,4,5,6,8,2] => [1,4,5,6,8,2,3,7] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2,3,6,7},{4},{5},{8}} => [1,3,6,4,5,7,2,8] => [1,4,5,7,2,3,6,8] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,3,6,8},{4},{5},{7}} => [1,3,6,4,5,8,7,2] => [1,4,5,7,8,2,3,6] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2,3,7},{4},{5,6},{8}} => [1,3,7,4,6,5,2,8] => [1,4,6,5,7,2,3,8] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2,8},{3,7},{4},{5,6}} => [1,8,7,4,6,5,3,2] => [1,4,6,5,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 3
{{1},{2,3,5,7},{4},{6},{8}} => [1,3,5,4,7,6,2,8] => [1,4,6,7,2,3,5,8] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,8},{3,5,7},{4},{6}} => [1,8,5,4,7,6,3,2] => [1,4,6,7,3,5,8,2] => [[1,2,3,4,7],[5,6],[8]] => 2
{{1},{2,3,5,7,8},{4},{6}} => [1,3,5,4,7,6,8,2] => [1,4,6,8,2,3,5,7] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,3,5,6,7},{4},{8}} => [1,3,5,4,6,7,2,8] => [1,4,7,2,3,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,8},{3,5,6,7},{4}} => [1,8,5,4,6,7,3,2] => [1,4,7,3,5,6,8,2] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,3,8},{4},{5,6,7}} => [1,3,8,4,6,7,5,2] => [1,4,7,5,6,8,2,3] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,3,5,8},{4},{6,7}} => [1,3,5,4,8,7,6,2] => [1,4,7,6,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1},{2,3,5,6,8},{4},{7}} => [1,3,5,4,6,8,7,2] => [1,4,7,8,2,3,5,6] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,3,5,6,7,8},{4}} => [1,3,5,4,6,7,8,2] => [1,4,8,2,3,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,6,8},{3,4,5},{7}} => [1,6,4,5,3,8,7,2] => [1,5,3,4,7,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,7},{3,6},{4,5},{8}} => [1,7,6,5,4,3,2,8] => [1,5,4,6,3,7,2,8] => [[1,2,4,6,8],[3],[5],[7]] => 3
{{1},{2,8},{3,6},{4,5},{7}} => [1,8,6,5,4,3,7,2] => [1,5,4,6,3,7,8,2] => [[1,2,4,6,7],[3],[5],[8]] => 3
{{1},{2,7,8},{3,6},{4,5}} => [1,7,6,5,4,3,8,2] => [1,5,4,6,3,8,2,7] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1},{2,8},{3,7},{4,5},{6}} => [1,8,7,5,4,6,3,2] => [1,5,4,6,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 3
{{1},{2,3,8},{4,5},{6},{7}} => [1,3,8,5,4,6,7,2] => [1,5,4,6,7,8,2,3] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,8},{3,6,7},{4,5}} => [1,8,6,5,4,7,3,2] => [1,5,4,7,3,6,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1},{2,3,8},{4,5},{6,7}} => [1,3,8,5,4,7,6,2] => [1,5,4,7,6,8,2,3] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1},{2,3,4,6},{5},{7,8}} => [1,3,4,6,5,2,8,7] => [1,5,6,2,3,4,8,7] => [[1,2,3,6,7],[4,5,8]] => 2
{{1},{2,8},{3,4,6},{5},{7}} => [1,8,4,6,5,3,7,2] => [1,5,6,3,4,7,8,2] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,7,8},{3,4,6},{5}} => [1,7,4,6,5,3,8,2] => [1,5,6,3,4,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => [1,5,6,4,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 3
{{1},{2,3,4,8},{5},{6},{7}} => [1,3,4,8,5,6,7,2] => [1,5,6,7,8,2,3,4] => [[1,2,3,4,5],[6,7,8]] => 1
{{1},{2,3,4,7,8},{5},{6}} => [1,3,4,7,5,6,8,2] => [1,5,6,8,2,3,4,7] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,8},{3,4,6,7},{5}} => [1,8,4,6,5,7,3,2] => [1,5,7,3,4,6,8,2] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,3,4,6,8},{5},{7}} => [1,3,4,6,5,8,7,2] => [1,5,7,8,2,3,4,6] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,3,4,6,7,8},{5}} => [1,3,4,6,5,7,8,2] => [1,5,8,2,3,4,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,8},{3,7},{4,5,6}} => [1,8,7,5,6,4,3,2] => [1,6,4,5,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 3
{{1},{2,8},{3,4,7},{5,6}} => [1,8,4,7,6,5,3,2] => [1,6,5,7,3,4,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1},{2,3,4,8},{5,6},{7}} => [1,3,4,8,6,5,7,2] => [1,6,5,7,8,2,3,4] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1},{2,3,4,5,7},{6},{8}} => [1,3,4,5,7,6,2,8] => [1,6,7,2,3,4,5,8] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,8},{3,4,5,7},{6}} => [1,8,4,5,7,6,3,2] => [1,6,7,3,4,5,8,2] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,3,4,8},{5,7},{6}} => [1,3,4,8,7,6,5,2] => [1,6,7,5,8,2,3,4] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1},{2,3,4,5,8},{6},{7}} => [1,3,4,5,8,6,7,2] => [1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 1
{{1},{2,3,4,5,7,8},{6}} => [1,3,4,5,7,6,8,2] => [1,6,8,2,3,4,5,7] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,8},{3,4,5,6,7}} => [1,8,4,5,6,7,3,2] => [1,7,3,4,5,6,8,2] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1},{2,3,4,5,8},{6,7}} => [1,3,4,5,8,7,6,2] => [1,7,6,8,2,3,4,5] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1},{2,3,4,5,6,8},{7}} => [1,3,4,5,6,8,7,2] => [1,7,8,2,3,4,5,6] => [[1,2,3,6,7,8],[4,5]] => 1
{{1},{2,3,4,5,6,7,8}} => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 1
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,2},{3},{4},{5,8},{6,7}} => [2,1,3,4,8,7,6,5] => [2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,2},{3},{4},{5,6,7,8}} => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,2},{3},{4,6,7,8},{5}} => [2,1,3,6,5,7,8,4] => [2,1,3,5,8,4,6,7] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,5,6,4,8,7] => [2,1,3,6,4,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,2},{3},{4,5,6,8},{7}} => [2,1,3,5,6,8,7,4] => [2,1,3,7,8,4,5,6] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2},{3,4},{5},{6},{7},{8}} => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,2},{3,4},{5},{6,7,8}} => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,2},{3,4},{5,6},{7},{8}} => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,2},{3,4},{5,7,8},{6}} => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,5,7] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,2},{3,4},{5,6,7,8}} => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,5,6,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,2},{3,5},{4},{6},{7},{8}} => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,2},{3,6,7,8},{4},{5}} => [2,1,6,4,5,7,8,3] => [2,1,4,5,8,3,6,7] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2},{3,5,6},{4},{7,8}} => [2,1,5,4,6,3,8,7] => [2,1,4,6,3,5,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,2},{3,7,8},{4},{5,6}} => [2,1,7,4,6,5,8,3] => [2,1,4,6,5,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2},{3,5,7,8},{4},{6}} => [2,1,5,4,7,6,8,3] => [2,1,4,6,8,3,5,7] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2},{3,5,6,8},{4},{7}} => [2,1,5,4,6,8,7,3] => [2,1,4,7,8,3,5,6] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2},{3,5,6,7,8},{4}} => [2,1,5,4,6,7,8,3] => [2,1,4,8,3,5,6,7] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,2},{3,4,5},{6},{7},{8}} => [2,1,4,5,3,6,7,8] => [2,1,5,3,4,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,2},{3,6,7,8},{4,5}} => [2,1,6,5,4,7,8,3] => [2,1,5,4,8,3,6,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => [2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,2},{3,7,8},{4,6},{5}} => [2,1,7,6,5,4,8,3] => [2,1,5,6,4,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2},{3,4,7,8},{5},{6}} => [2,1,4,7,5,6,8,3] => [2,1,5,6,8,3,4,7] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2},{3,8},{4,6,7},{5}} => [2,1,8,6,5,7,4,3] => [2,1,5,7,4,6,8,3] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,2},{3,4,6,8},{5},{7}} => [2,1,4,6,5,8,7,3] => [2,1,5,7,8,3,4,6] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2},{3,4,6,7,8},{5}} => [2,1,4,6,5,7,8,3] => [2,1,5,8,3,4,6,7] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,2},{3,4,5,6},{7,8}} => [2,1,4,5,6,3,8,7] => [2,1,6,3,4,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,2},{3,8},{4,5,6},{7}} => [2,1,8,5,6,4,7,3] => [2,1,6,4,5,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,2},{3,4,8},{5,6},{7}} => [2,1,4,8,6,5,7,3] => [2,1,6,5,7,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,2},{3,4,8},{5,7},{6}} => [2,1,4,8,7,6,5,3] => [2,1,6,7,5,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2},{3,4,5,7,8},{6}} => [2,1,4,5,7,6,8,3] => [2,1,6,8,3,4,5,7] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,2},{3,4,8},{5,6,7}} => [2,1,4,8,6,7,5,3] => [2,1,7,5,6,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,2},{3,4,5,8},{6,7}} => [2,1,4,5,8,7,6,3] => [2,1,7,6,8,3,4,5] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,2},{3,4,5,6,8},{7}} => [2,1,4,5,6,8,7,3] => [2,1,7,8,3,4,5,6] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,2},{3,4,5,6,7,8}} => [2,1,4,5,6,7,8,3] => [2,1,8,3,4,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
{{1,3},{2},{4},{5},{6},{7,8}} => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 2
{{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 2
{{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,4,5,7,8,6] => [2,3,1,4,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 2
{{1,3},{2},{4},{5,8},{6,7}} => [3,2,1,4,8,7,6,5] => [2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,3},{2},{4},{5,6,7,8}} => [3,2,1,4,6,7,8,5] => [2,3,1,4,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => 2
{{1,3},{2},{4,5},{6,7},{8}} => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,3},{2},{4,8},{5},{6,7}} => [3,2,1,8,5,7,6,4] => [2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => [2,3,1,5,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 2
{{1,3},{2},{4,7},{5,6},{8}} => [3,2,1,7,6,5,4,8] => [2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1,3},{2},{4,8},{5,7},{6}} => [3,2,1,8,7,6,5,4] => [2,3,1,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,3},{2},{4,5,7,8},{6}} => [3,2,1,5,7,6,8,4] => [2,3,1,6,8,4,5,7] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,3},{2},{4,5,8},{6,7}} => [3,2,1,5,8,7,6,4] => [2,3,1,7,6,8,4,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,3},{2},{4,5,6,8},{7}} => [3,2,1,5,6,8,7,4] => [2,3,1,7,8,4,5,6] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,3},{2},{4,5,6,7,8}} => [3,2,1,5,6,7,8,4] => [2,3,1,8,4,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 2
{{1,4},{2},{3},{5},{6},{7},{8}} => [4,2,3,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
{{1,4},{2},{3},{5},{6,8},{7}} => [4,2,3,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 2
{{1,4},{2},{3},{5,6},{7,8}} => [4,2,3,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
{{1,4},{2},{3},{5,8},{6},{7}} => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 2
{{1,4},{2},{3},{5,8},{6,7}} => [4,2,3,1,8,7,6,5] => [2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1,4},{2},{3},{5,6,7,8}} => [4,2,3,1,6,7,8,5] => [2,3,4,1,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 2
{{1,5},{2},{3},{4},{6},{7},{8}} => [5,2,3,4,1,6,7,8] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
{{1,6},{2},{3},{4},{5},{7},{8}} => [6,2,3,4,5,1,7,8] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
{{1,6},{2},{3},{4},{5},{7,8}} => [6,2,3,4,5,1,8,7] => [2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]] => 2
{{1,7},{2},{3},{4},{5},{6},{8}} => [7,2,3,4,5,6,1,8] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => 1
{{1,8},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,1] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => 1
{{1,7,8},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,8,1] => [2,3,4,5,6,8,1,7] => [[1,2,3,4,5,6],[7,8]] => 1
{{1,8},{2},{3},{4},{5},{6,7}} => [8,2,3,4,5,7,6,1] => [2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]] => 2
{{1,6,7,8},{2},{3},{4},{5}} => [6,2,3,4,5,7,8,1] => [2,3,4,5,8,1,6,7] => [[1,2,3,4,5,8],[6,7]] => 1
{{1,7},{2},{3},{4},{5,6},{8}} => [7,2,3,4,6,5,1,8] => [2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 2
{{1,5,7},{2},{3},{4},{6},{8}} => [5,2,3,4,7,6,1,8] => [2,3,4,6,7,1,5,8] => [[1,2,3,4,5,8],[6,7]] => 1
{{1,8},{2},{3},{4},{5,7},{6}} => [8,2,3,4,7,6,5,1] => [2,3,4,6,7,5,8,1] => [[1,2,3,4,5,7],[6],[8]] => 2
{{1,8},{2},{3},{4},{5,6,7}} => [8,2,3,4,6,7,5,1] => [2,3,4,7,5,6,8,1] => [[1,2,3,4,6,7],[5],[8]] => 2
{{1,5,6,7,8},{2},{3},{4}} => [5,2,3,4,6,7,8,1] => [2,3,4,8,1,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 1
{{1,4,5},{2},{3},{6,7,8}} => [4,2,3,5,1,7,8,6] => [2,3,5,1,4,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,6},{2},{3},{4,5},{7},{8}} => [6,2,3,5,4,1,7,8] => [2,3,5,4,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 2
{{1,8},{2},{3},{4,5},{6},{7}} => [8,2,3,5,4,6,7,1] => [2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 2
{{1,7},{2},{3},{4,6},{5},{8}} => [7,2,3,6,5,4,1,8] => [2,3,5,6,4,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 2
{{1,4,5,6},{2},{3},{7,8}} => [4,2,3,5,6,1,8,7] => [2,3,6,1,4,5,8,7] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,4,8},{2},{3},{5,6},{7}} => [4,2,3,8,6,5,7,1] => [2,3,6,5,7,8,1,4] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1,4,7,8},{2},{3},{5,6}} => [4,2,3,7,6,5,8,1] => [2,3,6,5,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,5,6,7},{2},{3},{8}} => [4,2,3,5,6,7,1,8] => [2,3,7,1,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 1
{{1,4,8},{2},{3},{5,6,7}} => [4,2,3,8,6,7,5,1] => [2,3,7,5,6,8,1,4] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1,4,5,6,8},{2},{3},{7}} => [4,2,3,5,6,8,7,1] => [2,3,7,8,1,4,5,6] => [[1,2,3,4,8],[5,6,7]] => 1
{{1,4,5,6,7,8},{2},{3}} => [4,2,3,5,6,7,8,1] => [2,3,8,1,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 1
{{1,3,4},{2},{5},{6},{7},{8}} => [3,2,4,1,5,6,7,8] => [2,4,1,3,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,3,4},{2},{5},{6,8},{7}} => [3,2,4,1,5,8,7,6] => [2,4,1,3,5,7,8,6] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,3,4},{2},{5,6},{7,8}} => [3,2,4,1,6,5,8,7] => [2,4,1,3,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3,4},{2},{5,7,8},{6}} => [3,2,4,1,7,6,8,5] => [2,4,1,3,6,8,5,7] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,3,4},{2},{5,8},{6,7}} => [3,2,4,1,8,7,6,5] => [2,4,1,3,7,6,8,5] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,3,4},{2},{5,6,8},{7}} => [3,2,4,1,6,8,7,5] => [2,4,1,3,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,3,4},{2},{5,6,7,8}} => [3,2,4,1,6,7,8,5] => [2,4,1,3,8,5,6,7] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,5},{2},{3,4},{6},{7},{8}} => [5,2,4,3,1,6,7,8] => [2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 2
{{1,5},{2},{3,4},{6},{7,8}} => [5,2,4,3,1,6,8,7] => [2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => 3
{{1,5},{2},{3,4},{6,8},{7}} => [5,2,4,3,1,8,7,6] => [2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 3
{{1,5},{2},{3,4},{6,7,8}} => [5,2,4,3,1,7,8,6] => [2,4,3,5,1,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 3
{{1,8},{2},{3,4},{5},{6},{7}} => [8,2,4,3,5,6,7,1] => [2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1,5,6},{2},{3,4},{7,8}} => [5,2,4,3,6,1,8,7] => [2,4,3,6,1,5,8,7] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,7,8},{2},{3,4},{5,6}} => [7,2,4,3,6,5,8,1] => [2,4,3,6,5,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5,7},{2},{3,4},{6},{8}} => [5,2,4,3,7,6,1,8] => [2,4,3,6,7,1,5,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,5,7,8},{2},{3,4},{6}} => [5,2,4,3,7,6,8,1] => [2,4,3,6,8,1,5,7] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,8},{2},{3,4},{5,6,7}} => [8,2,4,3,6,7,5,1] => [2,4,3,7,5,6,8,1] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1,3,5},{2},{4},{6},{7},{8}} => [3,2,5,4,1,6,7,8] => [2,4,5,1,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 1
{{1,3,5},{2},{4},{6,7},{8}} => [3,2,5,4,1,7,6,8] => [2,4,5,1,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,3,5},{2},{4},{6,8},{7}} => [3,2,5,4,1,8,7,6] => [2,4,5,1,3,7,8,6] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,6},{2},{3,5},{4},{7,8}} => [6,2,5,4,3,1,8,7] => [2,4,5,3,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 3
{{1,3,7},{2},{4},{5},{6},{8}} => [3,2,7,4,5,6,1,8] => [2,4,5,6,7,1,3,8] => [[1,2,3,4,5,8],[6,7]] => 1
{{1,3,8},{2},{4},{5},{6},{7}} => [3,2,8,4,5,6,7,1] => [2,4,5,6,7,8,1,3] => [[1,2,3,4,5,6],[7,8]] => 1
{{1,3,5,6},{2},{4},{7,8}} => [3,2,5,4,6,1,8,7] => [2,4,6,1,3,5,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,7},{2},{3,5,6},{4},{8}} => [7,2,5,4,6,3,1,8] => [2,4,6,3,5,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 2
{{1,7,8},{2},{3,5,6},{4}} => [7,2,5,4,6,3,8,1] => [2,4,6,3,5,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,7,8},{2},{4},{5,6}} => [3,2,7,4,6,5,8,1] => [2,4,6,5,8,1,3,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,5,7},{2},{4},{6},{8}} => [3,2,5,4,7,6,1,8] => [2,4,6,7,1,3,5,8] => [[1,2,3,4,8],[5,6,7]] => 1
{{1,3,5,7,8},{2},{4},{6}} => [3,2,5,4,7,6,8,1] => [2,4,6,8,1,3,5,7] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,3,5,6,8},{2},{4},{7}} => [3,2,5,4,6,8,7,1] => [2,4,7,8,1,3,5,6] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,3,5,6,7,8},{2},{4}} => [3,2,5,4,6,7,8,1] => [2,4,8,1,3,5,6,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,8},{2},{3,4,5},{6},{7}} => [8,2,4,5,3,6,7,1] => [2,5,3,4,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1,7,8},{2},{3,4,5},{6}} => [7,2,4,5,3,6,8,1] => [2,5,3,4,6,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,8},{2},{3,4,5},{6,7}} => [8,2,4,5,3,7,6,1] => [2,5,3,4,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,7},{2},{3,6},{4,5},{8}} => [7,2,6,5,4,3,1,8] => [2,5,4,6,3,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 3
{{1,3,7},{2},{4,5},{6},{8}} => [3,2,7,5,4,6,1,8] => [2,5,4,6,7,1,3,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,3,8},{2},{4,5},{6,7}} => [3,2,8,5,4,7,6,1] => [2,5,4,7,6,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,3,6,8},{2},{4,5},{7}} => [3,2,6,5,4,8,7,1] => [2,5,4,7,8,1,3,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,3,4,6},{2},{5},{7,8}} => [3,2,4,6,5,1,8,7] => [2,5,6,1,3,4,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,7,8},{2},{3,4,6},{5}} => [7,2,4,6,5,3,8,1] => [2,5,6,3,4,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,7},{2},{4,6},{5},{8}} => [3,2,7,6,5,4,1,8] => [2,5,6,4,7,1,3,8] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1,3,7,8},{2},{4,6},{5}} => [3,2,7,6,5,4,8,1] => [2,5,6,4,8,1,3,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,8},{2},{4,6,7},{5}} => [3,2,8,6,5,7,4,1] => [2,5,7,4,6,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,3,4,5,6},{2},{7},{8}} => [3,2,4,5,6,1,7,8] => [2,6,1,3,4,5,7,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,8},{2},{3,4,5,6},{7}} => [8,2,4,5,6,3,7,1] => [2,6,3,4,5,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1,7,8},{2},{3,4,5,6}} => [7,2,4,5,6,3,8,1] => [2,6,3,4,5,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,3,7},{2},{4,5,6},{8}} => [3,2,7,5,6,4,1,8] => [2,6,4,5,7,1,3,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,3,8},{2},{4,5,6},{7}} => [3,2,8,5,6,4,7,1] => [2,6,4,5,7,8,1,3] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,8},{2},{3,4,7},{5,6}} => [8,2,4,7,6,5,3,1] => [2,6,5,7,3,4,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,3,8},{2},{4,5,7},{6}} => [3,2,8,5,7,6,4,1] => [2,6,7,4,5,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,3,4,8},{2},{5,7},{6}} => [3,2,4,8,7,6,5,1] => [2,6,7,5,8,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,4,5,7,8},{2},{6}} => [3,2,4,5,7,6,8,1] => [2,6,8,1,3,4,5,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,3,4,5,6,7},{2},{8}} => [3,2,4,5,6,7,1,8] => [2,7,1,3,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,3,4,5,6,8},{2},{7}} => [3,2,4,5,6,8,7,1] => [2,7,8,1,3,4,5,6] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => [2,8,1,3,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3},{4},{5},{6},{7},{8}} => [2,3,1,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => [3,1,2,4,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,2,3},{4},{5,6},{7,8}} => [2,3,1,4,6,5,8,7] => [3,1,2,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,3},{4},{5,8},{6,7}} => [2,3,1,4,8,7,6,5] => [3,1,2,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,2,3},{4},{5,6,8},{7}} => [2,3,1,4,6,8,7,5] => [3,1,2,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,2,3},{4,5},{6,7},{8}} => [2,3,1,5,4,7,6,8] => [3,1,2,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,2,3},{4,6,7},{5},{8}} => [2,3,1,6,5,7,4,8] => [3,1,2,5,7,4,6,8] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2,3},{4,8},{5},{6,7}} => [2,3,1,8,5,7,6,4] => [3,1,2,5,7,6,8,4] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,2,3},{4,5,6},{7,8}} => [2,3,1,5,6,4,8,7] => [3,1,2,6,4,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,2,3},{4,8},{5,7},{6}} => [2,3,1,8,7,6,5,4] => [3,1,2,6,7,5,8,4] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,2,3},{4,5,6,7},{8}} => [2,3,1,5,6,7,4,8] => [3,1,2,7,4,5,6,8] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,2,3},{4,8},{5,6,7}} => [2,3,1,8,6,7,5,4] => [3,1,2,7,5,6,8,4] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,2,3},{4,5,6,7,8}} => [2,3,1,5,6,7,8,4] => [3,1,2,8,4,5,6,7] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,4},{2,3},{5},{6},{7},{8}} => [4,3,2,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 2
{{1,4},{2,3},{5},{6},{7,8}} => [4,3,2,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => 3
{{1,4},{2,3},{5},{6,7},{8}} => [4,3,2,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 3
{{1,4},{2,3},{5},{6,8},{7}} => [4,3,2,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 3
{{1,4},{2,3},{5},{6,7,8}} => [4,3,2,1,5,7,8,6] => [3,2,4,1,5,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 3
{{1,4},{2,3},{5,6},{7},{8}} => [4,3,2,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => 3
{{1,4},{2,3},{5,7},{6},{8}} => [4,3,2,1,7,6,5,8] => [3,2,4,1,6,7,5,8] => [[1,3,5,6,8],[2,7],[4]] => 3
{{1,4},{2,3},{5,8},{6},{7}} => [4,3,2,1,8,6,7,5] => [3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 3
{{1,4},{2,3},{5,7,8},{6}} => [4,3,2,1,7,6,8,5] => [3,2,4,1,6,8,5,7] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,4},{2,3},{5,6,7},{8}} => [4,3,2,1,6,7,5,8] => [3,2,4,1,7,5,6,8] => [[1,3,5,7,8],[2,6],[4]] => 3
{{1,4},{2,3},{5,6,8},{7}} => [4,3,2,1,6,8,7,5] => [3,2,4,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,4},{2,3},{5,6,7,8}} => [4,3,2,1,6,7,8,5] => [3,2,4,1,8,5,6,7] => [[1,3,5,7,8],[2,6],[4]] => 3
{{1,8},{2,3},{4},{5},{6},{7}} => [8,3,2,4,5,6,7,1] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,6,8},{2,3},{4},{5},{7}} => [6,3,2,4,5,8,7,1] => [3,2,4,5,7,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,5,6},{2,3},{4},{7,8}} => [5,3,2,4,6,1,8,7] => [3,2,4,6,1,5,8,7] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,5,7,8},{2,3},{4},{6}} => [5,3,2,4,7,6,8,1] => [3,2,4,6,8,1,5,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,8},{2,3},{4},{5,6,7}} => [8,3,2,4,6,7,5,1] => [3,2,4,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,5,6,8},{2,3},{4},{7}} => [5,3,2,4,6,8,7,1] => [3,2,4,7,8,1,5,6] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,5,6,7,8},{2,3},{4}} => [5,3,2,4,6,7,8,1] => [3,2,4,8,1,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,4,5},{2,3},{6},{7,8}} => [4,3,2,5,1,6,8,7] => [3,2,5,1,4,6,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,4,5},{2,3},{6,7},{8}} => [4,3,2,5,1,7,6,8] => [3,2,5,1,4,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,4,5},{2,3},{6,8},{7}} => [4,3,2,5,1,8,7,6] => [3,2,5,1,4,7,8,6] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,6,7},{2,3},{4,5},{8}} => [6,3,2,5,4,7,1,8] => [3,2,5,4,7,1,6,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,6,8},{2,3},{4,5},{7}} => [6,3,2,5,4,8,7,1] => [3,2,5,4,7,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6,7,8},{2,3},{4,5}} => [6,3,2,5,4,7,8,1] => [3,2,5,4,8,1,6,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4,7,8},{2,3},{5},{6}} => [4,3,2,7,5,6,8,1] => [3,2,5,6,8,1,4,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4,6,7},{2,3},{5},{8}} => [4,3,2,6,5,7,1,8] => [3,2,5,7,1,4,6,8] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,8},{2,3},{4,6,7},{5}} => [8,3,2,6,5,7,4,1] => [3,2,5,7,4,6,8,1] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,4,8},{2,3},{5},{6,7}} => [4,3,2,8,5,7,6,1] => [3,2,5,7,6,8,1,4] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,4,6,7,8},{2,3},{5}} => [4,3,2,6,5,7,8,1] => [3,2,5,8,1,4,6,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,4,5,6},{2,3},{7,8}} => [4,3,2,5,6,1,8,7] => [3,2,6,1,4,5,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,4,7},{2,3},{5,6},{8}} => [4,3,2,7,6,5,1,8] => [3,2,6,5,7,1,4,8] => [[1,3,5,8],[2,4],[6,7]] => 3
{{1,4,8},{2,3},{5,6},{7}} => [4,3,2,8,6,5,7,1] => [3,2,6,5,7,8,1,4] => [[1,3,5,6],[2,4],[7,8]] => 3
{{1,4,8},{2,3},{5,7},{6}} => [4,3,2,8,7,6,5,1] => [3,2,6,7,5,8,1,4] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,4,5,7,8},{2,3},{6}} => [4,3,2,5,7,6,8,1] => [3,2,6,8,1,4,5,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,4,5,8},{2,3},{6,7}} => [4,3,2,5,8,7,6,1] => [3,2,7,6,8,1,4,5] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,4,5,6,8},{2,3},{7}} => [4,3,2,5,6,8,7,1] => [3,2,7,8,1,4,5,6] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => [3,2,8,1,4,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,4},{3},{5,6},{7,8}} => [2,4,3,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,2,4},{3},{5,7,8},{6}} => [2,4,3,1,7,6,8,5] => [3,4,1,2,6,8,5,7] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,4},{3},{5,8},{6,7}} => [2,4,3,1,8,7,6,5] => [3,4,1,2,7,6,8,5] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,2,4},{3},{5,6,8},{7}} => [2,4,3,1,6,8,7,5] => [3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,4},{3},{5,6,7,8}} => [2,4,3,1,6,7,8,5] => [3,4,1,2,8,5,6,7] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,5},{2,4},{3},{6},{7},{8}} => [5,4,3,2,1,6,7,8] => [3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 2
{{1,5},{2,4},{3},{6,7},{8}} => [5,4,3,2,1,7,6,8] => [3,4,2,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 3
{{1,5},{2,4},{3},{6,8},{7}} => [5,4,3,2,1,8,7,6] => [3,4,2,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 3
{{1,5},{2,4},{3},{6,7,8}} => [5,4,3,2,1,7,8,6] => [3,4,2,5,1,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 3
{{1,8},{2,4},{3},{5},{6},{7}} => [8,4,3,2,5,6,7,1] => [3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1,8},{2,4},{3},{5},{6,7}} => [8,4,3,2,5,7,6,1] => [3,4,2,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,7},{2,4},{3},{5,6},{8}} => [7,4,3,2,6,5,1,8] => [3,4,2,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1,7,8},{2,4},{3},{5,6}} => [7,4,3,2,6,5,8,1] => [3,4,2,6,5,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5,7},{2,4},{3},{6},{8}} => [5,4,3,2,7,6,1,8] => [3,4,2,6,7,1,5,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,8},{2,4},{3},{5,7},{6}} => [8,4,3,2,7,6,5,1] => [3,4,2,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,5,7,8},{2,4},{3},{6}} => [5,4,3,2,7,6,8,1] => [3,4,2,6,8,1,5,7] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,5,6,7},{2,4},{3},{8}} => [5,4,3,2,6,7,1,8] => [3,4,2,7,1,5,6,8] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,5,6,8},{2,4},{3},{7}} => [5,4,3,2,6,8,7,1] => [3,4,2,7,8,1,5,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,5,6,7,8},{2,4},{3}} => [5,4,3,2,6,7,8,1] => [3,4,2,8,1,5,6,7] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,8},{2,5},{3},{4},{6},{7}} => [8,5,3,4,2,6,7,1] => [3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 2
{{1,2,8},{3},{4},{5},{6},{7}} => [2,8,3,4,5,6,7,1] => [3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => 1
{{1,2,6,7,8},{3},{4},{5}} => [2,6,3,4,5,7,8,1] => [3,4,5,8,1,2,6,7] => [[1,2,3,4,8],[5,6,7]] => 1
{{1,2,5,6},{3},{4},{7,8}} => [2,5,3,4,6,1,8,7] => [3,4,6,1,2,5,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,2,5,8},{3},{4},{6,7}} => [2,5,3,4,8,7,6,1] => [3,4,7,6,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2,5,6,8},{3},{4},{7}} => [2,5,3,4,6,8,7,1] => [3,4,7,8,1,2,5,6] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,2,5,6,7,8},{3},{4}} => [2,5,3,4,6,7,8,1] => [3,4,8,1,2,5,6,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,6},{2,4,5},{3},{7,8}} => [6,4,3,5,2,1,8,7] => [3,5,2,4,6,1,8,7] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,7,8},{2,4,5},{3},{6}} => [7,4,3,5,2,6,8,1] => [3,5,2,4,6,8,1,7] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,6,7},{2,4,5},{3},{8}} => [6,4,3,5,2,7,1,8] => [3,5,2,4,7,1,6,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,8},{2,4,5},{3},{6,7}} => [8,4,3,5,2,7,6,1] => [3,5,2,4,7,6,8,1] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,2,6},{3},{4,5},{7,8}} => [2,6,3,5,4,1,8,7] => [3,5,4,6,1,2,8,7] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,7},{2,6},{3},{4,5},{8}} => [7,6,3,5,4,2,1,8] => [3,5,4,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 3
{{1,7,8},{2,6},{3},{4,5}} => [7,6,3,5,4,2,8,1] => [3,5,4,6,2,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,8},{2,6,7},{3},{4,5}} => [8,6,3,5,4,7,2,1] => [3,5,4,7,2,6,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,2,8},{3},{4,5},{6,7}} => [2,8,3,5,4,7,6,1] => [3,5,4,7,6,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,2,6,8},{3},{4,5},{7}} => [2,6,3,5,4,8,7,1] => [3,5,4,7,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,4,6},{3},{5},{7,8}} => [2,4,3,6,5,1,8,7] => [3,5,6,1,2,4,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,7},{2,4,6},{3},{5},{8}} => [7,4,3,6,5,2,1,8] => [3,5,6,2,4,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 2
{{1,7,8},{2,4,6},{3},{5}} => [7,4,3,6,5,2,8,1] => [3,5,6,2,4,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,8},{2,4,7},{3},{5},{6}} => [8,4,3,7,5,6,2,1] => [3,5,6,7,2,4,8,1] => [[1,2,3,4,7],[5,6],[8]] => 2
{{1,2,4,7,8},{3},{5},{6}} => [2,4,3,7,5,6,8,1] => [3,5,6,8,1,2,4,7] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,8},{2,4,6,7},{3},{5}} => [8,4,3,6,5,7,2,1] => [3,5,7,2,4,6,8,1] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,4,6,8},{3},{5},{7}} => [2,4,3,6,5,8,7,1] => [3,5,7,8,1,2,4,6] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,2,4,5,6},{3},{7,8}} => [2,4,3,5,6,1,8,7] => [3,6,1,2,4,5,8,7] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,8},{2,7},{3},{4,5,6}} => [8,7,3,5,6,4,2,1] => [3,6,4,5,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 3
{{1,2,8},{3},{4,7},{5,6}} => [2,8,3,7,6,5,4,1] => [3,6,5,7,4,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,8},{2,4,5,7},{3},{6}} => [8,4,3,5,7,6,2,1] => [3,6,7,2,4,5,8,1] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,8},{3},{4,5,7},{6}} => [2,8,3,5,7,6,4,1] => [3,6,7,4,5,8,1,2] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,2,4,8},{3},{5,7},{6}} => [2,4,3,8,7,6,5,1] => [3,6,7,5,8,1,2,4] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2,4,5,7,8},{3},{6}} => [2,4,3,5,7,6,8,1] => [3,6,8,1,2,4,5,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,4,5,6,7},{3},{8}} => [2,4,3,5,6,7,1,8] => [3,7,1,2,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,4,5,6,8},{3},{7}} => [2,4,3,5,6,8,7,1] => [3,7,8,1,2,4,5,6] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,4,5,6,7,8},{3}} => [2,4,3,5,6,7,8,1] => [3,8,1,2,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,4},{5},{6},{7},{8}} => [2,3,4,1,5,6,7,8] => [4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,2,3,4},{5},{6,7},{8}} => [2,3,4,1,5,7,6,8] => [4,1,2,3,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,2,3,4},{5,6},{7},{8}} => [2,3,4,1,6,5,7,8] => [4,1,2,3,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,2,3,4},{5,6},{7,8}} => [2,3,4,1,6,5,8,7] => [4,1,2,3,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,3,4},{5,7,8},{6}} => [2,3,4,1,7,6,8,5] => [4,1,2,3,6,8,5,7] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,2,3,4},{5,6,7},{8}} => [2,3,4,1,6,7,5,8] => [4,1,2,3,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,2,3,4},{5,8},{6,7}} => [2,3,4,1,8,7,6,5] => [4,1,2,3,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,2,3,4},{5,6,8},{7}} => [2,3,4,1,6,8,7,5] => [4,1,2,3,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => [4,1,2,3,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,5},{2,3,4},{6},{7},{8}} => [5,3,4,2,1,6,7,8] => [4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 2
{{1,5},{2,3,4},{6,8},{7}} => [5,3,4,2,1,8,7,6] => [4,2,3,5,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 3
{{1,5},{2,3,4},{6,7,8}} => [5,3,4,2,1,7,8,6] => [4,2,3,5,1,8,6,7] => [[1,3,4,6,8],[2,7],[5]] => 3
{{1,6},{2,3,4},{5},{7,8}} => [6,3,4,2,5,1,8,7] => [4,2,3,5,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,8},{2,3,4},{5},{6},{7}} => [8,3,4,2,5,6,7,1] => [4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,5,8},{2,3,4},{6},{7}} => [5,3,4,2,8,6,7,1] => [4,2,3,6,7,8,1,5] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,5,6,7,8},{2,3,4}} => [5,3,4,2,6,7,8,1] => [4,2,3,8,1,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,2,5},{3,4},{6,7},{8}} => [2,5,4,3,1,7,6,8] => [4,3,5,1,2,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,7,8},{2,5},{3,4},{6}} => [7,5,4,3,2,6,8,1] => [4,3,5,2,6,8,1,7] => [[1,3,5,6],[2,8],[4],[7]] => 3
{{1,6,7},{2,5},{3,4},{8}} => [6,5,4,3,2,7,1,8] => [4,3,5,2,7,1,6,8] => [[1,3,5,8],[2,7],[4],[6]] => 3
{{1,6,7,8},{2,5},{3,4}} => [6,5,4,3,2,7,8,1] => [4,3,5,2,8,1,6,7] => [[1,3,5,8],[2,7],[4],[6]] => 3
{{1,2,6},{3,4},{5},{7,8}} => [2,6,4,3,5,1,8,7] => [4,3,5,6,1,2,8,7] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,7},{2,6},{3,4},{5},{8}} => [7,6,4,3,5,2,1,8] => [4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 3
{{1,8},{2,6},{3,4},{5},{7}} => [8,6,4,3,5,2,7,1] => [4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 3
{{1,7,8},{2,6},{3,4},{5}} => [7,6,4,3,5,2,8,1] => [4,3,5,6,2,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,8},{2,6,7},{3,4},{5}} => [8,6,4,3,5,7,2,1] => [4,3,5,7,2,6,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 3
{{1,2,8},{3,4},{5},{6,7}} => [2,8,4,3,5,7,6,1] => [4,3,5,7,6,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,8},{2,5,6},{3,4},{7}} => [8,5,4,3,6,2,7,1] => [4,3,6,2,5,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 3
{{1,2,7},{3,4},{5,6},{8}} => [2,7,4,3,6,5,1,8] => [4,3,6,5,7,1,2,8] => [[1,3,5,8],[2,4],[6,7]] => 3
{{1,2,8},{3,4},{5,6},{7}} => [2,8,4,3,6,5,7,1] => [4,3,6,5,7,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 3
{{1,2,8},{3,4},{5,7},{6}} => [2,8,4,3,7,6,5,1] => [4,3,6,7,5,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,2,5,8},{3,4},{6},{7}} => [2,5,4,3,8,6,7,1] => [4,3,6,7,8,1,2,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,6,7,8},{2,3,5},{4}} => [6,3,5,4,2,7,8,1] => [4,5,2,3,8,1,6,7] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,2,6},{3,5},{4},{7,8}} => [2,6,5,4,3,1,8,7] => [4,5,3,6,1,2,8,7] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => [4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 3
{{1,7,8},{2,6},{3,5},{4}} => [7,6,5,4,3,2,8,1] => [4,5,3,6,2,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,2,7,8},{3,5},{4},{6}} => [2,7,5,4,3,6,8,1] => [4,5,3,6,8,1,2,7] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,8},{3,5},{4},{6,7}} => [2,8,5,4,3,7,6,1] => [4,5,3,7,6,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,2,6,8},{3,5},{4},{7}} => [2,6,5,4,3,8,7,1] => [4,5,3,7,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,3,6},{4},{5},{7,8}} => [2,3,6,4,5,1,8,7] => [4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,7,8},{2,3,6},{4},{5}} => [7,3,6,4,5,2,8,1] => [4,5,6,2,3,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2,3,8},{4},{5},{6},{7}} => [2,3,8,4,5,6,7,1] => [4,5,6,7,8,1,2,3] => [[1,2,3,4,5],[6,7,8]] => 1
{{1,2,3,7,8},{4},{5},{6}} => [2,3,7,4,5,6,8,1] => [4,5,6,8,1,2,3,7] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,8},{2,3,6,7},{4},{5}} => [8,3,6,4,5,7,2,1] => [4,5,7,2,3,6,8,1] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,3,6,8},{4},{5},{7}} => [2,3,6,4,5,8,7,1] => [4,5,7,8,1,2,3,6] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,2,3,6,7,8},{4},{5}} => [2,3,6,4,5,7,8,1] => [4,5,8,1,2,3,6,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,3,5,6},{4},{7},{8}} => [2,3,5,4,6,1,7,8] => [4,6,1,2,3,5,7,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,7},{2,3,5,6},{4},{8}} => [7,3,5,4,6,2,1,8] => [4,6,2,3,5,7,1,8] => [[1,2,5,6,8],[3,4],[7]] => 2
{{1,8},{2,7},{3,5,6},{4}} => [8,7,5,4,6,3,2,1] => [4,6,3,5,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,2,3,7},{4},{5,6},{8}} => [2,3,7,4,6,5,1,8] => [4,6,5,7,1,2,3,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,8},{2,3,7},{4},{5,6}} => [8,3,7,4,6,5,2,1] => [4,6,5,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,2,8},{3,7},{4},{5,6}} => [2,8,7,4,6,5,3,1] => [4,6,5,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,2,3,8},{4},{5,6},{7}} => [2,3,8,4,6,5,7,1] => [4,6,5,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,3,5,7},{4},{6},{8}} => [2,3,5,4,7,6,1,8] => [4,6,7,1,2,3,5,8] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,8},{2,3,5,7},{4},{6}} => [8,3,5,4,7,6,2,1] => [4,6,7,2,3,5,8,1] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,8},{3,5,7},{4},{6}} => [2,8,5,4,7,6,3,1] => [4,6,7,3,5,8,1,2] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,2,3,5,7,8},{4},{6}} => [2,3,5,4,7,6,8,1] => [4,6,8,1,2,3,5,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,3,5,6,7},{4},{8}} => [2,3,5,4,6,7,1,8] => [4,7,1,2,3,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,8},{4},{5,6,7}} => [2,3,8,4,6,7,5,1] => [4,7,5,6,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,3,5,6,7,8},{4}} => [2,3,5,4,6,7,8,1] => [4,8,1,2,3,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => [5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,2,3,4,5},{6,8},{7}} => [2,3,4,5,1,8,7,6] => [5,1,2,3,4,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,2,3,4,5},{6,7,8}} => [2,3,4,5,1,7,8,6] => [5,1,2,3,4,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,6,7,8},{2,3,4,5}} => [6,3,4,5,2,7,8,1] => [5,2,3,4,8,1,6,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,7},{2,6},{3,4,5},{8}} => [7,6,4,5,3,2,1,8] => [5,3,4,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 3
{{1,7,8},{2,6},{3,4,5}} => [7,6,4,5,3,2,8,1] => [5,3,4,6,2,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,2,3,6},{4,5},{7,8}} => [2,3,6,5,4,1,8,7] => [5,4,6,1,2,3,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,8},{2,3,6},{4,5},{7}} => [8,3,6,5,4,2,7,1] => [5,4,6,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 3
{{1,7,8},{2,3,6},{4,5}} => [7,3,6,5,4,2,8,1] => [5,4,6,2,3,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1,2,8},{3,6},{4,5},{7}} => [2,8,6,5,4,3,7,1] => [5,4,6,3,7,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 3
{{1,2,3,7},{4,5},{6},{8}} => [2,3,7,5,4,6,1,8] => [5,4,6,7,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,8},{2,3,7},{4,5},{6}} => [8,3,7,5,4,6,2,1] => [5,4,6,7,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 3
{{1,2,3,8},{4,5},{6},{7}} => [2,3,8,5,4,6,7,1] => [5,4,6,7,8,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,8},{2,3,6,7},{4,5}} => [8,3,6,5,4,7,2,1] => [5,4,7,2,3,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 3
{{1,2,3,8},{4,5},{6,7}} => [2,3,8,5,4,7,6,1] => [5,4,7,6,8,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,2,3,6,7,8},{4,5}} => [2,3,6,5,4,7,8,1] => [5,4,8,1,2,3,6,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,4,6},{5},{7,8}} => [2,3,4,6,5,1,8,7] => [5,6,1,2,3,4,8,7] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,2,7},{3,4,6},{5},{8}} => [2,7,4,6,5,3,1,8] => [5,6,3,4,7,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 2
{{1,8},{2,7},{3,4,6},{5}} => [8,7,4,6,5,3,2,1] => [5,6,3,4,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,2,8},{3,4,6},{5},{7}} => [2,8,4,6,5,3,7,1] => [5,6,3,4,7,8,1,2] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,8},{2,3,7},{4,6},{5}} => [8,3,7,6,5,4,2,1] => [5,6,4,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,2,8},{3,7},{4,6},{5}} => [2,8,7,6,5,4,3,1] => [5,6,4,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,2,3,8},{4,6},{5},{7}} => [2,3,8,6,5,4,7,1] => [5,6,4,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,3,4,7},{5},{6},{8}} => [2,3,4,7,5,6,1,8] => [5,6,7,1,2,3,4,8] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,8},{2,3,4,7},{5},{6}} => [8,3,4,7,5,6,2,1] => [5,6,7,2,3,4,8,1] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,3,8},{4,7},{5},{6}} => [2,3,8,7,5,6,4,1] => [5,6,7,4,8,1,2,3] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2,3,4,8},{5},{6},{7}} => [2,3,4,8,5,6,7,1] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 1
{{1,2,3,4,7,8},{5},{6}} => [2,3,4,7,5,6,8,1] => [5,6,8,1,2,3,4,7] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,3,4,6,7},{5},{8}} => [2,3,4,6,5,7,1,8] => [5,7,1,2,3,4,6,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,8},{2,3,4,6,7},{5}} => [8,3,4,6,5,7,2,1] => [5,7,2,3,4,6,8,1] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,3,4,8},{5},{6,7}} => [2,3,4,8,5,7,6,1] => [5,7,6,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,3,4,6,8},{5},{7}} => [2,3,4,6,5,8,7,1] => [5,7,8,1,2,3,4,6] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,3,4,6,7,8},{5}} => [2,3,4,6,5,7,8,1] => [5,8,1,2,3,4,6,7] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => [6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => [6,1,2,3,4,5,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,7},{2,3,4,5,6},{8}} => [7,3,4,5,6,2,1,8] => [6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 2
{{1,7,8},{2,3,4,5,6}} => [7,3,4,5,6,2,8,1] => [6,2,3,4,5,8,1,7] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,7,8},{3,4,5,6}} => [2,7,4,5,6,3,8,1] => [6,3,4,5,8,1,2,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,2,3,7,8},{4,5,6}} => [2,3,7,5,6,4,8,1] => [6,4,5,8,1,2,3,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,3,4,7},{5,6},{8}} => [2,3,4,7,6,5,1,8] => [6,5,7,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,8},{4,7},{5,6}} => [2,3,8,7,6,5,4,1] => [6,5,7,4,8,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,2,3,4,8},{5,6},{7}} => [2,3,4,8,6,5,7,1] => [6,5,7,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,3,4,7,8},{5,6}} => [2,3,4,7,6,5,8,1] => [6,5,8,1,2,3,4,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,4,5,7},{6},{8}} => [2,3,4,5,7,6,1,8] => [6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,8},{2,3,4,5,7},{6}} => [8,3,4,5,7,6,2,1] => [6,7,2,3,4,5,8,1] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,3,8},{4,5,7},{6}} => [2,3,8,5,7,6,4,1] => [6,7,4,5,8,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,2,3,4,8},{5,7},{6}} => [2,3,4,8,7,6,5,1] => [6,7,5,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,3,4,5,8},{6},{7}} => [2,3,4,5,8,6,7,1] => [6,7,8,1,2,3,4,5] => [[1,2,3,7,8],[4,5,6]] => 1
{{1,2,3,4,5,7,8},{6}} => [2,3,4,5,7,6,8,1] => [6,8,1,2,3,4,5,7] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => [7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,8},{2,3,4,5,6,7}} => [8,3,4,5,6,7,2,1] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,4,8},{5,6,7}} => [2,3,4,8,6,7,5,1] => [7,5,6,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,3,4,5,8},{6,7}} => [2,3,4,5,8,7,6,1] => [7,6,8,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,4,5,6,8},{7}} => [2,3,4,5,6,8,7,1] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => 1
{{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => 1
{{1,3,5,6,7,8},{2,4}} => [3,4,5,2,6,7,8,1] => [4,2,8,1,3,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => [6,2,8,1,3,4,5,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,4,5,7,8},{3,6}} => [2,4,6,5,7,3,8,1] => [6,3,8,1,2,4,5,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,5,7,8},{4,6}} => [2,3,5,6,7,4,8,1] => [6,4,8,1,2,3,5,7] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,3,4,5,6,8},{2,7}} => [3,7,4,5,6,8,2,1] => [7,2,8,1,3,4,5,6] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,4,5,6,8},{3,7}} => [2,4,7,5,6,8,3,1] => [7,3,8,1,2,4,5,6] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,5,6,8},{4,7}} => [2,3,5,7,6,8,4,1] => [7,4,8,1,2,3,5,6] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,4,6,8},{5,7}} => [2,3,4,6,7,8,5,1] => [7,5,8,1,2,3,4,6] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,3,4,5,6,7},{2,8}} => [3,8,4,5,6,7,1,2] => [7,1,3,4,5,6,8,2] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,4,5,6,7},{3,8}} => [2,4,8,5,6,7,1,3] => [7,1,2,4,5,6,8,3] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,5,6,7},{4,8}} => [2,3,5,8,6,7,1,4] => [7,1,2,3,5,6,8,4] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,4,6,7},{5,8}} => [2,3,4,6,8,7,1,5] => [7,1,2,3,4,6,8,5] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => [7,1,2,3,4,5,8,6] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,3,5,7,8},{2,4,6}} => [3,4,5,6,7,2,8,1] => [6,2,4,8,1,3,5,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,5,7,8},{3,4,6}} => [2,5,4,6,7,3,8,1] => [6,3,4,8,1,2,5,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,4,7,8},{2,5,6}} => [3,5,4,7,6,2,8,1] => [6,2,5,8,1,3,4,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,5,6,8},{2,4,7}} => [3,4,5,7,6,8,2,1] => [7,2,4,8,1,3,5,6] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,5,6,8},{3,4,7}} => [2,5,4,7,6,8,3,1] => [7,3,4,8,1,2,5,6] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,4,6,8},{3,5,7}} => [2,4,5,6,7,8,3,1] => [7,3,5,8,1,2,4,6] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,3,6,8},{4,5,7}} => [2,3,6,5,7,8,4,1] => [7,4,5,8,1,2,3,6] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,3,5,8},{4,6,7}} => [2,3,5,6,8,7,4,1] => [7,4,6,8,1,2,3,5] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,4,6,7},{2,5,8}} => [3,5,4,6,8,7,1,2] => [7,1,3,4,6,8,2,5] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,3,6,7},{4,5,8}} => [2,3,6,5,8,7,1,4] => [7,1,2,3,6,8,4,5] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,3,5,7},{4,6,8}} => [2,3,5,6,7,8,1,4] => [7,1,2,3,5,8,4,6] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,3,4,7},{5,6,8}} => [2,3,4,7,6,8,1,5] => [7,1,2,3,4,8,5,6] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,2,3,5,6},{4,7,8}} => [2,3,5,7,6,1,8,4] => [6,1,2,3,5,8,4,7] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,3,4,6},{5,7,8}} => [2,3,4,6,7,1,8,5] => [6,1,2,3,4,8,5,7] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,3,6,7,8},{2,4},{5}} => [3,4,6,2,5,7,8,1] => [4,2,5,8,1,3,6,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,2,5,7,8},{3,6},{4}} => [2,5,6,4,7,3,8,1] => [4,6,3,8,1,2,5,7] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,4,7,8},{2,6},{5}} => [3,6,4,7,5,2,8,1] => [5,6,2,8,1,3,4,7] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,4,7,8},{2,5},{6}} => [3,5,4,7,2,6,8,1] => [5,2,6,8,1,3,4,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,5,6,8},{2,7},{4}} => [3,7,5,4,6,8,2,1] => [4,7,2,8,1,3,5,6] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,5,6,8},{3,7},{4}} => [2,5,7,4,6,8,3,1] => [4,7,3,8,1,2,5,6] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,4,5,8},{2,7},{6}} => [3,7,4,5,8,6,2,1] => [6,7,2,8,1,3,4,5] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,4,5,8},{3,6},{7}} => [2,4,6,5,8,3,7,1] => [6,3,7,8,1,2,4,5] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,4,6,7},{2,8},{5}} => [3,8,4,6,5,7,1,2] => [5,7,1,3,4,6,8,2] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,3,4,5,7},{2,8},{6}} => [3,8,4,5,7,6,1,2] => [6,7,1,3,4,5,8,2] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,4,5,7},{3,8},{6}} => [2,4,8,5,7,6,1,3] => [6,7,1,2,4,5,8,3] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,3,5,7},{4,8},{6}} => [2,3,5,8,7,6,1,4] => [6,7,1,2,3,5,8,4] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,3,4,5,6},{2,8},{7}} => [3,8,4,5,6,1,7,2] => [6,1,3,4,5,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,5,6},{4,8},{7}} => [2,3,5,8,6,1,7,4] => [6,1,2,3,5,7,8,4] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,4,6},{5,8},{7}} => [2,3,4,6,8,1,7,5] => [6,1,2,3,4,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,2,4,6,7},{3,5},{8}} => [2,4,5,6,3,7,1,8] => [5,3,7,1,2,4,6,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,5,7},{4,6},{8}} => [2,3,5,6,7,4,1,8] => [6,4,7,1,2,3,5,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,3,5,6},{4,7},{8}} => [2,3,5,7,6,1,4,8] => [6,1,2,3,5,7,4,8] => [[1,3,4,5,6,8],[2],[7]] => 2
{{1,2,3,4,6},{5,7},{8}} => [2,3,4,6,7,1,5,8] => [6,1,2,3,4,7,5,8] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => [7,1,3,5,8,2,4,6] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,2,5,7},{3,4,6,8}} => [2,5,4,6,7,8,1,3] => [7,1,2,5,8,3,4,6] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,3,4,7},{2,5,6,8}} => [3,5,4,7,6,8,1,2] => [7,1,3,4,8,2,5,6] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,4,7},{3,5,6,8}} => [2,4,5,7,6,8,1,3] => [7,1,2,4,8,3,5,6] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,3,7},{4,5,6,8}} => [2,3,7,5,6,8,1,4] => [7,1,2,3,8,4,5,6] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,3,5,6},{2,4,7,8}} => [3,4,5,7,6,1,8,2] => [6,1,3,5,8,2,4,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,2,5,6},{3,4,7,8}} => [2,5,4,7,6,1,8,3] => [6,1,2,5,8,3,4,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,3,4,6},{2,5,7,8}} => [3,5,4,6,7,1,8,2] => [6,1,3,4,8,2,5,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => [6,1,2,4,8,3,5,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,3,6},{4,5,7,8}} => [2,3,6,5,7,1,8,4] => [6,1,2,3,8,4,5,7] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,3,4,5},{2,6,7,8}} => [3,6,4,5,1,7,8,2] => [5,1,3,4,8,2,6,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,4,5},{3,6,7,8}} => [2,4,6,5,1,7,8,3] => [5,1,2,4,8,3,6,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => [5,1,2,3,8,4,6,7] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,3,6,8},{2,5,7},{4}} => [3,5,6,4,7,8,2,1] => [4,7,2,5,8,1,3,6] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,2,6,8},{3,5,7},{4}} => [2,6,5,4,7,8,3,1] => [4,7,3,5,8,1,2,6] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,2,5,8},{3,6,7},{4}} => [2,5,6,4,8,7,3,1] => [4,7,3,6,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,3,4,8},{2,6,7},{5}} => [3,6,4,8,5,7,2,1] => [5,7,2,6,8,1,3,4] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,2,5,8},{3,4,7},{6}} => [2,5,4,7,8,6,3,1] => [6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 2
{{1,3,4,7},{2,6,8},{5}} => [3,6,4,7,5,8,1,2] => [5,7,1,3,4,8,2,6] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,3,5,7},{2,4,8},{6}} => [3,4,5,8,7,6,1,2] => [6,7,1,3,5,8,2,4] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,3,4,5},{2,7,8},{6}} => [3,7,4,5,1,6,8,2] => [5,1,3,4,6,8,2,7] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2,3,6},{4,5,8},{7}} => [2,3,6,5,8,1,7,4] => [6,1,2,3,7,8,4,5] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,2,4,5},{3,6,8},{7}} => [2,4,6,5,1,8,7,3] => [5,1,2,4,7,8,3,6] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,4,7,8},{2,5},{3,6}} => [4,5,6,7,2,3,8,1] => [5,2,6,3,8,1,4,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,3,6,8},{2,4},{5,7}} => [3,4,6,2,7,8,5,1] => [4,2,7,5,8,1,3,6] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,4,5,8},{2,6},{3,7}} => [4,6,7,5,8,2,3,1] => [6,2,7,3,8,1,4,5] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,3,5,8},{2,6},{4,7}} => [3,6,5,7,8,2,4,1] => [6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,2,5,8},{3,6},{4,7}} => [2,5,6,7,8,3,4,1] => [6,3,7,4,8,1,2,5] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,3,5,8},{2,4},{6,7}} => [3,4,5,2,8,7,6,1] => [4,2,7,6,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,2,4,8},{3,5},{6,7}} => [2,4,5,8,3,7,6,1] => [5,3,7,6,8,1,2,4] => [[1,3,5],[2,4,8],[6,7]] => 3
{{1,2,6,7},{3,4},{5,8}} => [2,6,4,3,8,7,1,5] => [4,3,7,1,2,6,8,5] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,3,4,7},{2,6},{5,8}} => [3,6,4,7,8,2,1,5] => [6,2,7,1,3,4,8,5] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,5,7},{3,4},{6,8}} => [2,5,4,3,7,8,1,6] => [4,3,7,1,2,5,8,6] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,5,6},{3,7},{4,8}} => [2,5,7,8,6,1,3,4] => [6,1,2,5,7,3,8,4] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,3,4,6},{2,7},{5,8}} => [3,7,4,6,8,1,2,5] => [6,1,3,4,7,2,8,5] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,4,6},{3,7},{5,8}} => [2,4,7,6,8,1,3,5] => [6,1,2,4,7,3,8,5] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,3,6},{4,7},{5,8}} => [2,3,6,7,8,1,4,5] => [6,1,2,3,7,4,8,5] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,3,5},{4,7},{6,8}} => [2,3,5,7,1,8,4,6] => [5,1,2,3,7,4,8,6] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,3,4},{5,7},{6,8}} => [2,3,4,1,7,8,5,6] => [4,1,2,3,7,5,8,6] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,3,4,6},{2,5},{7,8}} => [3,5,4,6,2,1,8,7] => [5,2,6,1,3,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,4,6},{3,5},{7,8}} => [2,4,5,6,3,1,8,7] => [5,3,6,1,2,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,4,5},{3,6},{7,8}} => [2,4,6,5,1,3,8,7] => [5,1,2,4,6,3,8,7] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,5,7,8},{2,6},{3},{4}} => [5,6,3,4,7,2,8,1] => [3,4,6,2,8,1,5,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,7,8},{2,6},{3},{5}} => [4,6,3,7,5,2,8,1] => [3,5,6,2,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,7,8},{2,5},{4},{6}} => [3,5,7,4,2,6,8,1] => [4,5,2,6,8,1,3,7] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,5,6,8},{2,7},{3},{4}} => [5,7,3,4,6,8,2,1] => [3,4,7,2,8,1,5,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,6,8},{2,7},{3},{5}} => [4,7,3,6,5,8,2,1] => [3,5,7,2,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,6,8},{2,7},{4},{5}} => [3,7,6,4,5,8,2,1] => [4,5,7,2,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,5,8},{2,7},{3},{6}} => [4,7,3,5,8,6,2,1] => [3,6,7,2,8,1,4,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,5,8},{2,7},{4},{6}} => [3,7,5,4,8,6,2,1] => [4,6,7,2,8,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2,5,8},{3,7},{4},{6}} => [2,5,7,4,8,6,3,1] => [4,6,7,3,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,4,8},{2,7},{5},{6}} => [3,7,4,8,5,6,2,1] => [5,6,7,2,8,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2,4,8},{3,7},{5},{6}} => [2,4,7,8,5,6,3,1] => [5,6,7,3,8,1,2,4] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3,6,8},{2,5},{4},{7}} => [3,5,6,4,2,8,7,1] => [4,5,2,7,8,1,3,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,4,5,8},{2,6},{3},{7}} => [4,6,3,5,8,2,7,1] => [3,6,2,7,8,1,4,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,3,5,8},{2,6},{4},{7}} => [3,6,5,4,8,2,7,1] => [4,6,2,7,8,1,3,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,5,8},{3,6},{4},{7}} => [2,5,6,4,8,3,7,1] => [4,6,3,7,8,1,2,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,2,4,8},{3,6},{5},{7}} => [2,4,6,8,5,3,7,1] => [5,6,3,7,8,1,2,4] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,3,4,8},{2,5},{6},{7}} => [3,5,4,8,2,6,7,1] => [5,2,6,7,8,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4,6,7},{2,8},{3},{5}} => [4,8,3,6,5,7,1,2] => [3,5,7,1,4,6,8,2] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,3,6,7},{2,8},{4},{5}} => [3,8,6,4,5,7,1,2] => [4,5,7,1,3,6,8,2] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,6,7},{3,8},{4},{5}} => [2,6,8,4,5,7,1,3] => [4,5,7,1,2,6,8,3] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,5,7},{3,8},{4},{6}} => [2,5,8,4,7,6,1,3] => [4,6,7,1,2,5,8,3] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,2,5,6},{3,8},{4},{7}} => [2,5,8,4,6,1,7,3] => [4,6,1,2,5,7,8,3] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,4,6},{3,8},{5},{7}} => [2,4,8,6,5,1,7,3] => [5,6,1,2,4,7,8,3] => [[1,2,5,6,7],[3,4],[8]] => 2
{{1,2,3,6},{4,8},{5},{7}} => [2,3,6,8,5,1,7,4] => [5,6,1,2,3,7,8,4] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,3,4,5},{2,8},{6},{7}} => [3,8,4,5,1,6,7,2] => [5,1,3,4,6,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,4,5},{3,8},{6},{7}} => [2,4,8,5,1,6,7,3] => [5,1,2,4,6,7,8,3] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,2,3,5},{4,8},{6},{7}} => [2,3,5,8,1,6,7,4] => [5,1,2,3,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,4,6,7},{2,5},{3},{8}} => [4,5,3,6,2,7,1,8] => [3,5,2,7,1,4,6,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,4,5,7},{2,6},{3},{8}} => [4,6,3,5,7,2,1,8] => [3,6,2,7,1,4,5,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,5,7},{2,6},{4},{8}} => [3,6,5,4,7,2,1,8] => [4,6,2,7,1,3,5,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,5,7},{3,6},{4},{8}} => [2,5,6,4,7,3,1,8] => [4,6,3,7,1,2,5,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,4,7},{2,6},{5},{8}} => [3,6,4,7,5,2,1,8] => [5,6,2,7,1,3,4,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,2,4,7},{3,6},{5},{8}} => [2,4,6,7,5,3,1,8] => [5,6,3,7,1,2,4,8] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,5,7},{2,4},{6},{8}} => [3,4,5,2,7,6,1,8] => [4,2,6,7,1,3,5,8] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,4,7},{2,5},{6},{8}} => [3,5,4,7,2,6,1,8] => [5,2,6,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,3,4,5},{2,7},{6},{8}} => [3,7,4,5,1,6,2,8] => [5,1,3,4,6,7,2,8] => [[1,3,4,5,6,8],[2],[7]] => 2
{{1,2,3,5},{4,7},{6},{8}} => [2,3,5,7,1,6,4,8] => [5,1,2,3,6,7,4,8] => [[1,3,4,5,6,8],[2,7]] => 2
{{1,3,5,6},{2,4},{7},{8}} => [3,4,5,2,6,1,7,8] => [4,2,6,1,3,5,7,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,2,4,6},{3,5},{7},{8}} => [2,4,5,6,3,1,7,8] => [5,3,6,1,2,4,7,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,3,4,5},{2,6},{7},{8}} => [3,6,4,5,1,2,7,8] => [5,1,3,4,6,2,7,8] => [[1,3,4,5,7,8],[2],[6]] => 2
{{1,2,3,5},{4,6},{7},{8}} => [2,3,5,6,1,4,7,8] => [5,1,2,3,6,4,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
{{1,4,7},{2,5,8},{3,6}} => [4,5,6,7,8,3,1,2] => [6,3,7,1,4,8,2,5] => [[1,3,6],[2,5,8],[4,7]] => 3
{{1,4,6},{2,5,8},{3,7}} => [4,5,7,6,8,1,3,2] => [6,1,4,7,3,8,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,3,6},{2,5,8},{4,7}} => [3,5,6,7,8,1,4,2] => [6,1,3,7,4,8,2,5] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2,6},{3,4,8},{5,7}} => [2,6,4,8,7,1,5,3] => [6,1,2,7,5,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,4,5},{2,6,8},{3,7}} => [4,6,7,5,1,8,3,2] => [5,1,4,7,3,8,2,6] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,3,5},{2,6,8},{4,7}} => [3,6,5,7,1,8,4,2] => [5,1,3,7,4,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2,5},{3,6,8},{4,7}} => [2,5,6,7,1,8,4,3] => [5,1,2,7,4,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,3,4},{2,6,8},{5,7}} => [3,6,4,1,7,8,5,2] => [4,1,3,7,5,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2,5},{3,4,8},{6,7}} => [2,5,4,8,1,7,6,3] => [5,1,2,7,6,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,3,4},{2,5,8},{6,7}} => [3,5,4,1,8,7,6,2] => [4,1,3,7,6,8,2,5] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,4,6},{2,5,7},{3,8}} => [4,5,8,6,7,1,2,3] => [6,1,4,7,2,5,8,3] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,2,4},{3,5,7},{6,8}} => [2,4,5,1,7,8,3,6] => [4,1,2,7,3,5,8,6] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,2,5},{3,4,6},{7,8}} => [2,5,4,6,1,3,8,7] => [5,1,2,6,3,4,8,7] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,3,4},{2,5,6},{7,8}} => [3,5,4,1,6,2,8,7] => [4,1,3,6,2,5,8,7] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,2,4},{3,5,6},{7,8}} => [2,4,5,1,6,3,8,7] => [4,1,2,6,3,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,5,7},{2,6,8},{3},{4}} => [5,6,3,4,7,8,1,2] => [3,4,7,1,5,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4,7},{2,6,8},{3},{5}} => [4,6,3,7,5,8,1,2] => [3,5,7,1,4,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,7},{2,6,8},{4},{5}} => [3,6,7,4,5,8,1,2] => [4,5,7,1,3,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2,7},{3,6,8},{4},{5}} => [2,7,6,4,5,8,1,3] => [4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,4,7},{2,5,8},{3},{6}} => [4,5,3,7,8,6,1,2] => [3,6,7,1,4,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,7},{2,5,8},{4},{6}} => [3,5,7,4,8,6,1,2] => [4,6,7,1,3,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2,7},{3,5,8},{4},{6}} => [2,7,5,4,8,6,1,3] => [4,6,7,1,2,8,3,5] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,3,7},{2,4,8},{5},{6}} => [3,4,7,8,5,6,1,2] => [5,6,7,1,3,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2,7},{3,4,8},{5},{6}} => [2,7,4,8,5,6,1,3] => [5,6,7,1,2,8,3,4] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,5,6},{2,7,8},{3},{4}} => [5,7,3,4,6,1,8,2] => [3,4,6,1,5,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4,6},{2,7,8},{3},{5}} => [4,7,3,6,5,1,8,2] => [3,5,6,1,4,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,6},{2,7,8},{4},{5}} => [3,7,6,4,5,1,8,2] => [4,5,6,1,3,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2,6},{3,7,8},{4},{5}} => [2,6,7,4,5,1,8,3] => [4,5,6,1,2,8,3,7] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,3,5},{2,7,8},{4},{6}} => [3,7,5,4,1,6,8,2] => [4,5,1,3,6,8,2,7] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,2,5},{3,7,8},{4},{6}} => [2,5,7,4,1,6,8,3] => [4,5,1,2,6,8,3,7] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,4},{3,7,8},{5},{6}} => [2,4,7,1,5,6,8,3] => [4,1,2,5,6,8,3,7] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,4,6},{2,5,8},{3},{7}} => [4,5,3,6,8,1,7,2] => [3,6,1,4,7,8,2,5] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,2,6},{3,5,8},{4},{7}} => [2,6,5,4,8,1,7,3] => [4,6,1,2,7,8,3,5] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,6},{3,4,8},{5},{7}} => [2,6,4,8,5,1,7,3] => [5,6,1,2,7,8,3,4] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,3,5},{2,6,8},{4},{7}} => [3,6,5,4,1,8,7,2] => [4,5,1,3,7,8,2,6] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,2,5},{3,6,8},{4},{7}} => [2,5,6,4,1,8,7,3] => [4,5,1,2,7,8,3,6] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,4},{3,6,8},{5},{7}} => [2,4,6,1,5,8,7,3] => [4,1,2,5,7,8,3,6] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,2,5},{3,4,8},{6},{7}} => [2,5,4,8,1,6,7,3] => [5,1,2,6,7,8,3,4] => [[1,3,4,5,6],[2,7,8]] => 2
{{1,3,4},{2,5,8},{6},{7}} => [3,5,4,1,8,6,7,2] => [4,1,3,6,7,8,2,5] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,4,6},{2,5,7},{3},{8}} => [4,5,3,6,7,1,2,8] => [3,6,1,4,7,2,5,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,2,6},{3,5,7},{4},{8}} => [2,6,5,4,7,1,3,8] => [4,6,1,2,7,3,5,8] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,2,5},{3,6,7},{4},{8}} => [2,5,6,4,1,7,3,8] => [4,5,1,2,7,3,6,8] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,3,4},{2,5,7},{6},{8}} => [3,5,4,1,7,6,2,8] => [4,1,3,6,7,2,5,8] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,4},{3,5,7},{6},{8}} => [2,4,5,1,7,6,3,8] => [4,1,2,6,7,3,5,8] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,3,5},{2,4,6},{7},{8}} => [3,4,5,6,1,2,7,8] => [5,1,3,6,2,4,7,8] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,2,5},{3,4,6},{7},{8}} => [2,5,4,6,1,3,7,8] => [5,1,2,6,3,4,7,8] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,5,8},{2,6},{3,7},{4}} => [5,6,7,4,8,2,3,1] => [4,6,2,7,3,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,4,8},{2,6},{3,7},{5}} => [4,6,7,8,5,2,3,1] => [5,6,2,7,3,8,1,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,3,8},{2,6},{4,7},{5}} => [3,6,8,7,5,2,4,1] => [5,6,2,7,4,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,2,8},{3,6},{4,7},{5}} => [2,8,6,7,5,3,4,1] => [5,6,3,7,4,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,2,8},{3,5},{4,7},{6}} => [2,8,5,7,3,6,4,1] => [5,3,6,7,4,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,3,8},{2,4},{5,7},{6}} => [3,4,8,2,7,6,5,1] => [4,2,6,7,5,8,1,3] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,2,8},{3,5},{4,6},{7}} => [2,8,5,6,3,4,7,1] => [5,3,6,4,7,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 3
{{1,4,7},{2,6},{3,8},{5}} => [4,6,8,7,5,2,1,3] => [5,6,2,7,1,4,8,3] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,3,7},{2,6},{4,8},{5}} => [3,6,7,8,5,2,1,4] => [5,6,2,7,1,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,4,7},{2,5},{3,8},{6}} => [4,5,8,7,2,6,1,3] => [5,2,6,7,1,4,8,3] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,2,7},{3,5},{4,8},{6}} => [2,7,5,8,3,6,1,4] => [5,3,6,7,1,2,8,4] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,3,7},{2,4},{5,8},{6}} => [3,4,7,2,8,6,1,5] => [4,2,6,7,1,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,5,6},{2,7},{3,8},{4}} => [5,7,8,4,6,1,2,3] => [4,6,1,5,7,2,8,3] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,4,6},{2,7},{3,8},{5}} => [4,7,8,6,5,1,2,3] => [5,6,1,4,7,2,8,3] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,3,6},{2,7},{4,8},{5}} => [3,7,6,8,5,1,2,4] => [5,6,1,3,7,2,8,4] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,2,6},{3,7},{4,8},{5}} => [2,6,7,8,5,1,3,4] => [5,6,1,2,7,3,8,4] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,4,5},{2,7},{3,8},{6}} => [4,7,8,5,1,6,2,3] => [5,1,4,6,7,2,8,3] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,5},{3,7},{4,8},{6}} => [2,5,7,8,1,6,3,4] => [5,1,2,6,7,3,8,4] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,3,4},{2,7},{5,8},{6}} => [3,7,4,1,8,6,2,5] => [4,1,3,6,7,2,8,5] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,4},{3,7},{5,8},{6}} => [2,4,7,1,8,6,3,5] => [4,1,2,6,7,3,8,5] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,3},{4,7},{5,8},{6}} => [2,3,1,7,8,6,4,5] => [3,1,2,6,7,4,8,5] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,4,6},{2,5},{3,8},{7}} => [4,5,8,6,2,1,7,3] => [5,2,6,1,4,7,8,3] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,3,6},{2,5},{4,8},{7}} => [3,5,6,8,2,1,7,4] => [5,2,6,1,3,7,8,4] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,6},{3,5},{4,8},{7}} => [2,6,5,8,3,1,7,4] => [5,3,6,1,2,7,8,4] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,3,6},{2,4},{5,8},{7}} => [3,4,6,2,8,1,7,5] => [4,2,6,1,3,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,2,6},{3,4},{5,8},{7}} => [2,6,4,3,8,1,7,5] => [4,3,6,1,2,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,4,5},{2,6},{3,8},{7}} => [4,6,8,5,1,2,7,3] => [5,1,4,6,2,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 3
{{1,2,5},{3,6},{4,8},{7}} => [2,5,6,8,1,3,7,4] => [5,1,2,6,3,7,8,4] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,2,4},{3,6},{5,8},{7}} => [2,4,6,1,8,3,7,5] => [4,1,2,6,3,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,2,3},{4,6},{5,8},{7}} => [2,3,1,6,8,4,7,5] => [3,1,2,6,4,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 3
{{1,3,5},{2,4},{6,8},{7}} => [3,4,5,2,1,8,7,6] => [4,2,5,1,3,7,8,6] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,3,4},{2,5},{6,8},{7}} => [3,5,4,1,2,8,7,6] => [4,1,3,5,2,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 3
{{1,2,6},{3,5},{4,7},{8}} => [2,6,5,7,3,1,4,8] => [5,3,6,1,2,7,4,8] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,3,6},{2,4},{5,7},{8}} => [3,4,6,2,7,1,5,8] => [4,2,6,1,3,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,2,5},{3,6},{4,7},{8}} => [2,5,6,7,1,3,4,8] => [5,1,2,6,3,7,4,8] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,2,3},{4,6},{5,7},{8}} => [2,3,1,6,7,4,5,8] => [3,1,2,6,4,7,5,8] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,3,8},{2,4},{5},{6},{7}} => [3,4,8,2,5,6,7,1] => [4,2,5,6,7,8,1,3] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,3,4},{2,8},{5},{6},{7}} => [3,8,4,1,5,6,7,2] => [4,1,3,5,6,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 2
{{1,4,7},{2,6},{3},{5},{8}} => [4,6,3,7,5,2,1,8] => [3,5,6,2,7,1,4,8] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1,3,7},{2,4},{5},{6},{8}} => [3,4,7,2,5,6,1,8] => [4,2,5,6,7,1,3,8] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,3,5},{2,4},{6},{7},{8}} => [3,4,5,2,1,6,7,8] => [4,2,5,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 2
{{1,5},{2,6},{3,7},{4},{8}} => [5,6,7,4,1,2,3,8] => [4,5,1,6,2,7,3,8] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,4},{2,5},{3,6},{7},{8}} => [4,5,6,1,2,3,7,8] => [4,1,5,2,6,3,7,8] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,7},{2,8},{3},{4},{5},{6}} => [7,8,3,4,5,6,1,2] => [3,4,5,6,7,1,8,2] => [[1,2,3,4,5,7],[6,8]] => 2
{{1,6},{2,8},{3},{4},{5},{7}} => [6,8,3,4,5,1,7,2] => [3,4,5,6,1,7,8,2] => [[1,2,3,4,6,7],[5,8]] => 2
{{1,4},{2,8},{3},{5},{6},{7}} => [4,8,3,1,5,6,7,2] => [3,4,1,5,6,7,8,2] => [[1,2,4,5,6,7],[3,8]] => 2
{{1,3},{2,8},{4},{5},{6},{7}} => [3,8,1,4,5,6,7,2] => [3,1,4,5,6,7,8,2] => [[1,3,4,5,6,7],[2,8]] => 2
{{1,5},{2,6},{3},{4},{7},{8}} => [5,6,3,4,1,2,7,8] => [3,4,5,1,6,2,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
{{1,4},{2,5},{3},{6},{7},{8}} => [4,5,3,1,2,6,7,8] => [3,4,1,5,2,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 2
{{1,3},{2,4},{5},{6},{7},{8}} => [3,4,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,3,5,7},{2},{4},{6,8}} => [3,2,5,4,7,8,1,6] => [2,4,7,1,3,5,8,6] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,5},{2,4,8},{3},{6,7}} => [5,4,3,8,1,7,6,2] => [3,5,1,7,6,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5,8},{2,4},{3,6},{7}} => [5,4,6,2,8,3,7,1] => [4,2,6,3,7,8,1,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1},{2,3,5,8},{4,6},{7}} => [1,3,5,6,8,4,7,2] => [1,6,4,7,8,2,3,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,4},{2,5,8},{3},{6,7}} => [4,5,3,1,8,7,6,2] => [3,4,1,7,6,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,4,7},{2,5},{3},{6,8}} => [4,5,3,7,2,8,1,6] => [3,5,2,7,1,4,8,6] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,4},{2},{3,6},{5,7,8}} => [4,2,6,1,7,3,8,5] => [2,4,1,6,3,8,5,7] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,4},{2},{3,7},{5,6,8}} => [4,2,7,1,6,8,3,5] => [2,4,1,7,3,8,5,6] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,5},{2},{3,4,8},{6,7}} => [5,2,4,8,1,7,6,3] => [2,5,1,7,6,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,2,5},{3},{4,7,8},{6}} => [2,5,3,7,1,6,8,4] => [3,5,1,2,6,8,4,7] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,5,7},{3},{4,8},{6}} => [2,5,3,8,7,6,1,4] => [3,6,7,1,2,5,8,4] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1},{2,3,5,7},{4},{6,8}} => [1,3,5,4,7,8,2,6] => [1,4,7,2,3,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,4,6},{2},{3,8},{5,7}} => [4,2,8,6,7,1,5,3] => [2,6,1,4,7,5,8,3] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,4,6},{2},{3,7},{5,8}} => [4,2,7,6,8,1,3,5] => [2,6,1,4,7,3,8,5] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1},{2,6},{3,4,7},{5,8}} => [1,6,4,7,8,2,3,5] => [1,6,2,7,3,4,8,5] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,2},{3,6,7},{4,8},{5}} => [2,1,6,8,5,7,3,4] => [2,1,5,7,3,6,8,4] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,2},{3,7},{4,6,8},{5}} => [2,1,7,6,5,8,3,4] => [2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,2},{3,5,8},{4,7},{6}} => [2,1,5,7,8,6,4,3] => [2,1,6,7,4,8,3,5] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,7},{2,3,8},{4,5},{6}} => [7,3,8,5,4,6,1,2] => [5,4,6,7,1,8,2,3] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1},{2,5},{3,4,8},{6,7}} => [1,5,4,8,2,7,6,3] => [1,5,2,7,6,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,4},{3,5,8},{6,7}} => [1,4,5,2,8,7,6,3] => [1,4,2,7,6,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,4},{3,7},{5,6,8}} => [1,4,7,2,6,8,3,5] => [1,4,2,7,3,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,4},{3,6},{5,7,8}} => [1,4,6,2,7,3,8,5] => [1,4,2,6,3,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,4},{3,6,7},{5,8}} => [1,4,6,2,8,7,3,5] => [1,4,2,7,3,6,8,5] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1,3},{2,6},{4},{5,7,8}} => [3,6,1,4,7,2,8,5] => [3,1,4,6,2,8,5,7] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,4,8},{2,3,7},{5},{6}} => [4,3,7,8,5,6,2,1] => [5,6,7,2,3,8,1,4] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,4,6},{3,7},{5,8}} => [1,4,7,6,8,2,3,5] => [1,6,2,4,7,3,8,5] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1},{2,4,6},{3,8},{5,7}} => [1,4,8,6,7,2,5,3] => [1,6,2,4,7,5,8,3] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2,5,7},{3,4},{6,8}} => [1,5,4,3,7,8,2,6] => [1,4,3,7,2,5,8,6] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,8},{2,3,6},{4},{5,7}} => [8,3,6,4,7,2,5,1] => [4,6,2,3,7,5,8,1] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,2,6},{3,8},{4,7},{5}} => [2,6,8,7,5,1,4,3] => [5,6,1,2,7,4,8,3] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,7},{2,3,6},{4},{5,8}} => [7,3,6,4,8,2,1,5] => [4,6,2,3,7,1,8,5] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,2},{3,6,8},{4,7},{5}} => [2,1,6,7,5,8,4,3] => [2,1,5,7,4,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,3,7},{2,8},{4},{5,6}} => [3,8,7,4,6,5,1,2] => [4,6,5,7,1,3,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,3,7},{2,8},{4,6},{5}} => [3,8,7,6,5,4,1,2] => [5,6,4,7,1,3,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,3,7},{2},{4,5,8},{6}} => [3,2,7,5,8,6,1,4] => [2,6,7,1,3,8,4,5] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,7},{2,3,8},{4,6},{5}} => [7,3,8,6,5,4,1,2] => [5,6,4,7,1,8,2,3] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,7},{2,3,8},{4},{5,6}} => [7,3,8,4,6,5,1,2] => [4,6,5,7,1,8,2,3] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,7,8},{2,5},{3,6},{4}} => [7,5,6,4,2,3,8,1] => [4,5,2,6,3,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,4,6},{2,5},{3},{7,8}} => [4,5,3,6,2,1,8,7] => [3,5,2,6,1,4,8,7] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,5,7,8},{2},{3,6},{4}} => [5,2,6,4,7,3,8,1] => [2,4,6,3,8,1,5,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,5,8},{2,7},{3,6},{4}} => [5,7,6,4,8,3,2,1] => [4,6,3,7,2,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,8},{2,5,7},{3,6},{4}} => [8,5,6,4,7,3,2,1] => [4,6,3,7,2,5,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,5,8},{2,6,7},{3},{4}} => [5,6,3,4,8,7,2,1] => [3,4,7,2,6,8,1,5] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,4,5,7},{2},{3,8},{6}} => [4,2,8,5,7,6,1,3] => [2,6,7,1,4,5,8,3] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,3,5},{2,6},{4},{7,8}} => [3,6,5,4,1,2,8,7] => [4,5,1,3,6,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,4,6,8},{2},{3,7},{5}} => [4,2,7,6,5,8,3,1] => [2,5,7,3,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,8},{2,4,6},{3,7},{5}} => [8,4,7,6,5,2,3,1] => [5,6,2,4,7,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,3,5},{2,8},{4},{6,7}} => [3,8,5,4,1,7,6,2] => [4,5,1,3,7,6,8,2] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,5},{2,3,8},{4},{6,7}} => [5,3,8,4,1,7,6,2] => [4,5,1,7,6,8,2,3] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,8},{2,6},{3,4,7},{5}} => [8,6,4,7,5,2,3,1] => [5,6,2,7,3,4,8,1] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,6,8},{2},{3,4,7},{5}} => [6,2,4,7,5,8,3,1] => [2,5,7,3,4,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,6,8},{2,4},{3,7},{5}} => [6,4,7,2,5,8,3,1] => [4,2,5,7,3,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,6},{2,3,8},{4,7},{5}} => [6,3,8,7,5,1,4,2] => [5,6,1,7,4,8,2,3] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6},{2,3,7,8},{4},{5}} => [6,3,7,4,5,1,8,2] => [4,5,6,1,8,2,3,7] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,5},{2,3,7},{4,8},{6}} => [5,3,7,8,1,6,2,4] => [5,1,6,7,2,3,8,4] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,5},{2,3,6},{4},{7,8}} => [5,3,6,4,1,2,8,7] => [4,5,1,6,2,3,8,7] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,6,7},{2,4,8},{3},{5}} => [6,4,3,8,5,7,1,2] => [3,5,7,1,6,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,6,8},{2,5,7},{3},{4}} => [6,5,3,4,7,8,2,1] => [3,4,7,2,5,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,6,8},{2,7},{3,5},{4}} => [6,7,5,4,3,8,2,1] => [4,5,3,7,2,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,6,7},{2,8},{3,4},{5}} => [6,8,4,3,5,7,1,2] => [4,3,5,7,1,6,8,2] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,4,8},{2,3,6},{5},{7}} => [4,3,6,8,5,2,7,1] => [5,6,2,3,7,8,1,4] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,5},{2,4,8},{3,6},{7}} => [5,4,6,8,1,3,7,2] => [5,1,6,3,7,8,2,4] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6},{2,4,8},{3,5},{7}} => [6,4,5,8,3,1,7,2] => [5,3,6,1,7,8,2,4] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,6},{2,3,5},{4,8},{7}} => [6,3,5,8,2,1,7,4] => [5,2,3,6,1,7,8,4] => [[1,3,4,6,7],[2,8],[5]] => 3
{{1,5},{2,3,6},{4,8},{7}} => [5,3,6,8,1,2,7,4] => [5,1,6,2,3,7,8,4] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,4,8},{2,7},{3,6},{5}} => [4,7,6,8,5,3,2,1] => [5,6,3,7,2,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,4,7},{2,8},{3,6},{5}} => [4,8,6,7,5,3,1,2] => [5,6,3,7,1,4,8,2] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,4,6},{2,8},{3,7},{5}} => [4,8,7,6,5,1,3,2] => [5,6,1,4,7,3,8,2] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,5},{2,8},{3,4,7},{6}} => [5,8,4,7,1,6,3,2] => [5,1,6,7,3,4,8,2] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,5},{2,3,8},{4,7},{6}} => [5,3,8,7,1,6,4,2] => [5,1,6,7,4,8,2,3] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,2,5},{3,8},{4,7},{6}} => [2,5,8,7,1,6,4,3] => [5,1,2,6,7,4,8,3] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,5},{2,7},{3,4,8},{6}} => [5,7,4,8,1,6,2,3] => [5,1,6,7,2,8,3,4] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,7},{2,6},{3,4,8},{5}} => [7,6,4,8,5,2,1,3] => [5,6,2,7,1,8,3,4] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,8},{2,3,5},{4,7},{6}} => [8,3,5,7,2,6,4,1] => [5,2,3,6,7,4,8,1] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,8},{2,5},{3,4,7},{6}} => [8,5,4,7,2,6,3,1] => [5,2,6,7,3,4,8,1] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,8},{2,4,7},{3,5},{6}} => [8,4,5,7,3,6,2,1] => [5,3,6,7,2,4,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 3
{{1,8},{2,4,7},{3,6},{5}} => [8,4,6,7,5,3,2,1] => [5,6,3,7,2,4,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,7},{2,4,8},{3,6},{5}} => [7,4,6,8,5,3,1,2] => [5,6,3,7,1,8,2,4] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,3,8},{2,7},{4,6},{5}} => [3,7,8,6,5,4,2,1] => [5,6,4,7,2,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,6},{2,4,8},{3,7},{5}} => [6,4,7,8,5,1,3,2] => [5,6,1,7,3,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6},{2,4,7},{3,8},{5}} => [6,4,8,7,5,1,2,3] => [5,6,1,7,2,4,8,3] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,7},{2,4,6},{3,8},{5}} => [7,4,8,6,5,2,1,3] => [5,6,2,4,7,1,8,3] => [[1,2,5,7],[3,4],[6,8]] => 3
{{1,7},{2,4,8},{3,5},{6}} => [7,4,5,8,3,6,1,2] => [5,3,6,7,1,8,2,4] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,7},{2,3,5},{4,8},{6}} => [7,3,5,8,2,6,1,4] => [5,2,3,6,7,1,8,4] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,7},{3,8},{4,6},{5}} => [2,7,8,6,5,4,1,3] => [5,6,4,7,1,2,8,3] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,7},{2,8},{3,4,6},{5}} => [7,8,4,6,5,3,1,2] => [5,6,3,4,7,1,8,2] => [[1,2,5,7],[3,4],[6,8]] => 3
{{1,6},{2,3,7},{4,8},{5}} => [6,3,7,8,5,1,2,4] => [5,6,1,7,2,3,8,4] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,3,5},{2},{4,6,8},{7}} => [3,2,5,6,1,8,7,4] => [2,5,1,3,7,8,4,6] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,3},{2,4,6,8},{5},{7}} => [3,4,1,6,5,8,7,2] => [3,1,5,7,8,2,4,6] => [[1,3,4,5],[2,6,7,8]] => 2
{{1},{2,4,6,8},{3},{5,7}} => [1,4,3,6,7,8,5,2] => [1,3,7,5,8,2,4,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3},{2},{4,6,8},{5,7}} => [3,2,1,6,7,8,5,4] => [2,3,1,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,3,6},{2},{4,7},{5,8}} => [3,2,6,7,8,1,4,5] => [2,6,1,3,7,4,8,5] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3,5},{2},{4,7},{6,8}} => [3,2,5,7,1,8,4,6] => [2,5,1,3,7,4,8,6] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3,7},{2},{4,6},{5,8}} => [3,2,7,6,8,4,1,5] => [2,6,4,7,1,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,3,5,7},{2},{4,8},{6}} => [3,2,5,8,7,6,1,4] => [2,6,7,1,3,5,8,4] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,3},{2,4,8},{5,7},{6}} => [3,4,1,8,7,6,5,2] => [3,1,6,7,5,8,2,4] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,3},{2,7},{4,6,8},{5}} => [3,7,1,6,5,8,2,4] => [3,1,5,7,2,8,4,6] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,7},{2,4,6},{3},{5,8}} => [7,4,3,6,8,2,1,5] => [3,6,2,4,7,1,8,5] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,5,7},{2,4,8},{3},{6}} => [5,4,3,8,7,6,1,2] => [3,6,7,1,5,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,7},{2,4,6},{3,5},{8}} => [7,4,5,6,3,2,1,8] => [5,3,6,2,4,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 3
{{1,4,7},{2,6},{3,5},{8}} => [4,6,5,7,3,2,1,8] => [5,3,6,2,7,1,4,8] => [[1,3,5,8],[2,7],[4],[6]] => 3
{{1},{2,5,8},{3,7},{4,6}} => [1,5,7,6,8,4,3,2] => [1,6,4,7,3,8,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1},{2,4,8},{3,6},{5,7}} => [1,4,6,8,7,3,5,2] => [1,6,3,7,5,8,2,4] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,4},{2,6,8},{3,5},{7}} => [4,6,5,1,3,8,7,2] => [4,1,5,3,7,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,4},{2,5},{3,6,8},{7}} => [4,5,6,1,2,8,7,3] => [4,1,5,2,7,8,3,6] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,3},{2,5},{4,6,8},{7}} => [3,5,1,6,2,8,7,4] => [3,1,5,2,7,8,4,6] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,5},{2,4,6,8},{3},{7}} => [5,4,3,6,1,8,7,2] => [3,5,1,7,8,2,4,6] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,5},{2,4},{3,6,8},{7}} => [5,4,6,2,1,8,7,3] => [4,2,5,1,7,8,3,6] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1},{2,6,8},{3,5,7},{4}} => [1,6,5,4,7,8,3,2] => [1,4,7,3,5,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,6},{2,4,8},{3},{5,7}} => [6,4,3,8,7,1,5,2] => [3,6,1,7,5,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6},{2,4,7},{3},{5,8}} => [6,4,3,7,8,1,2,5] => [3,6,1,7,2,4,8,5] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,5},{2,4,7},{3},{6,8}} => [5,4,3,7,1,8,2,6] => [3,5,1,7,2,4,8,6] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,5,7},{2,4,6},{3},{8}} => [5,4,3,6,7,2,1,8] => [3,6,2,4,7,1,5,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,5,7},{2,4},{3,6},{8}} => [5,4,6,2,7,3,1,8] => [4,2,6,3,7,1,5,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1},{2,6,8},{3,5},{4,7}} => [1,6,5,7,3,8,4,2] => [1,5,3,7,4,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6},{2,7},{3,5,8},{4}} => [6,7,5,4,8,1,2,3] => [4,6,1,7,2,8,3,5] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,3,5},{2,7},{4},{6,8}} => [3,7,5,4,1,8,2,6] => [4,5,1,3,7,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,7},{2,6,8},{3,5},{4}} => [7,6,5,4,3,8,1,2] => [4,5,3,7,1,8,2,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,7},{2,6},{3,5,8},{4}} => [7,6,5,4,8,2,1,3] => [4,6,2,7,1,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,2},{3,4,6},{5,8},{7}} => [2,1,4,6,8,3,7,5] => [2,1,6,3,4,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,2},{3,6},{4,5,8},{7}} => [2,1,6,5,8,3,7,4] => [2,1,6,3,7,8,4,5] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,2},{3,5,6},{4,8},{7}} => [2,1,5,8,6,3,7,4] => [2,1,6,3,5,7,8,4] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,2,6},{3},{4,5,8},{7}} => [2,6,3,5,8,1,7,4] => [3,6,1,2,7,8,4,5] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,6},{2,3},{4,5,8},{7}} => [6,3,2,5,8,1,7,4] => [3,2,6,1,7,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,5,6},{2,3},{4,8},{7}} => [5,3,2,8,6,1,7,4] => [3,2,6,1,5,7,8,4] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,5},{2,8},{3,4,6},{7}} => [5,8,4,6,1,3,7,2] => [5,1,6,3,4,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,5},{2,3,8},{4,6},{7}} => [5,3,8,6,1,4,7,2] => [5,1,6,4,7,8,2,3] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6},{2,3,5,8},{4},{7}} => [6,3,5,4,8,1,7,2] => [4,6,1,7,8,2,3,5] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,2,4},{3,6},{5},{7,8}} => [2,4,6,1,5,3,8,7] => [4,1,2,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,4,6},{3},{5,8},{7}} => [2,4,3,6,8,1,7,5] => [3,6,1,2,4,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,3,4},{2,8},{5,7},{6}} => [3,8,4,1,7,6,5,2] => [4,1,3,6,7,5,8,2] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,4},{2,3,8},{5,7},{6}} => [4,3,8,1,7,6,5,2] => [4,1,6,7,5,8,2,3] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,4,6},{2,3},{5,8},{7}} => [4,3,2,6,8,1,7,5] => [3,2,6,1,4,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1,4},{2,3,6},{5},{7,8}} => [4,3,6,1,5,2,8,7] => [4,1,5,6,2,3,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,4},{2,3,6},{5,8},{7}} => [4,3,6,1,8,2,7,5] => [4,1,6,2,3,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,3,8},{2,6},{4,5},{7}} => [3,6,8,5,4,2,7,1] => [5,4,6,2,7,8,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 3
{{1,3,4},{2,6},{5},{7,8}} => [3,6,4,1,5,2,8,7] => [4,1,3,5,6,2,8,7] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,5},{2,4},{3,7,8},{6}} => [5,4,7,2,1,6,8,3] => [4,2,5,1,6,8,3,7] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,5,6},{2,4},{3,8},{7}} => [5,4,8,2,6,1,7,3] => [4,2,6,1,5,7,8,3] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,4},{2,8},{3,5,6},{7}} => [4,8,5,1,6,3,7,2] => [4,1,6,3,5,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,4},{2,7,8},{3,5},{6}} => [4,7,5,1,3,6,8,2] => [4,1,5,3,6,8,2,7] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,4,7},{2,8},{3},{5,6}} => [4,8,3,7,6,5,1,2] => [3,6,5,7,1,4,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,5,7},{2,8},{3,4},{6}} => [5,8,4,3,7,6,1,2] => [4,3,6,7,1,5,8,2] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,5},{2,3,7},{4},{6,8}} => [5,3,7,4,1,8,2,6] => [4,5,1,7,2,3,8,6] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,4,5},{2,7},{3},{6,8}} => [4,7,3,5,1,8,2,6] => [3,5,1,4,7,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,4},{2,6,7},{3},{5,8}} => [4,6,3,1,8,7,2,5] => [3,4,1,7,2,6,8,5] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,4},{2,6},{3},{5,7,8}} => [4,6,3,1,7,2,8,5] => [3,4,1,6,2,8,5,7] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,6,7},{2,5,8},{3},{4}} => [6,5,3,4,8,7,1,2] => [3,4,7,1,6,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,7},{2,5,6,8},{3},{4}} => [7,5,3,4,6,8,1,2] => [3,4,7,1,8,2,5,6] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,2,8},{3,6},{4},{5,7}} => [2,8,6,4,7,3,5,1] => [4,6,3,7,5,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,8},{2,5,6},{3},{4,7}} => [8,5,3,7,6,2,4,1] => [3,6,2,5,7,4,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,8},{2,5},{3},{4,6,7}} => [8,5,3,6,2,7,4,1] => [3,5,2,7,4,6,8,1] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,7,8},{2,5},{3},{4,6}} => [7,5,3,6,2,4,8,1] => [3,5,2,6,4,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,8},{2,4},{3,6,7},{5}} => [8,4,6,2,5,7,3,1] => [4,2,5,7,3,6,8,1] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,7,8},{2,4},{3,6},{5}} => [7,4,6,2,5,3,8,1] => [4,2,5,6,3,8,1,7] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,4},{2,3,7},{5,8},{6}} => [4,3,7,1,8,6,2,5] => [4,1,6,7,2,3,8,5] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,3},{2,7},{4,5,8},{6}} => [3,7,1,5,8,6,2,4] => [3,1,6,7,2,8,4,5] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,3},{2,6,7},{4,8},{5}} => [3,6,1,8,5,7,2,4] => [3,1,5,7,2,6,8,4] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,3},{2,6},{4,7,8},{5}} => [3,6,1,7,5,2,8,4] => [3,1,5,6,2,8,4,7] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,6},{2,4,7,8},{3},{5}} => [6,4,3,7,5,1,8,2] => [3,5,6,1,8,2,4,7] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,7},{2,5,8},{3,4},{6}} => [7,5,4,3,8,6,1,2] => [4,3,6,7,1,8,2,5] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,7},{2,3,5,8},{4},{6}} => [7,3,5,4,8,6,1,2] => [4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,2,7},{3},{4,6},{5,8}} => [2,7,3,6,8,4,1,5] => [3,6,4,7,1,2,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,6,7},{2},{3,5},{4,8}} => [6,2,5,8,3,7,1,4] => [2,5,3,7,1,6,8,4] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,6},{2},{3,5},{4,7,8}} => [6,2,5,7,3,1,8,4] => [2,5,3,6,1,8,4,7] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,5},{2},{3,7,8},{4,6}} => [5,2,7,6,1,4,8,3] => [2,5,1,6,4,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5,6},{2},{3,8},{4,7}} => [5,2,8,7,6,1,4,3] => [2,6,1,5,7,4,8,3] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,6},{2},{3,4,8},{5,7}} => [6,2,4,8,7,1,5,3] => [2,6,1,7,5,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,2,6},{3},{4,8},{5,7}} => [2,6,3,8,7,1,5,4] => [3,6,1,2,7,5,8,4] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,6,8},{2,3},{4,7},{5}} => [6,3,2,7,5,8,4,1] => [3,2,5,7,4,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,6,8},{2},{3,7},{4,5}} => [6,2,7,5,4,8,3,1] => [2,5,4,7,3,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,5,6,8},{2},{3,7},{4}} => [5,2,7,4,6,8,3,1] => [2,4,7,3,8,1,5,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,5,8},{2},{3,6,7},{4}} => [5,2,6,4,8,7,3,1] => [2,4,7,3,6,8,1,5] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 0
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3},{4},{5},{6},{7,9},{8}} => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3},{4},{5},{6,9},{7},{8}} => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3},{4},{5,9},{6},{7},{8}} => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3},{4,9},{5},{6},{7},{8}} => [1,2,3,9,5,6,7,8,4] => [1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3,9},{4},{5},{6},{7},{8}} => [1,2,9,4,5,6,7,8,3] => [1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2,9},{3},{4},{5},{6},{7},{8}} => [1,9,3,4,5,6,7,8,2] => [1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,9,1] => [[1,2,3,4,5,6,7,8],[9]] => 1
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => [1,2,3,4,5,10,7,8,9,6] => [1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [1,2,3,4,10,6,7,8,9,5] => [1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => [1,2,3,10,5,6,7,8,9,4] => [1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => [1,2,10,4,5,6,7,8,9,3] => [1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => [1,10,3,4,5,6,7,8,9,2] => [1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [10,2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,10,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
{{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => [8,1,2,3,4,5,6,7,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1},{2,3,4,5,6,7,8,9}} => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 1
{{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => [9,1,2,3,4,5,6,7,8,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4,5,6,8},{7},{9}} => [2,3,4,5,6,8,7,1,9] => [7,8,1,2,3,4,5,6,9] => [[1,2,5,6,7,8,9],[3,4]] => 1
{{1},{2,3,4,5,6,7,8,9,10}} => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
{{1,2,3,4,5,6,7,9},{8},{10}} => [2,3,4,5,6,7,9,8,1,10] => [8,9,1,2,3,4,5,6,7,10] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
{{1,2,3,4,5,7,8},{6},{9}} => [2,3,4,5,7,6,8,1,9] => [6,8,1,2,3,4,5,7,9] => [[1,2,5,6,7,8,9],[3,4]] => 1
{{1,3,6,8},{2},{4},{5,7}} => [3,2,6,4,7,8,5,1] => [2,4,7,5,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,8},{2},{3,6},{5,7}} => [4,2,6,8,7,3,5,1] => [2,6,3,7,5,8,1,4] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,3,8},{2},{4,6},{5,7}} => [3,2,8,6,7,4,5,1] => [2,6,4,7,5,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,4,7,8},{2},{3,6},{5}} => [4,2,6,7,5,3,8,1] => [2,5,6,3,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,8},{2},{3,7},{5,6}} => [4,2,7,8,6,5,3,1] => [2,6,5,7,3,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,5,8},{2},{3,6},{4,7}} => [5,2,6,7,8,3,4,1] => [2,6,3,7,4,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,4,7,8},{3},{6}} => [5,4,3,7,1,6,8,2] => [3,5,1,6,8,2,4,7] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,3},{2,4,6,7},{5},{8}} => [3,4,1,6,5,7,2,8] => [3,1,5,7,2,4,6,8] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,3},{2,5,8},{4,6},{7}} => [3,5,1,6,8,4,7,2] => [3,1,6,4,7,8,2,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6},{2,4},{3,5,8},{7}} => [6,4,5,2,8,1,7,3] => [4,2,6,1,7,8,3,5] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,4},{2,5,6},{3,7},{8}} => [4,5,7,1,6,2,3,8] => [4,1,6,2,5,7,3,8] => [[1,3,5,6,8],[2,4],[7]] => 3
{{1,2,5},{3,6},{4},{7,8}} => [2,5,6,4,1,3,8,7] => [4,5,1,2,6,3,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,6,7},{2,8},{3},{4,5}} => [6,8,3,5,4,7,1,2] => [3,5,4,7,1,6,8,2] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,5,6},{2,3},{4,7},{8}} => [5,3,2,7,6,1,4,8] => [3,2,6,1,5,7,4,8] => [[1,3,6,8],[2,5],[4,7]] => 3
{{1,4,6},{2,3},{5,7},{8}} => [4,3,2,6,7,1,5,8] => [3,2,6,1,4,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,4},{2,3,6},{5,7},{8}} => [4,3,6,1,7,2,5,8] => [4,1,6,2,3,7,5,8] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,2,4},{3,7},{5},{6,8}} => [2,4,7,1,5,8,3,6] => [4,1,2,5,7,3,8,6] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,7},{3},{4,5},{6,8}} => [2,7,3,5,4,8,1,6] => [3,5,4,7,1,2,8,6] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,4},{2,7},{3,6,8},{5}} => [4,7,6,1,5,8,2,3] => [4,1,5,7,2,8,3,6] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,4},{2,6},{3,5,7},{8}} => [4,6,5,1,7,2,3,8] => [4,1,6,2,7,3,5,8] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,6},{2,4},{3,5,7},{8}} => [6,4,5,2,7,1,3,8] => [4,2,6,1,7,3,5,8] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,3},{2,5,7},{4,6},{8}} => [3,5,1,6,7,4,2,8] => [3,1,6,4,7,2,5,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,5},{2,7,8},{3},{4,6}} => [5,7,3,6,1,4,8,2] => [3,5,1,6,4,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,7},{2,4},{3,5,6},{8}} => [7,4,5,2,6,3,1,8] => [4,2,6,3,5,7,1,8] => [[1,3,5,6,8],[2,4],[7]] => 3
{{1,5},{2,6},{3,7,8},{4}} => [5,6,7,4,1,2,8,3] => [4,5,1,6,2,8,3,7] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,3},{2,4,5,6},{7,8}} => [3,4,1,5,6,2,8,7] => [3,1,6,2,4,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,4},{2,3,5,6},{7,8}} => [4,3,5,1,6,2,8,7] => [4,1,6,2,3,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,4},{2,3,5,7},{6,8}} => [4,3,5,1,7,8,2,6] => [4,1,7,2,3,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,3},{2,4,5,7},{6,8}} => [3,4,1,5,7,8,2,6] => [3,1,7,2,4,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,2},{3,4,5,7},{6,8}} => [2,1,4,5,7,8,3,6] => [2,1,7,3,4,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,3},{2,4,5,6,7,8}} => [3,4,1,5,6,7,8,2] => [3,1,8,2,4,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,4},{2,3,5,6,7,8}} => [4,3,5,1,6,7,8,2] => [4,1,8,2,3,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,5},{2,3,4,6,7,8}} => [5,3,4,6,1,7,8,2] => [5,1,8,2,3,4,6,7] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,2},{3,4,6,7},{5,8}} => [2,1,4,6,8,7,3,5] => [2,1,7,3,4,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,3},{2,4,6,7},{5,8}} => [3,4,1,6,8,7,2,5] => [3,1,7,2,4,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,4},{2,3,6,7},{5,8}} => [4,3,6,1,8,7,2,5] => [4,1,7,2,3,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,5},{2,3,6,7},{4,8}} => [5,3,6,8,1,7,2,4] => [5,1,7,2,3,6,8,4] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,3},{2,4},{5,6,7,8}} => [3,4,1,2,6,7,8,5] => [3,1,4,2,8,5,6,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,4},{2,5},{3,6,7,8}} => [4,5,6,1,2,7,8,3] => [4,1,5,2,8,3,6,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,3},{2,5},{4,6,7,8}} => [3,5,1,6,2,7,8,4] => [3,1,5,2,8,4,6,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,2},{3,5},{4,6,7,8}} => [2,1,5,6,3,7,8,4] => [2,1,5,3,8,4,6,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,2},{3,6},{4,5,7,8}} => [2,1,6,5,7,3,8,4] => [2,1,6,3,8,4,5,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,3},{2,6},{4,5,7,8}} => [3,6,1,5,7,2,8,4] => [3,1,6,2,8,4,5,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,4},{2,6},{3,5,7,8}} => [4,6,5,1,7,2,8,3] => [4,1,6,2,8,3,5,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,5},{2,6},{3,4,7,8}} => [5,6,4,7,1,2,8,3] => [5,1,6,2,8,3,4,7] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,2},{3,5,6,8},{4,7}} => [2,1,5,7,6,8,4,3] => [2,1,7,4,8,3,5,6] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4},{2,5,6,8},{3,7}} => [4,5,7,1,6,8,3,2] => [4,1,7,3,8,2,5,6] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,5},{2,4,6,8},{3,7}} => [5,4,7,6,1,8,3,2] => [5,1,7,3,8,2,4,6] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => [7,2,3,6,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4},{2},{3,5,6},{7,8}} => [4,2,5,1,6,3,8,7] => [2,4,1,6,3,5,8,7] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,4,5},{2},{3,6},{7,8}} => [4,2,6,5,1,3,8,7] => [2,5,1,4,6,3,8,7] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,5},{2},{3,4,6},{7,8}} => [5,2,4,6,1,3,8,7] => [2,5,1,6,3,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,5},{2},{3,4,7,8},{6}} => [5,2,4,7,1,6,8,3] => [2,5,1,6,8,3,4,7] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,7},{2},{3,4,8},{5,6}} => [7,2,4,8,6,5,1,3] => [2,6,5,7,1,8,3,4] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,4,6,7},{2},{3,8},{5}} => [4,2,8,6,5,7,1,3] => [2,5,7,1,4,6,8,3] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,4,6},{2},{3,7,8},{5}} => [4,2,7,6,5,1,8,3] => [2,5,6,1,4,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,6},{2},{4},{5,7,8}} => [3,2,6,4,7,1,8,5] => [2,4,6,1,3,8,5,7] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,2},{3,6},{4},{5,7,8}} => [2,1,6,4,7,3,8,5] => [2,1,4,6,3,8,5,7] => [[1,3,4,6],[2,5,7,8]] => 3
{{1,4},{2},{3,5,7,8},{6}} => [4,2,5,1,7,6,8,3] => [2,4,1,6,8,3,5,7] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,7},{2,4},{3},{5,6,8}} => [7,4,3,2,6,8,1,5] => [3,4,2,7,1,8,5,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,2},{3,6,7},{4},{5,8}} => [2,1,6,4,8,7,3,5] => [2,1,4,7,3,6,8,5] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,3,6,7},{2},{4},{5,8}} => [3,2,6,4,8,7,1,5] => [2,4,7,1,3,6,8,5] => [[1,2,3,7],[4,5,6],[8]] => 2
{{1,4,7},{2},{3,8},{5,6}} => [4,2,8,7,6,5,1,3] => [2,6,5,7,1,4,8,3] => [[1,2,4,7],[3,6],[5],[8]] => 3
{{1,7},{2,4,5},{3},{6,8}} => [7,4,3,5,2,8,1,6] => [3,5,2,4,7,1,8,6] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,8},{2,4},{3,5,6},{7}} => [8,4,5,2,6,3,7,1] => [4,2,6,3,5,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,5,8},{2,3},{4,6},{7}} => [5,3,2,6,8,4,7,1] => [3,2,6,4,7,8,1,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,4,8},{2},{3,5,6},{7}} => [4,2,5,8,6,3,7,1] => [2,6,3,5,7,8,1,4] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,4},{2},{3,6,8},{5,7}} => [4,2,6,1,7,8,5,3] => [2,4,1,7,5,8,3,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,4,6},{2},{3},{5,7,8}} => [4,2,3,6,7,1,8,5] => [2,3,6,1,4,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,5,6},{3,7},{4,8}} => [1,5,7,8,6,2,3,4] => [1,6,2,5,7,3,8,4] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1},{2,5,6},{3},{4,7,8}} => [1,5,3,7,6,2,8,4] => [1,3,6,2,5,8,4,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,5},{3,7},{4,6,8}} => [1,5,7,6,2,8,3,4] => [1,5,2,7,3,8,4,6] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2},{3,6,7},{4,5,8}} => [1,2,6,5,8,7,3,4] => [1,2,7,3,6,8,4,5] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,3,6,7},{4},{5,8}} => [1,3,6,4,8,7,2,5] => [1,4,7,2,3,6,8,5] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,3,6},{4,8},{5,7}} => [1,3,6,8,7,2,5,4] => [1,6,2,3,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2},{3,4,6,8},{5,7}} => [1,2,4,6,7,8,5,3] => [1,2,7,5,8,3,4,6] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,6},{4,5,7,8}} => [1,2,6,5,7,3,8,4] => [1,2,6,3,8,4,5,7] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2,5},{3},{4,6,7,8}} => [1,5,3,6,2,7,8,4] => [1,3,5,2,8,4,6,7] => [[1,2,3,5,8],[4,6,7]] => 2
{{1},{2,5},{3,6},{4,7,8}} => [1,5,6,7,2,3,8,4] => [1,5,2,6,3,8,4,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2},{3,5},{4,6,7,8}} => [1,2,5,6,3,7,8,4] => [1,2,5,3,8,4,6,7] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2,4,7},{3,6},{5,8}} => [1,4,6,7,8,3,2,5] => [1,6,3,7,2,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,3},{2,4,7,8},{5},{6}} => [3,4,1,7,5,6,8,2] => [3,1,5,6,8,2,4,7] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,7},{2,3,4,8},{5},{6}} => [7,3,4,8,5,6,1,2] => [5,6,7,1,8,2,3,4] => [[1,2,3,5],[4,6,7,8]] => 2
{{1},{2,4,7},{3},{5,6,8}} => [1,4,3,7,6,8,2,5] => [1,3,7,2,4,8,5,6] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,7},{2},{3,4,5},{6,8}} => [7,2,4,5,3,8,1,6] => [2,5,3,4,7,1,8,6] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1},{2,3,7},{4,8},{5,6}} => [1,3,7,8,6,5,2,4] => [1,6,5,7,2,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1},{2},{3,7},{4,5,6,8}} => [1,2,7,5,6,8,3,4] => [1,2,7,3,8,4,5,6] => [[1,2,3,5,7,8],[4,6]] => 2
{{1},{2},{3,5,7},{4,6,8}} => [1,2,5,6,7,8,3,4] => [1,2,7,3,5,8,4,6] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1,5},{2},{3},{4,6,7,8}} => [5,2,3,6,1,7,8,4] => [2,3,5,1,8,4,6,7] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,2,6},{3},{4,7,8},{5}} => [2,6,3,7,5,1,8,4] => [3,5,6,1,2,8,4,7] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,6},{2},{3,4,7},{5,8}} => [6,2,4,7,8,1,3,5] => [2,6,1,7,3,4,8,5] => [[1,2,4,7],[3,5,6,8]] => 3
{{1},{2,6},{3,7},{4,5,8}} => [1,6,7,5,8,2,3,4] => [1,6,2,7,3,8,4,5] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,3,6},{2,5},{4},{7,8}} => [3,5,6,4,2,1,8,7] => [4,5,2,6,1,3,8,7] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,5},{2,4,6},{3},{7,8}} => [5,4,3,6,1,2,8,7] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,4,5},{2,6},{3},{7,8}} => [4,6,3,5,1,2,8,7] => [3,5,1,4,6,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,5,8},{2,7},{3,4},{6}} => [5,7,4,3,8,6,2,1] => [4,3,6,7,2,8,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,4,5},{2,8},{3},{6,7}} => [4,8,3,5,1,7,6,2] => [3,5,1,4,7,6,8,2] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,6,7},{2,8},{3,5},{4}} => [6,8,5,4,3,7,1,2] => [4,5,3,7,1,6,8,2] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,6},{2,5,8},{3},{4,7}} => [6,5,3,7,8,1,4,2] => [3,6,1,7,4,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6},{2,4,5,8},{3},{7}} => [6,4,3,5,8,1,7,2] => [3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,5},{2,7},{3},{4,6,8}} => [5,7,3,6,1,8,2,4] => [3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,5,8},{2,3},{4,7},{6}} => [5,3,2,7,8,6,4,1] => [3,2,6,7,4,8,1,5] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,7},{2,3},{4,6,8},{5}} => [7,3,2,6,5,8,1,4] => [3,2,5,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,6,7},{2,3},{4,8},{5}} => [6,3,2,8,5,7,1,4] => [3,2,5,7,1,6,8,4] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,8},{2,5,6},{3,7},{4}} => [8,5,7,4,6,2,3,1] => [4,6,2,5,7,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 3
{{1,3,8},{2,6},{4},{5,7}} => [3,6,8,4,7,2,5,1] => [4,6,2,7,5,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,6,7},{2,5},{3,8},{4}} => [6,5,8,4,2,7,1,3] => [4,5,2,7,1,6,8,3] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,5},{2,6,7},{3},{4,8}} => [5,6,3,8,1,7,2,4] => [3,5,1,7,2,6,8,4] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,3,8},{2,7},{4,5},{6}} => [3,7,8,5,4,6,2,1] => [5,4,6,7,2,8,1,3] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,6,8},{2,5},{3},{4,7}} => [6,5,3,7,2,8,4,1] => [3,5,2,7,4,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,6,8},{3},{4,7}} => [5,6,3,7,1,8,4,2] => [3,5,1,7,4,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5,7},{2,6},{3},{4,8}} => [5,6,3,8,7,2,1,4] => [3,6,2,7,1,5,8,4] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,6},{2,5,7},{3},{4,8}} => [6,5,3,8,7,1,2,4] => [3,6,1,7,2,5,8,4] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,5,6},{2},{3,7},{4,8}} => [5,2,7,8,6,1,3,4] => [2,6,1,5,7,3,8,4] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1,5,8},{2,6},{3},{4,7}} => [5,6,3,7,8,2,4,1] => [3,6,2,7,4,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,6,7},{2,5},{3},{4,8}} => [6,5,3,8,2,7,1,4] => [3,5,2,7,1,6,8,4] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,5,8},{2,7},{3},{4,6}} => [5,7,3,6,8,4,2,1] => [3,6,4,7,2,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,6},{2,5,8},{3,7},{4}} => [6,5,7,4,8,1,3,2] => [4,6,1,7,3,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,7,8},{3,6},{4}} => [5,7,6,4,1,3,8,2] => [4,5,1,6,3,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,7},{3,6,8},{4}} => [5,7,6,4,1,8,2,3] => [4,5,1,7,2,8,3,6] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,7},{2,5},{3},{4,6,8}} => [7,5,3,6,2,8,1,4] => [3,5,2,7,1,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,6,8},{2,5},{3,7},{4}} => [6,5,7,4,2,8,3,1] => [4,5,2,7,3,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,6,8},{3,7},{4}} => [5,6,7,4,1,8,3,2] => [4,5,1,7,3,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,5},{2,8},{3},{4,6,7}} => [5,8,3,6,1,7,4,2] => [3,5,1,7,4,6,8,2] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,6},{2,7,8},{3,5},{4}} => [6,7,5,4,3,1,8,2] => [4,5,3,6,1,8,2,7] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,3,8},{2,4,6},{5},{7}} => [3,4,8,6,5,2,7,1] => [5,6,2,4,7,8,1,3] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,7},{2,8},{3,4,5},{6}} => [7,8,4,5,3,6,1,2] => [5,3,4,6,7,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,2,7},{3,8},{4,5},{6}} => [2,7,8,5,4,6,1,3] => [5,4,6,7,1,2,8,3] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,3,5},{2},{4,6},{7,8}} => [3,2,5,6,1,4,8,7] => [2,5,1,3,6,4,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3,6},{2},{4,7,8},{5}} => [3,2,6,7,5,1,8,4] => [2,5,6,1,3,8,4,7] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,4,8},{2},{3,6,7},{5}} => [4,2,6,8,5,7,3,1] => [2,5,7,3,6,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,5,6},{2},{3,4,8},{7}} => [5,2,4,8,6,1,7,3] => [2,6,1,5,7,8,3,4] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,6},{2},{3,5,7,8},{4}} => [6,2,5,4,7,1,8,3] => [2,4,6,1,8,3,5,7] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,6,7},{2},{3,5,8},{4}} => [6,2,5,4,8,7,1,3] => [2,4,7,1,6,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4},{2,6,8},{3},{5,7}} => [4,6,3,1,7,8,5,2] => [3,4,1,7,5,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,8},{2,4,6},{3},{5,7}} => [8,4,3,6,7,2,5,1] => [3,6,2,4,7,5,8,1] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,7},{2},{3,6,8},{4,5}} => [7,2,6,5,4,8,1,3] => [2,5,4,7,1,8,3,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,4},{2},{3,5,7},{6,8}} => [4,2,5,1,7,8,3,6] => [2,4,1,7,3,5,8,6] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,2},{3,5,7},{4},{6,8}} => [2,1,5,4,7,8,3,6] => [2,1,4,7,3,5,8,6] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,5,8},{2},{3,4,7},{6}} => [5,2,4,7,8,6,3,1] => [2,6,7,3,4,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2},{3,4,7},{5},{6,8}} => [2,1,4,7,5,8,3,6] => [2,1,5,7,3,4,8,6] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,2,5},{3},{4,7},{6,8}} => [2,5,3,7,1,8,4,6] => [3,5,1,2,7,4,8,6] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,2,5,8},{3},{4,7},{6}} => [2,5,3,7,8,6,4,1] => [3,6,7,4,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2},{3,4,7},{5,8},{6}} => [2,1,4,7,8,6,3,5] => [2,1,6,7,3,4,8,5] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,2},{3,5},{4,6,8},{7}} => [2,1,5,6,3,8,7,4] => [2,1,5,3,7,8,4,6] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,2,6},{3},{4,7},{5,8}} => [2,6,3,7,8,1,4,5] => [3,6,1,2,7,4,8,5] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3,7},{2,6},{4},{5,8}} => [3,6,7,4,8,2,1,5] => [4,6,2,7,1,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,2,5},{3},{4,6,8},{7}} => [2,5,3,6,1,8,7,4] => [3,5,1,2,7,8,4,6] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2,5},{3},{4,6},{7,8}} => [2,5,3,6,1,4,8,7] => [3,5,1,2,6,4,8,7] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,2,4,7},{3},{5,8},{6}} => [2,4,3,7,8,6,1,5] => [3,6,7,1,2,4,8,5] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,2,4,7},{3},{5},{6,8}} => [2,4,3,7,5,8,1,6] => [3,5,7,1,2,4,8,6] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,2,4},{3},{5,7},{6,8}} => [2,4,3,1,7,8,5,6] => [3,4,1,2,7,5,8,6] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3},{2,4},{5,6,8},{7}} => [3,4,1,2,6,8,7,5] => [3,1,4,2,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,3},{2,4,7},{5},{6,8}} => [3,4,1,7,5,8,2,6] => [3,1,5,7,2,4,8,6] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,3},{2,4,6},{5},{7,8}} => [3,4,1,6,5,2,8,7] => [3,1,5,6,2,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,6},{2,3,4,8},{5},{7}} => [6,3,4,8,5,1,7,2] => [5,6,1,7,8,2,3,4] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,4,6},{2,8},{3,5},{7}} => [4,8,5,6,3,1,7,2] => [5,3,6,1,4,7,8,2] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,2,5,7},{3},{4},{6,8}} => [2,5,3,4,7,8,1,6] => [3,4,7,1,2,5,8,6] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,2,5,8},{3},{4,6},{7}} => [2,5,3,6,8,4,7,1] => [3,6,4,7,8,1,2,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,3,6},{2,8},{4,5},{7}} => [3,8,6,5,4,1,7,2] => [5,4,6,1,3,7,8,2] => [[1,3,6,7],[2,5],[4],[8]] => 3
{{1,2},{3,5,8},{4,6},{7}} => [2,1,5,6,8,4,7,3] => [2,1,6,4,7,8,3,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,3},{2,5,7},{4},{6,8}} => [3,5,1,4,7,8,2,6] => [3,1,4,7,2,5,8,6] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,2,7},{3,5},{4},{6,8}} => [2,7,5,4,3,8,1,6] => [4,5,3,7,1,2,8,6] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1},{2,3,4,7},{5},{6,8}} => [1,3,4,7,5,8,2,6] => [1,5,7,2,3,4,8,6] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,3},{2,4,6},{5,8},{7}} => [3,4,1,6,8,2,7,5] => [3,1,6,2,4,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 3
{{1},{2,3,4},{5,7},{6,8}} => [1,3,4,2,7,8,5,6] => [1,4,2,3,7,5,8,6] => [[1,2,4,5,7],[3,6,8]] => 3
{{1},{2,4,5},{3,7},{6,8}} => [1,4,7,5,2,8,3,6] => [1,5,2,4,7,3,8,6] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1},{2,3,5},{4,7},{6,8}} => [1,3,5,7,2,8,4,6] => [1,5,2,3,7,4,8,6] => [[1,2,4,5,7],[3,6,8]] => 3
{{1},{2,3,5},{4,6},{7,8}} => [1,3,5,6,2,4,8,7] => [1,5,2,3,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => 3
{{1,4,6,7},{2,3,5,8}} => [4,3,5,6,8,7,1,2] => [7,1,4,6,8,2,3,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,6},{2,4},{3,7,8},{5}} => [6,4,7,2,5,1,8,3] => [4,2,5,6,1,8,3,7] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,6},{2,4},{3,7},{5},{8}} => [6,4,7,2,5,1,3,8] => [4,2,5,6,1,7,3,8] => [[1,3,4,6,8],[2,7],[5]] => 3
{{1,5,6},{2,3,4,7,8}} => [5,3,4,7,6,1,8,2] => [6,1,5,8,2,3,4,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,5,6,7},{2,3,4,8}} => [5,3,4,8,6,7,1,2] => [7,1,5,6,8,2,3,4] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,7},{2,8},{3,4},{5},{6}} => [7,8,4,3,5,6,1,2] => [4,3,5,6,7,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,5,6,7},{2,4,8},{3}} => [5,4,3,8,6,7,1,2] => [3,7,1,5,6,8,2,4] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,5,7},{2,4,6,8},{3}} => [5,4,3,6,7,8,1,2] => [3,7,1,5,8,2,4,6] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,5},{2,3},{4,6,7},{8}} => [5,3,2,6,1,7,4,8] => [3,2,5,1,7,4,6,8] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,5},{2,3},{4,6,7,8}} => [5,3,2,6,1,7,8,4] => [3,2,5,1,8,4,6,7] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,5},{2,3},{4,6,8},{7}} => [5,3,2,6,1,8,7,4] => [3,2,5,1,7,8,4,6] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,6},{2,4},{3,8},{5},{7}} => [6,4,8,2,5,1,7,3] => [4,2,5,6,1,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 3
{{1,5},{2,3},{4,6},{7},{8}} => [5,3,2,6,1,4,7,8] => [3,2,5,1,6,4,7,8] => [[1,3,5,7,8],[2,6],[4]] => 3
{{1,5},{2,3},{4,7,8},{6}} => [5,3,2,7,1,6,8,4] => [3,2,5,1,6,8,4,7] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,5},{2,3},{4,8},{6},{7}} => [5,3,2,8,1,6,7,4] => [3,2,5,1,6,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 3
{{1,5},{2,3},{4,7},{6},{8}} => [5,3,2,7,1,6,4,8] => [3,2,5,1,6,7,4,8] => [[1,3,5,6,8],[2,7],[4]] => 3
{{1,6},{2,4},{3,5,7,8}} => [6,4,5,2,7,1,8,3] => [4,2,6,1,8,3,5,7] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,6},{2,5},{3,4,7,8}} => [6,5,4,7,2,1,8,3] => [5,2,6,1,8,3,4,7] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,5,6,8},{2,3,4,7}} => [5,3,4,7,6,8,2,1] => [7,2,3,4,8,1,5,6] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,3,6},{2},{4,7},{5},{8}} => [3,2,6,7,5,1,4,8] => [2,5,6,1,3,7,4,8] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,7},{3,4,5,8},{6}} => [1,7,4,5,8,6,2,3] => [1,6,7,2,8,3,4,5] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,6},{2,3,4,7},{5},{8}} => [6,3,4,7,5,1,2,8] => [5,6,1,7,2,3,4,8] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,4,8},{2,6,7},{3},{5}} => [4,6,3,8,5,7,2,1] => [3,5,7,2,6,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,7},{2,4},{3,5,8},{6}} => [7,4,5,2,8,6,1,3] => [4,2,6,7,1,8,3,5] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,5,8},{2,3,7},{4},{6}} => [5,3,7,4,8,6,2,1] => [4,6,7,2,3,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,5,8},{3,7},{4},{6}} => [1,5,7,4,8,6,3,2] => [1,4,6,7,3,8,2,5] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1},{2,7},{3,5,8},{4,6}} => [1,7,5,6,8,4,2,3] => [1,6,4,7,2,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,7},{2,5},{3,4,6},{8}} => [7,5,4,6,2,3,1,8] => [5,2,6,3,4,7,1,8] => [[1,3,5,6,8],[2,4],[7]] => 3
{{1},{2,8},{3,6},{4,5,7}} => [1,8,6,5,7,3,4,2] => [1,6,3,7,4,5,8,2] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1,4},{2,5,7},{3},{6},{8}} => [4,5,3,1,7,6,2,8] => [3,4,1,6,7,2,5,8] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,5},{2,3,6,8},{4},{7}} => [5,3,6,4,1,8,7,2] => [4,5,1,7,8,2,3,6] => [[1,2,4,5],[3,6,7,8]] => 2
{{1},{2,5},{3,6,8},{4},{7}} => [1,5,6,4,2,8,7,3] => [1,4,5,2,7,8,3,6] => [[1,2,3,5,6],[4,7,8]] => 2
{{1},{2,5,6,7},{3,8},{4}} => [1,5,8,4,6,7,2,3] => [1,4,7,2,5,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1,5,6},{2,3,7},{4},{8}} => [5,3,7,4,6,1,2,8] => [4,6,1,5,7,2,3,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1},{2,6},{3,7},{4},{5},{8}} => [1,6,7,4,5,2,3,8] => [1,4,5,6,2,7,3,8] => [[1,2,3,4,6,8],[5,7]] => 2
{{1},{2,5,6},{3,4,7},{8}} => [1,5,4,7,6,2,3,8] => [1,6,2,5,7,3,4,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,6,7},{2,3,8},{4},{5}} => [6,3,8,4,5,7,1,2] => [4,5,7,1,6,8,2,3] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,4,6},{3,5,7},{8}} => [1,4,5,6,7,2,3,8] => [1,6,2,4,7,3,5,8] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => [1,5,2,3,7,4,6,8] => [[1,2,4,5,7,8],[3,6]] => 2
{{1,4,6},{2},{3,5,8},{7}} => [4,2,5,6,8,1,7,3] => [2,6,1,4,7,8,3,5] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,6},{2},{3,8},{4},{5},{7}} => [6,2,8,4,5,1,7,3] => [2,4,5,6,1,7,8,3] => [[1,2,3,4,6,7],[5,8]] => 2
{{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => [1,2,5,3,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
{{1,5},{2},{3},{4,8},{6},{7}} => [5,2,3,8,1,6,7,4] => [2,3,5,1,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2,5},{3},{4,7},{6},{8}} => [1,5,3,7,2,6,4,8] => [1,3,5,2,6,7,4,8] => [[1,2,3,5,6,8],[4,7]] => 2
{{1,7},{2},{3,4},{5,6,8}} => [7,2,4,3,6,8,1,5] => [2,4,3,7,1,8,5,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,2,7},{3},{4,5,8},{6}} => [2,7,3,5,8,6,1,4] => [3,6,7,1,2,8,4,5] => [[1,2,3,6],[4,5,7,8]] => 2
{{1,6,7},{2},{3,4},{5,8}} => [6,2,4,3,8,7,1,5] => [2,4,3,7,1,6,8,5] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1},{2,4,8},{3,7},{5,6}} => [1,4,7,8,6,5,3,2] => [1,6,5,7,3,8,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1,3,8},{2,7},{4},{5,6}} => [3,7,8,4,6,5,2,1] => [4,6,5,7,2,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 3
{{1},{2,4},{3,7,8},{5,6}} => [1,4,7,2,6,5,8,3] => [1,4,2,6,5,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,6,8},{3,4},{5,7}} => [1,6,4,3,7,8,5,2] => [1,4,3,7,5,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,3,6,8},{2},{4,7},{5}} => [3,2,6,7,5,8,4,1] => [2,5,7,4,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,7},{2,6},{3},{5,8}} => [4,6,3,7,8,2,1,5] => [3,6,2,7,1,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,6,8},{2,4,7},{3},{5}} => [6,4,3,7,5,8,2,1] => [3,5,7,2,4,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4,5,7},{2},{3},{6,8}} => [4,2,3,5,7,8,1,6] => [2,3,7,1,4,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,3,4},{2},{5,7},{6,8}} => [3,2,4,1,7,8,5,6] => [2,4,1,3,7,5,8,6] => [[1,2,5,7],[3,4,6,8]] => 3
{{1,3},{2,4},{5,7,8},{6}} => [3,4,1,2,7,6,8,5] => [3,1,4,2,6,8,5,7] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,4},{2,5,6},{3},{7,8}} => [4,5,3,1,6,2,8,7] => [3,4,1,6,2,5,8,7] => [[1,2,4,7],[3,5,6,8]] => 3
{{1,5},{2},{3,6,7,8},{4}} => [5,2,6,4,1,7,8,3] => [2,4,5,1,8,3,6,7] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,5},{2,4,6},{3,8},{7}} => [5,4,8,6,1,2,7,3] => [5,1,6,2,4,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 3
{{1,4,5},{2},{3,7},{6,8}} => [4,2,7,5,1,8,3,6] => [2,5,1,4,7,3,8,6] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1},{2,6},{3,4,8},{5,7}} => [1,6,4,8,7,2,5,3] => [1,6,2,7,5,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,3},{4,6,8},{5,7}} => [1,3,2,6,7,8,5,4] => [1,3,2,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,3,5,7},{4,8},{6}} => [1,3,5,8,7,6,2,4] => [1,6,7,2,3,5,8,4] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1},{2,3,7},{4,6},{5,8}} => [1,3,7,6,8,4,2,5] => [1,6,4,7,2,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1},{2,3,6},{4,7},{5,8}} => [1,3,6,7,8,2,4,5] => [1,6,2,3,7,4,8,5] => [[1,2,4,5,7],[3,6,8]] => 3
{{1,3},{2,5,7,8},{4,6}} => [3,5,1,6,7,4,8,2] => [3,1,6,4,8,2,5,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4,5,7},{2},{3,6},{8}} => [4,2,6,5,7,3,1,8] => [2,6,3,7,1,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,4},{2},{3,5,6,8},{7}} => [4,2,5,1,6,8,7,3] => [2,4,1,7,8,3,5,6] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,3,8},{2,5,7},{4},{6}} => [3,5,8,4,7,6,2,1] => [4,6,7,2,5,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1,5,8},{2,4,7},{3},{6}} => [5,4,3,7,8,6,2,1] => [3,6,7,2,4,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,7},{2},{3,4,6,8},{5}} => [7,2,4,6,5,8,1,3] => [2,5,7,1,8,3,4,6] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,7},{2,4},{3,5,6,8}} => [7,4,5,2,6,8,1,3] => [4,2,7,1,8,3,5,6] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,4},{2,7},{3,5,6,8}} => [4,7,5,1,6,8,2,3] => [4,1,7,2,8,3,5,6] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,6,8},{2,4},{3,5,7}} => [6,4,5,2,7,8,3,1] => [4,2,7,3,5,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,3,8},{2,5,7},{4,6}} => [3,5,8,6,7,4,2,1] => [6,4,7,2,5,8,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 3
{{1},{2,4,8},{3,5,6},{7}} => [1,4,5,8,6,3,7,2] => [1,6,3,5,7,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,6},{2,4,5},{3,7},{8}} => [6,4,7,5,2,1,3,8] => [5,2,4,6,1,7,3,8] => [[1,3,4,6,8],[2,7],[5]] => 3
{{1},{2,7},{3,5,6},{4,8}} => [1,7,5,8,6,3,2,4] => [1,6,3,5,7,2,8,4] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1,4,7},{2,5,6},{3},{8}} => [4,5,3,7,6,2,1,8] => [3,6,2,5,7,1,4,8] => [[1,2,5,8],[3,4],[6,7]] => 2
{{1,4},{2,3,8},{5,6},{7}} => [4,3,8,1,6,5,7,2] => [4,1,6,5,7,8,2,3] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,2,6},{3,8},{4},{5,7}} => [2,6,8,4,7,1,5,3] => [4,6,1,2,7,5,8,3] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1},{2,6},{3,8},{4},{5,7}} => [1,6,8,4,7,2,5,3] => [1,4,6,2,7,5,8,3] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1},{2,5,6,7},{3,4,8}} => [1,5,4,8,6,7,2,3] => [1,7,2,5,6,8,3,4] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,7},{2,8},{3},{4},{5,6}} => [7,8,3,4,6,5,1,2] => [3,4,6,5,7,1,8,2] => [[1,2,3,5,7],[4,8],[6]] => 3
{{1,5,6,7},{2,3,8},{4}} => [5,3,8,4,6,7,1,2] => [4,7,1,5,6,8,2,3] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,5,7},{2,3,4,8},{6}} => [5,3,4,8,7,6,1,2] => [6,7,1,5,8,2,3,4] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1},{2,3,5},{4,8},{6,7}} => [1,3,5,8,2,7,6,4] => [1,5,2,3,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1,2,3,5},{4,8},{6,7}} => [2,3,5,8,1,7,6,4] => [5,1,2,3,7,6,8,4] => [[1,3,4,5,7],[2,6],[8]] => 3
{{1,3,5},{2},{4,8},{6,7}} => [3,2,5,8,1,7,6,4] => [2,5,1,3,7,6,8,4] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,6},{2},{3,8},{4},{5,7}} => [6,2,8,4,7,1,5,3] => [2,4,6,1,7,5,8,3] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1},{2},{3,5},{4,8},{6,7}} => [1,2,5,8,3,7,6,4] => [1,2,5,3,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1,2,5},{3},{4,8},{6,7}} => [2,5,3,8,1,7,6,4] => [3,5,1,2,7,6,8,4] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,5},{2},{3},{4,8},{6,7}} => [5,2,3,8,1,7,6,4] => [2,3,5,1,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1},{2,5},{3},{4,8},{6,7}} => [1,5,3,8,2,7,6,4] => [1,3,5,2,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1,3,4,8},{2,5,6,7}} => [3,5,4,8,6,7,2,1] => [7,2,5,6,8,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1},{2,7},{3,8},{4,5,6}} => [1,7,8,5,6,4,2,3] => [1,6,4,5,7,2,8,3] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1,4,6},{2,7},{3},{5,8}} => [4,7,3,6,8,1,2,5] => [3,6,1,4,7,2,8,5] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1},{2,5},{3,8},{4,6,7}} => [1,5,8,6,2,7,4,3] => [1,5,2,7,4,6,8,3] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,3,7},{4,8},{5},{6}} => [1,3,7,8,5,6,2,4] => [1,5,6,7,2,3,8,4] => [[1,2,3,4,7],[5,6,8]] => 2
{{1,4,7},{2,3},{5},{6,8}} => [4,3,2,7,5,8,1,6] => [3,2,5,7,1,4,8,6] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1},{2,4},{3,7,8},{5},{6}} => [1,4,7,2,5,6,8,3] => [1,4,2,5,6,8,3,7] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,5,7},{3,4,8},{6}} => [1,5,4,8,7,6,2,3] => [1,6,7,2,5,8,3,4] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,4},{3,5},{6,7},{8}} => [1,4,5,2,3,7,6,8] => [1,4,2,5,3,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,4,8},{3,5},{6},{7}} => [1,4,5,8,3,6,7,2] => [1,5,3,6,7,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,5},{3,6},{4},{7,8}} => [1,5,6,4,2,3,8,7] => [1,4,5,2,6,3,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
{{1},{2,5,7},{3,8},{4,6}} => [1,5,8,6,7,4,2,3] => [1,6,4,7,2,5,8,3] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,8},{2,4},{3,5,7},{6}} => [8,4,5,2,7,6,3,1] => [4,2,6,7,3,5,8,1] => [[1,3,4,7],[2,5,6],[8]] => 3
{{1,6,7},{2,4},{3,5},{8}} => [6,4,5,2,3,7,1,8] => [4,2,5,3,7,1,6,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1},{2,5},{3,6},{4,7},{8}} => [1,5,6,7,2,3,4,8] => [1,5,2,6,3,7,4,8] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,3,6,7},{4,8},{5}} => [1,3,6,8,5,7,2,4] => [1,5,7,2,3,6,8,4] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1,3,5,8},{2},{4,7},{6}} => [3,2,5,7,8,6,4,1] => [2,6,7,4,8,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,5,6},{2},{3,7,8},{4}} => [5,2,7,4,6,1,8,3] => [2,4,6,1,5,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4,7},{2},{3,5,8},{6}} => [4,2,5,7,8,6,1,3] => [2,6,7,1,4,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,4},{2,6,8},{3,7},{5}} => [4,6,7,1,5,8,3,2] => [4,1,5,7,3,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,5},{2,3,7,8},{4},{6}} => [5,3,7,4,1,6,8,2] => [4,5,1,6,8,2,3,7] => [[1,2,4,5],[3,6,7,8]] => 2
{{1},{2,5,6,8},{3},{4,7}} => [1,5,3,7,6,8,4,2] => [1,3,7,4,8,2,5,6] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,5,6,8},{4,7}} => [1,2,5,7,6,8,4,3] => [1,2,7,4,8,3,5,6] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2},{3,6,8},{4,5,7}} => [1,2,6,5,7,8,4,3] => [1,2,7,4,5,8,3,6] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,3},{4,7},{5,6,8}} => [1,3,2,7,6,8,4,5] => [1,3,2,7,4,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,4,6,8},{2},{3},{5,7}} => [4,2,3,6,7,8,5,1] => [2,3,7,5,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,3},{2},{4,6},{5,7,8}} => [3,2,1,6,7,4,8,5] => [2,3,1,6,4,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1},{2,5},{3,7,8},{4,6}} => [1,5,7,6,2,4,8,3] => [1,5,2,6,4,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,3},{2,4,5},{6,7},{8}} => [3,4,1,5,2,7,6,8] => [3,1,5,2,4,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,4},{2,3,7,8},{5},{6}} => [4,3,7,1,5,6,8,2] => [4,1,5,6,8,2,3,7] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,4,6},{2,3,7},{5},{8}} => [4,3,7,6,5,1,2,8] => [5,6,1,4,7,2,3,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,6},{2,5,8},{3,4,7}} => [6,5,4,7,8,1,3,2] => [6,1,7,3,4,8,2,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,3,6,7},{2,4,5,8}} => [3,4,6,5,8,7,1,2] => [7,1,3,6,8,2,4,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1},{2,8},{3,5,6},{4,7}} => [1,8,5,7,6,3,4,2] => [1,6,3,5,7,4,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 3
{{1,5},{2,7},{3,4,6,8}} => [5,7,4,6,1,8,2,3] => [5,1,7,2,8,3,4,6] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,7},{2},{3,8},{4,5,6}} => [7,2,8,5,6,4,1,3] => [2,6,4,5,7,1,8,3] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1,7},{2,4,5},{3,6,8}} => [7,4,6,5,2,8,1,3] => [5,2,4,7,1,8,3,6] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1},{2,4,5},{3,7,8},{6}} => [1,4,7,5,2,6,8,3] => [1,5,2,4,6,8,3,7] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,6},{3,8},{4,5,7}} => [1,6,8,5,7,2,4,3] => [1,6,2,7,4,5,8,3] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,4,6,7},{3,8},{5}} => [1,4,8,6,5,7,2,3] => [1,5,7,2,4,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1,5},{2,7,8},{3,4},{6}} => [5,7,4,3,1,6,8,2] => [4,3,5,1,6,8,2,7] => [[1,3,5,6],[2,7,8],[4]] => 3
{{1,3,5},{2},{4,7,8},{6}} => [3,2,5,7,1,6,8,4] => [2,5,1,3,6,8,4,7] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,3},{2,5},{4,7,8},{6}} => [3,5,1,7,2,6,8,4] => [3,1,5,2,6,8,4,7] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,7},{2,6},{3},{4,5,8}} => [7,6,3,5,8,2,1,4] => [3,6,2,7,1,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,4,5},{2,8},{3,7},{6}} => [4,8,7,5,1,6,3,2] => [5,1,4,6,7,3,8,2] => [[1,3,4,5,7],[2],[6],[8]] => 3
{{1,3,6},{2},{4,5,8},{7}} => [3,2,6,5,8,1,7,4] => [2,6,1,3,7,8,4,5] => [[1,2,5,6],[3,4,7,8]] => 2
{{1,2},{3,5},{4,7,8},{6}} => [2,1,5,7,3,6,8,4] => [2,1,5,3,6,8,4,7] => [[1,3,5,6],[2,4,7,8]] => 3
{{1},{2,3,4,7},{5,8},{6}} => [1,3,4,7,8,6,2,5] => [1,6,7,2,3,4,8,5] => [[1,2,3,6,7],[4,5,8]] => 2
{{1,4,8},{2,5,7},{3},{6}} => [4,5,3,8,7,6,2,1] => [3,6,7,2,5,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1},{2,3,4,6},{5,8},{7}} => [1,3,4,6,8,2,7,5] => [1,6,2,3,4,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 2
{{1},{2,4,5,8},{3,6},{7}} => [1,4,6,5,8,3,7,2] => [1,6,3,7,8,2,4,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,6},{2},{3,4,5,8},{7}} => [6,2,4,5,8,1,7,3] => [2,6,1,7,8,3,4,5] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,3},{2,5},{4},{6,8},{7}} => [3,5,1,4,2,8,7,6] => [3,1,4,5,2,7,8,6] => [[1,3,4,6,7],[2,5,8]] => 3
{{1},{2,6},{3,5},{4,8},{7}} => [1,6,5,8,3,2,7,4] => [1,5,3,6,2,7,8,4] => [[1,2,4,6,7],[3,8],[5]] => 3
{{1,5},{2,4,6,7},{3},{8}} => [5,4,3,6,1,7,2,8] => [3,5,1,7,2,4,6,8] => [[1,2,4,7,8],[3,5,6]] => 2
{{1},{2,6},{3,5,7,8},{4}} => [1,6,5,4,7,2,8,3] => [1,4,6,2,8,3,5,7] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,3},{2,6,7,8},{4},{5}} => [3,6,1,4,5,7,8,2] => [3,1,4,5,8,2,6,7] => [[1,3,4,5,8],[2,6,7]] => 2
{{1},{2,4},{3,6,7,8},{5}} => [1,4,6,2,5,7,8,3] => [1,4,2,5,8,3,6,7] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,4,7},{3,6,8},{5}} => [1,4,6,7,5,8,2,3] => [1,5,7,2,4,8,3,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,5,8},{3,4,6},{7}} => [1,5,4,6,8,3,7,2] => [1,6,3,4,7,8,2,5] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,3,6},{4,5,7},{8}} => [1,3,6,5,7,2,4,8] => [1,6,2,3,7,4,5,8] => [[1,2,4,5,7,8],[3,6]] => 2
{{1,6},{2,3},{4,5,7},{8}} => [6,3,2,5,7,1,4,8] => [3,2,6,1,7,4,5,8] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,4},{2,3,5},{6,7},{8}} => [4,3,5,1,2,7,6,8] => [4,1,5,2,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,6},{2,5,7},{3,4},{8}} => [6,5,4,3,7,1,2,8] => [4,3,6,1,7,2,5,8] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,4},{2,3,5},{6,8},{7}} => [4,3,5,1,2,8,7,6] => [4,1,5,2,3,7,8,6] => [[1,3,5,6,7],[2,4,8]] => 3
{{1},{2,3,6},{4,5,8},{7}} => [1,3,6,5,8,2,7,4] => [1,6,2,3,7,8,4,5] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,3,7},{4,6,8},{5}} => [1,3,7,6,5,8,2,4] => [1,5,7,2,3,8,4,6] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,3,7},{4,5,8},{6}} => [1,3,7,5,8,6,2,4] => [1,6,7,2,3,8,4,5] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,4,8},{2},{3,5},{6,7}} => [4,2,5,8,3,7,6,1] => [2,5,3,7,6,8,1,4] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1,6,8},{2},{3,5},{4,7}} => [6,2,5,7,3,8,4,1] => [2,5,3,7,4,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1,4},{2,3,5,8},{6},{7}} => [4,3,5,1,8,6,7,2] => [4,1,6,7,8,2,3,5] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,2,6,8},{3},{4},{5,7}} => [2,6,3,4,7,8,5,1] => [3,4,7,5,8,1,2,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,3},{2},{4},{5},{6},{7},{8},{9}} => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 1
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3},{4},{5},{6},{7},{8},{9}} => [2,3,1,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
{{1,8,9},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,9,1] => [2,3,4,5,6,7,9,1,8] => [[1,2,3,4,5,6,7],[8,9]] => 1
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [9,2,3,4,5,6,7,8,1,10] => [2,3,4,5,6,7,8,9,1,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
{{1,5,8},{2},{3,4,6},{7}} => [5,2,4,6,8,3,7,1] => [2,6,3,4,7,8,1,5] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1,3},{2,4,8},{5},{6,7}} => [3,4,1,8,5,7,6,2] => [3,1,5,7,6,8,2,4] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,5},{2,6},{3,4,7},{8}} => [5,6,4,7,1,2,3,8] => [5,1,6,2,7,3,4,8] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,5},{2,3,6},{4,7},{8}} => [5,3,6,7,1,2,4,8] => [5,1,6,2,3,7,4,8] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,5},{2,3,4,6},{7},{8}} => [5,3,4,6,1,2,7,8] => [5,1,6,2,3,4,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,5,7},{2,3},{4,6},{8}} => [5,3,2,6,7,4,1,8] => [3,2,6,4,7,1,5,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4},{2,5,7},{3,6},{8}} => [4,5,6,1,7,3,2,8] => [4,1,6,3,7,2,5,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,2,4},{3,8},{5,6},{7}} => [2,4,8,1,6,5,7,3] => [4,1,2,6,5,7,8,3] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => [9,1,2,3,4,5,6,7,8] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => [7,1,2,3,4,5,6,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,2,3,4,5,6},{7},{8},{9}} => [2,3,4,5,6,1,7,8,9] => [6,1,2,3,4,5,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,2,3,4,5},{6},{7},{8},{9}} => [2,3,4,5,1,6,7,8,9] => [5,1,2,3,4,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,2,3,4},{5},{6},{7},{8},{9}} => [2,3,4,1,5,6,7,8,9] => [4,1,2,3,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
{{1,2},{3,4},{5,6},{7,8},{9}} => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
{{1,2},{3,4},{5,6},{7},{8},{9}} => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => [[1,3,5,7,8,9],[2,4,6]] => 3
{{1,2},{3,4},{5},{6},{7},{8},{9}} => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4]] => 2
{{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => [10,1,2,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4,5,6,7,8},{9},{10}} => [2,3,4,5,6,7,8,1,9,10] => [8,1,2,3,4,5,6,7,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4,5,6,7},{8},{9},{10}} => [2,3,4,5,6,7,1,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4,5,6},{7},{8},{9},{10}} => [2,3,4,5,6,1,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4,5},{6},{7},{8},{9},{10}} => [2,3,4,5,1,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [2,3,4,1,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [2,3,1,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
{{1,2},{3,4},{5,6},{7,8},{9},{10}} => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => [[1,3,5,7,9,10],[2,4,6,8]] => 4
{{1,2},{3,4},{5,6},{7},{8},{9},{10}} => [2,1,4,3,6,5,7,8,9,10] => [2,1,4,3,6,5,7,8,9,10] => [[1,3,5,7,8,9,10],[2,4,6]] => 3
{{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]] => 2
{{1,2,3},{4,7},{5},{6,8}} => [2,3,1,7,5,8,4,6] => [3,1,2,5,7,4,8,6] => [[1,3,4,5,7],[2,6,8]] => 3
{{1,2,5},{3},{4,6,7},{8}} => [2,5,3,6,1,7,4,8] => [3,5,1,2,7,4,6,8] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,2,5},{3,8},{4},{6,7}} => [2,5,8,4,1,7,6,3] => [4,5,1,2,7,6,8,3] => [[1,2,5,7],[3,4,6],[8]] => 3
{{1,4},{2,5,7,8},{3},{6}} => [4,5,3,1,7,6,8,2] => [3,4,1,6,8,2,5,7] => [[1,2,4,5],[3,6,7,8]] => 2
{{1,3},{2},{4,7},{5,6,8}} => [3,2,1,7,6,8,4,5] => [2,3,1,7,4,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,4},{2},{3,6,7,8},{5}} => [4,2,6,1,5,7,8,3] => [2,4,1,5,8,3,6,7] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,3,7},{4},{5,6,8}} => [1,3,7,4,6,8,2,5] => [1,4,7,2,3,8,5,6] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,3,6},{4},{5,7,8}} => [1,3,6,4,7,2,8,5] => [1,4,6,2,3,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1},{2,3},{4,6,7},{5,8}} => [1,3,2,6,8,7,4,5] => [1,3,2,7,4,6,8,5] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1},{2,3},{4,6},{5,7,8}} => [1,3,2,6,7,4,8,5] => [1,3,2,6,4,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,4},{2,6},{3,7,8},{5}} => [4,6,7,1,5,2,8,3] => [4,1,5,6,2,8,3,7] => [[1,3,4,6],[2,5,7,8]] => 3
{{1},{2,3,5,6},{4,8},{7}} => [1,3,5,8,6,2,7,4] => [1,6,2,3,5,7,8,4] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1},{2,3,5},{4,7,8},{6}} => [1,3,5,7,2,6,8,4] => [1,5,2,3,6,8,4,7] => [[1,2,4,5,6],[3,7,8]] => 2
{{1},{2,5},{3,4,7,8},{6}} => [1,5,4,7,2,6,8,3] => [1,5,2,6,8,3,4,7] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,4,7},{2},{3,6},{5,8}} => [4,2,6,7,8,3,1,5] => [2,6,3,7,1,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1},{2,4,8},{3,6,7},{5}} => [1,4,6,8,5,7,3,2] => [1,5,7,3,6,8,2,4] => [[1,2,3,6],[4,5],[7,8]] => 2
{{1},{2,3,6},{4,7,8},{5}} => [1,3,6,7,5,2,8,4] => [1,5,6,2,3,8,4,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,4,5,7},{2,3,6,8}} => [4,3,6,5,7,8,1,2] => [7,1,4,5,8,2,3,6] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,5},{2,3,7},{4,6,8}} => [5,3,7,6,1,8,2,4] => [5,1,7,2,3,8,4,6] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,5},{2,3,6,8},{4,7}} => [5,3,6,7,1,8,4,2] => [5,1,7,4,8,2,3,6] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1},{2,5},{3,4,7},{6,8}} => [1,5,4,7,2,8,3,6] => [1,5,2,7,3,4,8,6] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,5},{2,6,8},{3,4,7}} => [5,6,4,7,1,8,3,2] => [5,1,7,3,4,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6},{2,5,7},{3,4,8}} => [6,5,4,8,7,1,2,3] => [6,1,7,2,5,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1},{2,7},{3,6},{4,5,8}} => [1,7,6,5,8,3,2,4] => [1,6,3,7,2,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,7},{2,4,5,8},{3,6}} => [7,4,6,5,8,3,1,2] => [6,3,7,1,8,2,4,5] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,7},{2,5,8},{3,4,6}} => [7,5,4,6,8,3,1,2] => [6,3,4,7,1,8,2,5] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,6},{2,5},{3,4,7},{8}} => [6,5,4,7,2,1,3,8] => [5,2,6,1,7,3,4,8] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,6},{2,4,5,8},{3,7}} => [6,4,7,5,8,1,3,2] => [6,1,7,3,8,2,4,5] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1},{2,4,5,7},{3,6},{8}} => [1,4,6,5,7,3,2,8] => [1,6,3,7,2,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,4,5},{2,7},{3,6,8}} => [4,7,6,5,1,8,2,3] => [5,1,4,7,2,8,3,6] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,7},{2,5},{3,4,6,8}} => [7,5,4,6,2,8,1,3] => [5,2,7,1,8,3,4,6] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1},{2,6},{3,4,5,7},{8}} => [1,6,4,5,7,2,3,8] => [1,6,2,7,3,4,5,8] => [[1,2,4,6,7,8],[3,5]] => 2
{{1},{2,7},{3,6,8},{4,5}} => [1,7,6,5,4,8,2,3] => [1,5,4,7,2,8,3,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1},{2,6,8},{3},{4,7},{5}} => [1,6,3,7,5,8,4,2] => [1,3,5,7,4,8,2,6] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1,3,4,7},{2},{5},{6,8}} => [3,2,4,7,5,8,1,6] => [2,5,7,1,3,4,8,6] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,4},{2},{3,5},{6,8},{7}} => [4,2,5,1,3,8,7,6] => [2,4,1,5,3,7,8,6] => [[1,2,4,6,7],[3,5,8]] => 3
{{1},{2,7},{3,5},{4},{6,8}} => [1,7,5,4,3,8,2,6] => [1,4,5,3,7,2,8,6] => [[1,2,3,5,7],[4,8],[6]] => 3
{{1,6},{2,4},{3},{5,7},{8}} => [6,4,3,2,7,1,5,8] => [3,4,2,6,1,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 3
{{1},{2,7},{3,5,6,8},{4}} => [1,7,5,4,6,8,2,3] => [1,4,7,2,8,3,5,6] => [[1,2,3,5,8],[4,6,7]] => 2
{{1},{2,8},{3,6},{4},{5,7}} => [1,8,6,4,7,3,5,2] => [1,4,6,3,7,5,8,2] => [[1,2,3,5,7],[4,6],[8]] => 3
{{1,7},{2,5},{3},{4,6},{8}} => [7,5,3,6,2,4,1,8] => [3,5,2,6,4,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1},{2,7},{3,4,6,8},{5}} => [1,7,4,6,5,8,2,3] => [1,5,7,2,8,3,4,6] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,6},{2,3,5,7},{4},{8}} => [6,3,5,4,7,1,2,8] => [4,6,1,7,2,3,5,8] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,4,5,8},{2},{3,6},{7}} => [4,2,6,5,8,3,7,1] => [2,6,3,7,8,1,4,5] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1,3,4,6},{2},{5,8},{7}} => [3,2,4,6,8,1,7,5] => [2,6,1,3,4,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,5},{2},{3,7},{4,6},{8}} => [5,2,7,6,1,4,3,8] => [2,5,1,6,4,7,3,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1},{2,6},{3,5,8},{4,7}} => [1,6,5,7,8,2,4,3] => [1,6,2,7,4,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,5},{3,4,6,8},{7}} => [1,5,4,6,2,8,7,3] => [1,5,2,7,8,3,4,6] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,4},{2,3,5,7},{6},{8}} => [4,3,5,1,7,6,2,8] => [4,1,6,7,2,3,5,8] => [[1,3,4,7,8],[2,5,6]] => 2
{{1},{2,5,6,8},{3,7},{4}} => [1,5,7,4,6,8,3,2] => [1,4,7,3,8,2,5,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,5},{2,3,7},{4},{6},{8}} => [5,3,7,4,1,6,2,8] => [4,5,1,6,7,2,3,8] => [[1,2,4,5,8],[3,6,7]] => 2
{{1,5},{2,3,8},{4},{6},{7}} => [5,3,8,4,1,6,7,2] => [4,5,1,6,7,8,2,3] => [[1,2,4,5,6],[3,7,8]] => 2
{{1,5,8},{2,3,6},{4},{7}} => [5,3,6,4,8,2,7,1] => [4,6,2,3,7,8,1,5] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1,6},{2,3,8},{4},{5},{7}} => [6,3,8,4,5,1,7,2] => [4,5,6,1,7,8,2,3] => [[1,2,3,5,6],[4,7,8]] => 2
{{1,6},{2,4,8},{3},{5},{7}} => [6,4,3,8,5,1,7,2] => [3,5,6,1,7,8,2,4] => [[1,2,3,5,6],[4,7,8]] => 2
{{1,6,8},{2,3,7},{4},{5}} => [6,3,7,4,5,8,2,1] => [4,5,7,2,3,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,6},{2,3},{4,7,8},{5}} => [6,3,2,7,5,1,8,4] => [3,2,5,6,1,8,4,7] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,7},{2,4},{3,8},{5},{6}} => [7,4,8,2,5,6,1,3] => [4,2,5,6,7,1,8,3] => [[1,3,4,5,7],[2,8],[6]] => 3
{{1,5},{2},{3,4,7},{6,8}} => [5,2,4,7,1,8,3,6] => [2,5,1,7,3,4,8,6] => [[1,2,4,7],[3,5,6,8]] => 3
{{1},{2,4},{3,5,7},{6,8}} => [1,4,5,2,7,8,3,6] => [1,4,2,7,3,5,8,6] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,7},{2,5},{3},{4,8},{6}} => [7,5,3,8,2,6,1,4] => [3,5,2,6,7,1,8,4] => [[1,2,4,5,7],[3,8],[6]] => 3
{{1,5,8},{2,4,6},{3},{7}} => [5,4,3,6,8,2,7,1] => [3,6,2,4,7,8,1,5] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1},{2,4},{3,5,7},{6},{8}} => [1,4,5,2,7,6,3,8] => [1,4,2,6,7,3,5,8] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,4},{3,5,8},{6},{7}} => [1,4,5,2,8,6,7,3] => [1,4,2,6,7,8,3,5] => [[1,2,4,5,6],[3,7,8]] => 2
{{1,7},{2,3,5},{4},{6,8}} => [7,3,5,4,2,8,1,6] => [4,5,2,3,7,1,8,6] => [[1,2,5,7],[3,4,8],[6]] => 3
{{1},{2,4,5},{3,8},{6,7}} => [1,4,8,5,2,7,6,3] => [1,5,2,4,7,6,8,3] => [[1,2,4,5,7],[3,6],[8]] => 3
{{1},{2,4,5,7},{3},{6,8}} => [1,4,3,5,7,8,2,6] => [1,3,7,2,4,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 2
{{1},{2,4,7},{3,5,8},{6}} => [1,4,5,7,8,6,2,3] => [1,6,7,2,4,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,5,7,8},{2},{3},{4,6}} => [5,2,3,6,7,4,8,1] => [2,3,6,4,8,1,5,7] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1},{2,5,7,8},{3},{4,6}} => [1,5,3,6,7,4,8,2] => [1,3,6,4,8,2,5,7] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1,3,4,5,6,7,8,9},{2}} => [3,2,4,5,6,7,8,9,1] => [2,9,1,3,4,5,6,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 1
{{1,3,4,5,6,7,8,9,10},{2}} => [3,2,4,5,6,7,8,9,10,1] => [2,10,1,3,4,5,6,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
{{1,6,7,8,9,10},{2},{3},{4},{5}} => [6,2,3,4,5,7,8,9,10,1] => [2,3,4,5,10,1,6,7,8,9] => [[1,2,3,4,5,8,9,10],[6,7]] => 1
{{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,10,1] => [2,3,4,5,6,7,8,10,1,9] => [[1,2,3,4,5,6,7,8],[9,10]] => 1
{{1,5,6,7},{2},{3,8},{4}} => [5,2,8,4,6,7,1,3] => [2,4,7,1,5,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 2
{{1,3,4,5,6,7,8},{2},{9}} => [3,2,4,5,6,7,8,1,9] => [2,8,1,3,4,5,6,7,9] => [[1,2,5,6,7,8,9],[3,4]] => 1
{{1},{2,3,5},{4,6,7,8}} => [1,3,5,6,2,7,8,4] => [1,5,2,3,8,4,6,7] => [[1,2,4,5,7,8],[3,6]] => 2
{{1},{2,3,5},{4,6,8},{7}} => [1,3,5,6,2,8,7,4] => [1,5,2,3,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 2
{{1,4},{2},{3,5,6,7,8}} => [4,2,5,1,6,7,8,3] => [2,4,1,8,3,5,6,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,3},{2,5,6},{4},{7,8}} => [3,5,1,4,6,2,8,7] => [3,1,4,6,2,5,8,7] => [[1,3,4,7],[2,5,6,8]] => 3
{{1,4},{2,5},{3,7,8},{6}} => [4,5,7,1,2,6,8,3] => [4,1,5,2,6,8,3,7] => [[1,3,5,6],[2,4,7,8]] => 3
{{1,7},{2},{3,5},{4,6,8}} => [7,2,5,6,3,8,1,4] => [2,5,3,7,1,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,3},{2,5,7,8},{4},{6}} => [3,5,1,4,7,6,8,2] => [3,1,4,6,8,2,5,7] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,7},{2},{3,5,6,8},{4}} => [7,2,5,4,6,8,1,3] => [2,4,7,1,8,3,5,6] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,6},{2},{3,5,7},{4,8}} => [6,2,5,8,7,1,3,4] => [2,6,1,7,3,5,8,4] => [[1,2,4,7],[3,5,6],[8]] => 3
{{1,4,6},{2,3,5},{7},{8}} => [4,3,5,6,2,1,7,8] => [5,2,3,6,1,4,7,8] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,6},{2,3,5,7,8},{4}} => [6,3,5,4,7,1,8,2] => [4,6,1,8,2,3,5,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,3,5,6,8},{2},{4,7}} => [3,2,5,7,6,8,4,1] => [2,7,4,8,1,3,5,6] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,4,5,8},{2,7},{3,6}} => [4,7,6,5,8,3,2,1] => [6,3,7,2,8,1,4,5] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,3,6},{2},{4,5,7,8}} => [3,2,6,5,7,1,8,4] => [2,6,1,3,8,4,5,7] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,5,6,8},{2,4,7},{3}} => [5,4,3,7,6,8,2,1] => [3,7,2,4,8,1,5,6] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,6},{2,4,5,7,8},{3}} => [6,4,3,5,7,1,8,2] => [3,6,1,8,2,4,5,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,4},{2,3,5,6,8},{7}} => [4,3,5,1,6,8,7,2] => [4,1,7,8,2,3,5,6] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,3,7},{2,4,6,8},{5}} => [3,4,7,6,5,8,1,2] => [5,7,1,3,8,2,4,6] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,4},{2,3,5,7,8},{6}} => [4,3,5,1,7,6,8,2] => [4,1,6,8,2,3,5,7] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,3},{2},{4,5,7},{6,8}} => [3,2,1,5,7,8,4,6] => [2,3,1,7,4,5,8,6] => [[1,2,4,6,7],[3,5,8]] => 3
{{1},{2},{3,4,6},{5,7,8}} => [1,2,4,6,7,3,8,5] => [1,2,6,3,4,8,5,7] => [[1,2,3,5,6,8],[4,7]] => 2
{{1},{2},{3,4,7},{5,6,8}} => [1,2,4,7,6,8,3,5] => [1,2,7,3,4,8,5,6] => [[1,2,3,5,6,8],[4,7]] => 2
{{1,2},{3},{4,6,8},{5,7}} => [2,1,3,6,7,8,5,4] => [2,1,3,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1,3},{2,4},{5},{6,7,8}} => [3,4,1,2,5,7,8,6] => [3,1,4,2,5,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,4},{2,8},{3},{5,6,7}} => [4,8,3,1,6,7,5,2] => [3,4,1,7,5,6,8,2] => [[1,2,4,6,7],[3,5],[8]] => 3
{{1,4,8},{2,5,6},{3},{7}} => [4,5,3,8,6,2,7,1] => [3,6,2,5,7,8,1,4] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,2,4,6},{3},{5,7},{8}} => [2,4,3,6,7,1,5,8] => [3,6,1,2,4,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 2
{{1,3,4,6},{2},{5,7},{8}} => [3,2,4,6,7,1,5,8] => [2,6,1,3,4,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 2
{{1,6,7},{2,4},{3,8},{5}} => [6,4,8,2,5,7,1,3] => [4,2,5,7,1,6,8,3] => [[1,3,4,7],[2,6],[5,8]] => 3
{{1,4},{2},{3,5},{6,7,8}} => [4,2,5,1,3,7,8,6] => [2,4,1,5,3,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,6},{2,7},{3},{4,5,8}} => [6,7,3,5,8,1,2,4] => [3,6,1,7,2,8,4,5] => [[1,2,4,6],[3,5,7,8]] => 3
{{1,6},{2,7,8},{3},{4,5}} => [6,7,3,5,4,1,8,2] => [3,5,4,6,1,8,2,7] => [[1,2,4,6],[3,7,8],[5]] => 3
{{1,6},{2},{3,5,8},{4,7}} => [6,2,5,7,8,1,4,3] => [2,6,1,7,4,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,6,8},{3},{4,5,7}} => [1,6,3,5,7,8,4,2] => [1,3,7,4,5,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1},{2,6,7},{3,8},{4,5}} => [1,6,8,5,4,7,2,3] => [1,5,4,7,2,6,8,3] => [[1,2,4,7],[3,6],[5,8]] => 3
{{1,2,7},{3,6},{4},{5,8}} => [2,7,6,4,8,3,1,5] => [4,6,3,7,1,2,8,5] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,2,8},{3},{4,6},{5,7}} => [2,8,3,6,7,4,5,1] => [3,6,4,7,5,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 3
{{1},{2,5,8},{3},{4,6,7}} => [1,5,3,6,8,7,4,2] => [1,3,7,4,6,8,2,5] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1,4},{2,7,8},{3,6},{5}} => [4,7,6,1,5,3,8,2] => [4,1,5,6,3,8,2,7] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1},{2,5,6},{3,7,8},{4}} => [1,5,7,4,6,2,8,3] => [1,4,6,2,5,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1},{2,4},{3,5,6},{7,8}} => [1,4,5,2,6,3,8,7] => [1,4,2,6,3,5,8,7] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,4,6},{2,3,8},{5,7}} => [4,3,8,6,7,1,5,2] => [6,1,4,7,5,8,2,3] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,3,6},{2,7},{4,5,8}} => [3,7,6,5,8,1,2,4] => [6,1,3,7,2,8,4,5] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,4,6},{2,3,5,7,8}} => [4,3,5,6,7,1,8,2] => [6,1,4,8,2,3,5,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,5,6},{2,4,7},{3,8}} => [5,4,8,7,6,1,2,3] => [6,1,5,7,2,4,8,3] => [[1,3,4,7],[2,6],[5],[8]] => 3
{{1},{2,4,6,7,8},{3,5}} => [1,4,5,6,3,7,8,2] => [1,5,3,8,2,4,6,7] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1},{2,3,5,8},{4,7},{6}} => [1,3,5,7,8,6,4,2] => [1,6,7,4,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,7},{2,3,5,6,8}} => [4,3,5,7,6,8,1,2] => [7,1,4,8,2,3,5,6] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,5,7,8},{2,3,4,6}} => [5,3,4,6,7,2,8,1] => [6,2,3,4,8,1,5,7] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,2,6,8},{3,4,5,7}} => [2,6,4,5,7,8,3,1] => [7,3,4,5,8,1,2,6] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,6},{2,3,4,5,7,8}} => [6,3,4,5,7,1,8,2] => [6,1,8,2,3,4,5,7] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,2,6},{3,4,5,8},{7}} => [2,6,4,5,8,1,7,3] => [6,1,2,7,8,3,4,5] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2,4},{3,5,6,7,8}} => [2,4,5,1,6,7,8,3] => [4,1,2,8,3,5,6,7] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,3,4},{2,5,6,7,8}} => [3,5,4,1,6,7,8,2] => [4,1,3,8,2,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,4,6,7},{2,3,8},{5}} => [4,3,8,6,5,7,1,2] => [5,7,1,4,6,8,2,3] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,3,8},{2,4,6,7},{5}} => [3,4,8,6,5,7,2,1] => [5,7,2,4,6,8,1,3] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,6},{2,3,5},{4,7,8}} => [6,3,5,7,2,1,8,4] => [5,2,3,6,1,8,4,7] => [[1,3,4,6],[2,7,8],[5]] => 3
{{1,2,6},{3,5},{4,7,8}} => [2,6,5,7,3,1,8,4] => [5,3,6,1,2,8,4,7] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,2,5},{3,6},{4,7,8}} => [2,5,6,7,1,3,8,4] => [5,1,2,6,3,8,4,7] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,5},{2,3,6},{4,7,8}} => [5,3,6,7,1,2,8,4] => [5,1,6,2,3,8,4,7] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,4,7,8},{2,6},{3,5}} => [4,6,5,7,3,2,8,1] => [5,3,6,2,8,1,4,7] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,7,8},{2,4,6},{3,5}} => [7,4,5,6,3,2,8,1] => [5,3,6,2,4,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1,2,5},{3,4,6,7,8}} => [2,5,4,6,1,7,8,3] => [5,1,2,8,3,4,6,7] => [[1,3,4,6,7,8],[2,5]] => 2
{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}} => [7,8,9,10,11,12,1,2,3,4,5,6] => [7,1,8,2,9,3,10,4,11,5,12,6] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 6
{{1},{2},{3},{4},{5,7},{6,8}} => [1,2,3,4,7,8,5,6] => [1,2,3,4,7,5,8,6] => [[1,2,3,4,5,7],[6,8]] => 2
{{1},{2},{3},{4,6},{5,8},{7}} => [1,2,3,6,8,4,7,5] => [1,2,3,6,4,7,8,5] => [[1,2,3,4,6,7],[5,8]] => 2
{{1},{2},{3,5},{4,8},{6},{7}} => [1,2,5,8,3,6,7,4] => [1,2,5,3,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2,4},{3,8},{5},{6},{7}} => [1,4,8,2,5,6,7,3] => [1,4,2,5,6,7,8,3] => [[1,2,4,5,6,7],[3,8]] => 2
{{1},{2},{3},{4},{5},{6,8},{7,9}} => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,8,6,9,7] => [[1,2,3,4,5,6,8],[7,9]] => 2
{{1},{2},{3},{4,7},{5,8},{6}} => [1,2,3,7,8,6,4,5] => [1,2,3,6,7,4,8,5] => [[1,2,3,4,5,7],[6,8]] => 2
{{1},{2},{3,6},{4,8},{5},{7}} => [1,2,6,8,5,3,7,4] => [1,2,5,6,3,7,8,4] => [[1,2,3,4,6,7],[5,8]] => 2
{{1},{2},{3},{4,6,7},{5,8}} => [1,2,3,6,8,7,4,5] => [1,2,3,7,4,6,8,5] => [[1,2,3,4,6,7],[5],[8]] => 2
{{1},{2,5},{3,8},{4},{6},{7}} => [1,5,8,4,2,6,7,3] => [1,4,5,2,6,7,8,3] => [[1,2,3,5,6,7],[4,8]] => 2
{{1},{2,4,5},{3,8},{6},{7}} => [1,4,8,5,2,6,7,3] => [1,5,2,4,6,7,8,3] => [[1,2,4,5,6,7],[3],[8]] => 2
{{1,7},{2,3,4,5,6,8}} => [7,3,4,5,6,8,1,2] => [7,1,8,2,3,4,5,6] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,4,6,7,8},{2,3,5}} => [4,3,5,6,2,7,8,1] => [5,2,3,8,1,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,3,6,7,8},{2,4,5}} => [3,4,6,5,2,7,8,1] => [5,2,4,8,1,3,6,7] => [[1,3,4,8],[2,6,7],[5]] => 2
{{1,6},{2,3,7},{4,5,8}} => [6,3,7,5,8,1,2,4] => [6,1,7,2,3,8,4,5] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,4,5,7,8},{2,3,6}} => [4,3,6,5,7,2,8,1] => [6,2,3,8,1,4,5,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,3,7},{2,4,6},{5,8}} => [3,4,7,6,8,2,1,5] => [6,2,4,7,1,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,5,7},{2,3,6,8},{4}} => [5,3,6,4,7,8,1,2] => [4,7,1,5,8,2,3,6] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,3,7},{2,4,5,8},{6}} => [3,4,7,5,8,6,1,2] => [6,7,1,3,8,2,4,5] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,3,7},{2,4,5,6,8}} => [3,4,7,5,6,8,1,2] => [7,1,3,8,2,4,5,6] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,6},{2,3,4,7,8},{5}} => [6,3,4,7,5,1,8,2] => [5,6,1,8,2,3,4,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1},{2,3,5,7,8},{4,6}} => [1,3,5,6,7,4,8,2] => [1,6,4,8,2,3,5,7] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1},{2,3,5,7},{4,6,8}} => [1,3,5,6,7,8,2,4] => [1,7,2,3,5,8,4,6] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,3,4,5,7},{6,8}} => [1,3,4,5,7,8,2,6] => [1,7,2,3,4,5,8,6] => [[1,2,4,5,6,7],[3,8]] => 2
{{1,3},{2,6,8},{4,5},{7}} => [3,6,1,5,4,8,7,2] => [3,1,5,4,7,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1},{2,4,7,8},{3,5},{6}} => [1,4,5,7,3,6,8,2] => [1,5,3,6,8,2,4,7] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1},{2,4,7,8},{3,6},{5}} => [1,4,6,7,5,3,8,2] => [1,5,6,3,8,2,4,7] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4},{2},{3,7,8},{5,6}} => [4,2,7,1,6,5,8,3] => [2,4,1,6,5,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 3
{{1},{2,3,4,6,8},{5,7}} => [1,3,4,6,7,8,5,2] => [1,7,5,8,2,3,4,6] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,5,6},{2,3},{4,7,8}} => [5,3,2,7,6,1,8,4] => [3,2,6,1,5,8,4,7] => [[1,3,6],[2,5,8],[4,7]] => 3
{{1,2,9},{3},{4},{5},{6},{7},{8}} => [2,9,3,4,5,6,7,8,1] => [3,4,5,6,7,8,9,1,2] => [[1,2,3,4,5,6,7],[8,9]] => 1
{{1,3},{2,4,5,6,8},{7}} => [3,4,1,5,6,8,7,2] => [3,1,7,8,2,4,5,6] => [[1,3,4,7,8],[2,5,6]] => 2
{{1,6,7},{2,3,4,5,8}} => [6,3,4,5,8,7,1,2] => [7,1,6,8,2,3,4,5] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,4,5},{2,3,7,8},{6}} => [4,3,7,5,1,6,8,2] => [5,1,4,6,8,2,3,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4,6,8},{2,3,5,7}} => [4,3,5,6,7,8,2,1] => [7,2,3,5,8,1,4,6] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4,8},{2,3,6,7},{5}} => [4,3,6,8,5,7,2,1] => [5,7,2,3,6,8,1,4] => [[1,2,5,6],[3,4],[7,8]] => 2
{{1,2,6},{3,7},{4,5,8}} => [2,6,7,5,8,1,3,4] => [6,1,2,7,3,8,4,5] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,2},{3,4,6},{5,7,8}} => [2,1,4,6,7,3,8,5] => [2,1,6,3,4,8,5,7] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,2,3},{4,7},{5,6,8}} => [2,3,1,7,6,8,4,5] => [3,1,2,7,4,8,5,6] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,2,6},{3,5,7,8},{4}} => [2,6,5,4,7,1,8,3] => [4,6,1,2,8,3,5,7] => [[1,2,5,7,8],[3,4,6]] => 2
{{1},{2,3,6},{4,5,7,8}} => [1,3,6,5,7,2,8,4] => [1,6,2,3,8,4,5,7] => [[1,2,4,5,7,8],[3,6]] => 2
{{1,7,8},{2,4},{3,5,6}} => [7,4,5,2,6,3,8,1] => [4,2,6,3,5,8,1,7] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1},{2},{3},{4},{5},{6,7,9},{8}} => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 1
{{1},{2,3,9},{4},{5},{6},{7},{8}} => [1,3,9,4,5,6,7,8,2] => [1,4,5,6,7,8,9,2,3] => [[1,2,3,4,5,6,7],[8,9]] => 1
{{1,3},{2,5,8},{4},{6,7}} => [3,5,1,4,8,7,6,2] => [3,1,4,7,6,8,2,5] => [[1,3,4,6],[2,5,8],[7]] => 3
{{1},{2,4},{3,5,6,7,8}} => [1,4,5,2,6,7,8,3] => [1,4,2,8,3,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 2
{{1,5,6},{2},{3},{4,7,8}} => [5,2,3,7,6,1,8,4] => [2,3,6,1,5,8,4,7] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,3,5},{2},{4,6},{7},{8}} => [3,2,5,6,1,4,7,8] => [2,5,1,3,6,4,7,8] => [[1,2,5,7,8],[3,4,6]] => 2
{{1},{2},{3,7},{4,8},{5},{6}} => [1,2,7,8,5,6,3,4] => [1,2,5,6,7,3,8,4] => [[1,2,3,4,5,7],[6,8]] => 2
{{1,7},{2},{3},{4},{5},{6,8}} => [7,2,3,4,5,8,1,6] => [2,3,4,5,7,1,8,6] => [[1,2,3,4,5,7],[6,8]] => 2
{{1,6},{2},{3},{4},{5,8},{7}} => [6,2,3,4,8,1,7,5] => [2,3,4,6,1,7,8,5] => [[1,2,3,4,6,7],[5,8]] => 2
{{1,4},{2,6},{3},{5,8},{7}} => [4,6,3,1,8,2,7,5] => [3,4,1,6,2,7,8,5] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,5},{2,6},{3},{4,8},{7}} => [5,6,3,8,1,2,7,4] => [3,5,1,6,2,7,8,4] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,5,7},{2},{3},{4},{6,8}} => [5,2,3,4,7,8,1,6] => [2,3,4,7,1,5,8,6] => [[1,2,3,4,7],[5,6,8]] => 2
{{1,5},{2},{3},{4,6},{7},{8}} => [5,2,3,6,1,4,7,8] => [2,3,5,1,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
{{1,4},{2},{3,6},{5},{7},{8}} => [4,2,6,1,5,3,7,8] => [2,4,1,5,6,3,7,8] => [[1,2,4,5,7,8],[3,6]] => 2
{{1},{2,5},{3,6},{4},{7},{8}} => [1,5,6,4,2,3,7,8] => [1,4,5,2,6,3,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
{{1,4,6},{2},{3,5,7},{8}} => [4,2,5,6,7,1,3,8] => [2,6,1,4,7,3,5,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,5},{2},{3},{4,7},{6,8}} => [5,2,3,7,1,8,4,6] => [2,3,5,1,7,4,8,6] => [[1,2,3,5,7],[4,6,8]] => 3
{{1,5,7},{2},{3},{4,6},{8}} => [5,2,3,6,7,4,1,8] => [2,3,6,4,7,1,5,8] => [[1,2,3,5,8],[4,7],[6]] => 2
{{1,4},{2},{3,7},{5},{6,8}} => [4,2,7,1,5,8,3,6] => [2,4,1,5,7,3,8,6] => [[1,2,4,5,7],[3,6,8]] => 3
{{1,5},{2},{3,7},{4,8},{6}} => [5,2,7,8,1,6,3,4] => [2,5,1,6,7,3,8,4] => [[1,2,4,5,7],[3,6,8]] => 3
{{1,7},{2,5},{3,6},{4},{8}} => [7,5,6,4,2,3,1,8] => [4,5,2,6,3,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 3
{{1},{2,6},{3},{4,8},{5},{7}} => [1,6,3,8,5,2,7,4] => [1,3,5,6,2,7,8,4] => [[1,2,3,4,6,7],[5,8]] => 2
{{1,5},{2,3,4,8},{6},{7}} => [5,3,4,8,1,6,7,2] => [5,1,6,7,8,2,3,4] => [[1,3,4,5],[2,6,7,8]] => 2
{{1,4,5},{2,3,8},{6},{7}} => [4,3,8,5,1,6,7,2] => [5,1,4,6,7,8,2,3] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,3},{2,5},{4,6,7},{8}} => [3,5,1,6,2,7,4,8] => [3,1,5,2,7,4,6,8] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,4,5,8},{2,3,7},{6}} => [4,3,7,5,8,6,2,1] => [6,7,2,3,8,1,4,5] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,7},{2,3},{4,5,6,8}} => [7,3,2,5,6,8,1,4] => [3,2,7,1,8,4,5,6] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,4,7,8},{2,3,5,6}} => [4,3,5,7,6,2,8,1] => [6,2,3,5,8,1,4,7] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,5,7,8},{2,4},{3,6}} => [5,4,6,2,7,3,8,1] => [4,2,6,3,8,1,5,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,5,7,8},{2,3},{4,6}} => [5,3,2,6,7,4,8,1] => [3,2,6,4,8,1,5,7] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,6},{2},{3},{4,5,7,8}} => [6,2,3,5,7,1,8,4] => [2,3,6,1,8,4,5,7] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,3,4,7},{2},{5,8},{6}} => [3,2,4,7,8,6,1,5] => [2,6,7,1,3,4,8,5] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,4,6},{2,3,5},{7,8}} => [4,3,5,6,2,1,8,7] => [5,2,3,6,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 3
{{1,6,8},{2,3,4,5,7}} => [6,3,4,5,7,8,2,1] => [7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,2},{3,6,8},{4,5,7}} => [2,1,6,5,7,8,4,3] => [2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6,7},{2,4,5,8},{3}} => [6,4,3,5,8,7,1,2] => [3,7,1,6,8,2,4,5] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,2,7},{3,6,8},{4,5}} => [2,7,6,5,4,8,1,3] => [5,4,7,1,2,8,3,6] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,3,5,8},{2,7},{4,6}} => [3,7,5,6,8,4,2,1] => [6,4,7,2,8,1,3,5] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,4,5,8},{2,3,6},{7}} => [4,3,6,5,8,2,7,1] => [6,2,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,5,7},{2,3,4,6,8}} => [5,3,4,6,7,8,1,2] => [7,1,5,8,2,3,4,6] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,5},{2,4,6,7,8},{3}} => [5,4,3,6,1,7,8,2] => [3,5,1,8,2,4,6,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,3},{2,4,5,6,7},{8}} => [3,4,1,5,6,7,2,8] => [3,1,7,2,4,5,6,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1},{2,5},{3,4,6,7,8}} => [1,5,4,6,2,7,8,3] => [1,5,2,8,3,4,6,7] => [[1,2,4,6,7,8],[3,5]] => 2
{{1,2,4},{3,5,6,7},{8}} => [2,4,5,1,6,7,3,8] => [4,1,2,7,3,5,6,8] => [[1,3,4,6,7,8],[2,5]] => 2
{{1},{2,3,4,6},{5,7,8}} => [1,3,4,6,7,2,8,5] => [1,6,2,3,4,8,5,7] => [[1,2,4,5,6,8],[3,7]] => 2
{{1,5},{2,3,4,6,7},{8}} => [5,3,4,6,1,7,2,8] => [5,1,7,2,3,4,6,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,2,4,6,8,10},{3},{5},{7},{9}} => [2,4,3,6,5,8,7,10,9,1] => [3,5,7,9,10,1,2,4,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 1
{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} => [2,4,3,6,5,8,7,10,9,12,11,1] => [3,5,7,9,11,12,1,2,4,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 1
{{1},{2,4,6},{3},{5,7,8}} => [1,4,3,6,7,2,8,5] => [1,3,6,2,4,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 2
{{1,2,4,5,7},{3},{6,8}} => [2,4,3,5,7,8,1,6] => [3,7,1,2,4,5,8,6] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,3,4,6,8},{2},{5,7}} => [3,2,4,6,7,8,5,1] => [2,7,5,8,1,3,4,6] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1},{2,5,7},{3},{4,6,8}} => [1,5,3,6,7,8,2,4] => [1,3,7,2,5,8,4,6] => [[1,2,3,6],[4,5,8],[7]] => 2
{{1,2},{3,5,7},{4,6,8}} => [2,1,5,6,7,8,3,4] => [2,1,7,3,5,8,4,6] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,3,4,5,7},{2},{6,8}} => [3,2,4,5,7,8,1,6] => [2,7,1,3,4,5,8,6] => [[1,2,5,6,7],[3,4,8]] => 2
{{1,4,5,7,8},{2},{3,6}} => [4,2,6,5,7,3,8,1] => [2,6,3,8,1,4,5,7] => [[1,2,4,7,8],[3,6],[5]] => 2
{{1,8},{2,9},{3},{4},{5},{6},{7}} => [8,9,3,4,5,6,7,1,2] => [3,4,5,6,7,8,1,9,2] => [[1,2,3,4,5,6,8],[7,9]] => 2
{{1},{2,7},{3,8},{4},{5},{6}} => [1,7,8,4,5,6,2,3] => [1,4,5,6,7,2,8,3] => [[1,2,3,4,5,7],[6,8]] => 2
{{1},{2},{3},{4,6,8},{5,7}} => [1,2,3,6,7,8,5,4] => [1,2,3,7,5,8,4,6] => [[1,2,3,4,6],[5,8],[7]] => 2
{{1},{2},{3,5,8},{4,6},{7}} => [1,2,5,6,8,4,7,3] => [1,2,6,4,7,8,3,5] => [[1,2,3,5,6],[4,8],[7]] => 2
{{1,4,5,6,7,8,9},{2,3}} => [4,3,2,5,6,7,8,9,1] => [3,2,9,1,4,5,6,7,8] => [[1,3,6,7,8,9],[2,5],[4]] => 2
{{1,4,6},{2,3},{5,7,8}} => [4,3,2,6,7,1,8,5] => [3,2,6,1,4,8,5,7] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1},{2,4,8},{3,5,6,7}} => [1,4,5,8,6,7,3,2] => [1,7,3,5,6,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 2
{{1},{2,7},{3,6},{4},{5,8}} => [1,7,6,4,8,3,2,5] => [1,4,6,3,7,2,8,5] => [[1,2,3,5,7],[4,8],[6]] => 3
{{1,3,5},{2,4,6,7,8}} => [3,4,5,6,1,7,8,2] => [5,1,3,8,2,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 2
{{1,5},{2},{3,7},{4},{6,8}} => [5,2,7,4,1,8,3,6] => [2,4,5,1,7,3,8,6] => [[1,2,3,5,7],[4,6,8]] => 3
{{1,5,6,7},{2,4},{3,8}} => [5,4,8,2,6,7,1,3] => [4,2,7,1,5,6,8,3] => [[1,3,6,7],[2,5],[4,8]] => 3
{{1,5,6},{2,4,8},{3,7}} => [5,4,7,8,6,1,3,2] => [6,1,5,7,3,8,2,4] => [[1,3,4,6],[2,8],[5],[7]] => 3
{{1,2,7},{3,8},{4},{5,6}} => [2,7,8,4,6,5,1,3] => [4,6,5,7,1,2,8,3] => [[1,2,4,7],[3,6,8],[5]] => 3
{{1,5},{2,3,4,7},{6,8}} => [5,3,4,7,1,8,2,6] => [5,1,7,2,3,4,8,6] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,2,4,6,8},{3},{5,7}} => [2,4,3,6,7,8,5,1] => [3,7,5,8,1,2,4,6] => [[1,2,4,8],[3,6,7],[5]] => 2
{{1,3,8},{2,4,5,6,7}} => [3,4,8,5,6,7,2,1] => [7,2,4,5,6,8,1,3] => [[1,3,4,5,6],[2,8],[7]] => 2
{{1,3},{2,7},{4,5,6,8}} => [3,7,1,5,6,8,2,4] => [3,1,7,2,8,4,5,6] => [[1,3,5,7,8],[2,4,6]] => 3
{{1},{2,7},{3},{4,5,6,8}} => [1,7,3,5,6,8,2,4] => [1,3,7,2,8,4,5,6] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,3,8},{2,6},{4,5,7}} => [3,6,8,5,7,2,4,1] => [6,2,7,4,5,8,1,3] => [[1,3,5,6],[2,4],[7,8]] => 3
{{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => [4,1,2,6,3,8,5,7] => [[1,3,4,6,8],[2,5,7]] => 3
{{1,2,7},{3,4,6,8},{5}} => [2,7,4,6,5,8,1,3] => [5,7,1,2,8,3,4,6] => [[1,2,5,7,8],[3,4,6]] => 2
{{1,3,4,8},{2,7},{5,6}} => [3,7,4,8,6,5,2,1] => [6,5,7,2,8,1,3,4] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1},{2,5},{3},{4,7},{6,8}} => [1,5,3,7,2,8,4,6] => [1,3,5,2,7,4,8,6] => [[1,2,3,5,7],[4,6,8]] => 3
{{1,2},{3,4,7},{5,6,8}} => [2,1,4,7,6,8,3,5] => [2,1,7,3,4,8,5,6] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,4,7},{2,3},{5,6,8}} => [4,3,2,7,6,8,1,5] => [3,2,7,1,4,8,5,6] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,3,7},{2,4},{5,6,8}} => [3,4,7,2,6,8,1,5] => [4,2,7,1,3,8,5,6] => [[1,3,6,8],[2,5,7],[4]] => 3
{{1,3,7},{2,6,8},{4,5}} => [3,6,7,5,4,8,1,2] => [5,4,7,1,3,8,2,6] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1,7},{2,3,5,8},{4,6}} => [7,3,5,6,8,4,1,2] => [6,4,7,1,8,2,3,5] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,2,6},{3,8},{4,5,7}} => [2,6,8,5,7,1,4,3] => [6,1,2,7,4,5,8,3] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,5,7,8},{2,6},{3,4}} => [5,6,4,3,7,2,8,1] => [4,3,6,2,8,1,5,7] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,6,8},{2,5,7},{3,4}} => [6,5,4,3,7,8,2,1] => [4,3,7,2,5,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1,6,8},{2,4,7},{3,5}} => [6,4,5,7,3,8,2,1] => [5,3,7,2,4,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1},{2,4},{3,5},{6,7,8}} => [1,4,5,2,3,7,8,6] => [1,4,2,5,3,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 3
{{1,5},{2,3,4,6},{7,8}} => [5,3,4,6,1,2,8,7] => [5,1,6,2,3,4,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
{{1,3,4},{2,8},{5,6,7}} => [3,8,4,1,6,7,5,2] => [4,1,3,7,5,6,8,2] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,8},{2,3,6},{4,5,7}} => [8,3,6,5,7,2,4,1] => [6,2,3,7,4,5,8,1] => [[1,3,4,6,7],[2,5],[8]] => 3
{{1,2},{3,5,6},{4,7,8}} => [2,1,5,7,6,3,8,4] => [2,1,6,3,5,8,4,7] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,5,6},{2,7,8},{3,4}} => [5,7,4,3,6,1,8,2] => [4,3,6,1,5,8,2,7] => [[1,3,6],[2,5,8],[4,7]] => 3
{{1,7},{2,6},{3,4,5,8}} => [7,6,4,5,8,2,1,3] => [6,2,7,1,8,3,4,5] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,2},{3,7},{4,5,6,8}} => [2,1,7,5,6,8,3,4] => [2,1,7,3,8,4,5,6] => [[1,3,5,7,8],[2,4,6]] => 3
{{1,7},{2,5,6,8},{3,4}} => [7,5,4,3,6,8,1,2] => [4,3,7,1,8,2,5,6] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,2,3,7},{4},{5,8},{6}} => [2,3,7,4,8,6,1,5] => [4,6,7,1,2,3,8,5] => [[1,2,3,7],[4,5,6,8]] => 2
{{1,7},{2},{3,4,5,8},{6}} => [7,2,4,5,8,6,1,3] => [2,6,7,1,8,3,4,5] => [[1,2,3,5],[4,6,7,8]] => 2
{{1,4},{2,3,5,6},{7},{8}} => [4,3,5,1,6,2,7,8] => [4,1,6,2,3,5,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
{{1,3,5},{2,4},{6},{7,8}} => [3,4,5,2,1,6,8,7] => [4,2,5,1,3,6,8,7] => [[1,3,6,7],[2,5,8],[4]] => 3
{{1},{2},{3,4,5,7},{6,8}} => [1,2,4,5,7,8,3,6] => [1,2,7,3,4,5,8,6] => [[1,2,3,5,6,7],[4,8]] => 2
{{1,6},{2,4,7,8},{3,5}} => [6,4,5,7,3,1,8,2] => [5,3,6,1,8,2,4,7] => [[1,3,5,8],[2,6,7],[4]] => 3
{{1,4,5},{2},{3,6,7},{8}} => [4,2,6,5,1,7,3,8] => [2,5,1,4,7,3,6,8] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1},{2,5},{3,4,6,7},{8}} => [1,5,4,6,2,7,3,8] => [1,5,2,7,3,4,6,8] => [[1,2,4,6,7,8],[3,5]] => 2
{{1,4,5},{2},{3,6,8},{7}} => [4,2,6,5,1,8,7,3] => [2,5,1,4,7,8,3,6] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1},{2,3,6},{4},{5,8},{7}} => [1,3,6,4,8,2,7,5] => [1,4,6,2,3,7,8,5] => [[1,2,3,6,7],[4,5,8]] => 2
{{1},{2,4},{3,7},{5},{6,8}} => [1,4,7,2,5,8,3,6] => [1,4,2,5,7,3,8,6] => [[1,2,4,5,7],[3,6,8]] => 3
{{1},{2,5},{3},{4,6,8},{7}} => [1,5,3,6,2,8,7,4] => [1,3,5,2,7,8,4,6] => [[1,2,3,5,6],[4,7,8]] => 2
{{1},{2,5},{3},{4,6,7},{8}} => [1,5,3,6,2,7,4,8] => [1,3,5,2,7,4,6,8] => [[1,2,3,5,8],[4,6,7]] => 2
{{1,5,8},{2,3,7},{4,6}} => [5,3,7,6,8,4,2,1] => [6,4,7,2,3,8,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 3
{{1,2},{3,4,6,8},{5,7}} => [2,1,4,6,7,8,5,3] => [2,1,7,5,8,3,4,6] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,3},{2,6,7},{4,5},{8}} => [3,6,1,5,4,7,2,8] => [3,1,5,4,7,2,6,8] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,3,7},{2,4,5},{6},{8}} => [3,4,7,5,2,6,1,8] => [5,2,4,6,7,1,3,8] => [[1,3,4,5,8],[2,7],[6]] => 2
{{1,6},{2},{3,4,5,7,8}} => [6,2,4,5,7,1,8,3] => [2,6,1,8,3,4,5,7] => [[1,2,4,7,8],[3,5,6]] => 2
{{1,4,5},{2,3,8},{6,7}} => [4,3,8,5,1,7,6,2] => [5,1,4,7,6,8,2,3] => [[1,3,4,6],[2,5],[7,8]] => 3
{{1,3,6,8},{2,7},{4,5}} => [3,7,6,5,4,8,2,1] => [5,4,7,2,8,1,3,6] => [[1,3,5],[2,7,8],[4],[6]] => 3
{{1,2,8},{3,6},{4,5,7}} => [2,8,6,5,7,3,4,1] => [6,3,7,4,5,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 3
{{1,2},{3,6,7},{4,5,8}} => [2,1,6,5,8,7,3,4] => [2,1,7,3,6,8,4,5] => [[1,3,5,6],[2,4,8],[7]] => 3
{{1,6,7},{2,3},{4,5,8}} => [6,3,2,5,8,7,1,4] => [3,2,7,1,6,8,4,5] => [[1,3,6],[2,5,8],[4,7]] => 3
{{1,6,7},{2,5,8},{3,4}} => [6,5,4,3,8,7,1,2] => [4,3,7,1,6,8,2,5] => [[1,3,6],[2,5,8],[4,7]] => 3
{{1,2,4},{3,6,7,8},{5}} => [2,4,6,1,5,7,8,3] => [4,1,2,5,8,3,6,7] => [[1,3,4,5,8],[2,6,7]] => 2
{{1,2,4},{3,5,6,8},{7}} => [2,4,5,1,6,8,7,3] => [4,1,2,7,8,3,5,6] => [[1,3,4,5,8],[2,6,7]] => 2
{{1},{2,4},{3,5,6,8},{7}} => [1,4,5,2,6,8,7,3] => [1,4,2,7,8,3,5,6] => [[1,2,4,5,8],[3,6,7]] => 2
{{1},{2,5},{3,4,6},{7,8}} => [1,5,4,6,2,3,8,7] => [1,5,2,6,3,4,8,7] => [[1,2,4,6,7],[3,5,8]] => 3
{{1,6,7},{2,3,5,8},{4}} => [6,3,5,4,8,7,1,2] => [4,7,1,6,8,2,3,5] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,3,5,8},{2,4,6,7}} => [3,4,5,6,8,7,2,1] => [7,2,4,6,8,1,3,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,4},{2,3,6},{5,7,8}} => [4,3,6,1,7,2,8,5] => [4,1,6,2,3,8,5,7] => [[1,3,5,6,8],[2,4,7]] => 3
{{1,5,7,8},{2,3,6},{4}} => [5,3,6,4,7,2,8,1] => [4,6,2,3,8,1,5,7] => [[1,2,5,8],[3,4,7],[6]] => 2
{{1,2,3,6},{4},{5,7,8}} => [2,3,6,4,7,1,8,5] => [4,6,1,2,3,8,5,7] => [[1,2,5,6,8],[3,4,7]] => 2
{{1,3,4,6},{2},{5,7,8}} => [3,2,4,6,7,1,8,5] => [2,6,1,3,4,8,5,7] => [[1,2,5,6,8],[3,4,7]] => 2
{{1,4,6},{2,3,5,8},{7}} => [4,3,5,6,8,1,7,2] => [6,1,4,7,8,2,3,5] => [[1,3,4,5],[2,7,8],[6]] => 2
{{1,6},{2,3,5,8},{4,7}} => [6,3,5,7,8,1,4,2] => [6,1,7,4,8,2,3,5] => [[1,3,5,8],[2,4,7],[6]] => 3
{{1,4,5,6},{2},{3,7,8}} => [4,2,7,5,6,1,8,3] => [2,6,1,4,5,8,3,7] => [[1,2,5,6],[3,4,8],[7]] => 2
{{1},{2,3,6,8},{4,7},{5}} => [1,3,6,7,5,8,4,2] => [1,5,7,4,8,2,3,6] => [[1,2,3,5],[4,7,8],[6]] => 2
{{1,4,8},{2,5,7},{3,6}} => [4,5,6,8,7,3,2,1] => [6,3,7,2,5,8,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 3
{{1},{2,4,7},{3,5,6,8}} => [1,4,5,7,6,8,2,3] => [1,7,2,4,8,3,5,6] => [[1,2,4,5,8],[3,7],[6]] => 2
{{1,2,6,8},{3},{4,5,7}} => [2,6,3,5,7,8,4,1] => [3,7,4,5,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 2
{{1},{2,5,7},{3},{4,8},{6}} => [1,5,3,8,7,6,2,4] => [1,3,6,7,2,5,8,4] => [[1,2,3,4,7],[5,6],[8]] => 2
{{1},{2,4,6,7},{3,5},{8}} => [1,4,5,6,3,7,2,8] => [1,5,3,7,2,4,6,8] => [[1,2,4,7,8],[3,6],[5]] => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4 1,11,3 1,26,25 1,57,130,15 1,120,546,210
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 4\ q$
$F_{4} = 1 + 11\ q + 3\ q^{2}$
$F_{5} = 1 + 26\ q + 25\ q^{2}$
$F_{6} = 1 + 57\ q + 130\ q^{2} + 15\ q^{3}$
$F_{7} = 1 + 120\ q + 546\ q^{2} + 210\ q^{3}$
Description
The number of descents of a standard tableau.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
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