Identifier
-
Mp00084:
Standard tableaux
—conjugate⟶
Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00164: Set partitions —Chen Deng Du Stanley Yan⟶ Set partitions
St000839: Set partitions ⟶ ℤ
Values
[[1]] => [[1]] => {{1}} => {{1}} => 1
[[1,2]] => [[1],[2]] => {{1},{2}} => {{1},{2}} => 2
[[1],[2]] => [[1,2]] => {{1,2}} => {{1,2}} => 1
[[1,2,3]] => [[1],[2],[3]] => {{1},{2},{3}} => {{1},{2},{3}} => 3
[[1,3],[2]] => [[1,2],[3]] => {{1,2},{3}} => {{1,2},{3}} => 3
[[1,2],[3]] => [[1,3],[2]] => {{1,3},{2}} => {{1,3},{2}} => 2
[[1],[2],[3]] => [[1,2,3]] => {{1,2,3}} => {{1,2,3}} => 1
[[1,2,3,4]] => [[1],[2],[3],[4]] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => 4
[[1,3,4],[2]] => [[1,2],[3],[4]] => {{1,2},{3},{4}} => {{1,2},{3},{4}} => 4
[[1,2,4],[3]] => [[1,3],[2],[4]] => {{1,3},{2},{4}} => {{1,3},{2},{4}} => 4
[[1,2,3],[4]] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => 3
[[1,3],[2,4]] => [[1,2],[3,4]] => {{1,2},{3,4}} => {{1,2},{3,4}} => 3
[[1,2],[3,4]] => [[1,3],[2,4]] => {{1,3},{2,4}} => {{1,4},{2,3}} => 2
[[1,4],[2],[3]] => [[1,2,3],[4]] => {{1,2,3},{4}} => {{1,2,3},{4}} => 4
[[1,3],[2],[4]] => [[1,2,4],[3]] => {{1,2,4},{3}} => {{1,2,4},{3}} => 3
[[1,2],[3],[4]] => [[1,3,4],[2]] => {{1,3,4},{2}} => {{1,3,4},{2}} => 2
[[1],[2],[3],[4]] => [[1,2,3,4]] => {{1,2,3,4}} => {{1,2,3,4}} => 1
[[1,2,3,4,5]] => [[1],[2],[3],[4],[5]] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => 5
[[1,3,4,5],[2]] => [[1,2],[3],[4],[5]] => {{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}} => 5
[[1,2,4,5],[3]] => [[1,3],[2],[4],[5]] => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}} => 5
[[1,2,3,5],[4]] => [[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}} => 5
[[1,2,3,4],[5]] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => 4
[[1,3,5],[2,4]] => [[1,2],[3,4],[5]] => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}} => 5
[[1,2,5],[3,4]] => [[1,3],[2,4],[5]] => {{1,3},{2,4},{5}} => {{1,4},{2,3},{5}} => 5
[[1,3,4],[2,5]] => [[1,2],[3,5],[4]] => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}} => 4
[[1,2,4],[3,5]] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => {{1,5},{2,3},{4}} => 4
[[1,2,3],[4,5]] => [[1,4],[2,5],[3]] => {{1,4},{2,5},{3}} => {{1,5},{2,4},{3}} => 3
[[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}} => 5
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}} => 5
[[1,2,5],[3],[4]] => [[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => {{1,3,4},{2},{5}} => 5
[[1,3,4],[2],[5]] => [[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}} => 4
[[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => 4
[[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => {{1,4,5},{2},{3}} => 3
[[1,4],[2,5],[3]] => [[1,2,3],[4,5]] => {{1,2,3},{4,5}} => {{1,2,3},{4,5}} => 4
[[1,3],[2,5],[4]] => [[1,2,4],[3,5]] => {{1,2,4},{3,5}} => {{1,2,5},{3,4}} => 3
[[1,2],[3,5],[4]] => [[1,3,4],[2,5]] => {{1,3,4},{2,5}} => {{1,4},{2,3,5}} => 2
[[1,3],[2,4],[5]] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => {{1,2,4},{3,5}} => 3
[[1,2],[3,4],[5]] => [[1,3,5],[2,4]] => {{1,3,5},{2,4}} => {{1,5},{2,3,4}} => 2
[[1,5],[2],[3],[4]] => [[1,2,3,4],[5]] => {{1,2,3,4},{5}} => {{1,2,3,4},{5}} => 5
[[1,4],[2],[3],[5]] => [[1,2,3,5],[4]] => {{1,2,3,5},{4}} => {{1,2,3,5},{4}} => 4
[[1,3],[2],[4],[5]] => [[1,2,4,5],[3]] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}} => 3
[[1,2],[3],[4],[5]] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => {{1,3,4,5},{2}} => 2
[[1],[2],[3],[4],[5]] => [[1,2,3,4,5]] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => 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}} => 6
[[1,3,4,5,6],[2]] => [[1,2],[3],[4],[5],[6]] => {{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}} => 6
[[1,2,4,5,6],[3]] => [[1,3],[2],[4],[5],[6]] => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => 6
[[1,2,3,5,6],[4]] => [[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}} => 6
[[1,2,3,4,6],[5]] => [[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}} => 6
[[1,2,3,4,5],[6]] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => 5
[[1,3,5,6],[2,4]] => [[1,2],[3,4],[5],[6]] => {{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}} => 6
[[1,2,5,6],[3,4]] => [[1,3],[2,4],[5],[6]] => {{1,3},{2,4},{5},{6}} => {{1,4},{2,3},{5},{6}} => 6
[[1,3,4,6],[2,5]] => [[1,2],[3,5],[4],[6]] => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}} => 6
[[1,2,4,6],[3,5]] => [[1,3],[2,5],[4],[6]] => {{1,3},{2,5},{4},{6}} => {{1,5},{2,3},{4},{6}} => 6
[[1,2,3,6],[4,5]] => [[1,4],[2,5],[3],[6]] => {{1,4},{2,5},{3},{6}} => {{1,5},{2,4},{3},{6}} => 6
[[1,3,4,5],[2,6]] => [[1,2],[3,6],[4],[5]] => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}} => 5
[[1,2,4,5],[3,6]] => [[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => {{1,6},{2,3},{4},{5}} => 5
[[1,2,3,5],[4,6]] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => {{1,6},{2,4},{3},{5}} => 5
[[1,2,3,4],[5,6]] => [[1,5],[2,6],[3],[4]] => {{1,5},{2,6},{3},{4}} => {{1,6},{2,5},{3},{4}} => 4
[[1,4,5,6],[2],[3]] => [[1,2,3],[4],[5],[6]] => {{1,2,3},{4},{5},{6}} => {{1,2,3},{4},{5},{6}} => 6
[[1,3,5,6],[2],[4]] => [[1,2,4],[3],[5],[6]] => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}} => 6
[[1,2,5,6],[3],[4]] => [[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => {{1,3,4},{2},{5},{6}} => 6
[[1,3,4,6],[2],[5]] => [[1,2,5],[3],[4],[6]] => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}} => 6
[[1,2,4,6],[3],[5]] => [[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => {{1,3,5},{2},{4},{6}} => 6
[[1,2,3,6],[4],[5]] => [[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => {{1,4,5},{2},{3},{6}} => 6
[[1,3,4,5],[2],[6]] => [[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}} => 5
[[1,2,4,5],[3],[6]] => [[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => {{1,3,6},{2},{4},{5}} => 5
[[1,2,3,5],[4],[6]] => [[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => {{1,4,6},{2},{3},{5}} => 5
[[1,2,3,4],[5],[6]] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => {{1,5,6},{2},{3},{4}} => 4
[[1,3,5],[2,4,6]] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => 5
[[1,2,5],[3,4,6]] => [[1,3],[2,4],[5,6]] => {{1,3},{2,4},{5,6}} => {{1,4},{2,3},{5,6}} => 5
[[1,3,4],[2,5,6]] => [[1,2],[3,5],[4,6]] => {{1,2},{3,5},{4,6}} => {{1,2},{3,6},{4,5}} => 4
[[1,2,4],[3,5,6]] => [[1,3],[2,5],[4,6]] => {{1,3},{2,5},{4,6}} => {{1,6},{2,3},{4,5}} => 4
[[1,2,3],[4,5,6]] => [[1,4],[2,5],[3,6]] => {{1,4},{2,5},{3,6}} => {{1,6},{2,5},{3,4}} => 3
[[1,4,6],[2,5],[3]] => [[1,2,3],[4,5],[6]] => {{1,2,3},{4,5},{6}} => {{1,2,3},{4,5},{6}} => 6
[[1,3,6],[2,5],[4]] => [[1,2,4],[3,5],[6]] => {{1,2,4},{3,5},{6}} => {{1,2,5},{3,4},{6}} => 6
[[1,2,6],[3,5],[4]] => [[1,3,4],[2,5],[6]] => {{1,3,4},{2,5},{6}} => {{1,4},{2,3,5},{6}} => 6
[[1,3,6],[2,4],[5]] => [[1,2,5],[3,4],[6]] => {{1,2,5},{3,4},{6}} => {{1,2,4},{3,5},{6}} => 6
[[1,2,6],[3,4],[5]] => [[1,3,5],[2,4],[6]] => {{1,3,5},{2,4},{6}} => {{1,5},{2,3,4},{6}} => 6
[[1,4,5],[2,6],[3]] => [[1,2,3],[4,6],[5]] => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}} => 5
[[1,3,5],[2,6],[4]] => [[1,2,4],[3,6],[5]] => {{1,2,4},{3,6},{5}} => {{1,2,6},{3,4},{5}} => 5
[[1,2,5],[3,6],[4]] => [[1,3,4],[2,6],[5]] => {{1,3,4},{2,6},{5}} => {{1,4},{2,3,6},{5}} => 5
[[1,3,4],[2,6],[5]] => [[1,2,5],[3,6],[4]] => {{1,2,5},{3,6},{4}} => {{1,2,6},{3,5},{4}} => 4
[[1,2,4],[3,6],[5]] => [[1,3,5],[2,6],[4]] => {{1,3,5},{2,6},{4}} => {{1,5},{2,3,6},{4}} => 4
[[1,2,3],[4,6],[5]] => [[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => {{1,5},{2,4,6},{3}} => 3
[[1,3,5],[2,4],[6]] => [[1,2,6],[3,4],[5]] => {{1,2,6},{3,4},{5}} => {{1,2,4},{3,6},{5}} => 5
[[1,2,5],[3,4],[6]] => [[1,3,6],[2,4],[5]] => {{1,3,6},{2,4},{5}} => {{1,6},{2,3,4},{5}} => 5
[[1,3,4],[2,5],[6]] => [[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => {{1,2,5},{3,6},{4}} => 4
[[1,2,4],[3,5],[6]] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => {{1,6},{2,3,5},{4}} => 4
[[1,2,3],[4,5],[6]] => [[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => {{1,6},{2,4,5},{3}} => 3
[[1,5,6],[2],[3],[4]] => [[1,2,3,4],[5],[6]] => {{1,2,3,4},{5},{6}} => {{1,2,3,4},{5},{6}} => 6
[[1,4,6],[2],[3],[5]] => [[1,2,3,5],[4],[6]] => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}} => 6
[[1,3,6],[2],[4],[5]] => [[1,2,4,5],[3],[6]] => {{1,2,4,5},{3},{6}} => {{1,2,4,5},{3},{6}} => 6
[[1,2,6],[3],[4],[5]] => [[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => {{1,3,4,5},{2},{6}} => 6
[[1,4,5],[2],[3],[6]] => [[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}} => 5
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => {{1,2,4,6},{3},{5}} => 5
[[1,2,5],[3],[4],[6]] => [[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => 5
[[1,3,4],[2],[5],[6]] => [[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => 4
[[1,2,4],[3],[5],[6]] => [[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => {{1,3,5,6},{2},{4}} => 4
[[1,2,3],[4],[5],[6]] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => {{1,4,5,6},{2},{3}} => 3
[[1,4],[2,5],[3,6]] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => 4
[[1,3],[2,5],[4,6]] => [[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => {{1,2,5,6},{3,4}} => 3
>>> Load all 645 entries. <<<[[1,2],[3,5],[4,6]] => [[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => {{1,4},{2,3,5,6}} => 2
[[1,3],[2,4],[5,6]] => [[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => {{1,2,4,5},{3,6}} => 3
[[1,2],[3,4],[5,6]] => [[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => {{1,6},{2,3,4,5}} => 2
[[1,5],[2,6],[3],[4]] => [[1,2,3,4],[5,6]] => {{1,2,3,4},{5,6}} => {{1,2,3,4},{5,6}} => 5
[[1,4],[2,6],[3],[5]] => [[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => {{1,2,3,6},{4,5}} => 4
[[1,3],[2,6],[4],[5]] => [[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => {{1,2,5},{3,4,6}} => 3
[[1,2],[3,6],[4],[5]] => [[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => {{1,4,6},{2,3,5}} => 2
[[1,4],[2,5],[3],[6]] => [[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}} => 4
[[1,3],[2,5],[4],[6]] => [[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => {{1,2,6},{3,4,5}} => 3
[[1,2],[3,5],[4],[6]] => [[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => {{1,4,5},{2,3,6}} => 2
[[1,3],[2,4],[5],[6]] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => {{1,2,4},{3,5,6}} => 3
[[1,2],[3,4],[5],[6]] => [[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => {{1,5,6},{2,3,4}} => 2
[[1,6],[2],[3],[4],[5]] => [[1,2,3,4,5],[6]] => {{1,2,3,4,5},{6}} => {{1,2,3,4,5},{6}} => 6
[[1,5],[2],[3],[4],[6]] => [[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}} => 5
[[1,4],[2],[3],[5],[6]] => [[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => {{1,2,3,5,6},{4}} => 4
[[1,3],[2],[4],[5],[6]] => [[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => {{1,2,4,5,6},{3}} => 3
[[1,2],[3],[4],[5],[6]] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => {{1,3,4,5,6},{2}} => 2
[[1],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6]] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => 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}} => 7
[[1,3,4,5,6,7],[2]] => [[1,2],[3],[4],[5],[6],[7]] => {{1,2},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7}} => 7
[[1,2,4,5,6,7],[3]] => [[1,3],[2],[4],[5],[6],[7]] => {{1,3},{2},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => 7
[[1,2,3,5,6,7],[4]] => [[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => 7
[[1,2,3,4,6,7],[5]] => [[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => 7
[[1,2,3,4,5,7],[6]] => [[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => {{1,6},{2},{3},{4},{5},{7}} => 7
[[1,2,3,4,5,6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => 6
[[1,3,5,6,7],[2,4]] => [[1,2],[3,4],[5],[6],[7]] => {{1,2},{3,4},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}} => 7
[[1,2,5,6,7],[3,4]] => [[1,3],[2,4],[5],[6],[7]] => {{1,3},{2,4},{5},{6},{7}} => {{1,4},{2,3},{5},{6},{7}} => 7
[[1,3,4,6,7],[2,5]] => [[1,2],[3,5],[4],[6],[7]] => {{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}} => 7
[[1,2,4,6,7],[3,5]] => [[1,3],[2,5],[4],[6],[7]] => {{1,3},{2,5},{4},{6},{7}} => {{1,5},{2,3},{4},{6},{7}} => 7
[[1,2,3,6,7],[4,5]] => [[1,4],[2,5],[3],[6],[7]] => {{1,4},{2,5},{3},{6},{7}} => {{1,5},{2,4},{3},{6},{7}} => 7
[[1,3,4,5,7],[2,6]] => [[1,2],[3,6],[4],[5],[7]] => {{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}} => 7
[[1,2,4,5,7],[3,6]] => [[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => {{1,6},{2,3},{4},{5},{7}} => 7
[[1,2,3,5,7],[4,6]] => [[1,4],[2,6],[3],[5],[7]] => {{1,4},{2,6},{3},{5},{7}} => {{1,6},{2,4},{3},{5},{7}} => 7
[[1,2,3,4,7],[5,6]] => [[1,5],[2,6],[3],[4],[7]] => {{1,5},{2,6},{3},{4},{7}} => {{1,6},{2,5},{3},{4},{7}} => 7
[[1,3,4,5,6],[2,7]] => [[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}} => 6
[[1,2,4,5,6],[3,7]] => [[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => {{1,7},{2,3},{4},{5},{6}} => 6
[[1,2,3,5,6],[4,7]] => [[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => {{1,7},{2,4},{3},{5},{6}} => 6
[[1,2,3,4,6],[5,7]] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => {{1,7},{2,5},{3},{4},{6}} => 6
[[1,2,3,4,5],[6,7]] => [[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => 5
[[1,4,5,6,7],[2],[3]] => [[1,2,3],[4],[5],[6],[7]] => {{1,2,3},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}} => 7
[[1,3,5,6,7],[2],[4]] => [[1,2,4],[3],[5],[6],[7]] => {{1,2,4},{3},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => 7
[[1,2,5,6,7],[3],[4]] => [[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => 7
[[1,3,4,6,7],[2],[5]] => [[1,2,5],[3],[4],[6],[7]] => {{1,2,5},{3},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => 7
[[1,2,4,6,7],[3],[5]] => [[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => 7
[[1,2,3,6,7],[4],[5]] => [[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => 7
[[1,3,4,5,7],[2],[6]] => [[1,2,6],[3],[4],[5],[7]] => {{1,2,6},{3},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}} => 7
[[1,2,4,5,7],[3],[6]] => [[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => {{1,3,6},{2},{4},{5},{7}} => 7
[[1,2,3,5,7],[4],[6]] => [[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => {{1,4,6},{2},{3},{5},{7}} => 7
[[1,2,3,4,7],[5],[6]] => [[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => {{1,5,6},{2},{3},{4},{7}} => 7
[[1,3,4,5,6],[2],[7]] => [[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}} => 6
[[1,2,4,5,6],[3],[7]] => [[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => {{1,3,7},{2},{4},{5},{6}} => 6
[[1,2,3,5,6],[4],[7]] => [[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => 6
[[1,2,3,4,6],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => {{1,5,7},{2},{3},{4},{6}} => 6
[[1,2,3,4,5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => {{1,6,7},{2},{3},{4},{5}} => 5
[[1,3,5,7],[2,4,6]] => [[1,2],[3,4],[5,6],[7]] => {{1,2},{3,4},{5,6},{7}} => {{1,2},{3,4},{5,6},{7}} => 7
[[1,2,5,7],[3,4,6]] => [[1,3],[2,4],[5,6],[7]] => {{1,3},{2,4},{5,6},{7}} => {{1,4},{2,3},{5,6},{7}} => 7
[[1,3,4,7],[2,5,6]] => [[1,2],[3,5],[4,6],[7]] => {{1,2},{3,5},{4,6},{7}} => {{1,2},{3,6},{4,5},{7}} => 7
[[1,2,4,7],[3,5,6]] => [[1,3],[2,5],[4,6],[7]] => {{1,3},{2,5},{4,6},{7}} => {{1,6},{2,3},{4,5},{7}} => 7
[[1,2,3,7],[4,5,6]] => [[1,4],[2,5],[3,6],[7]] => {{1,4},{2,5},{3,6},{7}} => {{1,6},{2,5},{3,4},{7}} => 7
[[1,3,5,6],[2,4,7]] => [[1,2],[3,4],[5,7],[6]] => {{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}} => 6
[[1,2,5,6],[3,4,7]] => [[1,3],[2,4],[5,7],[6]] => {{1,3},{2,4},{5,7},{6}} => {{1,4},{2,3},{5,7},{6}} => 6
[[1,3,4,6],[2,5,7]] => [[1,2],[3,5],[4,7],[6]] => {{1,2},{3,5},{4,7},{6}} => {{1,2},{3,7},{4,5},{6}} => 6
[[1,2,4,6],[3,5,7]] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => {{1,7},{2,3},{4,5},{6}} => 6
[[1,2,3,6],[4,5,7]] => [[1,4],[2,5],[3,7],[6]] => {{1,4},{2,5},{3,7},{6}} => {{1,7},{2,5},{3,4},{6}} => 6
[[1,3,4,5],[2,6,7]] => [[1,2],[3,6],[4,7],[5]] => {{1,2},{3,6},{4,7},{5}} => {{1,2},{3,7},{4,6},{5}} => 5
[[1,2,4,5],[3,6,7]] => [[1,3],[2,6],[4,7],[5]] => {{1,3},{2,6},{4,7},{5}} => {{1,7},{2,3},{4,6},{5}} => 5
[[1,2,3,5],[4,6,7]] => [[1,4],[2,6],[3,7],[5]] => {{1,4},{2,6},{3,7},{5}} => {{1,7},{2,6},{3,4},{5}} => 5
[[1,2,3,4],[5,6,7]] => [[1,5],[2,6],[3,7],[4]] => {{1,5},{2,6},{3,7},{4}} => {{1,7},{2,6},{3,5},{4}} => 4
[[1,4,6,7],[2,5],[3]] => [[1,2,3],[4,5],[6],[7]] => {{1,2,3},{4,5},{6},{7}} => {{1,2,3},{4,5},{6},{7}} => 7
[[1,3,6,7],[2,5],[4]] => [[1,2,4],[3,5],[6],[7]] => {{1,2,4},{3,5},{6},{7}} => {{1,2,5},{3,4},{6},{7}} => 7
[[1,2,6,7],[3,5],[4]] => [[1,3,4],[2,5],[6],[7]] => {{1,3,4},{2,5},{6},{7}} => {{1,4},{2,3,5},{6},{7}} => 7
[[1,3,6,7],[2,4],[5]] => [[1,2,5],[3,4],[6],[7]] => {{1,2,5},{3,4},{6},{7}} => {{1,2,4},{3,5},{6},{7}} => 7
[[1,2,6,7],[3,4],[5]] => [[1,3,5],[2,4],[6],[7]] => {{1,3,5},{2,4},{6},{7}} => {{1,5},{2,3,4},{6},{7}} => 7
[[1,4,5,7],[2,6],[3]] => [[1,2,3],[4,6],[5],[7]] => {{1,2,3},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}} => 7
[[1,3,5,7],[2,6],[4]] => [[1,2,4],[3,6],[5],[7]] => {{1,2,4},{3,6},{5},{7}} => {{1,2,6},{3,4},{5},{7}} => 7
[[1,2,5,7],[3,6],[4]] => [[1,3,4],[2,6],[5],[7]] => {{1,3,4},{2,6},{5},{7}} => {{1,4},{2,3,6},{5},{7}} => 7
[[1,3,4,7],[2,6],[5]] => [[1,2,5],[3,6],[4],[7]] => {{1,2,5},{3,6},{4},{7}} => {{1,2,6},{3,5},{4},{7}} => 7
[[1,2,4,7],[3,6],[5]] => [[1,3,5],[2,6],[4],[7]] => {{1,3,5},{2,6},{4},{7}} => {{1,5},{2,3,6},{4},{7}} => 7
[[1,2,3,7],[4,6],[5]] => [[1,4,5],[2,6],[3],[7]] => {{1,4,5},{2,6},{3},{7}} => {{1,5},{2,4,6},{3},{7}} => 7
[[1,3,5,7],[2,4],[6]] => [[1,2,6],[3,4],[5],[7]] => {{1,2,6},{3,4},{5},{7}} => {{1,2,4},{3,6},{5},{7}} => 7
[[1,2,5,7],[3,4],[6]] => [[1,3,6],[2,4],[5],[7]] => {{1,3,6},{2,4},{5},{7}} => {{1,6},{2,3,4},{5},{7}} => 7
[[1,3,4,7],[2,5],[6]] => [[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => {{1,2,5},{3,6},{4},{7}} => 7
[[1,2,4,7],[3,5],[6]] => [[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => {{1,6},{2,3,5},{4},{7}} => 7
[[1,2,3,7],[4,5],[6]] => [[1,4,6],[2,5],[3],[7]] => {{1,4,6},{2,5},{3},{7}} => {{1,6},{2,4,5},{3},{7}} => 7
[[1,4,5,6],[2,7],[3]] => [[1,2,3],[4,7],[5],[6]] => {{1,2,3},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}} => 6
[[1,3,5,6],[2,7],[4]] => [[1,2,4],[3,7],[5],[6]] => {{1,2,4},{3,7},{5},{6}} => {{1,2,7},{3,4},{5},{6}} => 6
[[1,2,5,6],[3,7],[4]] => [[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => {{1,4},{2,3,7},{5},{6}} => 6
[[1,3,4,6],[2,7],[5]] => [[1,2,5],[3,7],[4],[6]] => {{1,2,5},{3,7},{4},{6}} => {{1,2,7},{3,5},{4},{6}} => 6
[[1,2,4,6],[3,7],[5]] => [[1,3,5],[2,7],[4],[6]] => {{1,3,5},{2,7},{4},{6}} => {{1,5},{2,3,7},{4},{6}} => 6
[[1,2,3,6],[4,7],[5]] => [[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => {{1,5},{2,4,7},{3},{6}} => 6
[[1,3,4,5],[2,7],[6]] => [[1,2,6],[3,7],[4],[5]] => {{1,2,6},{3,7},{4},{5}} => {{1,2,7},{3,6},{4},{5}} => 5
[[1,2,4,5],[3,7],[6]] => [[1,3,6],[2,7],[4],[5]] => {{1,3,6},{2,7},{4},{5}} => {{1,6},{2,3,7},{4},{5}} => 5
[[1,2,3,5],[4,7],[6]] => [[1,4,6],[2,7],[3],[5]] => {{1,4,6},{2,7},{3},{5}} => {{1,6},{2,4,7},{3},{5}} => 5
[[1,2,3,4],[5,7],[6]] => [[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => {{1,6},{2,5,7},{3},{4}} => 4
[[1,3,5,6],[2,4],[7]] => [[1,2,7],[3,4],[5],[6]] => {{1,2,7},{3,4},{5},{6}} => {{1,2,4},{3,7},{5},{6}} => 6
[[1,2,5,6],[3,4],[7]] => [[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => {{1,7},{2,3,4},{5},{6}} => 6
[[1,3,4,6],[2,5],[7]] => [[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => {{1,2,5},{3,7},{4},{6}} => 6
[[1,2,4,6],[3,5],[7]] => [[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => {{1,7},{2,3,5},{4},{6}} => 6
[[1,2,3,6],[4,5],[7]] => [[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => {{1,7},{2,4,5},{3},{6}} => 6
[[1,3,4,5],[2,6],[7]] => [[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => {{1,2,6},{3,7},{4},{5}} => 5
[[1,2,4,5],[3,6],[7]] => [[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => {{1,7},{2,3,6},{4},{5}} => 5
[[1,2,3,5],[4,6],[7]] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => {{1,7},{2,4,6},{3},{5}} => 5
[[1,2,3,4],[5,6],[7]] => [[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => {{1,7},{2,5,6},{3},{4}} => 4
[[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => {{1,2,3,4},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}} => 7
[[1,4,6,7],[2],[3],[5]] => [[1,2,3,5],[4],[6],[7]] => {{1,2,3,5},{4},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => 7
[[1,3,6,7],[2],[4],[5]] => [[1,2,4,5],[3],[6],[7]] => {{1,2,4,5},{3},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => 7
[[1,2,6,7],[3],[4],[5]] => [[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => 7
[[1,4,5,7],[2],[3],[6]] => [[1,2,3,6],[4],[5],[7]] => {{1,2,3,6},{4},{5},{7}} => {{1,2,3,6},{4},{5},{7}} => 7
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => {{1,2,4,6},{3},{5},{7}} => {{1,2,4,6},{3},{5},{7}} => 7
[[1,2,5,7],[3],[4],[6]] => [[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => {{1,3,4,6},{2},{5},{7}} => 7
[[1,3,4,7],[2],[5],[6]] => [[1,2,5,6],[3],[4],[7]] => {{1,2,5,6},{3},{4},{7}} => {{1,2,5,6},{3},{4},{7}} => 7
[[1,2,4,7],[3],[5],[6]] => [[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => {{1,3,5,6},{2},{4},{7}} => 7
[[1,2,3,7],[4],[5],[6]] => [[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => {{1,4,5,6},{2},{3},{7}} => 7
[[1,4,5,6],[2],[3],[7]] => [[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => {{1,2,3,7},{4},{5},{6}} => 6
[[1,3,5,6],[2],[4],[7]] => [[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => {{1,2,4,7},{3},{5},{6}} => 6
[[1,2,5,6],[3],[4],[7]] => [[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => {{1,3,4,7},{2},{5},{6}} => 6
[[1,3,4,6],[2],[5],[7]] => [[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => {{1,2,5,7},{3},{4},{6}} => 6
[[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => 6
[[1,2,3,6],[4],[5],[7]] => [[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => {{1,4,5,7},{2},{3},{6}} => 6
[[1,3,4,5],[2],[6],[7]] => [[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => 5
[[1,2,4,5],[3],[6],[7]] => [[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => {{1,3,6,7},{2},{4},{5}} => 5
[[1,2,3,5],[4],[6],[7]] => [[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => {{1,4,6,7},{2},{3},{5}} => 5
[[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => {{1,5,6,7},{2},{3},{4}} => 4
[[1,4,6],[2,5,7],[3]] => [[1,2,3],[4,5],[6,7]] => {{1,2,3},{4,5},{6,7}} => {{1,2,3},{4,5},{6,7}} => 6
[[1,3,6],[2,5,7],[4]] => [[1,2,4],[3,5],[6,7]] => {{1,2,4},{3,5},{6,7}} => {{1,2,5},{3,4},{6,7}} => 6
[[1,2,6],[3,5,7],[4]] => [[1,3,4],[2,5],[6,7]] => {{1,3,4},{2,5},{6,7}} => {{1,4},{2,3,5},{6,7}} => 6
[[1,3,6],[2,4,7],[5]] => [[1,2,5],[3,4],[6,7]] => {{1,2,5},{3,4},{6,7}} => {{1,2,4},{3,5},{6,7}} => 6
[[1,2,6],[3,4,7],[5]] => [[1,3,5],[2,4],[6,7]] => {{1,3,5},{2,4},{6,7}} => {{1,5},{2,3,4},{6,7}} => 6
[[1,4,5],[2,6,7],[3]] => [[1,2,3],[4,6],[5,7]] => {{1,2,3},{4,6},{5,7}} => {{1,2,3},{4,7},{5,6}} => 5
[[1,3,5],[2,6,7],[4]] => [[1,2,4],[3,6],[5,7]] => {{1,2,4},{3,6},{5,7}} => {{1,2,7},{3,4},{5,6}} => 5
[[1,2,5],[3,6,7],[4]] => [[1,3,4],[2,6],[5,7]] => {{1,3,4},{2,6},{5,7}} => {{1,4},{2,3,7},{5,6}} => 5
[[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,6],[4,7]] => {{1,2,5},{3,6},{4,7}} => {{1,2,7},{3,6},{4,5}} => 4
[[1,2,4],[3,6,7],[5]] => [[1,3,5],[2,6],[4,7]] => {{1,3,5},{2,6},{4,7}} => {{1,5},{2,3,7},{4,6}} => 4
[[1,2,3],[4,6,7],[5]] => [[1,4,5],[2,6],[3,7]] => {{1,4,5},{2,6},{3,7}} => {{1,7},{2,5},{3,4,6}} => 3
[[1,3,5],[2,4,7],[6]] => [[1,2,6],[3,4],[5,7]] => {{1,2,6},{3,4},{5,7}} => {{1,2,4},{3,7},{5,6}} => 5
[[1,2,5],[3,4,7],[6]] => [[1,3,6],[2,4],[5,7]] => {{1,3,6},{2,4},{5,7}} => {{1,7},{2,3,4},{5,6}} => 5
[[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5],[4,7]] => {{1,2,6},{3,5},{4,7}} => {{1,2,5},{3,7},{4,6}} => 4
[[1,2,4],[3,5,7],[6]] => [[1,3,6],[2,5],[4,7]] => {{1,3,6},{2,5},{4,7}} => {{1,7},{2,3,6},{4,5}} => 4
[[1,2,3],[4,5,7],[6]] => [[1,4,6],[2,5],[3,7]] => {{1,4,6},{2,5},{3,7}} => {{1,6},{2,5},{3,4,7}} => 3
[[1,3,5],[2,4,6],[7]] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => {{1,2,4},{3,6},{5,7}} => 5
[[1,2,5],[3,4,6],[7]] => [[1,3,7],[2,4],[5,6]] => {{1,3,7},{2,4},{5,6}} => {{1,6},{2,3,4},{5,7}} => 5
[[1,3,4],[2,5,6],[7]] => [[1,2,7],[3,5],[4,6]] => {{1,2,7},{3,5},{4,6}} => {{1,2,6},{3,7},{4,5}} => 4
[[1,2,4],[3,5,6],[7]] => [[1,3,7],[2,5],[4,6]] => {{1,3,7},{2,5},{4,6}} => {{1,6},{2,3,5},{4,7}} => 4
[[1,2,3],[4,5,6],[7]] => [[1,4,7],[2,5],[3,6]] => {{1,4,7},{2,5},{3,6}} => {{1,7},{2,6},{3,4,5}} => 3
[[1,4,7],[2,5],[3,6]] => [[1,2,3],[4,5,6],[7]] => {{1,2,3},{4,5,6},{7}} => {{1,2,3},{4,5,6},{7}} => 7
[[1,3,7],[2,5],[4,6]] => [[1,2,4],[3,5,6],[7]] => {{1,2,4},{3,5,6},{7}} => {{1,2,5,6},{3,4},{7}} => 7
[[1,2,7],[3,5],[4,6]] => [[1,3,4],[2,5,6],[7]] => {{1,3,4},{2,5,6},{7}} => {{1,4},{2,3,5,6},{7}} => 7
[[1,3,7],[2,4],[5,6]] => [[1,2,5],[3,4,6],[7]] => {{1,2,5},{3,4,6},{7}} => {{1,2,4,5},{3,6},{7}} => 7
[[1,2,7],[3,4],[5,6]] => [[1,3,5],[2,4,6],[7]] => {{1,3,5},{2,4,6},{7}} => {{1,6},{2,3,4,5},{7}} => 7
[[1,4,6],[2,5],[3,7]] => [[1,2,3],[4,5,7],[6]] => {{1,2,3},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}} => 6
[[1,3,6],[2,5],[4,7]] => [[1,2,4],[3,5,7],[6]] => {{1,2,4},{3,5,7},{6}} => {{1,2,5,7},{3,4},{6}} => 6
[[1,2,6],[3,5],[4,7]] => [[1,3,4],[2,5,7],[6]] => {{1,3,4},{2,5,7},{6}} => {{1,4},{2,3,5,7},{6}} => 6
[[1,3,6],[2,4],[5,7]] => [[1,2,5],[3,4,7],[6]] => {{1,2,5},{3,4,7},{6}} => {{1,2,4,5},{3,7},{6}} => 6
[[1,2,6],[3,4],[5,7]] => [[1,3,5],[2,4,7],[6]] => {{1,3,5},{2,4,7},{6}} => {{1,7},{2,3,4,5},{6}} => 6
[[1,4,5],[2,6],[3,7]] => [[1,2,3],[4,6,7],[5]] => {{1,2,3},{4,6,7},{5}} => {{1,2,3},{4,6,7},{5}} => 5
[[1,3,5],[2,6],[4,7]] => [[1,2,4],[3,6,7],[5]] => {{1,2,4},{3,6,7},{5}} => {{1,2,6,7},{3,4},{5}} => 5
[[1,2,5],[3,6],[4,7]] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => {{1,4},{2,3,6,7},{5}} => 5
[[1,3,4],[2,6],[5,7]] => [[1,2,5],[3,6,7],[4]] => {{1,2,5},{3,6,7},{4}} => {{1,2,6,7},{3,5},{4}} => 4
[[1,2,4],[3,6],[5,7]] => [[1,3,5],[2,6,7],[4]] => {{1,3,5},{2,6,7},{4}} => {{1,5},{2,3,6,7},{4}} => 4
[[1,2,3],[4,6],[5,7]] => [[1,4,5],[2,6,7],[3]] => {{1,4,5},{2,6,7},{3}} => {{1,5},{2,4,6,7},{3}} => 3
[[1,3,5],[2,4],[6,7]] => [[1,2,6],[3,4,7],[5]] => {{1,2,6},{3,4,7},{5}} => {{1,2,4,6},{3,7},{5}} => 5
[[1,2,5],[3,4],[6,7]] => [[1,3,6],[2,4,7],[5]] => {{1,3,6},{2,4,7},{5}} => {{1,7},{2,3,4,6},{5}} => 5
[[1,3,4],[2,5],[6,7]] => [[1,2,6],[3,5,7],[4]] => {{1,2,6},{3,5,7},{4}} => {{1,2,5,6},{3,7},{4}} => 4
[[1,2,4],[3,5],[6,7]] => [[1,3,6],[2,5,7],[4]] => {{1,3,6},{2,5,7},{4}} => {{1,7},{2,3,5,6},{4}} => 4
[[1,2,3],[4,5],[6,7]] => [[1,4,6],[2,5,7],[3]] => {{1,4,6},{2,5,7},{3}} => {{1,7},{2,4,5,6},{3}} => 3
[[1,5,7],[2,6],[3],[4]] => [[1,2,3,4],[5,6],[7]] => {{1,2,3,4},{5,6},{7}} => {{1,2,3,4},{5,6},{7}} => 7
[[1,4,7],[2,6],[3],[5]] => [[1,2,3,5],[4,6],[7]] => {{1,2,3,5},{4,6},{7}} => {{1,2,3,6},{4,5},{7}} => 7
[[1,3,7],[2,6],[4],[5]] => [[1,2,4,5],[3,6],[7]] => {{1,2,4,5},{3,6},{7}} => {{1,2,5},{3,4,6},{7}} => 7
[[1,2,7],[3,6],[4],[5]] => [[1,3,4,5],[2,6],[7]] => {{1,3,4,5},{2,6},{7}} => {{1,4,6},{2,3,5},{7}} => 7
[[1,4,7],[2,5],[3],[6]] => [[1,2,3,6],[4,5],[7]] => {{1,2,3,6},{4,5},{7}} => {{1,2,3,5},{4,6},{7}} => 7
[[1,3,7],[2,5],[4],[6]] => [[1,2,4,6],[3,5],[7]] => {{1,2,4,6},{3,5},{7}} => {{1,2,6},{3,4,5},{7}} => 7
[[1,2,7],[3,5],[4],[6]] => [[1,3,4,6],[2,5],[7]] => {{1,3,4,6},{2,5},{7}} => {{1,4,5},{2,3,6},{7}} => 7
[[1,3,7],[2,4],[5],[6]] => [[1,2,5,6],[3,4],[7]] => {{1,2,5,6},{3,4},{7}} => {{1,2,4},{3,5,6},{7}} => 7
[[1,2,7],[3,4],[5],[6]] => [[1,3,5,6],[2,4],[7]] => {{1,3,5,6},{2,4},{7}} => {{1,5,6},{2,3,4},{7}} => 7
[[1,5,6],[2,7],[3],[4]] => [[1,2,3,4],[5,7],[6]] => {{1,2,3,4},{5,7},{6}} => {{1,2,3,4},{5,7},{6}} => 6
[[1,4,6],[2,7],[3],[5]] => [[1,2,3,5],[4,7],[6]] => {{1,2,3,5},{4,7},{6}} => {{1,2,3,7},{4,5},{6}} => 6
[[1,3,6],[2,7],[4],[5]] => [[1,2,4,5],[3,7],[6]] => {{1,2,4,5},{3,7},{6}} => {{1,2,5},{3,4,7},{6}} => 6
[[1,2,6],[3,7],[4],[5]] => [[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => {{1,4,7},{2,3,5},{6}} => 6
[[1,4,5],[2,7],[3],[6]] => [[1,2,3,6],[4,7],[5]] => {{1,2,3,6},{4,7},{5}} => {{1,2,3,7},{4,6},{5}} => 5
[[1,3,5],[2,7],[4],[6]] => [[1,2,4,6],[3,7],[5]] => {{1,2,4,6},{3,7},{5}} => {{1,2,6},{3,4,7},{5}} => 5
[[1,2,5],[3,7],[4],[6]] => [[1,3,4,6],[2,7],[5]] => {{1,3,4,6},{2,7},{5}} => {{1,4,7},{2,3,6},{5}} => 5
[[1,3,4],[2,7],[5],[6]] => [[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => {{1,2,6},{3,5,7},{4}} => 4
[[1,2,4],[3,7],[5],[6]] => [[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => {{1,5,7},{2,3,6},{4}} => 4
[[1,2,3],[4,7],[5],[6]] => [[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => {{1,5,7},{2,4,6},{3}} => 3
[[1,4,6],[2,5],[3],[7]] => [[1,2,3,7],[4,5],[6]] => {{1,2,3,7},{4,5},{6}} => {{1,2,3,5},{4,7},{6}} => 6
[[1,3,6],[2,5],[4],[7]] => [[1,2,4,7],[3,5],[6]] => {{1,2,4,7},{3,5},{6}} => {{1,2,7},{3,4,5},{6}} => 6
[[1,2,6],[3,5],[4],[7]] => [[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => {{1,4,5},{2,3,7},{6}} => 6
[[1,3,6],[2,4],[5],[7]] => [[1,2,5,7],[3,4],[6]] => {{1,2,5,7},{3,4},{6}} => {{1,2,4},{3,5,7},{6}} => 6
[[1,2,6],[3,4],[5],[7]] => [[1,3,5,7],[2,4],[6]] => {{1,3,5,7},{2,4},{6}} => {{1,5,7},{2,3,4},{6}} => 6
[[1,4,5],[2,6],[3],[7]] => [[1,2,3,7],[4,6],[5]] => {{1,2,3,7},{4,6},{5}} => {{1,2,3,6},{4,7},{5}} => 5
[[1,3,5],[2,6],[4],[7]] => [[1,2,4,7],[3,6],[5]] => {{1,2,4,7},{3,6},{5}} => {{1,2,7},{3,4,6},{5}} => 5
[[1,2,5],[3,6],[4],[7]] => [[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => {{1,4,6},{2,3,7},{5}} => 5
[[1,3,4],[2,6],[5],[7]] => [[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => {{1,2,7},{3,5,6},{4}} => 4
[[1,2,4],[3,6],[5],[7]] => [[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => {{1,5,6},{2,3,7},{4}} => 4
[[1,2,3],[4,6],[5],[7]] => [[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => {{1,5,6},{2,4,7},{3}} => 3
[[1,3,5],[2,4],[6],[7]] => [[1,2,6,7],[3,4],[5]] => {{1,2,6,7},{3,4},{5}} => {{1,2,4},{3,6,7},{5}} => 5
[[1,2,5],[3,4],[6],[7]] => [[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => {{1,6,7},{2,3,4},{5}} => 5
[[1,3,4],[2,5],[6],[7]] => [[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => {{1,2,5},{3,6,7},{4}} => 4
[[1,2,4],[3,5],[6],[7]] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => {{1,6,7},{2,3,5},{4}} => 4
[[1,2,3],[4,5],[6],[7]] => [[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => {{1,6,7},{2,4,5},{3}} => 3
[[1,6,7],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7]] => {{1,2,3,4,5},{6},{7}} => {{1,2,3,4,5},{6},{7}} => 7
[[1,5,7],[2],[3],[4],[6]] => [[1,2,3,4,6],[5],[7]] => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4,6},{5},{7}} => 7
[[1,4,7],[2],[3],[5],[6]] => [[1,2,3,5,6],[4],[7]] => {{1,2,3,5,6},{4},{7}} => {{1,2,3,5,6},{4},{7}} => 7
[[1,3,7],[2],[4],[5],[6]] => [[1,2,4,5,6],[3],[7]] => {{1,2,4,5,6},{3},{7}} => {{1,2,4,5,6},{3},{7}} => 7
[[1,2,7],[3],[4],[5],[6]] => [[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => {{1,3,4,5,6},{2},{7}} => 7
[[1,5,6],[2],[3],[4],[7]] => [[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4,7},{5},{6}} => 6
[[1,4,6],[2],[3],[5],[7]] => [[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => {{1,2,3,5,7},{4},{6}} => 6
[[1,3,6],[2],[4],[5],[7]] => [[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => {{1,2,4,5,7},{3},{6}} => 6
[[1,2,6],[3],[4],[5],[7]] => [[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}} => 6
[[1,4,5],[2],[3],[6],[7]] => [[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => {{1,2,3,6,7},{4},{5}} => 5
[[1,3,5],[2],[4],[6],[7]] => [[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}} => 5
[[1,2,5],[3],[4],[6],[7]] => [[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => {{1,3,4,6,7},{2},{5}} => 5
[[1,3,4],[2],[5],[6],[7]] => [[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => {{1,2,5,6,7},{3},{4}} => 4
[[1,2,4],[3],[5],[6],[7]] => [[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => {{1,3,5,6,7},{2},{4}} => 4
[[1,2,3],[4],[5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => {{1,4,5,6,7},{2},{3}} => 3
[[1,5],[2,6],[3,7],[4]] => [[1,2,3,4],[5,6,7]] => {{1,2,3,4},{5,6,7}} => {{1,2,3,4},{5,6,7}} => 5
[[1,4],[2,6],[3,7],[5]] => [[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => {{1,2,3,6,7},{4,5}} => 4
[[1,3],[2,6],[4,7],[5]] => [[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => {{1,2,5},{3,4,6,7}} => 3
[[1,2],[3,6],[4,7],[5]] => [[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => {{1,4,6,7},{2,3,5}} => 2
[[1,4],[2,5],[3,7],[6]] => [[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => {{1,2,3,5,6},{4,7}} => 4
[[1,3],[2,5],[4,7],[6]] => [[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => {{1,2,7},{3,4,5,6}} => 3
[[1,2],[3,5],[4,7],[6]] => [[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => {{1,4,5,6},{2,3,7}} => 2
[[1,3],[2,4],[5,7],[6]] => [[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => {{1,2,4,5,7},{3,6}} => 3
[[1,2],[3,4],[5,7],[6]] => [[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => {{1,6},{2,3,4,5,7}} => 2
[[1,4],[2,5],[3,6],[7]] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => {{1,2,3,5,7},{4,6}} => 4
[[1,3],[2,5],[4,6],[7]] => [[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => {{1,2,6},{3,4,5,7}} => 3
[[1,2],[3,5],[4,6],[7]] => [[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => {{1,4,5,7},{2,3,6}} => 2
[[1,3],[2,4],[5,6],[7]] => [[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => {{1,2,4,5,6},{3,7}} => 3
[[1,2],[3,4],[5,6],[7]] => [[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => {{1,7},{2,3,4,5,6}} => 2
[[1,6],[2,7],[3],[4],[5]] => [[1,2,3,4,5],[6,7]] => {{1,2,3,4,5},{6,7}} => {{1,2,3,4,5},{6,7}} => 6
[[1,5],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => {{1,2,3,4,7},{5,6}} => 5
[[1,4],[2,7],[3],[5],[6]] => [[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => {{1,2,3,6},{4,5,7}} => 4
[[1,3],[2,7],[4],[5],[6]] => [[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => {{1,2,5,7},{3,4,6}} => 3
[[1,2],[3,7],[4],[5],[6]] => [[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => {{1,4,6},{2,3,5,7}} => 2
[[1,5],[2,6],[3],[4],[7]] => [[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => {{1,2,3,4,6},{5,7}} => 5
[[1,4],[2,6],[3],[5],[7]] => [[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => {{1,2,3,7},{4,5,6}} => 4
[[1,3],[2,6],[4],[5],[7]] => [[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => {{1,2,5,6},{3,4,7}} => 3
[[1,2],[3,6],[4],[5],[7]] => [[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => {{1,4,7},{2,3,5,6}} => 2
[[1,4],[2,5],[3],[6],[7]] => [[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => {{1,2,3,5},{4,6,7}} => 4
[[1,3],[2,5],[4],[6],[7]] => [[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => {{1,2,6,7},{3,4,5}} => 3
[[1,2],[3,5],[4],[6],[7]] => [[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => {{1,4,5},{2,3,6,7}} => 2
[[1,3],[2,4],[5],[6],[7]] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => {{1,2,4},{3,5,6,7}} => 3
[[1,2],[3,4],[5],[6],[7]] => [[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,3,4}} => 2
[[1,7],[2],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7]] => {{1,2,3,4,5,6},{7}} => {{1,2,3,4,5,6},{7}} => 7
[[1,6],[2],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5,7},{6}} => 6
[[1,5],[2],[3],[4],[6],[7]] => [[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => {{1,2,3,4,6,7},{5}} => 5
[[1,4],[2],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}} => 4
[[1,3],[2],[4],[5],[6],[7]] => [[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => {{1,2,4,5,6,7},{3}} => 3
[[1,2],[3],[4],[5],[6],[7]] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => {{1,3,4,5,6,7},{2}} => 2
[[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}} => 1
[[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}} => 8
[[1,2,3,4,5,6,7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => {{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}} => 7
[[1,2,4,5,6,7],[3,8]] => [[1,3],[2,8],[4],[5],[6],[7]] => {{1,3},{2,8},{4},{5},{6},{7}} => {{1,8},{2,3},{4},{5},{6},{7}} => 7
[[1,2,3,5,6,7],[4,8]] => [[1,4],[2,8],[3],[5],[6],[7]] => {{1,4},{2,8},{3},{5},{6},{7}} => {{1,8},{2,4},{3},{5},{6},{7}} => 7
[[1,2,3,4,8],[5,6,7]] => [[1,5],[2,6],[3,7],[4],[8]] => {{1,5},{2,6},{3,7},{4},{8}} => {{1,7},{2,6},{3,5},{4},{8}} => 8
[[1,2,3,5,8],[4,6],[7]] => [[1,4,7],[2,6],[3],[5],[8]] => {{1,4,7},{2,6},{3},{5},{8}} => {{1,7},{2,4,6},{3},{5},{8}} => 8
[[1,2,5,6,7],[3,4],[8]] => [[1,3,8],[2,4],[5],[6],[7]] => {{1,3,8},{2,4},{5},{6},{7}} => {{1,8},{2,3,4},{5},{6},{7}} => 7
[[1,2,4,6,8],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6],[8]] => {{1,3,5,7},{2},{4},{6},{8}} => {{1,3,5,7},{2},{4},{6},{8}} => 8
[[1,3,5,7],[2,4,6,8]] => [[1,2],[3,4],[5,6],[7,8]] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => 7
[[1,2,5,7],[3,4,6,8]] => [[1,3],[2,4],[5,6],[7,8]] => {{1,3},{2,4},{5,6},{7,8}} => {{1,4},{2,3},{5,6},{7,8}} => 7
[[1,3,4,7],[2,5,6,8]] => [[1,2],[3,5],[4,6],[7,8]] => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => 7
[[1,2,4,7],[3,5,6,8]] => [[1,3],[2,5],[4,6],[7,8]] => {{1,3},{2,5},{4,6},{7,8}} => {{1,6},{2,3},{4,5},{7,8}} => 7
[[1,2,3,7],[4,5,6,8]] => [[1,4],[2,5],[3,6],[7,8]] => {{1,4},{2,5},{3,6},{7,8}} => {{1,6},{2,5},{3,4},{7,8}} => 7
[[1,3,5,6],[2,4,7,8]] => [[1,2],[3,4],[5,7],[6,8]] => {{1,2},{3,4},{5,7},{6,8}} => {{1,2},{3,4},{5,8},{6,7}} => 6
[[1,2,5,6],[3,4,7,8]] => [[1,3],[2,4],[5,7],[6,8]] => {{1,3},{2,4},{5,7},{6,8}} => {{1,4},{2,3},{5,8},{6,7}} => 6
[[1,3,4,6],[2,5,7,8]] => [[1,2],[3,5],[4,7],[6,8]] => {{1,2},{3,5},{4,7},{6,8}} => {{1,2},{3,8},{4,5},{6,7}} => 6
[[1,2,4,6],[3,5,7,8]] => [[1,3],[2,5],[4,7],[6,8]] => {{1,3},{2,5},{4,7},{6,8}} => {{1,8},{2,3},{4,5},{6,7}} => 6
[[1,2,3,6],[4,5,7,8]] => [[1,4],[2,5],[3,7],[6,8]] => {{1,4},{2,5},{3,7},{6,8}} => {{1,8},{2,5},{3,4},{6,7}} => 6
[[1,3,4,5],[2,6,7,8]] => [[1,2],[3,6],[4,7],[5,8]] => {{1,2},{3,6},{4,7},{5,8}} => {{1,2},{3,8},{4,7},{5,6}} => 5
[[1,2,4,5],[3,6,7,8]] => [[1,3],[2,6],[4,7],[5,8]] => {{1,3},{2,6},{4,7},{5,8}} => {{1,8},{2,3},{4,7},{5,6}} => 5
[[1,2,3,5],[4,6,7,8]] => [[1,4],[2,6],[3,7],[5,8]] => {{1,4},{2,6},{3,7},{5,8}} => {{1,8},{2,7},{3,4},{5,6}} => 5
[[1,2,3,4],[5,6,7,8]] => [[1,5],[2,6],[3,7],[4,8]] => {{1,5},{2,6},{3,7},{4,8}} => {{1,8},{2,7},{3,6},{4,5}} => 4
[[1,2,4,7],[3,6,8],[5]] => [[1,3,5],[2,6],[4,8],[7]] => {{1,3,5},{2,6},{4,8},{7}} => {{1,5},{2,3,8},{4,6},{7}} => 7
[[1,2,3,7],[4,6,8],[5]] => [[1,4,5],[2,6],[3,8],[7]] => {{1,4,5},{2,6},{3,8},{7}} => {{1,8},{2,5},{3,4,6},{7}} => 7
[[1,3,4,7],[2,5,8],[6]] => [[1,2,6],[3,5],[4,8],[7]] => {{1,2,6},{3,5},{4,8},{7}} => {{1,2,5},{3,8},{4,6},{7}} => 7
[[1,2,4,7],[3,5,8],[6]] => [[1,3,6],[2,5],[4,8],[7]] => {{1,3,6},{2,5},{4,8},{7}} => {{1,8},{2,3,6},{4,5},{7}} => 7
[[1,2,3,7],[4,5,8],[6]] => [[1,4,6],[2,5],[3,8],[7]] => {{1,4,6},{2,5},{3,8},{7}} => {{1,6},{2,5},{3,4,8},{7}} => 7
[[1,2,5,6],[3,7,8],[4]] => [[1,3,4],[2,7],[5,8],[6]] => {{1,3,4},{2,7},{5,8},{6}} => {{1,4},{2,3,8},{5,7},{6}} => 6
[[1,2,4,6],[3,7,8],[5]] => [[1,3,5],[2,7],[4,8],[6]] => {{1,3,5},{2,7},{4,8},{6}} => {{1,5},{2,3,8},{4,7},{6}} => 6
[[1,2,3,6],[4,7,8],[5]] => [[1,4,5],[2,7],[3,8],[6]] => {{1,4,5},{2,7},{3,8},{6}} => {{1,8},{2,5},{3,4,7},{6}} => 6
[[1,3,4,5],[2,7,8],[6]] => [[1,2,6],[3,7],[4,8],[5]] => {{1,2,6},{3,7},{4,8},{5}} => {{1,2,8},{3,7},{4,6},{5}} => 5
[[1,2,4,5],[3,7,8],[6]] => [[1,3,6],[2,7],[4,8],[5]] => {{1,3,6},{2,7},{4,8},{5}} => {{1,6},{2,3,8},{4,7},{5}} => 5
[[1,2,3,5],[4,7,8],[6]] => [[1,4,6],[2,7],[3,8],[5]] => {{1,4,6},{2,7},{3,8},{5}} => {{1,8},{2,6},{3,4,7},{5}} => 5
[[1,3,5,6],[2,4,8],[7]] => [[1,2,7],[3,4],[5,8],[6]] => {{1,2,7},{3,4},{5,8},{6}} => {{1,2,4},{3,8},{5,7},{6}} => 6
[[1,3,4,6],[2,5,8],[7]] => [[1,2,7],[3,5],[4,8],[6]] => {{1,2,7},{3,5},{4,8},{6}} => {{1,2,5},{3,8},{4,7},{6}} => 6
[[1,2,4,6],[3,5,8],[7]] => [[1,3,7],[2,5],[4,8],[6]] => {{1,3,7},{2,5},{4,8},{6}} => {{1,8},{2,3,7},{4,5},{6}} => 6
[[1,2,3,6],[4,5,8],[7]] => [[1,4,7],[2,5],[3,8],[6]] => {{1,4,7},{2,5},{3,8},{6}} => {{1,7},{2,5},{3,4,8},{6}} => 6
[[1,3,4,5],[2,6,8],[7]] => [[1,2,7],[3,6],[4,8],[5]] => {{1,2,7},{3,6},{4,8},{5}} => {{1,2,6},{3,8},{4,7},{5}} => 5
[[1,2,4,5],[3,6,8],[7]] => [[1,3,7],[2,6],[4,8],[5]] => {{1,3,7},{2,6},{4,8},{5}} => {{1,8},{2,3,7},{4,6},{5}} => 5
[[1,2,3,5],[4,6,8],[7]] => [[1,4,7],[2,6],[3,8],[5]] => {{1,4,7},{2,6},{3,8},{5}} => {{1,7},{2,6},{3,4,8},{5}} => 5
[[1,2,3,4],[5,6,8],[7]] => [[1,5,7],[2,6],[3,8],[4]] => {{1,5,7},{2,6},{3,8},{4}} => {{1,7},{2,6},{3,5,8},{4}} => 4
[[1,3,5,7],[2,4,6],[8]] => [[1,2,8],[3,4],[5,6],[7]] => {{1,2,8},{3,4},{5,6},{7}} => {{1,2,4},{3,6},{5,8},{7}} => 7
[[1,2,4,7],[3,5,6],[8]] => [[1,3,8],[2,5],[4,6],[7]] => {{1,3,8},{2,5},{4,6},{7}} => {{1,6},{2,3,5},{4,8},{7}} => 7
[[1,3,5,6],[2,4,7],[8]] => [[1,2,8],[3,4],[5,7],[6]] => {{1,2,8},{3,4},{5,7},{6}} => {{1,2,4},{3,7},{5,8},{6}} => 6
[[1,2,4,6],[3,5,7],[8]] => [[1,3,8],[2,5],[4,7],[6]] => {{1,3,8},{2,5},{4,7},{6}} => {{1,7},{2,3,5},{4,8},{6}} => 6
[[1,3,4,5],[2,6,7],[8]] => [[1,2,8],[3,6],[4,7],[5]] => {{1,2,8},{3,6},{4,7},{5}} => {{1,2,7},{3,8},{4,6},{5}} => 5
[[1,2,4,5],[3,6,7],[8]] => [[1,3,8],[2,6],[4,7],[5]] => {{1,3,8},{2,6},{4,7},{5}} => {{1,7},{2,3,6},{4,8},{5}} => 5
[[1,2,3,5],[4,6,7],[8]] => [[1,4,8],[2,6],[3,7],[5]] => {{1,4,8},{2,6},{3,7},{5}} => {{1,8},{2,7},{3,4,6},{5}} => 5
[[1,2,3,4],[5,6,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => {{1,5,8},{2,6},{3,7},{4}} => {{1,8},{2,7},{3,5,6},{4}} => 4
[[1,2,5,7],[3,6],[4,8]] => [[1,3,4],[2,6,8],[5],[7]] => {{1,3,4},{2,6,8},{5},{7}} => {{1,4},{2,3,6,8},{5},{7}} => 7
[[1,3,4,7],[2,6],[5,8]] => [[1,2,5],[3,6,8],[4],[7]] => {{1,2,5},{3,6,8},{4},{7}} => {{1,2,6,8},{3,5},{4},{7}} => 7
[[1,2,3,7],[4,6],[5,8]] => [[1,4,5],[2,6,8],[3],[7]] => {{1,4,5},{2,6,8},{3},{7}} => {{1,5},{2,4,6,8},{3},{7}} => 7
[[1,3,4,7],[2,5],[6,8]] => [[1,2,6],[3,5,8],[4],[7]] => {{1,2,6},{3,5,8},{4},{7}} => {{1,2,5,6},{3,8},{4},{7}} => 7
[[1,2,4,5],[3,7],[6,8]] => [[1,3,6],[2,7,8],[4],[5]] => {{1,3,6},{2,7,8},{4},{5}} => {{1,6},{2,3,7,8},{4},{5}} => 5
[[1,2,3,5],[4,7],[6,8]] => [[1,4,6],[2,7,8],[3],[5]] => {{1,4,6},{2,7,8},{3},{5}} => {{1,6},{2,4,7,8},{3},{5}} => 5
[[1,2,3,4],[5,7],[6,8]] => [[1,5,6],[2,7,8],[3],[4]] => {{1,5,6},{2,7,8},{3},{4}} => {{1,6},{2,5,7,8},{3},{4}} => 4
[[1,3,5,6],[2,4],[7,8]] => [[1,2,7],[3,4,8],[5],[6]] => {{1,2,7},{3,4,8},{5},{6}} => {{1,2,4,7},{3,8},{5},{6}} => 6
[[1,3,4,6],[2,5],[7,8]] => [[1,2,7],[3,5,8],[4],[6]] => {{1,2,7},{3,5,8},{4},{6}} => {{1,2,5,7},{3,8},{4},{6}} => 6
[[1,2,4,6],[3,5],[7,8]] => [[1,3,7],[2,5,8],[4],[6]] => {{1,3,7},{2,5,8},{4},{6}} => {{1,8},{2,3,5,7},{4},{6}} => 6
[[1,2,3,4],[5,6],[7,8]] => [[1,5,7],[2,6,8],[3],[4]] => {{1,5,7},{2,6,8},{3},{4}} => {{1,8},{2,5,6,7},{3},{4}} => 4
[[1,2,3,8],[4,7],[5],[6]] => [[1,4,5,6],[2,7],[3],[8]] => {{1,4,5,6},{2,7},{3},{8}} => {{1,5,7},{2,4,6},{3},{8}} => 8
[[1,2,5,7],[3,8],[4],[6]] => [[1,3,4,6],[2,8],[5],[7]] => {{1,3,4,6},{2,8},{5},{7}} => {{1,4,8},{2,3,6},{5},{7}} => 7
[[1,3,4,7],[2,8],[5],[6]] => [[1,2,5,6],[3,8],[4],[7]] => {{1,2,5,6},{3,8},{4},{7}} => {{1,2,6},{3,5,8},{4},{7}} => 7
[[1,2,5,6],[3,8],[4],[7]] => [[1,3,4,7],[2,8],[5],[6]] => {{1,3,4,7},{2,8},{5},{6}} => {{1,4,8},{2,3,7},{5},{6}} => 6
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,5,7],[3,8],[4],[6]] => {{1,2,5,7},{3,8},{4},{6}} => {{1,2,7},{3,5,8},{4},{6}} => 6
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,6,7],[3,8],[4],[5]] => {{1,2,6,7},{3,8},{4},{5}} => {{1,2,7},{3,6,8},{4},{5}} => 5
[[1,2,3,4],[5,8],[6],[7]] => [[1,5,6,7],[2,8],[3],[4]] => {{1,5,6,7},{2,8},{3},{4}} => {{1,6,8},{2,5,7},{3},{4}} => 4
[[1,3,4,7],[2,6],[5],[8]] => [[1,2,5,8],[3,6],[4],[7]] => {{1,2,5,8},{3,6},{4},{7}} => {{1,2,8},{3,5,6},{4},{7}} => 7
[[1,2,4,7],[3,6],[5],[8]] => [[1,3,5,8],[2,6],[4],[7]] => {{1,3,5,8},{2,6},{4},{7}} => {{1,5,6},{2,3,8},{4},{7}} => 7
[[1,3,5,7],[2,4],[6],[8]] => [[1,2,6,8],[3,4],[5],[7]] => {{1,2,6,8},{3,4},{5},{7}} => {{1,2,4},{3,6,8},{5},{7}} => 7
[[1,2,5,7],[3,4],[6],[8]] => [[1,3,6,8],[2,4],[5],[7]] => {{1,3,6,8},{2,4},{5},{7}} => {{1,6,8},{2,3,4},{5},{7}} => 7
[[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,5],[4],[7]] => {{1,3,6,8},{2,5},{4},{7}} => {{1,6,8},{2,3,5},{4},{7}} => 7
[[1,2,5,6],[3,7],[4],[8]] => [[1,3,4,8],[2,7],[5],[6]] => {{1,3,4,8},{2,7},{5},{6}} => {{1,4,7},{2,3,8},{5},{6}} => 6
[[1,3,4,6],[2,7],[5],[8]] => [[1,2,5,8],[3,7],[4],[6]] => {{1,2,5,8},{3,7},{4},{6}} => {{1,2,8},{3,5,7},{4},{6}} => 6
[[1,2,4,6],[3,7],[5],[8]] => [[1,3,5,8],[2,7],[4],[6]] => {{1,3,5,8},{2,7},{4},{6}} => {{1,5,7},{2,3,8},{4},{6}} => 6
[[1,2,3,6],[4,7],[5],[8]] => [[1,4,5,8],[2,7],[3],[6]] => {{1,4,5,8},{2,7},{3},{6}} => {{1,5,7},{2,4,8},{3},{6}} => 6
[[1,2,3,5],[4,7],[6],[8]] => [[1,4,6,8],[2,7],[3],[5]] => {{1,4,6,8},{2,7},{3},{5}} => {{1,6,7},{2,4,8},{3},{5}} => 5
[[1,2,3,4],[5,7],[6],[8]] => [[1,5,6,8],[2,7],[3],[4]] => {{1,5,6,8},{2,7},{3},{4}} => {{1,6,7},{2,5,8},{3},{4}} => 4
[[1,3,5,6],[2,4],[7],[8]] => [[1,2,7,8],[3,4],[5],[6]] => {{1,2,7,8},{3,4},{5},{6}} => {{1,2,4},{3,7,8},{5},{6}} => 6
[[1,2,3,4],[5,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => {{1,5,7,8},{2,6},{3},{4}} => {{1,7,8},{2,5,6},{3},{4}} => 4
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,3,4,7],[5],[6],[8]] => {{1,2,3,4,7},{5},{6},{8}} => {{1,2,3,4,7},{5},{6},{8}} => 8
[[1,3,5,7],[2],[4],[6],[8]] => [[1,2,4,6,8],[3],[5],[7]] => {{1,2,4,6,8},{3},{5},{7}} => {{1,2,4,6,8},{3},{5},{7}} => 7
[[1,2,3,4],[5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => {{1,5,6,7,8},{2},{3},{4}} => {{1,5,6,7,8},{2},{3},{4}} => 4
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3,4,6],[5,7],[8]] => {{1,2,3,4,6},{5,7},{8}} => {{1,2,3,4,7},{5,6},{8}} => 8
[[1,4,8],[2,6],[3],[5],[7]] => [[1,2,3,5,7],[4,6],[8]] => {{1,2,3,5,7},{4,6},{8}} => {{1,2,3,7},{4,5,6},{8}} => 8
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5,7},{6},{8}} => 8
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,3,4,6,7],[5],[8]] => {{1,2,3,4,6,7},{5},{8}} => {{1,2,3,4,6,7},{5},{8}} => 8
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,3,5,6,7],[4],[8]] => {{1,2,3,5,6,7},{4},{8}} => {{1,2,3,5,6,7},{4},{8}} => 8
[[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,5,6,7,8],[2],[4]] => {{1,3,5,6,7,8},{2},{4}} => {{1,3,5,6,7,8},{2},{4}} => 4
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => {{1,4,5,6,7,8},{2},{3}} => 3
[[1,4],[2,6],[3,7],[5,8]] => [[1,2,3,5],[4,6,7,8]] => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,6,7,8},{4,5}} => 4
[[1,3],[2,4],[5,7],[6,8]] => [[1,2,5,6],[3,4,7,8]] => {{1,2,5,6},{3,4,7,8}} => {{1,2,4,5,7,8},{3,6}} => 3
[[1,2],[3,4],[5,7],[6,8]] => [[1,3,5,6],[2,4,7,8]] => {{1,3,5,6},{2,4,7,8}} => {{1,6},{2,3,4,5,7,8}} => 2
[[1,3],[2,4],[5,6],[7,8]] => [[1,2,5,7],[3,4,6,8]] => {{1,2,5,7},{3,4,6,8}} => {{1,2,4,5,6,7},{3,8}} => 3
[[1,2],[3,4],[5,6],[7,8]] => [[1,3,5,7],[2,4,6,8]] => {{1,3,5,7},{2,4,6,8}} => {{1,8},{2,3,4,5,6,7}} => 2
[[1,5],[2,7],[3,8],[4],[6]] => [[1,2,3,4,6],[5,7,8]] => {{1,2,3,4,6},{5,7,8}} => {{1,2,3,4,7,8},{5,6}} => 5
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2,3,4,7],[5,6,8]] => {{1,2,3,4,7},{5,6,8}} => {{1,2,3,4,6,7},{5,8}} => 5
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2,3,6,7],[4,5,8]] => {{1,2,3,6,7},{4,5,8}} => {{1,2,3,5,6,8},{4,7}} => 4
[[1,5],[2,6],[3,7],[4],[8]] => [[1,2,3,4,8],[5,6,7]] => {{1,2,3,4,8},{5,6,7}} => {{1,2,3,4,6,8},{5,7}} => 5
[[1,4],[2,5],[3,7],[6],[8]] => [[1,2,3,6,8],[4,5,7]] => {{1,2,3,6,8},{4,5,7}} => {{1,2,3,5,6,7},{4,8}} => 4
[[1,4],[2,5],[3,6],[7],[8]] => [[1,2,3,7,8],[4,5,6]] => {{1,2,3,7,8},{4,5,6}} => {{1,2,3,5,7,8},{4,6}} => 4
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2,3,4,5,6],[7,8]] => {{1,2,3,4,5,6},{7,8}} => {{1,2,3,4,5,6},{7,8}} => 7
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => {{1,2,3,4,5,8},{6,7}} => 6
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => {{1,2,3,4,5,7},{6,8}} => 6
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4,5,6,7],[8]] => {{1,2,3,4,5,6,7},{8}} => {{1,2,3,4,5,6,7},{8}} => 8
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6,8},{7}} => 7
[[1,6],[2],[3],[4],[5],[7],[8]] => [[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5,7,8},{6}} => 6
[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4,6,7,8},{5}} => 5
[[1,4],[2],[3],[5],[6],[7],[8]] => [[1,2,3,5,6,7,8],[4]] => {{1,2,3,5,6,7,8},{4}} => {{1,2,3,5,6,7,8},{4}} => 4
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,2,4,5,6,7,8],[3]] => {{1,2,4,5,6,7,8},{3}} => {{1,2,4,5,6,7,8},{3}} => 3
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => {{1,3,4,5,6,7,8},{2}} => 2
[[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}} => 1
[[1,3,5,7,9],[2,4,6,8,10]] => [[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}} => 9
[[1,3,5,7,8],[2,4,6,9,10]] => [[1,2],[3,4],[5,6],[7,9],[8,10]] => {{1,2},{3,4},{5,6},{7,9},{8,10}} => {{1,2},{3,4},{5,6},{7,10},{8,9}} => 8
[[1,3,5,6,9],[2,4,7,8,10]] => [[1,2],[3,4],[5,7],[6,8],[9,10]] => {{1,2},{3,4},{5,7},{6,8},{9,10}} => {{1,2},{3,4},{5,8},{6,7},{9,10}} => 9
[[1,3,5,6,8],[2,4,7,9,10]] => [[1,2],[3,4],[5,7],[6,9],[8,10]] => {{1,2},{3,4},{5,7},{6,9},{8,10}} => {{1,2},{3,4},{5,10},{6,7},{8,9}} => 8
[[1,3,5,6,7],[2,4,8,9,10]] => [[1,2],[3,4],[5,8],[6,9],[7,10]] => {{1,2},{3,4},{5,8},{6,9},{7,10}} => {{1,2},{3,4},{5,10},{6,9},{7,8}} => 7
[[1,3,4,7,9],[2,5,6,8,10]] => [[1,2],[3,5],[4,6],[7,8],[9,10]] => {{1,2},{3,5},{4,6},{7,8},{9,10}} => {{1,2},{3,6},{4,5},{7,8},{9,10}} => 9
[[1,3,4,7,8],[2,5,6,9,10]] => [[1,2],[3,5],[4,6],[7,9],[8,10]] => {{1,2},{3,5},{4,6},{7,9},{8,10}} => {{1,2},{3,6},{4,5},{7,10},{8,9}} => 8
[[1,3,4,6,9],[2,5,7,8,10]] => [[1,2],[3,5],[4,7],[6,8],[9,10]] => {{1,2},{3,5},{4,7},{6,8},{9,10}} => {{1,2},{3,8},{4,5},{6,7},{9,10}} => 9
[[1,3,4,6,8],[2,5,7,9,10]] => [[1,2],[3,5],[4,7],[6,9],[8,10]] => {{1,2},{3,5},{4,7},{6,9},{8,10}} => {{1,2},{3,10},{4,5},{6,7},{8,9}} => 8
[[1,3,4,6,7],[2,5,8,9,10]] => [[1,2],[3,5],[4,8],[6,9],[7,10]] => {{1,2},{3,5},{4,8},{6,9},{7,10}} => {{1,2},{3,10},{4,5},{6,9},{7,8}} => 7
[[1,3,4,5,9],[2,6,7,8,10]] => [[1,2],[3,6],[4,7],[5,8],[9,10]] => {{1,2},{3,6},{4,7},{5,8},{9,10}} => {{1,2},{3,8},{4,7},{5,6},{9,10}} => 9
[[1,3,4,5,8],[2,6,7,9,10]] => [[1,2],[3,6],[4,7],[5,9],[8,10]] => {{1,2},{3,6},{4,7},{5,9},{8,10}} => {{1,2},{3,10},{4,7},{5,6},{8,9}} => 8
[[1,3,4,5,7],[2,6,8,9,10]] => [[1,2],[3,6],[4,8],[5,9],[7,10]] => {{1,2},{3,6},{4,8},{5,9},{7,10}} => {{1,2},{3,10},{4,9},{5,6},{7,8}} => 7
[[1,3,4,5,6],[2,7,8,9,10]] => [[1,2],[3,7],[4,8],[5,9],[6,10]] => {{1,2},{3,7},{4,8},{5,9},{6,10}} => {{1,2},{3,10},{4,9},{5,8},{6,7}} => 6
[[1,2,5,7,9],[3,4,6,8,10]] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => {{1,3},{2,4},{5,6},{7,8},{9,10}} => {{1,4},{2,3},{5,6},{7,8},{9,10}} => 9
[[1,2,5,7,8],[3,4,6,9,10]] => [[1,3],[2,4],[5,6],[7,9],[8,10]] => {{1,3},{2,4},{5,6},{7,9},{8,10}} => {{1,4},{2,3},{5,6},{7,10},{8,9}} => 8
[[1,2,5,6,9],[3,4,7,8,10]] => [[1,3],[2,4],[5,7],[6,8],[9,10]] => {{1,3},{2,4},{5,7},{6,8},{9,10}} => {{1,4},{2,3},{5,8},{6,7},{9,10}} => 9
[[1,2,5,6,8],[3,4,7,9,10]] => [[1,3],[2,4],[5,7],[6,9],[8,10]] => {{1,3},{2,4},{5,7},{6,9},{8,10}} => {{1,4},{2,3},{5,10},{6,7},{8,9}} => 8
[[1,2,5,6,7],[3,4,8,9,10]] => [[1,3],[2,4],[5,8],[6,9],[7,10]] => {{1,3},{2,4},{5,8},{6,9},{7,10}} => {{1,4},{2,3},{5,10},{6,9},{7,8}} => 7
[[1,2,4,7,9],[3,5,6,8,10]] => [[1,3],[2,5],[4,6],[7,8],[9,10]] => {{1,3},{2,5},{4,6},{7,8},{9,10}} => {{1,6},{2,3},{4,5},{7,8},{9,10}} => 9
[[1,2,4,7,8],[3,5,6,9,10]] => [[1,3],[2,5],[4,6],[7,9],[8,10]] => {{1,3},{2,5},{4,6},{7,9},{8,10}} => {{1,6},{2,3},{4,5},{7,10},{8,9}} => 8
[[1,2,4,6,9],[3,5,7,8,10]] => [[1,3],[2,5],[4,7],[6,8],[9,10]] => {{1,3},{2,5},{4,7},{6,8},{9,10}} => {{1,8},{2,3},{4,5},{6,7},{9,10}} => 9
[[1,2,4,6,8],[3,5,7,9,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => {{1,3},{2,5},{4,7},{6,9},{8,10}} => {{1,10},{2,3},{4,5},{6,7},{8,9}} => 8
[[1,2,4,6,7],[3,5,8,9,10]] => [[1,3],[2,5],[4,8],[6,9],[7,10]] => {{1,3},{2,5},{4,8},{6,9},{7,10}} => {{1,10},{2,3},{4,5},{6,9},{7,8}} => 7
[[1,2,4,5,9],[3,6,7,8,10]] => [[1,3],[2,6],[4,7],[5,8],[9,10]] => {{1,3},{2,6},{4,7},{5,8},{9,10}} => {{1,8},{2,3},{4,7},{5,6},{9,10}} => 9
[[1,2,4,5,8],[3,6,7,9,10]] => [[1,3],[2,6],[4,7],[5,9],[8,10]] => {{1,3},{2,6},{4,7},{5,9},{8,10}} => {{1,10},{2,3},{4,7},{5,6},{8,9}} => 8
[[1,2,4,5,7],[3,6,8,9,10]] => [[1,3],[2,6],[4,8],[5,9],[7,10]] => {{1,3},{2,6},{4,8},{5,9},{7,10}} => {{1,10},{2,3},{4,9},{5,6},{7,8}} => 7
[[1,2,4,5,6],[3,7,8,9,10]] => [[1,3],[2,7],[4,8],[5,9],[6,10]] => {{1,3},{2,7},{4,8},{5,9},{6,10}} => {{1,10},{2,3},{4,9},{5,8},{6,7}} => 6
[[1,2,3,7,9],[4,5,6,8,10]] => [[1,4],[2,5],[3,6],[7,8],[9,10]] => {{1,4},{2,5},{3,6},{7,8},{9,10}} => {{1,6},{2,5},{3,4},{7,8},{9,10}} => 9
[[1,2,3,7,8],[4,5,6,9,10]] => [[1,4],[2,5],[3,6],[7,9],[8,10]] => {{1,4},{2,5},{3,6},{7,9},{8,10}} => {{1,6},{2,5},{3,4},{7,10},{8,9}} => 8
[[1,2,3,6,9],[4,5,7,8,10]] => [[1,4],[2,5],[3,7],[6,8],[9,10]] => {{1,4},{2,5},{3,7},{6,8},{9,10}} => {{1,8},{2,5},{3,4},{6,7},{9,10}} => 9
[[1,2,3,6,8],[4,5,7,9,10]] => [[1,4],[2,5],[3,7],[6,9],[8,10]] => {{1,4},{2,5},{3,7},{6,9},{8,10}} => {{1,10},{2,5},{3,4},{6,7},{8,9}} => 8
[[1,2,3,6,7],[4,5,8,9,10]] => [[1,4],[2,5],[3,8],[6,9],[7,10]] => {{1,4},{2,5},{3,8},{6,9},{7,10}} => {{1,10},{2,5},{3,4},{6,9},{7,8}} => 7
[[1,2,3,5,9],[4,6,7,8,10]] => [[1,4],[2,6],[3,7],[5,8],[9,10]] => {{1,4},{2,6},{3,7},{5,8},{9,10}} => {{1,8},{2,7},{3,4},{5,6},{9,10}} => 9
[[1,2,3,5,8],[4,6,7,9,10]] => [[1,4],[2,6],[3,7],[5,9],[8,10]] => {{1,4},{2,6},{3,7},{5,9},{8,10}} => {{1,10},{2,7},{3,4},{5,6},{8,9}} => 8
[[1,2,3,5,7],[4,6,8,9,10]] => [[1,4],[2,6],[3,8],[5,9],[7,10]] => {{1,4},{2,6},{3,8},{5,9},{7,10}} => {{1,10},{2,9},{3,4},{5,6},{7,8}} => 7
[[1,2,3,5,6],[4,7,8,9,10]] => [[1,4],[2,7],[3,8],[5,9],[6,10]] => {{1,4},{2,7},{3,8},{5,9},{6,10}} => {{1,10},{2,9},{3,4},{5,8},{6,7}} => 6
[[1,2,3,4,9],[5,6,7,8,10]] => [[1,5],[2,6],[3,7],[4,8],[9,10]] => {{1,5},{2,6},{3,7},{4,8},{9,10}} => {{1,8},{2,7},{3,6},{4,5},{9,10}} => 9
[[1,2,3,4,8],[5,6,7,9,10]] => [[1,5],[2,6],[3,7],[4,9],[8,10]] => {{1,5},{2,6},{3,7},{4,9},{8,10}} => {{1,10},{2,7},{3,6},{4,5},{8,9}} => 8
[[1,2,3,4,7],[5,6,8,9,10]] => [[1,5],[2,6],[3,8],[4,9],[7,10]] => {{1,5},{2,6},{3,8},{4,9},{7,10}} => {{1,10},{2,9},{3,6},{4,5},{7,8}} => 7
[[1,2,3,4,6],[5,7,8,9,10]] => [[1,5],[2,7],[3,8],[4,9],[6,10]] => {{1,5},{2,7},{3,8},{4,9},{6,10}} => {{1,10},{2,9},{3,8},{4,5},{6,7}} => 6
[[1,2,3,4,5],[6,7,8,9,10]] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => {{1,6},{2,7},{3,8},{4,9},{5,10}} => {{1,10},{2,9},{3,8},{4,7},{5,6}} => 5
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 11
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] => {{1,2},{3,4},{5,6},{7,8},{9,11},{10,12}} => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 10
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] => {{1,2},{3,4},{5,6},{7,9},{8,10},{11,12}} => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 11
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] => {{1,2},{3,4},{5,6},{7,9},{8,11},{10,12}} => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => 10
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] => {{1,2},{3,4},{5,6},{7,10},{8,11},{9,12}} => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => 9
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] => {{1,2},{3,4},{5,7},{6,8},{9,10},{11,12}} => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => 11
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] => {{1,2},{3,4},{5,7},{6,8},{9,11},{10,12}} => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => 10
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] => {{1,2},{3,4},{5,7},{6,9},{8,10},{11,12}} => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => 11
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] => {{1,2},{3,4},{5,7},{6,9},{8,11},{10,12}} => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => 10
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] => {{1,2},{3,4},{5,7},{6,10},{8,11},{9,12}} => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => 9
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] => {{1,2},{3,4},{5,8},{6,9},{7,10},{11,12}} => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => 11
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] => {{1,2},{3,4},{5,8},{6,9},{7,11},{10,12}} => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => 10
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] => {{1,2},{3,4},{5,8},{6,10},{7,11},{9,12}} => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => 9
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] => {{1,2},{3,4},{5,9},{6,10},{7,11},{8,12}} => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => 8
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] => {{1,2},{3,5},{4,6},{7,8},{9,10},{11,12}} => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => 11
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] => {{1,2},{3,5},{4,6},{7,8},{9,11},{10,12}} => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => 10
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => {{1,2},{3,5},{4,6},{7,9},{8,10},{11,12}} => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 11
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] => {{1,2},{3,5},{4,6},{7,9},{8,11},{10,12}} => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => 10
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] => {{1,2},{3,5},{4,6},{7,10},{8,11},{9,12}} => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => 9
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] => {{1,2},{3,5},{4,7},{6,8},{9,10},{11,12}} => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => 11
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] => {{1,2},{3,5},{4,7},{6,8},{9,11},{10,12}} => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => 10
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] => {{1,2},{3,5},{4,7},{6,9},{8,10},{11,12}} => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => 11
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] => {{1,2},{3,5},{4,7},{6,9},{8,11},{10,12}} => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => 10
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] => {{1,2},{3,5},{4,7},{6,10},{8,11},{9,12}} => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => 9
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] => {{1,2},{3,5},{4,8},{6,9},{7,10},{11,12}} => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => 11
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] => {{1,2},{3,5},{4,8},{6,9},{7,11},{10,12}} => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => 10
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] => {{1,2},{3,5},{4,8},{6,10},{7,11},{9,12}} => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => 9
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] => {{1,2},{3,5},{4,9},{6,10},{7,11},{8,12}} => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => 8
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] => {{1,2},{3,6},{4,7},{5,8},{9,10},{11,12}} => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => 11
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] => {{1,2},{3,6},{4,7},{5,8},{9,11},{10,12}} => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => 10
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] => {{1,2},{3,6},{4,7},{5,9},{8,10},{11,12}} => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => 11
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] => {{1,2},{3,6},{4,7},{5,9},{8,11},{10,12}} => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => 10
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => {{1,2},{3,6},{4,7},{5,10},{8,11},{9,12}} => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => 9
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] => {{1,2},{3,6},{4,8},{5,9},{7,10},{11,12}} => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => 11
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] => {{1,2},{3,6},{4,8},{5,9},{7,11},{10,12}} => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => 10
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] => {{1,2},{3,6},{4,8},{5,10},{7,11},{9,12}} => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => 9
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] => {{1,2},{3,6},{4,9},{5,10},{7,11},{8,12}} => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => 8
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => {{1,2},{3,7},{4,8},{5,9},{6,10},{11,12}} => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => 11
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] => {{1,2},{3,7},{4,8},{5,9},{6,11},{10,12}} => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => 10
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] => {{1,2},{3,7},{4,8},{5,10},{6,11},{9,12}} => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => 9
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] => {{1,2},{3,7},{4,9},{5,10},{6,11},{8,12}} => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => 8
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => {{1,2},{3,8},{4,9},{5,10},{6,11},{7,12}} => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => 7
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => {{1,3},{2,4},{5,6},{7,8},{9,10},{11,12}} => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => 11
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] => {{1,3},{2,4},{5,6},{7,8},{9,11},{10,12}} => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => 10
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] => {{1,3},{2,4},{5,6},{7,9},{8,10},{11,12}} => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 11
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] => {{1,3},{2,4},{5,6},{7,9},{8,11},{10,12}} => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => 10
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] => {{1,3},{2,4},{5,6},{7,10},{8,11},{9,12}} => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => 9
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] => {{1,3},{2,4},{5,7},{6,8},{9,10},{11,12}} => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => 11
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] => {{1,3},{2,4},{5,7},{6,8},{9,11},{10,12}} => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => 10
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] => {{1,3},{2,4},{5,7},{6,9},{8,10},{11,12}} => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => 11
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] => {{1,3},{2,4},{5,7},{6,9},{8,11},{10,12}} => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => 10
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] => {{1,3},{2,4},{5,7},{6,10},{8,11},{9,12}} => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => 9
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] => {{1,3},{2,4},{5,8},{6,9},{7,10},{11,12}} => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => 11
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] => {{1,3},{2,4},{5,8},{6,9},{7,11},{10,12}} => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => 10
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] => {{1,3},{2,4},{5,8},{6,10},{7,11},{9,12}} => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => 9
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] => {{1,3},{2,4},{5,9},{6,10},{7,11},{8,12}} => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => 8
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] => {{1,3},{2,5},{4,6},{7,8},{9,10},{11,12}} => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => 11
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] => {{1,3},{2,5},{4,6},{7,8},{9,11},{10,12}} => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => 10
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] => {{1,3},{2,5},{4,6},{7,9},{8,10},{11,12}} => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => 11
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] => {{1,3},{2,5},{4,6},{7,9},{8,11},{10,12}} => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => 10
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] => {{1,3},{2,5},{4,6},{7,10},{8,11},{9,12}} => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => 9
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] => {{1,3},{2,5},{4,7},{6,8},{9,10},{11,12}} => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => 11
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] => {{1,3},{2,5},{4,7},{6,8},{9,11},{10,12}} => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => 10
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] => {{1,3},{2,5},{4,7},{6,9},{8,10},{11,12}} => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 11
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => {{1,3},{2,5},{4,7},{6,9},{8,11},{10,12}} => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 10
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] => {{1,3},{2,5},{4,7},{6,10},{8,11},{9,12}} => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => 9
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] => {{1,3},{2,5},{4,8},{6,9},{7,10},{11,12}} => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => 11
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] => {{1,3},{2,5},{4,8},{6,9},{7,11},{10,12}} => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 10
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] => {{1,3},{2,5},{4,8},{6,10},{7,11},{9,12}} => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => 9
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] => {{1,3},{2,5},{4,9},{6,10},{7,11},{8,12}} => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => 8
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] => {{1,3},{2,6},{4,7},{5,8},{9,10},{11,12}} => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => 11
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] => {{1,3},{2,6},{4,7},{5,8},{9,11},{10,12}} => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => 10
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] => {{1,3},{2,6},{4,7},{5,9},{8,10},{11,12}} => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 11
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] => {{1,3},{2,6},{4,7},{5,9},{8,11},{10,12}} => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 10
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] => {{1,3},{2,6},{4,7},{5,10},{8,11},{9,12}} => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => 9
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] => {{1,3},{2,6},{4,8},{5,9},{7,10},{11,12}} => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => 11
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] => {{1,3},{2,6},{4,8},{5,9},{7,11},{10,12}} => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 10
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] => {{1,3},{2,6},{4,8},{5,10},{7,11},{9,12}} => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => 9
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] => {{1,3},{2,6},{4,9},{5,10},{7,11},{8,12}} => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => 8
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] => {{1,3},{2,7},{4,8},{5,9},{6,10},{11,12}} => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => 11
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] => {{1,3},{2,7},{4,8},{5,9},{6,11},{10,12}} => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => 10
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] => {{1,3},{2,7},{4,8},{5,10},{6,11},{9,12}} => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => 9
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] => {{1,3},{2,7},{4,9},{5,10},{6,11},{8,12}} => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => 8
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] => {{1,3},{2,8},{4,9},{5,10},{6,11},{7,12}} => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => 7
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] => {{1,4},{2,5},{3,6},{7,8},{9,10},{11,12}} => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => 11
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] => {{1,4},{2,5},{3,6},{7,8},{9,11},{10,12}} => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => 10
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] => {{1,4},{2,5},{3,6},{7,9},{8,10},{11,12}} => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => 11
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] => {{1,4},{2,5},{3,6},{7,9},{8,11},{10,12}} => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => 10
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => {{1,4},{2,5},{3,6},{7,10},{8,11},{9,12}} => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => 9
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] => {{1,4},{2,5},{3,7},{6,8},{9,10},{11,12}} => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => 11
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] => {{1,4},{2,5},{3,7},{6,8},{9,11},{10,12}} => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => 10
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => {{1,4},{2,5},{3,7},{6,9},{8,10},{11,12}} => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 11
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] => {{1,4},{2,5},{3,7},{6,9},{8,11},{10,12}} => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 10
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] => {{1,4},{2,5},{3,7},{6,10},{8,11},{9,12}} => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => 9
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => {{1,4},{2,5},{3,8},{6,9},{7,10},{11,12}} => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => 11
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] => {{1,4},{2,5},{3,8},{6,9},{7,11},{10,12}} => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 10
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => {{1,4},{2,5},{3,8},{6,10},{7,11},{9,12}} => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => 9
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] => {{1,4},{2,5},{3,9},{6,10},{7,11},{8,12}} => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => 8
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => {{1,4},{2,6},{3,7},{5,8},{9,10},{11,12}} => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => 11
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] => {{1,4},{2,6},{3,7},{5,8},{9,11},{10,12}} => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => 10
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] => {{1,4},{2,6},{3,7},{5,9},{8,10},{11,12}} => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 11
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] => {{1,4},{2,6},{3,7},{5,9},{8,11},{10,12}} => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 10
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => {{1,4},{2,6},{3,7},{5,10},{8,11},{9,12}} => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => 9
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] => {{1,4},{2,6},{3,8},{5,9},{7,10},{11,12}} => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => 11
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] => {{1,4},{2,6},{3,8},{5,9},{7,11},{10,12}} => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 10
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] => {{1,4},{2,6},{3,8},{5,10},{7,11},{9,12}} => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => 9
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] => {{1,4},{2,6},{3,9},{5,10},{7,11},{8,12}} => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => 8
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => {{1,4},{2,7},{3,8},{5,9},{6,10},{11,12}} => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => 11
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] => {{1,4},{2,7},{3,8},{5,9},{6,11},{10,12}} => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => 10
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] => {{1,4},{2,7},{3,8},{5,10},{6,11},{9,12}} => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => 9
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] => {{1,4},{2,7},{3,9},{5,10},{6,11},{8,12}} => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => 8
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => {{1,4},{2,8},{3,9},{5,10},{6,11},{7,12}} => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => 7
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] => {{1,5},{2,6},{3,7},{4,8},{9,10},{11,12}} => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => 11
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] => {{1,5},{2,6},{3,7},{4,8},{9,11},{10,12}} => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => 10
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] => {{1,5},{2,6},{3,7},{4,9},{8,10},{11,12}} => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => 11
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] => {{1,5},{2,6},{3,7},{4,9},{8,11},{10,12}} => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => 10
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] => {{1,5},{2,6},{3,7},{4,10},{8,11},{9,12}} => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => 9
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] => {{1,5},{2,6},{3,8},{4,9},{7,10},{11,12}} => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => 11
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] => {{1,5},{2,6},{3,8},{4,9},{7,11},{10,12}} => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => 10
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] => {{1,5},{2,6},{3,8},{4,10},{7,11},{9,12}} => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => 9
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] => {{1,5},{2,6},{3,9},{4,10},{7,11},{8,12}} => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => 8
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] => {{1,5},{2,7},{3,8},{4,9},{6,10},{11,12}} => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => 11
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] => {{1,5},{2,7},{3,8},{4,9},{6,11},{10,12}} => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => 10
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] => {{1,5},{2,7},{3,8},{4,10},{6,11},{9,12}} => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => 9
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] => {{1,5},{2,7},{3,9},{4,10},{6,11},{8,12}} => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => 8
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] => {{1,5},{2,8},{3,9},{4,10},{6,11},{7,12}} => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => 7
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => {{1,6},{2,7},{3,8},{4,9},{5,10},{11,12}} => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => 11
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] => {{1,6},{2,7},{3,8},{4,9},{5,11},{10,12}} => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => 10
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => {{1,6},{2,7},{3,8},{4,10},{5,11},{9,12}} => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => 9
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] => {{1,6},{2,7},{3,9},{4,10},{5,11},{8,12}} => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => 8
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => {{1,6},{2,8},{3,9},{4,10},{5,11},{7,12}} => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => 7
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}} => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => 6
[[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}} => 9
[[1,2,3,4,5,6,7,8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => 8
[[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}} => 10
[[1,2,3,4,5,6,7,8,9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => 9
[[1,6,9],[2,8],[3],[4],[5],[7]] => [[1,2,3,4,5,7],[6,8],[9]] => {{1,2,3,4,5,7},{6,8},{9}} => {{1,2,3,4,5,8},{6,7},{9}} => 9
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[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}} => 9
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [[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}} => 10
[[1,2,4,5,6,7,8],[3,9]] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => {{1,3},{2,9},{4},{5},{6},{7},{8}} => {{1,9},{2,3},{4},{5},{6},{7},{8}} => 8
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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 1,1,2 1,2,3,4 1,3,5,7,10 1,6,10,14,19,26 1,10,19,29,41,56,76
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + q^{2} + 2\ q^{3}$
$F_{4} = q + 2\ q^{2} + 3\ q^{3} + 4\ q^{4}$
$F_{5} = q + 3\ q^{2} + 5\ q^{3} + 7\ q^{4} + 10\ q^{5}$
$F_{6} = q + 6\ q^{2} + 10\ q^{3} + 14\ q^{4} + 19\ q^{5} + 26\ q^{6}$
$F_{7} = q + 10\ q^{2} + 19\ q^{3} + 29\ q^{4} + 41\ q^{5} + 56\ q^{6} + 76\ q^{7}$
Description
The largest opener of a set partition.
An opener (or left hand endpoint) of a set partition is a number that is minimal in its block. For this statistic, singletons are considered as openers.
An opener (or left hand endpoint) of a set partition is a number that is minimal in its block. For this statistic, singletons are considered as openers.
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
Map
Chen Deng Du Stanley Yan
Description
A map that swaps the crossing number and the nesting number of a set partition.
Map
conjugate
Description
Sends a standard tableau to its conjugate tableau.
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