- FindStat

Identifier

Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00164: Set partitions —Chen Deng Du Stanley Yan⟶ Set partitions
Mp00216: Set partitions —inverse Wachs-White⟶ Set partitions
St001050: Set partitions ⟶ ℤ

Values

[[1]] => {{1}} => {{1}} => {{1}} => 1

[[1,2]] => {{1,2}} => {{1,2}} => {{1,2}} => 1

[[1],[2]] => {{1},{2}} => {{1},{2}} => {{1},{2}} => 2

[[1,2,3]] => {{1,2,3}} => {{1,2,3}} => {{1,2,3}} => 1

[[1,3],[2]] => {{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]] => {{1},{2},{3}} => {{1},{2},{3}} => {{1},{2},{3}} => 3

[[1,2,3,4]] => {{1,2,3,4}} => {{1,2,3,4}} => {{1,2,3,4}} => 1

[[1,3,4],[2]] => {{1,3,4},{2}} => {{1,3,4},{2}} => {{1,3},{2,4}} => 2

[[1,2,4],[3]] => {{1,2,4},{3}} => {{1,2,4},{3}} => {{1,3,4},{2}} => 1

[[1,2,3],[4]] => {{1,2,3},{4}} => {{1,2,3},{4}} => {{1},{2,3,4}} => 1

[[1,3],[2,4]] => {{1,3},{2,4}} => {{1,4},{2,3}} => {{1,4},{2,3}} => 2

[[1,2],[3,4]] => {{1,2},{3,4}} => {{1,2},{3,4}} => {{1,2},{3,4}} => 1

[[1,4],[2],[3]] => {{1,4},{2},{3}} => {{1,4},{2},{3}} => {{1,4},{2},{3}} => 3

[[1,3],[2],[4]] => {{1,3},{2},{4}} => {{1,3},{2},{4}} => {{1},{2,4},{3}} => 2

[[1,2],[3],[4]] => {{1,2},{3},{4}} => {{1,2},{3},{4}} => {{1},{2},{3,4}} => 1

[[1],[2],[3],[4]] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => {{1},{2},{3},{4}} => 4

[[1,2,3,4,5]] => {{1,2,3,4,5}} => {{1,2,3,4,5}} => {{1,2,3,4,5}} => 1

[[1,3,4,5],[2]] => {{1,3,4,5},{2}} => {{1,3,4,5},{2}} => {{1,3,5},{2,4}} => 2

[[1,2,4,5],[3]] => {{1,2,4,5},{3}} => {{1,2,4,5},{3}} => {{1,3},{2,4,5}} => 1

[[1,2,3,5],[4]] => {{1,2,3,5},{4}} => {{1,2,3,5},{4}} => {{1,3,4,5},{2}} => 1

[[1,2,3,4],[5]] => {{1,2,3,4},{5}} => {{1,2,3,4},{5}} => {{1},{2,3,4,5}} => 1

[[1,3,5],[2,4]] => {{1,3,5},{2,4}} => {{1,5},{2,3,4}} => {{1,5},{2,3,4}} => 2

[[1,2,5],[3,4]] => {{1,2,5},{3,4}} => {{1,2,4},{3,5}} => {{1,2,4,5},{3}} => 1

[[1,3,4],[2,5]] => {{1,3,4},{2,5}} => {{1,4},{2,3,5}} => {{1,2,5},{3,4}} => 2

[[1,2,4],[3,5]] => {{1,2,4},{3,5}} => {{1,2,5},{3,4}} => {{1,4,5},{2,3}} => 1

[[1,2,3],[4,5]] => {{1,2,3},{4,5}} => {{1,2,3},{4,5}} => {{1,2},{3,4,5}} => 1

[[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => {{1,4,5},{2},{3}} => {{1,4},{2,5},{3}} => 3

[[1,3,5],[2],[4]] => {{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => {{1,4},{2},{3,5}} => 2

[[1,2,5],[3],[4]] => {{1,2,5},{3},{4}} => {{1,2,5},{3},{4}} => {{1,4,5},{2},{3}} => 1

[[1,3,4],[2],[5]] => {{1,3,4},{2},{5}} => {{1,3,4},{2},{5}} => {{1},{2,4},{3,5}} => 2

[[1,2,4],[3],[5]] => {{1,2,4},{3},{5}} => {{1,2,4},{3},{5}} => {{1},{2,4,5},{3}} => 1

[[1,2,3],[4],[5]] => {{1,2,3},{4},{5}} => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}} => 1

[[1,4],[2,5],[3]] => {{1,4},{2,5},{3}} => {{1,5},{2,4},{3}} => {{1,5},{2,4},{3}} => 3

[[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => {{1,5},{2,3},{4}} => {{1,5},{2},{3,4}} => 2

[[1,2],[3,5],[4]] => {{1,2},{3,5},{4}} => {{1,2},{3,5},{4}} => {{1,3},{2},{4,5}} => 1

[[1,3],[2,4],[5]] => {{1,3},{2,4},{5}} => {{1,4},{2,3},{5}} => {{1},{2,5},{3,4}} => 2

[[1,2],[3,4],[5]] => {{1,2},{3,4},{5}} => {{1,2},{3,4},{5}} => {{1},{2,3},{4,5}} => 1

[[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => 4

[[1,4],[2],[3],[5]] => {{1,4},{2},{3},{5}} => {{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}} => 3

[[1,3],[2],[4],[5]] => {{1,3},{2},{4},{5}} => {{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}} => 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]] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => 5

[[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

[[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => {{1,3,4,5,6},{2}} => {{1,3,5},{2,4,6}} => 2

[[1,2,4,5,6],[3]] => {{1,2,4,5,6},{3}} => {{1,2,4,5,6},{3}} => {{1,3,5,6},{2,4}} => 1

[[1,2,3,5,6],[4]] => {{1,2,3,5,6},{4}} => {{1,2,3,5,6},{4}} => {{1,3},{2,4,5,6}} => 1

[[1,2,3,4,6],[5]] => {{1,2,3,4,6},{5}} => {{1,2,3,4,6},{5}} => {{1,3,4,5,6},{2}} => 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}} => 1

[[1,3,5,6],[2,4]] => {{1,3,5,6},{2,4}} => {{1,5,6},{2,3,4}} => {{1,3,4,5},{2,6}} => 2

[[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => {{1,2,4},{3,5,6}} => {{1,2,3,5,6},{4}} => 1

[[1,3,4,6],[2,5]] => {{1,3,4,6},{2,5}} => {{1,4,5},{2,3,6}} => {{1,2,4,5},{3,6}} => 2

[[1,2,4,6],[3,5]] => {{1,2,4,6},{3,5}} => {{1,2,6},{3,4,5}} => {{1,5,6},{2,3,4}} => 1

[[1,2,3,6],[4,5]] => {{1,2,3,6},{4,5}} => {{1,2,3,5},{4,6}} => {{1,2,4,5,6},{3}} => 1

[[1,3,4,5],[2,6]] => {{1,3,4,5},{2,6}} => {{1,4,6},{2,3,5}} => {{1,4,5},{2,3,6}} => 2

[[1,2,4,5],[3,6]] => {{1,2,4,5},{3,6}} => {{1,2,5},{3,4,6}} => {{1,2,5,6},{3,4}} => 1

[[1,2,3,5],[4,6]] => {{1,2,3,5},{4,6}} => {{1,2,3,6},{4,5}} => {{1,4,5,6},{2,3}} => 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}} => 1

[[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => {{1,4,5,6},{2},{3}} => {{1,4},{2,5},{3,6}} => 3

[[1,3,5,6],[2],[4]] => {{1,3,5,6},{2},{4}} => {{1,3,5,6},{2},{4}} => {{1,4,6},{2,5},{3}} => 2

[[1,2,5,6],[3],[4]] => {{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => {{1,4},{2,5,6},{3}} => 1

[[1,3,4,6],[2],[5]] => {{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => {{1,4,6},{2},{3,5}} => 2

[[1,2,4,6],[3],[5]] => {{1,2,4,6},{3},{5}} => {{1,2,4,6},{3},{5}} => {{1,4},{2},{3,5,6}} => 1

[[1,2,3,6],[4],[5]] => {{1,2,3,6},{4},{5}} => {{1,2,3,6},{4},{5}} => {{1,4,5,6},{2},{3}} => 1

[[1,3,4,5],[2],[6]] => {{1,3,4,5},{2},{6}} => {{1,3,4,5},{2},{6}} => {{1},{2,4,6},{3,5}} => 2

[[1,2,4,5],[3],[6]] => {{1,2,4,5},{3},{6}} => {{1,2,4,5},{3},{6}} => {{1},{2,4},{3,5,6}} => 1

[[1,2,3,5],[4],[6]] => {{1,2,3,5},{4},{6}} => {{1,2,3,5},{4},{6}} => {{1},{2,4,5,6},{3}} => 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}} => 1

[[1,3,5],[2,4,6]] => {{1,3,5},{2,4,6}} => {{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => 2

[[1,2,5],[3,4,6]] => {{1,2,5},{3,4,6}} => {{1,2,4,5},{3,6}} => {{1,2,4},{3,5,6}} => 1

[[1,3,4],[2,5,6]] => {{1,3,4},{2,5,6}} => {{1,4},{2,3,5,6}} => {{1,2,3,6},{4,5}} => 2

[[1,2,4],[3,5,6]] => {{1,2,4},{3,5,6}} => {{1,2,5,6},{3,4}} => {{1,3,4},{2,5,6}} => 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}} => 1

[[1,4,6],[2,5],[3]] => {{1,4,6},{2,5},{3}} => {{1,6},{2,4,5},{3}} => {{1,6},{2,4},{3,5}} => 3

[[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => {{1,6},{2,3,5},{4}} => {{1,6},{2,4,5},{3}} => 2

[[1,2,6],[3,5],[4]] => {{1,2,6},{3,5},{4}} => {{1,2,5},{3,6},{4}} => {{1,3},{2,5,6},{4}} => 1

[[1,3,6],[2,4],[5]] => {{1,3,6},{2,4},{5}} => {{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}} => 2

[[1,2,6],[3,4],[5]] => {{1,2,6},{3,4},{5}} => {{1,2,4},{3,6},{5}} => {{1,3,5,6},{2},{4}} => 1

[[1,4,5],[2,6],[3]] => {{1,4,5},{2,6},{3}} => {{1,5},{2,4,6},{3}} => {{1,3,5},{2,6},{4}} => 3

[[1,3,5],[2,6],[4]] => {{1,3,5},{2,6},{4}} => {{1,5},{2,3,6},{4}} => {{1,3},{2,6},{4,5}} => 2

[[1,2,5],[3,6],[4]] => {{1,2,5},{3,6},{4}} => {{1,2,6},{3,5},{4}} => {{1,5,6},{2,4},{3}} => 1

[[1,3,4],[2,6],[5]] => {{1,3,4},{2,6},{5}} => {{1,4},{2,3,6},{5}} => {{1,3,6},{2},{4,5}} => 2

[[1,2,4],[3,6],[5]] => {{1,2,4},{3,6},{5}} => {{1,2,6},{3,4},{5}} => {{1,5,6},{2},{3,4}} => 1

[[1,2,3],[4,6],[5]] => {{1,2,3},{4,6},{5}} => {{1,2,3},{4,6},{5}} => {{1,3},{2},{4,5,6}} => 1

[[1,3,5],[2,4],[6]] => {{1,3,5},{2,4},{6}} => {{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}} => 2

[[1,2,5],[3,4],[6]] => {{1,2,5},{3,4},{6}} => {{1,2,4},{3,5},{6}} => {{1},{2,3,5,6},{4}} => 1

[[1,3,4],[2,5],[6]] => {{1,3,4},{2,5},{6}} => {{1,4},{2,3,5},{6}} => {{1},{2,3,6},{4,5}} => 2

[[1,2,4],[3,5],[6]] => {{1,2,4},{3,5},{6}} => {{1,2,5},{3,4},{6}} => {{1},{2,5,6},{3,4}} => 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}} => 1

[[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => {{1,5,6},{2},{3},{4}} => {{1,5},{2,6},{3},{4}} => 4

[[1,4,6],[2],[3],[5]] => {{1,4,6},{2},{3},{5}} => {{1,4,6},{2},{3},{5}} => {{1,5},{2},{3,6},{4}} => 3

[[1,3,6],[2],[4],[5]] => {{1,3,6},{2},{4},{5}} => {{1,3,6},{2},{4},{5}} => {{1,5},{2},{3},{4,6}} => 2

[[1,2,6],[3],[4],[5]] => {{1,2,6},{3},{4},{5}} => {{1,2,6},{3},{4},{5}} => {{1,5,6},{2},{3},{4}} => 1

[[1,4,5],[2],[3],[6]] => {{1,4,5},{2},{3},{6}} => {{1,4,5},{2},{3},{6}} => {{1},{2,5},{3,6},{4}} => 3

[[1,3,5],[2],[4],[6]] => {{1,3,5},{2},{4},{6}} => {{1,3,5},{2},{4},{6}} => {{1},{2,5},{3},{4,6}} => 2

[[1,2,5],[3],[4],[6]] => {{1,2,5},{3},{4},{6}} => {{1,2,5},{3},{4},{6}} => {{1},{2,5,6},{3},{4}} => 1

[[1,3,4],[2],[5],[6]] => {{1,3,4},{2},{5},{6}} => {{1,3,4},{2},{5},{6}} => {{1},{2},{3,5},{4,6}} => 2

[[1,2,4],[3],[5],[6]] => {{1,2,4},{3},{5},{6}} => {{1,2,4},{3},{5},{6}} => {{1},{2},{3,5,6},{4}} => 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}} => 1

[[1,4],[2,5],[3,6]] => {{1,4},{2,5},{3,6}} => {{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => 3

[[1,3],[2,5],[4,6]] => {{1,3},{2,5},{4,6}} => {{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => 2

>>> Load all 580 entries. <<<

[[1,2],[3,5],[4,6]] => {{1,2},{3,5},{4,6}} => {{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => 1

[[1,3],[2,4],[5,6]] => {{1,3},{2,4},{5,6}} => {{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => 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

[[1,5],[2,6],[3],[4]] => {{1,5},{2,6},{3},{4}} => {{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}} => 4

[[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => {{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}} => 3

[[1,3],[2,6],[4],[5]] => {{1,3},{2,6},{4},{5}} => {{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}} => 2

[[1,2],[3,6],[4],[5]] => {{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}} => {{1,4},{2},{3},{5,6}} => 1

[[1,4],[2,5],[3],[6]] => {{1,4},{2,5},{3},{6}} => {{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}} => 3

[[1,3],[2,5],[4],[6]] => {{1,3},{2,5},{4},{6}} => {{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}} => 2

[[1,2],[3,5],[4],[6]] => {{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}} => {{1},{2,4},{3},{5,6}} => 1

[[1,3],[2,4],[5],[6]] => {{1,3},{2,4},{5},{6}} => {{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}} => 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

[[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => 5

[[1,5],[2],[3],[4],[6]] => {{1,5},{2},{3},{4},{6}} => {{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}} => 4

[[1,4],[2],[3],[5],[6]] => {{1,4},{2},{3},{5},{6}} => {{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}} => 3

[[1,3],[2],[4],[5],[6]] => {{1,3},{2},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}} => 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]] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => 6

[[1,2,3,4,5,6,7]] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => 1

[[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => {{1,3,4,5,6,7},{2}} => {{1,3,5,7},{2,4,6}} => 2

[[1,2,4,5,6,7],[3]] => {{1,2,4,5,6,7},{3}} => {{1,2,4,5,6,7},{3}} => {{1,3,5},{2,4,6,7}} => 1

[[1,2,3,5,6,7],[4]] => {{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}} => {{1,3,5,6,7},{2,4}} => 1

[[1,2,3,4,6,7],[5]] => {{1,2,3,4,6,7},{5}} => {{1,2,3,4,6,7},{5}} => {{1,3},{2,4,5,6,7}} => 1

[[1,2,3,4,5,7],[6]] => {{1,2,3,4,5,7},{6}} => {{1,2,3,4,5,7},{6}} => {{1,3,4,5,6,7},{2}} => 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}} => 1

[[1,3,5,6,7],[2,4]] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,3,4}} => {{1,3,7},{2,4,5,6}} => 2

[[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => {{1,2,4},{3,5,6,7}} => {{1,2,3,4,6,7},{5}} => 1

[[1,3,4,6,7],[2,5]] => {{1,3,4,6,7},{2,5}} => {{1,4,5},{2,3,6,7}} => {{1,2,3,5,6},{4,7}} => 2

[[1,2,4,6,7],[3,5]] => {{1,2,4,6,7},{3,5}} => {{1,2,6,7},{3,4,5}} => {{1,3,4,5},{2,6,7}} => 1

[[1,2,3,6,7],[4,5]] => {{1,2,3,6,7},{4,5}} => {{1,2,3,5},{4,6,7}} => {{1,2,3,5,6,7},{4}} => 1

[[1,3,4,5,7],[2,6]] => {{1,3,4,5,7},{2,6}} => {{1,4,7},{2,3,5,6}} => {{1,5,6},{2,3,4,7}} => 2

[[1,2,4,5,7],[3,6]] => {{1,2,4,5,7},{3,6}} => {{1,2,5,6},{3,4,7}} => {{1,2,4,5},{3,6,7}} => 1

[[1,2,3,5,7],[4,6]] => {{1,2,3,5,7},{4,6}} => {{1,2,3,7},{4,5,6}} => {{1,5,6,7},{2,3,4}} => 1

[[1,2,3,4,7],[5,6]] => {{1,2,3,4,7},{5,6}} => {{1,2,3,4,6},{5,7}} => {{1,2,4,5,6,7},{3}} => 1

[[1,3,4,5,6],[2,7]] => {{1,3,4,5,6},{2,7}} => {{1,4,6},{2,3,5,7}} => {{1,2,5,6},{3,4,7}} => 2

[[1,2,4,5,6],[3,7]] => {{1,2,4,5,6},{3,7}} => {{1,2,5,7},{3,4,6}} => {{1,4,5},{2,3,6,7}} => 1

[[1,2,3,5,6],[4,7]] => {{1,2,3,5,6},{4,7}} => {{1,2,3,6},{4,5,7}} => {{1,2,5,6,7},{3,4}} => 1

[[1,2,3,4,6],[5,7]] => {{1,2,3,4,6},{5,7}} => {{1,2,3,4,7},{5,6}} => {{1,4,5,6,7},{2,3}} => 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}} => 1

[[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => {{1,4,5,6,7},{2},{3}} => {{1,4,7},{2,5},{3,6}} => 3

[[1,3,5,6,7],[2],[4]] => {{1,3,5,6,7},{2},{4}} => {{1,3,5,6,7},{2},{4}} => {{1,4},{2,5,7},{3,6}} => 2

[[1,2,5,6,7],[3],[4]] => {{1,2,5,6,7},{3},{4}} => {{1,2,5,6,7},{3},{4}} => {{1,4},{2,5},{3,6,7}} => 1

[[1,3,4,6,7],[2],[5]] => {{1,3,4,6,7},{2},{5}} => {{1,3,4,6,7},{2},{5}} => {{1,4,6},{2,5,7},{3}} => 2

[[1,2,4,6,7],[3],[5]] => {{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}} => {{1,4,6,7},{2,5},{3}} => 1

[[1,2,3,6,7],[4],[5]] => {{1,2,3,6,7},{4},{5}} => {{1,2,3,6,7},{4},{5}} => {{1,4},{2,5,6,7},{3}} => 1

[[1,3,4,5,7],[2],[6]] => {{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}} => {{1,4,6},{2},{3,5,7}} => 2

[[1,2,4,5,7],[3],[6]] => {{1,2,4,5,7},{3},{6}} => {{1,2,4,5,7},{3},{6}} => {{1,4,6,7},{2},{3,5}} => 1

[[1,2,3,5,7],[4],[6]] => {{1,2,3,5,7},{4},{6}} => {{1,2,3,5,7},{4},{6}} => {{1,4},{2},{3,5,6,7}} => 1

[[1,2,3,4,7],[5],[6]] => {{1,2,3,4,7},{5},{6}} => {{1,2,3,4,7},{5},{6}} => {{1,4,5,6,7},{2},{3}} => 1

[[1,3,4,5,6],[2],[7]] => {{1,3,4,5,6},{2},{7}} => {{1,3,4,5,6},{2},{7}} => {{1},{2,4,6},{3,5,7}} => 2

[[1,2,4,5,6],[3],[7]] => {{1,2,4,5,6},{3},{7}} => {{1,2,4,5,6},{3},{7}} => {{1},{2,4,6,7},{3,5}} => 1

[[1,2,3,5,6],[4],[7]] => {{1,2,3,5,6},{4},{7}} => {{1,2,3,5,6},{4},{7}} => {{1},{2,4},{3,5,6,7}} => 1

[[1,2,3,4,6],[5],[7]] => {{1,2,3,4,6},{5},{7}} => {{1,2,3,4,6},{5},{7}} => {{1},{2,4,5,6,7},{3}} => 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}} => 1

[[1,3,5,7],[2,4,6]] => {{1,3,5,7},{2,4,6}} => {{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => 2

[[1,2,5,7],[3,4,6]] => {{1,2,5,7},{3,4,6}} => {{1,2,4,5,6},{3,7}} => {{1,2,4,6,7},{3,5}} => 1

[[1,3,4,7],[2,5,6]] => {{1,3,4,7},{2,5,6}} => {{1,4,5,7},{2,3,6}} => {{1,4,7},{2,3,5,6}} => 2

[[1,2,4,7],[3,5,6]] => {{1,2,4,7},{3,5,6}} => {{1,2,6},{3,4,5,7}} => {{1,2,6,7},{3,4,5}} => 1

[[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => {{1,2,3,5,7},{4,6}} => {{1,4},{2,3,5,6,7}} => 1

[[1,3,5,6],[2,4,7]] => {{1,3,5,6},{2,4,7}} => {{1,6},{2,3,4,5,7}} => {{1,2,7},{3,4,5,6}} => 2

[[1,2,5,6],[3,4,7]] => {{1,2,5,6},{3,4,7}} => {{1,2,4,5,7},{3,6}} => {{1,4,6,7},{2,3,5}} => 1

[[1,3,4,6],[2,5,7]] => {{1,3,4,6},{2,5,7}} => {{1,4,5,6},{2,3,7}} => {{1,2,4,7},{3,5,6}} => 2

[[1,2,4,6],[3,5,7]] => {{1,2,4,6},{3,5,7}} => {{1,2,7},{3,4,5,6}} => {{1,6,7},{2,3,4,5}} => 1

[[1,2,3,6],[4,5,7]] => {{1,2,3,6},{4,5,7}} => {{1,2,3,5,6},{4,7}} => {{1,2,4},{3,5,6,7}} => 1

[[1,3,4,5],[2,6,7]] => {{1,3,4,5},{2,6,7}} => {{1,4,6,7},{2,3,5}} => {{1,3,4,7},{2,5,6}} => 2

[[1,2,4,5],[3,6,7]] => {{1,2,4,5},{3,6,7}} => {{1,2,5},{3,4,6,7}} => {{1,2,3,6,7},{4,5}} => 1

[[1,2,3,5],[4,6,7]] => {{1,2,3,5},{4,6,7}} => {{1,2,3,6,7},{4,5}} => {{1,3,4},{2,5,6,7}} => 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}} => 1

[[1,4,6,7],[2,5],[3]] => {{1,4,6,7},{2,5},{3}} => {{1,6,7},{2,4,5},{3}} => {{1,4,6},{2,7},{3,5}} => 3

[[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => {{1,6,7},{2,3,5},{4}} => {{1,4},{2,7},{3,5,6}} => 2

[[1,2,6,7],[3,5],[4]] => {{1,2,6,7},{3,5},{4}} => {{1,2,5},{3,6,7},{4}} => {{1,3,6,7},{2,4},{5}} => 1

[[1,3,6,7],[2,4],[5]] => {{1,3,6,7},{2,4},{5}} => {{1,6,7},{2,3,4},{5}} => {{1,4,5,6},{2,7},{3}} => 2

[[1,2,6,7],[3,4],[5]] => {{1,2,6,7},{3,4},{5}} => {{1,2,4},{3,6,7},{5}} => {{1,3},{2,4,6,7},{5}} => 1

[[1,4,5,7],[2,6],[3]] => {{1,4,5,7},{2,6},{3}} => {{1,5,6},{2,4,7},{3}} => {{1,3,7},{2,5},{4,6}} => 3

[[1,3,5,7],[2,6],[4]] => {{1,3,5,7},{2,6},{4}} => {{1,5,6},{2,3,7},{4}} => {{1,3,7},{2,5,6},{4}} => 2

[[1,2,5,7],[3,6],[4]] => {{1,2,5,7},{3,6},{4}} => {{1,2,7},{3,5,6},{4}} => {{1,6,7},{2,4},{3,5}} => 1

[[1,3,4,7],[2,6],[5]] => {{1,3,4,7},{2,6},{5}} => {{1,4,6},{2,3,7},{5}} => {{1,3},{2,5,6},{4,7}} => 2

[[1,2,4,7],[3,6],[5]] => {{1,2,4,7},{3,6},{5}} => {{1,2,7},{3,4,6},{5}} => {{1,6,7},{2,4,5},{3}} => 1

[[1,2,3,7],[4,6],[5]] => {{1,2,3,7},{4,6},{5}} => {{1,2,3,6},{4,7},{5}} => {{1,3},{2,5,6,7},{4}} => 1

[[1,3,5,7],[2,4],[6]] => {{1,3,5,7},{2,4},{6}} => {{1,5,7},{2,3,4},{6}} => {{1,4,5,6},{2},{3,7}} => 2

[[1,2,5,7],[3,4],[6]] => {{1,2,5,7},{3,4},{6}} => {{1,2,4},{3,5,7},{6}} => {{1,3,4,6,7},{2},{5}} => 1

[[1,3,4,7],[2,5],[6]] => {{1,3,4,7},{2,5},{6}} => {{1,4,5},{2,3,7},{6}} => {{1,3,5,6},{2},{4,7}} => 2

[[1,2,4,7],[3,5],[6]] => {{1,2,4,7},{3,5},{6}} => {{1,2,7},{3,4,5},{6}} => {{1,6,7},{2},{3,4,5}} => 1

[[1,2,3,7],[4,5],[6]] => {{1,2,3,7},{4,5},{6}} => {{1,2,3,5},{4,7},{6}} => {{1,3,5,6,7},{2},{4}} => 1

[[1,4,5,6],[2,7],[3]] => {{1,4,5,6},{2,7},{3}} => {{1,5,7},{2,4,6},{3}} => {{1,5},{2,4,6},{3,7}} => 3

[[1,3,5,6],[2,7],[4]] => {{1,3,5,6},{2,7},{4}} => {{1,5,7},{2,3,6},{4}} => {{1,5,6},{2,4},{3,7}} => 2

[[1,2,5,6],[3,7],[4]] => {{1,2,5,6},{3,7},{4}} => {{1,2,6},{3,5,7},{4}} => {{1,3,5},{2,6,7},{4}} => 1

[[1,3,4,6],[2,7],[5]] => {{1,3,4,6},{2,7},{5}} => {{1,4,7},{2,3,6},{5}} => {{1,5,6},{2,4,7},{3}} => 2

[[1,2,4,6],[3,7],[5]] => {{1,2,4,6},{3,7},{5}} => {{1,2,6},{3,4,7},{5}} => {{1,3},{2,6,7},{4,5}} => 1

[[1,2,3,6],[4,7],[5]] => {{1,2,3,6},{4,7},{5}} => {{1,2,3,7},{4,6},{5}} => {{1,5,6,7},{2,4},{3}} => 1

[[1,3,4,5],[2,7],[6]] => {{1,3,4,5},{2,7},{6}} => {{1,4,7},{2,3,5},{6}} => {{1,5,6},{2},{3,4,7}} => 2

[[1,2,4,5],[3,7],[6]] => {{1,2,4,5},{3,7},{6}} => {{1,2,5},{3,4,7},{6}} => {{1,3,6,7},{2},{4,5}} => 1

[[1,2,3,5],[4,7],[6]] => {{1,2,3,5},{4,7},{6}} => {{1,2,3,7},{4,5},{6}} => {{1,5,6,7},{2},{3,4}} => 1

[[1,2,3,4],[5,7],[6]] => {{1,2,3,4},{5,7},{6}} => {{1,2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6,7}} => 1

[[1,3,5,6],[2,4],[7]] => {{1,3,5,6},{2,4},{7}} => {{1,5,6},{2,3,4},{7}} => {{1},{2,4,5,6},{3,7}} => 2

[[1,2,5,6],[3,4],[7]] => {{1,2,5,6},{3,4},{7}} => {{1,2,4},{3,5,6},{7}} => {{1},{2,3,4,6,7},{5}} => 1

[[1,3,4,6],[2,5],[7]] => {{1,3,4,6},{2,5},{7}} => {{1,4,5},{2,3,6},{7}} => {{1},{2,3,5,6},{4,7}} => 2

[[1,2,4,6],[3,5],[7]] => {{1,2,4,6},{3,5},{7}} => {{1,2,6},{3,4,5},{7}} => {{1},{2,6,7},{3,4,5}} => 1

[[1,2,3,6],[4,5],[7]] => {{1,2,3,6},{4,5},{7}} => {{1,2,3,5},{4,6},{7}} => {{1},{2,3,5,6,7},{4}} => 1

[[1,3,4,5],[2,6],[7]] => {{1,3,4,5},{2,6},{7}} => {{1,4,6},{2,3,5},{7}} => {{1},{2,5,6},{3,4,7}} => 2

[[1,2,4,5],[3,6],[7]] => {{1,2,4,5},{3,6},{7}} => {{1,2,5},{3,4,6},{7}} => {{1},{2,3,6,7},{4,5}} => 1

[[1,2,3,5],[4,6],[7]] => {{1,2,3,5},{4,6},{7}} => {{1,2,3,6},{4,5},{7}} => {{1},{2,5,6,7},{3,4}} => 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}} => 1

[[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => {{1,5,6,7},{2},{3},{4}} => {{1,5},{2,6},{3,7},{4}} => 4

[[1,4,6,7],[2],[3],[5]] => {{1,4,6,7},{2},{3},{5}} => {{1,4,6,7},{2},{3},{5}} => {{1,5},{2,6},{3},{4,7}} => 3

[[1,3,6,7],[2],[4],[5]] => {{1,3,6,7},{2},{4},{5}} => {{1,3,6,7},{2},{4},{5}} => {{1,5,7},{2,6},{3},{4}} => 2

[[1,2,6,7],[3],[4],[5]] => {{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => {{1,5},{2,6,7},{3},{4}} => 1

[[1,4,5,7],[2],[3],[6]] => {{1,4,5,7},{2},{3},{6}} => {{1,4,5,7},{2},{3},{6}} => {{1,5},{2},{3,6},{4,7}} => 3

[[1,3,5,7],[2],[4],[6]] => {{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => {{1,5,7},{2},{3,6},{4}} => 2

[[1,2,5,7],[3],[4],[6]] => {{1,2,5,7},{3},{4},{6}} => {{1,2,5,7},{3},{4},{6}} => {{1,5},{2},{3,6,7},{4}} => 1

[[1,3,4,7],[2],[5],[6]] => {{1,3,4,7},{2},{5},{6}} => {{1,3,4,7},{2},{5},{6}} => {{1,5,7},{2},{3},{4,6}} => 2

[[1,2,4,7],[3],[5],[6]] => {{1,2,4,7},{3},{5},{6}} => {{1,2,4,7},{3},{5},{6}} => {{1,5},{2},{3},{4,6,7}} => 1

[[1,2,3,7],[4],[5],[6]] => {{1,2,3,7},{4},{5},{6}} => {{1,2,3,7},{4},{5},{6}} => {{1,5,6,7},{2},{3},{4}} => 1

[[1,4,5,6],[2],[3],[7]] => {{1,4,5,6},{2},{3},{7}} => {{1,4,5,6},{2},{3},{7}} => {{1},{2,5},{3,6},{4,7}} => 3

[[1,3,5,6],[2],[4],[7]] => {{1,3,5,6},{2},{4},{7}} => {{1,3,5,6},{2},{4},{7}} => {{1},{2,5,7},{3,6},{4}} => 2

[[1,2,5,6],[3],[4],[7]] => {{1,2,5,6},{3},{4},{7}} => {{1,2,5,6},{3},{4},{7}} => {{1},{2,5},{3,6,7},{4}} => 1

[[1,3,4,6],[2],[5],[7]] => {{1,3,4,6},{2},{5},{7}} => {{1,3,4,6},{2},{5},{7}} => {{1},{2,5,7},{3},{4,6}} => 2

[[1,2,4,6],[3],[5],[7]] => {{1,2,4,6},{3},{5},{7}} => {{1,2,4,6},{3},{5},{7}} => {{1},{2,5},{3},{4,6,7}} => 1

[[1,2,3,6],[4],[5],[7]] => {{1,2,3,6},{4},{5},{7}} => {{1,2,3,6},{4},{5},{7}} => {{1},{2,5,6,7},{3},{4}} => 1

[[1,3,4,5],[2],[6],[7]] => {{1,3,4,5},{2},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,5,7},{4,6}} => 2

[[1,2,4,5],[3],[6],[7]] => {{1,2,4,5},{3},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,5},{4,6,7}} => 1

[[1,2,3,5],[4],[6],[7]] => {{1,2,3,5},{4},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => {{1},{2},{3,5,6,7},{4}} => 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}} => 1

[[1,4,6],[2,5,7],[3]] => {{1,4,6},{2,5,7},{3}} => {{1,7},{2,4,5,6},{3}} => {{1,7},{2,4,6},{3,5}} => 3

[[1,3,6],[2,5,7],[4]] => {{1,3,6},{2,5,7},{4}} => {{1,7},{2,3,5,6},{4}} => {{1,7},{2,4},{3,5,6}} => 2

[[1,2,6],[3,5,7],[4]] => {{1,2,6},{3,5,7},{4}} => {{1,2,5,6},{3,7},{4}} => {{1,3,6,7},{2,5},{4}} => 1

[[1,3,6],[2,4,7],[5]] => {{1,3,6},{2,4,7},{5}} => {{1,7},{2,3,4,6},{5}} => {{1,7},{2,4,5,6},{3}} => 2

[[1,2,6],[3,4,7],[5]] => {{1,2,6},{3,4,7},{5}} => {{1,2,4,6},{3,7},{5}} => {{1,3},{2,5},{4,6,7}} => 1

[[1,4,5],[2,6,7],[3]] => {{1,4,5},{2,6,7},{3}} => {{1,5},{2,4,6,7},{3}} => {{1,3,7},{2,4,6},{5}} => 3

[[1,3,5],[2,6,7],[4]] => {{1,3,5},{2,6,7},{4}} => {{1,5},{2,3,6,7},{4}} => {{1,3,7},{2,4},{5,6}} => 2

[[1,2,5],[3,6,7],[4]] => {{1,2,5},{3,6,7},{4}} => {{1,2,6,7},{3,5},{4}} => {{1,4},{2,6,7},{3,5}} => 1

[[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => {{1,4},{2,3,6,7},{5}} => {{1,3},{2,4,7},{5,6}} => 2

[[1,2,4],[3,6,7],[5]] => {{1,2,4},{3,6,7},{5}} => {{1,2,6,7},{3,4},{5}} => {{1,4,5},{2,6,7},{3}} => 1

[[1,2,3],[4,6,7],[5]] => {{1,2,3},{4,6,7},{5}} => {{1,2,3},{4,6,7},{5}} => {{1,3},{2,4},{5,6,7}} => 1

[[1,3,5],[2,4,7],[6]] => {{1,3,5},{2,4,7},{6}} => {{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}} => 2

[[1,2,5],[3,4,7],[6]] => {{1,2,5},{3,4,7},{6}} => {{1,2,4,5},{3,7},{6}} => {{1,3,5},{2},{4,6,7}} => 1

[[1,3,4],[2,5,7],[6]] => {{1,3,4},{2,5,7},{6}} => {{1,4},{2,3,5,7},{6}} => {{1,3,4,7},{2},{5,6}} => 2

[[1,2,4],[3,5,7],[6]] => {{1,2,4},{3,5,7},{6}} => {{1,2,5,7},{3,4},{6}} => {{1,4,5},{2},{3,6,7}} => 1

[[1,2,3],[4,5,7],[6]] => {{1,2,3},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}} => {{1,3,4},{2},{5,6,7}} => 1

[[1,3,5],[2,4,6],[7]] => {{1,3,5},{2,4,6},{7}} => {{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}} => 2

[[1,2,5],[3,4,6],[7]] => {{1,2,5},{3,4,6},{7}} => {{1,2,4,5},{3,6},{7}} => {{1},{2,3,5},{4,6,7}} => 1

[[1,3,4],[2,5,6],[7]] => {{1,3,4},{2,5,6},{7}} => {{1,4},{2,3,5,6},{7}} => {{1},{2,3,4,7},{5,6}} => 2

[[1,2,4],[3,5,6],[7]] => {{1,2,4},{3,5,6},{7}} => {{1,2,5,6},{3,4},{7}} => {{1},{2,4,5},{3,6,7}} => 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}} => 1

[[1,4,7],[2,5],[3,6]] => {{1,4,7},{2,5},{3,6}} => {{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => 3

[[1,3,7],[2,5],[4,6]] => {{1,3,7},{2,5},{4,6}} => {{1,6},{2,3,5},{4,7}} => {{1,2,7},{3,5,6},{4}} => 2

[[1,2,7],[3,5],[4,6]] => {{1,2,7},{3,5},{4,6}} => {{1,2,6},{3,7},{4,5}} => {{1,3,4},{2,6,7},{5}} => 1

[[1,3,7],[2,4],[5,6]] => {{1,3,7},{2,4},{5,6}} => {{1,6},{2,3,4},{5,7}} => {{1,2,7},{3},{4,5,6}} => 2

[[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => {{1,2,4},{3,6},{5,7}} => {{1,2,4,6,7},{3},{5}} => 1

[[1,4,6],[2,5],[3,7]] => {{1,4,6},{2,5},{3,7}} => {{1,6},{2,5},{3,4,7}} => {{1,2,7},{3,6},{4,5}} => 3

[[1,3,6],[2,5],[4,7]] => {{1,3,6},{2,5},{4,7}} => {{1,7},{2,3,6},{4,5}} => {{1,7},{2,5,6},{3,4}} => 2

[[1,2,6],[3,5],[4,7]] => {{1,2,6},{3,5},{4,7}} => {{1,2,5},{3,7},{4,6}} => {{1,4},{2,3,6,7},{5}} => 1

[[1,3,6],[2,4],[5,7]] => {{1,3,6},{2,4},{5,7}} => {{1,7},{2,3,4},{5,6}} => {{1,7},{2,3},{4,5,6}} => 2

[[1,2,6],[3,4],[5,7]] => {{1,2,6},{3,4},{5,7}} => {{1,2,4},{3,7},{5,6}} => {{1,4,6,7},{2,3},{5}} => 1

[[1,4,5],[2,6],[3,7]] => {{1,4,5},{2,6},{3,7}} => {{1,7},{2,5},{3,4,6}} => {{1,7},{2,3,6},{4,5}} => 3

[[1,3,5],[2,6],[4,7]] => {{1,3,5},{2,6},{4,7}} => {{1,5},{2,3,7},{4,6}} => {{1,4},{2,3,7},{5,6}} => 2

[[1,2,5],[3,6],[4,7]] => {{1,2,5},{3,6},{4,7}} => {{1,2,7},{3,6},{4,5}} => {{1,6,7},{2,5},{3,4}} => 1

[[1,3,4],[2,6],[5,7]] => {{1,3,4},{2,6},{5,7}} => {{1,4},{2,3,7},{5,6}} => {{1,4,7},{2,3},{5,6}} => 2

[[1,2,4],[3,6],[5,7]] => {{1,2,4},{3,6},{5,7}} => {{1,2,7},{3,4},{5,6}} => {{1,6,7},{2,3},{4,5}} => 1

[[1,2,3],[4,6],[5,7]] => {{1,2,3},{4,6},{5,7}} => {{1,2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6,7}} => 1

[[1,3,5],[2,4],[6,7]] => {{1,3,5},{2,4},{6,7}} => {{1,5},{2,3,4},{6,7}} => {{1,2},{3,7},{4,5,6}} => 2

[[1,2,5],[3,4],[6,7]] => {{1,2,5},{3,4},{6,7}} => {{1,2,4},{3,5},{6,7}} => {{1,2},{3,4,6,7},{5}} => 1

[[1,3,4],[2,5],[6,7]] => {{1,3,4},{2,5},{6,7}} => {{1,4},{2,3,5},{6,7}} => {{1,2},{3,4,7},{5,6}} => 2

[[1,2,4],[3,5],[6,7]] => {{1,2,4},{3,5},{6,7}} => {{1,2,5},{3,4},{6,7}} => {{1,2},{3,6,7},{4,5}} => 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}} => 1

[[1,5,7],[2,6],[3],[4]] => {{1,5,7},{2,6},{3},{4}} => {{1,7},{2,5,6},{3},{4}} => {{1,7},{2,5},{3,6},{4}} => 4

[[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => {{1,7},{2,4,6},{3},{5}} => {{1,7},{2,5},{3},{4,6}} => 3

[[1,3,7],[2,6],[4],[5]] => {{1,3,7},{2,6},{4},{5}} => {{1,7},{2,3,6},{4},{5}} => {{1,7},{2,5,6},{3},{4}} => 2

[[1,2,7],[3,6],[4],[5]] => {{1,2,7},{3,6},{4},{5}} => {{1,2,6},{3,7},{4},{5}} => {{1,4},{2,6,7},{3},{5}} => 1

[[1,4,7],[2,5],[3],[6]] => {{1,4,7},{2,5},{3},{6}} => {{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,5},{4,6}} => 3

[[1,3,7],[2,5],[4],[6]] => {{1,3,7},{2,5},{4},{6}} => {{1,7},{2,3,5},{4},{6}} => {{1,7},{2},{3,5,6},{4}} => 2

[[1,2,7],[3,5],[4],[6]] => {{1,2,7},{3,5},{4},{6}} => {{1,2,5},{3,7},{4},{6}} => {{1,4},{2},{3,6,7},{5}} => 1

[[1,3,7],[2,4],[5],[6]] => {{1,3,7},{2,4},{5},{6}} => {{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}} => 2

[[1,2,7],[3,4],[5],[6]] => {{1,2,7},{3,4},{5},{6}} => {{1,2,4},{3,7},{5},{6}} => {{1,4,6,7},{2},{3},{5}} => 1

[[1,5,6],[2,7],[3],[4]] => {{1,5,6},{2,7},{3},{4}} => {{1,6},{2,5,7},{3},{4}} => {{1,4},{2,7},{3,6},{5}} => 4

[[1,4,6],[2,7],[3],[5]] => {{1,4,6},{2,7},{3},{5}} => {{1,6},{2,4,7},{3},{5}} => {{1,4,6},{2,7},{3},{5}} => 3

[[1,3,6],[2,7],[4],[5]] => {{1,3,6},{2,7},{4},{5}} => {{1,6},{2,3,7},{4},{5}} => {{1,4},{2,7},{3},{5,6}} => 2

[[1,2,6],[3,7],[4],[5]] => {{1,2,6},{3,7},{4},{5}} => {{1,2,7},{3,6},{4},{5}} => {{1,6,7},{2,5},{3},{4}} => 1

[[1,4,5],[2,7],[3],[6]] => {{1,4,5},{2,7},{3},{6}} => {{1,5},{2,4,7},{3},{6}} => {{1,4,6},{2},{3,7},{5}} => 3

[[1,3,5],[2,7],[4],[6]] => {{1,3,5},{2,7},{4},{6}} => {{1,5},{2,3,7},{4},{6}} => {{1,4},{2},{3,7},{5,6}} => 2

[[1,2,5],[3,7],[4],[6]] => {{1,2,5},{3,7},{4},{6}} => {{1,2,7},{3,5},{4},{6}} => {{1,6,7},{2},{3,5},{4}} => 1

[[1,3,4],[2,7],[5],[6]] => {{1,3,4},{2,7},{5},{6}} => {{1,4},{2,3,7},{5},{6}} => {{1,4,7},{2},{3},{5,6}} => 2

[[1,2,4],[3,7],[5],[6]] => {{1,2,4},{3,7},{5},{6}} => {{1,2,7},{3,4},{5},{6}} => {{1,6,7},{2},{3},{4,5}} => 1

[[1,2,3],[4,7],[5],[6]] => {{1,2,3},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6,7}} => 1

[[1,4,6],[2,5],[3],[7]] => {{1,4,6},{2,5},{3},{7}} => {{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,5},{4,6}} => 3

[[1,3,6],[2,5],[4],[7]] => {{1,3,6},{2,5},{4},{7}} => {{1,6},{2,3,5},{4},{7}} => {{1},{2,7},{3,5,6},{4}} => 2

[[1,2,6],[3,5],[4],[7]] => {{1,2,6},{3,5},{4},{7}} => {{1,2,5},{3,6},{4},{7}} => {{1},{2,4},{3,6,7},{5}} => 1

[[1,3,6],[2,4],[5],[7]] => {{1,3,6},{2,4},{5},{7}} => {{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}} => 2

[[1,2,6],[3,4],[5],[7]] => {{1,2,6},{3,4},{5},{7}} => {{1,2,4},{3,6},{5},{7}} => {{1},{2,4,6,7},{3},{5}} => 1

[[1,4,5],[2,6],[3],[7]] => {{1,4,5},{2,6},{3},{7}} => {{1,5},{2,4,6},{3},{7}} => {{1},{2,4,6},{3,7},{5}} => 3

[[1,3,5],[2,6],[4],[7]] => {{1,3,5},{2,6},{4},{7}} => {{1,5},{2,3,6},{4},{7}} => {{1},{2,4},{3,7},{5,6}} => 2

[[1,2,5],[3,6],[4],[7]] => {{1,2,5},{3,6},{4},{7}} => {{1,2,6},{3,5},{4},{7}} => {{1},{2,6,7},{3,5},{4}} => 1

[[1,3,4],[2,6],[5],[7]] => {{1,3,4},{2,6},{5},{7}} => {{1,4},{2,3,6},{5},{7}} => {{1},{2,4,7},{3},{5,6}} => 2

[[1,2,4],[3,6],[5],[7]] => {{1,2,4},{3,6},{5},{7}} => {{1,2,6},{3,4},{5},{7}} => {{1},{2,6,7},{3},{4,5}} => 1

[[1,2,3],[4,6],[5],[7]] => {{1,2,3},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6,7}} => 1

[[1,3,5],[2,4],[6],[7]] => {{1,3,5},{2,4},{6},{7}} => {{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}} => 2

[[1,2,5],[3,4],[6],[7]] => {{1,2,5},{3,4},{6},{7}} => {{1,2,4},{3,5},{6},{7}} => {{1},{2},{3,4,6,7},{5}} => 1

[[1,3,4],[2,5],[6],[7]] => {{1,3,4},{2,5},{6},{7}} => {{1,4},{2,3,5},{6},{7}} => {{1},{2},{3,4,7},{5,6}} => 2

[[1,2,4],[3,5],[6],[7]] => {{1,2,4},{3,5},{6},{7}} => {{1,2,5},{3,4},{6},{7}} => {{1},{2},{3,6,7},{4,5}} => 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}} => 1

[[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => {{1,6,7},{2},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}} => 5

[[1,5,7],[2],[3],[4],[6]] => {{1,5,7},{2},{3},{4},{6}} => {{1,5,7},{2},{3},{4},{6}} => {{1,6},{2},{3,7},{4},{5}} => 4

[[1,4,7],[2],[3],[5],[6]] => {{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => {{1,6},{2},{3},{4,7},{5}} => 3

[[1,3,7],[2],[4],[5],[6]] => {{1,3,7},{2},{4},{5},{6}} => {{1,3,7},{2},{4},{5},{6}} => {{1,6},{2},{3},{4},{5,7}} => 2

[[1,2,7],[3],[4],[5],[6]] => {{1,2,7},{3},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}} => {{1,6,7},{2},{3},{4},{5}} => 1

[[1,5,6],[2],[3],[4],[7]] => {{1,5,6},{2},{3},{4},{7}} => {{1,5,6},{2},{3},{4},{7}} => {{1},{2,6},{3,7},{4},{5}} => 4

[[1,4,6],[2],[3],[5],[7]] => {{1,4,6},{2},{3},{5},{7}} => {{1,4,6},{2},{3},{5},{7}} => {{1},{2,6},{3},{4,7},{5}} => 3

[[1,3,6],[2],[4],[5],[7]] => {{1,3,6},{2},{4},{5},{7}} => {{1,3,6},{2},{4},{5},{7}} => {{1},{2,6},{3},{4},{5,7}} => 2

[[1,2,6],[3],[4],[5],[7]] => {{1,2,6},{3},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}} => {{1},{2,6,7},{3},{4},{5}} => 1

[[1,4,5],[2],[3],[6],[7]] => {{1,4,5},{2},{3},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,6},{4,7},{5}} => 3

[[1,3,5],[2],[4],[6],[7]] => {{1,3,5},{2},{4},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => {{1},{2},{3,6},{4},{5,7}} => 2

[[1,2,5],[3],[4],[6],[7]] => {{1,2,5},{3},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => {{1},{2},{3,6,7},{4},{5}} => 1

[[1,3,4],[2],[5],[6],[7]] => {{1,3,4},{2},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}} => 2

[[1,2,4],[3],[5],[6],[7]] => {{1,2,4},{3},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6,7},{5}} => 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}} => 1

[[1,5],[2,6],[3,7],[4]] => {{1,5},{2,6},{3,7},{4}} => {{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}} => 4

[[1,4],[2,6],[3,7],[5]] => {{1,4},{2,6},{3,7},{5}} => {{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}} => 3

[[1,3],[2,6],[4,7],[5]] => {{1,3},{2,6},{4,7},{5}} => {{1,7},{2,3},{4,6},{5}} => {{1,7},{2,4},{3},{5,6}} => 2

[[1,2],[3,6],[4,7],[5]] => {{1,2},{3,6},{4,7},{5}} => {{1,2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6,7}} => 1

[[1,4],[2,5],[3,7],[6]] => {{1,4},{2,5},{3,7},{6}} => {{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}} => 3

[[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => {{1,7},{2,3},{4,5},{6}} => {{1,7},{2},{3,4},{5,6}} => 2

[[1,2],[3,5],[4,7],[6]] => {{1,2},{3,5},{4,7},{6}} => {{1,2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6,7}} => 1

[[1,3],[2,4],[5,7],[6]] => {{1,3},{2,4},{5,7},{6}} => {{1,4},{2,3},{5,7},{6}} => {{1,3},{2},{4,7},{5,6}} => 2

[[1,2],[3,4],[5,7],[6]] => {{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6,7}} => 1

[[1,4],[2,5],[3,6],[7]] => {{1,4},{2,5},{3,6},{7}} => {{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}} => 3

[[1,3],[2,5],[4,6],[7]] => {{1,3},{2,5},{4,6},{7}} => {{1,6},{2,3},{4,5},{7}} => {{1},{2,7},{3,4},{5,6}} => 2

[[1,2],[3,5],[4,6],[7]] => {{1,2},{3,5},{4,6},{7}} => {{1,2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6,7}} => 1

[[1,3],[2,4],[5,6],[7]] => {{1,3},{2,4},{5,6},{7}} => {{1,4},{2,3},{5,6},{7}} => {{1},{2,3},{4,7},{5,6}} => 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

[[1,6],[2,7],[3],[4],[5]] => {{1,6},{2,7},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => 5

[[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => {{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}} => 4

[[1,4],[2,7],[3],[5],[6]] => {{1,4},{2,7},{3},{5},{6}} => {{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}} => 3

[[1,3],[2,7],[4],[5],[6]] => {{1,3},{2,7},{4},{5},{6}} => {{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}} => 2

[[1,2],[3,7],[4],[5],[6]] => {{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6,7}} => 1

[[1,5],[2,6],[3],[4],[7]] => {{1,5},{2,6},{3},{4},{7}} => {{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}} => 4

[[1,4],[2,6],[3],[5],[7]] => {{1,4},{2,6},{3},{5},{7}} => {{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}} => 3

[[1,3],[2,6],[4],[5],[7]] => {{1,3},{2,6},{4},{5},{7}} => {{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}} => 2

[[1,2],[3,6],[4],[5],[7]] => {{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6,7}} => 1

[[1,4],[2,5],[3],[6],[7]] => {{1,4},{2,5},{3},{6},{7}} => {{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}} => 3

[[1,3],[2,5],[4],[6],[7]] => {{1,3},{2,5},{4},{6},{7}} => {{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}} => 2

[[1,2],[3,5],[4],[6],[7]] => {{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6,7}} => 1

[[1,3],[2,4],[5],[6],[7]] => {{1,3},{2,4},{5},{6},{7}} => {{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}} => 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

[[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => 6

[[1,6],[2],[3],[4],[5],[7]] => {{1,6},{2},{3},{4},{5},{7}} => {{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}} => 5

[[1,5],[2],[3],[4],[6],[7]] => {{1,5},{2},{3},{4},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}} => 4

[[1,4],[2],[3],[5],[6],[7]] => {{1,4},{2},{3},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}} => 3

[[1,3],[2],[4],[5],[6],[7]] => {{1,3},{2},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}} => 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]] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => 7

[[1,2,3,4,5,6,7,8]] => {{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

[[1,2,3,4,6,7,8],[5]] => {{1,2,3,4,6,7,8},{5}} => {{1,2,3,4,6,7,8},{5}} => {{1,3,5,6,7,8},{2,4}} => 1

[[1,2,3,4,5,7,8],[6]] => {{1,2,3,4,5,7,8},{6}} => {{1,2,3,4,5,7,8},{6}} => {{1,3},{2,4,5,6,7,8}} => 1

[[1,2,3,4,5,6,8],[7]] => {{1,2,3,4,5,6,8},{7}} => {{1,2,3,4,5,6,8},{7}} => {{1,3,4,5,6,7,8},{2}} => 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}} => 1

[[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => {{1,2,4},{3,5,6,7,8}} => {{1,2,3,4,5,7,8},{6}} => 1

[[1,3,4,6,7,8],[2,5]] => {{1,3,4,6,7,8},{2,5}} => {{1,4,5},{2,3,6,7,8}} => {{1,2,3,4,6,7},{5,8}} => 2

[[1,2,3,6,7,8],[4,5]] => {{1,2,3,6,7,8},{4,5}} => {{1,2,3,5},{4,6,7,8}} => {{1,2,3,4,6,7,8},{5}} => 1

[[1,2,3,4,7,8],[5,6]] => {{1,2,3,4,7,8},{5,6}} => {{1,2,3,4,6},{5,7,8}} => {{1,2,3,5,6,7,8},{4}} => 1

[[1,2,3,4,5,8],[6,7]] => {{1,2,3,4,5,8},{6,7}} => {{1,2,3,4,5,7},{6,8}} => {{1,2,4,5,6,7,8},{3}} => 1

[[1,2,3,4,6,7],[5,8]] => {{1,2,3,4,6,7},{5,8}} => {{1,2,3,4,7},{5,6,8}} => {{1,2,5,6,7,8},{3,4}} => 1

[[1,2,3,4,5,7],[6,8]] => {{1,2,3,4,5,7},{6,8}} => {{1,2,3,4,5,8},{6,7}} => {{1,4,5,6,7,8},{2,3}} => 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}} => 1

[[1,2,3,4,5,8],[6],[7]] => {{1,2,3,4,5,8},{6},{7}} => {{1,2,3,4,5,8},{6},{7}} => {{1,4,5,6,7,8},{2},{3}} => 1

[[1,2,3,4,5,7],[6],[8]] => {{1,2,3,4,5,7},{6},{8}} => {{1,2,3,4,5,7},{6},{8}} => {{1},{2,4,5,6,7,8},{3}} => 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}} => 1

[[1,3,5,7,8],[2,4,6]] => {{1,3,5,7,8},{2,4,6}} => {{1,7,8},{2,3,4,5,6}} => {{1,3,4,5,6,7},{2,8}} => 2

[[1,2,5,7,8],[3,4,6]] => {{1,2,5,7,8},{3,4,6}} => {{1,2,4,5,6},{3,7,8}} => {{1,2,3,5,7,8},{4,6}} => 1

[[1,2,3,7,8],[4,5,6]] => {{1,2,3,7,8},{4,5,6}} => {{1,2,3,5,7,8},{4,6}} => {{1,3,4,6,7,8},{2,5}} => 1

[[1,3,5,6,8],[2,4,7]] => {{1,3,5,6,8},{2,4,7}} => {{1,6,7},{2,3,4,5,8}} => {{1,2,4,5,6,7},{3,8}} => 2

[[1,2,3,6,8],[4,5,7]] => {{1,2,3,6,8},{4,5,7}} => {{1,2,3,5,6,7},{4,8}} => {{1,2,4,6,7,8},{3,5}} => 1

[[1,2,3,4,8],[5,6,7]] => {{1,2,3,4,8},{5,6,7}} => {{1,2,3,4,6,8},{5,7}} => {{1,4},{2,3,5,6,7,8}} => 1

[[1,2,3,5,6],[4,7,8]] => {{1,2,3,5,6},{4,7,8}} => {{1,2,3,6},{4,5,7,8}} => {{1,2,3,6,7,8},{4,5}} => 1

[[1,2,3,4,8],[5,6],[7]] => {{1,2,3,4,8},{5,6},{7}} => {{1,2,3,4,6},{5,8},{7}} => {{1,3,5,6,7,8},{2},{4}} => 1

[[1,2,3,6,7],[4,5],[8]] => {{1,2,3,6,7},{4,5},{8}} => {{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,4,6,7,8},{5}} => 1

[[1,2,3,4,7],[5,6],[8]] => {{1,2,3,4,7},{5,6},{8}} => {{1,2,3,4,6},{5,7},{8}} => {{1},{2,3,5,6,7,8},{4}} => 1

[[1,5,6,7,8],[2],[3],[4]] => {{1,5,6,7,8},{2},{3},{4}} => {{1,5,6,7,8},{2},{3},{4}} => {{1,5},{2,6},{3,7},{4,8}} => 4

[[1,3,5,7],[2,4,6,8]] => {{1,3,5,7},{2,4,6,8}} => {{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}} => 2

[[1,2,3,7],[4,5,6,8]] => {{1,2,3,7},{4,5,6,8}} => {{1,2,3,5,8},{4,6,7}} => {{1,5},{2,3,4,6,7,8}} => 1

[[1,2,4,5],[3,6,7,8]] => {{1,2,4,5},{3,6,7,8}} => {{1,2,5},{3,4,6,7,8}} => {{1,2,3,4,7,8},{5,6}} => 1

[[1,5,7,8],[2,6],[3],[4]] => {{1,5,7,8},{2,6},{3},{4}} => {{1,7,8},{2,5,6},{3},{4}} => {{1,5},{2,8},{3,6},{4,7}} => 4

[[1,4,6,8],[2,7],[3],[5]] => {{1,4,6,8},{2,7},{3},{5}} => {{1,6,7},{2,4,8},{3},{5}} => {{1,4},{2,6},{3,8},{5,7}} => 3

[[1,5,6,7],[2,8],[3],[4]] => {{1,5,6,7},{2,8},{3},{4}} => {{1,6,8},{2,5,7},{3},{4}} => {{1,6},{2,5},{3,8},{4,7}} => 4

[[1,5,7],[2,6,8],[3],[4]] => {{1,5,7},{2,6,8},{3},{4}} => {{1,8},{2,5,6,7},{3},{4}} => {{1,8},{2,5},{3,6},{4,7}} => 4

[[1,3,6],[2,7,8],[4],[5]] => {{1,3,6},{2,7,8},{4},{5}} => {{1,6},{2,3,7,8},{4},{5}} => {{1,4},{2,5},{3,8},{6,7}} => 2

[[1,5,8],[2,6],[3,7],[4]] => {{1,5,8},{2,6},{3,7},{4}} => {{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,5},{4,6}} => 4

[[1,4,7],[2,5],[3,8],[6]] => {{1,4,7},{2,5},{3,8},{6}} => {{1,7},{2,5},{3,4,8},{6}} => {{1,3},{2,8},{4,7},{5,6}} => 3

[[1,4,6],[2,7],[3,8],[5]] => {{1,4,6},{2,7},{3,8},{5}} => {{1,8},{2,6},{3,4,7},{5}} => {{1,8},{2,4},{3,7},{5,6}} => 3

[[1,3,6],[2,7],[4,8],[5]] => {{1,3,6},{2,7},{4,8},{5}} => {{1,6},{2,3,8},{4,7},{5}} => {{1,5},{2,4},{3,8},{6,7}} => 2

[[1,5],[2,6],[3,7],[4,8]] => {{1,5},{2,6},{3,7},{4,8}} => {{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}} => 4

[[1,4],[2,6],[3,7],[5,8]] => {{1,4},{2,6},{3,7},{5,8}} => {{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => 3

[[1,3],[2,6],[4,7],[5,8]] => {{1,3},{2,6},{4,7},{5,8}} => {{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}} => 2

[[1,2],[3,6],[4,7],[5,8]] => {{1,2},{3,6},{4,7},{5,8}} => {{1,2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7,8}} => 1

[[1,4],[2,5],[3,7],[6,8]] => {{1,4},{2,5},{3,7},{6,8}} => {{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}} => 3

[[1,3],[2,5],[4,7],[6,8]] => {{1,3},{2,5},{4,7},{6,8}} => {{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => 2

[[1,2],[3,5],[4,7],[6,8]] => {{1,2},{3,5},{4,7},{6,8}} => {{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}} => 1

[[1,3],[2,4],[5,7],[6,8]] => {{1,3},{2,4},{5,7},{6,8}} => {{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => 2

[[1,2],[3,4],[5,7],[6,8]] => {{1,2},{3,4},{5,7},{6,8}} => {{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}} => 1

[[1,4],[2,5],[3,6],[7,8]] => {{1,4},{2,5},{3,6},{7,8}} => {{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}} => 3

[[1,3],[2,5],[4,6],[7,8]] => {{1,3},{2,5},{4,6},{7,8}} => {{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}} => 2

[[1,2],[3,5],[4,6],[7,8]] => {{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => 1

[[1,3],[2,4],[5,6],[7,8]] => {{1,3},{2,4},{5,6},{7,8}} => {{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}} => 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

[[1,2,3,4,5,6,7,8],[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}} => 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}} => 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}} => 1

[[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}} => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,8},{4,7},{5,6}} => 5

[[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}} => {{1,4},{2,3},{5,6},{7,8},{9,10}} => 1

[[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}} => {{1,2},{3,6},{4,5},{7,8},{9,10}} => 1

[[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}} => {{1,6},{2,3},{4,5},{7,8},{9,10}} => 1

[[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}} => {{1,6},{2,5},{3,4},{7,8},{9,10}} => 1

[[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}} => {{1,2},{3,4},{5,8},{6,7},{9,10}} => 1

[[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}} => {{1,4},{2,3},{5,8},{6,7},{9,10}} => 1

[[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}} => {{1,2},{3,8},{4,5},{6,7},{9,10}} => 1

[[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}} => {{1,8},{2,3},{4,5},{6,7},{9,10}} => 1

[[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}} => {{1,8},{2,5},{3,4},{6,7},{9,10}} => 1

[[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}} => {{1,2},{3,8},{4,7},{5,6},{9,10}} => 1

[[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}} => {{1,8},{2,3},{4,7},{5,6},{9,10}} => 1

[[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}} => {{1,8},{2,7},{3,4},{5,6},{9,10}} => 1

[[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}} => {{1,8},{2,7},{3,6},{4,5},{9,10}} => 1

[[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}} => {{1,2},{3,4},{5,6},{7,10},{8,9}} => 2

[[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}} => {{1,4},{2,3},{5,6},{7,10},{8,9}} => 2

[[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}} => {{1,2},{3,6},{4,5},{7,10},{8,9}} => 2

[[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}} => {{1,6},{2,3},{4,5},{7,10},{8,9}} => 2

[[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}} => {{1,6},{2,5},{3,4},{7,10},{8,9}} => 2

[[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}} => {{1,2},{3,4},{5,10},{6,7},{8,9}} => 2

[[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}} => {{1,4},{2,3},{5,10},{6,7},{8,9}} => 2

[[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}} => {{1,2},{3,10},{4,5},{6,7},{8,9}} => 2

[[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}} => {{1,10},{2,3},{4,5},{6,7},{8,9}} => 2

[[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}} => {{1,10},{2,5},{3,4},{6,7},{8,9}} => 2

[[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}} => {{1,2},{3,10},{4,7},{5,6},{8,9}} => 2

[[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}} => {{1,10},{2,3},{4,7},{5,6},{8,9}} => 2

[[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}} => {{1,10},{2,7},{3,4},{5,6},{8,9}} => 2

[[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}} => {{1,10},{2,7},{3,6},{4,5},{8,9}} => 2

[[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}} => {{1,2},{3,4},{5,10},{6,9},{7,8}} => 3

[[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}} => {{1,4},{2,3},{5,10},{6,9},{7,8}} => 3

[[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}} => {{1,2},{3,10},{4,5},{6,9},{7,8}} => 3

[[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}} => {{1,10},{2,3},{4,5},{6,9},{7,8}} => 3

[[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}} => {{1,10},{2,5},{3,4},{6,9},{7,8}} => 3

[[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}} => {{1,2},{3,10},{4,9},{5,6},{7,8}} => 3

[[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}} => {{1,10},{2,3},{4,9},{5,6},{7,8}} => 3

[[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}} => {{1,10},{2,9},{3,4},{5,6},{7,8}} => 3

[[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}} => {{1,10},{2,9},{3,6},{4,5},{7,8}} => 3

[[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}} => {{1,2},{3,10},{4,9},{5,8},{6,7}} => 4

[[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}} => {{1,10},{2,3},{4,9},{5,8},{6,7}} => 4

[[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}} => {{1,10},{2,9},{3,4},{5,8},{6,7}} => 4

[[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}} => {{1,10},{2,9},{3,8},{4,5},{6,7}} => 4

[[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}} => {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => 1

[[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}} => {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => 1

[[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}} => {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => 1

[[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}} => {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => 1

[[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}} => {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => 1

[[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}} => {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => 1

[[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}} => {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => 1

[[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}} => {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => 1

[[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}} => {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => 1

[[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}} => {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => 1

[[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}} => {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => 1

[[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}} => {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => 1

[[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}} => {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => 1

[[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}} => {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 1

[[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}} => {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 1

[[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}} => {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 1

[[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}} => {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => 1

[[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}} => {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => 1

[[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}} => {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => 1

[[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}} => {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => 1

[[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}} => {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => 1

[[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}} => {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 1

[[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}} => {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 1

[[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}} => {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => 1

[[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}} => {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 1

[[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}} => {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 1

[[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}} => {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => 1

[[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}} => {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => 1

[[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}} => {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => 1

[[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}} => {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => 1

[[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}} => {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => 1

[[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}} => {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => 1

[[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}} => {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => 1

[[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}} => {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => 1

[[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}} => {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => 1

[[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}} => {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => 1

[[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}} => {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => 1

[[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}} => {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 2

[[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}} => {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => 2

[[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}} => {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => 2

[[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}} => {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => 2

[[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}} => {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => 2

[[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}} => {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => 2

[[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}} => {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => 2

[[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}} => {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => 2

[[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}} => {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => 2

[[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}} => {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => 2

[[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}} => {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => 2

[[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}} => {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => 2

[[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}} => {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => 2

[[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}} => {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => 2

[[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}} => {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => 2

[[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}} => {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => 2

[[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}} => {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => 2

[[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}} => {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => 2

[[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}} => {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => 2

[[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}} => {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => 2

[[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}} => {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => 2

[[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}} => {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => 2

[[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}} => {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 2

[[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}} => {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 2

[[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}} => {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => 2

[[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}} => {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 2

[[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}} => {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 2

[[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}} => {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => 2

[[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}} => {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => 2

[[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}} => {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => 2

[[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}} => {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => 2

[[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}} => {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 2

[[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}} => {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 2

[[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}} => {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => 2

[[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}} => {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 2

[[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}} => {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 2

[[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}} => {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => 2

[[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}} => {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => 2

[[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}} => {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => 2

[[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}} => {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => 2

[[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}} => {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => 2

[[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}} => {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => 2

[[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}} => {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => 3

[[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}} => {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => 3

[[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}} => {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => 3

[[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}} => {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => 3

[[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}} => {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => 3

[[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}} => {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => 3

[[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}} => {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => 3

[[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}} => {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => 3

[[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}} => {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => 3

[[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}} => {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => 3

[[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}} => {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => 3

[[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}} => {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => 3

[[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}} => {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => 3

[[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}} => {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => 3

[[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}} => {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => 3

[[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}} => {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => 3

[[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}} => {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => 3

[[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}} => {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => 3

[[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}} => {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => 3

[[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}} => {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => 3

[[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}} => {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => 3

[[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}} => {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => 3

[[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}} => {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => 3

[[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}} => {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => 3

[[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}} => {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => 3

[[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}} => {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => 3

[[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}} => {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => 3

[[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}} => {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => 3

[[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}} => {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => 4

[[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}} => {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => 4

[[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}} => {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => 4

[[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}} => {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => 4

[[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}} => {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => 4

[[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}} => {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => 4

[[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}} => {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => 4

[[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}} => {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => 4

[[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}} => {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => 4

[[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}} => {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => 4

[[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}} => {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => 4

[[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}} => {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => 4

[[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}} => {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => 4

[[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}} => {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => 4

[[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}} => {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => 5

[[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}} => {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => 5

[[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}} => {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => 5

[[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}} => {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => 5

[[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}} => {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => 5

[[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}} => {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => 6

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 2\ q + q^{2} + q^{3}$

$F_{4} = 5\ q + 3\ q^{2} + q^{3} + q^{4}$

$F_{5} = 13\ q + 8\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$

$F_{6} = 38\ q + 24\ q^{2} + 9\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$

$F_{7} = 116\ q + 74\ q^{2} + 28\ q^{3} + 9\ q^{4} + 3\ q^{5} + q^{6} + q^{7}$

Description

The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.

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

inverse Wachs-White

Description

The inverse of a transformation of set partitions due to Wachs and White.
Return the set partition of

$\{1,...,n\}$ corresponding to the set of arcs, interpreted as a rook placement, applying Wachs and White's bijection

$\gamma^{-1}$ .
Note that our index convention differs from the convention in [1]: regarding the rook board as a lower-right triangular grid, we refer with

$(i,j)$ to the cell in the

$i$ -th column from the right and the

$j$ -th row from the top.