Identifier
-
Mp00079:
Set partitions
—shape⟶
Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
St000561: Set partitions ⟶ ℤ
Values
{{1,2}} => [2] => [[1,2]] => {{1,2}} => 0
{{1},{2}} => [1,1] => [[1],[2]] => {{1},{2}} => 0
{{1,2,3}} => [3] => [[1,2,3]] => {{1,2,3}} => 1
{{1,2},{3}} => [2,1] => [[1,3],[2]] => {{1,3},{2}} => 0
{{1,3},{2}} => [2,1] => [[1,3],[2]] => {{1,3},{2}} => 0
{{1},{2,3}} => [2,1] => [[1,3],[2]] => {{1,3},{2}} => 0
{{1},{2},{3}} => [1,1,1] => [[1],[2],[3]] => {{1},{2},{3}} => 0
{{1,2,3,4}} => [4] => [[1,2,3,4]] => {{1,2,3,4}} => 4
{{1,2,3},{4}} => [3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
{{1,2,4},{3}} => [3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
{{1,2},{3,4}} => [2,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => 0
{{1,2},{3},{4}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1,3,4},{2}} => [3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
{{1,3},{2,4}} => [2,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => 0
{{1,3},{2},{4}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1,4},{2,3}} => [2,2] => [[1,2],[3,4]] => {{1,2},{3,4}} => 0
{{1},{2,3,4}} => [3,1] => [[1,3,4],[2]] => {{1,3,4},{2}} => 1
{{1},{2,3},{4}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1,4},{2},{3}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1},{2,4},{3}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1},{2},{3,4}} => [2,1,1] => [[1,4],[2],[3]] => {{1,4},{2},{3}} => 0
{{1},{2},{3},{4}} => [1,1,1,1] => [[1],[2],[3],[4]] => {{1},{2},{3},{4}} => 0
{{1,2,3,4,5}} => [5] => [[1,2,3,4,5]] => {{1,2,3,4,5}} => 10
{{1,2,3,4},{5}} => [4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 4
{{1,2,3,5},{4}} => [4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 4
{{1,2,3},{4,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,2,3},{4},{5}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,2,4,5},{3}} => [4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 4
{{1,2,4},{3,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,2,4},{3},{5}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,2,5},{3,4}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,2},{3,4,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,2},{3,4},{5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,2,5},{3},{4}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,2},{3,5},{4}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,2},{3},{4,5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,3,4,5},{2}} => [4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 4
{{1,3,4},{2,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,3,4},{2},{5}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,3,5},{2,4}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,3},{2,4,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,3},{2,4},{5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,3,5},{2},{4}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,3},{2,5},{4}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,3},{2},{4,5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,4,5},{2,3}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,4},{2,3,5}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1,4},{2,3},{5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,5},{2,3,4}} => [3,2] => [[1,2,5],[3,4]] => {{1,2,5},{3,4}} => 1
{{1},{2,3,4,5}} => [4,1] => [[1,3,4,5],[2]] => {{1,3,4,5},{2}} => 4
{{1},{2,3,4},{5}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,5},{2,3},{4}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2,3,5},{4}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1},{2,3},{4,5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2,3},{4},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,4,5},{2},{3}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1,4},{2,5},{3}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,4},{2},{3,5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,5},{2,4},{3}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2,4,5},{3}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1},{2,4},{3,5}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2,4},{3},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,5},{2},{3,4}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2,5},{3,4}} => [2,2,1] => [[1,3],[2,5],[4]] => {{1,3},{2,5},{4}} => 0
{{1},{2},{3,4,5}} => [3,1,1] => [[1,4,5],[2],[3]] => {{1,4,5},{2},{3}} => 1
{{1},{2},{3,4},{5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1},{2,5},{3},{4}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1},{2},{3,5},{4}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1},{2},{3},{4,5}} => [2,1,1,1] => [[1,5],[2],[3],[4]] => {{1,5},{2},{3},{4}} => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => {{1},{2},{3},{4},{5}} => 0
{{1,2,3,4,5,6}} => [6] => [[1,2,3,4,5,6]] => {{1,2,3,4,5,6}} => 20
{{1,2,3,4,5},{6}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1,2,3,4,6},{5}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1,2,3,4},{5,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,3,4},{5},{6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,3,5,6},{4}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1,2,3,5},{4,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,3,5},{4},{6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,3,6},{4,5}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,3},{4,5,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,2,3},{4,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,3,6},{4},{5}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,3},{4,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,3},{4},{5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,2,4,5,6},{3}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1,2,4,5},{3,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,4,5},{3},{6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,4,6},{3,5}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,4},{3,5,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,2,4},{3,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,4,6},{3},{5}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,4},{3,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,4},{3},{5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,2,5,6},{3,4}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2,5},{3,4,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
>>> Load all 1200 entries. <<<{{1,2,5},{3,4},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,6},{3,4,5}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,2},{3,4,5,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,2},{3,4,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,6},{3,4},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3,4,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3,4},{5,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2,5,6},{3},{4}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,2,5},{3,6},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,5},{3},{4,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,2,6},{3,5},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3,5,6},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3,5},{4,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2,6},{3},{4,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3,6},{4,5}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,2},{3},{4,5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,2},{3},{4,5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2},{3},{4,6},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2},{3},{4},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,3,4,5,6},{2}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1,3,4,5},{2,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,3,4,5},{2},{6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,3,4,6},{2,5}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,3,4},{2,5,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,3,4},{2,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,4,6},{2},{5}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,3,4},{2,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,4},{2},{5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,3,5,6},{2,4}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,3,5},{2,4,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,3,5},{2,4},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,6},{2,4,5}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,3},{2,4,5,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,3},{2,4,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,6},{2,4},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2,4,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2,4},{5,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3,5,6},{2},{4}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,3,5},{2,6},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,5},{2},{4,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,3,6},{2,5},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2,5,6},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2,5},{4,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3,6},{2},{4,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2,6},{4,5}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,3},{2},{4,5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,3},{2},{4,5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3},{2},{4,6},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3},{2},{4},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,4,5,6},{2,3}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,4,5},{2,3,6}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,4,5},{2,3},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4,6},{2,3,5}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,4},{2,3,5,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,4},{2,3,5},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4,6},{2,3},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2,3,6},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2,3},{5,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,5,6},{2,3,4}} => [3,3] => [[1,2,3],[4,5,6]] => {{1,2,3},{4,5,6}} => 2
{{1,5},{2,3,4,6}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1,5},{2,3,4},{6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,6},{2,3,4,5}} => [4,2] => [[1,2,5,6],[3,4]] => {{1,2,5,6},{3,4}} => 4
{{1},{2,3,4,5,6}} => [5,1] => [[1,3,4,5,6],[2]] => {{1,3,4,5,6},{2}} => 10
{{1},{2,3,4,5},{6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,6},{2,3,4},{5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3,4,6},{5}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1},{2,3,4},{5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3,4},{5},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,5,6},{2,3},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2,3,6},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2,3},{4,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2,3,5},{4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3,5,6},{4}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1},{2,3,5},{4,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3,5},{4},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,6},{2,3},{4,5}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1},{2,3,6},{4,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3},{4,5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,3},{4,5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,3,6},{4},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2,3},{4,6},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,3},{4},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,3},{4},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,4,5,6},{2},{3}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1,4,5},{2,6},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4,5},{2},{3,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,4,6},{2,5},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2,5,6},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2,5},{3,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,4,6},{2},{3,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2,6},{3,5}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,4},{2},{3,5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,4},{2},{3,5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,4},{2},{3,6},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,4},{2},{3},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,5,6},{2,4},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2,4,6},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2,4},{3,6}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2,4,5},{3}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,4,5,6},{3}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1},{2,4,5},{3,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,4,5},{3},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,6},{2,4},{3,5}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1},{2,4,6},{3,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,4},{3,5,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,4},{3,5},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,4,6},{3},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2,4},{3,6},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,4},{3},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,4},{3},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,5,6},{2},{3,4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2,6},{3,4}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1,5},{2},{3,4,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1,5},{2},{3,4},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2,5},{3,4}} => [2,2,2] => [[1,2],[3,4],[5,6]] => {{1,2},{3,4},{5,6}} => 0
{{1},{2,5,6},{3,4}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,5},{3,4,6}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,5},{3,4},{6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,6},{2},{3,4,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2,6},{3,4,5}} => [3,2,1] => [[1,3,6],[2,5],[4]] => {{1,3,6},{2,5},{4}} => 1
{{1},{2},{3,4,5,6}} => [4,1,1] => [[1,4,5,6],[2],[3]] => {{1,4,5,6},{2},{3}} => 4
{{1},{2},{3,4,5},{6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,6},{2},{3,4},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,6},{3,4},{5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3,4,6},{5}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2},{3,4},{5,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3,4},{5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,5},{2},{3,6},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,5},{2},{3},{4,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,5,6},{3},{4}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2,5},{3,6},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,5},{3},{4,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,5},{3},{4},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,6},{2},{3,5},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,6},{3,5},{4}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3,5,6},{4}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2},{3,5},{4,6}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3,5},{4},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,6},{2},{3},{4,5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2,6},{3},{4,5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3,6},{4,5}} => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => {{1,4},{2,6},{3},{5}} => 0
{{1},{2},{3},{4,5,6}} => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => {{1,5,6},{2},{3},{4}} => 1
{{1},{2},{3},{4,5},{6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1},{2,6},{3},{4},{5}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1},{2},{3,6},{4},{5}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1},{2},{3},{4,6},{5}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1},{2},{3},{4},{5,6}} => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => {{1,6},{2},{3},{4},{5}} => 0
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => {{1},{2},{3},{4},{5},{6}} => 0
{{1,2,3,4,5,6,7}} => [7] => [[1,2,3,4,5,6,7]] => {{1,2,3,4,5,6,7}} => 35
{{1,2,3,4,5,6},{7}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,2,3,4,5,7},{6}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,2,3,4,5},{6,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,4,6,7},{5}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,2,3,4,6},{5,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,4,7},{5,6}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,4},{5,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,4},{5},{6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,3,5,6,7},{4}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,2,3,5,6},{4,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,5,7},{4,6}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,5},{4,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,5},{4},{6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,3,6,7},{4,5}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,3,6},{4,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,7},{4,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,3},{4,5,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,3},{4,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,6},{4},{5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,3},{4,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3,7},{4},{5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,3},{4,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,3},{4},{5,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,3},{4},{5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3},{4},{5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3},{4},{5},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,2,4,5,6,7},{3}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,2,4,5,6},{3,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,4,5,7},{3,6}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,4,5},{3,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,5},{3},{6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,4,6,7},{3,5}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,4,6},{3,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,7},{3,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,4},{3,5,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,4},{3,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,6},{3},{5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,4},{3,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4,7},{3},{5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,4},{3,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,4},{3},{5,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,4},{3},{5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4},{3},{5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4},{3},{5},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,2,5,6,7},{3,4}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2,5,6},{3,4,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5,7},{3,4,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,5},{3,4,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,5},{3,4},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,6,7},{3,4,5}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,6},{3,4,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,7},{3,4,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,2},{3,4,5,6,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,2},{3,4,5,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2},{3,4,5,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2},{3,4,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,6},{3,4},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2},{3,4,6,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2},{3,4,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3,4},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4},{5,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,4,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,4},{5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5,6},{3},{4,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,5},{3,6},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,5,7},{3},{4,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,5},{3,7},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,5},{3},{4,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,5},{3},{4,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,5},{3},{4,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,5},{3},{4},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,6},{3,5},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2},{3,5,6,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2},{3,5,6},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,5,6},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3,5},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,5,7},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,5},{4,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,5,7},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,5},{4},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,6,7},{3},{4,5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2,6},{3,7},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2,6},{3},{4,5,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2,6},{3},{4,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3,6},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,6,7},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,6},{4,5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2,7},{3},{4,5,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,2},{3,7},{4,5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3},{4,5,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,2},{3},{4,5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,7},{3},{4,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4,5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3},{4,5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4,5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,6},{3},{4,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,6},{3},{4},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,6,7},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,6},{4},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,7},{3},{4,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4,6,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3},{4,6},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4,6},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,7},{3},{4},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3,7},{4},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4,7},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,2},{3},{4},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,2},{3},{4},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2},{3},{4,7},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2},{3},{4},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2},{3},{4},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,3,4,5,6,7},{2}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1,3,4,5,6},{2,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,3,4,5,7},{2,6}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,3,4,5},{2,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,5},{2},{6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,4,6,7},{2,5}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,3,4,6},{2,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,7},{2,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,4},{2,5,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,4},{2,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,6},{2},{5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,4},{2,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4,7},{2},{5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,4},{2,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,4},{2},{5,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,4},{2},{5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4},{2},{5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4},{2},{5},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,3,5,6,7},{2,4}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,3,5,6},{2,4,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5,7},{2,4,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,5},{2,4,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,5},{2,4},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,6,7},{2,4,5}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,6},{2,4,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,7},{2,4,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,3},{2,4,5,6,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,3},{2,4,5,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3},{2,4,5,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3},{2,4,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,4,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,6},{2,4},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3},{2,4,6,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3},{2,4,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,4,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2,4},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,4,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,4},{5,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,4,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,4},{5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5,6},{2},{4,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,5},{2,6},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,5,7},{2},{4,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,5},{2,7},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,5},{2},{4,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,5},{2},{4,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,5},{2},{4,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,5},{2},{4},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,6},{2,5},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3},{2,5,6,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3},{2,5,6},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,5,6},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2,5},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,5,7},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,5},{4,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,5,7},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,5},{4},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,6,7},{2},{4,5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3,6},{2,7},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3,6},{2},{4,5,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3,6},{2},{4,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2,6},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,6,7},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,6},{4,5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3,7},{2},{4,5,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,3},{2,7},{4,5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,3},{2},{4,5,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,3},{2},{4,5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,7},{2},{4,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4,5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2},{4,5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4,5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,6},{2},{4,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,6},{2},{4},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,6,7},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,6},{4},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,7},{2},{4,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4,6,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2},{4,6},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4,6},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,7},{2},{4},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2,7},{4},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4,7},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,3},{2},{4},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,3},{2},{4},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3},{2},{4,7},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3},{2},{4},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3},{2},{4},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,4,5,6,7},{2,3}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,4,5,6},{2,3,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5,7},{2,3,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4,5},{2,3,6,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,5},{2,3},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,6,7},{2,3,5}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4,6},{2,3,5,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,7},{2,3,5,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,4},{2,3,5,6,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,4},{2,3,5,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4},{2,3,5,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4},{2,3,5},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,3,5},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,6},{2,3},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4},{2,3,6,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4},{2,3,6},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,3,6},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2,3},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,3,7},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,3},{5,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,3,7},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,3},{5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5,6,7},{2,3,4}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,5,6},{2,3,4,7}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5,7},{2,3,4,6}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,5},{2,3,4,6,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,5},{2,3,4,6},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5},{2,3,4,7},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5},{2,3,4},{6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,3,4},{6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6,7},{2,3,4,5}} => [4,3] => [[1,2,3,7],[4,5,6]] => {{1,2,3,7},{4,5,6}} => 5
{{1,6},{2,3,4,5,7}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1,6},{2,3,4,5},{7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,7},{2,3,4,5,6}} => [5,2] => [[1,2,5,6,7],[3,4]] => {{1,2,5,6,7},{3,4}} => 10
{{1},{2,3,4,5,6,7}} => [6,1] => [[1,3,4,5,6,7],[2]] => {{1,3,4,5,6,7},{2}} => 20
{{1},{2,3,4,5,6},{7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,7},{2,3,4,5},{6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,4,5,7},{6}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1},{2,3,4,5},{6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,4,5},{6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,6},{2,3,4,7},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,6},{2,3,4},{5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,3,4},{5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3,4,6},{5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,4,6,7},{5}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1},{2,3,4,6},{5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,4,6},{5},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,7},{2,3,4},{5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,3,4,7},{5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,4},{5,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,3,4},{5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3,4},{5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,4,7},{5},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,3,4},{5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,4},{5},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5,6},{2,3},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5},{2,3,6,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5},{2,3,6},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,3,6},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2,3},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,3,7},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,3},{4,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,3,7},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,3},{4},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,6},{2,3,5,7},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,6},{2,3,5},{4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,3,5},{4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3,5,6},{4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,5,6,7},{4}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1},{2,3,5,6},{4,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,5,6},{4},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,7},{2,3,5},{4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,3,5,7},{4,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,5},{4,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,3,5},{4,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3,5},{4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,5,7},{4},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,3,5},{4,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,5},{4},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,5},{4},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,6,7},{2,3},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,3,7},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,3},{4,5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,7},{2,3,6},{4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,3,6,7},{4,5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3,6},{4,5,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,3,6},{4,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3},{4,5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,3,7},{4,5,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,3},{4,5,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,3},{4,5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3,7},{4,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4,5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4,5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3},{4,5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,3,7},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,3},{4},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,3,6},{4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,6,7},{4},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,3,6},{4,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,6},{4},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3,6},{4},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3,7},{4,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4,6,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4,6},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3},{4,6},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,3},{4},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3,7},{4},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4,7},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,3},{4},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,3},{4},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,3,7},{4},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2,3},{4,7},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,3},{4},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,3},{4},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5,6},{2},{3,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,5},{2,6},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,5,7},{2},{3,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,5},{2,7},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,5},{2},{3,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,5},{2},{3,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,5},{2},{3,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,5},{2},{3},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,6},{2,5},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4},{2,5,6,7},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4},{2,5,6},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,5,6},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2,5},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,5,7},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,5},{3,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,5,7},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,5},{3},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4,6,7},{2},{3,5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,6},{2,7},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4,6},{2},{3,5,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4,6},{2},{3,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2,6},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,6,7},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,6},{3,5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4,7},{2},{3,5,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,4},{2,7},{3,5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,4},{2},{3,5,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,4},{2},{3,5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,7},{2},{3,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3,5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2},{3,5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3,5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,6},{2},{3,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,6},{2},{3},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,6,7},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,6},{3},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4,7},{2},{3,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3,6,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2},{3,6},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3,6},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4,7},{2},{3},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,7},{3},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3,7},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,4},{2},{3},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2},{3},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4},{2},{3,7},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4},{2},{3},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4},{2},{3},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5,6},{2,4},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5},{2,4,6,7},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5},{2,4,6},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,4,6},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2,4},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,4,7},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,4},{3,6,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,4,7},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,4},{3},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,6},{2,4,5,7},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,6},{2,4,5},{3,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,4,5},{3},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,4,5,6},{3}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,4,5,6,7},{3}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1},{2,4,5,6},{3,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,7},{2,4,5},{3,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,4,5,7},{3,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,4,5},{3,6,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,4,5},{3,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,4,5},{3},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,4,5},{3,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,5},{3},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,6,7},{2,4},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,4,7},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,4},{3,5,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,7},{2,4,6},{3,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,4,6,7},{3,5}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,4,6},{3,5,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,4,6},{3,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,4},{3,5,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,4,7},{3,5,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,4},{3,5,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,4},{3,5,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4,7},{3,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3,5,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3,5},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4},{3,5},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,4,7},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,4},{3},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,4,6},{3},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,4,6},{3,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,6},{3},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4,7},{3,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3,6,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3,6},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4},{3,6},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,4},{3},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4,7},{3},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3,7},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,4},{3},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,4},{3},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2,4},{3,7},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,4},{3},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,4},{3},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,4},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,5,6,7},{2},{3,4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5,6},{2,7},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5,6},{2},{3,4,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5,6},{2},{3,4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2,6},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,6,7},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,6},{3,4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5,7},{2},{3,4,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,5},{2,7},{3,4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,5},{2},{3,4,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,5},{2},{3,4,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,7},{2},{3,4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3,4,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2},{3,4},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3,4},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2,5},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,5,7},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,5},{3,4,7}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,7},{2,5,6},{3,4}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,5,6,7},{3,4}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,5,6},{3,4,7}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,5,6},{3,4},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,5},{3,4,6}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,5,7},{3,4,6}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,5},{3,4,6,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,5},{3,4,6},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5,7},{3,4},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3,4,7},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3,4},{6,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5},{3,4},{6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6,7},{2},{3,4,5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1,6},{2,7},{3,4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1,6},{2},{3,4,5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1,6},{2},{3,4,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2,6},{3,4,5}} => [3,2,2] => [[1,2,7],[3,4],[5,6]] => {{1,2,7},{3,4},{5,6}} => 1
{{1},{2,6,7},{3,4,5}} => [3,3,1] => [[1,3,4],[2,6,7],[5]] => {{1,3,4},{2,6,7},{5}} => 2
{{1},{2,6},{3,4,5,7}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,6},{3,4,5},{7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,7},{2},{3,4,5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2,7},{3,4,5,6}} => [4,2,1] => [[1,3,6,7],[2,5],[4]] => {{1,3,6,7},{2,5},{4}} => 4
{{1},{2},{3,4,5,6,7}} => [5,1,1] => [[1,4,5,6,7],[2],[3]] => {{1,4,5,6,7},{2},{3}} => 10
{{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,7},{2},{3,4,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,7},{3,4,5},{6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2},{3,4,5},{6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,6,7},{2},{3,4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3,4,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2},{3,4},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3,4},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6,7},{3,4},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3,4,7},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3,4},{5,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6},{3,4},{5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3,4,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,7},{3,4,6},{5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2},{3,4,6},{5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2},{3,4},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,7},{3,4},{5,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2},{3,4,7},{5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4},{5,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,4},{5,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3,4},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3,4},{5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3,4},{5,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,4},{5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,6},{2},{3,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,6},{2},{3},{4,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,6,7},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,6},{3},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5,7},{2},{3,6},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3,6,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2},{3,6},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3,6},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5,7},{2},{3},{4,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2,7},{3},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3,7},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,5},{2},{3},{4,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,5},{2},{3},{4,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5},{2},{3,7},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5},{2},{3},{4,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5},{2},{3},{4},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,5,7},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,5},{3},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,5,6},{3},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2,5,6},{3,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5,6},{3},{4,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5,7},{3,6},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3,6,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3,6},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5},{3,6},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,5},{3},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5,7},{3},{4,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3,7},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,5},{3},{4,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,5},{3},{4,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2,5},{3,7},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,5},{3},{4,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,5},{3},{4},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,5},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,6,7},{2},{3,5},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3,5,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2},{3,5},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3,5},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6,7},{3,5},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3,5,7},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3,5},{4,7}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6},{3,5},{4},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3,5,6},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,7},{3,5,6},{4}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2},{3,5,6},{4,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2},{3,5},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,7},{3,5},{4,6}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2},{3,5,7},{4,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,5},{4,6,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,5},{4,6},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3,5},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3,5},{4},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3,5},{4,7},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,5},{4},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,5},{4},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,6,7},{2},{3},{4,5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2,7},{3},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3,7},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1,6},{2},{3},{4,5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1,6},{2},{3},{4,5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2,6},{3},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6,7},{3},{4,5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3,7},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,6},{3},{4,5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,6},{3},{4,5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3,6},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2,7},{3,6},{4,5}} => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => {{1,3},{2,5},{4,7},{6}} => 0
{{1},{2},{3,6,7},{4,5}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,6},{4,5,7}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,6},{4,5},{7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,7},{2},{3},{4,5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2,7},{3},{4,5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3,7},{4,5,6}} => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => {{1,4,7},{2,6},{3},{5}} => 1
{{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => {{1,5,6,7},{2},{3},{4}} => 4
{{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,7},{2},{3},{4,5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3},{4,5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,7},{4,5},{6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3},{4,5},{6,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6},{2},{3,7},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6},{2},{3},{4,7},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6},{2},{3},{4},{5,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2,6},{3,7},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,6},{3},{4,7},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,6},{3},{4},{5,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,6},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,7},{2},{3,6},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3,6},{4},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3,6},{4,7},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,6},{4},{5,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,6},{4},{5},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,7},{2},{3},{4,6},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3},{4,6},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,7},{4,6},{5}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3},{4,6},{5,7}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4,6},{5},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,7},{2},{3},{4},{5,6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2,7},{3},{4},{5,6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3,7},{4},{5,6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4,7},{5,6}} => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => {{1,5},{2,7},{3},{4},{6}} => 0
{{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => {{1,6,7},{2},{3},{4},{5}} => 1
{{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2,7},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2},{3,7},{4},{5},{6}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2},{3},{4,7},{5},{6}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2},{3},{4},{5,7},{6}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => {{1,7},{2},{3},{4},{5},{6}} => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => {{1},{2},{3},{4},{5},{6},{7}} => 0
{{1},{2},{3,4,5,6,7,8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1},{2,4,5,6,7,8},{3}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1},{2,3,4,6,7,8},{5}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1},{2,3,4,5,7,8},{6}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1},{2,3,4,5,6,8},{7}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1},{2,3,4,5,6,7,8}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2},{3,4,5,6,7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,3,4,5,6,7},{2},{8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,3,4,5,6,8},{2},{7}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,3,4,5,6,7,8},{2}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,4,5,6,7,8},{2,3}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,4,6,7,8},{3},{5}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,4,5,7,8},{3},{6}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,4,5,6,8},{3},{7}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,4,5,6,7,8},{3}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2,3,6,7,8},{4},{5}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,5,7,8},{4},{6}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,5,6,7},{4},{8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,5,6,7,8},{4}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2,3,6,7,8},{4,5}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,4,7,8},{5},{6}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,4,6,7},{5},{8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,4,6,8},{5},{7}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,4,6,7,8},{5}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2,3,4,5,6},{7},{8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,4,5,6},{7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,4,5,7},{6},{8}} => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => {{1,4,5,6,7,8},{2},{3}} => 20
{{1,2,3,4,5,7,8},{6}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2,3,4,5,6,7},{8}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,8},{2,3,4,5,6,7}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,4,5,8},{6,7}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,4,5,6,8},{7}} => [7,1] => [[1,3,4,5,6,7,8],[2]] => {{1,3,4,5,6,7,8},{2}} => 35
{{1,2,3,4,5,6,7,8}} => [8] => [[1,2,3,4,5,6,7,8]] => {{1,2,3,4,5,6,7,8}} => 56
{{1,3,5,6,7,8},{2,4}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,3,4,6,7,8},{2,5}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,4,6,7,8},{3,5}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,4,5,7,8},{3,6}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,5,7,8},{4,6}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,4,5,6,8},{3,7}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,5,6,8},{4,7}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,3,4,6,8},{5,7}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,2,4,5,6,7},{3,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,3},{2,4,5,6,7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,4},{2,3,5,6,7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,5},{2,3,4,6,7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
{{1,6},{2,3,4,5,7,8}} => [6,2] => [[1,2,5,6,7,8],[3,4]] => {{1,2,5,6,7,8},{3,4}} => 20
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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:
4,1 10,4,0,0,1 26,20,0,0,5,0,0,0,0,0,1 76,80,10,0,30,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,1 232,350,70,0,140,35,0,0,0,0,42,0,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
F2=2
F3=4+q
F4=10+4 q+q4
F5=26+20 q+5 q4+q10
F6=76+80 q+10 q2+30 q4+6 q10+q20
F7=232+350 q+70 q2+140 q4+35 q5+42 q10+7 q20+q35
Description
The number of occurrences of the pattern {{1,2,3}} in a set partition.
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shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
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reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau T labeled down (in English convention) each column to the shape of a partition.
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rows
Description
The set partition whose blocks are the rows of the tableau.
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