Identifier
-
Mp00249:
Set partitions
—Callan switch⟶
Set partitions
St000971: Set partitions ⟶ ℤ
Values
{{1}} => {{1}} => 1
{{1,2}} => {{1,2}} => 2
{{1},{2}} => {{1},{2}} => 1
{{1,2,3}} => {{1,3},{2}} => 2
{{1,2},{3}} => {{1,2},{3}} => 2
{{1,3},{2}} => {{1,2,3}} => 3
{{1},{2,3}} => {{1},{2,3}} => 1
{{1},{2},{3}} => {{1},{2},{3}} => 1
{{1,2,3,4}} => {{1,4},{2},{3}} => 2
{{1,2,3},{4}} => {{1,3},{2},{4}} => 2
{{1,2,4},{3}} => {{1,3,4},{2}} => 2
{{1,2},{3,4}} => {{1,2},{3,4}} => 2
{{1,2},{3},{4}} => {{1,2},{3},{4}} => 2
{{1,3,4},{2}} => {{1,2,4},{3}} => 3
{{1,3},{2,4}} => {{1,3},{2,4}} => 3
{{1,3},{2},{4}} => {{1,2,3},{4}} => 3
{{1,4},{2,3}} => {{1,4},{2,3}} => 3
{{1},{2,3,4}} => {{1},{2,3,4}} => 1
{{1},{2,3},{4}} => {{1},{2,3},{4}} => 1
{{1,4},{2},{3}} => {{1,2,3,4}} => 4
{{1},{2,4},{3}} => {{1},{2,4},{3}} => 1
{{1},{2},{3,4}} => {{1},{2},{3,4}} => 1
{{1},{2},{3},{4}} => {{1},{2},{3},{4}} => 1
{{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
{{1,2,3,4},{5}} => {{1,4},{2},{3},{5}} => 2
{{1,2,3,5},{4}} => {{1,4,5},{2},{3}} => 2
{{1,2,3},{4,5}} => {{1,3},{2},{4,5}} => 2
{{1,2,3},{4},{5}} => {{1,3},{2},{4},{5}} => 2
{{1,2,4,5},{3}} => {{1,3,4,5},{2}} => 2
{{1,2,4},{3,5}} => {{1,4},{2},{3,5}} => 2
{{1,2,4},{3},{5}} => {{1,3,4},{2},{5}} => 2
{{1,2,5},{3,4}} => {{1,5},{2},{3,4}} => 2
{{1,2},{3,4,5}} => {{1,2},{3,4,5}} => 2
{{1,2},{3,4},{5}} => {{1,2},{3,4},{5}} => 2
{{1,2,5},{3},{4}} => {{1,3,5},{2},{4}} => 2
{{1,2},{3,5},{4}} => {{1,2},{3,5},{4}} => 2
{{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => 2
{{1,2},{3},{4},{5}} => {{1,2},{3},{4},{5}} => 2
{{1,3,4,5},{2}} => {{1,2,4,5},{3}} => 3
{{1,3,4},{2,5}} => {{1,4},{2,5},{3}} => 3
{{1,3,4},{2},{5}} => {{1,2,4},{3},{5}} => 3
{{1,3,5},{2,4}} => {{1,5},{2,4},{3}} => 3
{{1,3},{2,4,5}} => {{1,3},{2,4,5}} => 3
{{1,3},{2,4},{5}} => {{1,3},{2,4},{5}} => 3
{{1,3,5},{2},{4}} => {{1,2,5},{3},{4}} => 3
{{1,3},{2,5},{4}} => {{1,3},{2,5},{4}} => 3
{{1,3},{2},{4,5}} => {{1,2,3},{4,5}} => 3
{{1,3},{2},{4},{5}} => {{1,2,3},{4},{5}} => 3
{{1,4,5},{2,3}} => {{1,4,5},{2,3}} => 3
{{1,4},{2,3,5}} => {{1,4},{2,3,5}} => 4
{{1,4},{2,3},{5}} => {{1,4},{2,3},{5}} => 3
{{1,5},{2,3,4}} => {{1,5},{2,3,4}} => 4
{{1},{2,3,4,5}} => {{1},{2,3,4,5}} => 1
{{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => 1
{{1,5},{2,3},{4}} => {{1,5},{2,3},{4}} => 3
{{1},{2,3,5},{4}} => {{1},{2,3,5},{4}} => 1
{{1},{2,3},{4,5}} => {{1},{2,3},{4,5}} => 1
{{1},{2,3},{4},{5}} => {{1},{2,3},{4},{5}} => 1
{{1,4,5},{2},{3}} => {{1,2,3,5},{4}} => 4
{{1,4},{2,5},{3}} => {{1,3,4},{2,5}} => 4
{{1,4},{2},{3,5}} => {{1,2,4},{3,5}} => 4
{{1,4},{2},{3},{5}} => {{1,2,3,4},{5}} => 4
{{1,5},{2,4},{3}} => {{1,3,5},{2,4}} => 4
{{1},{2,4,5},{3}} => {{1},{2,4,5},{3}} => 1
{{1},{2,4},{3,5}} => {{1},{2,4},{3,5}} => 1
{{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => 1
{{1,5},{2},{3,4}} => {{1,2,5},{3,4}} => 4
{{1},{2,5},{3,4}} => {{1},{2,5},{3,4}} => 1
{{1},{2},{3,4,5}} => {{1},{2},{3,4,5}} => 1
{{1},{2},{3,4},{5}} => {{1},{2},{3,4},{5}} => 1
{{1,5},{2},{3},{4}} => {{1,2,3,4,5}} => 5
{{1},{2,5},{3},{4}} => {{1},{2,5},{3},{4}} => 1
{{1},{2},{3,5},{4}} => {{1},{2},{3,5},{4}} => 1
{{1},{2},{3},{4,5}} => {{1},{2},{3},{4,5}} => 1
{{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => 1
{{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
{{1,2,3,4,5},{6}} => {{1,5},{2},{3},{4},{6}} => 2
{{1,2,3,4,6},{5}} => {{1,5,6},{2},{3},{4}} => 2
{{1,2,3,4},{5,6}} => {{1,4},{2},{3},{5,6}} => 2
{{1,2,3,4},{5},{6}} => {{1,4},{2},{3},{5},{6}} => 2
{{1,2,3,5,6},{4}} => {{1,4,5,6},{2},{3}} => 2
{{1,2,3,5},{4,6}} => {{1,5},{2},{3},{4,6}} => 2
{{1,2,3,5},{4},{6}} => {{1,4,5},{2},{3},{6}} => 2
{{1,2,3,6},{4,5}} => {{1,6},{2},{3},{4,5}} => 2
{{1,2,3},{4,5,6}} => {{1,3},{2},{4,5,6}} => 2
{{1,2,3},{4,5},{6}} => {{1,3},{2},{4,5},{6}} => 2
{{1,2,3,6},{4},{5}} => {{1,4,6},{2},{3},{5}} => 2
{{1,2,3},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => 2
{{1,2,3},{4},{5,6}} => {{1,3},{2},{4},{5,6}} => 2
{{1,2,3},{4},{5},{6}} => {{1,3},{2},{4},{5},{6}} => 2
{{1,2,4,5,6},{3}} => {{1,3,4,5,6},{2}} => 2
{{1,2,4,5},{3,6}} => {{1,5},{2},{3,6},{4}} => 2
{{1,2,4,5},{3},{6}} => {{1,3,4,5},{2},{6}} => 2
{{1,2,4,6},{3,5}} => {{1,6},{2},{3,5},{4}} => 2
{{1,2,4},{3,5,6}} => {{1,4},{2},{3,5,6}} => 2
{{1,2,4},{3,5},{6}} => {{1,4},{2},{3,5},{6}} => 2
{{1,2,4,6},{3},{5}} => {{1,3,4,6},{2},{5}} => 2
{{1,2,4},{3,6},{5}} => {{1,4},{2},{3,6},{5}} => 2
{{1,2,4},{3},{5,6}} => {{1,3,4},{2},{5,6}} => 2
{{1,2,4},{3},{5},{6}} => {{1,3,4},{2},{5},{6}} => 2
{{1,2,5,6},{3,4}} => {{1,5,6},{2},{3,4}} => 2
>>> Load all 1283 entries. <<<{{1,2,5},{3,4,6}} => {{1,5},{2},{3,4,6}} => 2
{{1,2,5},{3,4},{6}} => {{1,5},{2},{3,4},{6}} => 2
{{1,2,6},{3,4,5}} => {{1,6},{2},{3,4,5}} => 2
{{1,2},{3,4,5,6}} => {{1,2},{3,4,5,6}} => 2
{{1,2},{3,4,5},{6}} => {{1,2},{3,4,5},{6}} => 2
{{1,2,6},{3,4},{5}} => {{1,6},{2},{3,4},{5}} => 2
{{1,2},{3,4,6},{5}} => {{1,2},{3,4,6},{5}} => 2
{{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => 2
{{1,2},{3,4},{5},{6}} => {{1,2},{3,4},{5},{6}} => 2
{{1,2,5,6},{3},{4}} => {{1,3,5,6},{2},{4}} => 2
{{1,2,5},{3,6},{4}} => {{1,4,5},{2},{3,6}} => 2
{{1,2,5},{3},{4,6}} => {{1,3,5},{2},{4,6}} => 2
{{1,2,5},{3},{4},{6}} => {{1,3,5},{2},{4},{6}} => 2
{{1,2,6},{3,5},{4}} => {{1,4,6},{2},{3,5}} => 2
{{1,2},{3,5,6},{4}} => {{1,2},{3,5,6},{4}} => 2
{{1,2},{3,5},{4,6}} => {{1,2},{3,5},{4,6}} => 2
{{1,2},{3,5},{4},{6}} => {{1,2},{3,5},{4},{6}} => 2
{{1,2,6},{3},{4,5}} => {{1,3,6},{2},{4,5}} => 2
{{1,2},{3,6},{4,5}} => {{1,2},{3,6},{4,5}} => 2
{{1,2},{3},{4,5,6}} => {{1,2},{3},{4,5,6}} => 2
{{1,2},{3},{4,5},{6}} => {{1,2},{3},{4,5},{6}} => 2
{{1,2,6},{3},{4},{5}} => {{1,3,6},{2},{4},{5}} => 2
{{1,2},{3,6},{4},{5}} => {{1,2},{3,6},{4},{5}} => 2
{{1,2},{3},{4,6},{5}} => {{1,2},{3},{4,6},{5}} => 2
{{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => 2
{{1,2},{3},{4},{5},{6}} => {{1,2},{3},{4},{5},{6}} => 2
{{1,3,4,5,6},{2}} => {{1,2,4,5,6},{3}} => 3
{{1,3,4,5},{2,6}} => {{1,5},{2,6},{3},{4}} => 3
{{1,3,4,5},{2},{6}} => {{1,2,4,5},{3},{6}} => 3
{{1,3,4,6},{2,5}} => {{1,6},{2,5},{3},{4}} => 3
{{1,3,4},{2,5,6}} => {{1,4},{2,5,6},{3}} => 3
{{1,3,4},{2,5},{6}} => {{1,4},{2,5},{3},{6}} => 3
{{1,3,4,6},{2},{5}} => {{1,2,4,6},{3},{5}} => 3
{{1,3,4},{2,6},{5}} => {{1,4},{2,6},{3},{5}} => 3
{{1,3,4},{2},{5,6}} => {{1,2,4},{3},{5,6}} => 3
{{1,3,4},{2},{5},{6}} => {{1,2,4},{3},{5},{6}} => 3
{{1,3,5,6},{2,4}} => {{1,5,6},{2,4},{3}} => 3
{{1,3,5},{2,4,6}} => {{1,5},{2,4,6},{3}} => 3
{{1,3,5},{2,4},{6}} => {{1,5},{2,4},{3},{6}} => 3
{{1,3,6},{2,4,5}} => {{1,6},{2,4,5},{3}} => 3
{{1,3},{2,4,5,6}} => {{1,3},{2,4,5,6}} => 3
{{1,3},{2,4,5},{6}} => {{1,3},{2,4,5},{6}} => 3
{{1,3,6},{2,4},{5}} => {{1,6},{2,4},{3},{5}} => 3
{{1,3},{2,4,6},{5}} => {{1,3},{2,4,6},{5}} => 3
{{1,3},{2,4},{5,6}} => {{1,3},{2,4},{5,6}} => 3
{{1,3},{2,4},{5},{6}} => {{1,3},{2,4},{5},{6}} => 3
{{1,3,5,6},{2},{4}} => {{1,2,5,6},{3},{4}} => 3
{{1,3,5},{2,6},{4}} => {{1,4,5},{2,6},{3}} => 3
{{1,3,5},{2},{4,6}} => {{1,2,5},{3},{4,6}} => 3
{{1,3,5},{2},{4},{6}} => {{1,2,5},{3},{4},{6}} => 3
{{1,3,6},{2,5},{4}} => {{1,4,6},{2,5},{3}} => 3
{{1,3},{2,5,6},{4}} => {{1,3},{2,5,6},{4}} => 3
{{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}} => 3
{{1,3},{2,5},{4},{6}} => {{1,3},{2,5},{4},{6}} => 3
{{1,3,6},{2},{4,5}} => {{1,2,6},{3},{4,5}} => 3
{{1,3},{2,6},{4,5}} => {{1,3},{2,6},{4,5}} => 3
{{1,3},{2},{4,5,6}} => {{1,2,3},{4,5,6}} => 3
{{1,3},{2},{4,5},{6}} => {{1,2,3},{4,5},{6}} => 3
{{1,3,6},{2},{4},{5}} => {{1,2,6},{3},{4},{5}} => 3
{{1,3},{2,6},{4},{5}} => {{1,3},{2,6},{4},{5}} => 3
{{1,3},{2},{4,6},{5}} => {{1,2,3},{4,6},{5}} => 3
{{1,3},{2},{4},{5,6}} => {{1,2,3},{4},{5,6}} => 3
{{1,3},{2},{4},{5},{6}} => {{1,2,3},{4},{5},{6}} => 3
{{1,4,5,6},{2,3}} => {{1,4,5,6},{2,3}} => 3
{{1,4,5},{2,3,6}} => {{1,5},{2,3,6},{4}} => 4
{{1,4,5},{2,3},{6}} => {{1,4,5},{2,3},{6}} => 3
{{1,4,6},{2,3,5}} => {{1,6},{2,3,5},{4}} => 4
{{1,4},{2,3,5,6}} => {{1,4},{2,3,5,6}} => 4
{{1,4},{2,3,5},{6}} => {{1,4},{2,3,5},{6}} => 4
{{1,4,6},{2,3},{5}} => {{1,4,6},{2,3},{5}} => 3
{{1,4},{2,3,6},{5}} => {{1,4},{2,3,6},{5}} => 4
{{1,4},{2,3},{5,6}} => {{1,4},{2,3},{5,6}} => 3
{{1,4},{2,3},{5},{6}} => {{1,4},{2,3},{5},{6}} => 3
{{1,5,6},{2,3,4}} => {{1,5,6},{2,3,4}} => 4
{{1,5},{2,3,4,6}} => {{1,5},{2,3,4,6}} => 5
{{1,5},{2,3,4},{6}} => {{1,5},{2,3,4},{6}} => 4
{{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => 5
{{1},{2,3,4,5,6}} => {{1},{2,3,4,5,6}} => 1
{{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => 1
{{1,6},{2,3,4},{5}} => {{1,6},{2,3,4},{5}} => 4
{{1},{2,3,4,6},{5}} => {{1},{2,3,4,6},{5}} => 1
{{1},{2,3,4},{5,6}} => {{1},{2,3,4},{5,6}} => 1
{{1},{2,3,4},{5},{6}} => {{1},{2,3,4},{5},{6}} => 1
{{1,5,6},{2,3},{4}} => {{1,5,6},{2,3},{4}} => 3
{{1,5},{2,3,6},{4}} => {{1,4,5},{2,3,6}} => 5
{{1,5},{2,3},{4,6}} => {{1,5},{2,3},{4,6}} => 3
{{1,5},{2,3},{4},{6}} => {{1,5},{2,3},{4},{6}} => 3
{{1,6},{2,3,5},{4}} => {{1,4,6},{2,3,5}} => 5
{{1},{2,3,5,6},{4}} => {{1},{2,3,5,6},{4}} => 1
{{1},{2,3,5},{4,6}} => {{1},{2,3,5},{4,6}} => 1
{{1},{2,3,5},{4},{6}} => {{1},{2,3,5},{4},{6}} => 1
{{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => 3
{{1},{2,3,6},{4,5}} => {{1},{2,3,6},{4,5}} => 1
{{1},{2,3},{4,5,6}} => {{1},{2,3},{4,5,6}} => 1
{{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => 1
{{1,6},{2,3},{4},{5}} => {{1,6},{2,3},{4},{5}} => 3
{{1},{2,3,6},{4},{5}} => {{1},{2,3,6},{4},{5}} => 1
{{1},{2,3},{4,6},{5}} => {{1},{2,3},{4,6},{5}} => 1
{{1},{2,3},{4},{5,6}} => {{1},{2,3},{4},{5,6}} => 1
{{1},{2,3},{4},{5},{6}} => {{1},{2,3},{4},{5},{6}} => 1
{{1,4,5,6},{2},{3}} => {{1,2,3,5,6},{4}} => 4
{{1,4,5},{2,6},{3}} => {{1,3,5},{2,6},{4}} => 4
{{1,4,5},{2},{3,6}} => {{1,2,5},{3,6},{4}} => 4
{{1,4,5},{2},{3},{6}} => {{1,2,3,5},{4},{6}} => 4
{{1,4,6},{2,5},{3}} => {{1,3,6},{2,5},{4}} => 4
{{1,4},{2,5,6},{3}} => {{1,3,4},{2,5,6}} => 4
{{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}} => 4
{{1,4},{2,5},{3},{6}} => {{1,3,4},{2,5},{6}} => 4
{{1,4,6},{2},{3,5}} => {{1,2,6},{3,5},{4}} => 4
{{1,4},{2,6},{3,5}} => {{1,4},{2,6},{3,5}} => 4
{{1,4},{2},{3,5,6}} => {{1,2,4},{3,5,6}} => 4
{{1,4},{2},{3,5},{6}} => {{1,2,4},{3,5},{6}} => 4
{{1,4,6},{2},{3},{5}} => {{1,2,3,6},{4},{5}} => 4
{{1,4},{2,6},{3},{5}} => {{1,3,4},{2,6},{5}} => 4
{{1,4},{2},{3,6},{5}} => {{1,2,4},{3,6},{5}} => 4
{{1,4},{2},{3},{5,6}} => {{1,2,3,4},{5,6}} => 4
{{1,4},{2},{3},{5},{6}} => {{1,2,3,4},{5},{6}} => 4
{{1,5,6},{2,4},{3}} => {{1,3,5,6},{2,4}} => 4
{{1,5},{2,4,6},{3}} => {{1,3,5},{2,4,6}} => 5
{{1,5},{2,4},{3,6}} => {{1,5},{2,4},{3,6}} => 4
{{1,5},{2,4},{3},{6}} => {{1,3,5},{2,4},{6}} => 4
{{1,6},{2,4,5},{3}} => {{1,3,6},{2,4,5}} => 5
{{1},{2,4,5,6},{3}} => {{1},{2,4,5,6},{3}} => 1
{{1},{2,4,5},{3,6}} => {{1},{2,4,5},{3,6}} => 1
{{1},{2,4,5},{3},{6}} => {{1},{2,4,5},{3},{6}} => 1
{{1,6},{2,4},{3,5}} => {{1,6},{2,4},{3,5}} => 4
{{1},{2,4,6},{3,5}} => {{1},{2,4,6},{3,5}} => 1
{{1},{2,4},{3,5,6}} => {{1},{2,4},{3,5,6}} => 1
{{1},{2,4},{3,5},{6}} => {{1},{2,4},{3,5},{6}} => 1
{{1,6},{2,4},{3},{5}} => {{1,3,6},{2,4},{5}} => 4
{{1},{2,4,6},{3},{5}} => {{1},{2,4,6},{3},{5}} => 1
{{1},{2,4},{3,6},{5}} => {{1},{2,4},{3,6},{5}} => 1
{{1},{2,4},{3},{5,6}} => {{1},{2,4},{3},{5,6}} => 1
{{1},{2,4},{3},{5},{6}} => {{1},{2,4},{3},{5},{6}} => 1
{{1,5,6},{2},{3,4}} => {{1,2,5,6},{3,4}} => 4
{{1,5},{2,6},{3,4}} => {{1,5},{2,6},{3,4}} => 4
{{1,5},{2},{3,4,6}} => {{1,2,5},{3,4,6}} => 5
{{1,5},{2},{3,4},{6}} => {{1,2,5},{3,4},{6}} => 4
{{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => 4
{{1},{2,5,6},{3,4}} => {{1},{2,5,6},{3,4}} => 1
{{1},{2,5},{3,4,6}} => {{1},{2,5},{3,4,6}} => 1
{{1},{2,5},{3,4},{6}} => {{1},{2,5},{3,4},{6}} => 1
{{1,6},{2},{3,4,5}} => {{1,2,6},{3,4,5}} => 5
{{1},{2,6},{3,4,5}} => {{1},{2,6},{3,4,5}} => 1
{{1},{2},{3,4,5,6}} => {{1},{2},{3,4,5,6}} => 1
{{1},{2},{3,4,5},{6}} => {{1},{2},{3,4,5},{6}} => 1
{{1,6},{2},{3,4},{5}} => {{1,2,6},{3,4},{5}} => 4
{{1},{2,6},{3,4},{5}} => {{1},{2,6},{3,4},{5}} => 1
{{1},{2},{3,4,6},{5}} => {{1},{2},{3,4,6},{5}} => 1
{{1},{2},{3,4},{5,6}} => {{1},{2},{3,4},{5,6}} => 1
{{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => 1
{{1,5,6},{2},{3},{4}} => {{1,2,3,4,6},{5}} => 5
{{1,5},{2,6},{3},{4}} => {{1,3,4,5},{2,6}} => 5
{{1,5},{2},{3,6},{4}} => {{1,2,4,5},{3,6}} => 5
{{1,5},{2},{3},{4,6}} => {{1,2,3,5},{4,6}} => 5
{{1,5},{2},{3},{4},{6}} => {{1,2,3,4,5},{6}} => 5
{{1,6},{2,5},{3},{4}} => {{1,3,4,6},{2,5}} => 5
{{1},{2,5,6},{3},{4}} => {{1},{2,5,6},{3},{4}} => 1
{{1},{2,5},{3,6},{4}} => {{1},{2,5},{3,6},{4}} => 1
{{1},{2,5},{3},{4,6}} => {{1},{2,5},{3},{4,6}} => 1
{{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => 1
{{1,6},{2},{3,5},{4}} => {{1,2,4,6},{3,5}} => 5
{{1},{2,6},{3,5},{4}} => {{1},{2,6},{3,5},{4}} => 1
{{1},{2},{3,5,6},{4}} => {{1},{2},{3,5,6},{4}} => 1
{{1},{2},{3,5},{4,6}} => {{1},{2},{3,5},{4,6}} => 1
{{1},{2},{3,5},{4},{6}} => {{1},{2},{3,5},{4},{6}} => 1
{{1,6},{2},{3},{4,5}} => {{1,2,3,6},{4,5}} => 5
{{1},{2,6},{3},{4,5}} => {{1},{2,6},{3},{4,5}} => 1
{{1},{2},{3,6},{4,5}} => {{1},{2},{3,6},{4,5}} => 1
{{1},{2},{3},{4,5,6}} => {{1},{2},{3},{4,5,6}} => 1
{{1},{2},{3},{4,5},{6}} => {{1},{2},{3},{4,5},{6}} => 1
{{1,6},{2},{3},{4},{5}} => {{1,2,3,4,5,6}} => 6
{{1},{2,6},{3},{4},{5}} => {{1},{2,6},{3},{4},{5}} => 1
{{1},{2},{3,6},{4},{5}} => {{1},{2},{3,6},{4},{5}} => 1
{{1},{2},{3},{4,6},{5}} => {{1},{2},{3},{4,6},{5}} => 1
{{1},{2},{3},{4},{5,6}} => {{1},{2},{3},{4},{5,6}} => 1
{{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => 1
{{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
{{1,2,3,4,5,6},{7}} => {{1,6},{2},{3},{4},{5},{7}} => 2
{{1,2,3,4,5,7},{6}} => {{1,6,7},{2},{3},{4},{5}} => 2
{{1,2,3,4,5},{6,7}} => {{1,5},{2},{3},{4},{6,7}} => 2
{{1,2,3,4,5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7}} => 2
{{1,2,3,4,6,7},{5}} => {{1,5,6,7},{2},{3},{4}} => 2
{{1,2,3,4,6},{5,7}} => {{1,6},{2},{3},{4},{5,7}} => 2
{{1,2,3,4,6},{5},{7}} => {{1,5,6},{2},{3},{4},{7}} => 2
{{1,2,3,4,7},{5,6}} => {{1,7},{2},{3},{4},{5,6}} => 2
{{1,2,3,4},{5,6,7}} => {{1,4},{2},{3},{5,6,7}} => 2
{{1,2,3,4},{5,6},{7}} => {{1,4},{2},{3},{5,6},{7}} => 2
{{1,2,3,4,7},{5},{6}} => {{1,5,7},{2},{3},{4},{6}} => 2
{{1,2,3,4},{5,7},{6}} => {{1,4},{2},{3},{5,7},{6}} => 2
{{1,2,3,4},{5},{6,7}} => {{1,4},{2},{3},{5},{6,7}} => 2
{{1,2,3,4},{5},{6},{7}} => {{1,4},{2},{3},{5},{6},{7}} => 2
{{1,2,3,5,6,7},{4}} => {{1,4,5,6,7},{2},{3}} => 2
{{1,2,3,5,6},{4,7}} => {{1,6},{2},{3},{4,7},{5}} => 2
{{1,2,3,5,6},{4},{7}} => {{1,4,5,6},{2},{3},{7}} => 2
{{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
{{1,2,3,5},{4,6,7}} => {{1,5},{2},{3},{4,6,7}} => 2
{{1,2,3,5},{4,6},{7}} => {{1,5},{2},{3},{4,6},{7}} => 2
{{1,2,3,5,7},{4},{6}} => {{1,4,5,7},{2},{3},{6}} => 2
{{1,2,3,5},{4,7},{6}} => {{1,5},{2},{3},{4,7},{6}} => 2
{{1,2,3,5},{4},{6,7}} => {{1,4,5},{2},{3},{6,7}} => 2
{{1,2,3,5},{4},{6},{7}} => {{1,4,5},{2},{3},{6},{7}} => 2
{{1,2,3,6,7},{4,5}} => {{1,6,7},{2},{3},{4,5}} => 2
{{1,2,3,6},{4,5,7}} => {{1,6},{2},{3},{4,5,7}} => 2
{{1,2,3,6},{4,5},{7}} => {{1,6},{2},{3},{4,5},{7}} => 2
{{1,2,3,7},{4,5,6}} => {{1,7},{2},{3},{4,5,6}} => 2
{{1,2,3},{4,5,6,7}} => {{1,3},{2},{4,5,6,7}} => 2
{{1,2,3},{4,5,6},{7}} => {{1,3},{2},{4,5,6},{7}} => 2
{{1,2,3,7},{4,5},{6}} => {{1,7},{2},{3},{4,5},{6}} => 2
{{1,2,3},{4,5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => 2
{{1,2,3},{4,5},{6,7}} => {{1,3},{2},{4,5},{6,7}} => 2
{{1,2,3},{4,5},{6},{7}} => {{1,3},{2},{4,5},{6},{7}} => 2
{{1,2,3,6,7},{4},{5}} => {{1,4,6,7},{2},{3},{5}} => 2
{{1,2,3,6},{4,7},{5}} => {{1,5,6},{2},{3},{4,7}} => 2
{{1,2,3,6},{4},{5,7}} => {{1,4,6},{2},{3},{5,7}} => 2
{{1,2,3,6},{4},{5},{7}} => {{1,4,6},{2},{3},{5},{7}} => 2
{{1,2,3,7},{4,6},{5}} => {{1,5,7},{2},{3},{4,6}} => 2
{{1,2,3},{4,6,7},{5}} => {{1,3},{2},{4,6,7},{5}} => 2
{{1,2,3},{4,6},{5,7}} => {{1,3},{2},{4,6},{5,7}} => 2
{{1,2,3},{4,6},{5},{7}} => {{1,3},{2},{4,6},{5},{7}} => 2
{{1,2,3,7},{4},{5,6}} => {{1,4,7},{2},{3},{5,6}} => 2
{{1,2,3},{4,7},{5,6}} => {{1,3},{2},{4,7},{5,6}} => 2
{{1,2,3},{4},{5,6,7}} => {{1,3},{2},{4},{5,6,7}} => 2
{{1,2,3},{4},{5,6},{7}} => {{1,3},{2},{4},{5,6},{7}} => 2
{{1,2,3,7},{4},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => 2
{{1,2,3},{4,7},{5},{6}} => {{1,3},{2},{4,7},{5},{6}} => 2
{{1,2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => 2
{{1,2,3},{4},{5},{6,7}} => {{1,3},{2},{4},{5},{6,7}} => 2
{{1,2,3},{4},{5},{6},{7}} => {{1,3},{2},{4},{5},{6},{7}} => 2
{{1,2,4,5,6,7},{3}} => {{1,3,4,5,6,7},{2}} => 2
{{1,2,4,5,6},{3,7}} => {{1,6},{2},{3,7},{4},{5}} => 2
{{1,2,4,5,6},{3},{7}} => {{1,3,4,5,6},{2},{7}} => 2
{{1,2,4,5,7},{3,6}} => {{1,7},{2},{3,6},{4},{5}} => 2
{{1,2,4,5},{3,6,7}} => {{1,5},{2},{3,6,7},{4}} => 2
{{1,2,4,5},{3,6},{7}} => {{1,5},{2},{3,6},{4},{7}} => 2
{{1,2,4,5,7},{3},{6}} => {{1,3,4,5,7},{2},{6}} => 2
{{1,2,4,5},{3,7},{6}} => {{1,5},{2},{3,7},{4},{6}} => 2
{{1,2,4,5},{3},{6,7}} => {{1,3,4,5},{2},{6,7}} => 2
{{1,2,4,5},{3},{6},{7}} => {{1,3,4,5},{2},{6},{7}} => 2
{{1,2,4,6,7},{3,5}} => {{1,6,7},{2},{3,5},{4}} => 2
{{1,2,4,6},{3,5,7}} => {{1,6},{2},{3,5,7},{4}} => 2
{{1,2,4,6},{3,5},{7}} => {{1,6},{2},{3,5},{4},{7}} => 2
{{1,2,4,7},{3,5,6}} => {{1,7},{2},{3,5,6},{4}} => 2
{{1,2,4},{3,5,6,7}} => {{1,4},{2},{3,5,6,7}} => 2
{{1,2,4},{3,5,6},{7}} => {{1,4},{2},{3,5,6},{7}} => 2
{{1,2,4,7},{3,5},{6}} => {{1,7},{2},{3,5},{4},{6}} => 2
{{1,2,4},{3,5,7},{6}} => {{1,4},{2},{3,5,7},{6}} => 2
{{1,2,4},{3,5},{6,7}} => {{1,4},{2},{3,5},{6,7}} => 2
{{1,2,4},{3,5},{6},{7}} => {{1,4},{2},{3,5},{6},{7}} => 2
{{1,2,4,6,7},{3},{5}} => {{1,3,4,6,7},{2},{5}} => 2
{{1,2,4,6},{3,7},{5}} => {{1,5,6},{2},{3,7},{4}} => 2
{{1,2,4,6},{3},{5,7}} => {{1,3,4,6},{2},{5,7}} => 2
{{1,2,4,6},{3},{5},{7}} => {{1,3,4,6},{2},{5},{7}} => 2
{{1,2,4,7},{3,6},{5}} => {{1,5,7},{2},{3,6},{4}} => 2
{{1,2,4},{3,6,7},{5}} => {{1,4},{2},{3,6,7},{5}} => 2
{{1,2,4},{3,6},{5,7}} => {{1,4},{2},{3,6},{5,7}} => 2
{{1,2,4},{3,6},{5},{7}} => {{1,4},{2},{3,6},{5},{7}} => 2
{{1,2,4,7},{3},{5,6}} => {{1,3,4,7},{2},{5,6}} => 2
{{1,2,4},{3,7},{5,6}} => {{1,4},{2},{3,7},{5,6}} => 2
{{1,2,4},{3},{5,6,7}} => {{1,3,4},{2},{5,6,7}} => 2
{{1,2,4},{3},{5,6},{7}} => {{1,3,4},{2},{5,6},{7}} => 2
{{1,2,4,7},{3},{5},{6}} => {{1,3,4,7},{2},{5},{6}} => 2
{{1,2,4},{3,7},{5},{6}} => {{1,4},{2},{3,7},{5},{6}} => 2
{{1,2,4},{3},{5,7},{6}} => {{1,3,4},{2},{5,7},{6}} => 2
{{1,2,4},{3},{5},{6,7}} => {{1,3,4},{2},{5},{6,7}} => 2
{{1,2,4},{3},{5},{6},{7}} => {{1,3,4},{2},{5},{6},{7}} => 2
{{1,2,5,6,7},{3,4}} => {{1,5,6,7},{2},{3,4}} => 2
{{1,2,5,6},{3,4,7}} => {{1,6},{2},{3,4,7},{5}} => 2
{{1,2,5,6},{3,4},{7}} => {{1,5,6},{2},{3,4},{7}} => 2
{{1,2,5,7},{3,4,6}} => {{1,7},{2},{3,4,6},{5}} => 2
{{1,2,5},{3,4,6,7}} => {{1,5},{2},{3,4,6,7}} => 2
{{1,2,5},{3,4,6},{7}} => {{1,5},{2},{3,4,6},{7}} => 2
{{1,2,5,7},{3,4},{6}} => {{1,5,7},{2},{3,4},{6}} => 2
{{1,2,5},{3,4,7},{6}} => {{1,5},{2},{3,4,7},{6}} => 2
{{1,2,5},{3,4},{6,7}} => {{1,5},{2},{3,4},{6,7}} => 2
{{1,2,5},{3,4},{6},{7}} => {{1,5},{2},{3,4},{6},{7}} => 2
{{1,2,6,7},{3,4,5}} => {{1,6,7},{2},{3,4,5}} => 2
{{1,2,6},{3,4,5,7}} => {{1,6},{2},{3,4,5,7}} => 2
{{1,2,6},{3,4,5},{7}} => {{1,6},{2},{3,4,5},{7}} => 2
{{1,2,7},{3,4,5,6}} => {{1,7},{2},{3,4,5,6}} => 2
{{1,2},{3,4,5,6,7}} => {{1,2},{3,4,5,6,7}} => 2
{{1,2},{3,4,5,6},{7}} => {{1,2},{3,4,5,6},{7}} => 2
{{1,2,7},{3,4,5},{6}} => {{1,7},{2},{3,4,5},{6}} => 2
{{1,2},{3,4,5,7},{6}} => {{1,2},{3,4,5,7},{6}} => 2
{{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => 2
{{1,2},{3,4,5},{6},{7}} => {{1,2},{3,4,5},{6},{7}} => 2
{{1,2,6,7},{3,4},{5}} => {{1,6,7},{2},{3,4},{5}} => 2
{{1,2,6},{3,4,7},{5}} => {{1,5,6},{2},{3,4,7}} => 2
{{1,2,6},{3,4},{5,7}} => {{1,6},{2},{3,4},{5,7}} => 2
{{1,2,6},{3,4},{5},{7}} => {{1,6},{2},{3,4},{5},{7}} => 2
{{1,2,7},{3,4,6},{5}} => {{1,5,7},{2},{3,4,6}} => 2
{{1,2},{3,4,6,7},{5}} => {{1,2},{3,4,6,7},{5}} => 2
{{1,2},{3,4,6},{5,7}} => {{1,2},{3,4,6},{5,7}} => 2
{{1,2},{3,4,6},{5},{7}} => {{1,2},{3,4,6},{5},{7}} => 2
{{1,2,7},{3,4},{5,6}} => {{1,7},{2},{3,4},{5,6}} => 2
{{1,2},{3,4,7},{5,6}} => {{1,2},{3,4,7},{5,6}} => 2
{{1,2},{3,4},{5,6,7}} => {{1,2},{3,4},{5,6,7}} => 2
{{1,2},{3,4},{5,6},{7}} => {{1,2},{3,4},{5,6},{7}} => 2
{{1,2,7},{3,4},{5},{6}} => {{1,7},{2},{3,4},{5},{6}} => 2
{{1,2},{3,4,7},{5},{6}} => {{1,2},{3,4,7},{5},{6}} => 2
{{1,2},{3,4},{5,7},{6}} => {{1,2},{3,4},{5,7},{6}} => 2
{{1,2},{3,4},{5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => 2
{{1,2},{3,4},{5},{6},{7}} => {{1,2},{3,4},{5},{6},{7}} => 2
{{1,2,5,6,7},{3},{4}} => {{1,3,5,6,7},{2},{4}} => 2
{{1,2,5,6},{3,7},{4}} => {{1,4,5,6},{2},{3,7}} => 2
{{1,2,5,6},{3},{4,7}} => {{1,3,5,6},{2},{4,7}} => 2
{{1,2,5,6},{3},{4},{7}} => {{1,3,5,6},{2},{4},{7}} => 2
{{1,2,5,7},{3,6},{4}} => {{1,4,5,7},{2},{3,6}} => 2
{{1,2,5},{3,6,7},{4}} => {{1,4,5},{2},{3,6,7}} => 2
{{1,2,5},{3,6},{4,7}} => {{1,5},{2},{3,6},{4,7}} => 2
{{1,2,5},{3,6},{4},{7}} => {{1,4,5},{2},{3,6},{7}} => 2
{{1,2,5,7},{3},{4,6}} => {{1,3,5,7},{2},{4,6}} => 2
{{1,2,5},{3,7},{4,6}} => {{1,5},{2},{3,7},{4,6}} => 2
{{1,2,5},{3},{4,6,7}} => {{1,3,5},{2},{4,6,7}} => 2
{{1,2,5},{3},{4,6},{7}} => {{1,3,5},{2},{4,6},{7}} => 2
{{1,2,5,7},{3},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => 2
{{1,2,5},{3,7},{4},{6}} => {{1,4,5},{2},{3,7},{6}} => 2
{{1,2,5},{3},{4,7},{6}} => {{1,3,5},{2},{4,7},{6}} => 2
{{1,2,5},{3},{4},{6,7}} => {{1,3,5},{2},{4},{6,7}} => 2
{{1,2,5},{3},{4},{6},{7}} => {{1,3,5},{2},{4},{6},{7}} => 2
{{1,2,6,7},{3,5},{4}} => {{1,4,6,7},{2},{3,5}} => 2
{{1,2,6},{3,5,7},{4}} => {{1,4,6},{2},{3,5,7}} => 2
{{1,2,6},{3,5},{4,7}} => {{1,6},{2},{3,5},{4,7}} => 2
{{1,2,6},{3,5},{4},{7}} => {{1,4,6},{2},{3,5},{7}} => 2
{{1,2,7},{3,5,6},{4}} => {{1,4,7},{2},{3,5,6}} => 2
{{1,2},{3,5,6,7},{4}} => {{1,2},{3,5,6,7},{4}} => 2
{{1,2},{3,5,6},{4,7}} => {{1,2},{3,5,6},{4,7}} => 2
{{1,2},{3,5,6},{4},{7}} => {{1,2},{3,5,6},{4},{7}} => 2
{{1,2,7},{3,5},{4,6}} => {{1,7},{2},{3,5},{4,6}} => 2
{{1,2},{3,5,7},{4,6}} => {{1,2},{3,5,7},{4,6}} => 2
{{1,2},{3,5},{4,6,7}} => {{1,2},{3,5},{4,6,7}} => 2
{{1,2},{3,5},{4,6},{7}} => {{1,2},{3,5},{4,6},{7}} => 2
{{1,2,7},{3,5},{4},{6}} => {{1,4,7},{2},{3,5},{6}} => 2
{{1,2},{3,5,7},{4},{6}} => {{1,2},{3,5,7},{4},{6}} => 2
{{1,2},{3,5},{4,7},{6}} => {{1,2},{3,5},{4,7},{6}} => 2
{{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => 2
{{1,2},{3,5},{4},{6},{7}} => {{1,2},{3,5},{4},{6},{7}} => 2
{{1,2,6,7},{3},{4,5}} => {{1,3,6,7},{2},{4,5}} => 2
{{1,2,6},{3,7},{4,5}} => {{1,6},{2},{3,7},{4,5}} => 2
{{1,2,6},{3},{4,5,7}} => {{1,3,6},{2},{4,5,7}} => 2
{{1,2,6},{3},{4,5},{7}} => {{1,3,6},{2},{4,5},{7}} => 2
{{1,2,7},{3,6},{4,5}} => {{1,7},{2},{3,6},{4,5}} => 2
{{1,2},{3,6,7},{4,5}} => {{1,2},{3,6,7},{4,5}} => 2
{{1,2},{3,6},{4,5,7}} => {{1,2},{3,6},{4,5,7}} => 2
{{1,2},{3,6},{4,5},{7}} => {{1,2},{3,6},{4,5},{7}} => 2
{{1,2,7},{3},{4,5,6}} => {{1,3,7},{2},{4,5,6}} => 2
{{1,2},{3,7},{4,5,6}} => {{1,2},{3,7},{4,5,6}} => 2
{{1,2},{3},{4,5,6,7}} => {{1,2},{3},{4,5,6,7}} => 2
{{1,2},{3},{4,5,6},{7}} => {{1,2},{3},{4,5,6},{7}} => 2
{{1,2,7},{3},{4,5},{6}} => {{1,3,7},{2},{4,5},{6}} => 2
{{1,2},{3,7},{4,5},{6}} => {{1,2},{3,7},{4,5},{6}} => 2
{{1,2},{3},{4,5,7},{6}} => {{1,2},{3},{4,5,7},{6}} => 2
{{1,2},{3},{4,5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => 2
{{1,2},{3},{4,5},{6},{7}} => {{1,2},{3},{4,5},{6},{7}} => 2
{{1,2,6,7},{3},{4},{5}} => {{1,3,6,7},{2},{4},{5}} => 2
{{1,2,6},{3,7},{4},{5}} => {{1,4,6},{2},{3,7},{5}} => 2
{{1,2,6},{3},{4,7},{5}} => {{1,3,6},{2},{4,7},{5}} => 2
{{1,2,6},{3},{4},{5,7}} => {{1,3,6},{2},{4},{5,7}} => 2
{{1,2,6},{3},{4},{5},{7}} => {{1,3,6},{2},{4},{5},{7}} => 2
{{1,2,7},{3,6},{4},{5}} => {{1,4,7},{2},{3,6},{5}} => 2
{{1,2},{3,6,7},{4},{5}} => {{1,2},{3,6,7},{4},{5}} => 2
{{1,2},{3,6},{4,7},{5}} => {{1,2},{3,6},{4,7},{5}} => 2
{{1,2},{3,6},{4},{5,7}} => {{1,2},{3,6},{4},{5,7}} => 2
{{1,2},{3,6},{4},{5},{7}} => {{1,2},{3,6},{4},{5},{7}} => 2
{{1,2,7},{3},{4,6},{5}} => {{1,3,7},{2},{4,6},{5}} => 2
{{1,2},{3,7},{4,6},{5}} => {{1,2},{3,7},{4,6},{5}} => 2
{{1,2},{3},{4,6,7},{5}} => {{1,2},{3},{4,6,7},{5}} => 2
{{1,2},{3},{4,6},{5,7}} => {{1,2},{3},{4,6},{5,7}} => 2
{{1,2},{3},{4,6},{5},{7}} => {{1,2},{3},{4,6},{5},{7}} => 2
{{1,2,7},{3},{4},{5,6}} => {{1,3,7},{2},{4},{5,6}} => 2
{{1,2},{3,7},{4},{5,6}} => {{1,2},{3,7},{4},{5,6}} => 2
{{1,2},{3},{4,7},{5,6}} => {{1,2},{3},{4,7},{5,6}} => 2
{{1,2},{3},{4},{5,6,7}} => {{1,2},{3},{4},{5,6,7}} => 2
{{1,2},{3},{4},{5,6},{7}} => {{1,2},{3},{4},{5,6},{7}} => 2
{{1,2,7},{3},{4},{5},{6}} => {{1,3,7},{2},{4},{5},{6}} => 2
{{1,2},{3,7},{4},{5},{6}} => {{1,2},{3,7},{4},{5},{6}} => 2
{{1,2},{3},{4,7},{5},{6}} => {{1,2},{3},{4,7},{5},{6}} => 2
{{1,2},{3},{4},{5,7},{6}} => {{1,2},{3},{4},{5,7},{6}} => 2
{{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => 2
{{1,2},{3},{4},{5},{6},{7}} => {{1,2},{3},{4},{5},{6},{7}} => 2
{{1,3,4,5,6,7},{2}} => {{1,2,4,5,6,7},{3}} => 3
{{1,3,4,5,6},{2,7}} => {{1,6},{2,7},{3},{4},{5}} => 3
{{1,3,4,5,6},{2},{7}} => {{1,2,4,5,6},{3},{7}} => 3
{{1,3,4,5,7},{2,6}} => {{1,7},{2,6},{3},{4},{5}} => 3
{{1,3,4,5},{2,6,7}} => {{1,5},{2,6,7},{3},{4}} => 3
{{1,3,4,5},{2,6},{7}} => {{1,5},{2,6},{3},{4},{7}} => 3
{{1,3,4,5,7},{2},{6}} => {{1,2,4,5,7},{3},{6}} => 3
{{1,3,4,5},{2,7},{6}} => {{1,5},{2,7},{3},{4},{6}} => 3
{{1,3,4,5},{2},{6,7}} => {{1,2,4,5},{3},{6,7}} => 3
{{1,3,4,5},{2},{6},{7}} => {{1,2,4,5},{3},{6},{7}} => 3
{{1,3,4,6,7},{2,5}} => {{1,6,7},{2,5},{3},{4}} => 3
{{1,3,4,6},{2,5,7}} => {{1,6},{2,5,7},{3},{4}} => 3
{{1,3,4,6},{2,5},{7}} => {{1,6},{2,5},{3},{4},{7}} => 3
{{1,3,4,7},{2,5,6}} => {{1,7},{2,5,6},{3},{4}} => 3
{{1,3,4},{2,5,6,7}} => {{1,4},{2,5,6,7},{3}} => 3
{{1,3,4},{2,5,6},{7}} => {{1,4},{2,5,6},{3},{7}} => 3
{{1,3,4,7},{2,5},{6}} => {{1,7},{2,5},{3},{4},{6}} => 3
{{1,3,4},{2,5,7},{6}} => {{1,4},{2,5,7},{3},{6}} => 3
{{1,3,4},{2,5},{6,7}} => {{1,4},{2,5},{3},{6,7}} => 3
{{1,3,4},{2,5},{6},{7}} => {{1,4},{2,5},{3},{6},{7}} => 3
{{1,3,4,6,7},{2},{5}} => {{1,2,4,6,7},{3},{5}} => 3
{{1,3,4,6},{2,7},{5}} => {{1,5,6},{2,7},{3},{4}} => 3
{{1,3,4,6},{2},{5,7}} => {{1,2,4,6},{3},{5,7}} => 3
{{1,3,4,6},{2},{5},{7}} => {{1,2,4,6},{3},{5},{7}} => 3
{{1,3,4,7},{2,6},{5}} => {{1,5,7},{2,6},{3},{4}} => 3
{{1,3,4},{2,6,7},{5}} => {{1,4},{2,6,7},{3},{5}} => 3
{{1,3,4},{2,6},{5,7}} => {{1,4},{2,6},{3},{5,7}} => 3
{{1,3,4},{2,6},{5},{7}} => {{1,4},{2,6},{3},{5},{7}} => 3
{{1,3,4,7},{2},{5,6}} => {{1,2,4,7},{3},{5,6}} => 3
{{1,3,4},{2,7},{5,6}} => {{1,4},{2,7},{3},{5,6}} => 3
{{1,3,4},{2},{5,6,7}} => {{1,2,4},{3},{5,6,7}} => 3
{{1,3,4},{2},{5,6},{7}} => {{1,2,4},{3},{5,6},{7}} => 3
{{1,3,4,7},{2},{5},{6}} => {{1,2,4,7},{3},{5},{6}} => 3
{{1,3,4},{2,7},{5},{6}} => {{1,4},{2,7},{3},{5},{6}} => 3
{{1,3,4},{2},{5,7},{6}} => {{1,2,4},{3},{5,7},{6}} => 3
{{1,3,4},{2},{5},{6,7}} => {{1,2,4},{3},{5},{6,7}} => 3
{{1,3,4},{2},{5},{6},{7}} => {{1,2,4},{3},{5},{6},{7}} => 3
{{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
{{1,3,5,6},{2,4,7}} => {{1,6},{2,4,7},{3},{5}} => 3
{{1,3,5,6},{2,4},{7}} => {{1,5,6},{2,4},{3},{7}} => 3
{{1,3,5,7},{2,4,6}} => {{1,7},{2,4,6},{3},{5}} => 3
{{1,3,5},{2,4,6,7}} => {{1,5},{2,4,6,7},{3}} => 3
{{1,3,5},{2,4,6},{7}} => {{1,5},{2,4,6},{3},{7}} => 3
{{1,3,5,7},{2,4},{6}} => {{1,5,7},{2,4},{3},{6}} => 3
{{1,3,5},{2,4,7},{6}} => {{1,5},{2,4,7},{3},{6}} => 3
{{1,3,5},{2,4},{6,7}} => {{1,5},{2,4},{3},{6,7}} => 3
{{1,3,5},{2,4},{6},{7}} => {{1,5},{2,4},{3},{6},{7}} => 3
{{1,3,6,7},{2,4,5}} => {{1,6,7},{2,4,5},{3}} => 3
{{1,3,6},{2,4,5,7}} => {{1,6},{2,4,5,7},{3}} => 3
{{1,3,6},{2,4,5},{7}} => {{1,6},{2,4,5},{3},{7}} => 3
{{1,3,7},{2,4,5,6}} => {{1,7},{2,4,5,6},{3}} => 3
{{1,3},{2,4,5,6,7}} => {{1,3},{2,4,5,6,7}} => 3
{{1,3},{2,4,5,6},{7}} => {{1,3},{2,4,5,6},{7}} => 3
{{1,3,7},{2,4,5},{6}} => {{1,7},{2,4,5},{3},{6}} => 3
{{1,3},{2,4,5,7},{6}} => {{1,3},{2,4,5,7},{6}} => 3
{{1,3},{2,4,5},{6,7}} => {{1,3},{2,4,5},{6,7}} => 3
{{1,3},{2,4,5},{6},{7}} => {{1,3},{2,4,5},{6},{7}} => 3
{{1,3,6,7},{2,4},{5}} => {{1,6,7},{2,4},{3},{5}} => 3
{{1,3,6},{2,4,7},{5}} => {{1,5,6},{2,4,7},{3}} => 3
{{1,3,6},{2,4},{5,7}} => {{1,6},{2,4},{3},{5,7}} => 3
{{1,3,6},{2,4},{5},{7}} => {{1,6},{2,4},{3},{5},{7}} => 3
{{1,3,7},{2,4,6},{5}} => {{1,5,7},{2,4,6},{3}} => 3
{{1,3},{2,4,6,7},{5}} => {{1,3},{2,4,6,7},{5}} => 3
{{1,3},{2,4,6},{5,7}} => {{1,3},{2,4,6},{5,7}} => 3
{{1,3},{2,4,6},{5},{7}} => {{1,3},{2,4,6},{5},{7}} => 3
{{1,3,7},{2,4},{5,6}} => {{1,7},{2,4},{3},{5,6}} => 3
{{1,3},{2,4,7},{5,6}} => {{1,3},{2,4,7},{5,6}} => 3
{{1,3},{2,4},{5,6,7}} => {{1,3},{2,4},{5,6,7}} => 3
{{1,3},{2,4},{5,6},{7}} => {{1,3},{2,4},{5,6},{7}} => 3
{{1,3,7},{2,4},{5},{6}} => {{1,7},{2,4},{3},{5},{6}} => 3
{{1,3},{2,4,7},{5},{6}} => {{1,3},{2,4,7},{5},{6}} => 3
{{1,3},{2,4},{5,7},{6}} => {{1,3},{2,4},{5,7},{6}} => 3
{{1,3},{2,4},{5},{6,7}} => {{1,3},{2,4},{5},{6,7}} => 3
{{1,3},{2,4},{5},{6},{7}} => {{1,3},{2,4},{5},{6},{7}} => 3
{{1,3,5,6,7},{2},{4}} => {{1,2,5,6,7},{3},{4}} => 3
{{1,3,5,6},{2,7},{4}} => {{1,4,5,6},{2,7},{3}} => 3
{{1,3,5,6},{2},{4,7}} => {{1,2,5,6},{3},{4,7}} => 3
{{1,3,5,6},{2},{4},{7}} => {{1,2,5,6},{3},{4},{7}} => 3
{{1,3,5,7},{2,6},{4}} => {{1,4,5,7},{2,6},{3}} => 3
{{1,3,5},{2,6,7},{4}} => {{1,4,5},{2,6,7},{3}} => 3
{{1,3,5},{2,6},{4,7}} => {{1,5},{2,6},{3},{4,7}} => 3
{{1,3,5},{2,6},{4},{7}} => {{1,4,5},{2,6},{3},{7}} => 3
{{1,3,5,7},{2},{4,6}} => {{1,2,5,7},{3},{4,6}} => 3
{{1,3,5},{2,7},{4,6}} => {{1,5},{2,7},{3},{4,6}} => 3
{{1,3,5},{2},{4,6,7}} => {{1,2,5},{3},{4,6,7}} => 3
{{1,3,5},{2},{4,6},{7}} => {{1,2,5},{3},{4,6},{7}} => 3
{{1,3,5,7},{2},{4},{6}} => {{1,2,5,7},{3},{4},{6}} => 3
{{1,3,5},{2,7},{4},{6}} => {{1,4,5},{2,7},{3},{6}} => 3
{{1,3,5},{2},{4,7},{6}} => {{1,2,5},{3},{4,7},{6}} => 3
{{1,3,5},{2},{4},{6,7}} => {{1,2,5},{3},{4},{6,7}} => 3
{{1,3,5},{2},{4},{6},{7}} => {{1,2,5},{3},{4},{6},{7}} => 3
{{1,3,6,7},{2,5},{4}} => {{1,4,6,7},{2,5},{3}} => 3
{{1,3,6},{2,5,7},{4}} => {{1,4,6},{2,5,7},{3}} => 3
{{1,3,6},{2,5},{4,7}} => {{1,6},{2,5},{3},{4,7}} => 3
{{1,3,6},{2,5},{4},{7}} => {{1,4,6},{2,5},{3},{7}} => 3
{{1,3,7},{2,5,6},{4}} => {{1,4,7},{2,5,6},{3}} => 3
{{1,3},{2,5,6,7},{4}} => {{1,3},{2,5,6,7},{4}} => 3
{{1,3},{2,5,6},{4,7}} => {{1,3},{2,5,6},{4,7}} => 3
{{1,3},{2,5,6},{4},{7}} => {{1,3},{2,5,6},{4},{7}} => 3
{{1,3,7},{2,5},{4,6}} => {{1,7},{2,5},{3},{4,6}} => 3
{{1,3},{2,5,7},{4,6}} => {{1,3},{2,5,7},{4,6}} => 3
{{1,3},{2,5},{4,6,7}} => {{1,3},{2,5},{4,6,7}} => 3
{{1,3},{2,5},{4,6},{7}} => {{1,3},{2,5},{4,6},{7}} => 3
{{1,3,7},{2,5},{4},{6}} => {{1,4,7},{2,5},{3},{6}} => 3
{{1,3},{2,5,7},{4},{6}} => {{1,3},{2,5,7},{4},{6}} => 3
{{1,3},{2,5},{4,7},{6}} => {{1,3},{2,5},{4,7},{6}} => 3
{{1,3},{2,5},{4},{6,7}} => {{1,3},{2,5},{4},{6,7}} => 3
{{1,3},{2,5},{4},{6},{7}} => {{1,3},{2,5},{4},{6},{7}} => 3
{{1,3,6,7},{2},{4,5}} => {{1,2,6,7},{3},{4,5}} => 3
{{1,3,6},{2,7},{4,5}} => {{1,6},{2,7},{3},{4,5}} => 3
{{1,3,6},{2},{4,5,7}} => {{1,2,6},{3},{4,5,7}} => 3
{{1,3,6},{2},{4,5},{7}} => {{1,2,6},{3},{4,5},{7}} => 3
{{1,3,7},{2,6},{4,5}} => {{1,7},{2,6},{3},{4,5}} => 3
{{1,3},{2,6,7},{4,5}} => {{1,3},{2,6,7},{4,5}} => 3
{{1,3},{2,6},{4,5,7}} => {{1,3},{2,6},{4,5,7}} => 3
{{1,3},{2,6},{4,5},{7}} => {{1,3},{2,6},{4,5},{7}} => 3
{{1,3,7},{2},{4,5,6}} => {{1,2,7},{3},{4,5,6}} => 3
{{1,3},{2,7},{4,5,6}} => {{1,3},{2,7},{4,5,6}} => 3
{{1,3},{2},{4,5,6,7}} => {{1,2,3},{4,5,6,7}} => 3
{{1,3},{2},{4,5,6},{7}} => {{1,2,3},{4,5,6},{7}} => 3
{{1,3,7},{2},{4,5},{6}} => {{1,2,7},{3},{4,5},{6}} => 3
{{1,3},{2,7},{4,5},{6}} => {{1,3},{2,7},{4,5},{6}} => 3
{{1,3},{2},{4,5,7},{6}} => {{1,2,3},{4,5,7},{6}} => 3
{{1,3},{2},{4,5},{6,7}} => {{1,2,3},{4,5},{6,7}} => 3
{{1,3},{2},{4,5},{6},{7}} => {{1,2,3},{4,5},{6},{7}} => 3
{{1,3,6,7},{2},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => 3
{{1,3,6},{2,7},{4},{5}} => {{1,4,6},{2,7},{3},{5}} => 3
{{1,3,6},{2},{4,7},{5}} => {{1,2,6},{3},{4,7},{5}} => 3
{{1,3,6},{2},{4},{5,7}} => {{1,2,6},{3},{4},{5,7}} => 3
{{1,3,6},{2},{4},{5},{7}} => {{1,2,6},{3},{4},{5},{7}} => 3
{{1,3,7},{2,6},{4},{5}} => {{1,4,7},{2,6},{3},{5}} => 3
{{1,3},{2,6,7},{4},{5}} => {{1,3},{2,6,7},{4},{5}} => 3
{{1,3},{2,6},{4,7},{5}} => {{1,3},{2,6},{4,7},{5}} => 3
{{1,3},{2,6},{4},{5,7}} => {{1,3},{2,6},{4},{5,7}} => 3
{{1,3},{2,6},{4},{5},{7}} => {{1,3},{2,6},{4},{5},{7}} => 3
{{1,3,7},{2},{4,6},{5}} => {{1,2,7},{3},{4,6},{5}} => 3
{{1,3},{2,7},{4,6},{5}} => {{1,3},{2,7},{4,6},{5}} => 3
{{1,3},{2},{4,6,7},{5}} => {{1,2,3},{4,6,7},{5}} => 3
{{1,3},{2},{4,6},{5,7}} => {{1,2,3},{4,6},{5,7}} => 3
{{1,3},{2},{4,6},{5},{7}} => {{1,2,3},{4,6},{5},{7}} => 3
{{1,3,7},{2},{4},{5,6}} => {{1,2,7},{3},{4},{5,6}} => 3
{{1,3},{2,7},{4},{5,6}} => {{1,3},{2,7},{4},{5,6}} => 3
{{1,3},{2},{4,7},{5,6}} => {{1,2,3},{4,7},{5,6}} => 3
{{1,3},{2},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => 3
{{1,3},{2},{4},{5,6},{7}} => {{1,2,3},{4},{5,6},{7}} => 3
{{1,3,7},{2},{4},{5},{6}} => {{1,2,7},{3},{4},{5},{6}} => 3
{{1,3},{2,7},{4},{5},{6}} => {{1,3},{2,7},{4},{5},{6}} => 3
{{1,3},{2},{4,7},{5},{6}} => {{1,2,3},{4,7},{5},{6}} => 3
{{1,3},{2},{4},{5,7},{6}} => {{1,2,3},{4},{5,7},{6}} => 3
{{1,3},{2},{4},{5},{6,7}} => {{1,2,3},{4},{5},{6,7}} => 3
{{1,3},{2},{4},{5},{6},{7}} => {{1,2,3},{4},{5},{6},{7}} => 3
{{1,4,5,6,7},{2,3}} => {{1,4,5,6,7},{2,3}} => 3
{{1,4,5,6},{2,3,7}} => {{1,6},{2,3,7},{4},{5}} => 4
{{1,4,5,6},{2,3},{7}} => {{1,4,5,6},{2,3},{7}} => 3
{{1,4,5,7},{2,3,6}} => {{1,7},{2,3,6},{4},{5}} => 4
{{1,4,5},{2,3,6,7}} => {{1,5},{2,3,6,7},{4}} => 4
{{1,4,5},{2,3,6},{7}} => {{1,5},{2,3,6},{4},{7}} => 4
{{1,4,5,7},{2,3},{6}} => {{1,4,5,7},{2,3},{6}} => 3
{{1,4,5},{2,3,7},{6}} => {{1,5},{2,3,7},{4},{6}} => 4
{{1,4,5},{2,3},{6,7}} => {{1,4,5},{2,3},{6,7}} => 3
{{1,4,5},{2,3},{6},{7}} => {{1,4,5},{2,3},{6},{7}} => 3
{{1,4,6,7},{2,3,5}} => {{1,6,7},{2,3,5},{4}} => 4
{{1,4,6},{2,3,5,7}} => {{1,6},{2,3,5,7},{4}} => 4
{{1,4,6},{2,3,5},{7}} => {{1,6},{2,3,5},{4},{7}} => 4
{{1,4,7},{2,3,5,6}} => {{1,7},{2,3,5,6},{4}} => 4
{{1,4},{2,3,5,6,7}} => {{1,4},{2,3,5,6,7}} => 4
{{1,4},{2,3,5,6},{7}} => {{1,4},{2,3,5,6},{7}} => 4
{{1,4,7},{2,3,5},{6}} => {{1,7},{2,3,5},{4},{6}} => 4
{{1,4},{2,3,5,7},{6}} => {{1,4},{2,3,5,7},{6}} => 4
{{1,4},{2,3,5},{6,7}} => {{1,4},{2,3,5},{6,7}} => 4
{{1,4},{2,3,5},{6},{7}} => {{1,4},{2,3,5},{6},{7}} => 4
{{1,4,6,7},{2,3},{5}} => {{1,4,6,7},{2,3},{5}} => 3
{{1,4,6},{2,3,7},{5}} => {{1,5,6},{2,3,7},{4}} => 4
{{1,4,6},{2,3},{5,7}} => {{1,4,6},{2,3},{5,7}} => 3
{{1,4,6},{2,3},{5},{7}} => {{1,4,6},{2,3},{5},{7}} => 3
{{1,4,7},{2,3,6},{5}} => {{1,5,7},{2,3,6},{4}} => 4
{{1,4},{2,3,6,7},{5}} => {{1,4},{2,3,6,7},{5}} => 4
{{1,4},{2,3,6},{5,7}} => {{1,4},{2,3,6},{5,7}} => 4
{{1,4},{2,3,6},{5},{7}} => {{1,4},{2,3,6},{5},{7}} => 4
{{1,4,7},{2,3},{5,6}} => {{1,4,7},{2,3},{5,6}} => 3
{{1,4},{2,3,7},{5,6}} => {{1,4},{2,3,7},{5,6}} => 4
{{1,4},{2,3},{5,6,7}} => {{1,4},{2,3},{5,6,7}} => 3
{{1,4},{2,3},{5,6},{7}} => {{1,4},{2,3},{5,6},{7}} => 3
{{1,4,7},{2,3},{5},{6}} => {{1,4,7},{2,3},{5},{6}} => 3
{{1,4},{2,3,7},{5},{6}} => {{1,4},{2,3,7},{5},{6}} => 4
{{1,4},{2,3},{5,7},{6}} => {{1,4},{2,3},{5,7},{6}} => 3
{{1,4},{2,3},{5},{6,7}} => {{1,4},{2,3},{5},{6,7}} => 3
{{1,4},{2,3},{5},{6},{7}} => {{1,4},{2,3},{5},{6},{7}} => 3
{{1,5,6,7},{2,3,4}} => {{1,5,6,7},{2,3,4}} => 4
{{1,5,6},{2,3,4,7}} => {{1,6},{2,3,4,7},{5}} => 5
{{1,5,6},{2,3,4},{7}} => {{1,5,6},{2,3,4},{7}} => 4
{{1,5,7},{2,3,4,6}} => {{1,7},{2,3,4,6},{5}} => 5
{{1,5},{2,3,4,6,7}} => {{1,5},{2,3,4,6,7}} => 5
{{1,5},{2,3,4,6},{7}} => {{1,5},{2,3,4,6},{7}} => 5
{{1,5,7},{2,3,4},{6}} => {{1,5,7},{2,3,4},{6}} => 4
{{1,5},{2,3,4,7},{6}} => {{1,5},{2,3,4,7},{6}} => 5
{{1,5},{2,3,4},{6,7}} => {{1,5},{2,3,4},{6,7}} => 4
{{1,5},{2,3,4},{6},{7}} => {{1,5},{2,3,4},{6},{7}} => 4
{{1,6,7},{2,3,4,5}} => {{1,6,7},{2,3,4,5}} => 5
{{1,6},{2,3,4,5,7}} => {{1,6},{2,3,4,5,7}} => 6
{{1,6},{2,3,4,5},{7}} => {{1,6},{2,3,4,5},{7}} => 5
{{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => 6
{{1},{2,3,4,5,6,7}} => {{1},{2,3,4,5,6,7}} => 1
{{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => 1
{{1,7},{2,3,4,5},{6}} => {{1,7},{2,3,4,5},{6}} => 5
{{1},{2,3,4,5,7},{6}} => {{1},{2,3,4,5,7},{6}} => 1
{{1},{2,3,4,5},{6,7}} => {{1},{2,3,4,5},{6,7}} => 1
{{1},{2,3,4,5},{6},{7}} => {{1},{2,3,4,5},{6},{7}} => 1
{{1,6,7},{2,3,4},{5}} => {{1,6,7},{2,3,4},{5}} => 4
{{1,6},{2,3,4,7},{5}} => {{1,5,6},{2,3,4,7}} => 6
{{1,6},{2,3,4},{5,7}} => {{1,6},{2,3,4},{5,7}} => 4
{{1,6},{2,3,4},{5},{7}} => {{1,6},{2,3,4},{5},{7}} => 4
{{1,7},{2,3,4,6},{5}} => {{1,5,7},{2,3,4,6}} => 6
{{1},{2,3,4,6,7},{5}} => {{1},{2,3,4,6,7},{5}} => 1
{{1},{2,3,4,6},{5,7}} => {{1},{2,3,4,6},{5,7}} => 1
{{1},{2,3,4,6},{5},{7}} => {{1},{2,3,4,6},{5},{7}} => 1
{{1,7},{2,3,4},{5,6}} => {{1,7},{2,3,4},{5,6}} => 4
{{1},{2,3,4,7},{5,6}} => {{1},{2,3,4,7},{5,6}} => 1
{{1},{2,3,4},{5,6,7}} => {{1},{2,3,4},{5,6,7}} => 1
{{1},{2,3,4},{5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => 1
{{1,7},{2,3,4},{5},{6}} => {{1,7},{2,3,4},{5},{6}} => 4
{{1},{2,3,4,7},{5},{6}} => {{1},{2,3,4,7},{5},{6}} => 1
{{1},{2,3,4},{5,7},{6}} => {{1},{2,3,4},{5,7},{6}} => 1
{{1},{2,3,4},{5},{6,7}} => {{1},{2,3,4},{5},{6,7}} => 1
{{1},{2,3,4},{5},{6},{7}} => {{1},{2,3,4},{5},{6},{7}} => 1
{{1,5,6,7},{2,3},{4}} => {{1,5,6,7},{2,3},{4}} => 3
{{1,5,6},{2,3,7},{4}} => {{1,4,6},{2,3,7},{5}} => 5
{{1,5,6},{2,3},{4,7}} => {{1,5,6},{2,3},{4,7}} => 3
{{1,5,6},{2,3},{4},{7}} => {{1,5,6},{2,3},{4},{7}} => 3
{{1,5,7},{2,3,6},{4}} => {{1,4,7},{2,3,6},{5}} => 5
{{1,5},{2,3,6,7},{4}} => {{1,4,5},{2,3,6,7}} => 5
{{1,5},{2,3,6},{4,7}} => {{1,5},{2,3,6},{4,7}} => 5
{{1,5},{2,3,6},{4},{7}} => {{1,4,5},{2,3,6},{7}} => 5
{{1,5,7},{2,3},{4,6}} => {{1,5,7},{2,3},{4,6}} => 3
{{1,5},{2,3,7},{4,6}} => {{1,5},{2,3,7},{4,6}} => 5
{{1,5},{2,3},{4,6,7}} => {{1,5},{2,3},{4,6,7}} => 3
{{1,5},{2,3},{4,6},{7}} => {{1,5},{2,3},{4,6},{7}} => 3
{{1,5,7},{2,3},{4},{6}} => {{1,5,7},{2,3},{4},{6}} => 3
{{1,5},{2,3,7},{4},{6}} => {{1,4,5},{2,3,7},{6}} => 5
{{1,5},{2,3},{4,7},{6}} => {{1,5},{2,3},{4,7},{6}} => 3
{{1,5},{2,3},{4},{6,7}} => {{1,5},{2,3},{4},{6,7}} => 3
{{1,5},{2,3},{4},{6},{7}} => {{1,5},{2,3},{4},{6},{7}} => 3
{{1,6,7},{2,3,5},{4}} => {{1,4,6,7},{2,3,5}} => 5
{{1,6},{2,3,5,7},{4}} => {{1,4,6},{2,3,5,7}} => 6
{{1,6},{2,3,5},{4,7}} => {{1,6},{2,3,5},{4,7}} => 5
{{1,6},{2,3,5},{4},{7}} => {{1,4,6},{2,3,5},{7}} => 5
{{1,7},{2,3,5,6},{4}} => {{1,4,7},{2,3,5,6}} => 6
{{1},{2,3,5,6,7},{4}} => {{1},{2,3,5,6,7},{4}} => 1
{{1},{2,3,5,6},{4,7}} => {{1},{2,3,5,6},{4,7}} => 1
{{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}} => 1
{{1,7},{2,3,5},{4,6}} => {{1,7},{2,3,5},{4,6}} => 5
{{1},{2,3,5,7},{4,6}} => {{1},{2,3,5,7},{4,6}} => 1
{{1},{2,3,5},{4,6,7}} => {{1},{2,3,5},{4,6,7}} => 1
{{1},{2,3,5},{4,6},{7}} => {{1},{2,3,5},{4,6},{7}} => 1
{{1,7},{2,3,5},{4},{6}} => {{1,4,7},{2,3,5},{6}} => 5
{{1},{2,3,5,7},{4},{6}} => {{1},{2,3,5,7},{4},{6}} => 1
{{1},{2,3,5},{4,7},{6}} => {{1},{2,3,5},{4,7},{6}} => 1
{{1},{2,3,5},{4},{6,7}} => {{1},{2,3,5},{4},{6,7}} => 1
{{1},{2,3,5},{4},{6},{7}} => {{1},{2,3,5},{4},{6},{7}} => 1
{{1,6,7},{2,3},{4,5}} => {{1,6,7},{2,3},{4,5}} => 3
{{1,6},{2,3,7},{4,5}} => {{1,6},{2,3,7},{4,5}} => 5
{{1,6},{2,3},{4,5,7}} => {{1,6},{2,3},{4,5,7}} => 3
{{1,6},{2,3},{4,5},{7}} => {{1,6},{2,3},{4,5},{7}} => 3
{{1,7},{2,3,6},{4,5}} => {{1,7},{2,3,6},{4,5}} => 5
{{1},{2,3,6,7},{4,5}} => {{1},{2,3,6,7},{4,5}} => 1
{{1},{2,3,6},{4,5,7}} => {{1},{2,3,6},{4,5,7}} => 1
{{1},{2,3,6},{4,5},{7}} => {{1},{2,3,6},{4,5},{7}} => 1
{{1,7},{2,3},{4,5,6}} => {{1,7},{2,3},{4,5,6}} => 3
{{1},{2,3,7},{4,5,6}} => {{1},{2,3,7},{4,5,6}} => 1
{{1},{2,3},{4,5,6,7}} => {{1},{2,3},{4,5,6,7}} => 1
{{1},{2,3},{4,5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => 1
{{1,7},{2,3},{4,5},{6}} => {{1,7},{2,3},{4,5},{6}} => 3
{{1},{2,3,7},{4,5},{6}} => {{1},{2,3,7},{4,5},{6}} => 1
{{1},{2,3},{4,5,7},{6}} => {{1},{2,3},{4,5,7},{6}} => 1
{{1},{2,3},{4,5},{6,7}} => {{1},{2,3},{4,5},{6,7}} => 1
{{1},{2,3},{4,5},{6},{7}} => {{1},{2,3},{4,5},{6},{7}} => 1
{{1,6,7},{2,3},{4},{5}} => {{1,6,7},{2,3},{4},{5}} => 3
{{1,6},{2,3,7},{4},{5}} => {{1,4,5,6},{2,3,7}} => 6
{{1,6},{2,3},{4,7},{5}} => {{1,6},{2,3},{4,7},{5}} => 3
{{1,6},{2,3},{4},{5,7}} => {{1,6},{2,3},{4},{5,7}} => 3
{{1,6},{2,3},{4},{5},{7}} => {{1,6},{2,3},{4},{5},{7}} => 3
{{1,7},{2,3,6},{4},{5}} => {{1,4,5,7},{2,3,6}} => 6
{{1},{2,3,6,7},{4},{5}} => {{1},{2,3,6,7},{4},{5}} => 1
{{1},{2,3,6},{4,7},{5}} => {{1},{2,3,6},{4,7},{5}} => 1
{{1},{2,3,6},{4},{5,7}} => {{1},{2,3,6},{4},{5,7}} => 1
{{1},{2,3,6},{4},{5},{7}} => {{1},{2,3,6},{4},{5},{7}} => 1
{{1,7},{2,3},{4,6},{5}} => {{1,7},{2,3},{4,6},{5}} => 3
{{1},{2,3,7},{4,6},{5}} => {{1},{2,3,7},{4,6},{5}} => 1
{{1},{2,3},{4,6,7},{5}} => {{1},{2,3},{4,6,7},{5}} => 1
{{1},{2,3},{4,6},{5,7}} => {{1},{2,3},{4,6},{5,7}} => 1
{{1},{2,3},{4,6},{5},{7}} => {{1},{2,3},{4,6},{5},{7}} => 1
{{1,7},{2,3},{4},{5,6}} => {{1,7},{2,3},{4},{5,6}} => 3
{{1},{2,3,7},{4},{5,6}} => {{1},{2,3,7},{4},{5,6}} => 1
{{1},{2,3},{4,7},{5,6}} => {{1},{2,3},{4,7},{5,6}} => 1
{{1},{2,3},{4},{5,6,7}} => {{1},{2,3},{4},{5,6,7}} => 1
{{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => 1
{{1,7},{2,3},{4},{5},{6}} => {{1,7},{2,3},{4},{5},{6}} => 3
{{1},{2,3,7},{4},{5},{6}} => {{1},{2,3,7},{4},{5},{6}} => 1
{{1},{2,3},{4,7},{5},{6}} => {{1},{2,3},{4,7},{5},{6}} => 1
{{1},{2,3},{4},{5,7},{6}} => {{1},{2,3},{4},{5,7},{6}} => 1
{{1},{2,3},{4},{5},{6,7}} => {{1},{2,3},{4},{5},{6,7}} => 1
{{1},{2,3},{4},{5},{6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2},{3}} => {{1,2,3,5,6,7},{4}} => 4
{{1,4,5,6},{2,7},{3}} => {{1,3,5,6},{2,7},{4}} => 4
{{1,4,5,6},{2},{3,7}} => {{1,2,5,6},{3,7},{4}} => 4
{{1,4,5,6},{2},{3},{7}} => {{1,2,3,5,6},{4},{7}} => 4
{{1,4,5,7},{2,6},{3}} => {{1,3,5,7},{2,6},{4}} => 4
{{1,4,5},{2,6,7},{3}} => {{1,3,5},{2,6,7},{4}} => 4
{{1,4,5},{2,6},{3,7}} => {{1,5},{2,6},{3,7},{4}} => 4
{{1,4,5},{2,6},{3},{7}} => {{1,3,5},{2,6},{4},{7}} => 4
{{1,4,5,7},{2},{3,6}} => {{1,2,5,7},{3,6},{4}} => 4
{{1,4,5},{2,7},{3,6}} => {{1,5},{2,7},{3,6},{4}} => 4
{{1,4,5},{2},{3,6,7}} => {{1,2,5},{3,6,7},{4}} => 4
{{1,4,5},{2},{3,6},{7}} => {{1,2,5},{3,6},{4},{7}} => 4
{{1,4,5,7},{2},{3},{6}} => {{1,2,3,5,7},{4},{6}} => 4
{{1,4,5},{2,7},{3},{6}} => {{1,3,5},{2,7},{4},{6}} => 4
{{1,4,5},{2},{3,7},{6}} => {{1,2,5},{3,7},{4},{6}} => 4
{{1,4,5},{2},{3},{6,7}} => {{1,2,3,5},{4},{6,7}} => 4
{{1,4,5},{2},{3},{6},{7}} => {{1,2,3,5},{4},{6},{7}} => 4
{{1,4,6,7},{2,5},{3}} => {{1,3,6,7},{2,5},{4}} => 4
{{1,4,6},{2,5,7},{3}} => {{1,3,6},{2,5,7},{4}} => 4
{{1,4,6},{2,5},{3,7}} => {{1,6},{2,5},{3,7},{4}} => 4
{{1,4,6},{2,5},{3},{7}} => {{1,3,6},{2,5},{4},{7}} => 4
{{1,4,7},{2,5,6},{3}} => {{1,3,7},{2,5,6},{4}} => 4
{{1,4},{2,5,6,7},{3}} => {{1,3,4},{2,5,6,7}} => 4
{{1,4},{2,5,6},{3,7}} => {{1,4},{2,5,6},{3,7}} => 4
{{1,4},{2,5,6},{3},{7}} => {{1,3,4},{2,5,6},{7}} => 4
{{1,4,7},{2,5},{3,6}} => {{1,7},{2,5},{3,6},{4}} => 4
{{1,4},{2,5,7},{3,6}} => {{1,4},{2,5,7},{3,6}} => 4
{{1,4},{2,5},{3,6,7}} => {{1,4},{2,5},{3,6,7}} => 4
{{1,4},{2,5},{3,6},{7}} => {{1,4},{2,5},{3,6},{7}} => 4
{{1,4,7},{2,5},{3},{6}} => {{1,3,7},{2,5},{4},{6}} => 4
{{1,4},{2,5,7},{3},{6}} => {{1,3,4},{2,5,7},{6}} => 4
{{1,4},{2,5},{3,7},{6}} => {{1,4},{2,5},{3,7},{6}} => 4
{{1,4},{2,5},{3},{6,7}} => {{1,3,4},{2,5},{6,7}} => 4
{{1,4},{2,5},{3},{6},{7}} => {{1,3,4},{2,5},{6},{7}} => 4
{{1,4,6,7},{2},{3,5}} => {{1,2,6,7},{3,5},{4}} => 4
{{1,4,6},{2,7},{3,5}} => {{1,6},{2,7},{3,5},{4}} => 4
{{1,4,6},{2},{3,5,7}} => {{1,2,6},{3,5,7},{4}} => 4
{{1,4,6},{2},{3,5},{7}} => {{1,2,6},{3,5},{4},{7}} => 4
{{1,4,7},{2,6},{3,5}} => {{1,7},{2,6},{3,5},{4}} => 4
{{1,4},{2,6,7},{3,5}} => {{1,4},{2,6,7},{3,5}} => 4
{{1,4},{2,6},{3,5,7}} => {{1,4},{2,6},{3,5,7}} => 4
{{1,4},{2,6},{3,5},{7}} => {{1,4},{2,6},{3,5},{7}} => 4
{{1,4,7},{2},{3,5,6}} => {{1,2,7},{3,5,6},{4}} => 4
{{1,4},{2,7},{3,5,6}} => {{1,4},{2,7},{3,5,6}} => 4
{{1,4},{2},{3,5,6,7}} => {{1,2,4},{3,5,6,7}} => 4
{{1,4},{2},{3,5,6},{7}} => {{1,2,4},{3,5,6},{7}} => 4
{{1,4,7},{2},{3,5},{6}} => {{1,2,7},{3,5},{4},{6}} => 4
{{1,4},{2,7},{3,5},{6}} => {{1,4},{2,7},{3,5},{6}} => 4
{{1,4},{2},{3,5,7},{6}} => {{1,2,4},{3,5,7},{6}} => 4
{{1,4},{2},{3,5},{6,7}} => {{1,2,4},{3,5},{6,7}} => 4
{{1,4},{2},{3,5},{6},{7}} => {{1,2,4},{3,5},{6},{7}} => 4
{{1,4,6,7},{2},{3},{5}} => {{1,2,3,6,7},{4},{5}} => 4
{{1,4,6},{2,7},{3},{5}} => {{1,3,6},{2,7},{4},{5}} => 4
{{1,4,6},{2},{3,7},{5}} => {{1,2,6},{3,7},{4},{5}} => 4
{{1,4,6},{2},{3},{5,7}} => {{1,2,3,6},{4},{5,7}} => 4
{{1,4,6},{2},{3},{5},{7}} => {{1,2,3,6},{4},{5},{7}} => 4
{{1,4,7},{2,6},{3},{5}} => {{1,3,7},{2,6},{4},{5}} => 4
{{1,4},{2,6,7},{3},{5}} => {{1,3,4},{2,6,7},{5}} => 4
{{1,4},{2,6},{3,7},{5}} => {{1,4},{2,6},{3,7},{5}} => 4
{{1,4},{2,6},{3},{5,7}} => {{1,3,4},{2,6},{5,7}} => 4
{{1,4},{2,6},{3},{5},{7}} => {{1,3,4},{2,6},{5},{7}} => 4
{{1,4,7},{2},{3,6},{5}} => {{1,2,7},{3,6},{4},{5}} => 4
{{1,4},{2,7},{3,6},{5}} => {{1,4},{2,7},{3,6},{5}} => 4
{{1,4},{2},{3,6,7},{5}} => {{1,2,4},{3,6,7},{5}} => 4
{{1,4},{2},{3,6},{5,7}} => {{1,2,4},{3,6},{5,7}} => 4
{{1,4},{2},{3,6},{5},{7}} => {{1,2,4},{3,6},{5},{7}} => 4
{{1,4,7},{2},{3},{5,6}} => {{1,2,3,7},{4},{5,6}} => 4
{{1,4},{2,7},{3},{5,6}} => {{1,3,4},{2,7},{5,6}} => 4
{{1,4},{2},{3,7},{5,6}} => {{1,2,4},{3,7},{5,6}} => 4
{{1,4},{2},{3},{5,6,7}} => {{1,2,3,4},{5,6,7}} => 4
{{1,4},{2},{3},{5,6},{7}} => {{1,2,3,4},{5,6},{7}} => 4
{{1,4,7},{2},{3},{5},{6}} => {{1,2,3,7},{4},{5},{6}} => 4
{{1,4},{2,7},{3},{5},{6}} => {{1,3,4},{2,7},{5},{6}} => 4
{{1,4},{2},{3,7},{5},{6}} => {{1,2,4},{3,7},{5},{6}} => 4
{{1,4},{2},{3},{5,7},{6}} => {{1,2,3,4},{5,7},{6}} => 4
{{1,4},{2},{3},{5},{6,7}} => {{1,2,3,4},{5},{6,7}} => 4
{{1,4},{2},{3},{5},{6},{7}} => {{1,2,3,4},{5},{6},{7}} => 4
{{1,5,6,7},{2,4},{3}} => {{1,3,5,6,7},{2,4}} => 4
{{1,5,6},{2,4,7},{3}} => {{1,3,6},{2,4,7},{5}} => 5
{{1,5,6},{2,4},{3,7}} => {{1,5,6},{2,4},{3,7}} => 4
{{1,5,6},{2,4},{3},{7}} => {{1,3,5,6},{2,4},{7}} => 4
{{1,5,7},{2,4,6},{3}} => {{1,3,7},{2,4,6},{5}} => 5
{{1,5},{2,4,6,7},{3}} => {{1,3,5},{2,4,6,7}} => 5
{{1,5},{2,4,6},{3,7}} => {{1,5},{2,4,6},{3,7}} => 5
{{1,5},{2,4,6},{3},{7}} => {{1,3,5},{2,4,6},{7}} => 5
{{1,5,7},{2,4},{3,6}} => {{1,5,7},{2,4},{3,6}} => 4
{{1,5},{2,4,7},{3,6}} => {{1,5},{2,4,7},{3,6}} => 5
{{1,5},{2,4},{3,6,7}} => {{1,5},{2,4},{3,6,7}} => 4
{{1,5},{2,4},{3,6},{7}} => {{1,5},{2,4},{3,6},{7}} => 4
{{1,5,7},{2,4},{3},{6}} => {{1,3,5,7},{2,4},{6}} => 4
{{1,5},{2,4,7},{3},{6}} => {{1,3,5},{2,4,7},{6}} => 5
{{1,5},{2,4},{3,7},{6}} => {{1,5},{2,4},{3,7},{6}} => 4
{{1,5},{2,4},{3},{6,7}} => {{1,3,5},{2,4},{6,7}} => 4
{{1,5},{2,4},{3},{6},{7}} => {{1,3,5},{2,4},{6},{7}} => 4
{{1,6,7},{2,4,5},{3}} => {{1,3,6,7},{2,4,5}} => 5
{{1,6},{2,4,5,7},{3}} => {{1,3,6},{2,4,5,7}} => 6
{{1,6},{2,4,5},{3,7}} => {{1,6},{2,4,5},{3,7}} => 5
{{1,6},{2,4,5},{3},{7}} => {{1,3,6},{2,4,5},{7}} => 5
{{1,7},{2,4,5,6},{3}} => {{1,3,7},{2,4,5,6}} => 6
{{1},{2,4,5,6,7},{3}} => {{1},{2,4,5,6,7},{3}} => 1
{{1},{2,4,5,6},{3,7}} => {{1},{2,4,5,6},{3,7}} => 1
{{1},{2,4,5,6},{3},{7}} => {{1},{2,4,5,6},{3},{7}} => 1
{{1,7},{2,4,5},{3,6}} => {{1,7},{2,4,5},{3,6}} => 5
{{1},{2,4,5,7},{3,6}} => {{1},{2,4,5,7},{3,6}} => 1
{{1},{2,4,5},{3,6,7}} => {{1},{2,4,5},{3,6,7}} => 1
{{1},{2,4,5},{3,6},{7}} => {{1},{2,4,5},{3,6},{7}} => 1
{{1,7},{2,4,5},{3},{6}} => {{1,3,7},{2,4,5},{6}} => 5
{{1},{2,4,5,7},{3},{6}} => {{1},{2,4,5,7},{3},{6}} => 1
{{1},{2,4,5},{3,7},{6}} => {{1},{2,4,5},{3,7},{6}} => 1
{{1},{2,4,5},{3},{6,7}} => {{1},{2,4,5},{3},{6,7}} => 1
{{1},{2,4,5},{3},{6},{7}} => {{1},{2,4,5},{3},{6},{7}} => 1
{{1,6,7},{2,4},{3,5}} => {{1,6,7},{2,4},{3,5}} => 4
{{1,6},{2,4,7},{3,5}} => {{1,6},{2,4,7},{3,5}} => 5
{{1,6},{2,4},{3,5,7}} => {{1,6},{2,4},{3,5,7}} => 4
{{1,6},{2,4},{3,5},{7}} => {{1,6},{2,4},{3,5},{7}} => 4
{{1,7},{2,4,6},{3,5}} => {{1,7},{2,4,6},{3,5}} => 5
{{1},{2,4,6,7},{3,5}} => {{1},{2,4,6,7},{3,5}} => 1
{{1},{2,4,6},{3,5,7}} => {{1},{2,4,6},{3,5,7}} => 1
{{1},{2,4,6},{3,5},{7}} => {{1},{2,4,6},{3,5},{7}} => 1
{{1,7},{2,4},{3,5,6}} => {{1,7},{2,4},{3,5,6}} => 4
{{1},{2,4,7},{3,5,6}} => {{1},{2,4,7},{3,5,6}} => 1
{{1},{2,4},{3,5,6,7}} => {{1},{2,4},{3,5,6,7}} => 1
{{1},{2,4},{3,5,6},{7}} => {{1},{2,4},{3,5,6},{7}} => 1
{{1,7},{2,4},{3,5},{6}} => {{1,7},{2,4},{3,5},{6}} => 4
{{1},{2,4,7},{3,5},{6}} => {{1},{2,4,7},{3,5},{6}} => 1
{{1},{2,4},{3,5,7},{6}} => {{1},{2,4},{3,5,7},{6}} => 1
{{1},{2,4},{3,5},{6,7}} => {{1},{2,4},{3,5},{6,7}} => 1
{{1},{2,4},{3,5},{6},{7}} => {{1},{2,4},{3,5},{6},{7}} => 1
{{1,6,7},{2,4},{3},{5}} => {{1,3,6,7},{2,4},{5}} => 4
{{1,6},{2,4,7},{3},{5}} => {{1,3,5,6},{2,4,7}} => 6
{{1,6},{2,4},{3,7},{5}} => {{1,6},{2,4},{3,7},{5}} => 4
{{1,6},{2,4},{3},{5,7}} => {{1,3,6},{2,4},{5,7}} => 4
{{1,6},{2,4},{3},{5},{7}} => {{1,3,6},{2,4},{5},{7}} => 4
{{1,7},{2,4,6},{3},{5}} => {{1,3,5,7},{2,4,6}} => 6
{{1},{2,4,6,7},{3},{5}} => {{1},{2,4,6,7},{3},{5}} => 1
{{1},{2,4,6},{3,7},{5}} => {{1},{2,4,6},{3,7},{5}} => 1
{{1},{2,4,6},{3},{5,7}} => {{1},{2,4,6},{3},{5,7}} => 1
{{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}} => 1
{{1,7},{2,4},{3,6},{5}} => {{1,7},{2,4},{3,6},{5}} => 4
{{1},{2,4,7},{3,6},{5}} => {{1},{2,4,7},{3,6},{5}} => 1
{{1},{2,4},{3,6,7},{5}} => {{1},{2,4},{3,6,7},{5}} => 1
{{1},{2,4},{3,6},{5,7}} => {{1},{2,4},{3,6},{5,7}} => 1
{{1},{2,4},{3,6},{5},{7}} => {{1},{2,4},{3,6},{5},{7}} => 1
{{1,7},{2,4},{3},{5,6}} => {{1,3,7},{2,4},{5,6}} => 4
{{1},{2,4,7},{3},{5,6}} => {{1},{2,4,7},{3},{5,6}} => 1
{{1},{2,4},{3,7},{5,6}} => {{1},{2,4},{3,7},{5,6}} => 1
{{1},{2,4},{3},{5,6,7}} => {{1},{2,4},{3},{5,6,7}} => 1
{{1},{2,4},{3},{5,6},{7}} => {{1},{2,4},{3},{5,6},{7}} => 1
{{1,7},{2,4},{3},{5},{6}} => {{1,3,7},{2,4},{5},{6}} => 4
{{1},{2,4,7},{3},{5},{6}} => {{1},{2,4,7},{3},{5},{6}} => 1
{{1},{2,4},{3,7},{5},{6}} => {{1},{2,4},{3,7},{5},{6}} => 1
{{1},{2,4},{3},{5,7},{6}} => {{1},{2,4},{3},{5,7},{6}} => 1
{{1},{2,4},{3},{5},{6,7}} => {{1},{2,4},{3},{5},{6,7}} => 1
{{1},{2,4},{3},{5},{6},{7}} => {{1},{2,4},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3,4}} => {{1,2,5,6,7},{3,4}} => 4
{{1,5,6},{2,7},{3,4}} => {{1,5,6},{2,7},{3,4}} => 4
{{1,5,6},{2},{3,4,7}} => {{1,2,6},{3,4,7},{5}} => 5
{{1,5,6},{2},{3,4},{7}} => {{1,2,5,6},{3,4},{7}} => 4
{{1,5,7},{2,6},{3,4}} => {{1,5,7},{2,6},{3,4}} => 4
{{1,5},{2,6,7},{3,4}} => {{1,5},{2,6,7},{3,4}} => 4
{{1,5},{2,6},{3,4,7}} => {{1,5},{2,6},{3,4,7}} => 5
{{1,5},{2,6},{3,4},{7}} => {{1,5},{2,6},{3,4},{7}} => 4
{{1,5,7},{2},{3,4,6}} => {{1,2,7},{3,4,6},{5}} => 5
{{1,5},{2,7},{3,4,6}} => {{1,5},{2,7},{3,4,6}} => 5
{{1,5},{2},{3,4,6,7}} => {{1,2,5},{3,4,6,7}} => 5
{{1,5},{2},{3,4,6},{7}} => {{1,2,5},{3,4,6},{7}} => 5
{{1,5,7},{2},{3,4},{6}} => {{1,2,5,7},{3,4},{6}} => 4
{{1,5},{2,7},{3,4},{6}} => {{1,5},{2,7},{3,4},{6}} => 4
{{1,5},{2},{3,4,7},{6}} => {{1,2,5},{3,4,7},{6}} => 5
{{1,5},{2},{3,4},{6,7}} => {{1,2,5},{3,4},{6,7}} => 4
{{1,5},{2},{3,4},{6},{7}} => {{1,2,5},{3,4},{6},{7}} => 4
{{1,6,7},{2,5},{3,4}} => {{1,6,7},{2,5},{3,4}} => 4
{{1,6},{2,5,7},{3,4}} => {{1,6},{2,5,7},{3,4}} => 4
{{1,6},{2,5},{3,4,7}} => {{1,6},{2,5},{3,4,7}} => 5
{{1,6},{2,5},{3,4},{7}} => {{1,6},{2,5},{3,4},{7}} => 4
{{1,7},{2,5,6},{3,4}} => {{1,7},{2,5,6},{3,4}} => 4
{{1},{2,5,6,7},{3,4}} => {{1},{2,5,6,7},{3,4}} => 1
{{1},{2,5,6},{3,4,7}} => {{1},{2,5,6},{3,4,7}} => 1
{{1},{2,5,6},{3,4},{7}} => {{1},{2,5,6},{3,4},{7}} => 1
{{1,7},{2,5},{3,4,6}} => {{1,7},{2,5},{3,4,6}} => 5
{{1},{2,5,7},{3,4,6}} => {{1},{2,5,7},{3,4,6}} => 1
{{1},{2,5},{3,4,6,7}} => {{1},{2,5},{3,4,6,7}} => 1
{{1},{2,5},{3,4,6},{7}} => {{1},{2,5},{3,4,6},{7}} => 1
{{1,7},{2,5},{3,4},{6}} => {{1,7},{2,5},{3,4},{6}} => 4
{{1},{2,5,7},{3,4},{6}} => {{1},{2,5,7},{3,4},{6}} => 1
{{1},{2,5},{3,4,7},{6}} => {{1},{2,5},{3,4,7},{6}} => 1
{{1},{2,5},{3,4},{6,7}} => {{1},{2,5},{3,4},{6,7}} => 1
{{1},{2,5},{3,4},{6},{7}} => {{1},{2,5},{3,4},{6},{7}} => 1
{{1,6,7},{2},{3,4,5}} => {{1,2,6,7},{3,4,5}} => 5
{{1,6},{2,7},{3,4,5}} => {{1,6},{2,7},{3,4,5}} => 5
{{1,6},{2},{3,4,5,7}} => {{1,2,6},{3,4,5,7}} => 6
{{1,6},{2},{3,4,5},{7}} => {{1,2,6},{3,4,5},{7}} => 5
{{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => 5
{{1},{2,6,7},{3,4,5}} => {{1},{2,6,7},{3,4,5}} => 1
{{1},{2,6},{3,4,5,7}} => {{1},{2,6},{3,4,5,7}} => 1
{{1},{2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5},{7}} => 1
{{1,7},{2},{3,4,5,6}} => {{1,2,7},{3,4,5,6}} => 6
{{1},{2,7},{3,4,5,6}} => {{1},{2,7},{3,4,5,6}} => 1
{{1},{2},{3,4,5,6,7}} => {{1},{2},{3,4,5,6,7}} => 1
{{1},{2},{3,4,5,6},{7}} => {{1},{2},{3,4,5,6},{7}} => 1
{{1,7},{2},{3,4,5},{6}} => {{1,2,7},{3,4,5},{6}} => 5
{{1},{2,7},{3,4,5},{6}} => {{1},{2,7},{3,4,5},{6}} => 1
{{1},{2},{3,4,5,7},{6}} => {{1},{2},{3,4,5,7},{6}} => 1
{{1},{2},{3,4,5},{6,7}} => {{1},{2},{3,4,5},{6,7}} => 1
{{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => 1
{{1,6,7},{2},{3,4},{5}} => {{1,2,6,7},{3,4},{5}} => 4
{{1,6},{2,7},{3,4},{5}} => {{1,6},{2,7},{3,4},{5}} => 4
{{1,6},{2},{3,4,7},{5}} => {{1,2,5,6},{3,4,7}} => 6
{{1,6},{2},{3,4},{5,7}} => {{1,2,6},{3,4},{5,7}} => 4
{{1,6},{2},{3,4},{5},{7}} => {{1,2,6},{3,4},{5},{7}} => 4
{{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3,4},{5}} => 4
{{1},{2,6,7},{3,4},{5}} => {{1},{2,6,7},{3,4},{5}} => 1
{{1},{2,6},{3,4,7},{5}} => {{1},{2,6},{3,4,7},{5}} => 1
{{1},{2,6},{3,4},{5,7}} => {{1},{2,6},{3,4},{5,7}} => 1
{{1},{2,6},{3,4},{5},{7}} => {{1},{2,6},{3,4},{5},{7}} => 1
{{1,7},{2},{3,4,6},{5}} => {{1,2,5,7},{3,4,6}} => 6
{{1},{2,7},{3,4,6},{5}} => {{1},{2,7},{3,4,6},{5}} => 1
{{1},{2},{3,4,6,7},{5}} => {{1},{2},{3,4,6,7},{5}} => 1
{{1},{2},{3,4,6},{5,7}} => {{1},{2},{3,4,6},{5,7}} => 1
{{1},{2},{3,4,6},{5},{7}} => {{1},{2},{3,4,6},{5},{7}} => 1
{{1,7},{2},{3,4},{5,6}} => {{1,2,7},{3,4},{5,6}} => 4
{{1},{2,7},{3,4},{5,6}} => {{1},{2,7},{3,4},{5,6}} => 1
{{1},{2},{3,4,7},{5,6}} => {{1},{2},{3,4,7},{5,6}} => 1
{{1},{2},{3,4},{5,6,7}} => {{1},{2},{3,4},{5,6,7}} => 1
{{1},{2},{3,4},{5,6},{7}} => {{1},{2},{3,4},{5,6},{7}} => 1
{{1,7},{2},{3,4},{5},{6}} => {{1,2,7},{3,4},{5},{6}} => 4
{{1},{2,7},{3,4},{5},{6}} => {{1},{2,7},{3,4},{5},{6}} => 1
{{1},{2},{3,4,7},{5},{6}} => {{1},{2},{3,4,7},{5},{6}} => 1
{{1},{2},{3,4},{5,7},{6}} => {{1},{2},{3,4},{5,7},{6}} => 1
{{1},{2},{3,4},{5},{6,7}} => {{1},{2},{3,4},{5},{6,7}} => 1
{{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3},{4}} => {{1,2,3,4,6,7},{5}} => 5
{{1,5,6},{2,7},{3},{4}} => {{1,3,4,6},{2,7},{5}} => 5
{{1,5,6},{2},{3,7},{4}} => {{1,2,4,6},{3,7},{5}} => 5
{{1,5,6},{2},{3},{4,7}} => {{1,2,3,6},{4,7},{5}} => 5
{{1,5,6},{2},{3},{4},{7}} => {{1,2,3,4,6},{5},{7}} => 5
{{1,5,7},{2,6},{3},{4}} => {{1,3,4,7},{2,6},{5}} => 5
{{1,5},{2,6,7},{3},{4}} => {{1,3,4,5},{2,6,7}} => 5
{{1,5},{2,6},{3,7},{4}} => {{1,4,5},{2,6},{3,7}} => 5
{{1,5},{2,6},{3},{4,7}} => {{1,3,5},{2,6},{4,7}} => 5
{{1,5},{2,6},{3},{4},{7}} => {{1,3,4,5},{2,6},{7}} => 5
{{1,5,7},{2},{3,6},{4}} => {{1,2,4,7},{3,6},{5}} => 5
{{1,5},{2,7},{3,6},{4}} => {{1,4,5},{2,7},{3,6}} => 5
{{1,5},{2},{3,6,7},{4}} => {{1,2,4,5},{3,6,7}} => 5
{{1,5},{2},{3,6},{4,7}} => {{1,2,5},{3,6},{4,7}} => 5
{{1,5},{2},{3,6},{4},{7}} => {{1,2,4,5},{3,6},{7}} => 5
{{1,5,7},{2},{3},{4,6}} => {{1,2,3,7},{4,6},{5}} => 5
{{1,5},{2,7},{3},{4,6}} => {{1,3,5},{2,7},{4,6}} => 5
{{1,5},{2},{3,7},{4,6}} => {{1,2,5},{3,7},{4,6}} => 5
{{1,5},{2},{3},{4,6,7}} => {{1,2,3,5},{4,6,7}} => 5
{{1,5},{2},{3},{4,6},{7}} => {{1,2,3,5},{4,6},{7}} => 5
{{1,5,7},{2},{3},{4},{6}} => {{1,2,3,4,7},{5},{6}} => 5
{{1,5},{2,7},{3},{4},{6}} => {{1,3,4,5},{2,7},{6}} => 5
{{1,5},{2},{3,7},{4},{6}} => {{1,2,4,5},{3,7},{6}} => 5
{{1,5},{2},{3},{4,7},{6}} => {{1,2,3,5},{4,7},{6}} => 5
{{1,5},{2},{3},{4},{6,7}} => {{1,2,3,4,5},{6,7}} => 5
{{1,5},{2},{3},{4},{6},{7}} => {{1,2,3,4,5},{6},{7}} => 5
{{1,6,7},{2,5},{3},{4}} => {{1,3,4,6,7},{2,5}} => 5
{{1,6},{2,5,7},{3},{4}} => {{1,3,4,6},{2,5,7}} => 6
{{1,6},{2,5},{3,7},{4}} => {{1,4,6},{2,5},{3,7}} => 5
{{1,6},{2,5},{3},{4,7}} => {{1,3,6},{2,5},{4,7}} => 5
{{1,6},{2,5},{3},{4},{7}} => {{1,3,4,6},{2,5},{7}} => 5
{{1,7},{2,5,6},{3},{4}} => {{1,3,4,7},{2,5,6}} => 6
{{1},{2,5,6,7},{3},{4}} => {{1},{2,5,6,7},{3},{4}} => 1
{{1},{2,5,6},{3,7},{4}} => {{1},{2,5,6},{3,7},{4}} => 1
{{1},{2,5,6},{3},{4,7}} => {{1},{2,5,6},{3},{4,7}} => 1
{{1},{2,5,6},{3},{4},{7}} => {{1},{2,5,6},{3},{4},{7}} => 1
{{1,7},{2,5},{3,6},{4}} => {{1,4,7},{2,5},{3,6}} => 5
{{1},{2,5,7},{3,6},{4}} => {{1},{2,5,7},{3,6},{4}} => 1
{{1},{2,5},{3,6,7},{4}} => {{1},{2,5},{3,6,7},{4}} => 1
{{1},{2,5},{3,6},{4,7}} => {{1},{2,5},{3,6},{4,7}} => 1
{{1},{2,5},{3,6},{4},{7}} => {{1},{2,5},{3,6},{4},{7}} => 1
{{1,7},{2,5},{3},{4,6}} => {{1,3,7},{2,5},{4,6}} => 5
{{1},{2,5,7},{3},{4,6}} => {{1},{2,5,7},{3},{4,6}} => 1
{{1},{2,5},{3,7},{4,6}} => {{1},{2,5},{3,7},{4,6}} => 1
{{1},{2,5},{3},{4,6,7}} => {{1},{2,5},{3},{4,6,7}} => 1
{{1},{2,5},{3},{4,6},{7}} => {{1},{2,5},{3},{4,6},{7}} => 1
{{1,7},{2,5},{3},{4},{6}} => {{1,3,4,7},{2,5},{6}} => 5
{{1},{2,5,7},{3},{4},{6}} => {{1},{2,5,7},{3},{4},{6}} => 1
{{1},{2,5},{3,7},{4},{6}} => {{1},{2,5},{3,7},{4},{6}} => 1
{{1},{2,5},{3},{4,7},{6}} => {{1},{2,5},{3},{4,7},{6}} => 1
{{1},{2,5},{3},{4},{6,7}} => {{1},{2,5},{3},{4},{6,7}} => 1
{{1},{2,5},{3},{4},{6},{7}} => {{1},{2,5},{3},{4},{6},{7}} => 1
{{1,6,7},{2},{3,5},{4}} => {{1,2,4,6,7},{3,5}} => 5
{{1,6},{2,7},{3,5},{4}} => {{1,4,6},{2,7},{3,5}} => 5
{{1,6},{2},{3,5,7},{4}} => {{1,2,4,6},{3,5,7}} => 6
{{1,6},{2},{3,5},{4,7}} => {{1,2,6},{3,5},{4,7}} => 5
{{1,6},{2},{3,5},{4},{7}} => {{1,2,4,6},{3,5},{7}} => 5
{{1,7},{2,6},{3,5},{4}} => {{1,4,7},{2,6},{3,5}} => 5
{{1},{2,6,7},{3,5},{4}} => {{1},{2,6,7},{3,5},{4}} => 1
{{1},{2,6},{3,5,7},{4}} => {{1},{2,6},{3,5,7},{4}} => 1
{{1},{2,6},{3,5},{4,7}} => {{1},{2,6},{3,5},{4,7}} => 1
{{1},{2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4},{7}} => 1
{{1,7},{2},{3,5,6},{4}} => {{1,2,4,7},{3,5,6}} => 6
{{1},{2,7},{3,5,6},{4}} => {{1},{2,7},{3,5,6},{4}} => 1
{{1},{2},{3,5,6,7},{4}} => {{1},{2},{3,5,6,7},{4}} => 1
{{1},{2},{3,5,6},{4,7}} => {{1},{2},{3,5,6},{4,7}} => 1
{{1},{2},{3,5,6},{4},{7}} => {{1},{2},{3,5,6},{4},{7}} => 1
{{1,7},{2},{3,5},{4,6}} => {{1,2,7},{3,5},{4,6}} => 5
{{1},{2,7},{3,5},{4,6}} => {{1},{2,7},{3,5},{4,6}} => 1
{{1},{2},{3,5,7},{4,6}} => {{1},{2},{3,5,7},{4,6}} => 1
{{1},{2},{3,5},{4,6,7}} => {{1},{2},{3,5},{4,6,7}} => 1
{{1},{2},{3,5},{4,6},{7}} => {{1},{2},{3,5},{4,6},{7}} => 1
{{1,7},{2},{3,5},{4},{6}} => {{1,2,4,7},{3,5},{6}} => 5
{{1},{2,7},{3,5},{4},{6}} => {{1},{2,7},{3,5},{4},{6}} => 1
{{1},{2},{3,5,7},{4},{6}} => {{1},{2},{3,5,7},{4},{6}} => 1
{{1},{2},{3,5},{4,7},{6}} => {{1},{2},{3,5},{4,7},{6}} => 1
{{1},{2},{3,5},{4},{6,7}} => {{1},{2},{3,5},{4},{6,7}} => 1
{{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => 1
{{1,6,7},{2},{3},{4,5}} => {{1,2,3,6,7},{4,5}} => 5
{{1,6},{2,7},{3},{4,5}} => {{1,3,6},{2,7},{4,5}} => 5
{{1,6},{2},{3,7},{4,5}} => {{1,2,6},{3,7},{4,5}} => 5
{{1,6},{2},{3},{4,5,7}} => {{1,2,3,6},{4,5,7}} => 6
{{1,6},{2},{3},{4,5},{7}} => {{1,2,3,6},{4,5},{7}} => 5
{{1,7},{2,6},{3},{4,5}} => {{1,3,7},{2,6},{4,5}} => 5
{{1},{2,6,7},{3},{4,5}} => {{1},{2,6,7},{3},{4,5}} => 1
{{1},{2,6},{3,7},{4,5}} => {{1},{2,6},{3,7},{4,5}} => 1
{{1},{2,6},{3},{4,5,7}} => {{1},{2,6},{3},{4,5,7}} => 1
{{1},{2,6},{3},{4,5},{7}} => {{1},{2,6},{3},{4,5},{7}} => 1
{{1,7},{2},{3,6},{4,5}} => {{1,2,7},{3,6},{4,5}} => 5
{{1},{2,7},{3,6},{4,5}} => {{1},{2,7},{3,6},{4,5}} => 1
{{1},{2},{3,6,7},{4,5}} => {{1},{2},{3,6,7},{4,5}} => 1
{{1},{2},{3,6},{4,5,7}} => {{1},{2},{3,6},{4,5,7}} => 1
{{1},{2},{3,6},{4,5},{7}} => {{1},{2},{3,6},{4,5},{7}} => 1
{{1,7},{2},{3},{4,5,6}} => {{1,2,3,7},{4,5,6}} => 6
{{1},{2,7},{3},{4,5,6}} => {{1},{2,7},{3},{4,5,6}} => 1
{{1},{2},{3,7},{4,5,6}} => {{1},{2},{3,7},{4,5,6}} => 1
{{1},{2},{3},{4,5,6,7}} => {{1},{2},{3},{4,5,6,7}} => 1
{{1},{2},{3},{4,5,6},{7}} => {{1},{2},{3},{4,5,6},{7}} => 1
{{1,7},{2},{3},{4,5},{6}} => {{1,2,3,7},{4,5},{6}} => 5
{{1},{2,7},{3},{4,5},{6}} => {{1},{2,7},{3},{4,5},{6}} => 1
{{1},{2},{3,7},{4,5},{6}} => {{1},{2},{3,7},{4,5},{6}} => 1
{{1},{2},{3},{4,5,7},{6}} => {{1},{2},{3},{4,5,7},{6}} => 1
{{1},{2},{3},{4,5},{6,7}} => {{1},{2},{3},{4,5},{6,7}} => 1
{{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => 1
{{1,6,7},{2},{3},{4},{5}} => {{1,2,3,4,5,7},{6}} => 6
{{1,6},{2,7},{3},{4},{5}} => {{1,3,4,5,6},{2,7}} => 6
{{1,6},{2},{3,7},{4},{5}} => {{1,2,4,5,6},{3,7}} => 6
{{1,6},{2},{3},{4,7},{5}} => {{1,2,3,5,6},{4,7}} => 6
{{1,6},{2},{3},{4},{5,7}} => {{1,2,3,4,6},{5,7}} => 6
{{1,6},{2},{3},{4},{5},{7}} => {{1,2,3,4,5,6},{7}} => 6
{{1,7},{2,6},{3},{4},{5}} => {{1,3,4,5,7},{2,6}} => 6
{{1},{2,6,7},{3},{4},{5}} => {{1},{2,6,7},{3},{4},{5}} => 1
{{1},{2,6},{3,7},{4},{5}} => {{1},{2,6},{3,7},{4},{5}} => 1
{{1},{2,6},{3},{4,7},{5}} => {{1},{2,6},{3},{4,7},{5}} => 1
{{1},{2,6},{3},{4},{5,7}} => {{1},{2,6},{3},{4},{5,7}} => 1
{{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => 1
{{1,7},{2},{3,6},{4},{5}} => {{1,2,4,5,7},{3,6}} => 6
{{1},{2,7},{3,6},{4},{5}} => {{1},{2,7},{3,6},{4},{5}} => 1
{{1},{2},{3,6,7},{4},{5}} => {{1},{2},{3,6,7},{4},{5}} => 1
{{1},{2},{3,6},{4,7},{5}} => {{1},{2},{3,6},{4,7},{5}} => 1
{{1},{2},{3,6},{4},{5,7}} => {{1},{2},{3,6},{4},{5,7}} => 1
{{1},{2},{3,6},{4},{5},{7}} => {{1},{2},{3,6},{4},{5},{7}} => 1
{{1,7},{2},{3},{4,6},{5}} => {{1,2,3,5,7},{4,6}} => 6
{{1},{2,7},{3},{4,6},{5}} => {{1},{2,7},{3},{4,6},{5}} => 1
{{1},{2},{3,7},{4,6},{5}} => {{1},{2},{3,7},{4,6},{5}} => 1
{{1},{2},{3},{4,6,7},{5}} => {{1},{2},{3},{4,6,7},{5}} => 1
{{1},{2},{3},{4,6},{5,7}} => {{1},{2},{3},{4,6},{5,7}} => 1
{{1},{2},{3},{4,6},{5},{7}} => {{1},{2},{3},{4,6},{5},{7}} => 1
{{1,7},{2},{3},{4},{5,6}} => {{1,2,3,4,7},{5,6}} => 6
{{1},{2,7},{3},{4},{5,6}} => {{1},{2,7},{3},{4},{5,6}} => 1
{{1},{2},{3,7},{4},{5,6}} => {{1},{2},{3,7},{4},{5,6}} => 1
{{1},{2},{3},{4,7},{5,6}} => {{1},{2},{3},{4,7},{5,6}} => 1
{{1},{2},{3},{4},{5,6,7}} => {{1},{2},{3},{4},{5,6,7}} => 1
{{1},{2},{3},{4},{5,6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => 1
{{1,7},{2},{3},{4},{5},{6}} => {{1,2,3,4,5,6,7}} => 7
{{1},{2,7},{3},{4},{5},{6}} => {{1},{2,7},{3},{4},{5},{6}} => 1
{{1},{2},{3,7},{4},{5},{6}} => {{1},{2},{3,7},{4},{5},{6}} => 1
{{1},{2},{3},{4,7},{5},{6}} => {{1},{2},{3},{4,7},{5},{6}} => 1
{{1},{2},{3},{4},{5,7},{6}} => {{1},{2},{3},{4},{5,7},{6}} => 1
{{1},{2},{3},{4},{5},{6,7}} => {{1},{2},{3},{4},{5},{6,7}} => 1
{{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => 1
{{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => 2
{{1,3},{2,4},{5,6},{7,8}} => {{1,3},{2,4},{5,6},{7,8}} => 3
{{1,4},{2,3},{5,6},{7,8}} => {{1,4},{2,3},{5,6},{7,8}} => 3
{{1,5},{2,3},{4,6},{7,8}} => {{1,5},{2,3},{4,6},{7,8}} => 3
{{1,6},{2,3},{4,5},{7,8}} => {{1,6},{2,3},{4,5},{7,8}} => 3
{{1,7},{2,3},{4,5},{6,8}} => {{1,7},{2,3},{4,5},{6,8}} => 3
{{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => 3
{{1,8},{2,4},{3,5},{6,7}} => {{1,8},{2,4},{3,5},{6,7}} => 4
{{1,7},{2,4},{3,5},{6,8}} => {{1,7},{2,4},{3,5},{6,8}} => 4
{{1,6},{2,4},{3,5},{7,8}} => {{1,6},{2,4},{3,5},{7,8}} => 4
{{1,5},{2,4},{3,6},{7,8}} => {{1,5},{2,4},{3,6},{7,8}} => 4
{{1,4},{2,5},{3,6},{7,8}} => {{1,4},{2,5},{3,6},{7,8}} => 4
{{1,3},{2,5},{4,6},{7,8}} => {{1,3},{2,5},{4,6},{7,8}} => 3
{{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => 2
{{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => 2
{{1,3},{2,6},{4,5},{7,8}} => {{1,3},{2,6},{4,5},{7,8}} => 3
{{1,4},{2,6},{3,5},{7,8}} => {{1,4},{2,6},{3,5},{7,8}} => 4
{{1,5},{2,6},{3,4},{7,8}} => {{1,5},{2,6},{3,4},{7,8}} => 4
{{1,6},{2,5},{3,4},{7,8}} => {{1,6},{2,5},{3,4},{7,8}} => 4
{{1,7},{2,5},{3,4},{6,8}} => {{1,7},{2,5},{3,4},{6,8}} => 4
{{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,5},{3,4},{6,7}} => 4
{{1,8},{2,6},{3,4},{5,7}} => {{1,8},{2,6},{3,4},{5,7}} => 4
{{1,7},{2,6},{3,4},{5,8}} => {{1,7},{2,6},{3,4},{5,8}} => 4
{{1,6},{2,7},{3,4},{5,8}} => {{1,6},{2,7},{3,4},{5,8}} => 4
{{1,5},{2,7},{3,4},{6,8}} => {{1,5},{2,7},{3,4},{6,8}} => 4
{{1,4},{2,7},{3,5},{6,8}} => {{1,4},{2,7},{3,5},{6,8}} => 4
{{1,3},{2,7},{4,5},{6,8}} => {{1,3},{2,7},{4,5},{6,8}} => 3
{{1,2},{3,7},{4,5},{6,8}} => {{1,2},{3,7},{4,5},{6,8}} => 2
{{1,2},{3,8},{4,5},{6,7}} => {{1,2},{3,8},{4,5},{6,7}} => 2
{{1,3},{2,8},{4,5},{6,7}} => {{1,3},{2,8},{4,5},{6,7}} => 3
{{1,4},{2,8},{3,5},{6,7}} => {{1,4},{2,8},{3,5},{6,7}} => 4
{{1,5},{2,8},{3,4},{6,7}} => {{1,5},{2,8},{3,4},{6,7}} => 4
{{1,6},{2,8},{3,4},{5,7}} => {{1,6},{2,8},{3,4},{5,7}} => 4
{{1,7},{2,8},{3,4},{5,6}} => {{1,7},{2,8},{3,4},{5,6}} => 4
{{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => 4
{{1,8},{2,7},{3,5},{4,6}} => {{1,8},{2,7},{3,5},{4,6}} => 5
{{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}} => 5
{{1,6},{2,8},{3,5},{4,7}} => {{1,6},{2,8},{3,5},{4,7}} => 5
{{1,5},{2,8},{3,6},{4,7}} => {{1,5},{2,8},{3,6},{4,7}} => 5
{{1,4},{2,8},{3,6},{5,7}} => {{1,4},{2,8},{3,6},{5,7}} => 4
{{1,3},{2,8},{4,6},{5,7}} => {{1,3},{2,8},{4,6},{5,7}} => 3
{{1,2},{3,8},{4,6},{5,7}} => {{1,2},{3,8},{4,6},{5,7}} => 2
{{1,2},{3,7},{4,6},{5,8}} => {{1,2},{3,7},{4,6},{5,8}} => 2
{{1,3},{2,7},{4,6},{5,8}} => {{1,3},{2,7},{4,6},{5,8}} => 3
{{1,4},{2,7},{3,6},{5,8}} => {{1,4},{2,7},{3,6},{5,8}} => 4
{{1,5},{2,7},{3,6},{4,8}} => {{1,5},{2,7},{3,6},{4,8}} => 5
{{1,6},{2,7},{3,5},{4,8}} => {{1,6},{2,7},{3,5},{4,8}} => 5
{{1,7},{2,6},{3,5},{4,8}} => {{1,7},{2,6},{3,5},{4,8}} => 5
{{1,8},{2,6},{3,5},{4,7}} => {{1,8},{2,6},{3,5},{4,7}} => 5
{{1,8},{2,5},{3,6},{4,7}} => {{1,8},{2,5},{3,6},{4,7}} => 5
{{1,7},{2,5},{3,6},{4,8}} => {{1,7},{2,5},{3,6},{4,8}} => 5
{{1,6},{2,5},{3,7},{4,8}} => {{1,6},{2,5},{3,7},{4,8}} => 5
{{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}} => 5
{{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}} => 4
{{1,3},{2,6},{4,7},{5,8}} => {{1,3},{2,6},{4,7},{5,8}} => 3
{{1,2},{3,6},{4,7},{5,8}} => {{1,2},{3,6},{4,7},{5,8}} => 2
{{1,2},{3,5},{4,7},{6,8}} => {{1,2},{3,5},{4,7},{6,8}} => 2
{{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}} => 3
{{1,4},{2,5},{3,7},{6,8}} => {{1,4},{2,5},{3,7},{6,8}} => 4
{{1,5},{2,4},{3,7},{6,8}} => {{1,5},{2,4},{3,7},{6,8}} => 4
{{1,6},{2,4},{3,7},{5,8}} => {{1,6},{2,4},{3,7},{5,8}} => 4
{{1,7},{2,4},{3,6},{5,8}} => {{1,7},{2,4},{3,6},{5,8}} => 4
{{1,8},{2,4},{3,6},{5,7}} => {{1,8},{2,4},{3,6},{5,7}} => 4
{{1,8},{2,3},{4,6},{5,7}} => {{1,8},{2,3},{4,6},{5,7}} => 3
{{1,7},{2,3},{4,6},{5,8}} => {{1,7},{2,3},{4,6},{5,8}} => 3
{{1,6},{2,3},{4,7},{5,8}} => {{1,6},{2,3},{4,7},{5,8}} => 3
{{1,5},{2,3},{4,7},{6,8}} => {{1,5},{2,3},{4,7},{6,8}} => 3
{{1,4},{2,3},{5,7},{6,8}} => {{1,4},{2,3},{5,7},{6,8}} => 3
{{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}} => 3
{{1,2},{3,4},{5,7},{6,8}} => {{1,2},{3,4},{5,7},{6,8}} => 2
{{1,2},{3,4},{5,8},{6,7}} => {{1,2},{3,4},{5,8},{6,7}} => 2
{{1,3},{2,4},{5,8},{6,7}} => {{1,3},{2,4},{5,8},{6,7}} => 3
{{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => 3
{{1,5},{2,3},{4,8},{6,7}} => {{1,5},{2,3},{4,8},{6,7}} => 3
{{1,6},{2,3},{4,8},{5,7}} => {{1,6},{2,3},{4,8},{5,7}} => 3
{{1,7},{2,3},{4,8},{5,6}} => {{1,7},{2,3},{4,8},{5,6}} => 3
{{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,3},{4,7},{5,6}} => 3
{{1,8},{2,4},{3,7},{5,6}} => {{1,8},{2,4},{3,7},{5,6}} => 4
{{1,7},{2,4},{3,8},{5,6}} => {{1,7},{2,4},{3,8},{5,6}} => 4
{{1,6},{2,4},{3,8},{5,7}} => {{1,6},{2,4},{3,8},{5,7}} => 4
{{1,5},{2,4},{3,8},{6,7}} => {{1,5},{2,4},{3,8},{6,7}} => 4
{{1,4},{2,5},{3,8},{6,7}} => {{1,4},{2,5},{3,8},{6,7}} => 4
{{1,3},{2,5},{4,8},{6,7}} => {{1,3},{2,5},{4,8},{6,7}} => 3
{{1,2},{3,5},{4,8},{6,7}} => {{1,2},{3,5},{4,8},{6,7}} => 2
{{1,2},{3,6},{4,8},{5,7}} => {{1,2},{3,6},{4,8},{5,7}} => 2
{{1,3},{2,6},{4,8},{5,7}} => {{1,3},{2,6},{4,8},{5,7}} => 3
{{1,4},{2,6},{3,8},{5,7}} => {{1,4},{2,6},{3,8},{5,7}} => 4
{{1,5},{2,6},{3,8},{4,7}} => {{1,5},{2,6},{3,8},{4,7}} => 5
{{1,6},{2,5},{3,8},{4,7}} => {{1,6},{2,5},{3,8},{4,7}} => 5
{{1,7},{2,5},{3,8},{4,6}} => {{1,7},{2,5},{3,8},{4,6}} => 5
{{1,8},{2,5},{3,7},{4,6}} => {{1,8},{2,5},{3,7},{4,6}} => 5
{{1,8},{2,6},{3,7},{4,5}} => {{1,8},{2,6},{3,7},{4,5}} => 5
{{1,7},{2,6},{3,8},{4,5}} => {{1,7},{2,6},{3,8},{4,5}} => 5
{{1,6},{2,7},{3,8},{4,5}} => {{1,6},{2,7},{3,8},{4,5}} => 5
{{1,5},{2,7},{3,8},{4,6}} => {{1,5},{2,7},{3,8},{4,6}} => 5
{{1,4},{2,7},{3,8},{5,6}} => {{1,4},{2,7},{3,8},{5,6}} => 4
{{1,3},{2,7},{4,8},{5,6}} => {{1,3},{2,7},{4,8},{5,6}} => 3
{{1,2},{3,7},{4,8},{5,6}} => {{1,2},{3,7},{4,8},{5,6}} => 2
{{1,2},{3,8},{4,7},{5,6}} => {{1,2},{3,8},{4,7},{5,6}} => 2
{{1,3},{2,8},{4,7},{5,6}} => {{1,3},{2,8},{4,7},{5,6}} => 3
{{1,4},{2,8},{3,7},{5,6}} => {{1,4},{2,8},{3,7},{5,6}} => 4
{{1,5},{2,8},{3,7},{4,6}} => {{1,5},{2,8},{3,7},{4,6}} => 5
{{1,6},{2,8},{3,7},{4,5}} => {{1,6},{2,8},{3,7},{4,5}} => 5
{{1,7},{2,8},{3,6},{4,5}} => {{1,7},{2,8},{3,6},{4,5}} => 5
{{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}} => 5
{{1},{2,3,4,6,7,8},{5}} => {{1},{2,3,4,6,7,8},{5}} => 1
{{1},{2,3,4,5,8},{6},{7}} => {{1},{2,3,4,5,8},{6},{7}} => 1
{{1},{2,3,4,5,7,8},{6}} => {{1},{2,3,4,5,7,8},{6}} => 1
{{1},{2,3,4,8},{5,6,7}} => {{1},{2,3,4,8},{5,6,7}} => 1
{{1},{2,3,4,5,8},{6,7}} => {{1},{2,3,4,5,8},{6,7}} => 1
{{1},{2,3,4,5,6,8},{7}} => {{1},{2,3,4,5,6,8},{7}} => 1
{{1},{2,3,4,5,6,7,8}} => {{1},{2,3,4,5,6,7,8}} => 1
{{1,2},{3,4,5,6,7,8}} => {{1,2},{3,4,5,6,7,8}} => 2
{{1,8},{2},{3},{4},{5},{6},{7}} => {{1,2,3,4,5,6,7,8}} => 8
{{1,5,6,7,8},{2},{3},{4}} => {{1,2,3,4,6,7,8},{5}} => 5
{{1,6,7,8},{2},{3},{4,5}} => {{1,2,3,6,7,8},{4,5}} => 5
{{1,6,7,8},{2},{3,5},{4}} => {{1,2,4,6,7,8},{3,5}} => 5
{{1,6,7,8},{2,5},{3},{4}} => {{1,3,4,6,7,8},{2,5}} => 5
{{1},{2,3,4,5,6,7,8,9}} => {{1},{2,3,4,5,6,7,8,9}} => 1
{{1},{2,3,4,5,6,7,9},{8}} => {{1},{2,3,4,5,6,7,9},{8}} => 1
{{1},{2,3,4,5,6,7,8,9,10}} => {{1},{2,3,4,5,6,7,8,9,10}} => 1
{{1},{2,3,4,5,6,9},{7,8}} => {{1},{2,3,4,5,6,9},{7,8}} => 1
{{1},{2,3,4,5,6,8,9},{7}} => {{1},{2,3,4,5,6,8,9},{7}} => 1
{{1},{2,3,4,5,6,7,8,10},{9}} => {{1},{2,3,4,5,6,7,8,10},{9}} => 1
{{1},{2,3,4,5,6,7,8,9,10,11}} => {{1},{2,3,4,5,6,7,8,9,10,11}} => 1
{{1,3},{2,4,5,6,7,8}} => {{1,3},{2,4,5,6,7,8}} => 3
{{1,4},{2,3,5,6,7,8}} => {{1,4},{2,3,5,6,7,8}} => 4
{{1,5},{2,3,4,6,7,8}} => {{1,5},{2,3,4,6,7,8}} => 5
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,1 5,5,4,1 15,15,13,8,1 52,52,47,35,16,1 203,203,188,153,97,32,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 5\ q + 5\ q^{2} + 4\ q^{3} + q^{4}$
$F_{5} = 15\ q + 15\ q^{2} + 13\ q^{3} + 8\ q^{4} + q^{5}$
$F_{6} = 52\ q + 52\ q^{2} + 47\ q^{3} + 35\ q^{4} + 16\ q^{5} + q^{6}$
$F_{7} = 203\ q + 203\ q^{2} + 188\ q^{3} + 153\ q^{4} + 97\ q^{5} + 32\ q^{6} + q^{7}$
Description
The smallest closer of a set partition.
A closer (or right hand endpoint) of a set partition is a number that is maximal in its block. For this statistic, singletons are considered as closers.
In other words, this is the smallest among the maximal elements of the blocks.
A closer (or right hand endpoint) of a set partition is a number that is maximal in its block. For this statistic, singletons are considered as closers.
In other words, this is the smallest among the maximal elements of the blocks.
Map
Callan switch
Description
Switch the first closer and the minimum of the smallest closer and the second element of the block containing 1 in a set partition.
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..
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