Identifier
-
Mp00128:
Set partitions
—to composition⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000759: Integer partitions ⟶ ℤ
Values
{{1}} => [1] => [1,0] => [] => 1
{{1,2}} => [2] => [1,1,0,0] => [] => 1
{{1},{2}} => [1,1] => [1,0,1,0] => [1] => 2
{{1,2,3}} => [3] => [1,1,1,0,0,0] => [] => 1
{{1,2},{3}} => [2,1] => [1,1,0,0,1,0] => [2] => 1
{{1,3},{2}} => [2,1] => [1,1,0,0,1,0] => [2] => 1
{{1},{2,3}} => [1,2] => [1,0,1,1,0,0] => [1,1] => 2
{{1},{2},{3}} => [1,1,1] => [1,0,1,0,1,0] => [2,1] => 3
{{1,2,3,4}} => [4] => [1,1,1,1,0,0,0,0] => [] => 1
{{1,2,3},{4}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 1
{{1,2,4},{3}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 1
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 1
{{1,2},{3},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 1
{{1,3,4},{2}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 1
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 1
{{1,3},{2},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 1
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 1
{{1},{2,3,4}} => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 2
{{1},{2,3},{4}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
{{1,4},{2},{3}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 1
{{1},{2,4},{3}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,1] => 2
{{1},{2},{3,4}} => [1,1,2] => [1,0,1,0,1,1,0,0] => [2,2,1] => 3
{{1},{2},{3},{4}} => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [3,2,1] => 4
{{1,2,3,4,5}} => [5] => [1,1,1,1,1,0,0,0,0,0] => [] => 1
{{1,2,3,4},{5}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
{{1,2,3,5},{4}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
{{1,2,3},{4,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,2,4,5},{3}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
{{1,2,4},{3,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,2,5},{3,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,2},{3,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
{{1,3,4,5},{2}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 1
{{1,3,4},{2,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,3,5},{2,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,3},{2,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
{{1,4,5},{2,3}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 1
{{1,4},{2,3,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,5},{2,3,4}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 1
{{1},{2,3,4,5}} => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 2
{{1},{2,3,4},{5}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 2
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1},{2,3,5},{4}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 2
{{1},{2,3},{4,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 2
{{1},{2,3},{4},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 1
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
{{1},{2,4,5},{3}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 2
{{1},{2,4},{3,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 2
{{1},{2,4},{3},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 1
{{1},{2,5},{3,4}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 2
{{1},{2},{3,4,5}} => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 3
{{1},{2},{3,4},{5}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 3
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 1
{{1},{2,5},{3},{4}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 2
{{1},{2},{3,5},{4}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 3
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 4
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 5
{{1,2,3,4,5,6}} => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => 1
{{1,2,3,4,5},{6}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
{{1,2,3,4,6},{5}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
{{1,2,3,4},{5,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,3,5,6},{4}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
{{1,2,3,5},{4,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,3,6},{4,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,2,3},{4,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,2,3},{4,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,3},{4,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,3},{4},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,2,4,5,6},{3}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
{{1,2,4,5},{3,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,4,6},{3,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,2,4},{3,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,2,4},{3,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,4},{3,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,4},{3},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,2,5,6},{3,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
>>> Load all 1319 entries. <<<{{1,2,5},{3,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,2,5},{3,4},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,6},{3,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,2},{3,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
{{1,2},{3,4,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,2,6},{3,4},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2},{3,4,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,2},{3,4},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,2,5},{3,6},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2,5},{3},{4,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,2,6},{3,5},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,2},{3,5,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,2},{3,5},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,2,6},{3},{4,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,2},{3,6},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,2},{3},{4,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
{{1,2},{3},{4,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,2},{3,6},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,2},{3},{4,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,2},{3},{4},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
{{1,3,4,5,6},{2}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
{{1,3,4,5},{2,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,3,4,6},{2,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,3,4},{2,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,3,4},{2,5},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,3,4},{2,6},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3,4},{2},{5,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,3,5,6},{2,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,3,5},{2,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,3,5},{2,4},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3,6},{2,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,3},{2,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
{{1,3},{2,4,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,3,6},{2,4},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3},{2,4,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,3},{2,4},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,3,5},{2,6},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3,5},{2},{4,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,3,6},{2,5},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,3},{2,5,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,3},{2,5},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,3,6},{2},{4,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,3},{2,6},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,3},{2},{4,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
{{1,3},{2},{4,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,3},{2,6},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,3},{2},{4,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,3},{2},{4},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
{{1,4,5,6},{2,3}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
{{1,4,5},{2,3,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,4,5},{2,3},{6}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,4,6},{2,3,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,4},{2,3,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
{{1,4},{2,3,5},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,4,6},{2,3},{5}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,4},{2,3,6},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,4},{2,3},{5,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,5,6},{2,3,4}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 1
{{1,5},{2,3,4,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
{{1,5},{2,3,4},{6}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,6},{2,3,4,5}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
{{1},{2,3,4,5,6}} => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 2
{{1},{2,3,4,5},{6}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 2
{{1,6},{2,3,4},{5}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1},{2,3,4,6},{5}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 2
{{1},{2,3,4},{5,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,3,4},{5},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1,5,6},{2,3},{4}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,5},{2,3,6},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,5},{2,3},{4,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,6},{2,3,5},{4}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1},{2,3,5,6},{4}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 2
{{1},{2,3,5},{4,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,3,5},{4},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1,6},{2,3},{4,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1},{2,3,6},{4,5}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,3},{4,5,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
{{1},{2,3},{4,5},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1},{2,3,6},{4},{5}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1},{2,3},{4,6},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 2
{{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 2
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 1
{{1,4,5},{2,6},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,4,5},{2},{3,6}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,4,6},{2,5},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,4},{2,5,6},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,4},{2,5},{3,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,4,6},{2},{3,5}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,4},{2,6},{3,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,4},{2},{3,5,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
{{1,4},{2},{3,5},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,4},{2,6},{3},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,4},{2},{3,6},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,4},{2},{3},{5,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
{{1,5,6},{2,4},{3}} => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 1
{{1,5},{2,4,6},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1,5},{2,4},{3,6}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,6},{2,4,5},{3}} => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 1
{{1},{2,4,5,6},{3}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 2
{{1},{2,4,5},{3,6}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,4,5},{3},{6}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1,6},{2,4},{3,5}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1},{2,4,6},{3,5}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,4},{3,5,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
{{1},{2,4},{3,5},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1},{2,4,6},{3},{5}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1},{2,4},{3,6},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 2
{{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 2
{{1,5,6},{2},{3,4}} => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 1
{{1,5},{2,6},{3,4}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1,5},{2},{3,4,6}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
{{1,5},{2},{3,4},{6}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,6},{2,5},{3,4}} => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 1
{{1},{2,5,6},{3,4}} => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 2
{{1},{2,5},{3,4,6}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
{{1},{2,5},{3,4},{6}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1,6},{2},{3,4,5}} => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 1
{{1},{2,6},{3,4,5}} => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 2
{{1},{2},{3,4,5,6}} => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 3
{{1},{2},{3,4,5},{6}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 3
{{1,6},{2},{3,4},{5}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1},{2,6},{3,4},{5}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1},{2},{3,4,6},{5}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 3
{{1},{2},{3,4},{5,6}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 3
{{1},{2},{3,4},{5},{6}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 1
{{1,5},{2,6},{3},{4}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1,5},{2},{3,6},{4}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1,5},{2},{3},{4,6}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
{{1,6},{2,5},{3},{4}} => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 1
{{1},{2,5,6},{3},{4}} => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 2
{{1},{2,5},{3,6},{4}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 2
{{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 2
{{1,6},{2},{3,5},{4}} => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 1
{{1},{2,6},{3,5},{4}} => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 2
{{1},{2},{3,5,6},{4}} => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 3
{{1},{2},{3,5},{4,6}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 3
{{1},{2},{3,5},{4},{6}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3
{{1,6},{2},{3},{4,5}} => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 1
{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 2
{{1},{2},{3,6},{4,5}} => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 3
{{1},{2},{3},{4,5,6}} => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 4
{{1},{2},{3},{4,5},{6}} => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 4
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 1
{{1},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 2
{{1},{2},{3,6},{4},{5}} => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 3
{{1},{2},{3},{4,6},{5}} => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 4
{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 5
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 6
{{1,2,3,4,5,6,7}} => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 1
{{1,2,3,4,5,6},{7}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,2,3,4,5,7},{6}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,2,3,4,5},{6,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,4,6,7},{5}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,2,3,4,6},{5,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,4,7},{5,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,4},{5,6,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,3,4},{5,6},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,4},{5,7},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,4},{5},{6,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,3,5,6,7},{4}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,2,3,5,6},{4,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,5,7},{4,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,5},{4,6,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,3,5},{4,6},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,5},{4,7},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,5},{4},{6,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,3,6,7},{4,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,3,6},{4,5,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,3,6},{4,5},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,7},{4,5,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,3},{4,5,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,3,7},{4,5},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,3},{4,5},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,3,6},{4,7},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3,6},{4},{5,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,3,7},{4,6},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,3},{4,6},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,3,7},{4},{5,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,3},{4,7},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,3},{4},{5,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,2,3},{4},{5,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,3},{4,7},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,3},{4},{5,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,2,4,5,6,7},{3}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,2,4,5,6},{3,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,4,5,7},{3,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,4,5},{3,6,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,4,5},{3,6},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,4,5},{3,7},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4,5},{3},{6,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,4,6,7},{3,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,4,6},{3,5,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,4,6},{3,5},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4,7},{3,5,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,4},{3,5,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,4,7},{3,5},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,4},{3,5},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,4,6},{3,7},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4,6},{3},{5,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,4,7},{3,6},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,4},{3,6},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,4,7},{3},{5,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,4},{3,7},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,4},{3},{5,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,2,4},{3},{5,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,4},{3,7},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,4},{3},{5,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,2,5,6,7},{3,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,2,5,6},{3,4,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,5,6},{3,4},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,5,7},{3,4,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,5},{3,4,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,5,7},{3,4},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,5},{3,4},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,6,7},{3,4,5}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,2,6},{3,4,5,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,7},{3,4,5,6}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,2},{3,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1,2},{3,4,5,6},{7}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2},{3,4,5,7},{6}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,2},{3,4,5},{6,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,4,5},{6},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2,6,7},{3,4},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,6},{3,4},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2},{3,4,6,7},{5}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,2},{3,4,6},{5,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,4,6},{5},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2,7},{3,4},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2},{3,4,7},{5,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,4},{5,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,2},{3,4},{5,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2},{3,4,7},{5},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2},{3,4},{5,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,2,5,6},{3,7},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,5,6},{3},{4,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,5,7},{3,6},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,5},{3,6},{4,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,5,7},{3},{4,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,5},{3,7},{4,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,5},{3},{4,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,2,5},{3},{4,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,5},{3,7},{4},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,5},{3},{4,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,2,6,7},{3,5},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2,6},{3,5},{4,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,2},{3,5,6,7},{4}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,2},{3,5,6},{4,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,5,6},{4},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2,7},{3,5},{4,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2},{3,5,7},{4,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,5},{4,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,2},{3,5},{4,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2},{3,5,7},{4},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2},{3,5},{4,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,2,6,7},{3},{4,5}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,2,6},{3,7},{4,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2,6},{3},{4,5,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,2,6},{3},{4,5},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,7},{3,6},{4,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,2},{3,6,7},{4,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,2},{3,6},{4,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,2},{3,6},{4,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2,7},{3},{4,5,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,2},{3,7},{4,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,2},{3},{4,5,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1,2},{3},{4,5,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,2,7},{3},{4,5},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2},{3,7},{4,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2},{3},{4,5,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,2},{3},{4,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,2},{3},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2,6},{3},{4,7},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,2,7},{3,6},{4},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,2},{3,6,7},{4},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,2},{3,6},{4,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,2,7},{3},{4,6},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,2},{3,7},{4,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,2},{3},{4,6,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,2},{3},{4,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,2},{3},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,2},{3},{4,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1,2},{3},{4},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,2},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,2},{3},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,2},{3},{4},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1,3,4,5,6,7},{2}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
{{1,3,4,5,6},{2,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,3,4,5,7},{2,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,3,4,5},{2,6,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,4,5},{2,6},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,3,4,5},{2,7},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4,5},{2},{6,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,4,6,7},{2,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,3,4,6},{2,5,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,4,6},{2,5},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4,7},{2,5,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,4},{2,5,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,4,7},{2,5},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,4},{2,5},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,3,4,6},{2,7},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4,6},{2},{5,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,4,7},{2,6},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,4},{2,6},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,4,7},{2},{5,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,4},{2,7},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,4},{2},{5,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,3,4},{2},{5,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,4},{2,7},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,4},{2},{5,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,3,5,6,7},{2,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,3,5,6},{2,4,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,5,6},{2,4},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,5,7},{2,4,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,5},{2,4,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,5,7},{2,4},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,5},{2,4},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,6,7},{2,4,5}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,3,6},{2,4,5,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,7},{2,4,5,6}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,3},{2,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1,3},{2,4,5,6},{7}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3},{2,4,5,7},{6}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,3},{2,4,5},{6,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,4,5},{6},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3,6,7},{2,4},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,6},{2,4},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3},{2,4,6,7},{5}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,3},{2,4,6},{5,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,4,6},{5},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3,7},{2,4},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3},{2,4,7},{5,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,4},{5,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,3},{2,4},{5,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3},{2,4,7},{5},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3},{2,4},{5,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,3,5,6},{2,7},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,5,6},{2},{4,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,5,7},{2,6},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,5},{2,6},{4,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,5,7},{2},{4,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,5},{2,7},{4,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,5},{2},{4,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,3,5},{2},{4,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,5},{2,7},{4},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,5},{2},{4,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,3,6,7},{2,5},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3,6},{2,5},{4,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,3},{2,5,6,7},{4}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,3},{2,5,6},{4,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,5,6},{4},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3,7},{2,5},{4,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3},{2,5,7},{4,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,5},{4,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,3},{2,5},{4,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3},{2,5,7},{4},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3},{2,5},{4,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,3,6,7},{2},{4,5}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,3,6},{2,7},{4,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3,6},{2},{4,5,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,3,6},{2},{4,5},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,7},{2,6},{4,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,3},{2,6,7},{4,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,3},{2,6},{4,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,3},{2,6},{4,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3,7},{2},{4,5,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,3},{2,7},{4,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,3},{2},{4,5,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1,3},{2},{4,5,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,3,7},{2},{4,5},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3},{2,7},{4,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3},{2},{4,5,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,3},{2},{4,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,3},{2},{4,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,3,6},{2,7},{4},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3,6},{2},{4,7},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,3,7},{2,6},{4},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,3},{2,6,7},{4},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,3},{2,6},{4,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,3,7},{2},{4,6},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,3},{2,7},{4,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,3},{2},{4,6,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,3},{2},{4,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,3},{2},{4,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,3},{2},{4,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1,3},{2},{4},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,3},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,3},{2},{4,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,3},{2},{4},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1,4,5,6,7},{2,3}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 1
{{1,4,5,6},{2,3,7}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,4,5,6},{2,3},{7}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,5,7},{2,3,6}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,4,5},{2,3,6,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,5,7},{2,3},{6}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,5},{2,3},{6,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,6,7},{2,3,5}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,4,6},{2,3,5,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,7},{2,3,5,6}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,4},{2,3,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1,4},{2,3,5,6},{7}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4},{2,3,5,7},{6}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,4},{2,3,5},{6,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,3,5},{6},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4,6,7},{2,3},{5}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,6},{2,3},{5,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4},{2,3,6,7},{5}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,4},{2,3,6},{5,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,3,6},{5},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4,7},{2,3},{5,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4},{2,3,7},{5,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,3},{5,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,4},{2,3},{5,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4},{2,3,7},{5},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4},{2,3},{5,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,5,6,7},{2,3,4}} => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 1
{{1,5,6},{2,3,4,7}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5,7},{2,3,4,6}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,5},{2,3,4,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1,5},{2,3,4,6},{7}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5},{2,3,4,7},{6}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,5},{2,3,4},{6,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,3,4},{6},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,6,7},{2,3,4,5}} => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
{{1,6},{2,3,4,5,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1,6},{2,3,4,5},{7}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,7},{2,3,4,5,6}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 1
{{1},{2,3,4,5,6,7}} => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 2
{{1},{2,3,4,5,6},{7}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
{{1,7},{2,3,4,5},{6}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1},{2,3,4,5,7},{6}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
{{1},{2,3,4,5},{6,7}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,4,5},{6},{7}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,6},{2,3,4,7},{5}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,6},{2,3,4},{5,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,3,4},{5},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,7},{2,3,4,6},{5}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1},{2,3,4,6,7},{5}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
{{1},{2,3,4,6},{5,7}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,4,6},{5},{7}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1,7},{2,3,4},{5,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,3,4,7},{5,6}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,4},{5,6,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,3,4},{5,6},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,3,4},{5},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,3,4,7},{5},{6}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,3,4},{5,7},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,3,4},{5},{6,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,3,4},{5},{6},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,5,6,7},{2,3},{4}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5,6},{2,3},{4,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5},{2,3,6,7},{4}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,5},{2,3,6},{4,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,3,6},{4},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,5,7},{2,3},{4,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5},{2,3,7},{4,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,3},{4,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,5},{2,3},{4,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5},{2,3,7},{4},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,5},{2,3},{4,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,6},{2,3,5,7},{4}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,6},{2,3,5},{4,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,3,5},{4},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,7},{2,3,5,6},{4}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1},{2,3,5,6,7},{4}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
{{1},{2,3,5,6},{4,7}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,5,6},{4},{7}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1,7},{2,3,5},{4,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,3,5,7},{4,6}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,5},{4,6,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,3,5},{4,6},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,3,5},{4},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,3,5,7},{4},{6}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,3,5},{4,7},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,3,5},{4},{6,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,3,5},{4},{6},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,6,7},{2,3},{4,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,6},{2,3,7},{4,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,3},{4,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,6},{2,3},{4,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,7},{2,3,6},{4,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,3,6,7},{4,5}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,3,6},{4,5,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,3,6},{4,5},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,3},{4,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1},{2,3,7},{4,5,6}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,3},{4,5,6,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 2
{{1},{2,3},{4,5,6},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,3,7},{4,5},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,3},{4,5,7},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,3},{4,5},{6,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,3},{4,5},{6},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,6},{2,3,7},{4},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,6},{2,3},{4,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,7},{2,3,6},{4},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,3,6,7},{4},{5}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,3,6},{4,7},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,3,6},{4},{5,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,3,6},{4},{5},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,3,7},{4,6},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,3},{4,6,7},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,3},{4,6},{5,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,3},{4,6},{5},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1},{2,3,7},{4},{5,6}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,3},{4,7},{5,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 2
{{1},{2,3},{4},{5,6},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1},{2,3,7},{4},{5},{6}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1},{2,3},{4,7},{5},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2,3},{4},{5,7},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2
{{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 2
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 1
{{1,4,5,6},{2,7},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,5,6},{2},{3,7}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,4,5,7},{2,6},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,5},{2,6},{3,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,5,7},{2},{3,6}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,4,5},{2,7},{3,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,5},{2},{3,6,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,4,5},{2},{3,6},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,4,5},{2,7},{3},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,5},{2},{3,7},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,4,6,7},{2,5},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4,6},{2,5},{3,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,4},{2,5,6,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,4},{2,5,6},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4,7},{2,5},{3,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4},{2,5,7},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,5},{3,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,4,6,7},{2},{3,5}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,4,6},{2,7},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4,6},{2},{3,5,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4,7},{2,6},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,4},{2,6,7},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,4},{2,6},{3,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4,7},{2},{3,5,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,4},{2,7},{3,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,4},{2},{3,5,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1,5,6,7},{2,4},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 1
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5,6},{2,4},{3,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,5},{2,4,6,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,5},{2,4,6},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,5,7},{2,4},{3,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5},{2,4,7},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,4},{3,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 1
{{1,6},{2,4,5,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1,6},{2,4,5},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,7},{2,4,5,6},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1
{{1},{2,4,5,6,7},{3}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 2
{{1},{2,4,5,6},{3,7}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1,7},{2,4,5},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,4,5,7},{3,6}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,4,5},{3,6,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,6,7},{2,4},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,6},{2,4,7},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,4},{3,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,7},{2,4,6},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,4,6,7},{3,5}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,4,6},{3,5,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,4},{3,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1},{2,4,7},{3,5,6}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,4},{3,5,6,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 2
{{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 2
{{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2
{{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 2
{{1,5,6,7},{2},{3,4}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 1
{{1,5,6},{2,7},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5,6},{2},{3,4,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,5,7},{2,6},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,5},{2,6,7},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,5},{2,6},{3,4,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5,7},{2},{3,4,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,5},{2,7},{3,4,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,5},{2},{3,4,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,6,7},{2,5},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 1
{{1,6},{2,5,7},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1,6},{2,5},{3,4,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,7},{2,5,6},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 1
{{1},{2,5,6,7},{3,4}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 2
{{1},{2,5,6},{3,4,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1,7},{2,5},{3,4,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1},{2,5,7},{3,4,6}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,5},{3,4,6,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 2
{{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,6,7},{2},{3,4,5}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 1
{{1,6},{2,7},{3,4,5}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1,6},{2},{3,4,5,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,7},{2,6},{3,4,5}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 1
{{1},{2,6,7},{3,4,5}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 2
{{1},{2,6},{3,4,5,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 2
{{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1,7},{2},{3,4,5,6}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1
{{1},{2,7},{3,4,5,6}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 2
{{1},{2},{3,4,5,6,7}} => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 3
{{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 3
{{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 3
{{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 3
{{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 3
{{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 3
{{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 3
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 1
{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 1
{{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 1
{{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 2
{{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 2
{{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2
{{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 2
{{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 1
{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 1
{{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 2
{{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 1
{{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 2
{{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 3
{{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 3
{{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 3
{{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 3
{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 1
{{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 1
{{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 2
{{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 2
{{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 1
{{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 2
{{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 3
{{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 3
{{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 1
{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 2
{{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 3
{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 4
{{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 4
{{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 4
{{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 4
{{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 1
{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 1
{{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 2
{{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2
{{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 2
{{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 1
{{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 2
{{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 3
{{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 3
{{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 3
{{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 1
{{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 2
{{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 3
{{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 4
{{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 4
{{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4
{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 1
{{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 2
{{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 3
{{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 4
{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 5
{{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 5
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 1
{{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 2
{{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 3
{{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 4
{{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 5
{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 6
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 7
{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 8
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 7
{{1},{2},{3},{4},{5},{6,7,8}} => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 6
{{1},{2},{3},{4},{5,6,7,8}} => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 5
{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 2
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,2},{3,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 1
{{1,3,4,5,6,7,8},{2}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3},{4,5,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,4,5,6,7,8},{3}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3,4},{5,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,5,6,7,8},{2,3,4}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,5,6,7,8},{3,4}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,5,6,7,8},{4}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3,4,5},{6,7,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,6,7,8},{2,3,4,5}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,6,7,8},{3,4,5}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,6,7,8},{5}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,7,8},{2,3,4,5,6}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,7,8},{3,4,5,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,7,8},{4,5,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,4,7,8},{5,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,5,7,8},{6}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3,4,5,6,7},{8}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,8},{2,3,4,5,6,7}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,2,8},{3,4,5,6,7}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,3,8},{4,5,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,4,8},{5,6,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,5,6,8},{7}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
{{1,2,3,4,5,6,7,8}} => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 1
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,3,4,5,7,8},{2,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,3,4,5,6,8},{2,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,3,4,5,6,7},{2,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,5,6,7},{4,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,6,7},{5,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,2,3,4,5,7},{6,8}} => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 1
{{1,3,5,7,8},{2,4,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,5,7,8},{3,4,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,4,7,8},{2,5,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,7,8},{3,5,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,5,6,8},{2,4,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,5,6,8},{3,4,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,4,6,8},{2,5,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,6,8},{3,5,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,6,8},{4,5,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,5,8},{3,6,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,5,8},{4,6,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,5,6,7},{2,4,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,5,6,7},{3,4,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,4,6,7},{2,5,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,6,7},{3,5,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,6,7},{4,5,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,4,5,7},{2,6,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,5,7},{3,6,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,5,7},{4,6,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,4,7},{5,6,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,4,5,6},{3,7,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,5,6},{4,7,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,3,4,6},{5,7,8}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,5,7},{2,4,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,5,7},{3,4,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,4,7},{2,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,4,7},{3,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,7},{4,5,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,5,6},{2,4,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,5,6},{3,4,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,4,6},{2,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,4,6},{3,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,6},{4,5,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,4,5},{2,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,4,5},{3,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,5},{4,6,7,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => 9
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,7,6,5,4,3,2,1] => 8
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => 10
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,8,7,6,5,4,3,2,1] => 9
{{1},{2},{3},{4},{5},{6},{7,8,9}} => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,6,6,5,4,3,2,1] => 7
{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1},{2,3,4,5,6,7,8,9}} => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 2
{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 2
{{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
{{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 2
{{1,3},{2,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,4},{2,3,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,5},{2,3,4,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,4,5,8},{2,3,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,4,6,7},{2,3,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,5,6},{2,3,4,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,5,6,7},{2,3,4,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,5,6,8},{2,3,4,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,4,8},{2,5,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,6,7},{2,4,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,4,5,6,7,8,9}} => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 1
{{1,2,3,4,5,6,7,8,9,10}} => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 1
{{1,4,5,7},{2,3,6,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,4,5,6,8},{2,3,7}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,4,6},{2,3,5,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,6},{3,4,5,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,4,7},{2,3,5,6,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
{{1,5,7,8},{2,3,4,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,6,8},{2,4,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,6,8},{3,4,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,6},{2,3,4,5,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,2,4},{3,5,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,5,8},{2,3,4,6,7}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,3,4},{2,5,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,5},{3,4,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
{{1,7},{2,3,4,5,6,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 1
{{1,4,6,7,8},{2,3,5}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,2,6,7},{3,4,5,8}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,6,7,8},{2,4,5}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,4,5,7,8},{2,3,6}} => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 1
{{1,3,7},{2,4,5,6,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,5,8},{3,4,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,6,7},{2,3,4,5,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,4,6,8},{2,3,5,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
{{1,4,7,8},{2,3,5,6}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,6,8},{2,3,4,5,7}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,5,7},{2,3,4,6,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,4,8},{2,3,5,6,7}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,3,5},{2,4,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,3,8},{2,4,5,6,7}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,7},{3,4,5,6,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
{{1,4,5},{2,3,6,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
{{1,3,5,8},{2,4,6,7}} => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 1
{{1,3,6},{2,4,5,7,8}} => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 1
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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 3,1,1 10,3,1,1 37,10,3,1,1 151,37,10,3,1,1 674,151,37,10,3,1,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 3\ q + q^{2} + q^{3}$
$F_{4} = 10\ q + 3\ q^{2} + q^{3} + q^{4}$
$F_{5} = 37\ q + 10\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$
$F_{6} = 151\ q + 37\ q^{2} + 10\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$
$F_{7} = 674\ q + 151\ q^{2} + 37\ q^{3} + 10\ q^{4} + 3\ q^{5} + q^{6} + q^{7}$
Description
The smallest missing part in an integer partition.
In [3], this is referred to as the mex, the minimal excluded part of the partition.
For compositions, this is studied in [sec.3.2., 1].
In [3], this is referred to as the mex, the minimal excluded part of the partition.
For compositions, this is studied in [sec.3.2., 1].
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
bounce path
Description
The bounce path determined by an integer composition.
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