Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000091: Integer compositions ⟶ ℤ
Values
{{1}} => [1] => [1] => 0
{{1,2}} => [2,1] => [1,1] => 0
{{1},{2}} => [1,2] => [2] => 0
{{1,2,3}} => [2,3,1] => [2,1] => 0
{{1,2},{3}} => [2,1,3] => [1,2] => 1
{{1,3},{2}} => [3,2,1] => [1,1,1] => 0
{{1},{2,3}} => [1,3,2] => [2,1] => 0
{{1},{2},{3}} => [1,2,3] => [3] => 0
{{1,2,3,4}} => [2,3,4,1] => [3,1] => 0
{{1,2,3},{4}} => [2,3,1,4] => [2,2] => 0
{{1,2,4},{3}} => [2,4,3,1] => [2,1,1] => 0
{{1,2},{3,4}} => [2,1,4,3] => [1,2,1] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [1,3] => 2
{{1,3,4},{2}} => [3,2,4,1] => [1,2,1] => 1
{{1,3},{2,4}} => [3,4,1,2] => [2,2] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [1,1,2] => 1
{{1,4},{2,3}} => [4,3,2,1] => [1,1,1,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => [3,1] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [2,2] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [1,2,1] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [2,1,1] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [3,1] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [4,1] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [3,2] => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => [3,1,1] => 0
{{1,2,3},{4,5}} => [2,3,1,5,4] => [2,2,1] => 0
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [2,3] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [2,2,1] => 0
{{1,2,4},{3,5}} => [2,4,5,1,3] => [3,2] => 0
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [2,1,2] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [2,1,1,1] => 0
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,3,1] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,2,2] => 1
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [2,2,1] => 0
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,2,1,1] => 1
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,3,1] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,4] => 3
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,3,1] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [2,1,2] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,2,2] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [3,1,1] => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => [2,2,1] => 0
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [2,3] => 1
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,2,1,1] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [2,2,1] => 0
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,1,2,1] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,1,3] => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,1,2,1] => 1
{{1,4},{2,3,5}} => [4,3,5,1,2] => [1,2,2] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,1,1,2] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,2,1,1] => 1
{{1},{2,3,4,5}} => [1,3,4,5,2] => [4,1] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [3,2] => 0
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,1,2,1] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [3,1,1] => 0
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [2,2,1] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [2,3] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,3,1] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [2,1,2] => 1
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [1,2,2] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,2,2] => 1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,1,1,1,1] => 0
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [2,2,1] => 0
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [3,2] => 0
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [2,1,2] => 1
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,2,1,1] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [2,1,1,1] => 0
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [4,1] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [3,2] => 0
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,3,1] => 2
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [2,2,1] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [3,1,1] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [4,1] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [5] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [5,1] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [4,2] => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [4,1,1] => 0
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [3,2,1] => 0
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [3,3] => 0
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [3,2,1] => 0
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [4,2] => 0
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [3,1,2] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [3,1,1,1] => 0
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [2,3,1] => 1
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [2,2,2] => 0
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [3,2,1] => 0
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [2,2,1,1] => 0
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [2,3,1] => 1
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [2,4] => 2
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [2,3,1] => 1
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [3,1,2] => 1
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [2,2,2] => 0
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [4,1,1] => 0
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [3,2,1] => 0
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [3,3] => 0
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [2,2,1,1] => 0
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [3,2,1] => 0
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [2,1,2,1] => 1
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [2,1,3] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [2,1,2,1] => 1
>>> Load all 1155 entries. <<<{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [2,2,2] => 0
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [2,1,1,2] => 1
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [2,2,1,1] => 0
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [1,4,1] => 3
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [1,3,2] => 2
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [2,1,2,1] => 1
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [1,3,1,1] => 2
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [1,2,2,1] => 1
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [1,2,3] => 2
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [2,3,1] => 1
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [3,1,2] => 1
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [2,2,2] => 0
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [2,2,2] => 0
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [2,1,1,1,1] => 0
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [1,2,2,1] => 1
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [1,3,2] => 2
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [1,2,1,2] => 2
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [2,2,1,1] => 0
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [1,2,1,1,1] => 1
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [1,4,1] => 3
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [1,3,2] => 2
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [2,3,1] => 1
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [1,2,2,1] => 1
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [1,3,1,1] => 2
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [1,4,1] => 3
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,5] => 4
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,4,1] => 3
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [2,2,2] => 0
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [1,3,2] => 2
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [2,2,1,1] => 0
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [2,1,2,1] => 1
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [2,1,3] => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [1,3,1,1] => 2
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [2,1,2,1] => 1
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [1,2,2,1] => 1
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [1,2,3] => 2
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [3,2,1] => 0
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [4,2] => 0
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [3,1,2] => 1
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [3,1,1,1] => 0
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [2,3,1] => 1
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [2,2,2] => 0
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [3,2,1] => 0
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [2,2,1,1] => 0
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [2,3,1] => 1
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [2,4] => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [1,2,2,1] => 1
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [2,1,1,2] => 1
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [1,3,2] => 2
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [1,2,1,2] => 2
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [3,1,1,1] => 0
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [2,3,1] => 1
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [2,2,2] => 0
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [2,2,2] => 0
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [1,2,1,1,1] => 1
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [2,2,1,1] => 0
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [1,1,3,1] => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [1,1,2,2] => 1
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [1,2,2,1] => 1
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [2,3,1] => 1
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [1,1,2,1,1] => 1
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [1,1,3,1] => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [1,1,4] => 3
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [1,1,3,1] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [1,2,1,2] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [1,1,2,2] => 1
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [1,3,1,1] => 2
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [1,2,2,1] => 1
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [1,2,3] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [1,1,2,1,1] => 1
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [1,2,2,1] => 1
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [1,1,1,2,1] => 1
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [1,1,1,3] => 2
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [1,2,2,1] => 1
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [1,3,2] => 2
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [1,2,1,2] => 2
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,3,1,1] => 2
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [5,1] => 0
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [4,2] => 0
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,2,2,1] => 1
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [4,1,1] => 0
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [3,2,1] => 0
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [3,3] => 0
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [1,1,3,1] => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [1,2,1,2] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [1,1,2,2] => 1
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [1,1,2,2] => 1
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,2,1,1,1] => 1
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [3,2,1] => 0
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [4,2] => 0
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [3,1,2] => 1
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,1,2,1,1] => 1
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [3,1,1,1] => 0
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [2,3,1] => 1
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [2,2,2] => 0
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,1,3,1] => 2
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [3,2,1] => 0
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [2,2,1,1] => 0
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [2,3,1] => 1
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [2,4] => 2
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [1,4,1] => 3
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [2,2,2] => 0
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [1,2,1,2] => 2
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [1,3,2] => 2
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [2,2,1,1] => 0
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [2,1,2,1] => 1
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [3,3] => 0
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [2,1,3] => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [1,3,1,1] => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [2,1,2,1] => 1
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [1,2,2,1] => 1
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [1,2,3] => 2
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [1,3,1,1] => 2
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [2,1,2,1] => 1
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [1,2,2,1] => 1
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [1,2,2,1] => 1
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [1,2,3] => 2
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [1,1,1,2,1] => 1
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [1,1,2,2] => 1
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [1,2,1,2] => 2
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [1,1,1,1,2] => 1
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,1,2,1,1] => 1
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [2,3,1] => 1
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [3,1,2] => 1
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [2,2,2] => 0
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,2,2,1] => 1
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [4,1,1] => 0
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [3,2,1] => 0
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [3,3] => 0
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,1,1,2,1] => 1
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [2,2,1,1] => 0
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [3,2,1] => 0
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [2,1,2,1] => 1
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [2,1,3] => 2
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [1,2,2,1] => 1
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [2,1,1,2] => 1
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [1,3,2] => 2
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [1,2,1,2] => 2
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,1,1,1,1,1] => 0
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [2,1,2,1] => 1
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [2,2,2] => 0
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [2,1,1,2] => 1
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,3,1,1] => 2
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [2,2,1,1] => 0
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [5,1] => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [4,2] => 0
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,2,2,1] => 1
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [2,1,2,1] => 1
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [4,1,1] => 0
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [3,2,1] => 0
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [3,3] => 0
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [1,4,1] => 3
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [2,2,2] => 0
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [1,2,1,2] => 2
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [1,3,2] => 2
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [1,3,2] => 2
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,1,2,1,1] => 1
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [2,3,1] => 1
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [3,1,2] => 1
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [2,2,2] => 0
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [2,2,2] => 0
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,2,1,1,1] => 1
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [2,1,1,1,1] => 0
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [3,2,1] => 0
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [4,2] => 0
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [3,1,2] => 1
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,3,1,1] => 2
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [2,2,1,1] => 0
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [3,1,1,1] => 0
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [5,1] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [4,2] => 0
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,4,1] => 3
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [2,3,1] => 1
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [3,2,1] => 0
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [4,1,1] => 0
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [5,1] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [6] => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [6,1] => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [5,2] => 0
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [5,1,1] => 0
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [4,2,1] => 0
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [4,3] => 0
{{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => [4,2,1] => 0
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [5,2] => 0
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [4,1,2] => 1
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [4,1,1,1] => 0
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [3,3,1] => 0
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [3,2,2] => 0
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [4,2,1] => 0
{{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => [3,2,1,1] => 0
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [3,3,1] => 0
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [3,4] => 1
{{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => [3,3,1] => 0
{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [4,1,2] => 1
{{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => [3,2,2] => 0
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [5,1,1] => 0
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [4,2,1] => 0
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [4,3] => 0
{{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => [3,2,1,1] => 0
{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [4,2,1] => 0
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [3,1,2,1] => 1
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [3,1,3] => 2
{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [3,1,2,1] => 1
{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [3,2,2] => 0
{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [3,1,1,2] => 1
{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [3,2,1,1] => 0
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [2,4,1] => 2
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [2,3,2] => 1
{{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => [3,1,2,1] => 1
{{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => [2,3,1,1] => 1
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [2,2,2,1] => 0
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [2,2,3] => 1
{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [3,3,1] => 0
{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [4,1,2] => 1
{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [3,2,2] => 0
{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [3,2,2] => 0
{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [3,1,1,1,1] => 0
{{1,2,3},{4,6,7},{5}} => [2,3,1,6,5,7,4] => [2,2,2,1] => 0
{{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => [2,3,2] => 1
{{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => [2,2,1,2] => 1
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [3,2,1,1] => 0
{{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => [2,2,1,1,1] => 0
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [2,4,1] => 2
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [2,3,2] => 1
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [3,3,1] => 0
{{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => [2,2,2,1] => 0
{{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => [2,3,1,1] => 1
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [2,4,1] => 2
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [2,5] => 3
{{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => [2,4,1] => 2
{{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => [3,2,2] => 0
{{1,2,4,5,6},{3},{7}} => [2,4,3,5,6,1,7] => [2,3,2] => 1
{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [3,2,1,1] => 0
{{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => [3,1,2,1] => 1
{{1,2,4,5},{3,6},{7}} => [2,4,6,5,1,3,7] => [3,1,3] => 2
{{1,2,4,5,7},{3},{6}} => [2,4,3,5,7,6,1] => [2,3,1,1] => 1
{{1,2,4,5},{3,7},{6}} => [2,4,7,5,1,6,3] => [3,1,2,1] => 1
{{1,2,4,5},{3},{6,7}} => [2,4,3,5,1,7,6] => [2,2,2,1] => 0
{{1,2,4,5},{3},{6},{7}} => [2,4,3,5,1,6,7] => [2,2,3] => 1
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [4,2,1] => 0
{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [5,2] => 0
{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [4,1,2] => 1
{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [4,1,1,1] => 0
{{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => [3,3,1] => 0
{{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => [3,2,2] => 0
{{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => [4,2,1] => 0
{{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => [3,2,1,1] => 0
{{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => [3,3,1] => 0
{{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => [3,4] => 1
{{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => [2,2,2,1] => 0
{{1,2,4,6},{3,7},{5}} => [2,4,7,6,5,1,3] => [3,1,1,2] => 1
{{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => [2,3,2] => 1
{{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => [2,2,1,2] => 1
{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [4,1,1,1] => 0
{{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => [3,3,1] => 0
{{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => [3,2,2] => 0
{{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => [3,2,2] => 0
{{1,2,4,7},{3},{5,6}} => [2,4,3,7,6,5,1] => [2,2,1,1,1] => 0
{{1,2,4},{3,7},{5,6}} => [2,4,7,1,6,5,3] => [3,2,1,1] => 0
{{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => [2,1,3,1] => 2
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [2,1,2,2] => 1
{{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => [2,2,2,1] => 0
{{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => [3,3,1] => 0
{{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => [2,1,2,1,1] => 1
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [2,1,3,1] => 2
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [2,1,4] => 3
{{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => [2,1,3,1] => 2
{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [2,2,1,2] => 1
{{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => [2,1,2,2] => 1
{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [2,3,1,1] => 1
{{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => [2,2,2,1] => 0
{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [2,2,3] => 1
{{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => [2,1,2,1,1] => 1
{{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => [2,2,2,1] => 0
{{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => [2,1,1,2,1] => 1
{{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => [2,1,1,3] => 2
{{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => [2,2,2,1] => 0
{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [2,3,2] => 1
{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [2,2,1,2] => 1
{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [2,3,1,1] => 1
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [1,5,1] => 4
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [1,4,2] => 3
{{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => [2,2,2,1] => 0
{{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => [1,4,1,1] => 3
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [1,3,2,1] => 2
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [1,3,3] => 2
{{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => [2,1,3,1] => 2
{{1,2,6},{3,4,7},{5}} => [2,6,4,7,5,1,3] => [2,2,1,2] => 1
{{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => [2,1,2,2] => 1
{{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => [2,1,2,2] => 1
{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [2,2,1,1,1] => 0
{{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => [1,3,2,1] => 2
{{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => [1,4,2] => 3
{{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => [1,3,1,2] => 3
{{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => [2,1,2,1,1] => 1
{{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => [1,3,1,1,1] => 2
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [1,2,3,1] => 2
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [1,2,2,2] => 1
{{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => [2,1,3,1] => 2
{{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => [1,3,2,1] => 2
{{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => [1,2,2,1,1] => 1
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [1,2,3,1] => 2
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [1,2,4] => 3
{{1,2,5,6,7},{3},{4}} => [2,5,3,4,6,7,1] => [2,4,1] => 2
{{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => [3,2,2] => 0
{{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => [2,2,1,2] => 1
{{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => [2,3,2] => 1
{{1,2,5,7},{3,6},{4}} => [2,5,6,4,7,3,1] => [3,2,1,1] => 0
{{1,2,5},{3,6,7},{4}} => [2,5,6,4,1,7,3] => [3,1,2,1] => 1
{{1,2,5},{3,6},{4,7}} => [2,5,6,7,1,3,4] => [4,3] => 0
{{1,2,5},{3,6},{4},{7}} => [2,5,6,4,1,3,7] => [3,1,3] => 2
{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [2,3,1,1] => 1
{{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => [3,1,2,1] => 1
{{1,2,5},{3},{4,6,7}} => [2,5,3,6,1,7,4] => [2,2,2,1] => 0
{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [2,2,3] => 1
{{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => [2,3,1,1] => 1
{{1,2,5},{3,7},{4},{6}} => [2,5,7,4,1,6,3] => [3,1,2,1] => 1
{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [2,2,2,1] => 0
{{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => [2,2,2,1] => 0
{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [2,2,3] => 1
{{1,2,6,7},{3,5},{4}} => [2,6,5,4,3,7,1] => [2,1,1,2,1] => 1
{{1,2,6},{3,5,7},{4}} => [2,6,5,4,7,1,3] => [2,1,2,2] => 1
{{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => [2,2,1,2] => 1
{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [2,1,1,1,2] => 1
{{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => [2,1,2,1,1] => 1
{{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => [1,2,3,1] => 2
{{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => [1,3,1,2] => 3
{{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => [1,2,2,2] => 1
{{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => [2,2,2,1] => 0
{{1,2},{3,5,7},{4,6}} => [2,1,5,6,7,4,3] => [1,4,1,1] => 3
{{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => [1,3,2,1] => 2
{{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => [1,3,3] => 2
{{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => [2,1,1,2,1] => 1
{{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => [1,2,2,1,1] => 1
{{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => [1,3,2,1] => 2
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [1,2,1,2,1] => 2
{{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => [1,2,1,3] => 3
{{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => [2,2,2,1] => 0
{{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => [3,1,1,2] => 1
{{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => [2,3,2] => 1
{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [2,2,1,2] => 1
{{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => [2,1,1,1,1,1] => 0
{{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => [1,2,1,2,1] => 2
{{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => [1,2,2,2] => 1
{{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => [1,2,1,1,2] => 2
{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [2,3,1,1] => 1
{{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => [1,2,2,1,1] => 1
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [1,5,1] => 4
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [1,4,2] => 3
{{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => [2,2,2,1] => 0
{{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => [1,2,1,2,1] => 2
{{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => [1,4,1,1] => 3
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [1,3,2,1] => 2
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [1,3,3] => 2
{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [2,4,1] => 2
{{1,2,6},{3,7},{4},{5}} => [2,6,7,4,5,1,3] => [3,2,2] => 0
{{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => [2,2,1,2] => 1
{{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => [2,3,2] => 1
{{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => [2,3,2] => 1
{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [2,1,2,1,1] => 1
{{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => [1,2,3,1] => 2
{{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => [1,3,1,2] => 3
{{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => [1,2,2,2] => 1
{{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => [1,2,2,2] => 1
{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [2,2,1,1,1] => 0
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [1,2,1,1,1,1] => 1
{{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => [1,3,2,1] => 2
{{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => [1,4,2] => 3
{{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => [1,3,1,2] => 3
{{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => [2,3,1,1] => 1
{{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => [1,2,2,1,1] => 1
{{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => [1,3,1,1,1] => 2
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [1,5,1] => 4
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [1,4,2] => 3
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [2,4,1] => 2
{{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => [1,2,3,1] => 2
{{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => [1,3,2,1] => 2
{{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => [1,4,1,1] => 3
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [1,5,1] => 4
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,6] => 5
{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [1,5,1] => 4
{{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => [2,3,2] => 1
{{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => [1,4,2] => 3
{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [2,3,1,1] => 1
{{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => [2,2,2,1] => 0
{{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => [2,2,3] => 1
{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [1,4,1,1] => 3
{{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => [2,2,2,1] => 0
{{1,3,4,5},{2},{6,7}} => [3,2,4,5,1,7,6] => [1,3,2,1] => 2
{{1,3,4,5},{2},{6},{7}} => [3,2,4,5,1,6,7] => [1,3,3] => 2
{{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => [2,2,2,1] => 0
{{1,3,4,6},{2,5,7}} => [3,5,4,6,7,1,2] => [2,3,2] => 1
{{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => [2,2,1,2] => 1
{{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => [2,2,1,1,1] => 0
{{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => [2,1,3,1] => 2
{{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => [2,1,2,2] => 1
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [2,2,2,1] => 0
{{1,3,4},{2,5,7},{6}} => [3,5,4,1,7,6,2] => [2,1,2,1,1] => 1
{{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => [2,1,3,1] => 2
{{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => [2,1,4] => 3
{{1,3,4,6,7},{2},{5}} => [3,2,4,6,5,7,1] => [1,3,2,1] => 2
{{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => [2,2,1,2] => 1
{{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => [1,4,2] => 3
{{1,3,4,6},{2},{5},{7}} => [3,2,4,6,5,1,7] => [1,3,1,2] => 3
{{1,3,4,7},{2,6},{5}} => [3,6,4,7,5,2,1] => [2,2,1,1,1] => 0
{{1,3,4},{2,6,7},{5}} => [3,6,4,1,5,7,2] => [2,1,3,1] => 2
{{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => [2,1,2,2] => 1
{{1,3,4},{2,6},{5},{7}} => [3,6,4,1,5,2,7] => [2,1,2,2] => 1
{{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => [1,3,1,1,1] => 2
{{1,3,4},{2,7},{5,6}} => [3,7,4,1,6,5,2] => [2,1,2,1,1] => 1
{{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => [1,2,3,1] => 2
{{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => [1,2,2,2] => 1
{{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => [1,3,2,1] => 2
{{1,3,4},{2,7},{5},{6}} => [3,7,4,1,5,6,2] => [2,1,3,1] => 2
{{1,3,4},{2},{5,7},{6}} => [3,2,4,1,7,6,5] => [1,2,2,1,1] => 1
{{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => [1,2,3,1] => 2
{{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => [1,2,4] => 3
{{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => [3,3,1] => 0
{{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => [4,1,2] => 1
{{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => [3,2,2] => 0
{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [5,1,1] => 0
{{1,3,5},{2,4,6,7}} => [3,4,5,6,1,7,2] => [4,2,1] => 0
{{1,3,5},{2,4,6},{7}} => [3,4,5,6,1,2,7] => [4,3] => 0
{{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => [3,2,1,1] => 0
{{1,3,5},{2,4,7},{6}} => [3,4,5,7,1,6,2] => [4,2,1] => 0
{{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => [3,1,2,1] => 1
{{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => [3,1,3] => 2
{{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => [3,1,2,1] => 1
{{1,3,6},{2,4,5,7}} => [3,4,6,5,7,1,2] => [3,2,2] => 0
{{1,3,6},{2,4,5},{7}} => [3,4,6,5,2,1,7] => [3,1,1,2] => 1
{{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => [3,2,1,1] => 0
{{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => [2,4,1] => 2
{{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => [2,3,2] => 1
{{1,3,7},{2,4,5},{6}} => [3,4,7,5,2,6,1] => [3,1,2,1] => 1
{{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => [2,3,1,1] => 1
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [2,2,2,1] => 0
{{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => [2,2,3] => 1
{{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => [3,3,1] => 0
{{1,3,6},{2,4,7},{5}} => [3,4,6,7,5,1,2] => [4,1,2] => 1
{{1,3,6},{2,4},{5,7}} => [3,4,6,2,7,1,5] => [3,2,2] => 0
{{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => [3,2,2] => 0
{{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => [3,1,1,1,1] => 0
{{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => [2,2,2,1] => 0
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [2,3,2] => 1
{{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => [2,2,1,2] => 1
{{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => [3,2,1,1] => 0
{{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => [2,2,1,1,1] => 0
{{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => [2,4,1] => 2
{{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => [2,3,2] => 1
{{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => [3,3,1] => 0
{{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => [2,2,2,1] => 0
{{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => [2,3,1,1] => 1
{{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => [2,4,1] => 2
{{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => [2,5] => 3
{{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => [1,2,3,1] => 2
{{1,3,5,6},{2,7},{4}} => [3,7,5,4,6,1,2] => [2,1,2,2] => 1
{{1,3,5,6},{2},{4,7}} => [3,2,5,7,6,1,4] => [1,3,1,2] => 3
{{1,3,5,6},{2},{4},{7}} => [3,2,5,4,6,1,7] => [1,2,2,2] => 1
{{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => [2,1,2,1,1] => 1
{{1,3,5},{2,6,7},{4}} => [3,6,5,4,1,7,2] => [2,1,1,2,1] => 1
{{1,3,5},{2,6},{4,7}} => [3,6,5,7,1,2,4] => [2,2,3] => 1
{{1,3,5},{2,6},{4},{7}} => [3,6,5,4,1,2,7] => [2,1,1,3] => 2
{{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => [1,4,1,1] => 3
{{1,3,5},{2,7},{4,6}} => [3,7,5,6,1,4,2] => [2,2,2,1] => 0
{{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => [1,3,2,1] => 2
{{1,3,5},{2},{4,6},{7}} => [3,2,5,6,1,4,7] => [1,3,3] => 2
{{1,3,5,7},{2},{4},{6}} => [3,2,5,4,7,6,1] => [1,2,2,1,1] => 1
{{1,3,5},{2,7},{4},{6}} => [3,7,5,4,1,6,2] => [2,1,1,2,1] => 1
{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [1,3,2,1] => 2
{{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => [1,2,1,2,1] => 2
{{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => [1,2,1,3] => 3
{{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => [3,1,2,1] => 1
{{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => [3,2,2] => 0
{{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => [4,1,2] => 1
{{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => [3,1,1,2] => 1
{{1,3,7},{2,5,6},{4}} => [3,5,7,4,6,2,1] => [3,2,1,1] => 0
{{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => [2,4,1] => 2
{{1,3},{2,5,6},{4,7}} => [3,5,1,7,6,2,4] => [2,2,1,2] => 1
{{1,3},{2,5,6},{4},{7}} => [3,5,1,4,6,2,7] => [2,3,2] => 1
{{1,3,7},{2,5},{4,6}} => [3,5,7,6,2,4,1] => [3,1,2,1] => 1
{{1,3},{2,5,7},{4,6}} => [3,5,1,6,7,4,2] => [2,3,1,1] => 1
{{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => [2,2,2,1] => 0
{{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => [2,2,3] => 1
{{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => [3,1,2,1] => 1
{{1,3},{2,5,7},{4},{6}} => [3,5,1,4,7,6,2] => [2,3,1,1] => 1
{{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => [2,2,2,1] => 0
{{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => [2,2,2,1] => 0
{{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => [2,2,3] => 1
{{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => [1,2,1,2,1] => 2
{{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => [2,1,1,1,2] => 1
{{1,3,6},{2},{4,5,7}} => [3,2,6,5,7,1,4] => [1,2,2,2] => 1
{{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => [1,2,1,1,2] => 2
{{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => [3,1,1,1,1] => 0
{{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => [2,2,2,1] => 0
{{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => [2,3,2] => 1
{{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => [2,2,1,2] => 1
{{1,3,7},{2},{4,5,6}} => [3,2,7,5,6,4,1] => [1,2,2,1,1] => 1
{{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => [2,3,1,1] => 1
{{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => [1,1,4,1] => 3
{{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => [1,1,3,2] => 2
{{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => [1,2,1,2,1] => 2
{{1,3},{2,7},{4,5},{6}} => [3,7,1,5,4,6,2] => [2,2,2,1] => 0
{{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => [1,1,3,1,1] => 2
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [1,1,2,2,1] => 1
{{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => [1,1,2,3] => 2
{{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => [1,2,3,1] => 2
{{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => [2,1,2,2] => 1
{{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => [1,3,1,2] => 3
{{1,3,6},{2},{4},{5,7}} => [3,2,6,4,7,1,5] => [1,2,2,2] => 1
{{1,3,6},{2},{4},{5},{7}} => [3,2,6,4,5,1,7] => [1,2,2,2] => 1
{{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => [3,2,1,1] => 0
{{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => [2,4,1] => 2
{{1,3},{2,6},{4,7},{5}} => [3,6,1,7,5,2,4] => [2,2,1,2] => 1
{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [2,3,2] => 1
{{1,3},{2,6},{4},{5},{7}} => [3,6,1,4,5,2,7] => [2,3,2] => 1
{{1,3,7},{2},{4,6},{5}} => [3,2,7,6,5,4,1] => [1,2,1,1,1,1] => 1
{{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => [2,2,1,1,1] => 0
{{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => [1,1,2,2,1] => 1
{{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => [1,1,3,2] => 2
{{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => [1,1,2,1,2] => 2
{{1,3,7},{2},{4},{5,6}} => [3,2,7,4,6,5,1] => [1,2,2,1,1] => 1
{{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => [2,3,1,1] => 1
{{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => [1,1,2,1,1,1] => 1
{{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => [1,1,4,1] => 3
{{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => [1,1,3,2] => 2
{{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => [1,2,3,1] => 2
{{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => [2,4,1] => 2
{{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => [1,1,2,2,1] => 1
{{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => [1,1,3,1,1] => 2
{{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => [1,1,4,1] => 3
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [1,1,5] => 4
{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [1,1,4,1] => 3
{{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => [1,2,2,2] => 1
{{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => [1,1,3,2] => 2
{{1,4,5,7},{2,3,6}} => [4,3,6,5,7,2,1] => [1,2,2,1,1] => 1
{{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => [1,2,1,2,1] => 2
{{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => [1,2,1,3] => 3
{{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => [1,1,3,1,1] => 2
{{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => [1,2,1,2,1] => 2
{{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => [1,1,2,2,1] => 1
{{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => [1,1,2,3] => 2
{{1,4,6,7},{2,3,5}} => [4,3,5,6,2,7,1] => [1,3,2,1] => 2
{{1,4,6},{2,3,5,7}} => [4,3,5,6,7,1,2] => [1,4,2] => 3
{{1,4,6},{2,3,5},{7}} => [4,3,5,6,2,1,7] => [1,3,1,2] => 3
{{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => [1,3,1,1,1] => 2
{{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => [1,2,3,1] => 2
{{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => [1,2,2,2] => 1
{{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => [1,3,2,1] => 2
{{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => [1,2,2,1,1] => 1
{{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => [1,2,3,1] => 2
{{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => [1,2,4] => 3
{{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => [1,1,2,2,1] => 1
{{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => [1,2,1,1,2] => 2
{{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => [1,1,3,2] => 2
{{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => [1,1,2,1,2] => 2
{{1,4,7},{2,3,6},{5}} => [4,3,6,7,5,2,1] => [1,3,1,1,1] => 2
{{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => [1,2,3,1] => 2
{{1,4},{2,3,6},{5,7}} => [4,3,6,1,7,2,5] => [1,2,2,2] => 1
{{1,4},{2,3,6},{5},{7}} => [4,3,6,1,5,2,7] => [1,2,2,2] => 1
{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [1,1,2,1,1,1] => 1
{{1,4},{2,3,7},{5,6}} => [4,3,7,1,6,5,2] => [1,2,2,1,1] => 1
{{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => [1,1,1,3,1] => 2
{{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => [1,1,1,2,2] => 1
{{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => [1,1,2,2,1] => 1
{{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => [1,2,3,1] => 2
{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [1,1,1,2,1,1] => 1
{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [1,1,1,3,1] => 2
{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [1,1,1,4] => 3
{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [1,2,3,1] => 2
{{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => [1,3,1,2] => 3
{{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => [1,2,2,2] => 1
{{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => [1,4,1,1] => 3
{{1,5},{2,3,4,6,7}} => [5,3,4,6,1,7,2] => [1,3,2,1] => 2
{{1,5},{2,3,4,6},{7}} => [5,3,4,6,1,2,7] => [1,3,3] => 2
{{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => [1,2,2,1,1] => 1
{{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => [1,3,2,1] => 2
{{1,5},{2,3,4},{6,7}} => [5,3,4,2,1,7,6] => [1,2,1,2,1] => 2
{{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => [1,2,1,3] => 3
{{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => [1,3,2,1] => 2
{{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => [1,4,2] => 3
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [1,3,1,2] => 3
{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [1,4,1,1] => 3
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [6,1] => 0
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [5,2] => 0
{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [1,3,2,1] => 2
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [5,1,1] => 0
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [4,2,1] => 0
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [4,3] => 0
{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [1,2,3,1] => 2
{{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => [1,3,1,2] => 3
{{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => [1,2,2,2] => 1
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [1,2,2,2] => 1
{{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => [1,3,1,1,1] => 2
{{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => [4,2,1] => 0
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [5,2] => 0
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [4,1,2] => 1
{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [1,2,2,1,1] => 1
{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [4,1,1,1] => 0
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [3,3,1] => 0
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [3,2,2] => 0
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [1,2,3,1] => 2
{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [4,2,1] => 0
{{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => [3,2,1,1] => 0
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [3,3,1] => 0
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [3,4] => 1
{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [1,1,4,1] => 3
{{1,5,6},{2,3,7},{4}} => [5,3,7,4,6,1,2] => [1,2,2,2] => 1
{{1,5,6},{2,3},{4,7}} => [5,3,2,7,6,1,4] => [1,1,2,1,2] => 2
{{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => [1,1,3,2] => 2
{{1,5,7},{2,3,6},{4}} => [5,3,6,4,7,2,1] => [1,2,2,1,1] => 1
{{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => [1,2,1,2,1] => 2
{{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => [1,3,3] => 2
{{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => [1,2,1,3] => 3
{{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => [1,1,3,1,1] => 2
{{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => [1,2,1,2,1] => 2
{{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => [1,1,2,2,1] => 1
{{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => [1,1,2,3] => 2
{{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => [1,1,3,1,1] => 2
{{1,5},{2,3,7},{4},{6}} => [5,3,7,4,1,6,2] => [1,2,1,2,1] => 2
{{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => [1,1,2,2,1] => 1
{{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => [1,1,2,2,1] => 1
{{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => [1,1,2,3] => 2
{{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => [1,2,1,2,1] => 2
{{1,6},{2,3,5,7},{4}} => [6,3,5,4,7,1,2] => [1,2,2,2] => 1
{{1,6},{2,3,5},{4,7}} => [6,3,5,7,2,1,4] => [1,3,1,2] => 3
{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [1,2,1,1,2] => 2
{{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => [1,2,2,1,1] => 1
{{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => [3,3,1] => 0
{{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => [4,1,2] => 1
{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [3,2,2] => 0
{{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => [1,3,2,1] => 2
{{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => [5,1,1] => 0
{{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => [4,2,1] => 0
{{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => [4,3] => 0
{{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => [1,2,1,2,1] => 2
{{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => [3,2,1,1] => 0
{{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => [4,2,1] => 0
{{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => [3,1,2,1] => 1
{{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => [3,1,3] => 2
{{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => [1,1,2,2,1] => 1
{{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => [1,2,1,1,2] => 2
{{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => [1,1,3,2] => 2
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [1,1,2,1,2] => 2
{{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => [1,2,1,1,1,1] => 1
{{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => [3,1,2,1] => 1
{{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => [3,2,2] => 0
{{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => [3,1,1,2] => 1
{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [1,1,3,1,1] => 2
{{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => [3,2,1,1] => 0
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [2,4,1] => 2
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [2,3,2] => 1
{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [1,1,2,2,1] => 1
{{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => [3,1,2,1] => 1
{{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => [2,3,1,1] => 1
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [2,2,2,1] => 0
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [2,2,3] => 1
{{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => [1,1,4,1] => 3
{{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => [1,2,2,2] => 1
{{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => [1,1,2,1,2] => 2
{{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => [1,1,3,2] => 2
{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [1,1,3,2] => 2
{{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => [1,2,2,1,1] => 1
{{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => [3,3,1] => 0
{{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => [4,1,2] => 1
{{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => [3,2,2] => 0
{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [3,2,2] => 0
{{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => [1,1,2,1,1,1] => 1
{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [3,1,1,1,1] => 0
{{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => [2,2,2,1] => 0
{{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => [2,3,2] => 1
{{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => [2,2,1,2] => 1
{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [1,1,3,1,1] => 2
{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [3,2,1,1] => 0
{{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => [2,2,1,1,1] => 0
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [2,4,1] => 2
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [2,3,2] => 1
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [1,1,4,1] => 3
{{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => [3,3,1] => 0
{{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => [2,2,2,1] => 0
{{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => [2,3,1,1] => 1
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [2,4,1] => 2
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [2,5] => 3
{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [1,5,1] => 4
{{1,4,5,6},{2,7},{3}} => [4,7,3,5,6,1,2] => [2,3,2] => 1
{{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => [1,2,2,2] => 1
{{1,4,5,6},{2},{3},{7}} => [4,2,3,5,6,1,7] => [1,4,2] => 3
{{1,4,5,7},{2,6},{3}} => [4,6,3,5,7,2,1] => [2,3,1,1] => 1
{{1,4,5},{2,6,7},{3}} => [4,6,3,5,1,7,2] => [2,2,2,1] => 0
{{1,4,5},{2,6},{3,7}} => [4,6,7,5,1,2,3] => [3,1,3] => 2
{{1,4,5},{2,6},{3},{7}} => [4,6,3,5,1,2,7] => [2,2,3] => 1
{{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => [1,2,2,1,1] => 1
{{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => [2,1,1,2,1] => 1
{{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => [1,2,1,2,1] => 2
{{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => [1,2,1,3] => 3
{{1,4,5,7},{2},{3},{6}} => [4,2,3,5,7,6,1] => [1,4,1,1] => 3
{{1,4,5},{2,7},{3},{6}} => [4,7,3,5,1,6,2] => [2,2,2,1] => 0
{{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => [1,2,1,2,1] => 2
{{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => [1,3,2,1] => 2
{{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => [1,3,3] => 2
{{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => [2,2,2,1] => 0
{{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => [2,3,2] => 1
{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [3,1,1,2] => 1
{{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => [2,2,1,2] => 1
{{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => [2,2,1,1,1] => 0
{{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => [2,1,3,1] => 2
{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [3,2,2] => 0
{{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => [2,1,2,2] => 1
{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [4,2,1] => 0
{{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => [3,2,1,1] => 0
{{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => [3,3,1] => 0
{{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => [3,4] => 1
{{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => [2,2,2,1] => 0
{{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => [2,1,2,1,1] => 1
{{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => [3,3,1] => 0
{{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => [2,1,3,1] => 2
{{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => [2,1,4] => 3
{{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => [1,3,2,1] => 2
{{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => [2,2,1,2] => 1
{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [1,4,2] => 3
{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [1,3,1,2] => 3
{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [2,2,1,1,1] => 0
{{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => [2,1,3,1] => 2
{{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => [2,1,2,2] => 1
{{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => [2,1,2,2] => 1
{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [1,3,1,1,1] => 2
{{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => [2,1,2,1,1] => 1
{{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => [1,2,3,1] => 2
{{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => [1,2,2,2] => 1
{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [1,3,2,1] => 2
{{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => [2,1,3,1] => 2
{{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => [1,2,2,1,1] => 1
{{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => [1,2,3,1] => 2
{{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => [1,2,4] => 3
{{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => [1,3,2,1] => 2
{{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => [2,2,1,2] => 1
{{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => [1,2,1,1,2] => 2
{{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => [1,4,2] => 3
{{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => [1,3,1,2] => 3
{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [2,2,1,1,1] => 0
{{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => [2,1,3,1] => 2
{{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => [3,2,2] => 0
{{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => [2,1,2,2] => 1
{{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => [2,1,2,2] => 1
{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [1,3,1,1,1] => 2
{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [2,1,2,1,1] => 1
{{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => [1,2,3,1] => 2
{{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => [1,2,2,2] => 1
{{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => [1,2,2,2] => 1
{{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => [1,3,1,1,1] => 2
{{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => [2,1,2,1,1] => 1
{{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => [1,2,2,1,1] => 1
{{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => [1,2,3,1] => 2
{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [1,2,2,2] => 1
{{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => [1,3,2,1] => 2
{{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => [2,1,3,1] => 2
{{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => [1,2,3,1] => 2
{{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => [1,2,2,1,1] => 1
{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [1,2,3,1] => 2
{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [1,2,4] => 3
{{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => [1,1,1,3,1] => 2
{{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => [1,1,2,1,2] => 2
{{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => [1,2,2,2] => 1
{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [1,1,1,2,2] => 1
{{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => [1,1,3,1,1] => 2
{{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => [1,1,2,2,1] => 1
{{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => [1,2,1,3] => 3
{{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => [1,1,2,3] => 2
{{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => [1,2,2,1,1] => 1
{{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => [1,3,2,1] => 2
{{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => [1,2,1,2,1] => 2
{{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => [1,2,1,3] => 3
{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [1,1,1,2,1,1] => 1
{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [1,1,2,2,1] => 1
{{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => [1,2,1,2,1] => 2
{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [1,1,1,1,2,1] => 1
{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [1,1,1,1,3] => 2
{{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => [1,1,2,2,1] => 1
{{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => [1,1,3,2] => 2
{{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => [1,2,1,1,2] => 2
{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [1,1,2,1,2] => 2
{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [1,1,3,1,1] => 2
{{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => [2,4,1] => 2
{{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => [3,2,2] => 0
{{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => [2,3,2] => 1
{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [1,2,1,2,1] => 2
{{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => [3,2,1,1] => 0
{{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => [3,1,2,1] => 1
{{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => [3,1,3] => 2
{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [1,1,2,2,1] => 1
{{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => [2,3,1,1] => 1
{{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => [3,1,2,1] => 1
{{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => [2,2,2,1] => 0
{{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => [2,2,3] => 1
{{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => [1,2,3,1] => 2
{{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => [1,3,1,2] => 3
{{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => [1,2,2,2] => 1
{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [1,2,2,2] => 1
{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [1,3,1,1,1] => 2
{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [4,2,1] => 0
{{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => [5,2] => 0
{{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => [4,1,2] => 1
{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [1,2,2,1,1] => 1
{{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => [4,1,1,1] => 0
{{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => [3,3,1] => 0
{{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => [3,2,2] => 0
{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [1,2,3,1] => 2
{{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => [4,2,1] => 0
{{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => [3,2,1,1] => 0
{{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => [3,3,1] => 0
{{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => [3,4] => 1
{{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => [1,1,1,3,1] => 2
{{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => [1,1,2,1,2] => 2
{{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => [1,2,2,2] => 1
{{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => [1,1,1,2,2] => 1
{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [1,1,1,2,2] => 1
{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [1,1,2,1,1,1] => 1
{{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => [2,2,2,1] => 0
{{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => [3,1,1,2] => 1
{{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => [2,3,2] => 1
{{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => [2,2,1,2] => 1
{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [1,2,2,1,1] => 1
{{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => [4,1,1,1] => 0
{{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => [3,3,1] => 0
{{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => [3,2,2] => 0
{{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => [3,2,2] => 0
{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [1,1,1,2,1,1] => 1
{{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => [2,2,1,1,1] => 0
{{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => [3,2,1,1] => 0
{{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => [2,1,3,1] => 2
{{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => [2,1,2,2] => 1
{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [1,1,1,3,1] => 2
{{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => [2,2,2,1] => 0
{{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => [3,3,1] => 0
{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [2,1,2,1,1] => 1
{{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => [2,1,3,1] => 2
{{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => [2,1,4] => 3
{{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => [1,2,3,1] => 2
{{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => [2,1,2,2] => 1
{{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => [1,3,1,2] => 3
{{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => [1,2,2,2] => 1
{{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => [2,1,2,1,1] => 1
{{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => [2,1,1,2,1] => 1
{{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => [2,2,3] => 1
{{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => [2,1,1,3] => 2
{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [1,4,1,1] => 3
{{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => [2,2,2,1] => 0
{{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => [1,3,2,1] => 2
{{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => [1,3,3] => 2
{{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => [1,2,2,1,1] => 1
{{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => [2,1,1,2,1] => 1
{{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => [1,3,2,1] => 2
{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [1,2,1,2,1] => 2
{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [1,2,1,3] => 3
{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [1,1,1,1,2,1] => 1
{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [1,1,1,2,2] => 1
{{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => [1,1,2,1,2] => 2
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [1,1,1,1,1,2] => 1
{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [1,1,1,2,1,1] => 1
{{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => [2,1,3,1] => 2
{{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => [2,2,1,2] => 1
{{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => [2,1,2,2] => 1
{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [1,1,2,2,1] => 1
{{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => [2,3,1,1] => 1
{{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => [2,2,2,1] => 0
{{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => [2,2,3] => 1
{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [1,1,1,1,2,1] => 1
{{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => [2,1,2,1,1] => 1
{{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => [2,2,2,1] => 0
{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [2,1,1,2,1] => 1
{{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => [2,1,1,3] => 2
{{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => [1,3,2,1] => 2
{{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => [2,2,1,2] => 1
{{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => [1,4,2] => 3
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [1,3,1,2] => 3
{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [1,1,2,1,1,1] => 1
{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [2,2,2,1] => 0
{{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => [2,3,2] => 1
{{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => [2,2,1,2] => 1
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [1,4,1,1] => 3
{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [2,3,1,1] => 1
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [6,1] => 0
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [5,2] => 0
{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [1,3,2,1] => 2
{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [2,2,2,1] => 0
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [5,1,1] => 0
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [4,2,1] => 0
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [4,3] => 0
{{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => [1,2,3,1] => 2
{{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => [2,1,2,2] => 1
{{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => [1,3,1,2] => 3
{{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => [1,2,2,2] => 1
{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [1,2,2,2] => 1
{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [1,1,1,2,1,1] => 1
{{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => [2,1,3,1] => 2
{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [2,2,1,2] => 1
{{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => [2,1,2,2] => 1
{{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => [2,1,2,2] => 1
{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [1,3,1,1,1] => 2
{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [2,2,1,1,1] => 0
{{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => [4,2,1] => 0
{{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => [5,2] => 0
{{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => [4,1,2] => 1
{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [1,2,2,1,1] => 1
{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [2,1,2,1,1] => 1
{{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => [4,1,1,1] => 0
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [3,3,1] => 0
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [3,2,2] => 0
{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [1,2,3,1] => 2
{{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => [2,1,3,1] => 2
{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [4,2,1] => 0
{{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => [3,2,1,1] => 0
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [3,3,1] => 0
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [3,4] => 1
{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [1,5,1] => 4
{{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => [2,3,2] => 1
{{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => [1,2,2,2] => 1
{{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => [1,3,1,2] => 3
{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [1,4,2] => 3
{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [2,3,1,1] => 1
{{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => [2,2,2,1] => 0
{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [3,1,3] => 2
{{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => [2,2,3] => 1
{{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => [2,2,3] => 1
{{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => [1,2,2,1,1] => 1
{{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => [2,1,1,2,1] => 1
{{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => [1,2,1,2,1] => 2
{{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => [1,3,3] => 2
{{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => [1,2,1,3] => 3
{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [1,4,1,1] => 3
{{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => [2,2,2,1] => 0
{{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => [1,2,1,2,1] => 2
{{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => [1,3,2,1] => 2
{{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => [1,3,3] => 2
{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [1,4,1,1] => 3
{{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => [2,2,2,1] => 0
{{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => [1,2,1,2,1] => 2
{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [1,3,2,1] => 2
{{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => [1,3,2,1] => 2
{{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => [1,3,3] => 2
{{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => [1,1,2,2,1] => 1
{{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => [1,1,3,2] => 2
{{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => [1,2,1,1,2] => 2
{{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => [1,1,2,1,2] => 2
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [1,1,2,1,2] => 2
{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [1,1,3,1,1] => 2
{{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => [2,4,1] => 2
{{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => [3,2,2] => 0
{{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => [2,2,1,2] => 1
{{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => [2,3,2] => 1
{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [1,2,1,2,1] => 2
{{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => [3,2,1,1] => 0
{{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => [3,1,2,1] => 1
{{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => [4,3] => 0
{{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => [3,1,3] => 2
{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [1,1,2,2,1] => 1
{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [2,3,1,1] => 1
{{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => [3,1,2,1] => 1
{{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => [2,2,2,1] => 0
{{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => [2,2,3] => 1
{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [1,1,2,2,1] => 1
{{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => [2,3,1,1] => 1
{{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => [3,1,2,1] => 1
{{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => [2,2,2,1] => 0
{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [2,2,2,1] => 0
{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [2,2,3] => 1
{{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => [1,2,1,2,1] => 2
{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [2,1,1,1,2] => 1
{{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => [1,2,2,2] => 1
{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [1,3,1,2] => 3
{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [1,2,1,1,2] => 2
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => 0
{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [2,1,1,2,1] => 1
{{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => [2,1,2,2] => 1
{{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => [2,2,1,2] => 1
{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [2,1,1,1,2] => 1
{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [1,2,2,1,1] => 1
{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [2,1,2,1,1] => 1
{{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => [3,3,1] => 0
{{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => [4,1,2] => 1
{{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => [3,2,2] => 0
{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [1,3,2,1] => 2
{{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => [2,2,2,1] => 0
{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [5,1,1] => 0
{{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => [4,2,1] => 0
{{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => [4,3] => 0
{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [1,2,1,2,1] => 2
{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [2,1,1,2,1] => 1
{{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => [3,2,1,1] => 0
{{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => [4,2,1] => 0
{{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => [3,1,2,1] => 1
{{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => [3,1,3] => 2
{{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => [1,3,2,1] => 2
{{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => [2,2,1,2] => 1
{{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => [1,2,1,1,2] => 2
{{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => [1,4,2] => 3
{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [1,3,1,2] => 3
{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [1,1,2,1,1,1] => 1
{{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => [2,2,2,1] => 0
{{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => [3,1,1,2] => 1
{{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => [2,3,2] => 1
{{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => [2,2,1,2] => 1
{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [1,2,1,1,1,1] => 1
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [2,1,1,1,1,1] => 0
{{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => [3,1,2,1] => 1
{{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => [3,2,2] => 0
{{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => [3,1,1,2] => 1
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [1,4,1,1] => 3
{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [2,3,1,1] => 1
{{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => [3,2,1,1] => 0
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [6,1] => 0
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [5,2] => 0
{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [1,3,2,1] => 2
{{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => [2,2,2,1] => 0
{{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => [3,1,2,1] => 1
{{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => [5,1,1] => 0
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [4,2,1] => 0
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [4,3] => 0
{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [1,5,1] => 4
{{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => [2,3,2] => 1
{{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => [1,2,2,2] => 1
{{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => [1,3,1,2] => 3
{{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => [1,4,2] => 3
{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [1,4,2] => 3
{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [1,1,3,1,1] => 2
{{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => [2,4,1] => 2
{{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => [3,2,2] => 0
{{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => [2,2,1,2] => 1
{{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => [2,3,2] => 1
{{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => [2,3,2] => 1
{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [1,2,2,1,1] => 1
{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [2,1,2,1,1] => 1
{{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => [3,3,1] => 0
{{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => [4,1,2] => 1
{{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => [3,2,2] => 0
{{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => [3,2,2] => 0
{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [1,3,1,1,1] => 2
{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [2,2,1,1,1] => 0
{{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => [3,1,1,1,1] => 0
{{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => [4,2,1] => 0
{{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => [5,2] => 0
{{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => [4,1,2] => 1
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [1,4,1,1] => 3
{{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => [2,3,1,1] => 1
{{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => [3,2,1,1] => 0
{{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => [4,1,1,1] => 0
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [6,1] => 0
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [5,2] => 0
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [1,5,1] => 4
{{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => [2,4,1] => 2
{{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => [3,3,1] => 0
{{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => [4,2,1] => 0
{{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => [5,1,1] => 0
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [6,1] => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [7] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 10,4,1 25,20,6,1 77,71,46,8,1 234,326,222,84,10,1
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 10 + 4\ q + q^{2}$
$F_{5} = 25 + 20\ q + 6\ q^{2} + q^{3}$
$F_{6} = 77 + 71\ q + 46\ q^{2} + 8\ q^{3} + q^{4}$
$F_{7} = 234 + 326\ q + 222\ q^{2} + 84\ q^{3} + 10\ q^{4} + q^{5}$
Description
The descent variation of a composition.
Defined in [1].
Defined in [1].
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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