Identifier
-
Mp00240:
Permutations
—weak exceedance partition⟶
Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000162: Permutations ⟶ ℤ
Values
[1] => {{1}} => [1] => 0
[1,2] => {{1},{2}} => [1,2] => 0
[2,1] => {{1,2}} => [2,1] => 1
[1,2,3] => {{1},{2},{3}} => [1,2,3] => 0
[1,3,2] => {{1},{2,3}} => [1,3,2] => 1
[2,1,3] => {{1,2},{3}} => [2,1,3] => 1
[2,3,1] => {{1,2,3}} => [2,3,1] => 1
[3,1,2] => {{1,3},{2}} => [3,2,1] => 1
[3,2,1] => {{1,3},{2}} => [3,2,1] => 1
[1,2,3,4] => {{1},{2},{3},{4}} => [1,2,3,4] => 0
[1,2,4,3] => {{1},{2},{3,4}} => [1,2,4,3] => 1
[1,3,2,4] => {{1},{2,3},{4}} => [1,3,2,4] => 1
[1,3,4,2] => {{1},{2,3,4}} => [1,3,4,2] => 1
[1,4,2,3] => {{1},{2,4},{3}} => [1,4,3,2] => 1
[1,4,3,2] => {{1},{2,4},{3}} => [1,4,3,2] => 1
[2,1,3,4] => {{1,2},{3},{4}} => [2,1,3,4] => 1
[2,1,4,3] => {{1,2},{3,4}} => [2,1,4,3] => 2
[2,3,1,4] => {{1,2,3},{4}} => [2,3,1,4] => 1
[2,3,4,1] => {{1,2,3,4}} => [2,3,4,1] => 1
[2,4,1,3] => {{1,2,4},{3}} => [2,4,3,1] => 1
[2,4,3,1] => {{1,2,4},{3}} => [2,4,3,1] => 1
[3,1,2,4] => {{1,3},{2},{4}} => [3,2,1,4] => 1
[3,1,4,2] => {{1,3,4},{2}} => [3,2,4,1] => 1
[3,2,1,4] => {{1,3},{2},{4}} => [3,2,1,4] => 1
[3,2,4,1] => {{1,3,4},{2}} => [3,2,4,1] => 1
[3,4,1,2] => {{1,3},{2,4}} => [3,4,1,2] => 2
[3,4,2,1] => {{1,3},{2,4}} => [3,4,1,2] => 2
[4,1,2,3] => {{1,4},{2},{3}} => [4,2,3,1] => 1
[4,1,3,2] => {{1,4},{2},{3}} => [4,2,3,1] => 1
[4,2,1,3] => {{1,4},{2},{3}} => [4,2,3,1] => 1
[4,2,3,1] => {{1,4},{2},{3}} => [4,2,3,1] => 1
[4,3,1,2] => {{1,4},{2,3}} => [4,3,2,1] => 2
[4,3,2,1] => {{1,4},{2,3}} => [4,3,2,1] => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
[1,2,3,5,4] => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => 1
[1,2,4,3,5] => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => 1
[1,2,4,5,3] => {{1},{2},{3,4,5}} => [1,2,4,5,3] => 1
[1,2,5,3,4] => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => 1
[1,2,5,4,3] => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => 1
[1,3,2,4,5] => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
[1,3,2,5,4] => {{1},{2,3},{4,5}} => [1,3,2,5,4] => 2
[1,3,4,2,5] => {{1},{2,3,4},{5}} => [1,3,4,2,5] => 1
[1,3,4,5,2] => {{1},{2,3,4,5}} => [1,3,4,5,2] => 1
[1,3,5,2,4] => {{1},{2,3,5},{4}} => [1,3,5,4,2] => 1
[1,3,5,4,2] => {{1},{2,3,5},{4}} => [1,3,5,4,2] => 1
[1,4,2,3,5] => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => 1
[1,4,2,5,3] => {{1},{2,4,5},{3}} => [1,4,3,5,2] => 1
[1,4,3,2,5] => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => 1
[1,4,3,5,2] => {{1},{2,4,5},{3}} => [1,4,3,5,2] => 1
[1,4,5,2,3] => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 2
[1,4,5,3,2] => {{1},{2,4},{3,5}} => [1,4,5,2,3] => 2
[1,5,2,3,4] => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 1
[1,5,2,4,3] => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 1
[1,5,3,2,4] => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 1
[1,5,3,4,2] => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => 1
[1,5,4,2,3] => {{1},{2,5},{3,4}} => [1,5,4,3,2] => 2
[1,5,4,3,2] => {{1},{2,5},{3,4}} => [1,5,4,3,2] => 2
[2,1,3,4,5] => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => 1
[2,1,3,5,4] => {{1,2},{3},{4,5}} => [2,1,3,5,4] => 2
[2,1,4,3,5] => {{1,2},{3,4},{5}} => [2,1,4,3,5] => 2
[2,1,4,5,3] => {{1,2},{3,4,5}} => [2,1,4,5,3] => 2
[2,1,5,3,4] => {{1,2},{3,5},{4}} => [2,1,5,4,3] => 2
[2,1,5,4,3] => {{1,2},{3,5},{4}} => [2,1,5,4,3] => 2
[2,3,1,4,5] => {{1,2,3},{4},{5}} => [2,3,1,4,5] => 1
[2,3,1,5,4] => {{1,2,3},{4,5}} => [2,3,1,5,4] => 2
[2,3,4,1,5] => {{1,2,3,4},{5}} => [2,3,4,1,5] => 1
[2,3,4,5,1] => {{1,2,3,4,5}} => [2,3,4,5,1] => 1
[2,3,5,1,4] => {{1,2,3,5},{4}} => [2,3,5,4,1] => 1
[2,3,5,4,1] => {{1,2,3,5},{4}} => [2,3,5,4,1] => 1
[2,4,1,3,5] => {{1,2,4},{3},{5}} => [2,4,3,1,5] => 1
[2,4,1,5,3] => {{1,2,4,5},{3}} => [2,4,3,5,1] => 1
[2,4,3,1,5] => {{1,2,4},{3},{5}} => [2,4,3,1,5] => 1
[2,4,3,5,1] => {{1,2,4,5},{3}} => [2,4,3,5,1] => 1
[2,4,5,1,3] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 2
[2,4,5,3,1] => {{1,2,4},{3,5}} => [2,4,5,1,3] => 2
[2,5,1,3,4] => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 1
[2,5,1,4,3] => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 1
[2,5,3,1,4] => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 1
[2,5,3,4,1] => {{1,2,5},{3},{4}} => [2,5,3,4,1] => 1
[2,5,4,1,3] => {{1,2,5},{3,4}} => [2,5,4,3,1] => 2
[2,5,4,3,1] => {{1,2,5},{3,4}} => [2,5,4,3,1] => 2
[3,1,2,4,5] => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => 1
[3,1,2,5,4] => {{1,3},{2},{4,5}} => [3,2,1,5,4] => 2
[3,1,4,2,5] => {{1,3,4},{2},{5}} => [3,2,4,1,5] => 1
[3,1,4,5,2] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 1
[3,1,5,2,4] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 1
[3,1,5,4,2] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 1
[3,2,1,4,5] => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => 1
[3,2,1,5,4] => {{1,3},{2},{4,5}} => [3,2,1,5,4] => 2
[3,2,4,1,5] => {{1,3,4},{2},{5}} => [3,2,4,1,5] => 1
[3,2,4,5,1] => {{1,3,4,5},{2}} => [3,2,4,5,1] => 1
[3,2,5,1,4] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 1
[3,2,5,4,1] => {{1,3,5},{2},{4}} => [3,2,5,4,1] => 1
[3,4,1,2,5] => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 2
[3,4,1,5,2] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 2
[3,4,2,1,5] => {{1,3},{2,4},{5}} => [3,4,1,2,5] => 2
[3,4,2,5,1] => {{1,3},{2,4,5}} => [3,4,1,5,2] => 2
[3,4,5,1,2] => {{1,3,5},{2,4}} => [3,4,5,2,1] => 2
[3,4,5,2,1] => {{1,3,5},{2,4}} => [3,4,5,2,1] => 2
[3,5,1,2,4] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
[3,5,1,4,2] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
>>> Load all 873 entries. <<<[3,5,2,1,4] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
[3,5,2,4,1] => {{1,3},{2,5},{4}} => [3,5,1,4,2] => 2
[3,5,4,1,2] => {{1,3,4},{2,5}} => [3,5,4,1,2] => 2
[3,5,4,2,1] => {{1,3,4},{2,5}} => [3,5,4,1,2] => 2
[4,1,2,3,5] => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 1
[4,1,2,5,3] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 1
[4,1,3,2,5] => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 1
[4,1,3,5,2] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 1
[4,1,5,2,3] => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
[4,1,5,3,2] => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
[4,2,1,3,5] => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 1
[4,2,1,5,3] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 1
[4,2,3,1,5] => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => 1
[4,2,3,5,1] => {{1,4,5},{2},{3}} => [4,2,3,5,1] => 1
[4,2,5,1,3] => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
[4,2,5,3,1] => {{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
[4,3,1,2,5] => {{1,4},{2,3},{5}} => [4,3,2,1,5] => 2
[4,3,1,5,2] => {{1,4,5},{2,3}} => [4,3,2,5,1] => 2
[4,3,2,1,5] => {{1,4},{2,3},{5}} => [4,3,2,1,5] => 2
[4,3,2,5,1] => {{1,4,5},{2,3}} => [4,3,2,5,1] => 2
[4,3,5,1,2] => {{1,4},{2,3,5}} => [4,3,5,1,2] => 2
[4,3,5,2,1] => {{1,4},{2,3,5}} => [4,3,5,1,2] => 2
[4,5,1,2,3] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[4,5,1,3,2] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[4,5,2,1,3] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[4,5,2,3,1] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[4,5,3,1,2] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[4,5,3,2,1] => {{1,4},{2,5},{3}} => [4,5,3,1,2] => 2
[5,1,2,3,4] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,1,2,4,3] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,1,3,2,4] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,1,3,4,2] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,1,4,2,3] => {{1,5},{2},{3,4}} => [5,2,4,3,1] => 2
[5,1,4,3,2] => {{1,5},{2},{3,4}} => [5,2,4,3,1] => 2
[5,2,1,3,4] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,2,1,4,3] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,2,3,1,4] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,2,3,4,1] => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
[5,2,4,1,3] => {{1,5},{2},{3,4}} => [5,2,4,3,1] => 2
[5,2,4,3,1] => {{1,5},{2},{3,4}} => [5,2,4,3,1] => 2
[5,3,1,2,4] => {{1,5},{2,3},{4}} => [5,3,2,4,1] => 2
[5,3,1,4,2] => {{1,5},{2,3},{4}} => [5,3,2,4,1] => 2
[5,3,2,1,4] => {{1,5},{2,3},{4}} => [5,3,2,4,1] => 2
[5,3,2,4,1] => {{1,5},{2,3},{4}} => [5,3,2,4,1] => 2
[5,3,4,1,2] => {{1,5},{2,3,4}} => [5,3,4,2,1] => 2
[5,3,4,2,1] => {{1,5},{2,3,4}} => [5,3,4,2,1] => 2
[5,4,1,2,3] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[5,4,1,3,2] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[5,4,2,1,3] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[5,4,2,3,1] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[5,4,3,1,2] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[5,4,3,2,1] => {{1,5},{2,4},{3}} => [5,4,3,2,1] => 2
[1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => 1
[1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => 1
[1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => 1
[1,2,5,3,6,4] => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => 1
[1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => 2
[1,2,6,3,4,5] => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 1
[1,2,6,3,5,4] => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 1
[1,2,6,4,3,5] => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 1
[1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => 1
[1,2,6,5,3,4] => {{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => 2
[1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => 2
[1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => 2
[1,3,2,6,4,5] => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => 2
[1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => 1
[1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => 1
[1,3,5,2,6,4] => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 1
[1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => 2
[1,3,6,2,4,5] => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 1
[1,3,6,2,5,4] => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 1
[1,3,6,4,2,5] => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 1
[1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => 1
[1,3,6,5,2,4] => {{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => 2
[1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => 1
[1,4,2,3,6,5] => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => 2
[1,4,2,5,3,6] => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => 1
[1,4,2,5,6,3] => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => 1
[1,4,2,6,3,5] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 1
[1,4,2,6,5,3] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 1
[1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 1
[1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => 1
[1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => 2
[1,4,5,3,6,2] => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => 2
[1,4,5,6,2,3] => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => 2
[1,4,5,6,3,2] => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => 2
[1,4,6,2,3,5] => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 2
[1,4,6,2,5,3] => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 2
[1,4,6,3,2,5] => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 2
[1,4,6,3,5,2] => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => 2
[1,4,6,5,2,3] => {{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => {{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => 2
[1,5,2,3,4,6] => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 1
[1,5,2,3,6,4] => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 1
[1,5,2,4,3,6] => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 1
[1,5,2,4,6,3] => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 1
[1,5,2,6,3,4] => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 2
[1,5,2,6,4,3] => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 2
[1,5,3,2,4,6] => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 1
[1,5,3,2,6,4] => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 1
[1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => 1
[1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 2
[1,5,3,6,4,2] => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => 2
[1,5,4,2,3,6] => {{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => 2
[1,5,4,2,6,3] => {{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => 2
[1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => 2
[1,5,4,6,2,3] => {{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => 2
[1,5,4,6,3,2] => {{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => 2
[1,5,6,2,3,4] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,5,6,2,4,3] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,5,6,3,2,4] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,5,6,3,4,2] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,5,6,4,2,3] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,5,6,4,3,2] => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => 2
[1,6,2,3,4,5] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,2,3,5,4] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,2,4,3,5] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,2,4,5,3] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,2,5,3,4] => {{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => 2
[1,6,2,5,4,3] => {{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => 2
[1,6,3,2,4,5] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,3,2,5,4] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,3,4,2,5] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => {{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => 2
[1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => {{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => 2
[1,6,4,2,5,3] => {{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => 2
[1,6,4,3,2,5] => {{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => 2
[1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => {{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => 2
[1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => 2
[1,6,5,2,3,4] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[1,6,5,2,4,3] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[1,6,5,3,2,4] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[1,6,5,3,4,2] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[1,6,5,4,2,3] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => 2
[2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => 2
[2,1,3,6,4,5] => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => 2
[2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => 2
[2,1,4,6,3,5] => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => 2
[2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => 2
[2,1,5,3,6,4] => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => 2
[2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => 3
[2,1,6,3,4,5] => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 2
[2,1,6,3,5,4] => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 2
[2,1,6,4,3,5] => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 2
[2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => {{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => 3
[2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => 3
[2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 2
[2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 2
[2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 1
[2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 1
[2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 1
[2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 2
[2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 1
[2,3,6,1,5,4] => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 1
[2,3,6,4,1,5] => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 1
[2,3,6,4,5,1] => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 1
[2,3,6,5,1,4] => {{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 2
[2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 2
[2,4,1,3,5,6] => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 1
[2,4,1,3,6,5] => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 2
[2,4,1,5,3,6] => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 1
[2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 1
[2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 1
[2,4,1,6,5,3] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 1
[2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 1
[2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 2
[2,4,5,3,6,1] => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 2
[2,4,5,6,1,3] => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 2
[2,4,5,6,3,1] => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
[2,4,6,1,5,3] => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
[2,4,6,3,5,1] => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
[2,4,6,5,1,3] => {{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => 2
[2,4,6,5,3,1] => {{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => 2
[2,5,1,3,4,6] => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 1
[2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 1
[2,5,1,4,3,6] => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 1
[2,5,1,4,6,3] => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 1
[2,5,1,6,3,4] => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 2
[2,5,1,6,4,3] => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 2
[2,5,3,1,4,6] => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 1
[2,5,3,1,6,4] => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 1
[2,5,3,4,1,6] => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => 1
[2,5,3,4,6,1] => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => 2
[2,5,4,1,3,6] => {{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => 2
[2,5,4,1,6,3] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 2
[2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 2
[2,5,4,6,1,3] => {{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => {{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => 2
[2,5,6,1,3,4] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,5,6,1,4,3] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,5,6,3,1,4] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,5,6,3,4,1] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,5,6,4,1,3] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => 2
[2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,1,3,5,4] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,1,4,3,5] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,1,4,5,3] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,1,5,3,4] => {{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => 2
[2,6,1,5,4,3] => {{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => 2
[2,6,3,1,4,5] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,3,1,5,4] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,3,4,1,5] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,3,4,5,1] => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => {{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => 2
[2,6,3,5,4,1] => {{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => 2
[2,6,4,1,3,5] => {{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => 2
[2,6,4,1,5,3] => {{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => 2
[2,6,4,3,1,5] => {{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => 2
[2,6,4,3,5,1] => {{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => {{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => 2
[2,6,4,5,3,1] => {{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => 2
[2,6,5,1,3,4] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[2,6,5,1,4,3] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[2,6,5,3,1,4] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[2,6,5,3,4,1] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[2,6,5,4,1,3] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => 1
[3,1,2,4,6,5] => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => 2
[3,1,2,5,4,6] => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => 2
[3,1,2,5,6,4] => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => 2
[3,1,2,6,4,5] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[3,1,2,6,5,4] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[3,1,4,2,5,6] => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => 1
[3,1,4,2,6,5] => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => 2
[3,1,4,5,2,6] => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => 1
[3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 1
[3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 1
[3,1,4,6,5,2] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 1
[3,1,5,2,4,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 1
[3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 1
[3,1,5,4,2,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 1
[3,1,5,4,6,2] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 1
[3,1,5,6,2,4] => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 2
[3,1,5,6,4,2] => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 2
[3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,1,6,2,5,4] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,1,6,4,2,5] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,1,6,4,5,2] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,1,6,5,2,4] => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => 2
[3,1,6,5,4,2] => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => 2
[3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => 2
[3,2,1,6,4,5] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 1
[3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 1
[3,2,5,1,6,4] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 1
[3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 2
[3,2,5,6,4,1] => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => 2
[3,2,6,1,4,5] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,2,6,1,5,4] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,2,6,4,1,5] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,2,6,4,5,1] => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => 1
[3,2,6,5,1,4] => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => 2
[3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => 2
[3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 3
[3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 2
[3,4,1,6,2,5] => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 2
[3,4,1,6,5,2] => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 2
[3,4,2,1,5,6] => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => 2
[3,4,2,1,6,5] => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => 3
[3,4,2,5,1,6] => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => 2
[3,4,2,5,6,1] => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => 2
[3,4,2,6,1,5] => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 2
[3,4,2,6,5,1] => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => 2
[3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => 2
[3,4,5,1,6,2] => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => 2
[3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => 2
[3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => 2
[3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => 2
[3,4,6,1,2,5] => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 2
[3,4,6,1,5,2] => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 2
[3,4,6,2,1,5] => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 2
[3,4,6,2,5,1] => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => {{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => 2
[3,4,6,5,2,1] => {{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => 2
[3,5,1,2,4,6] => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 2
[3,5,1,2,6,4] => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 2
[3,5,1,4,2,6] => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 2
[3,5,1,4,6,2] => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 2
[3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 3
[3,5,2,1,4,6] => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 2
[3,5,2,1,6,4] => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 2
[3,5,2,4,1,6] => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => 2
[3,5,2,4,6,1] => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => 2
[3,5,2,6,1,4] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 3
[3,5,2,6,4,1] => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => 3
[3,5,4,1,2,6] => {{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => {{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => {{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => 2
[3,5,4,2,6,1] => {{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => 2
[3,5,4,6,1,2] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 2
[3,5,4,6,2,1] => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => 2
[3,5,6,1,2,4] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,5,6,1,4,2] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,5,6,2,1,4] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,5,6,2,4,1] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,5,6,4,1,2] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,5,6,4,2,1] => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,1,2,5,4] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,1,4,2,5] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,1,4,5,2] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,1,5,2,4] => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => 3
[3,6,1,5,4,2] => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => 3
[3,6,2,1,4,5] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,2,1,5,4] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,2,4,1,5] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,2,4,5,1] => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => 2
[3,6,2,5,1,4] => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => 3
[3,6,2,5,4,1] => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => 3
[3,6,4,1,2,5] => {{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => 2
[3,6,4,1,5,2] => {{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => {{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => 2
[3,6,4,2,5,1] => {{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => 2
[3,6,4,5,1,2] => {{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => 2
[3,6,4,5,2,1] => {{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => 2
[3,6,5,1,2,4] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[3,6,5,1,4,2] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[3,6,5,2,1,4] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[3,6,5,2,4,1] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[3,6,5,4,1,2] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => 2
[4,1,2,3,5,6] => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 1
[4,1,2,3,6,5] => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 2
[4,1,2,5,3,6] => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 1
[4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 1
[4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,1,2,6,5,3] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,1,3,2,5,6] => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 1
[4,1,3,2,6,5] => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 2
[4,1,3,5,2,6] => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 1
[4,1,3,5,6,2] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 1
[4,1,3,6,2,5] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,1,3,6,5,2] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,1,5,2,3,6] => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 2
[4,1,5,2,6,3] => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 2
[4,1,5,3,2,6] => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 2
[4,1,5,3,6,2] => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 2
[4,1,5,6,2,3] => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 2
[4,1,5,6,3,2] => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 2
[4,1,6,2,3,5] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,1,6,2,5,3] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,1,6,3,2,5] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,1,6,3,5,2] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,1,6,5,2,3] => {{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => 2
[4,1,6,5,3,2] => {{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => 2
[4,2,1,3,5,6] => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 1
[4,2,1,3,6,5] => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 2
[4,2,1,5,3,6] => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 1
[4,2,1,5,6,3] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 1
[4,2,1,6,3,5] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,2,1,6,5,3] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => 1
[4,2,3,6,1,5] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,2,3,6,5,1] => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => 1
[4,2,5,1,3,6] => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 2
[4,2,5,1,6,3] => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => 2
[4,2,5,3,6,1] => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => 2
[4,2,5,6,1,3] => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 2
[4,2,5,6,3,1] => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,2,6,1,5,3] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,2,6,3,5,1] => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => 2
[4,2,6,5,1,3] => {{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => {{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => 2
[4,3,1,2,5,6] => {{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => 2
[4,3,1,2,6,5] => {{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => 3
[4,3,1,5,2,6] => {{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => 2
[4,3,1,5,6,2] => {{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => 2
[4,3,1,6,2,5] => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => 2
[4,3,1,6,5,2] => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => 2
[4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => 2
[4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => 3
[4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => 2
[4,3,2,6,1,5] => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => 2
[4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => 2
[4,3,5,1,2,6] => {{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => {{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => {{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => 2
[4,3,5,2,6,1] => {{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => 2
[4,3,5,6,1,2] => {{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => 2
[4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => 2
[4,3,6,1,2,5] => {{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => 2
[4,3,6,1,5,2] => {{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => {{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => 2
[4,3,6,2,5,1] => {{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => 2
[4,3,6,5,1,2] => {{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => 2
[4,3,6,5,2,1] => {{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => 2
[4,5,1,2,3,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,1,2,6,3] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,1,3,2,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,1,3,6,2] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,1,6,2,3] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,1,6,3,2] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,2,1,3,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,2,1,6,3] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,2,3,1,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,2,3,6,1] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,2,6,1,3] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,2,6,3,1] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,3,1,6,2] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => 2
[4,5,3,2,6,1] => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => 2
[4,5,3,6,1,2] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => 2
[4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,5,6,2,1,3] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,5,6,2,3,1] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,5,6,3,1,2] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,5,6,3,2,1] => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => 3
[4,6,1,2,3,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,1,2,5,3] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,1,3,2,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,1,3,5,2] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,1,5,2,3] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,1,5,3,2] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,2,1,3,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,2,1,5,3] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,2,3,1,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,2,3,5,1] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,2,5,1,3] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,2,5,3,1] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,3,1,2,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,3,1,5,2] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,3,2,1,5] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,3,2,5,1] => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => 2
[4,6,3,5,1,2] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => 2
[4,6,5,1,2,3] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[4,6,5,1,3,2] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[4,6,5,2,1,3] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[4,6,5,2,3,1] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[4,6,5,3,1,2] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[4,6,5,3,2,1] => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => 3
[5,1,2,3,4,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,1,2,4,3,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,1,2,4,6,3] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,1,2,6,3,4] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,1,2,6,4,3] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,1,3,2,4,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,1,3,2,6,4] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,1,3,4,2,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,1,3,4,6,2] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,1,3,6,2,4] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,1,3,6,4,2] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,1,4,2,3,6] => {{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => 2
[5,1,4,2,6,3] => {{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => 2
[5,1,4,3,2,6] => {{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => 2
[5,1,4,3,6,2] => {{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => 2
[5,1,4,6,2,3] => {{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => 2
[5,1,4,6,3,2] => {{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => 2
[5,1,6,2,3,4] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,1,6,2,4,3] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,1,6,3,2,4] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,1,6,3,4,2] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,1,6,4,2,3] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,1,6,4,3,2] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,1,3,4,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,2,1,3,6,4] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,2,1,4,3,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,2,1,4,6,3] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,2,1,6,3,4] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,2,1,6,4,3] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,2,3,1,4,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,2,3,1,6,4] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => 2
[5,2,4,1,3,6] => {{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => 2
[5,2,4,1,6,3] => {{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => 2
[5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => 2
[5,2,4,6,1,3] => {{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => {{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => 2
[5,2,6,1,3,4] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,6,1,4,3] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,6,3,1,4] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,6,3,4,1] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,6,4,1,3] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,2,6,4,3,1] => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => 2
[5,3,1,2,4,6] => {{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => 2
[5,3,1,2,6,4] => {{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => 2
[5,3,1,4,2,6] => {{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => 2
[5,3,1,4,6,2] => {{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => 2
[5,3,1,6,2,4] => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => 3
[5,3,1,6,4,2] => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => 3
[5,3,2,1,4,6] => {{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => 2
[5,3,2,1,6,4] => {{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => 2
[5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => 2
[5,3,2,6,1,4] => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => 3
[5,3,2,6,4,1] => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => 3
[5,3,4,1,2,6] => {{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => 2
[5,3,4,1,6,2] => {{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => 2
[5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => 2
[5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => 2
[5,3,4,6,1,2] => {{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => 2
[5,3,4,6,2,1] => {{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => 2
[5,3,6,1,2,4] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,3,6,1,4,2] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,3,6,2,1,4] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,3,6,2,4,1] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,3,6,4,1,2] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => 2
[5,4,1,2,3,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,1,2,6,3] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,1,3,2,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,1,3,6,2] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,1,6,2,3] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,1,6,3,2] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,2,1,3,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,2,1,6,3] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,2,3,1,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,2,3,6,1] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,2,6,1,3] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,2,6,3,1] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,3,1,2,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,3,1,6,2] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => 2
[5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => 2
[5,4,3,6,1,2] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => 2
[5,4,6,1,2,3] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,4,6,1,3,2] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,4,6,2,1,3] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,4,6,2,3,1] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,4,6,3,1,2] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,4,6,3,2,1] => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => 3
[5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,1,2,4,3] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,1,3,2,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,1,3,4,2] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,1,4,2,3] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,1,4,3,2] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,1,3,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,1,4,3] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,3,1,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,3,4,1] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,4,1,3] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,2,4,3,1] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,1,2,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,1,4,2] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,2,1,4] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,2,4,1] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => 2
[5,6,4,1,2,3] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[5,6,4,1,3,2] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[5,6,4,2,1,3] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[5,6,4,2,3,1] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[5,6,4,3,1,2] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[5,6,4,3,2,1] => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => 3
[6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,2,3,5,4] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,2,4,3,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,2,4,5,3] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,2,5,3,4] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,1,2,5,4,3] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,1,3,2,4,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,3,2,5,4] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,3,4,2,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,3,4,5,2] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,1,3,5,2,4] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,1,3,5,4,2] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,1,4,2,3,5] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,1,4,2,5,3] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,1,4,3,2,5] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,1,4,3,5,2] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,1,4,5,2,3] => {{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => 2
[6,1,4,5,3,2] => {{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => 2
[6,1,5,2,3,4] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,1,5,2,4,3] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,1,5,3,2,4] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,1,5,3,4,2] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,1,5,4,2,3] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,1,5,4,3,2] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,1,3,4,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,1,3,5,4] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,1,4,3,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,1,4,5,3] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,1,5,3,4] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,2,1,5,4,3] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,2,3,1,4,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,3,1,5,4] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,3,4,1,5] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => 2
[6,2,4,1,3,5] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,2,4,1,5,3] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,2,4,3,1,5] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => {{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => 2
[6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,5,1,4,3] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,5,3,1,4] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,5,3,4,1] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,5,4,1,3] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,2,5,4,3,1] => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,1,2,5,4] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,1,4,2,5] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,1,4,5,2] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,1,5,2,4] => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => 3
[6,3,1,5,4,2] => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => 3
[6,3,2,1,4,5] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,2,1,5,4] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,2,4,1,5] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => 2
[6,3,2,5,1,4] => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => 3
[6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => 3
[6,3,4,1,2,5] => {{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => 2
[6,3,4,1,5,2] => {{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => 2
[6,3,4,2,1,5] => {{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => 2
[6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => 2
[6,3,4,5,1,2] => {{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => 2
[6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => 2
[6,3,5,1,2,4] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,3,5,1,4,2] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,3,5,2,1,4] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,3,5,2,4,1] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,3,5,4,1,2] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,3,5,4,2,1] => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => 2
[6,4,1,2,3,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,1,2,5,3] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,1,3,2,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,1,3,5,2] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,1,5,2,3] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,1,5,3,2] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,2,1,3,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,2,1,5,3] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,2,3,1,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,2,3,5,1] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,2,5,1,3] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,2,5,3,1] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,3,1,2,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,3,1,5,2] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,3,2,1,5] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => 2
[6,4,3,5,1,2] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => 2
[6,4,5,1,2,3] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,4,5,1,3,2] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,4,5,2,1,3] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,4,5,2,3,1] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,4,5,3,1,2] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,4,5,3,2,1] => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => 3
[6,5,1,2,3,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,1,2,4,3] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,1,3,2,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,1,3,4,2] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,1,4,2,3] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,1,4,3,2] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,1,3,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,1,4,3] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,3,1,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,3,4,1] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,4,1,3] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,2,4,3,1] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,1,2,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,1,4,2] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,2,1,4] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,2,4,1] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,4,1,2] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
[6,5,4,1,3,2] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
[6,5,4,2,1,3] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
[6,5,4,2,3,1] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
[6,5,4,3,1,2] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
[6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => 3
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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 1,5 1,18,5 1,58,61 1,179,479,61
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 5\ q$
$F_{4} = 1 + 18\ q + 5\ q^{2}$
$F_{5} = 1 + 58\ q + 61\ q^{2}$
$F_{6} = 1 + 179\ q + 479\ q^{2} + 61\ q^{3}$
Description
The number of nontrivial cycles in the cycle decomposition of a permutation.
This statistic is equal to the difference of the number of cycles of $\pi$ (see St000031The number of cycles in the cycle decomposition of a permutation.) and the number of fixed points of $\pi$ (see St000022The number of fixed points of a permutation.).
This statistic is equal to the difference of the number of cycles of $\pi$ (see St000031The number of cycles in the cycle decomposition of a permutation.) and the number of fixed points of $\pi$ (see St000022The number of fixed points of a permutation.).
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to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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