Identifier
Values
{{1,2}} => [2,1] => [2,1] => [2,1] => 1
{{1},{2}} => [1,2] => [1,2] => [1,2] => 1
{{1,2,3}} => [2,3,1] => [3,1,2] => [1,3,2] => 1
{{1,2},{3}} => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}} => [3,2,1] => [3,2,1] => [3,2,1] => 1
{{1},{2,3}} => [1,3,2] => [1,3,2] => [3,1,2] => 2
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 1
{{1,2,3,4}} => [2,3,4,1] => [4,1,2,3] => [1,2,4,3] => 1
{{1,2,3},{4}} => [2,3,1,4] => [3,1,2,4] => [1,3,2,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [4,3,1,2] => [1,4,3,2] => 1
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [2,4,1,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}} => [3,2,4,1] => [4,1,3,2] => [4,1,3,2] => 2
{{1,3},{2,4}} => [3,4,1,2] => [2,4,1,3] => [4,2,1,3] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 1
{{1},{2,3,4}} => [1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [3,1,2,4] => 2
{{1,4},{2},{3}} => [4,2,3,1] => [3,1,4,2] => [1,3,4,2] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 3
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 2
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 1
{{1,2,3,4,5}} => [2,3,4,5,1] => [5,1,2,3,4] => [1,2,3,5,4] => 1
{{1,2,3,4},{5}} => [2,3,4,1,5] => [4,1,2,3,5] => [1,2,4,3,5] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => [5,4,1,2,3] => [1,2,5,4,3] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,1,2,5,4] => [1,3,5,2,4] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [5,1,2,4,3] => [5,1,2,4,3] => 4
{{1,2,4},{3,5}} => [2,4,5,1,3] => [3,5,1,2,4] => [1,5,3,2,4] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [4,3,1,2,5] => [1,4,3,2,5] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [5,4,3,1,2] => [1,5,4,3,2] => 1
{{1,2},{3,4,5}} => [2,1,4,5,3] => [2,1,5,3,4] => [5,2,1,3,4] => 4
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [2,1,4,3,5] => [2,4,1,3,5] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [4,1,2,5,3] => [1,2,4,5,3] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [2,1,5,4,3] => [5,2,4,1,3] => 6
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [2,1,3,5,4] => [2,5,1,3,4] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [5,1,3,2,4] => [3,1,2,5,4] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [2,5,4,1,3] => [5,4,2,1,3] => 3
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [4,1,3,2,5] => [4,1,3,2,5] => 2
{{1,3,5},{2,4}} => [3,4,5,2,1] => [5,2,1,3,4] => [2,1,3,5,4] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => [5,2,4,1,3] => [5,2,1,4,3] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [2,4,1,3,5] => [4,2,1,3,5] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [5,4,1,3,2] => [5,1,4,3,2] => 2
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [4,2,5,1,3] => [2,4,1,5,3] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,5,1,4] => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [5,1,4,3,2] => [5,4,1,3,2] => 3
{{1,4},{2,3,5}} => [4,3,5,1,2] => [2,5,1,4,3] => [2,5,4,1,3] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,2,1,5,3] => [2,1,4,5,3] => 2
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => 2
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [4,1,5,3,2] => [4,5,1,3,2] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,5,4,2,3] => [1,5,4,2,3] => 3
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [3,5,1,2,4] => 4
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => 2
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [5,1,3,4,2] => [1,5,3,4,2] => 3
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [2,5,3,1,4] => [2,5,3,1,4] => 4
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [3,5,1,4,2] => [3,5,1,4,2] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [3,1,4,2,5] => [1,3,4,2,5] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,5,2,4,3] => [5,1,4,2,3] => 4
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,3,5,2,4] => [5,3,1,2,4] => 4
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => 3
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [4,3,1,5,2] => [1,4,3,5,2] => 2
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 4
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,5,3,4] => [1,5,2,3,4] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => 2
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [4,1,3,5,2] => [4,1,3,5,2] => 4
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,4,2,5,3] => [1,4,5,2,3] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 3
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 4
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,2,3,4,6,5] => 1
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,2,3,5,4,6] => 1
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [6,5,1,2,3,4] => [1,2,3,6,5,4] => 1
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,2,4,6,3,5] => 2
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,2,4,3,5,6] => 1
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [6,1,2,3,5,4] => [6,1,2,3,5,4] => 2
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [4,6,1,2,3,5] => [1,2,6,4,3,5] => 2
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [5,4,1,2,3,6] => [1,2,5,4,3,6] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [6,5,4,1,2,3] => [1,2,6,5,4,3] => 1
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [3,1,6,2,4,5] => 2
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,3,5,2,4,6] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [5,1,2,3,6,4] => [1,2,3,5,6,4] => 2
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [6,1,3,5,2,4] => 8
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,3,6,2,4,5] => 2
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => 1
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [6,1,2,4,3,5] => [4,1,2,3,6,5] => 2
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [3,6,5,1,2,4] => [1,6,5,3,2,4] => 3
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [5,1,2,4,3,6] => [5,1,2,4,3,6] => 4
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [6,3,1,2,4,5] => [1,3,2,4,6,5] => 1
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [6,3,5,1,2,4] => [1,6,3,2,5,4] => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [3,5,1,2,4,6] => [1,5,3,2,4,6] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [6,5,1,2,4,3] => [6,1,2,5,4,3] => 4
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [5,3,6,1,2,4] => [3,1,5,2,6,4] => 2
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [4,3,1,2,6,5] => [1,4,3,6,2,5] => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [4,3,1,2,5,6] => [1,4,3,2,5,6] => 1
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [6,1,2,5,4,3] => [6,5,1,2,4,3] => 7
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [3,6,1,2,5,4] => [1,3,6,5,2,4] => 2
>>> Load all 403 entries. <<<
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [5,4,3,1,2,6] => [1,5,4,3,2,6] => 1
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [5,3,1,2,6,4] => [1,3,2,5,6,4] => 2
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 2
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [5,2,1,3,4,6] => 4
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [5,1,2,6,4,3] => [5,6,1,2,4,3] => 3
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [2,1,6,5,3,4] => [6,5,2,1,3,4] => 7
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => 8
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => 2
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [6,1,2,4,5,3] => [1,6,2,4,5,3] => 4
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [3,6,4,1,2,5] => [3,1,6,4,2,5] => 4
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [4,6,1,2,5,3] => [1,4,6,2,5,3] => 1
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [4,1,2,5,3,6] => [1,2,4,5,3,6] => 2
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [6,5,4,3,1,2] => [1,6,5,4,3,2] => 1
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [2,1,6,3,5,4] => [2,6,5,1,3,4] => 2
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [2,1,4,6,3,5] => [6,2,4,1,3,5] => 8
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => 6
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [5,4,1,2,6,3] => [1,2,5,4,6,3] => 2
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => 12
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [6,2,1,3,4,5] => 2
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => 2
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [5,1,2,4,6,3] => [5,1,2,4,6,3] => 8
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [2,1,5,3,6,4] => [5,2,6,1,3,4] => 6
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => 8
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => 4
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [6,1,3,2,4,5] => [3,1,2,4,6,5] => 2
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [2,5,1,3,6,4] => [2,1,5,6,3,4] => 1
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [5,1,3,2,4,6] => [3,1,2,5,4,6] => 2
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [6,2,1,3,5,4] => [2,6,1,3,5,4] => 4
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [6,2,5,4,1,3] => [6,5,2,1,4,3] => 4
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [2,5,4,1,3,6] => [5,4,2,1,3,6] => 3
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [6,5,1,3,2,4] => [3,1,2,6,5,4] => 2
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [5,2,6,4,1,3] => [5,6,2,1,4,3] => 4
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [4,1,3,2,6,5] => [4,1,3,6,2,5] => 4
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [4,1,3,2,5,6] => [4,1,3,2,5,6] => 2
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [6,1,5,2,3,4] => [1,2,6,3,5,4] => 2
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [2,6,1,3,4,5] => [2,1,3,6,4,5] => 2
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [5,2,1,3,4,6] => [2,1,3,5,4,6] => 1
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [6,5,2,1,3,4] => [2,1,3,6,5,4] => 1
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [6,2,4,1,3,5] => [4,2,1,3,6,5] => 2
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [5,2,4,1,3,6] => [5,2,1,4,3,6] => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [5,1,6,2,3,4] => [1,5,2,3,6,4] => 2
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [6,5,2,4,1,3] => [6,2,1,5,4,3] => 2
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [2,4,1,3,6,5] => [4,2,6,1,3,5] => 4
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [6,1,3,2,5,4] => [3,6,1,2,5,4] => 4
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [2,6,5,4,1,3] => [6,5,4,2,1,3] => 4
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [4,6,1,3,2,5] => [6,1,4,3,2,5] => 2
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [5,4,1,3,2,6] => [5,1,4,3,2,6] => 2
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [6,4,2,1,3,5] => [2,1,4,3,6,5] => 1
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [6,2,4,5,1,3] => [2,6,4,1,5,3] => 8
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [4,6,2,5,1,3] => [4,6,2,1,5,3] => 2
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => 2
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [6,5,4,1,3,2] => [6,1,5,4,3,2] => 2
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [5,4,2,6,1,3] => [2,5,4,1,6,3] => 4
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [3,2,1,6,4,5] => [3,6,2,1,4,5] => 4
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => 2
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [5,1,3,2,6,4] => [3,1,2,5,6,4] => 4
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [5,2,4,6,1,3] => [5,2,4,1,6,3] => 8
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => 6
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [6,1,4,3,2,5] => [4,3,1,2,6,5] => 3
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [2,6,5,1,4,3] => [2,6,5,4,1,3] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [5,1,4,3,2,6] => [5,4,1,3,2,6] => 3
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [6,2,1,4,3,5] => [2,4,1,3,6,5] => 2
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [6,2,5,1,4,3] => [2,6,5,1,4,3] => 2
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [2,5,1,4,3,6] => [2,5,4,1,3,6] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => 3
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [5,2,6,1,4,3] => [5,2,6,1,4,3] => 2
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => 2
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 1
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [6,1,4,2,5,3] => [1,2,6,4,5,3] => 3
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [2,6,1,4,5,3] => [2,4,6,5,1,3] => 2
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [4,2,1,5,3,6] => [2,1,4,5,3,6] => 2
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [5,2,1,4,6,3] => [2,5,1,4,6,3] => 4
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,2,3,6,4,5] => 2
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,2,5,3,4,6] => 2
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [5,1,4,2,6,3] => [1,5,2,4,6,3] => 4
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,6,5,2,3,4] => [1,2,6,5,3,4] => 3
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,4,6,2,3,5] => 4
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 2
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [6,1,4,5,3,2] => [4,6,5,1,3,2] => 1
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [2,6,4,1,5,3] => [4,2,6,5,1,3] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [4,6,1,5,3,2] => [6,1,4,5,3,2] => 6
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [4,1,5,3,2,6] => [4,5,1,3,2,6] => 2
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [5,4,2,1,6,3] => [2,1,5,4,6,3] => 2
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,6,2,3,5,4] => [6,1,2,5,3,4] => 8
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,4,6,2,3,5] => [1,6,4,2,3,5] => 4
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,5,4,2,3,6] => [1,5,4,2,3,6] => 3
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [5,4,1,6,3,2] => [5,1,4,6,3,2] => 6
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,6,5,4,2,3] => [1,6,5,4,2,3] => 4
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [6,3,1,2,4,5] => 8
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 4
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [5,1,4,6,3,2] => [5,4,6,1,3,2] => 6
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,5,2,3,6,4] => [1,2,5,6,3,4] => 1
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => 7
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => 4
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 2
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [6,1,3,4,2,5] => [3,4,1,2,6,5] => 1
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [2,5,1,6,3,4] => [2,5,1,6,3,4] => 4
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [3,6,5,1,4,2] => [3,6,5,1,4,2] => 2
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [5,1,3,4,2,6] => [1,5,3,4,2,6] => 3
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [6,2,1,5,3,4] => [6,2,1,3,5,4] => 3
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [6,2,5,3,1,4] => [2,6,3,1,5,4] => 4
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [2,3,6,1,4,5] => [2,6,3,1,4,5] => 8
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [2,5,3,1,4,6] => [2,5,3,1,4,6] => 4
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [6,3,1,4,2,5] => [1,3,4,2,6,5] => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [3,2,6,5,1,4] => [6,3,5,2,1,4] => 8
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [6,3,5,1,4,2] => [3,6,1,5,4,2] => 1
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [3,5,1,4,2,6] => [3,5,1,4,2,6] => 1
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [6,5,1,3,4,2] => [1,6,3,5,4,2] => 3
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [5,2,6,3,1,4] => [5,2,3,1,6,4] => 4
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [5,3,6,1,4,2] => [3,1,5,6,4,2] => 4
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [3,1,4,2,6,5] => [1,3,4,6,2,5] => 2
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [3,1,4,2,5,6] => [1,3,4,2,5,6] => 2
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [6,1,5,4,3,2] => [6,5,4,1,3,2] => 4
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [2,6,1,5,4,3] => [6,2,5,4,1,3] => 8
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [3,6,2,1,5,4] => [3,2,6,5,1,4] => 2
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 1
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [5,2,1,6,4,3] => [2,5,6,1,4,3] => 4
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,6,2,4,3,5] => [6,1,2,4,3,5] => 4
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,3,6,5,2,4] => [6,5,3,1,2,4] => 6
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,5,2,4,3,6] => [5,1,4,2,3,6] => 4
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [3,1,5,2,6,4] => [3,1,5,6,2,4] => 4
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,6,3,2,4,5] => [3,1,2,6,4,5] => 4
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,6,3,5,2,4] => [6,5,1,3,2,4] => 3
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,3,5,2,4,6] => [5,3,1,2,4,6] => 4
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [5,1,6,4,3,2] => [5,6,4,1,3,2] => 6
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,6,5,2,4,3] => [6,1,5,4,2,3] => 6
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,5,3,6,2,4] => [5,6,1,3,2,4] => 9
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => 4
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 3
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [6,1,4,3,5,2] => [6,1,4,3,5,2] => 4
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [2,6,4,3,1,5] => [6,2,4,3,1,5] => 4
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [3,6,1,4,5,2] => [6,3,1,4,5,2] => 8
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [4,3,1,5,2,6] => [1,4,3,5,2,6] => 2
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,6,2,5,4,3] => [6,5,1,4,2,3] => 6
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,3,6,2,5,4] => [3,6,5,1,2,4] => 8
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 4
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [5,3,1,4,6,2] => [1,3,5,4,6,2] => 2
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,5,3,2,6,4] => [5,1,3,6,2,4] => 4
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 2
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,5,2,3,4,6] => 2
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [5,1,4,3,6,2] => [5,4,1,3,6,2] => 6
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,5,2,6,4,3] => [5,6,1,4,2,3] => 8
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,6,5,3,4] => [1,6,5,2,3,4] => 3
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => 4
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 2
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [6,1,3,4,5,2] => [1,3,6,4,5,2] => 4
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [2,4,1,6,3,5] => [4,6,2,1,3,5] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [3,6,4,1,5,2] => [3,1,6,4,5,2] => 4
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [4,6,1,3,5,2] => [4,1,6,3,5,2] => 8
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [4,1,3,5,2,6] => [4,1,3,5,2,6] => 4
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [4,2,1,6,5,3] => [2,6,1,4,5,3] => 4
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,6,2,4,5,3] => [1,6,4,5,2,3] => 3
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,3,6,4,2,5] => [3,6,4,1,2,5] => 8
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,4,6,2,5,3] => [4,6,1,5,2,3] => 6
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [5,4,3,1,6,2] => [1,5,4,3,6,2] => 2
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 5
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,6,3,5,4] => [6,1,5,2,3,4] => 6
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,4,6,3,5] => [6,4,1,2,3,5] => 6
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 3
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [5,4,1,3,6,2] => [5,1,4,3,6,2] => 6
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,5,4,2,6,3] => [1,5,4,6,2,3] => 2
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 4
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,6,2,3,4,5] => 4
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 4
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [5,1,3,4,6,2] => [1,5,3,4,6,2] => 4
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,5,2,4,6,3] => [5,1,4,6,2,3] => 8
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,5,3,6,4] => [1,5,6,2,3,4] => 6
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 9
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 4
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [1,2,3,4,5,7,6] => 1
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7] => 1
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [7,6,1,2,3,4,5] => [1,2,3,4,7,6,5] => 1
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [5,1,2,3,4,7,6] => [1,2,3,5,7,4,6] => 2
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => [1,2,3,5,4,6,7] => 1
{{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => [5,7,1,2,3,4,6] => [1,2,3,7,5,4,6] => 2
{{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7] => 1
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 1
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [1,2,4,6,3,5,7] => 2
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [6,1,2,3,4,7,5] => [1,2,3,4,6,7,5] => 2
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [1,2,4,7,3,5,6] => 2
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7] => 1
{{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => [4,7,6,1,2,3,5] => [1,2,7,6,4,3,5] => 3
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [7,4,1,2,3,5,6] => [1,2,4,3,5,7,6] => 1
{{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => [7,4,6,1,2,3,5] => [1,2,7,4,3,6,5] => 2
{{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => [4,6,1,2,3,5,7] => [1,2,6,4,3,5,7] => 2
{{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => [6,4,7,1,2,3,5] => [1,4,2,6,3,7,5] => 2
{{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => [5,4,1,2,3,7,6] => [1,2,5,4,7,3,6] => 2
{{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => [5,4,1,2,3,6,7] => [1,2,5,4,3,6,7] => 1
{{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => [4,7,1,2,3,6,5] => [1,2,4,7,6,3,5] => 2
{{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7] => 1
{{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => [6,4,1,2,3,7,5] => [1,2,4,3,6,7,5] => 2
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,3,5,7,2,4,6] => 8
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,3,5,2,4,6,7] => 2
{{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => [4,7,5,1,2,3,6] => [1,4,2,7,5,3,6] => 4
{{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => [5,7,1,2,3,6,4] => [1,2,5,7,3,6,4] => 1
{{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => [5,1,2,3,6,4,7] => [1,2,3,5,6,4,7] => 2
{{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => [7,6,5,4,1,2,3] => [1,2,7,6,5,4,3] => 1
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [6,5,1,2,3,7,4] => [1,2,3,6,5,7,4] => 2
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,3,6,2,4,5,7] => 2
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,3,7,2,4,5,6] => 4
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1
{{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => [3,6,1,2,4,7,5] => [1,3,2,6,7,4,5] => 1
{{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => [7,3,1,2,4,6,5] => [1,3,7,2,4,6,5] => 4
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [7,1,2,6,3,4,5] => [1,2,7,3,4,6,5] => 4
{{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => [3,7,1,2,4,5,6] => [1,3,2,4,7,5,6] => 2
{{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => [6,3,1,2,4,5,7] => [1,3,2,4,6,5,7] => 1
{{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => [7,6,3,1,2,4,5] => [1,3,2,4,7,6,5] => 1
{{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => [7,5,3,1,2,4,6] => [1,3,2,5,4,7,6] => 1
{{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => [4,3,1,2,6,5,7] => [1,4,3,6,2,5,7] => 2
{{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => [4,3,1,2,5,7,6] => [1,4,3,7,2,5,6] => 2
{{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7] => 1
{{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => [3,7,6,1,2,5,4] => [1,3,7,6,5,2,4] => 2
{{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => [7,3,1,2,5,4,6] => [1,3,5,2,4,7,6] => 2
{{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => [7,3,6,1,2,5,4] => [1,3,7,6,2,5,4] => 2
{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [3,6,1,2,5,4,7] => [1,3,6,5,2,4,7] => 2
{{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => [7,1,2,5,3,6,4] => [1,2,7,3,5,6,4] => 4
{{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => [3,7,1,2,5,6,4] => [1,3,5,7,6,2,4] => 2
{{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => [5,3,1,2,6,4,7] => [1,3,2,5,6,4,7] => 2
{{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => [6,3,1,2,5,7,4] => [1,3,6,2,5,7,4] => 4
{{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => [6,5,3,1,2,7,4] => [1,3,2,6,5,7,4] => 2
{{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => [3,6,1,2,7,4,5] => [1,3,6,2,7,4,5] => 4
{{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => [7,4,1,2,5,3,6] => [1,2,4,5,3,7,6] => 2
{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [4,6,1,2,5,3,7] => [1,4,6,2,5,3,7] => 1
{{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => [6,4,7,1,2,5,3] => [1,4,2,6,7,5,3] => 4
{{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => [4,1,2,5,3,7,6] => [1,2,4,5,7,3,6] => 2
{{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => [4,1,2,5,3,6,7] => [1,2,4,5,3,6,7] => 2
{{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => [4,7,3,1,2,6,5] => [1,4,3,7,6,2,5] => 2
{{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => [6,3,1,2,7,5,4] => [1,3,6,7,2,5,4] => 4
{{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => [5,4,1,2,6,3,7] => [1,2,5,4,6,3,7] => 2
{{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => [6,4,1,2,5,7,3] => [1,2,4,6,5,7,3] => 2
{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [7,1,2,4,5,6,3] => [1,2,7,4,5,6,3] => 3
{{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => [4,7,5,1,2,6,3] => [1,4,2,7,5,6,3] => 4
{{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => [5,3,1,2,7,6,4] => [1,3,7,2,5,6,4] => 4
{{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => [6,5,4,1,2,7,3] => [1,2,6,5,4,7,3] => 2
{{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => [6,1,7,2,3,5,4] => [1,2,6,7,3,5,4] => 2
{{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => [7,1,5,2,3,4,6] => [1,2,5,3,4,7,6] => 2
{{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => [6,1,5,2,3,4,7] => [1,2,6,3,5,4,7] => 2
{{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => [7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 2
{{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => [7,1,6,5,2,3,4] => [1,2,7,6,3,5,4] => 3
{{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => [6,4,7,1,3,2,5] => [1,4,6,3,2,7,5] => 2
{{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => [7,1,4,2,5,3,6] => [1,4,5,2,3,7,6] => 1
{{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => [6,1,4,2,5,3,7] => [1,2,6,4,5,3,7] => 3
{{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => [7,6,1,4,2,5,3] => [1,2,7,4,6,5,3] => 3
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,2,3,4,7,5,6] => 2
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,2,3,6,4,5,7] => 2
{{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => [1,7,6,2,3,4,5] => [1,2,3,7,6,4,5] => 3
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,2,5,7,3,4,6] => 4
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,2,5,3,4,6,7] => 2
{{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => [7,1,4,2,5,6,3] => [1,2,4,7,5,6,3] => 4
{{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => [1,5,7,2,3,4,6] => [1,2,7,5,3,4,6] => 4
{{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => [1,6,5,2,3,4,7] => [1,2,6,5,3,4,7] => 3
{{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => [1,7,6,5,2,3,4] => [1,2,7,6,5,3,4] => 4
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,4,6,2,3,5,7] => 4
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [6,1,4,2,5,7,3] => [1,2,6,4,5,7,3] => 4
{{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => [1,6,2,3,4,7,5] => [1,2,3,6,7,4,5] => 1
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,4,2,3,5,6,7] => 2
{{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => [1,7,4,2,3,5,6] => [1,4,2,3,7,5,6] => 4
{{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => [1,5,2,3,6,4,7] => [1,2,5,6,3,4,7] => 1
{{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => [1,6,5,2,3,7,4] => [1,2,6,5,7,3,4] => 2
{{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => [3,6,1,4,2,7,5] => [1,3,6,4,7,2,5] => 4
{{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => [7,3,1,4,2,6,5] => [1,3,4,7,2,6,5] => 2
{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [3,1,7,2,4,5,6] => [1,3,2,7,4,5,6] => 2
{{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => [3,7,1,4,2,5,6] => [1,3,4,2,7,5,6] => 4
{{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => [6,3,1,4,2,5,7] => [1,3,4,2,6,5,7] => 2
{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [7,6,3,1,4,2,5] => [1,3,4,2,7,6,5] => 2
{{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => [7,5,3,1,4,2,6] => [1,3,5,4,2,7,6] => 2
{{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => [3,1,4,2,6,5,7] => [1,3,4,6,2,5,7] => 2
{{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => [3,1,4,2,5,7,6] => [1,3,4,7,2,5,6] => 2
{{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => [3,1,4,2,5,6,7] => [1,3,4,2,5,6,7] => 2
{{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => [1,7,2,6,3,4,5] => [1,2,7,3,6,4,5] => 4
{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [5,3,1,6,2,7,4] => [1,3,5,2,6,7,4] => 2
{{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => [7,3,1,4,5,2,6] => [1,3,4,5,2,7,6] => 2
{{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => [4,3,1,5,2,7,6] => [1,4,3,5,7,2,6] => 4
{{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => [4,3,1,5,2,6,7] => [1,4,3,5,2,6,7] => 2
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [5,3,1,4,6,2,7] => [1,3,5,4,6,2,7] => 2
{{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => [1,7,2,5,3,6,4] => [1,2,7,5,6,3,4] => 3
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [6,3,1,4,5,7,2] => [1,3,4,6,5,7,2] => 4
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,2,3,7,4,5,6] => 2
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,2,6,3,4,5,7] => 2
{{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => [1,2,7,6,3,4,5] => [1,2,7,6,3,4,5] => 3
{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [6,5,3,1,4,7,2] => [1,3,6,5,4,7,2] => 2
{{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => [1,2,6,3,4,7,5] => [1,2,6,7,3,4,5] => 6
{{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => [6,1,3,4,5,2,7] => [1,3,6,4,5,2,7] => 4
{{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => [7,6,1,3,4,5,2] => [1,3,7,4,6,5,2] => 8
{{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => [6,4,7,1,3,5,2] => [1,4,6,3,7,5,2] => 6
{{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => [1,7,4,2,5,3,6] => [1,2,7,4,5,3,6] => 4
{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [6,1,4,2,7,5,3] => [1,2,6,7,4,5,3] => 3
{{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => [1,4,2,5,3,7,6] => [1,4,5,7,2,3,6] => 8
{{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => [1,4,2,5,3,6,7] => [1,4,5,2,3,6,7] => 1
{{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => [4,7,3,1,5,6,2] => [1,4,3,7,5,6,2] => 6
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,2,7,3,4,5,6] => 4
{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [7,1,3,4,5,6,2] => [1,3,4,7,5,6,2] => 8
{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [5,3,1,6,4,7,2] => [1,3,5,6,4,7,2] => 6
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [6,1,3,4,5,7,2] => [1,3,6,4,5,7,2] => 6
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
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Description
The number of permutations with the same antidiagonal sums.
The X-ray of a permutation $\pi$ is the vector of the sums of the antidiagonals of the permutation matrix of $\pi$, read from left to right. For example, the permutation matrix of $\pi=[3,1,2,5,4]$ is
$$\left(\begin{array}{rrrrr} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right),$$
so its X-ray is $(0, 1, 1, 1, 0, 0, 0, 2, 0)$.
This statistic records the number of permutations having the same X-ray as the given permutation. In [1] this is called the degeneracy of the X-ray of the permutation.
By [prop.1, 1], the number of different X-rays of permutations of size $n$ equals the number of nondecreasing differences of permutations of size $n$, [2].
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.