Identifier
Values
{{1}} => [1] => [1] => [1] => 1
{{1,2}} => [2,1] => [2,1] => [2,1] => 1
{{1},{2}} => [1,2] => [1,2] => [1,2] => 2
{{1,2,3}} => [2,3,1] => [3,2,1] => [2,3,1] => 1
{{1,2},{3}} => [2,1,3] => [2,1,3] => [2,1,3] => 2
{{1,3},{2}} => [3,2,1] => [2,3,1] => [3,2,1] => 2
{{1},{2,3}} => [1,3,2] => [1,3,2] => [1,3,2] => 2
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 3
{{1,2,3,4}} => [2,3,4,1] => [4,3,2,1] => [2,3,4,1] => 1
{{1,2,3},{4}} => [2,3,1,4] => [3,2,1,4] => [2,3,1,4] => 2
{{1,2,4},{3}} => [2,4,3,1] => [3,4,2,1] => [2,4,3,1] => 2
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
{{1,3,4},{2}} => [3,2,4,1] => [2,4,3,1] => [3,2,4,1] => 2
{{1,3},{2,4}} => [3,4,1,2] => [4,1,3,2] => [4,3,1,2] => 1
{{1,3},{2},{4}} => [3,2,1,4] => [2,3,1,4] => [3,2,1,4] => 3
{{1,4},{2,3}} => [4,3,2,1] => [3,2,4,1] => [4,3,2,1] => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,4,3,2] => [1,3,4,2] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 3
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,4,1] => [4,2,3,1] => 3
{{1},{2,4},{3}} => [1,4,3,2] => [1,3,4,2] => [1,4,3,2] => 3
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 3
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
{{1,2,3,4,5}} => [2,3,4,5,1] => [5,4,3,2,1] => [2,3,4,5,1] => 1
{{1,2,3,4},{5}} => [2,3,4,1,5] => [4,3,2,1,5] => [2,3,4,1,5] => 2
{{1,2,3,5},{4}} => [2,3,5,4,1] => [4,5,3,2,1] => [2,3,5,4,1] => 2
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 3
{{1,2,4,5},{3}} => [2,4,3,5,1] => [3,5,4,2,1] => [2,4,3,5,1] => 2
{{1,2,4},{3,5}} => [2,4,5,1,3] => [5,2,1,4,3] => [2,5,4,1,3] => 1
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [3,4,2,1,5] => [2,4,3,1,5] => 3
{{1,2,5},{3,4}} => [2,5,4,3,1] => [4,3,5,2,1] => [2,5,4,3,1] => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 3
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [3,4,5,2,1] => [2,5,3,4,1] => 3
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [2,1,4,5,3] => [2,1,5,4,3] => 3
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 3
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 4
{{1,3,4,5},{2}} => [3,2,4,5,1] => [2,5,4,3,1] => [3,2,4,5,1] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [4,1,5,3,2] => [4,3,5,1,2] => 2
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [2,4,3,1,5] => [3,2,4,1,5] => 3
{{1,3,5},{2,4}} => [3,4,5,2,1] => [5,2,4,3,1] => [3,4,5,1,2] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => [5,4,1,3,2] => [4,3,1,5,2] => 1
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [4,1,3,2,5] => [4,3,1,2,5] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [2,4,5,3,1] => [3,2,5,4,1] => 3
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [4,5,1,3,2] => [5,3,1,4,2] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [2,3,1,5,4] => [3,2,1,5,4] => 3
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 4
{{1,4,5},{2,3}} => [4,3,2,5,1] => [3,2,5,4,1] => [4,3,2,5,1] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [5,3,1,4,2] => [3,5,4,2,1] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [3,2,4,1,5] => [4,3,2,1,5] => 3
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,3,2,5,1] => [5,3,4,2,1] => 2
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,5,4,3,2] => [1,3,4,5,2] => 2
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => 3
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [3,2,4,5,1] => [5,3,2,4,1] => 3
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,4,5,3,2] => [1,3,5,4,2] => 3
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 4
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [2,3,5,4,1] => [4,2,3,5,1] => 3
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [3,5,1,4,2] => [5,4,3,1,2] => 2
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [2,5,1,4,3] => [5,2,4,1,3] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [2,3,4,1,5] => [4,2,3,1,5] => 4
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [3,4,2,5,1] => [5,4,3,2,1] => 3
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,3,5,4,2] => [1,4,3,5,2] => 3
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,5,2,4,3] => [1,5,4,2,3] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,3,2,5] => 4
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,4,3,5,1] => [5,2,4,3,1] => 3
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,4,3,5,2] => [1,5,4,3,2] => 3
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => 3
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 4
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [2,3,4,5,1] => [5,2,3,4,1] => 4
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,3,4,5,2] => [1,5,3,4,2] => 4
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,4,3] => 4
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 4
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 5
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => 1
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => 2
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => 2
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => 2
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => 3
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => 2
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [6,3,2,1,5,4] => [2,3,6,5,1,4] => 1
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => 3
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => 2
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 2
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 3
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => 3
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => 3
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 3
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 4
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => 2
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [5,2,1,6,4,3] => [2,5,4,6,1,3] => 2
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => 3
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [6,3,5,4,2,1] => [2,4,5,6,1,3] => 1
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [6,5,2,1,4,3] => [2,5,4,1,6,3] => 1
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [5,2,1,4,3,6] => [2,5,4,1,3,6] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => 3
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [5,6,2,1,4,3] => [2,6,4,1,5,3] => 2
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => 3
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => 4
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => 2
>>> Load all 471 entries. <<<
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [6,4,2,1,5,3] => [2,4,6,5,3,1] => 1
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => 3
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => 2
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => 2
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => 3
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => 3
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => 3
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 4
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => 3
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [4,6,2,1,5,3] => [2,6,5,4,1,3] => 2
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [3,6,2,1,5,4] => [2,6,3,5,1,4] => 2
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => 4
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => 3
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => 3
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [2,1,6,5,3,4] => 2
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => 4
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => 3
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => 3
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => 3
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 4
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => 4
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => 4
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => 4
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 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] => 5
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => 2
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [5,4,1,6,3,2] => [4,3,5,6,2,1] => 2
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => 3
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [6,4,2,5,3,1] => [3,5,4,6,1,2] => 1
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [4,1,6,5,3,2] => [4,3,5,1,6,2] => 2
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [4,1,5,3,2,6] => [4,3,5,1,2,6] => 3
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => 3
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [4,1,5,6,3,2] => [4,3,6,1,5,2] => 3
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => 3
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => 4
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [6,5,2,4,3,1] => [3,4,5,1,6,2] => 1
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [6,1,5,4,3,2] => [6,3,4,5,1,2] => 1
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [5,2,4,3,1,6] => [3,4,5,1,2,6] => 2
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [5,2,6,4,3,1] => [3,4,6,5,2,1] => 2
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [6,5,4,1,3,2] => [4,3,1,5,6,2] => 1
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [5,4,1,3,2,6] => [4,3,1,5,2,6] => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [5,6,2,4,3,1] => [3,4,6,1,5,2] => 2
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [5,6,4,1,3,2] => [4,3,1,6,5,2] => 2
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [4,3,1,2,6,5] => 2
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [4,3,1,2,5,6] => 3
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => 3
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [4,5,1,6,3,2] => [5,3,6,4,1,2] => 3
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [2,6,3,1,5,4] => [3,2,6,5,1,4] => 2
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => 4
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [4,6,2,5,3,1] => [3,5,6,4,1,2] => 2
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => 2
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [6,1,3,2,5,4] => [6,3,1,5,2,4] => 1
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [4,5,1,3,2,6] => [5,3,1,4,2,6] => 3
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => 3
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [5,4,6,1,3,2] => [6,3,1,5,4,2] => 2
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => 3
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => 4
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => 4
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [4,5,6,1,3,2] => [6,3,1,4,5,2] => 3
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => 4
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => 4
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 5
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [5,3,1,6,4,2] => [3,5,4,6,2,1] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => 3
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => 1
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [6,5,3,1,4,2] => [3,5,4,2,6,1] => 1
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [5,3,1,4,2,6] => [3,5,4,2,1,6] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => 3
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [5,6,3,1,4,2] => [3,6,4,2,5,1] => 2
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => 3
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => 4
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => 2
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [6,4,3,1,5,2] => [3,4,6,5,1,2] => 1
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => 3
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => 2
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => 2
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => 3
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => 3
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => 3
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => 3
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 4
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => 3
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [4,6,3,1,5,2] => [3,6,5,4,2,1] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [3,2,6,1,5,4] => [6,3,2,5,1,4] => 2
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => 4
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => 3
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => 3
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,6,3,2,5,4] => [1,3,6,5,2,4] => 2
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => 4
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => 3
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => 3
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => 3
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 4
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => 4
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => 4
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => 4
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 4
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 5
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => 3
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [3,5,1,6,4,2] => [5,4,3,6,1,2] => 3
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [2,5,1,6,4,3] => [5,2,4,6,1,3] => 3
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => 4
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [3,6,2,5,4,1] => [4,5,3,6,1,2] => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [3,6,5,1,4,2] => [5,4,3,1,6,2] => 2
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [6,1,5,2,4,3] => [6,5,4,2,1,3] => 1
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [3,5,1,4,2,6] => [5,4,3,1,2,6] => 3
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [2,6,3,5,4,1] => [4,2,5,6,1,3] => 2
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [5,1,6,3,4,2] => [5,4,6,3,1,2] => 2
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [2,6,5,1,4,3] => [5,2,4,1,6,3] => 2
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [2,5,1,4,3,6] => [5,2,4,1,3,6] => 3
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => 4
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [3,5,6,1,4,2] => [6,4,3,1,5,2] => 3
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [2,5,6,1,4,3] => [6,2,4,1,5,3] => 3
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => 4
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 5
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => 3
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [3,6,4,1,5,2] => [4,6,3,5,2,1] => 2
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [6,2,4,1,5,3] => [4,6,5,2,1,3] => 1
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => 4
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => 3
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => 3
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,5,2,6,4,3] => [1,5,4,6,2,3] => 3
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => 4
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [5,2,4,3,6,1] => [6,5,4,2,3,1] => 2
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,6,3,5,4,2] => [1,4,5,6,2,3] => 2
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,6,5,2,4,3] => [1,5,4,2,6,3] => 2
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,5,2,4,3,6] => [1,5,4,2,3,6] => 3
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => 4
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => 4
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,5,6,2,4,3] => [1,6,4,2,5,3] => 3
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => 4
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 5
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => 3
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [4,3,6,1,5,2] => [6,5,4,3,1,2] => 2
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [2,6,4,1,5,3] => [4,2,6,5,3,1] => 2
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => 4
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => 3
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => 3
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,6,4,2,5,3] => [1,4,6,5,3,2] => 2
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => 4
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => 3
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => 3
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => 3
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => 4
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => 4
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => 4
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => 4
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 4
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 5
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => 4
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [3,4,6,1,5,2] => [6,5,3,4,1,2] => 3
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [2,4,6,1,5,3] => [6,2,5,4,1,3] => 3
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [2,3,6,1,5,4] => [6,2,3,5,1,4] => 3
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 5
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => 4
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => 4
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,4,6,2,5,3] => [1,6,5,4,2,3] => 3
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,3,6,2,5,4] => [1,6,3,5,2,4] => 3
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => 5
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => 4
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => 4
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => 4
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,6,3,5,4] => [1,2,6,5,3,4] => 3
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 5
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => 4
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => 4
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => 4
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => 4
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 5
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 5
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => 5
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 5
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 5
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 6
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => 1
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => 2
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [5,4,3,2,1,7,6] => [2,3,4,5,1,7,6] => 2
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => 3
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [4,3,2,1,5,7,6] => [2,3,4,1,5,7,6] => 3
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => 4
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [7,4,6,5,3,2,1] => [2,3,5,6,7,1,4] => 1
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => 5
{{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => [4,5,3,6,2,1,7] => [2,6,5,4,3,1,7] => 4
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [2,1,5,6,4,7,3] => [2,1,7,6,5,4,3] => 4
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 6
{{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => [2,7,6,5,4,3,1] => [3,2,4,5,6,7,1] => 2
{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [7,2,6,5,4,3,1] => [3,4,5,6,7,1,2] => 1
{{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => 6
{{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => [3,2,7,6,5,4,1] => [4,3,2,5,6,7,1] => 2
{{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => [3,2,4,1,5,6,7] => [4,3,2,1,5,6,7] => 5
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [5,4,3,2,6,1,7] => [6,3,4,5,2,1,7] => 3
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [4,3,2,5,6,1,7] => [6,3,4,2,5,1,7] => 4
{{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => [3,2,4,7,6,5,1] => [5,3,2,4,6,7,1] => 3
{{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => [4,6,3,1,5,2,7] => [3,6,5,4,2,1,7] => 3
{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [4,5,3,2,6,1,7] => [6,3,5,4,2,1,7] => 4
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [3,2,5,4,6,1,7] => [6,3,2,5,4,1,7] => 4
{{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => [1,5,6,4,7,3,2] => [1,3,7,6,5,4,2] => 4
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 6
{{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => [2,3,7,6,5,4,1] => [4,2,3,5,6,7,1] => 3
{{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => [6,2,7,1,5,4,3] => [7,6,4,5,1,2,3] => 2
{{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => [5,6,1,7,3,4,2] => [6,4,7,3,5,1,2] => 3
{{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => [3,4,2,6,5,1,7] => [5,4,3,2,6,1,7] => 4
{{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => [3,4,2,5,1,7,6] => [5,4,3,2,1,7,6] => 4
{{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => [3,4,2,5,1,6,7] => [5,4,3,2,1,6,7] => 5
{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [3,5,4,2,6,1,7] => [6,4,3,5,2,1,7] => 4
{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [3,4,2,5,6,1,7] => [6,4,3,2,5,1,7] => 5
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [4,3,5,2,6,1,7] => [6,5,4,3,2,1,7] => 4
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [2,5,4,3,6,1,7] => [6,2,4,5,3,1,7] => 4
{{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => [1,6,5,4,3,7,2] => [1,7,4,5,6,3,2] => 3
{{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => 4
{{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => [1,5,7,4,2,6,3] => [1,4,7,6,5,3,2] => 3
{{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => [1,5,6,4,3,7,2] => [1,7,4,6,5,3,2] => 4
{{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => 4
{{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => [2,3,4,7,6,5,1] => [5,2,3,4,6,7,1] => 4
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [3,4,5,2,6,1,7] => [6,5,3,4,2,1,7] => 5
{{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => [4,5,3,7,1,6,2] => [7,6,5,4,3,1,2] => 3
{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [2,4,5,3,6,1,7] => [6,2,5,4,3,1,7] => 5
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [4,5,3,6,2,7,1] => [7,6,5,4,3,2,1] => 4
{{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => 4
{{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => 4
{{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => 5
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [1,5,4,6,3,7,2] => [1,7,6,5,4,3,2] => 4
{{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => 4
{{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => [2,3,4,5,7,6,1] => [6,2,3,4,5,7,1] => 5
{{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => 5
{{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => 5
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 6
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 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] => 7
{{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
{{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => 4
{{1,6},{2,3},{4,5},{7,8}} => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => 4
{{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => 4
{{1,3},{2,5},{4,6},{7,8}} => [3,5,1,6,2,4,8,7] => [6,1,3,2,5,4,8,7] => [6,3,1,5,2,4,8,7] => 2
{{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => 4
{{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => [6,5,4,3,2,1,8,7] => 4
{{1,8},{2,5},{3,4},{6,7}} => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => [8,5,4,3,2,7,6,1] => 4
{{1,3},{2,7},{4,5},{6,8}} => [3,7,1,5,4,8,2,6] => [5,4,8,1,3,2,7,6] => [8,3,1,5,4,7,2,6] => 2
{{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => 4
{{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => [8,7,4,3,6,5,2,1] => 4
{{1,7},{2,8},{3,5},{4,6}} => [7,8,5,6,3,4,1,2] => [6,3,5,4,8,1,7,2] => [8,7,6,5,3,4,1,2] => 2
{{1,6},{2,8},{3,5},{4,7}} => [6,8,5,7,3,1,4,2] => [7,3,5,1,8,4,6,2] => [5,6,7,8,3,4,1,2] => 2
{{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => [2,1,8,3,5,4,7,6] => [2,1,8,5,3,7,4,6] => 2
{{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => [4,3,1,2,8,7,5,6] => 2
{{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => 4
{{1,4},{2,3},{5,8},{6,7}} => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => 4
{{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => [8,3,2,7,6,5,4,1] => 4
{{1,6},{2,5},{3,8},{4,7}} => [6,5,8,7,2,1,4,3] => [7,2,8,1,5,4,6,3] => [8,7,6,5,1,2,3,4] => 2
{{1,6},{2,7},{3,8},{4,5}} => [6,7,8,5,4,1,2,3] => [5,4,8,1,7,2,6,3] => [8,7,6,5,4,2,1,3] => 2
{{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => 4
{{1,7},{2,8},{3,6},{4,5}} => [7,8,6,5,4,3,1,2] => [5,4,6,3,8,1,7,2] => [8,7,6,5,4,3,1,2] => 3
{{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => [8,7,6,5,4,3,2,1] => 4
{{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => 5
{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 8
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => 7
{{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => [1,2,3,8,7,6,5,4] => [1,2,3,5,6,7,8,4] => 4
{{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 6
{{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => 6
{{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => 5
{{1},{2,4},{3},{5,7},{6},{8}} => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => 6
{{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => [1,3,5,7,8,6,4,2] => [1,4,3,6,5,8,7,2] => 5
{{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => [1,3,6,7,5,8,4,2] => [1,4,3,8,7,6,5,2] => 5
{{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => 4
{{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => [1,4,5,3,7,8,6,2] => [1,6,5,4,3,8,7,2] => 5
{{1},{2,8},{3,5,7},{4},{6}} => [1,8,5,4,7,6,3,2] => [1,4,6,7,5,3,8,2] => [1,8,5,4,7,6,3,2] => 5
{{1},{2,8},{3,7},{4,5},{6}} => [1,8,7,5,4,6,3,2] => [1,5,4,6,7,3,8,2] => [1,8,7,5,4,6,3,2] => 5
{{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => [1,5,6,4,7,3,8,2] => [1,8,7,6,5,4,3,2] => 5
{{1},{2,8},{3,4,7},{5,6}} => [1,8,4,7,6,5,3,2] => [1,6,5,7,4,3,8,2] => [1,8,4,7,6,5,3,2] => 4
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 7
{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 6
{{1,2},{3,4},{5,7,8},{6}} => [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => 4
{{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,8,6,5] => [2,1,4,3,6,8,7,5] => 4
{{1,2},{3,5,6},{4},{7,8}} => [2,1,5,4,6,3,8,7] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => 4
{{1,2},{3,5,7,8},{4},{6}} => [2,1,5,4,7,6,8,3] => [2,1,4,6,8,7,5,3] => [2,1,5,4,7,6,8,3] => 4
{{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => [2,1,5,6,4,3,8,7] => [2,1,4,6,5,3,8,7] => 4
{{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => [2,1,6,7,8,5,4,3] => [2,1,4,5,8,6,7,3] => 4
{{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => 7
{{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => 6
{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => [2,3,1,5,7,8,6,4] => [3,2,1,6,5,8,7,4] => 5
{{1,3},{2},{4,8},{5,7},{6}} => [3,2,1,8,7,6,5,4] => [2,3,1,6,7,5,8,4] => [3,2,1,8,7,6,5,4] => 5
{{1,4},{2},{3},{5,8},{6},{7}} => [4,2,3,1,8,6,7,5] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => 6
{{1,5,6,7,8},{2},{3},{4}} => [5,2,3,4,6,7,8,1] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => 4
{{1,4,5,6,7,8},{2},{3}} => [4,2,3,5,6,7,8,1] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => 3
{{1,3,4},{2},{5,6},{7,8}} => [3,2,4,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => 4
{{1,3,4},{2},{5,7,8},{6}} => [3,2,4,1,7,6,8,5] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => 4
{{1,3,4},{2},{5,6,8},{7}} => [3,2,4,1,6,8,7,5] => [2,4,3,1,7,8,6,5] => [3,2,4,1,6,8,7,5] => 4
{{1,3,5},{2},{4},{6,8},{7}} => [3,2,5,4,1,8,7,6] => [2,4,5,3,1,7,8,6] => [3,2,5,4,1,8,7,6] => 5
{{1,3,5,6},{2},{4},{7,8}} => [3,2,5,4,6,1,8,7] => [2,4,6,5,3,1,8,7] => [3,2,5,4,6,1,8,7] => 4
{{1,3,5,7},{2},{4},{6},{8}} => [3,2,5,4,7,6,1,8] => [2,4,6,7,5,3,1,8] => [3,2,5,4,7,6,1,8] => 5
{{1,3,5,7,8},{2},{4},{6}} => [3,2,5,4,7,6,8,1] => [2,4,6,8,7,5,3,1] => [3,2,5,4,7,6,8,1] => 4
{{1,3,6,8},{2},{4,5},{7}} => [3,2,6,5,4,8,7,1] => [2,5,4,7,8,6,3,1] => [3,2,6,5,4,8,7,1] => 4
{{1,3,7},{2},{4,6},{5},{8}} => [3,2,7,6,5,4,1,8] => [2,5,6,4,7,3,1,8] => [3,2,7,6,5,4,1,8] => 5
{{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => 2
{{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => 4
{{1,4},{2,3},{5},{6},{7},{8}} => [4,3,2,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => 6
{{1,4,8},{2,3},{5},{6,7}} => [4,3,2,8,5,7,6,1] => [3,2,5,7,6,8,4,1] => [4,3,2,8,5,7,6,1] => 4
{{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => 2
{{1,2,4},{3},{5,6},{7,8}} => [2,4,3,1,6,5,8,7] => [3,4,2,1,6,5,8,7] => [2,4,3,1,6,5,8,7] => 4
{{1,2,4},{3},{5,7,8},{6}} => [2,4,3,1,7,6,8,5] => [3,4,2,1,6,8,7,5] => [2,4,3,1,7,6,8,5] => 4
{{1,2,4},{3},{5,6,8},{7}} => [2,4,3,1,6,8,7,5] => [3,4,2,1,7,8,6,5] => [2,4,3,1,6,8,7,5] => 4
{{1,5},{2,4},{3},{6},{7},{8}} => [5,4,3,2,1,6,7,8] => [3,4,2,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => 6
{{1,5},{2,4},{3},{6,8},{7}} => [5,4,3,2,1,8,7,6] => [3,4,2,5,1,7,8,6] => [5,4,3,2,1,8,7,6] => 5
{{1,5,7},{2,4},{3},{6},{8}} => [5,4,3,2,7,6,1,8] => [3,4,2,6,7,5,1,8] => [5,4,3,2,7,6,1,8] => 5
{{1,7},{2,6},{3},{4,5},{8}} => [7,6,3,5,4,2,1,8] => [3,5,4,6,2,7,1,8] => [7,6,3,5,4,2,1,8] => 5
{{1,7},{2,4,6},{3},{5},{8}} => [7,4,3,6,5,2,1,8] => [3,5,6,4,2,7,1,8] => [7,4,3,6,5,2,1,8] => 5
{{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => 2
{{1,2,8},{3,4},{5},{6,7}} => [2,8,4,3,5,7,6,1] => [4,3,5,7,6,8,2,1] => [2,8,4,3,5,7,6,1] => 4
{{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => [4,5,3,6,2,7,1,8] => [7,6,5,4,3,2,1,8] => 5
{{1,7,8},{2,6},{3,5},{4}} => [7,6,5,4,3,2,8,1] => [4,5,3,6,2,8,7,1] => [7,6,5,4,3,2,8,1] => 4
{{1,2,3,6},{4},{5},{7,8}} => [2,3,6,4,5,1,8,7] => [4,5,6,3,2,1,8,7] => [2,3,6,4,5,1,8,7] => 4
{{1,2,3,7,8},{4},{5},{6}} => [2,3,7,4,5,6,8,1] => [4,5,6,8,7,3,2,1] => [2,3,7,4,5,6,8,1] => 4
{{1,8},{2,3,7},{4},{5,6}} => [8,3,7,4,6,5,2,1] => [4,6,5,7,3,2,8,1] => [8,3,7,4,6,5,2,1] => 4
{{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => 4
{{1,7},{2,6},{3,4,5},{8}} => [7,6,4,5,3,2,1,8] => [5,4,3,6,2,7,1,8] => [7,6,4,5,3,2,1,8] => 4
{{1,2,3,4,8},{5},{6},{7}} => [2,3,4,8,5,6,7,1] => [5,6,7,8,4,3,2,1] => [2,3,4,8,5,6,7,1] => 4
{{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => 3
{{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => 2
{{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => 2
{{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => 1
{{1,2,3,5,6,8},{4,7}} => [2,3,5,7,6,8,4,1] => [8,6,4,7,5,3,2,1] => [2,3,5,7,6,8,1,4] => 1
{{1,2,3,5,8},{4,6,7}} => [2,3,5,6,8,7,4,1] => [7,4,8,6,5,3,2,1] => [2,3,5,6,8,7,4,1] => 2
{{1,4,5,7},{2,6,8},{3}} => [4,6,3,5,7,8,1,2] => [3,8,5,1,7,6,4,2] => [5,4,3,8,6,7,2,1] => 2
{{1,2,6,7},{3,8},{4},{5}} => [2,6,8,4,5,7,1,3] => [4,5,7,2,1,8,6,3] => [2,7,6,4,5,8,1,3] => 4
{{1,2,8},{3,6},{4,7},{5}} => [2,8,6,7,5,3,4,1] => [5,7,3,6,4,8,2,1] => [2,8,7,6,5,3,4,1] => 3
{{1,2,4},{3,6},{5,8},{7}} => [2,4,6,1,8,3,7,5] => [7,8,2,1,4,3,6,5] => [2,8,4,1,6,3,7,5] => 2
{{1,2},{3,6,7},{4,8},{5}} => [2,1,6,8,5,7,3,4] => [2,1,5,7,3,8,6,4] => [2,1,7,6,5,8,3,4] => 4
{{1,2,6},{3,8},{4,7},{5}} => [2,6,8,7,5,1,4,3] => [5,7,2,1,8,4,6,3] => [2,7,6,8,5,4,1,3] => 3
{{1,5,7,8},{2},{3,6},{4}} => [5,2,6,4,7,3,8,1] => [2,4,8,7,3,6,5,1] => [5,2,6,4,7,1,8,3] => 3
{{1,6},{2,3,7,8},{4},{5}} => [6,3,7,4,5,1,8,2] => [4,5,8,7,3,1,6,2] => [3,7,6,4,5,2,8,1] => 3
{{1,5},{2,4,8},{3,7},{6}} => [5,4,7,8,1,6,3,2] => [6,8,1,7,4,3,5,2] => [8,5,4,7,3,6,1,2] => 2
{{1,5,7},{2,4,8},{3},{6}} => [5,4,3,8,7,6,1,2] => [3,6,7,4,1,8,5,2] => [4,7,3,5,8,6,2,1] => 4
{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 9
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => 8
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 10
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => 9
{{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => 2
{{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => 2
{{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => [7,5,3,2,8,6,4,1] => [4,3,6,5,8,7,2,1] => 2
{{1},{2,5},{3,7},{4,6,8}} => [1,5,7,6,2,8,3,4] => [1,8,6,2,7,3,5,4] => [1,6,8,5,3,7,4,2] => 2
{{1},{2,3,6,7},{4},{5,8}} => [1,3,6,4,8,7,2,5] => [1,4,7,3,2,8,6,5] => [1,3,7,4,6,8,2,5] => 4
{{1},{2,6},{3,7},{4,5,8}} => [1,6,7,5,8,2,3,4] => [1,8,5,2,7,3,6,4] => [1,5,8,7,6,4,3,2] => 2
{{1,4,5},{2,6},{3},{7,8}} => [4,6,3,5,1,2,8,7] => [3,5,1,6,4,2,8,7] => [5,4,3,6,1,2,8,7] => 4
{{1,5},{2,7},{3},{4,6,8}} => [5,7,3,6,1,8,2,4] => [3,8,6,1,7,2,5,4] => [6,8,3,5,2,7,4,1] => 2
{{1,5,6},{2},{3,4,8},{7}} => [5,2,4,8,6,1,7,3] => [2,6,4,1,7,8,5,3] => [4,2,6,5,8,3,7,1] => 4
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 8
{{1,3},{2},{4},{5},{6},{7},{8},{9}} => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => 8
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 9
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => 9
{{1,8},{2},{3,6},{4,5,7}} => [8,2,6,5,7,3,4,1] => [2,7,5,3,6,4,8,1] => [8,2,5,7,6,4,3,1] => 3
{{1,5},{2,6},{3,4,7},{8}} => [5,6,4,7,1,2,3,8] => [7,4,1,6,2,5,3,8] => [4,7,6,5,3,2,1,8] => 2
{{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => 1
{{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => 3
{{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => 1
{{1,4},{2,3},{5},{6},{7},{8},{9}} => [4,3,2,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => 7
{{1,5,7},{2,3,8},{4,6}} => [5,3,8,6,7,4,1,2] => [7,4,6,3,1,8,5,2] => [3,6,5,8,7,4,1,2] => 2
{{1,3,4,5,6,7,8,9},{2}} => [3,2,4,5,6,7,8,9,1] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => 2
{{1,4,5,6,7,8,9},{2},{3}} => [4,2,3,5,6,7,8,9,1] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => 3
{{1,3,4,5,6,7,8,9,10},{2}} => [3,2,4,5,6,7,8,9,10,1] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1] => 2
{{1,9},{2,8},{3,7},{4,6},{5},{10}} => [9,8,7,6,5,4,3,2,1,10] => [5,6,4,7,3,8,2,9,1,10] => [9,8,7,6,5,4,3,2,1,10] => 6
{{1},{2,10},{3,9},{4,8},{5,7},{6}} => [1,10,9,8,7,6,5,4,3,2] => [1,6,7,5,8,4,9,3,10,2] => [1,10,9,8,7,6,5,4,3,2] => 6
{{1,4,5,7,8},{2,3,6}} => [4,3,6,5,7,2,8,1] => [8,7,5,3,2,6,4,1] => [4,3,6,5,7,1,8,2] => 1
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => 10
{{1,2},{3,6,8},{4,5,7}} => [2,1,6,5,7,8,4,3] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => 2
{{1,4,5,7,8},{2},{3,6}} => [4,2,6,5,7,3,8,1] => [2,8,7,5,3,6,4,1] => [4,2,6,5,7,1,8,3] => 2
{{1,3,8},{2,4,5,6,7}} => [3,4,8,5,6,7,2,1] => [7,6,5,2,8,4,3,1] => [3,4,8,5,6,7,2,1] => 2
{{1,5,7,8},{2,3,6},{4}} => [5,3,6,4,7,2,8,1] => [4,8,7,3,2,6,5,1] => [5,3,6,4,7,1,8,2] => 2
{{1},{2,3,6,8},{4,7},{5}} => [1,3,6,7,5,8,4,2] => [1,5,8,4,7,6,3,2] => [1,3,6,7,5,8,2,4] => 3
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Description
The number of cycles in the cycle decomposition of a permutation.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.