Identifier
Values
{{1}} => [1] => [1,0] => [2,1] => 0
{{1,2}} => [2,1] => [1,1,0,0] => [2,3,1] => 0
{{1},{2}} => [1,2] => [1,0,1,0] => [3,1,2] => 0
{{1,2,3}} => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 1
{{1,2},{3}} => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 0
{{1,3},{2}} => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 0
{{1},{2,3}} => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 0
{{1},{2},{3}} => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 1
{{1,2,3},{4}} => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 1
{{1,2},{3,4}} => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 0
{{1,2},{3},{4}} => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 1
{{1,3},{2,4}} => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 0
{{1,4},{2,3}} => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
{{1},{2,4},{3}} => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 1
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 2
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 1
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 1
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 0
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 1
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 0
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 0
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 2
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 3
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 0
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 0
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 1
{{1,4},{2,3,5}} => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 0
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 1
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 1
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 3
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 0
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 0
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 0
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 1
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 0
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => 1
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => 0
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => 1
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => 0
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => 0
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => 2
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => 0
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => 0
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => 0
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => 0
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => 5
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => 0
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => 0
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => 0
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => 0
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
>>> Load all 337 entries. <<<
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => 0
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => 0
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => 0
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => 1
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => 1
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [8,3,1,2,4,7,5,6] => 2
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => 1
{{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => 3
{{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [8,3,1,5,6,2,4,7] => 3
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => 0
{{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => 4
{{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => 0
{{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => 4
{{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0
{{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => 2
{{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => 4
{{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => 4
{{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => 4
{{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8,3,4,1,6,7,2,5] => 4
{{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => 3
{{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => 3
{{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => 0
{{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [8,1,4,2,6,3,5,7] => 2
{{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => 0
{{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => 5
{{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => 3
{{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,7,6,5,1,3,8,4] => 3
{{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => 5
{{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,7,4,5,6,1,2,3] => 7
{{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [8,1,2,7,6,3,4,5] => 3
{{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => 0
{{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => 0
{{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3,5},{6,7}} => [8,4,5,2,3,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3,4},{6,7}} => [8,5,4,3,2,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6},{3,4},{5,7}} => [8,6,4,3,7,2,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3,5},{4,6}} => [8,7,5,6,3,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6},{3,5},{4,7}} => [8,6,5,7,3,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3,6},{4,7}} => [8,5,6,7,2,3,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3,6},{5,7}} => [8,4,6,2,7,3,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3},{4,6},{5,7}} => [8,3,2,6,7,4,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3,7},{5,6}} => [8,4,7,2,6,5,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3,7},{4,6}} => [8,5,7,6,2,4,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6},{3,7},{4,5}} => [8,6,7,5,4,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,2,3,4,5,6,7,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => 0
{{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => 0
{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,3,4,5,6,7,8] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => 0
{{1,7},{2},{3},{4},{5},{6},{8}} => [7,2,3,4,5,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3},{4},{5},{6,7}} => [8,2,3,4,5,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2},{3},{4},{5,6},{8}} => [7,2,3,4,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2},{3},{4},{5,7},{6}} => [8,2,3,4,7,6,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3},{4,5},{6},{7}} => [8,2,3,5,4,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2},{3},{4,6},{5},{8}} => [7,2,3,6,5,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,7},{2},{3},{4,5,6},{8}} => [7,2,3,5,6,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2},{3,4},{5,6,7}} => [8,2,4,3,6,7,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,4,5},{6,7}} => [8,2,4,5,3,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2},{3,6},{4,5},{8}} => [7,2,6,5,4,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2},{3,6,7},{4,5}} => [8,2,6,5,4,7,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,4,5,6},{7}} => [8,2,4,5,6,3,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,4,7},{5,6}} => [8,2,4,7,6,5,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,4,5,7},{6}} => [8,2,4,5,7,6,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,4,5,6,7}} => [8,2,4,5,6,7,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,2,3},{4},{5},{6},{7},{8}} => [2,3,1,4,5,6,7,8] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => 1
{{1,8},{2,3},{4},{5},{6},{7}} => [8,3,2,4,5,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3},{4},{5,6,7}} => [8,3,2,4,6,7,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,3},{4,5},{6},{8}} => [7,3,2,5,4,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,3},{4,6,7},{5}} => [8,3,2,6,5,7,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3},{4,5,7},{6}} => [8,3,2,5,7,6,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3},{5},{6},{7}} => [8,4,3,2,5,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3},{5},{6,7}} => [8,4,3,2,5,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,4},{3},{5,6},{8}} => [7,4,3,2,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4},{3},{5,7},{6}} => [8,4,3,2,7,6,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3},{5,6,7}} => [8,4,3,2,6,7,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3},{4},{6},{7}} => [8,5,3,4,2,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,7},{3},{4},{6}} => [8,5,3,4,7,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,6,7},{3},{4}} => [8,5,3,4,6,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,4,5},{3},{6},{8}} => [7,4,3,5,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4,5},{3},{6,7}} => [8,4,3,5,2,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,6},{3},{4,5},{8}} => [7,6,3,5,4,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,6,7},{3},{4,5}} => [8,6,3,5,4,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,4,6},{3},{5},{8}} => [7,4,3,6,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4,7},{3},{5},{6}} => [8,4,3,7,5,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,5,6},{3},{7}} => [8,4,3,5,6,2,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3},{4,5,6}} => [8,7,3,5,6,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,7},{3},{5,6}} => [8,4,3,7,6,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,5,7},{3},{6}} => [8,4,3,5,7,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,5,6,7},{3}} => [8,4,3,5,6,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,4},{5},{6},{7}} => [8,3,4,2,5,6,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,3,4},{5,6},{8}} => [7,3,4,2,6,5,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,3,4},{5,6},{7}} => [8,3,4,2,6,5,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,5},{3,4},{6},{8}} => [7,5,4,3,2,6,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,7},{2,6},{3,4},{5},{8}} => [7,6,4,3,5,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,6},{3,4},{5},{7}} => [8,6,4,3,5,2,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6,7},{3,4},{5}} => [8,6,4,3,5,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,6},{3,4},{7}} => [8,5,4,3,6,2,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,7},{3,4},{6}} => [8,5,4,3,7,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,5},{4},{6,7}} => [8,3,5,4,2,7,6,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,6,7},{3,5},{4}} => [8,6,5,4,3,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,6,7},{4},{5}} => [8,3,6,4,5,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,3,5,6},{4},{8}} => [7,3,5,4,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,7},{3,5,6},{4}} => [8,7,5,4,6,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,7},{4},{5,6}} => [8,3,7,4,6,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,5,7},{4},{6}} => [8,3,5,4,7,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,5,6,7},{4}} => [8,3,5,4,6,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,6},{3,4,5},{8}} => [7,6,4,5,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,6},{3,4,5},{7}} => [8,6,4,5,3,2,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3,4,5},{6}} => [8,7,4,5,3,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,6},{4,5},{7}} => [8,3,6,5,4,2,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,7},{4,5},{6}} => [8,3,7,5,4,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,6,7},{4,5}} => [8,3,6,5,4,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,7},{3,4,6},{5}} => [8,7,4,6,5,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,7},{4,6},{5}} => [8,3,7,6,5,4,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,3,4,5,6},{8}} => [7,3,4,5,6,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,3,4,7},{5,6}} => [8,3,4,7,6,5,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,4,5,7},{6}} => [8,3,4,5,7,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,4,5,6,7}} => [8,3,4,5,6,7,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => 0
{{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => 2
{{1,8},{2,3,6},{4},{5,7}} => [8,3,6,4,7,2,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,7},{3,6},{4}} => [8,5,6,4,7,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,6},{3,7},{5}} => [8,4,7,6,5,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6},{3,4,7},{5}} => [8,6,4,7,5,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,6},{4,7},{5}} => [8,3,6,7,5,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,3,5},{4,7},{6}} => [8,3,5,7,2,6,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3,4,7},{6}} => [8,5,4,7,2,6,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,7},{3,5},{6}} => [8,4,5,7,3,6,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,7},{3,6},{5}} => [8,4,6,7,5,3,2,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,4,6},{3,5},{8}} => [7,4,5,6,3,2,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4,5},{3,7},{6}} => [8,4,7,5,2,6,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,6},{3},{4,7}} => [8,5,3,7,6,2,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5},{3},{4,6,7}} => [8,5,3,6,2,7,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4},{3,6,7},{5}} => [8,4,6,2,5,7,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,2,3,4,5,6,7,8,9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => 0
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => 0
{{1,9},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,2,3,4,5,6,7,8,9,10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0
{{1,9},{2,3},{4},{5},{6},{7},{8}} => [9,3,2,4,5,6,7,8,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [10,2,3,4,5,6,7,8,9,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
{{1,7},{2,4},{3,5,6},{8}} => [7,4,5,2,6,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4},{3,5,6},{7}} => [8,4,5,2,6,3,7,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,6},{3,5,7},{4}} => [8,6,5,4,7,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,5,6},{3,7},{4}} => [8,5,7,4,6,2,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2,4,6},{3},{5,7}} => [8,4,3,6,7,2,5,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,5},{3,4,6},{8}} => [7,5,4,6,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2,4},{3,5,7},{6}} => [8,4,5,2,7,6,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,7},{2,4},{3,6},{5},{8}} => [7,4,6,2,5,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,10,1,3,4,5,6,7,8,9] => 0
{{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => 1
{{1,7},{2,5},{3},{4,6},{8}} => [7,5,3,6,2,4,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
{{1,8},{2},{3,5,7},{4,6}} => [8,2,5,6,7,4,3,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,8},{2},{3,5},{4,6,7}} => [8,2,5,6,3,7,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
{{1,9},{2,3,4,5,6,7,8}} => [9,3,4,5,6,7,8,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
{{1,10},{2,3,4,5,6,7,8,9}} => [10,3,4,5,6,7,8,9,2,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
{{1,9},{2,3,4,5,6,8},{7}} => [9,3,4,5,6,8,7,2,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
{{1,9},{2,4},{3},{5},{6},{7},{8}} => [9,4,3,2,5,6,7,8,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
{{1,10},{2,3},{4},{5},{6},{7},{8},{9}} => [10,3,2,4,5,6,7,8,9,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
{{1,7},{2,5},{3,6},{4},{8}} => [7,5,6,4,2,3,1,8] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => 0
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Description
The number of nestings in the permutation.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.