Identifier
Values
[1] => {{1}} => 1
[1,2] => {{1},{2}} => 3
[2,1] => {{1,2}} => 1
[1,2,3] => {{1},{2},{3}} => 6
[1,3,2] => {{1},{2,3}} => 3
[2,1,3] => {{1,2},{3}} => 4
[2,3,1] => {{1,2,3}} => 1
[3,1,2] => {{1,2,3}} => 1
[3,2,1] => {{1,3},{2}} => 3
[1,2,3,4] => {{1},{2},{3},{4}} => 10
[1,2,4,3] => {{1},{2},{3,4}} => 6
[1,3,2,4] => {{1},{2,3},{4}} => 7
[1,3,4,2] => {{1},{2,3,4}} => 3
[1,4,2,3] => {{1},{2,3,4}} => 3
[1,4,3,2] => {{1},{2,4},{3}} => 6
[2,1,3,4] => {{1,2},{3},{4}} => 8
[2,1,4,3] => {{1,2},{3,4}} => 4
[2,3,1,4] => {{1,2,3},{4}} => 5
[2,3,4,1] => {{1,2,3,4}} => 1
[2,4,1,3] => {{1,2,3,4}} => 1
[2,4,3,1] => {{1,2,4},{3}} => 4
[3,1,2,4] => {{1,2,3},{4}} => 5
[3,1,4,2] => {{1,2,3,4}} => 1
[3,2,1,4] => {{1,3},{2},{4}} => 7
[3,2,4,1] => {{1,3,4},{2}} => 3
[3,4,1,2] => {{1,3},{2,4}} => 3
[3,4,2,1] => {{1,2,3,4}} => 1
[4,1,2,3] => {{1,2,3,4}} => 1
[4,1,3,2] => {{1,2,4},{3}} => 4
[4,2,1,3] => {{1,3,4},{2}} => 3
[4,2,3,1] => {{1,4},{2},{3}} => 6
[4,3,1,2] => {{1,2,3,4}} => 1
[4,3,2,1] => {{1,4},{2,3}} => 3
[1,2,3,4,5] => {{1},{2},{3},{4},{5}} => 15
[1,2,3,5,4] => {{1},{2},{3},{4,5}} => 10
[1,2,4,3,5] => {{1},{2},{3,4},{5}} => 11
[1,2,4,5,3] => {{1},{2},{3,4,5}} => 6
[1,2,5,3,4] => {{1},{2},{3,4,5}} => 6
[1,2,5,4,3] => {{1},{2},{3,5},{4}} => 10
[1,3,2,4,5] => {{1},{2,3},{4},{5}} => 12
[1,3,2,5,4] => {{1},{2,3},{4,5}} => 7
[1,3,4,2,5] => {{1},{2,3,4},{5}} => 8
[1,3,4,5,2] => {{1},{2,3,4,5}} => 3
[1,3,5,2,4] => {{1},{2,3,4,5}} => 3
[1,3,5,4,2] => {{1},{2,3,5},{4}} => 7
[1,4,2,3,5] => {{1},{2,3,4},{5}} => 8
[1,4,2,5,3] => {{1},{2,3,4,5}} => 3
[1,4,3,2,5] => {{1},{2,4},{3},{5}} => 11
[1,4,3,5,2] => {{1},{2,4,5},{3}} => 6
[1,4,5,2,3] => {{1},{2,4},{3,5}} => 6
[1,4,5,3,2] => {{1},{2,3,4,5}} => 3
[1,5,2,3,4] => {{1},{2,3,4,5}} => 3
[1,5,2,4,3] => {{1},{2,3,5},{4}} => 7
[1,5,3,2,4] => {{1},{2,4,5},{3}} => 6
[1,5,3,4,2] => {{1},{2,5},{3},{4}} => 10
[1,5,4,2,3] => {{1},{2,3,4,5}} => 3
[1,5,4,3,2] => {{1},{2,5},{3,4}} => 6
[2,1,3,4,5] => {{1,2},{3},{4},{5}} => 13
[2,1,3,5,4] => {{1,2},{3},{4,5}} => 8
[2,1,4,3,5] => {{1,2},{3,4},{5}} => 9
[2,1,4,5,3] => {{1,2},{3,4,5}} => 4
[2,1,5,3,4] => {{1,2},{3,4,5}} => 4
[2,1,5,4,3] => {{1,2},{3,5},{4}} => 8
[2,3,1,4,5] => {{1,2,3},{4},{5}} => 10
[2,3,1,5,4] => {{1,2,3},{4,5}} => 5
[2,3,4,1,5] => {{1,2,3,4},{5}} => 6
[2,3,4,5,1] => {{1,2,3,4,5}} => 1
[2,3,5,1,4] => {{1,2,3,4,5}} => 1
[2,3,5,4,1] => {{1,2,3,5},{4}} => 5
[2,4,1,3,5] => {{1,2,3,4},{5}} => 6
[2,4,1,5,3] => {{1,2,3,4,5}} => 1
[2,4,3,1,5] => {{1,2,4},{3},{5}} => 9
[2,4,3,5,1] => {{1,2,4,5},{3}} => 4
[2,4,5,1,3] => {{1,2,4},{3,5}} => 4
[2,4,5,3,1] => {{1,2,3,4,5}} => 1
[2,5,1,3,4] => {{1,2,3,4,5}} => 1
[2,5,1,4,3] => {{1,2,3,5},{4}} => 5
[2,5,3,1,4] => {{1,2,4,5},{3}} => 4
[2,5,3,4,1] => {{1,2,5},{3},{4}} => 8
[2,5,4,1,3] => {{1,2,3,4,5}} => 1
[2,5,4,3,1] => {{1,2,5},{3,4}} => 4
[3,1,2,4,5] => {{1,2,3},{4},{5}} => 10
[3,1,2,5,4] => {{1,2,3},{4,5}} => 5
[3,1,4,2,5] => {{1,2,3,4},{5}} => 6
[3,1,4,5,2] => {{1,2,3,4,5}} => 1
[3,1,5,2,4] => {{1,2,3,4,5}} => 1
[3,1,5,4,2] => {{1,2,3,5},{4}} => 5
[3,2,1,4,5] => {{1,3},{2},{4},{5}} => 12
[3,2,1,5,4] => {{1,3},{2},{4,5}} => 7
[3,2,4,1,5] => {{1,3,4},{2},{5}} => 8
[3,2,4,5,1] => {{1,3,4,5},{2}} => 3
[3,2,5,1,4] => {{1,3,4,5},{2}} => 3
[3,2,5,4,1] => {{1,3,5},{2},{4}} => 7
[3,4,1,2,5] => {{1,3},{2,4},{5}} => 8
[3,4,1,5,2] => {{1,3},{2,4,5}} => 3
[3,4,2,1,5] => {{1,2,3,4},{5}} => 6
[3,4,2,5,1] => {{1,2,3,4,5}} => 1
[3,4,5,1,2] => {{1,2,3,4,5}} => 1
[3,4,5,2,1] => {{1,3,5},{2,4}} => 3
[3,5,1,2,4] => {{1,3},{2,4,5}} => 3
[3,5,1,4,2] => {{1,3},{2,5},{4}} => 7
>>> Load all 873 entries. <<<
[3,5,2,1,4] => {{1,2,3,4,5}} => 1
[3,5,2,4,1] => {{1,2,3,5},{4}} => 5
[3,5,4,1,2] => {{1,3,4},{2,5}} => 3
[3,5,4,2,1] => {{1,2,3,4,5}} => 1
[4,1,2,3,5] => {{1,2,3,4},{5}} => 6
[4,1,2,5,3] => {{1,2,3,4,5}} => 1
[4,1,3,2,5] => {{1,2,4},{3},{5}} => 9
[4,1,3,5,2] => {{1,2,4,5},{3}} => 4
[4,1,5,2,3] => {{1,2,4},{3,5}} => 4
[4,1,5,3,2] => {{1,2,3,4,5}} => 1
[4,2,1,3,5] => {{1,3,4},{2},{5}} => 8
[4,2,1,5,3] => {{1,3,4,5},{2}} => 3
[4,2,3,1,5] => {{1,4},{2},{3},{5}} => 11
[4,2,3,5,1] => {{1,4,5},{2},{3}} => 6
[4,2,5,1,3] => {{1,4},{2},{3,5}} => 6
[4,2,5,3,1] => {{1,3,4,5},{2}} => 3
[4,3,1,2,5] => {{1,2,3,4},{5}} => 6
[4,3,1,5,2] => {{1,2,3,4,5}} => 1
[4,3,2,1,5] => {{1,4},{2,3},{5}} => 8
[4,3,2,5,1] => {{1,4,5},{2,3}} => 3
[4,3,5,1,2] => {{1,4},{2,3,5}} => 3
[4,3,5,2,1] => {{1,2,3,4,5}} => 1
[4,5,1,2,3] => {{1,2,3,4,5}} => 1
[4,5,1,3,2] => {{1,3,4},{2,5}} => 3
[4,5,2,1,3] => {{1,4},{2,3,5}} => 3
[4,5,2,3,1] => {{1,2,3,4,5}} => 1
[4,5,3,1,2] => {{1,4},{2,5},{3}} => 6
[4,5,3,2,1] => {{1,2,4,5},{3}} => 4
[5,1,2,3,4] => {{1,2,3,4,5}} => 1
[5,1,2,4,3] => {{1,2,3,5},{4}} => 5
[5,1,3,2,4] => {{1,2,4,5},{3}} => 4
[5,1,3,4,2] => {{1,2,5},{3},{4}} => 8
[5,1,4,2,3] => {{1,2,3,4,5}} => 1
[5,1,4,3,2] => {{1,2,5},{3,4}} => 4
[5,2,1,3,4] => {{1,3,4,5},{2}} => 3
[5,2,1,4,3] => {{1,3,5},{2},{4}} => 7
[5,2,3,1,4] => {{1,4,5},{2},{3}} => 6
[5,2,3,4,1] => {{1,5},{2},{3},{4}} => 10
[5,2,4,1,3] => {{1,3,4,5},{2}} => 3
[5,2,4,3,1] => {{1,5},{2},{3,4}} => 6
[5,3,1,2,4] => {{1,2,3,4,5}} => 1
[5,3,1,4,2] => {{1,2,3,5},{4}} => 5
[5,3,2,1,4] => {{1,4,5},{2,3}} => 3
[5,3,2,4,1] => {{1,5},{2,3},{4}} => 7
[5,3,4,1,2] => {{1,2,3,4,5}} => 1
[5,3,4,2,1] => {{1,5},{2,3,4}} => 3
[5,4,1,2,3] => {{1,3,5},{2,4}} => 3
[5,4,1,3,2] => {{1,2,3,4,5}} => 1
[5,4,2,1,3] => {{1,2,3,4,5}} => 1
[5,4,2,3,1] => {{1,5},{2,3,4}} => 3
[5,4,3,1,2] => {{1,2,4,5},{3}} => 4
[5,4,3,2,1] => {{1,5},{2,4},{3}} => 6
[1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => 21
[1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => 15
[1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => 16
[1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => 10
[1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => 10
[1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => 15
[1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => 17
[1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => 11
[1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => 12
[1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => 6
[1,2,4,6,3,5] => {{1},{2},{3,4,5,6}} => 6
[1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => 11
[1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}} => 12
[1,2,5,3,6,4] => {{1},{2},{3,4,5,6}} => 6
[1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => 16
[1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => 10
[1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => 10
[1,2,5,6,4,3] => {{1},{2},{3,4,5,6}} => 6
[1,2,6,3,4,5] => {{1},{2},{3,4,5,6}} => 6
[1,2,6,3,5,4] => {{1},{2},{3,4,6},{5}} => 11
[1,2,6,4,3,5] => {{1},{2},{3,5,6},{4}} => 10
[1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => 15
[1,2,6,5,3,4] => {{1},{2},{3,4,5,6}} => 6
[1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => 10
[1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => 18
[1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => 12
[1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => 13
[1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => 7
[1,3,2,6,4,5] => {{1},{2,3},{4,5,6}} => 7
[1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => 12
[1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => 14
[1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => 8
[1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => 9
[1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => 3
[1,3,4,6,2,5] => {{1},{2,3,4,5,6}} => 3
[1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => 8
[1,3,5,2,4,6] => {{1},{2,3,4,5},{6}} => 9
[1,3,5,2,6,4] => {{1},{2,3,4,5,6}} => 3
[1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => 13
[1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => 7
[1,3,5,6,2,4] => {{1},{2,3,5},{4,6}} => 7
[1,3,5,6,4,2] => {{1},{2,3,4,5,6}} => 3
[1,3,6,2,4,5] => {{1},{2,3,4,5,6}} => 3
[1,3,6,2,5,4] => {{1},{2,3,4,6},{5}} => 8
[1,3,6,4,2,5] => {{1},{2,3,5,6},{4}} => 7
[1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}} => 12
[1,3,6,5,2,4] => {{1},{2,3,4,5,6}} => 3
[1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => 7
[1,4,2,3,5,6] => {{1},{2,3,4},{5},{6}} => 14
[1,4,2,3,6,5] => {{1},{2,3,4},{5,6}} => 8
[1,4,2,5,3,6] => {{1},{2,3,4,5},{6}} => 9
[1,4,2,5,6,3] => {{1},{2,3,4,5,6}} => 3
[1,4,2,6,3,5] => {{1},{2,3,4,5,6}} => 3
[1,4,2,6,5,3] => {{1},{2,3,4,6},{5}} => 8
[1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => 17
[1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => 11
[1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => 12
[1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => 6
[1,4,3,6,2,5] => {{1},{2,4,5,6},{3}} => 6
[1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => 11
[1,4,5,2,3,6] => {{1},{2,4},{3,5},{6}} => 12
[1,4,5,2,6,3] => {{1},{2,4},{3,5,6}} => 6
[1,4,5,3,2,6] => {{1},{2,3,4,5},{6}} => 9
[1,4,5,3,6,2] => {{1},{2,3,4,5,6}} => 3
[1,4,5,6,2,3] => {{1},{2,3,4,5,6}} => 3
[1,4,5,6,3,2] => {{1},{2,4,6},{3,5}} => 6
[1,4,6,2,3,5] => {{1},{2,4},{3,5,6}} => 6
[1,4,6,2,5,3] => {{1},{2,4},{3,6},{5}} => 11
[1,4,6,3,2,5] => {{1},{2,3,4,5,6}} => 3
[1,4,6,3,5,2] => {{1},{2,3,4,6},{5}} => 8
[1,4,6,5,2,3] => {{1},{2,4,5},{3,6}} => 6
[1,4,6,5,3,2] => {{1},{2,3,4,5,6}} => 3
[1,5,2,3,4,6] => {{1},{2,3,4,5},{6}} => 9
[1,5,2,3,6,4] => {{1},{2,3,4,5,6}} => 3
[1,5,2,4,3,6] => {{1},{2,3,5},{4},{6}} => 13
[1,5,2,4,6,3] => {{1},{2,3,5,6},{4}} => 7
[1,5,2,6,3,4] => {{1},{2,3,5},{4,6}} => 7
[1,5,2,6,4,3] => {{1},{2,3,4,5,6}} => 3
[1,5,3,2,4,6] => {{1},{2,4,5},{3},{6}} => 12
[1,5,3,2,6,4] => {{1},{2,4,5,6},{3}} => 6
[1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => 16
[1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => 10
[1,5,3,6,2,4] => {{1},{2,5},{3},{4,6}} => 10
[1,5,3,6,4,2] => {{1},{2,4,5,6},{3}} => 6
[1,5,4,2,3,6] => {{1},{2,3,4,5},{6}} => 9
[1,5,4,2,6,3] => {{1},{2,3,4,5,6}} => 3
[1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => 12
[1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => 6
[1,5,4,6,2,3] => {{1},{2,5},{3,4,6}} => 6
[1,5,4,6,3,2] => {{1},{2,3,4,5,6}} => 3
[1,5,6,2,3,4] => {{1},{2,3,4,5,6}} => 3
[1,5,6,2,4,3] => {{1},{2,4,5},{3,6}} => 6
[1,5,6,3,2,4] => {{1},{2,5},{3,4,6}} => 6
[1,5,6,3,4,2] => {{1},{2,3,4,5,6}} => 3
[1,5,6,4,2,3] => {{1},{2,5},{3,6},{4}} => 10
[1,5,6,4,3,2] => {{1},{2,3,5,6},{4}} => 7
[1,6,2,3,4,5] => {{1},{2,3,4,5,6}} => 3
[1,6,2,3,5,4] => {{1},{2,3,4,6},{5}} => 8
[1,6,2,4,3,5] => {{1},{2,3,5,6},{4}} => 7
[1,6,2,4,5,3] => {{1},{2,3,6},{4},{5}} => 12
[1,6,2,5,3,4] => {{1},{2,3,4,5,6}} => 3
[1,6,2,5,4,3] => {{1},{2,3,6},{4,5}} => 7
[1,6,3,2,4,5] => {{1},{2,4,5,6},{3}} => 6
[1,6,3,2,5,4] => {{1},{2,4,6},{3},{5}} => 11
[1,6,3,4,2,5] => {{1},{2,5,6},{3},{4}} => 10
[1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => 15
[1,6,3,5,2,4] => {{1},{2,4,5,6},{3}} => 6
[1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => 10
[1,6,4,2,3,5] => {{1},{2,3,4,5,6}} => 3
[1,6,4,2,5,3] => {{1},{2,3,4,6},{5}} => 8
[1,6,4,3,2,5] => {{1},{2,5,6},{3,4}} => 6
[1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => 11
[1,6,4,5,2,3] => {{1},{2,3,4,5,6}} => 3
[1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => 6
[1,6,5,2,3,4] => {{1},{2,4,6},{3,5}} => 6
[1,6,5,2,4,3] => {{1},{2,3,4,5,6}} => 3
[1,6,5,3,2,4] => {{1},{2,3,4,5,6}} => 3
[1,6,5,3,4,2] => {{1},{2,6},{3,4,5}} => 6
[1,6,5,4,2,3] => {{1},{2,3,5,6},{4}} => 7
[1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => 10
[2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => 19
[2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => 13
[2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => 14
[2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => 8
[2,1,3,6,4,5] => {{1,2},{3},{4,5,6}} => 8
[2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => 13
[2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => 15
[2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => 9
[2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => 10
[2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => 4
[2,1,4,6,3,5] => {{1,2},{3,4,5,6}} => 4
[2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => 9
[2,1,5,3,4,6] => {{1,2},{3,4,5},{6}} => 10
[2,1,5,3,6,4] => {{1,2},{3,4,5,6}} => 4
[2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => 14
[2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => 8
[2,1,5,6,3,4] => {{1,2},{3,5},{4,6}} => 8
[2,1,5,6,4,3] => {{1,2},{3,4,5,6}} => 4
[2,1,6,3,4,5] => {{1,2},{3,4,5,6}} => 4
[2,1,6,3,5,4] => {{1,2},{3,4,6},{5}} => 9
[2,1,6,4,3,5] => {{1,2},{3,5,6},{4}} => 8
[2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => 13
[2,1,6,5,3,4] => {{1,2},{3,4,5,6}} => 4
[2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => 8
[2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => 16
[2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => 10
[2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => 11
[2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => 5
[2,3,1,6,4,5] => {{1,2,3},{4,5,6}} => 5
[2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => 10
[2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => 12
[2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => 6
[2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => 7
[2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 1
[2,3,4,6,1,5] => {{1,2,3,4,5,6}} => 1
[2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => 6
[2,3,5,1,4,6] => {{1,2,3,4,5},{6}} => 7
[2,3,5,1,6,4] => {{1,2,3,4,5,6}} => 1
[2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => 11
[2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => 5
[2,3,5,6,1,4] => {{1,2,3,5},{4,6}} => 5
[2,3,5,6,4,1] => {{1,2,3,4,5,6}} => 1
[2,3,6,1,4,5] => {{1,2,3,4,5,6}} => 1
[2,3,6,1,5,4] => {{1,2,3,4,6},{5}} => 6
[2,3,6,4,1,5] => {{1,2,3,5,6},{4}} => 5
[2,3,6,4,5,1] => {{1,2,3,6},{4},{5}} => 10
[2,3,6,5,1,4] => {{1,2,3,4,5,6}} => 1
[2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => 5
[2,4,1,3,5,6] => {{1,2,3,4},{5},{6}} => 12
[2,4,1,3,6,5] => {{1,2,3,4},{5,6}} => 6
[2,4,1,5,3,6] => {{1,2,3,4,5},{6}} => 7
[2,4,1,5,6,3] => {{1,2,3,4,5,6}} => 1
[2,4,1,6,3,5] => {{1,2,3,4,5,6}} => 1
[2,4,1,6,5,3] => {{1,2,3,4,6},{5}} => 6
[2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => 15
[2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => 9
[2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => 10
[2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => 4
[2,4,3,6,1,5] => {{1,2,4,5,6},{3}} => 4
[2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => 9
[2,4,5,1,3,6] => {{1,2,4},{3,5},{6}} => 10
[2,4,5,1,6,3] => {{1,2,4},{3,5,6}} => 4
[2,4,5,3,1,6] => {{1,2,3,4,5},{6}} => 7
[2,4,5,3,6,1] => {{1,2,3,4,5,6}} => 1
[2,4,5,6,1,3] => {{1,2,3,4,5,6}} => 1
[2,4,5,6,3,1] => {{1,2,4,6},{3,5}} => 4
[2,4,6,1,3,5] => {{1,2,4},{3,5,6}} => 4
[2,4,6,1,5,3] => {{1,2,4},{3,6},{5}} => 9
[2,4,6,3,1,5] => {{1,2,3,4,5,6}} => 1
[2,4,6,3,5,1] => {{1,2,3,4,6},{5}} => 6
[2,4,6,5,1,3] => {{1,2,4,5},{3,6}} => 4
[2,4,6,5,3,1] => {{1,2,3,4,5,6}} => 1
[2,5,1,3,4,6] => {{1,2,3,4,5},{6}} => 7
[2,5,1,3,6,4] => {{1,2,3,4,5,6}} => 1
[2,5,1,4,3,6] => {{1,2,3,5},{4},{6}} => 11
[2,5,1,4,6,3] => {{1,2,3,5,6},{4}} => 5
[2,5,1,6,3,4] => {{1,2,3,5},{4,6}} => 5
[2,5,1,6,4,3] => {{1,2,3,4,5,6}} => 1
[2,5,3,1,4,6] => {{1,2,4,5},{3},{6}} => 10
[2,5,3,1,6,4] => {{1,2,4,5,6},{3}} => 4
[2,5,3,4,1,6] => {{1,2,5},{3},{4},{6}} => 14
[2,5,3,4,6,1] => {{1,2,5,6},{3},{4}} => 8
[2,5,3,6,1,4] => {{1,2,5},{3},{4,6}} => 8
[2,5,3,6,4,1] => {{1,2,4,5,6},{3}} => 4
[2,5,4,1,3,6] => {{1,2,3,4,5},{6}} => 7
[2,5,4,1,6,3] => {{1,2,3,4,5,6}} => 1
[2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => 10
[2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => 4
[2,5,4,6,1,3] => {{1,2,5},{3,4,6}} => 4
[2,5,4,6,3,1] => {{1,2,3,4,5,6}} => 1
[2,5,6,1,3,4] => {{1,2,3,4,5,6}} => 1
[2,5,6,1,4,3] => {{1,2,4,5},{3,6}} => 4
[2,5,6,3,1,4] => {{1,2,5},{3,4,6}} => 4
[2,5,6,3,4,1] => {{1,2,3,4,5,6}} => 1
[2,5,6,4,1,3] => {{1,2,5},{3,6},{4}} => 8
[2,5,6,4,3,1] => {{1,2,3,5,6},{4}} => 5
[2,6,1,3,4,5] => {{1,2,3,4,5,6}} => 1
[2,6,1,3,5,4] => {{1,2,3,4,6},{5}} => 6
[2,6,1,4,3,5] => {{1,2,3,5,6},{4}} => 5
[2,6,1,4,5,3] => {{1,2,3,6},{4},{5}} => 10
[2,6,1,5,3,4] => {{1,2,3,4,5,6}} => 1
[2,6,1,5,4,3] => {{1,2,3,6},{4,5}} => 5
[2,6,3,1,4,5] => {{1,2,4,5,6},{3}} => 4
[2,6,3,1,5,4] => {{1,2,4,6},{3},{5}} => 9
[2,6,3,4,1,5] => {{1,2,5,6},{3},{4}} => 8
[2,6,3,4,5,1] => {{1,2,6},{3},{4},{5}} => 13
[2,6,3,5,1,4] => {{1,2,4,5,6},{3}} => 4
[2,6,3,5,4,1] => {{1,2,6},{3},{4,5}} => 8
[2,6,4,1,3,5] => {{1,2,3,4,5,6}} => 1
[2,6,4,1,5,3] => {{1,2,3,4,6},{5}} => 6
[2,6,4,3,1,5] => {{1,2,5,6},{3,4}} => 4
[2,6,4,3,5,1] => {{1,2,6},{3,4},{5}} => 9
[2,6,4,5,1,3] => {{1,2,3,4,5,6}} => 1
[2,6,4,5,3,1] => {{1,2,6},{3,4,5}} => 4
[2,6,5,1,3,4] => {{1,2,4,6},{3,5}} => 4
[2,6,5,1,4,3] => {{1,2,3,4,5,6}} => 1
[2,6,5,3,1,4] => {{1,2,3,4,5,6}} => 1
[2,6,5,3,4,1] => {{1,2,6},{3,4,5}} => 4
[2,6,5,4,1,3] => {{1,2,3,5,6},{4}} => 5
[2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => 8
[3,1,2,4,5,6] => {{1,2,3},{4},{5},{6}} => 16
[3,1,2,4,6,5] => {{1,2,3},{4},{5,6}} => 10
[3,1,2,5,4,6] => {{1,2,3},{4,5},{6}} => 11
[3,1,2,5,6,4] => {{1,2,3},{4,5,6}} => 5
[3,1,2,6,4,5] => {{1,2,3},{4,5,6}} => 5
[3,1,2,6,5,4] => {{1,2,3},{4,6},{5}} => 10
[3,1,4,2,5,6] => {{1,2,3,4},{5},{6}} => 12
[3,1,4,2,6,5] => {{1,2,3,4},{5,6}} => 6
[3,1,4,5,2,6] => {{1,2,3,4,5},{6}} => 7
[3,1,4,5,6,2] => {{1,2,3,4,5,6}} => 1
[3,1,4,6,2,5] => {{1,2,3,4,5,6}} => 1
[3,1,4,6,5,2] => {{1,2,3,4,6},{5}} => 6
[3,1,5,2,4,6] => {{1,2,3,4,5},{6}} => 7
[3,1,5,2,6,4] => {{1,2,3,4,5,6}} => 1
[3,1,5,4,2,6] => {{1,2,3,5},{4},{6}} => 11
[3,1,5,4,6,2] => {{1,2,3,5,6},{4}} => 5
[3,1,5,6,2,4] => {{1,2,3,5},{4,6}} => 5
[3,1,5,6,4,2] => {{1,2,3,4,5,6}} => 1
[3,1,6,2,4,5] => {{1,2,3,4,5,6}} => 1
[3,1,6,2,5,4] => {{1,2,3,4,6},{5}} => 6
[3,1,6,4,2,5] => {{1,2,3,5,6},{4}} => 5
[3,1,6,4,5,2] => {{1,2,3,6},{4},{5}} => 10
[3,1,6,5,2,4] => {{1,2,3,4,5,6}} => 1
[3,1,6,5,4,2] => {{1,2,3,6},{4,5}} => 5
[3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => 18
[3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => 12
[3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => 13
[3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => 7
[3,2,1,6,4,5] => {{1,3},{2},{4,5,6}} => 7
[3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => 12
[3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => 14
[3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => 8
[3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => 9
[3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => 3
[3,2,4,6,1,5] => {{1,3,4,5,6},{2}} => 3
[3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => 8
[3,2,5,1,4,6] => {{1,3,4,5},{2},{6}} => 9
[3,2,5,1,6,4] => {{1,3,4,5,6},{2}} => 3
[3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => 13
[3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => 7
[3,2,5,6,1,4] => {{1,3,5},{2},{4,6}} => 7
[3,2,5,6,4,1] => {{1,3,4,5,6},{2}} => 3
[3,2,6,1,4,5] => {{1,3,4,5,6},{2}} => 3
[3,2,6,1,5,4] => {{1,3,4,6},{2},{5}} => 8
[3,2,6,4,1,5] => {{1,3,5,6},{2},{4}} => 7
[3,2,6,4,5,1] => {{1,3,6},{2},{4},{5}} => 12
[3,2,6,5,1,4] => {{1,3,4,5,6},{2}} => 3
[3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => 7
[3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => 14
[3,4,1,2,6,5] => {{1,3},{2,4},{5,6}} => 8
[3,4,1,5,2,6] => {{1,3},{2,4,5},{6}} => 9
[3,4,1,5,6,2] => {{1,3},{2,4,5,6}} => 3
[3,4,1,6,2,5] => {{1,3},{2,4,5,6}} => 3
[3,4,1,6,5,2] => {{1,3},{2,4,6},{5}} => 8
[3,4,2,1,5,6] => {{1,2,3,4},{5},{6}} => 12
[3,4,2,1,6,5] => {{1,2,3,4},{5,6}} => 6
[3,4,2,5,1,6] => {{1,2,3,4,5},{6}} => 7
[3,4,2,5,6,1] => {{1,2,3,4,5,6}} => 1
[3,4,2,6,1,5] => {{1,2,3,4,5,6}} => 1
[3,4,2,6,5,1] => {{1,2,3,4,6},{5}} => 6
[3,4,5,1,2,6] => {{1,2,3,4,5},{6}} => 7
[3,4,5,1,6,2] => {{1,2,3,4,5,6}} => 1
[3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => 9
[3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => 3
[3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => 3
[3,4,5,6,2,1] => {{1,2,3,4,5,6}} => 1
[3,4,6,1,2,5] => {{1,2,3,4,5,6}} => 1
[3,4,6,1,5,2] => {{1,2,3,4,6},{5}} => 6
[3,4,6,2,1,5] => {{1,3,5,6},{2,4}} => 3
[3,4,6,2,5,1] => {{1,3,6},{2,4},{5}} => 8
[3,4,6,5,1,2] => {{1,2,3,4,5,6}} => 1
[3,4,6,5,2,1] => {{1,3,6},{2,4,5}} => 3
[3,5,1,2,4,6] => {{1,3},{2,4,5},{6}} => 9
[3,5,1,2,6,4] => {{1,3},{2,4,5,6}} => 3
[3,5,1,4,2,6] => {{1,3},{2,5},{4},{6}} => 13
[3,5,1,4,6,2] => {{1,3},{2,5,6},{4}} => 7
[3,5,1,6,2,4] => {{1,3},{2,5},{4,6}} => 7
[3,5,1,6,4,2] => {{1,3},{2,4,5,6}} => 3
[3,5,2,1,4,6] => {{1,2,3,4,5},{6}} => 7
[3,5,2,1,6,4] => {{1,2,3,4,5,6}} => 1
[3,5,2,4,1,6] => {{1,2,3,5},{4},{6}} => 11
[3,5,2,4,6,1] => {{1,2,3,5,6},{4}} => 5
[3,5,2,6,1,4] => {{1,2,3,5},{4,6}} => 5
[3,5,2,6,4,1] => {{1,2,3,4,5,6}} => 1
[3,5,4,1,2,6] => {{1,3,4},{2,5},{6}} => 9
[3,5,4,1,6,2] => {{1,3,4},{2,5,6}} => 3
[3,5,4,2,1,6] => {{1,2,3,4,5},{6}} => 7
[3,5,4,2,6,1] => {{1,2,3,4,5,6}} => 1
[3,5,4,6,1,2] => {{1,2,3,4,5,6}} => 1
[3,5,4,6,2,1] => {{1,3,4,6},{2,5}} => 3
[3,5,6,1,2,4] => {{1,3,4,6},{2,5}} => 3
[3,5,6,1,4,2] => {{1,2,3,4,5,6}} => 1
[3,5,6,2,1,4] => {{1,2,3,4,5,6}} => 1
[3,5,6,2,4,1] => {{1,3,6},{2,4,5}} => 3
[3,5,6,4,1,2] => {{1,2,3,5,6},{4}} => 5
[3,5,6,4,2,1] => {{1,3,6},{2,5},{4}} => 7
[3,6,1,2,4,5] => {{1,3},{2,4,5,6}} => 3
[3,6,1,2,5,4] => {{1,3},{2,4,6},{5}} => 8
[3,6,1,4,2,5] => {{1,3},{2,5,6},{4}} => 7
[3,6,1,4,5,2] => {{1,3},{2,6},{4},{5}} => 12
[3,6,1,5,2,4] => {{1,3},{2,4,5,6}} => 3
[3,6,1,5,4,2] => {{1,3},{2,6},{4,5}} => 7
[3,6,2,1,4,5] => {{1,2,3,4,5,6}} => 1
[3,6,2,1,5,4] => {{1,2,3,4,6},{5}} => 6
[3,6,2,4,1,5] => {{1,2,3,5,6},{4}} => 5
[3,6,2,4,5,1] => {{1,2,3,6},{4},{5}} => 10
[3,6,2,5,1,4] => {{1,2,3,4,5,6}} => 1
[3,6,2,5,4,1] => {{1,2,3,6},{4,5}} => 5
[3,6,4,1,2,5] => {{1,3,4},{2,5,6}} => 3
[3,6,4,1,5,2] => {{1,3,4},{2,6},{5}} => 8
[3,6,4,2,1,5] => {{1,2,3,4,5,6}} => 1
[3,6,4,2,5,1] => {{1,2,3,4,6},{5}} => 6
[3,6,4,5,1,2] => {{1,3,4,5},{2,6}} => 3
[3,6,4,5,2,1] => {{1,2,3,4,5,6}} => 1
[3,6,5,1,2,4] => {{1,2,3,4,5,6}} => 1
[3,6,5,1,4,2] => {{1,3,4,5},{2,6}} => 3
[3,6,5,2,1,4] => {{1,3,5},{2,4,6}} => 3
[3,6,5,2,4,1] => {{1,2,3,4,5,6}} => 1
[3,6,5,4,1,2] => {{1,3,5},{2,6},{4}} => 7
[3,6,5,4,2,1] => {{1,2,3,5,6},{4}} => 5
[4,1,2,3,5,6] => {{1,2,3,4},{5},{6}} => 12
[4,1,2,3,6,5] => {{1,2,3,4},{5,6}} => 6
[4,1,2,5,3,6] => {{1,2,3,4,5},{6}} => 7
[4,1,2,5,6,3] => {{1,2,3,4,5,6}} => 1
[4,1,2,6,3,5] => {{1,2,3,4,5,6}} => 1
[4,1,2,6,5,3] => {{1,2,3,4,6},{5}} => 6
[4,1,3,2,5,6] => {{1,2,4},{3},{5},{6}} => 15
[4,1,3,2,6,5] => {{1,2,4},{3},{5,6}} => 9
[4,1,3,5,2,6] => {{1,2,4,5},{3},{6}} => 10
[4,1,3,5,6,2] => {{1,2,4,5,6},{3}} => 4
[4,1,3,6,2,5] => {{1,2,4,5,6},{3}} => 4
[4,1,3,6,5,2] => {{1,2,4,6},{3},{5}} => 9
[4,1,5,2,3,6] => {{1,2,4},{3,5},{6}} => 10
[4,1,5,2,6,3] => {{1,2,4},{3,5,6}} => 4
[4,1,5,3,2,6] => {{1,2,3,4,5},{6}} => 7
[4,1,5,3,6,2] => {{1,2,3,4,5,6}} => 1
[4,1,5,6,2,3] => {{1,2,3,4,5,6}} => 1
[4,1,5,6,3,2] => {{1,2,4,6},{3,5}} => 4
[4,1,6,2,3,5] => {{1,2,4},{3,5,6}} => 4
[4,1,6,2,5,3] => {{1,2,4},{3,6},{5}} => 9
[4,1,6,3,2,5] => {{1,2,3,4,5,6}} => 1
[4,1,6,3,5,2] => {{1,2,3,4,6},{5}} => 6
[4,1,6,5,2,3] => {{1,2,4,5},{3,6}} => 4
[4,1,6,5,3,2] => {{1,2,3,4,5,6}} => 1
[4,2,1,3,5,6] => {{1,3,4},{2},{5},{6}} => 14
[4,2,1,3,6,5] => {{1,3,4},{2},{5,6}} => 8
[4,2,1,5,3,6] => {{1,3,4,5},{2},{6}} => 9
[4,2,1,5,6,3] => {{1,3,4,5,6},{2}} => 3
[4,2,1,6,3,5] => {{1,3,4,5,6},{2}} => 3
[4,2,1,6,5,3] => {{1,3,4,6},{2},{5}} => 8
[4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => 17
[4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => 11
[4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => 12
[4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => 6
[4,2,3,6,1,5] => {{1,4,5,6},{2},{3}} => 6
[4,2,3,6,5,1] => {{1,4,6},{2},{3},{5}} => 11
[4,2,5,1,3,6] => {{1,4},{2},{3,5},{6}} => 12
[4,2,5,1,6,3] => {{1,4},{2},{3,5,6}} => 6
[4,2,5,3,1,6] => {{1,3,4,5},{2},{6}} => 9
[4,2,5,3,6,1] => {{1,3,4,5,6},{2}} => 3
[4,2,5,6,1,3] => {{1,3,4,5,6},{2}} => 3
[4,2,5,6,3,1] => {{1,4,6},{2},{3,5}} => 6
[4,2,6,1,3,5] => {{1,4},{2},{3,5,6}} => 6
[4,2,6,1,5,3] => {{1,4},{2},{3,6},{5}} => 11
[4,2,6,3,1,5] => {{1,3,4,5,6},{2}} => 3
[4,2,6,3,5,1] => {{1,3,4,6},{2},{5}} => 8
[4,2,6,5,1,3] => {{1,4,5},{2},{3,6}} => 6
[4,2,6,5,3,1] => {{1,3,4,5,6},{2}} => 3
[4,3,1,2,5,6] => {{1,2,3,4},{5},{6}} => 12
[4,3,1,2,6,5] => {{1,2,3,4},{5,6}} => 6
[4,3,1,5,2,6] => {{1,2,3,4,5},{6}} => 7
[4,3,1,5,6,2] => {{1,2,3,4,5,6}} => 1
[4,3,1,6,2,5] => {{1,2,3,4,5,6}} => 1
[4,3,1,6,5,2] => {{1,2,3,4,6},{5}} => 6
[4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => 14
[4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => 8
[4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => 9
[4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => 3
[4,3,2,6,1,5] => {{1,4,5,6},{2,3}} => 3
[4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => 8
[4,3,5,1,2,6] => {{1,4},{2,3,5},{6}} => 9
[4,3,5,1,6,2] => {{1,4},{2,3,5,6}} => 3
[4,3,5,2,1,6] => {{1,2,3,4,5},{6}} => 7
[4,3,5,2,6,1] => {{1,2,3,4,5,6}} => 1
[4,3,5,6,1,2] => {{1,2,3,4,5,6}} => 1
[4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => 3
[4,3,6,1,2,5] => {{1,4},{2,3,5,6}} => 3
[4,3,6,1,5,2] => {{1,4},{2,3,6},{5}} => 8
[4,3,6,2,1,5] => {{1,2,3,4,5,6}} => 1
[4,3,6,2,5,1] => {{1,2,3,4,6},{5}} => 6
[4,3,6,5,1,2] => {{1,4,5},{2,3,6}} => 3
[4,3,6,5,2,1] => {{1,2,3,4,5,6}} => 1
[4,5,1,2,3,6] => {{1,2,3,4,5},{6}} => 7
[4,5,1,2,6,3] => {{1,2,3,4,5,6}} => 1
[4,5,1,3,2,6] => {{1,3,4},{2,5},{6}} => 9
[4,5,1,3,6,2] => {{1,3,4},{2,5,6}} => 3
[4,5,1,6,2,3] => {{1,3,4,6},{2,5}} => 3
[4,5,1,6,3,2] => {{1,2,3,4,5,6}} => 1
[4,5,2,1,3,6] => {{1,4},{2,3,5},{6}} => 9
[4,5,2,1,6,3] => {{1,4},{2,3,5,6}} => 3
[4,5,2,3,1,6] => {{1,2,3,4,5},{6}} => 7
[4,5,2,3,6,1] => {{1,2,3,4,5,6}} => 1
[4,5,2,6,1,3] => {{1,2,3,4,5,6}} => 1
[4,5,2,6,3,1] => {{1,4,6},{2,3,5}} => 3
[4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}} => 12
[4,5,3,1,6,2] => {{1,4},{2,5,6},{3}} => 6
[4,5,3,2,1,6] => {{1,2,4,5},{3},{6}} => 10
[4,5,3,2,6,1] => {{1,2,4,5,6},{3}} => 4
[4,5,3,6,1,2] => {{1,2,4,5,6},{3}} => 4
[4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => 6
[4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => 6
[4,5,6,1,3,2] => {{1,4},{2,3,5,6}} => 3
[4,5,6,2,1,3] => {{1,2,4,5},{3,6}} => 4
[4,5,6,2,3,1] => {{1,2,3,4,5,6}} => 1
[4,5,6,3,1,2] => {{1,2,3,4,5,6}} => 1
[4,5,6,3,2,1] => {{1,3,4,6},{2,5}} => 3
[4,6,1,2,3,5] => {{1,2,3,4,5,6}} => 1
[4,6,1,2,5,3] => {{1,2,3,4,6},{5}} => 6
[4,6,1,3,2,5] => {{1,3,4},{2,5,6}} => 3
[4,6,1,3,5,2] => {{1,3,4},{2,6},{5}} => 8
[4,6,1,5,2,3] => {{1,2,3,4,5,6}} => 1
[4,6,1,5,3,2] => {{1,3,4,5},{2,6}} => 3
[4,6,2,1,3,5] => {{1,4},{2,3,5,6}} => 3
[4,6,2,1,5,3] => {{1,4},{2,3,6},{5}} => 8
[4,6,2,3,1,5] => {{1,2,3,4,5,6}} => 1
[4,6,2,3,5,1] => {{1,2,3,4,6},{5}} => 6
[4,6,2,5,1,3] => {{1,4,5},{2,3,6}} => 3
[4,6,2,5,3,1] => {{1,2,3,4,5,6}} => 1
[4,6,3,1,2,5] => {{1,4},{2,5,6},{3}} => 6
[4,6,3,1,5,2] => {{1,4},{2,6},{3},{5}} => 11
[4,6,3,2,1,5] => {{1,2,4,5,6},{3}} => 4
[4,6,3,2,5,1] => {{1,2,4,6},{3},{5}} => 9
[4,6,3,5,1,2] => {{1,4,5},{2,6},{3}} => 6
[4,6,3,5,2,1] => {{1,2,4,5,6},{3}} => 4
[4,6,5,1,2,3] => {{1,4},{2,3,5,6}} => 3
[4,6,5,1,3,2] => {{1,4},{2,6},{3,5}} => 6
[4,6,5,2,1,3] => {{1,2,3,4,5,6}} => 1
[4,6,5,2,3,1] => {{1,2,4,6},{3,5}} => 4
[4,6,5,3,1,2] => {{1,3,4,5},{2,6}} => 3
[4,6,5,3,2,1] => {{1,2,3,4,5,6}} => 1
[5,1,2,3,4,6] => {{1,2,3,4,5},{6}} => 7
[5,1,2,3,6,4] => {{1,2,3,4,5,6}} => 1
[5,1,2,4,3,6] => {{1,2,3,5},{4},{6}} => 11
[5,1,2,4,6,3] => {{1,2,3,5,6},{4}} => 5
[5,1,2,6,3,4] => {{1,2,3,5},{4,6}} => 5
[5,1,2,6,4,3] => {{1,2,3,4,5,6}} => 1
[5,1,3,2,4,6] => {{1,2,4,5},{3},{6}} => 10
[5,1,3,2,6,4] => {{1,2,4,5,6},{3}} => 4
[5,1,3,4,2,6] => {{1,2,5},{3},{4},{6}} => 14
[5,1,3,4,6,2] => {{1,2,5,6},{3},{4}} => 8
[5,1,3,6,2,4] => {{1,2,5},{3},{4,6}} => 8
[5,1,3,6,4,2] => {{1,2,4,5,6},{3}} => 4
[5,1,4,2,3,6] => {{1,2,3,4,5},{6}} => 7
[5,1,4,2,6,3] => {{1,2,3,4,5,6}} => 1
[5,1,4,3,2,6] => {{1,2,5},{3,4},{6}} => 10
[5,1,4,3,6,2] => {{1,2,5,6},{3,4}} => 4
[5,1,4,6,2,3] => {{1,2,5},{3,4,6}} => 4
[5,1,4,6,3,2] => {{1,2,3,4,5,6}} => 1
[5,1,6,2,3,4] => {{1,2,3,4,5,6}} => 1
[5,1,6,2,4,3] => {{1,2,4,5},{3,6}} => 4
[5,1,6,3,2,4] => {{1,2,5},{3,4,6}} => 4
[5,1,6,3,4,2] => {{1,2,3,4,5,6}} => 1
[5,1,6,4,2,3] => {{1,2,5},{3,6},{4}} => 8
[5,1,6,4,3,2] => {{1,2,3,5,6},{4}} => 5
[5,2,1,3,4,6] => {{1,3,4,5},{2},{6}} => 9
[5,2,1,3,6,4] => {{1,3,4,5,6},{2}} => 3
[5,2,1,4,3,6] => {{1,3,5},{2},{4},{6}} => 13
[5,2,1,4,6,3] => {{1,3,5,6},{2},{4}} => 7
[5,2,1,6,3,4] => {{1,3,5},{2},{4,6}} => 7
[5,2,1,6,4,3] => {{1,3,4,5,6},{2}} => 3
[5,2,3,1,4,6] => {{1,4,5},{2},{3},{6}} => 12
[5,2,3,1,6,4] => {{1,4,5,6},{2},{3}} => 6
[5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => 16
[5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => 10
[5,2,3,6,1,4] => {{1,5},{2},{3},{4,6}} => 10
[5,2,3,6,4,1] => {{1,4,5,6},{2},{3}} => 6
[5,2,4,1,3,6] => {{1,3,4,5},{2},{6}} => 9
[5,2,4,1,6,3] => {{1,3,4,5,6},{2}} => 3
[5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => 12
[5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => 6
[5,2,4,6,1,3] => {{1,5},{2},{3,4,6}} => 6
[5,2,4,6,3,1] => {{1,3,4,5,6},{2}} => 3
[5,2,6,1,3,4] => {{1,3,4,5,6},{2}} => 3
[5,2,6,1,4,3] => {{1,4,5},{2},{3,6}} => 6
[5,2,6,3,1,4] => {{1,5},{2},{3,4,6}} => 6
[5,2,6,3,4,1] => {{1,3,4,5,6},{2}} => 3
[5,2,6,4,1,3] => {{1,5},{2},{3,6},{4}} => 10
[5,2,6,4,3,1] => {{1,3,5,6},{2},{4}} => 7
[5,3,1,2,4,6] => {{1,2,3,4,5},{6}} => 7
[5,3,1,2,6,4] => {{1,2,3,4,5,6}} => 1
[5,3,1,4,2,6] => {{1,2,3,5},{4},{6}} => 11
[5,3,1,4,6,2] => {{1,2,3,5,6},{4}} => 5
[5,3,1,6,2,4] => {{1,2,3,5},{4,6}} => 5
[5,3,1,6,4,2] => {{1,2,3,4,5,6}} => 1
[5,3,2,1,4,6] => {{1,4,5},{2,3},{6}} => 9
[5,3,2,1,6,4] => {{1,4,5,6},{2,3}} => 3
[5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => 13
[5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => 7
[5,3,2,6,1,4] => {{1,5},{2,3},{4,6}} => 7
[5,3,2,6,4,1] => {{1,4,5,6},{2,3}} => 3
[5,3,4,1,2,6] => {{1,2,3,4,5},{6}} => 7
[5,3,4,1,6,2] => {{1,2,3,4,5,6}} => 1
[5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => 9
[5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => 3
[5,3,4,6,1,2] => {{1,5},{2,3,4,6}} => 3
[5,3,4,6,2,1] => {{1,2,3,4,5,6}} => 1
[5,3,6,1,2,4] => {{1,2,3,4,5,6}} => 1
[5,3,6,1,4,2] => {{1,4,5},{2,3,6}} => 3
[5,3,6,2,1,4] => {{1,5},{2,3,4,6}} => 3
[5,3,6,2,4,1] => {{1,2,3,4,5,6}} => 1
[5,3,6,4,1,2] => {{1,5},{2,3,6},{4}} => 7
[5,3,6,4,2,1] => {{1,2,3,5,6},{4}} => 5
[5,4,1,2,3,6] => {{1,3,5},{2,4},{6}} => 9
[5,4,1,2,6,3] => {{1,3,5,6},{2,4}} => 3
[5,4,1,3,2,6] => {{1,2,3,4,5},{6}} => 7
[5,4,1,3,6,2] => {{1,2,3,4,5,6}} => 1
[5,4,1,6,2,3] => {{1,2,3,4,5,6}} => 1
[5,4,1,6,3,2] => {{1,3,5},{2,4,6}} => 3
[5,4,2,1,3,6] => {{1,2,3,4,5},{6}} => 7
[5,4,2,1,6,3] => {{1,2,3,4,5,6}} => 1
[5,4,2,3,1,6] => {{1,5},{2,3,4},{6}} => 9
[5,4,2,3,6,1] => {{1,5,6},{2,3,4}} => 3
[5,4,2,6,1,3] => {{1,5},{2,3,4,6}} => 3
[5,4,2,6,3,1] => {{1,2,3,4,5,6}} => 1
[5,4,3,1,2,6] => {{1,2,4,5},{3},{6}} => 10
[5,4,3,1,6,2] => {{1,2,4,5,6},{3}} => 4
[5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => 12
[5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => 6
[5,4,3,6,1,2] => {{1,5},{2,4,6},{3}} => 6
[5,4,3,6,2,1] => {{1,2,4,5,6},{3}} => 4
[5,4,6,1,2,3] => {{1,2,4,5},{3,6}} => 4
[5,4,6,1,3,2] => {{1,2,3,4,5,6}} => 1
[5,4,6,2,1,3] => {{1,5},{2,4},{3,6}} => 6
[5,4,6,2,3,1] => {{1,3,5,6},{2,4}} => 3
[5,4,6,3,1,2] => {{1,5},{2,3,4,6}} => 3
[5,4,6,3,2,1] => {{1,2,3,4,5,6}} => 1
[5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => 3
[5,6,1,2,4,3] => {{1,2,3,4,5,6}} => 1
[5,6,1,3,2,4] => {{1,2,3,4,5,6}} => 1
[5,6,1,3,4,2] => {{1,3,4,5},{2,6}} => 3
[5,6,1,4,2,3] => {{1,2,3,5,6},{4}} => 5
[5,6,1,4,3,2] => {{1,3,5},{2,6},{4}} => 7
[5,6,2,1,3,4] => {{1,2,3,4,5,6}} => 1
[5,6,2,1,4,3] => {{1,4,5},{2,3,6}} => 3
[5,6,2,3,1,4] => {{1,5},{2,3,4,6}} => 3
[5,6,2,3,4,1] => {{1,2,3,4,5,6}} => 1
[5,6,2,4,1,3] => {{1,5},{2,3,6},{4}} => 7
[5,6,2,4,3,1] => {{1,2,3,5,6},{4}} => 5
[5,6,3,1,2,4] => {{1,2,4,5,6},{3}} => 4
[5,6,3,1,4,2] => {{1,4,5},{2,6},{3}} => 6
[5,6,3,2,1,4] => {{1,5},{2,4,6},{3}} => 6
[5,6,3,2,4,1] => {{1,2,4,5,6},{3}} => 4
[5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => 10
[5,6,3,4,2,1] => {{1,2,5,6},{3},{4}} => 8
[5,6,4,1,2,3] => {{1,2,3,4,5,6}} => 1
[5,6,4,1,3,2] => {{1,3,4,5},{2,6}} => 3
[5,6,4,2,1,3] => {{1,5},{2,3,4,6}} => 3
[5,6,4,2,3,1] => {{1,2,3,4,5,6}} => 1
[5,6,4,3,1,2] => {{1,5},{2,6},{3,4}} => 6
[5,6,4,3,2,1] => {{1,2,5,6},{3,4}} => 4
[6,1,2,3,4,5] => {{1,2,3,4,5,6}} => 1
[6,1,2,3,5,4] => {{1,2,3,4,6},{5}} => 6
[6,1,2,4,3,5] => {{1,2,3,5,6},{4}} => 5
[6,1,2,4,5,3] => {{1,2,3,6},{4},{5}} => 10
[6,1,2,5,3,4] => {{1,2,3,4,5,6}} => 1
[6,1,2,5,4,3] => {{1,2,3,6},{4,5}} => 5
[6,1,3,2,4,5] => {{1,2,4,5,6},{3}} => 4
[6,1,3,2,5,4] => {{1,2,4,6},{3},{5}} => 9
[6,1,3,4,2,5] => {{1,2,5,6},{3},{4}} => 8
[6,1,3,4,5,2] => {{1,2,6},{3},{4},{5}} => 13
[6,1,3,5,2,4] => {{1,2,4,5,6},{3}} => 4
[6,1,3,5,4,2] => {{1,2,6},{3},{4,5}} => 8
[6,1,4,2,3,5] => {{1,2,3,4,5,6}} => 1
[6,1,4,2,5,3] => {{1,2,3,4,6},{5}} => 6
[6,1,4,3,2,5] => {{1,2,5,6},{3,4}} => 4
[6,1,4,3,5,2] => {{1,2,6},{3,4},{5}} => 9
[6,1,4,5,2,3] => {{1,2,3,4,5,6}} => 1
[6,1,4,5,3,2] => {{1,2,6},{3,4,5}} => 4
[6,1,5,2,3,4] => {{1,2,4,6},{3,5}} => 4
[6,1,5,2,4,3] => {{1,2,3,4,5,6}} => 1
[6,1,5,3,2,4] => {{1,2,3,4,5,6}} => 1
[6,1,5,3,4,2] => {{1,2,6},{3,4,5}} => 4
[6,1,5,4,2,3] => {{1,2,3,5,6},{4}} => 5
[6,1,5,4,3,2] => {{1,2,6},{3,5},{4}} => 8
[6,2,1,3,4,5] => {{1,3,4,5,6},{2}} => 3
[6,2,1,3,5,4] => {{1,3,4,6},{2},{5}} => 8
[6,2,1,4,3,5] => {{1,3,5,6},{2},{4}} => 7
[6,2,1,4,5,3] => {{1,3,6},{2},{4},{5}} => 12
[6,2,1,5,3,4] => {{1,3,4,5,6},{2}} => 3
[6,2,1,5,4,3] => {{1,3,6},{2},{4,5}} => 7
[6,2,3,1,4,5] => {{1,4,5,6},{2},{3}} => 6
[6,2,3,1,5,4] => {{1,4,6},{2},{3},{5}} => 11
[6,2,3,4,1,5] => {{1,5,6},{2},{3},{4}} => 10
[6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => 15
[6,2,3,5,1,4] => {{1,4,5,6},{2},{3}} => 6
[6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => 10
[6,2,4,1,3,5] => {{1,3,4,5,6},{2}} => 3
[6,2,4,1,5,3] => {{1,3,4,6},{2},{5}} => 8
[6,2,4,3,1,5] => {{1,5,6},{2},{3,4}} => 6
[6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => 11
[6,2,4,5,1,3] => {{1,3,4,5,6},{2}} => 3
[6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => 6
[6,2,5,1,3,4] => {{1,4,6},{2},{3,5}} => 6
[6,2,5,1,4,3] => {{1,3,4,5,6},{2}} => 3
[6,2,5,3,1,4] => {{1,3,4,5,6},{2}} => 3
[6,2,5,3,4,1] => {{1,6},{2},{3,4,5}} => 6
[6,2,5,4,1,3] => {{1,3,5,6},{2},{4}} => 7
[6,2,5,4,3,1] => {{1,6},{2},{3,5},{4}} => 10
[6,3,1,2,4,5] => {{1,2,3,4,5,6}} => 1
[6,3,1,2,5,4] => {{1,2,3,4,6},{5}} => 6
[6,3,1,4,2,5] => {{1,2,3,5,6},{4}} => 5
[6,3,1,4,5,2] => {{1,2,3,6},{4},{5}} => 10
[6,3,1,5,2,4] => {{1,2,3,4,5,6}} => 1
[6,3,1,5,4,2] => {{1,2,3,6},{4,5}} => 5
[6,3,2,1,4,5] => {{1,4,5,6},{2,3}} => 3
[6,3,2,1,5,4] => {{1,4,6},{2,3},{5}} => 8
[6,3,2,4,1,5] => {{1,5,6},{2,3},{4}} => 7
[6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => 12
[6,3,2,5,1,4] => {{1,4,5,6},{2,3}} => 3
[6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => 7
[6,3,4,1,2,5] => {{1,2,3,4,5,6}} => 1
[6,3,4,1,5,2] => {{1,2,3,4,6},{5}} => 6
[6,3,4,2,1,5] => {{1,5,6},{2,3,4}} => 3
[6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => 8
[6,3,4,5,1,2] => {{1,2,3,4,5,6}} => 1
[6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => 3
[6,3,5,1,2,4] => {{1,4,6},{2,3,5}} => 3
[6,3,5,1,4,2] => {{1,2,3,4,5,6}} => 1
[6,3,5,2,1,4] => {{1,2,3,4,5,6}} => 1
[6,3,5,2,4,1] => {{1,6},{2,3,4,5}} => 3
[6,3,5,4,1,2] => {{1,2,3,5,6},{4}} => 5
[6,3,5,4,2,1] => {{1,6},{2,3,5},{4}} => 7
[6,4,1,2,3,5] => {{1,3,5,6},{2,4}} => 3
[6,4,1,2,5,3] => {{1,3,6},{2,4},{5}} => 8
[6,4,1,3,2,5] => {{1,2,3,4,5,6}} => 1
[6,4,1,3,5,2] => {{1,2,3,4,6},{5}} => 6
[6,4,1,5,2,3] => {{1,3,6},{2,4,5}} => 3
[6,4,1,5,3,2] => {{1,2,3,4,5,6}} => 1
[6,4,2,1,3,5] => {{1,2,3,4,5,6}} => 1
[6,4,2,1,5,3] => {{1,2,3,4,6},{5}} => 6
[6,4,2,3,1,5] => {{1,5,6},{2,3,4}} => 3
[6,4,2,3,5,1] => {{1,6},{2,3,4},{5}} => 8
[6,4,2,5,1,3] => {{1,2,3,4,5,6}} => 1
[6,4,2,5,3,1] => {{1,6},{2,3,4,5}} => 3
[6,4,3,1,2,5] => {{1,2,4,5,6},{3}} => 4
[6,4,3,1,5,2] => {{1,2,4,6},{3},{5}} => 9
[6,4,3,2,1,5] => {{1,5,6},{2,4},{3}} => 6
[6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => 11
[6,4,3,5,1,2] => {{1,2,4,5,6},{3}} => 4
[6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => 6
[6,4,5,1,2,3] => {{1,2,3,4,5,6}} => 1
[6,4,5,1,3,2] => {{1,2,4,6},{3,5}} => 4
[6,4,5,2,1,3] => {{1,3,5,6},{2,4}} => 3
[6,4,5,2,3,1] => {{1,6},{2,4},{3,5}} => 6
[6,4,5,3,1,2] => {{1,2,3,4,5,6}} => 1
[6,4,5,3,2,1] => {{1,6},{2,3,4,5}} => 3
[6,5,1,2,3,4] => {{1,2,3,4,5,6}} => 1
[6,5,1,2,4,3] => {{1,3,6},{2,4,5}} => 3
[6,5,1,3,2,4] => {{1,3,4,6},{2,5}} => 3
[6,5,1,3,4,2] => {{1,2,3,4,5,6}} => 1
[6,5,1,4,2,3] => {{1,3,6},{2,5},{4}} => 7
[6,5,1,4,3,2] => {{1,2,3,5,6},{4}} => 5
[6,5,2,1,3,4] => {{1,4,6},{2,3,5}} => 3
[6,5,2,1,4,3] => {{1,2,3,4,5,6}} => 1
[6,5,2,3,1,4] => {{1,2,3,4,5,6}} => 1
[6,5,2,3,4,1] => {{1,6},{2,3,4,5}} => 3
[6,5,2,4,1,3] => {{1,2,3,5,6},{4}} => 5
[6,5,2,4,3,1] => {{1,6},{2,3,5},{4}} => 7
[6,5,3,1,2,4] => {{1,4,6},{2,5},{3}} => 6
[6,5,3,1,4,2] => {{1,2,4,5,6},{3}} => 4
[6,5,3,2,1,4] => {{1,2,4,5,6},{3}} => 4
[6,5,3,2,4,1] => {{1,6},{2,4,5},{3}} => 6
[6,5,3,4,1,2] => {{1,2,5,6},{3},{4}} => 8
[6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => 10
[6,5,4,1,2,3] => {{1,3,4,6},{2,5}} => 3
[6,5,4,1,3,2] => {{1,2,3,4,5,6}} => 1
[6,5,4,2,1,3] => {{1,2,3,4,5,6}} => 1
[6,5,4,2,3,1] => {{1,6},{2,3,4,5}} => 3
[6,5,4,3,1,2] => {{1,2,5,6},{3,4}} => 4
[6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => 6
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Description
Sum of the minimal elements of the blocks of a set partition.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].