edit this statistic or download as text // json
Identifier
Values
[1] => 1
[1,2] => 2
[2,1] => 2
[1,2,3] => 2
[1,3,2] => 4
[2,1,3] => 4
[2,3,1] => 4
[3,1,2] => 4
[3,2,1] => 2
[1,2,3,4] => 2
[1,2,4,3] => 4
[1,3,2,4] => 2
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 2
[2,3,1,4] => 8
[2,3,4,1] => 4
[2,4,1,3] => 2
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 2
[3,2,1,4] => 4
[3,2,4,1] => 8
[3,4,1,2] => 2
[3,4,2,1] => 4
[4,1,2,3] => 4
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 2
[4,3,1,2] => 4
[4,3,2,1] => 2
[1,2,3,4,5] => 2
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 8
[1,2,5,3,4] => 8
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 8
[1,3,5,2,4] => 8
[1,3,5,4,2] => 8
[1,4,2,3,5] => 4
[1,4,2,5,3] => 8
[1,4,3,2,5] => 2
[1,4,3,5,2] => 8
[1,4,5,2,3] => 4
[1,4,5,3,2] => 8
[1,5,2,3,4] => 8
[1,5,2,4,3] => 8
[1,5,3,2,4] => 8
[1,5,3,4,2] => 4
[1,5,4,2,3] => 8
[1,5,4,3,2] => 4
[2,1,3,4,5] => 4
[2,1,3,5,4] => 2
[2,1,4,3,5] => 4
[2,1,4,5,3] => 8
[2,1,5,3,4] => 8
[2,1,5,4,3] => 4
[2,3,1,4,5] => 8
[2,3,1,5,4] => 8
[2,3,4,1,5] => 8
[2,3,4,5,1] => 4
[2,3,5,1,4] => 8
[2,3,5,4,1] => 8
[2,4,1,3,5] => 8
[2,4,1,5,3] => 4
[2,4,3,1,5] => 8
[2,4,3,5,1] => 4
[2,4,5,1,3] => 8
[2,4,5,3,1] => 8
[2,5,1,3,4] => 8
[2,5,1,4,3] => 8
[2,5,3,1,4] => 2
[2,5,3,4,1] => 8
[2,5,4,1,3] => 8
[2,5,4,3,1] => 8
[3,1,2,4,5] => 8
[3,1,2,5,4] => 8
[3,1,4,2,5] => 8
[3,1,4,5,2] => 8
[3,1,5,2,4] => 4
[3,1,5,4,2] => 8
[3,2,1,4,5] => 4
[3,2,1,5,4] => 4
[3,2,4,1,5] => 8
[3,2,4,5,1] => 8
[3,2,5,1,4] => 8
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 8
[3,4,2,1,5] => 8
[3,4,2,5,1] => 8
[3,4,5,1,2] => 4
[3,4,5,2,1] => 4
[3,5,1,2,4] => 8
[3,5,1,4,2] => 4
>>> Load all 1201 entries. <<<
[3,5,2,1,4] => 8
[3,5,2,4,1] => 8
[3,5,4,1,2] => 8
[3,5,4,2,1] => 8
[4,1,2,3,5] => 8
[4,1,2,5,3] => 8
[4,1,3,2,5] => 8
[4,1,3,5,2] => 2
[4,1,5,2,3] => 8
[4,1,5,3,2] => 8
[4,2,1,3,5] => 8
[4,2,1,5,3] => 8
[4,2,3,1,5] => 4
[4,2,3,5,1] => 8
[4,2,5,1,3] => 4
[4,2,5,3,1] => 8
[4,3,1,2,5] => 8
[4,3,1,5,2] => 8
[4,3,2,1,5] => 4
[4,3,2,5,1] => 8
[4,3,5,1,2] => 8
[4,3,5,2,1] => 8
[4,5,1,2,3] => 4
[4,5,1,3,2] => 8
[4,5,2,1,3] => 8
[4,5,2,3,1] => 4
[4,5,3,1,2] => 2
[4,5,3,2,1] => 4
[5,1,2,3,4] => 4
[5,1,2,4,3] => 8
[5,1,3,2,4] => 4
[5,1,3,4,2] => 8
[5,1,4,2,3] => 8
[5,1,4,3,2] => 8
[5,2,1,3,4] => 8
[5,2,1,4,3] => 4
[5,2,3,1,4] => 8
[5,2,3,4,1] => 2
[5,2,4,1,3] => 8
[5,2,4,3,1] => 4
[5,3,1,2,4] => 8
[5,3,1,4,2] => 8
[5,3,2,1,4] => 8
[5,3,2,4,1] => 4
[5,3,4,1,2] => 4
[5,3,4,2,1] => 4
[5,4,1,2,3] => 4
[5,4,1,3,2] => 8
[5,4,2,1,3] => 8
[5,4,2,3,1] => 4
[5,4,3,1,2] => 4
[5,4,3,2,1] => 2
[1,2,3,4,5,6] => 2
[1,2,3,4,6,5] => 4
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 8
[1,2,3,6,4,5] => 8
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 2
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 8
[1,2,4,5,6,3] => 8
[1,2,4,6,3,5] => 8
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 8
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 8
[1,2,6,3,4,5] => 8
[1,2,6,3,5,4] => 8
[1,2,6,4,3,5] => 8
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 8
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 4
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 8
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 8
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 8
[1,3,4,6,2,5] => 8
[1,3,4,6,5,2] => 8
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 8
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 8
[1,3,5,6,4,2] => 8
[1,3,6,2,4,5] => 8
[1,3,6,2,5,4] => 8
[1,3,6,4,2,5] => 8
[1,3,6,4,5,2] => 8
[1,3,6,5,2,4] => 8
[1,3,6,5,4,2] => 8
[1,4,2,3,5,6] => 8
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 4
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 8
[1,4,2,6,5,3] => 8
[1,4,3,2,5,6] => 4
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 8
[1,4,3,5,6,2] => 8
[1,4,3,6,2,5] => 8
[1,4,3,6,5,2] => 8
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 8
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 8
[1,4,5,6,3,2] => 8
[1,4,6,2,3,5] => 8
[1,4,6,2,5,3] => 4
[1,4,6,3,2,5] => 8
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 8
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 8
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 8
[1,5,2,6,4,3] => 8
[1,5,3,2,4,6] => 8
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 4
[1,5,3,6,4,2] => 8
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 8
[1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 8
[1,5,4,6,3,2] => 8
[1,5,6,2,3,4] => 8
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 8
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 8
[1,6,2,3,4,5] => 8
[1,6,2,3,5,4] => 8
[1,6,2,4,3,5] => 8
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 8
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 8
[1,6,3,2,5,4] => 8
[1,6,3,4,2,5] => 8
[1,6,3,4,5,2] => 4
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 8
[1,6,4,2,5,3] => 8
[1,6,4,3,2,5] => 8
[1,6,4,3,5,2] => 4
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 8
[1,6,5,2,4,3] => 8
[1,6,5,3,2,4] => 8
[1,6,5,3,4,2] => 8
[1,6,5,4,2,3] => 8
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 4
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 8
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 8
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 8
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 4
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 8
[2,3,1,4,6,5] => 8
[2,3,1,5,4,6] => 8
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 8
[2,3,4,1,5,6] => 8
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 8
[2,3,4,5,6,1] => 4
[2,3,4,6,1,5] => 8
[2,3,4,6,5,1] => 8
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 8
[2,3,5,4,1,6] => 8
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 8
[2,3,5,6,4,1] => 8
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 8
[2,3,6,4,1,5] => 8
[2,3,6,4,5,1] => 8
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 8
[2,4,1,3,5,6] => 8
[2,4,1,3,6,5] => 8
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 8
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 8
[2,4,3,1,5,6] => 8
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 8
[2,4,3,5,6,1] => 8
[2,4,3,6,1,5] => 8
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 4
[2,4,5,3,1,6] => 8
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 8
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 8
[2,4,6,3,1,5] => 8
[2,4,6,3,5,1] => 8
[2,4,6,5,1,3] => 8
[2,4,6,5,3,1] => 8
[2,5,1,3,4,6] => 8
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 8
[2,5,1,4,6,3] => 8
[2,5,1,6,3,4] => 8
[2,5,1,6,4,3] => 8
[2,5,3,1,4,6] => 8
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 8
[2,5,3,6,4,1] => 8
[2,5,4,1,3,6] => 8
[2,5,4,1,6,3] => 4
[2,5,4,3,1,6] => 8
[2,5,4,3,6,1] => 4
[2,5,4,6,1,3] => 8
[2,5,4,6,3,1] => 8
[2,5,6,1,3,4] => 8
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 8
[2,5,6,4,1,3] => 8
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 8
[2,6,1,3,5,4] => 8
[2,6,1,4,3,5] => 8
[2,6,1,4,5,3] => 8
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 8
[2,6,3,1,4,5] => 8
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 8
[2,6,3,5,1,4] => 8
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 8
[2,6,4,1,5,3] => 8
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 8
[2,6,4,5,1,3] => 8
[2,6,4,5,3,1] => 8
[2,6,5,1,3,4] => 8
[2,6,5,1,4,3] => 8
[2,6,5,3,1,4] => 8
[2,6,5,3,4,1] => 8
[2,6,5,4,1,3] => 8
[2,6,5,4,3,1] => 8
[3,1,2,4,5,6] => 8
[3,1,2,4,6,5] => 8
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 8
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 8
[3,1,4,5,2,6] => 8
[3,1,4,5,6,2] => 8
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 8
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 4
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 8
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 8
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 8
[3,1,6,4,5,2] => 8
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 8
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 4
[3,2,1,5,4,6] => 4
[3,2,1,5,6,4] => 8
[3,2,1,6,4,5] => 8
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 8
[3,2,4,6,1,5] => 8
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 8
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 8
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 8
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 8
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 8
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 4
[3,4,1,5,2,6] => 8
[3,4,1,5,6,2] => 8
[3,4,1,6,2,5] => 8
[3,4,1,6,5,2] => 8
[3,4,2,1,5,6] => 8
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 8
[3,4,2,5,6,1] => 8
[3,4,2,6,1,5] => 8
[3,4,2,6,5,1] => 8
[3,4,5,1,2,6] => 8
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 8
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 4
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 8
[3,4,6,2,1,5] => 8
[3,4,6,2,5,1] => 8
[3,4,6,5,1,2] => 8
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 8
[3,5,1,2,6,4] => 8
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 8
[3,5,2,1,4,6] => 8
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 8
[3,5,2,4,6,1] => 8
[3,5,2,6,1,4] => 8
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 8
[3,5,4,1,6,2] => 8
[3,5,4,2,1,6] => 8
[3,5,4,2,6,1] => 8
[3,5,4,6,1,2] => 4
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 8
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 8
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 8
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 8
[3,6,2,1,5,4] => 8
[3,6,2,4,1,5] => 8
[3,6,2,4,5,1] => 8
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 8
[3,6,4,1,2,5] => 8
[3,6,4,1,5,2] => 8
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 8
[3,6,5,1,2,4] => 8
[3,6,5,1,4,2] => 8
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 8
[3,6,5,4,2,1] => 8
[4,1,2,3,5,6] => 8
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 8
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 8
[4,1,2,6,5,3] => 8
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 8
[4,1,3,5,6,2] => 8
[4,1,3,6,2,5] => 8
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 8
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 8
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 8
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 8
[4,1,6,3,2,5] => 4
[4,1,6,3,5,2] => 8
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 8
[4,2,1,3,5,6] => 8
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 8
[4,2,1,5,6,3] => 8
[4,2,1,6,3,5] => 8
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 8
[4,2,3,6,1,5] => 8
[4,2,3,6,5,1] => 8
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 8
[4,2,5,3,1,6] => 8
[4,2,5,3,6,1] => 8
[4,2,5,6,1,3] => 8
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 8
[4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 8
[4,3,1,2,5,6] => 8
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 8
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 8
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 8
[4,3,2,5,6,1] => 8
[4,3,2,6,1,5] => 8
[4,3,2,6,5,1] => 8
[4,3,5,1,2,6] => 8
[4,3,5,1,6,2] => 8
[4,3,5,2,1,6] => 8
[4,3,5,2,6,1] => 8
[4,3,5,6,1,2] => 8
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 8
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 8
[4,3,6,5,1,2] => 4
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 8
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 8
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 4
[4,5,1,6,3,2] => 8
[4,5,2,1,3,6] => 8
[4,5,2,1,6,3] => 8
[4,5,2,3,1,6] => 8
[4,5,2,3,6,1] => 8
[4,5,2,6,1,3] => 8
[4,5,2,6,3,1] => 8
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 8
[4,5,3,2,1,6] => 8
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 8
[4,5,6,1,2,3] => 2
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 4
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 8
[4,6,1,2,5,3] => 8
[4,6,1,3,2,5] => 8
[4,6,1,3,5,2] => 8
[4,6,1,5,2,3] => 8
[4,6,1,5,3,2] => 8
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 8
[4,6,2,3,1,5] => 8
[4,6,2,3,5,1] => 8
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 8
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 8
[4,6,3,2,5,1] => 8
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 8
[4,6,5,1,2,3] => 8
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 8
[4,6,5,3,1,2] => 8
[4,6,5,3,2,1] => 8
[5,1,2,3,4,6] => 8
[5,1,2,3,6,4] => 8
[5,1,2,4,3,6] => 8
[5,1,2,4,6,3] => 8
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 8
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 8
[5,1,3,6,4,2] => 8
[5,1,4,2,3,6] => 8
[5,1,4,2,6,3] => 8
[5,1,4,3,2,6] => 8
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 8
[5,1,4,6,3,2] => 8
[5,1,6,2,3,4] => 8
[5,1,6,2,4,3] => 8
[5,1,6,3,2,4] => 8
[5,1,6,3,4,2] => 8
[5,1,6,4,2,3] => 8
[5,1,6,4,3,2] => 8
[5,2,1,3,4,6] => 8
[5,2,1,3,6,4] => 8
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 8
[5,2,1,6,4,3] => 8
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 8
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 8
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 8
[5,2,4,1,3,6] => 8
[5,2,4,1,6,3] => 8
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 8
[5,2,4,6,1,3] => 8
[5,2,4,6,3,1] => 8
[5,2,6,1,3,4] => 8
[5,2,6,1,4,3] => 8
[5,2,6,3,1,4] => 8
[5,2,6,3,4,1] => 8
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 8
[5,3,1,2,4,6] => 8
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 8
[5,3,1,4,6,2] => 8
[5,3,1,6,2,4] => 8
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 8
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 8
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 8
[5,3,4,1,2,6] => 8
[5,3,4,1,6,2] => 8
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 8
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 8
[5,3,6,1,2,4] => 8
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 8
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 8
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 8
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 8
[5,4,1,6,3,2] => 4
[5,4,2,1,3,6] => 8
[5,4,2,1,6,3] => 8
[5,4,2,3,1,6] => 8
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 8
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 8
[5,4,3,1,6,2] => 8
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 8
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 8
[5,4,6,1,2,3] => 8
[5,4,6,1,3,2] => 4
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 8
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 8
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 8
[5,6,1,3,2,4] => 4
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 8
[5,6,2,1,3,4] => 8
[5,6,2,1,4,3] => 4
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 4
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 8
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 8
[5,6,3,2,4,1] => 8
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 4
[5,6,4,1,3,2] => 8
[5,6,4,2,1,3] => 8
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 4
[6,1,2,3,4,5] => 4
[6,1,2,3,5,4] => 8
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 8
[6,1,2,5,3,4] => 8
[6,1,2,5,4,3] => 8
[6,1,3,2,4,5] => 8
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 8
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 8
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 4
[6,1,4,3,5,2] => 8
[6,1,4,5,2,3] => 8
[6,1,4,5,3,2] => 8
[6,1,5,2,3,4] => 8
[6,1,5,2,4,3] => 8
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 8
[6,1,5,4,2,3] => 8
[6,1,5,4,3,2] => 8
[6,2,1,3,4,5] => 8
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 8
[6,2,1,4,5,3] => 8
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 8
[6,2,3,1,4,5] => 8
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 8
[6,2,3,4,5,1] => 2
[6,2,3,5,1,4] => 8
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 8
[6,2,4,1,5,3] => 4
[6,2,4,3,1,5] => 8
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 8
[6,2,4,5,3,1] => 8
[6,2,5,1,3,4] => 8
[6,2,5,1,4,3] => 8
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 8
[6,2,5,4,1,3] => 8
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 8
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 8
[6,3,1,4,5,2] => 8
[6,3,1,5,2,4] => 4
[6,3,1,5,4,2] => 8
[6,3,2,1,4,5] => 8
[6,3,2,1,5,4] => 8
[6,3,2,4,1,5] => 8
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 8
[6,3,2,5,4,1] => 2
[6,3,4,1,2,5] => 8
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 4
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 8
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 8
[6,3,5,4,2,1] => 8
[6,4,1,2,3,5] => 8
[6,4,1,2,5,3] => 8
[6,4,1,3,2,5] => 8
[6,4,1,3,5,2] => 8
[6,4,1,5,2,3] => 8
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 8
[6,4,2,1,5,3] => 8
[6,4,2,3,1,5] => 8
[6,4,2,3,5,1] => 8
[6,4,2,5,1,3] => 8
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 8
[6,4,3,1,5,2] => 8
[6,4,3,2,1,5] => 8
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 8
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 8
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 4
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 4
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 8
[6,5,1,4,3,2] => 8
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 8
[6,5,2,4,3,1] => 8
[6,5,3,1,2,4] => 8
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 8
[6,5,3,2,4,1] => 8
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 8
[6,5,4,2,1,3] => 8
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 4
[6,5,4,3,2,1] => 2
[1,2,3,4,5,6,7] => 2
[1,2,3,4,5,7,6] => 4
[1,2,3,4,6,5,7] => 4
[1,2,3,4,6,7,5] => 8
[1,2,3,4,7,5,6] => 8
[1,2,3,4,7,6,5] => 4
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 8
[1,2,3,5,6,7,4] => 8
[1,2,3,5,7,4,6] => 8
[1,2,3,5,7,6,4] => 8
[1,2,3,6,4,5,7] => 8
[1,2,3,6,4,7,5] => 8
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 8
[1,2,3,6,7,4,5] => 4
[1,2,3,6,7,5,4] => 8
[1,2,3,7,4,5,6] => 8
[1,2,3,7,4,6,5] => 8
[1,2,3,7,5,4,6] => 8
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 8
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 8
[1,2,4,3,7,5,6] => 8
[1,2,4,3,7,6,5] => 4
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 8
[1,2,4,5,6,3,7] => 8
[1,2,4,5,6,7,3] => 8
[1,2,4,5,7,3,6] => 8
[1,2,4,5,7,6,3] => 8
[1,2,4,6,3,5,7] => 8
[1,2,4,6,3,7,5] => 8
[1,2,4,6,5,3,7] => 8
[1,2,4,6,5,7,3] => 8
[1,2,4,6,7,3,5] => 8
[1,2,4,6,7,5,3] => 8
[1,2,4,7,3,5,6] => 8
[1,2,4,7,3,6,5] => 8
[1,2,4,7,5,3,6] => 8
[1,2,4,7,5,6,3] => 8
[1,2,4,7,6,3,5] => 8
[1,2,4,7,6,5,3] => 8
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 8
[1,2,5,3,6,4,7] => 8
[1,2,5,3,6,7,4] => 8
[1,2,5,3,7,4,6] => 8
[1,2,5,3,7,6,4] => 8
[1,2,5,4,3,6,7] => 2
[1,2,5,4,3,7,6] => 4
[1,2,5,4,6,3,7] => 8
[1,2,5,4,6,7,3] => 8
[1,2,5,4,7,3,6] => 8
[1,2,5,4,7,6,3] => 8
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 8
[1,2,5,6,4,3,7] => 8
[1,2,5,6,4,7,3] => 8
[1,2,5,6,7,3,4] => 8
[1,2,5,6,7,4,3] => 8
[1,2,5,7,3,4,6] => 8
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 8
[1,2,5,7,4,6,3] => 8
[1,2,5,7,6,3,4] => 8
[1,2,5,7,6,4,3] => 8
[1,2,6,3,4,5,7] => 8
[1,2,6,3,4,7,5] => 8
[1,2,6,3,5,4,7] => 8
[1,2,6,3,5,7,4] => 8
[1,2,6,3,7,4,5] => 8
[1,2,6,3,7,5,4] => 8
[1,2,6,4,3,5,7] => 8
[1,2,6,4,3,7,5] => 8
[1,2,6,4,5,3,7] => 4
[1,2,6,4,5,7,3] => 8
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 8
[1,2,6,5,3,4,7] => 8
[1,2,6,5,3,7,4] => 8
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 8
[1,2,6,5,7,3,4] => 8
[1,2,6,5,7,4,3] => 8
[1,2,6,7,3,4,5] => 8
[1,2,6,7,3,5,4] => 8
[1,2,6,7,4,3,5] => 8
[1,2,6,7,4,5,3] => 8
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 8
[1,2,7,3,4,5,6] => 8
[1,2,7,3,4,6,5] => 8
[1,2,7,3,5,4,6] => 8
[1,2,7,3,5,6,4] => 8
[1,2,7,3,6,4,5] => 8
[1,2,7,3,6,5,4] => 8
[1,2,7,4,3,5,6] => 8
[1,2,7,4,3,6,5] => 8
[1,2,7,4,5,3,6] => 8
[1,2,7,4,5,6,3] => 4
[1,2,7,4,6,3,5] => 8
[1,2,7,4,6,5,3] => 4
[1,2,7,5,3,4,6] => 8
[1,2,7,5,3,6,4] => 8
[1,2,7,5,4,3,6] => 8
[1,2,7,5,4,6,3] => 4
[1,2,7,5,6,3,4] => 8
[1,2,7,5,6,4,3] => 8
[1,2,7,6,3,4,5] => 8
[1,2,7,6,3,5,4] => 8
[1,2,7,6,4,3,5] => 8
[1,2,7,6,4,5,3] => 8
[1,2,7,6,5,3,4] => 8
[1,2,7,6,5,4,3] => 4
[1,3,2,4,5,6,7] => 4
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 8
[1,3,2,4,7,5,6] => 8
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 4
[1,3,2,5,6,4,7] => 8
[1,3,2,5,6,7,4] => 8
[1,3,2,5,7,4,6] => 8
[1,3,2,5,7,6,4] => 8
[1,3,2,6,4,5,7] => 8
[1,3,2,6,4,7,5] => 8
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 8
[1,3,2,6,7,4,5] => 4
[1,3,2,6,7,5,4] => 8
[1,3,2,7,4,5,6] => 8
[1,3,2,7,4,6,5] => 8
[1,3,2,7,5,4,6] => 8
[1,3,2,7,5,6,4] => 4
[1,3,2,7,6,4,5] => 8
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 8
[1,3,4,2,5,7,6] => 8
[1,3,4,2,6,5,7] => 8
[1,3,4,2,6,7,5] => 8
[1,3,4,2,7,5,6] => 8
[1,3,4,2,7,6,5] => 8
[1,3,4,5,2,6,7] => 8
[1,3,4,5,2,7,6] => 8
[1,3,4,5,6,2,7] => 4
[1,3,4,5,6,7,2] => 8
[1,3,4,5,7,2,6] => 8
[1,3,4,5,7,6,2] => 8
[1,3,4,6,2,5,7] => 8
[1,3,4,6,2,7,5] => 8
[1,3,4,6,5,2,7] => 8
[1,3,4,6,5,7,2] => 8
[1,3,4,6,7,2,5] => 8
[1,3,4,6,7,5,2] => 8
[1,3,4,7,2,5,6] => 8
[1,3,4,7,2,6,5] => 8
[1,3,4,7,5,2,6] => 8
[1,3,4,7,5,6,2] => 8
[1,3,4,7,6,2,5] => 8
[1,3,4,7,6,5,2] => 8
[1,3,5,2,4,6,7] => 8
[1,3,5,2,4,7,6] => 8
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 8
[1,3,5,2,7,4,6] => 8
[1,3,5,2,7,6,4] => 8
[1,3,5,4,2,6,7] => 8
[1,3,5,4,2,7,6] => 8
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 8
[1,3,5,4,7,2,6] => 8
[1,3,5,4,7,6,2] => 8
[1,3,5,6,2,4,7] => 8
[1,3,5,6,2,7,4] => 8
[1,3,5,6,4,2,7] => 8
[1,3,5,6,4,7,2] => 8
[1,3,5,6,7,2,4] => 8
[1,3,5,6,7,4,2] => 8
[1,3,5,7,2,4,6] => 8
[1,3,5,7,2,6,4] => 8
[1,3,5,7,4,2,6] => 8
[1,3,5,7,4,6,2] => 8
[1,3,5,7,6,2,4] => 8
[1,3,5,7,6,4,2] => 8
[1,3,6,2,4,5,7] => 8
[1,3,6,2,4,7,5] => 8
[1,3,6,2,5,4,7] => 8
[1,3,6,2,5,7,4] => 8
[1,3,6,2,7,4,5] => 8
[1,3,6,2,7,5,4] => 8
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 8
[1,3,6,4,5,2,7] => 8
[1,3,6,4,5,7,2] => 8
[1,3,6,4,7,2,5] => 8
[1,3,6,4,7,5,2] => 8
[1,3,6,5,2,4,7] => 8
[1,3,6,5,2,7,4] => 8
[1,3,6,5,4,2,7] => 8
[1,3,6,5,4,7,2] => 8
[1,3,6,5,7,2,4] => 8
[1,3,6,5,7,4,2] => 8
[1,3,6,7,2,4,5] => 8
[1,3,6,7,2,5,4] => 8
[1,3,6,7,4,2,5] => 8
[1,3,6,7,4,5,2] => 8
[1,3,6,7,5,2,4] => 8
[1,3,6,7,5,4,2] => 8
[1,3,7,2,4,5,6] => 8
[1,3,7,2,4,6,5] => 8
[1,3,7,2,5,4,6] => 8
[1,3,7,2,5,6,4] => 8
[1,3,7,2,6,4,5] => 8
[1,3,7,2,6,5,4] => 8
[1,3,7,4,2,5,6] => 8
[1,3,7,4,2,6,5] => 8
[1,3,7,4,5,2,6] => 8
[1,3,7,4,5,6,2] => 8
[1,3,7,4,6,2,5] => 8
[1,3,7,4,6,5,2] => 8
[1,3,7,5,2,4,6] => 8
[1,3,7,5,2,6,4] => 8
[1,3,7,5,4,2,6] => 8
[1,3,7,5,4,6,2] => 8
[1,3,7,5,6,2,4] => 8
[1,3,7,5,6,4,2] => 8
[1,3,7,6,2,4,5] => 8
[1,3,7,6,2,5,4] => 8
[1,3,7,6,4,2,5] => 8
[1,3,7,6,4,5,2] => 8
[1,3,7,6,5,2,4] => 8
[1,3,7,6,5,4,2] => 8
[1,4,2,3,5,6,7] => 8
[1,4,2,3,5,7,6] => 8
[1,4,2,3,6,5,7] => 8
[1,4,2,3,6,7,5] => 8
[1,4,2,3,7,5,6] => 8
[1,4,2,3,7,6,5] => 8
[1,4,2,5,3,6,7] => 8
[1,4,2,5,3,7,6] => 8
[1,4,2,5,6,3,7] => 8
[1,4,2,5,6,7,3] => 8
[1,4,2,5,7,3,6] => 8
[1,4,2,5,7,6,3] => 8
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 8
[1,4,2,6,5,3,7] => 8
[1,4,2,6,5,7,3] => 8
[1,4,2,6,7,3,5] => 8
[1,4,2,6,7,5,3] => 8
[1,4,2,7,3,5,6] => 8
[1,4,2,7,3,6,5] => 8
[1,4,2,7,5,3,6] => 8
[1,4,2,7,5,6,3] => 8
[1,4,2,7,6,3,5] => 8
[1,4,2,7,6,5,3] => 8
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 4
[1,4,3,2,6,7,5] => 8
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 4
[1,4,3,5,2,6,7] => 8
[1,4,3,5,2,7,6] => 8
[1,4,3,5,6,2,7] => 8
[1,4,3,5,6,7,2] => 8
[1,4,3,5,7,2,6] => 8
[1,4,3,5,7,6,2] => 8
[1,4,3,6,2,5,7] => 8
[1,4,3,6,2,7,5] => 8
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 8
[1,4,3,6,7,2,5] => 8
[1,4,3,6,7,5,2] => 8
[1,4,3,7,2,5,6] => 8
[1,4,3,7,2,6,5] => 8
[1,4,3,7,5,2,6] => 8
[1,4,3,7,5,6,2] => 8
[1,4,3,7,6,2,5] => 8
[1,4,3,7,6,5,2] => 8
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 4
[1,4,5,2,6,3,7] => 8
[1,4,5,2,6,7,3] => 8
[1,4,5,2,7,3,6] => 8
[1,4,5,2,7,6,3] => 8
[1,4,5,3,2,6,7] => 8
[1,4,5,3,2,7,6] => 8
[1,4,5,3,6,2,7] => 8
[1,4,5,3,6,7,2] => 8
[1,4,5,3,7,2,6] => 8
[1,4,5,3,7,6,2] => 8
[1,4,5,6,2,3,7] => 4
[1,4,5,6,2,7,3] => 8
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 8
[1,4,5,6,7,2,3] => 8
[1,4,5,6,7,3,2] => 8
[1,4,5,7,2,3,6] => 8
[1,4,5,7,2,6,3] => 8
[1,4,5,7,3,2,6] => 8
[1,4,5,7,3,6,2] => 8
[1,4,5,7,6,2,3] => 8
[1,4,5,7,6,3,2] => 8
[1,4,6,2,3,5,7] => 8
[1,4,6,2,3,7,5] => 8
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 8
[1,4,6,2,7,3,5] => 4
[1,4,6,2,7,5,3] => 8
[1,4,6,3,2,5,7] => 8
[1,4,6,3,2,7,5] => 8
[1,4,6,3,5,2,7] => 8
[1,4,6,3,5,7,2] => 8
[1,4,6,3,7,2,5] => 8
[1,4,6,3,7,5,2] => 8
[1,4,6,5,2,3,7] => 8
[1,4,6,5,2,7,3] => 8
[1,4,6,5,3,2,7] => 8
[1,4,6,5,3,7,2] => 8
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Description
The size of the symmetry class of a permutation.
The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations inverse (Mp00066inverse), reverse (Mp00064reverse), and complement (Mp00069complement).
Two elements in the same symmetry class are also in the same Wilf-equivalence class, see for example [2].
References
[1] Callan, D., Mansour, T. Five subsets of permutations enumerated as weak sorting permutations arXiv:1602.05182
[2] Stankova-Frenkel, Z., West, J. A New Class of Wilf-Equivalent Permutations arXiv:math/0103152
Code
def eq_class(pi):
    cl = [pi]
    test = [pi]
    while test:
        tau = test.pop()
        tau1 = tau.reverse()
        tau2 = tau.complement()
        tau3 = tau.inverse()
        if tau1 not in cl:
            cl.append(tau1)
            test.append(tau1)
        if tau2 not in cl:
            cl.append(tau2)
            test.append(tau2)
        if tau3 not in cl:
            cl.append(tau3)
            test.append(tau3)
    return cl

def statistic(pi):
    return len(eq_class(pi))
Created
Feb 23, 2016 at 18:09 by Christian Stump
Updated
May 10, 2019 at 17:30 by Henning Ulfarsson