edit this statistic or download as text // json
Identifier
Values
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 5
[2,1,3] => 3
[2,3,1] => 5
[3,1,2] => 3
[3,2,1] => 3
[1,2,3,4] => 4
[1,2,4,3] => 6
[1,3,2,4] => 6
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 8
[2,1,3,4] => 4
[2,1,4,3] => 6
[2,3,1,4] => 6
[2,3,4,1] => 8
[2,4,1,3] => 6
[2,4,3,1] => 8
[3,1,2,4] => 4
[3,1,4,2] => 6
[3,2,1,4] => 4
[3,2,4,1] => 8
[3,4,1,2] => 6
[3,4,2,1] => 6
[4,1,2,3] => 4
[4,1,3,2] => 6
[4,2,1,3] => 4
[4,2,3,1] => 6
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 5
[1,2,3,5,4] => 7
[1,2,4,3,5] => 7
[1,2,4,5,3] => 9
[1,2,5,3,4] => 9
[1,2,5,4,3] => 9
[1,3,2,4,5] => 7
[1,3,2,5,4] => 9
[1,3,4,2,5] => 9
[1,3,4,5,2] => 11
[1,3,5,2,4] => 9
[1,3,5,4,2] => 11
[1,4,2,3,5] => 9
[1,4,2,5,3] => 11
[1,4,3,2,5] => 9
[1,4,3,5,2] => 13
[1,4,5,2,3] => 11
[1,4,5,3,2] => 11
[1,5,2,3,4] => 11
[1,5,2,4,3] => 13
[1,5,3,2,4] => 11
[1,5,3,4,2] => 13
[1,5,4,2,3] => 11
[1,5,4,3,2] => 11
[2,1,3,4,5] => 5
[2,1,3,5,4] => 7
[2,1,4,3,5] => 7
[2,1,4,5,3] => 9
[2,1,5,3,4] => 9
[2,1,5,4,3] => 9
[2,3,1,4,5] => 7
[2,3,1,5,4] => 9
[2,3,4,1,5] => 9
[2,3,4,5,1] => 11
[2,3,5,1,4] => 9
[2,3,5,4,1] => 11
[2,4,1,3,5] => 7
[2,4,1,5,3] => 11
[2,4,3,1,5] => 9
[2,4,3,5,1] => 13
[2,4,5,1,3] => 9
[2,4,5,3,1] => 11
[2,5,1,3,4] => 9
[2,5,1,4,3] => 11
[2,5,3,1,4] => 9
[2,5,3,4,1] => 13
[2,5,4,1,3] => 9
[2,5,4,3,1] => 11
[3,1,2,4,5] => 5
[3,1,2,5,4] => 7
[3,1,4,2,5] => 7
[3,1,4,5,2] => 9
[3,1,5,2,4] => 9
[3,1,5,4,2] => 9
[3,2,1,4,5] => 5
[3,2,1,5,4] => 7
[3,2,4,1,5] => 9
[3,2,4,5,1] => 11
[3,2,5,1,4] => 9
[3,2,5,4,1] => 11
[3,4,1,2,5] => 7
[3,4,1,5,2] => 11
[3,4,2,1,5] => 7
[3,4,2,5,1] => 13
[3,4,5,1,2] => 9
[3,4,5,2,1] => 9
[3,5,1,2,4] => 7
[3,5,1,4,2] => 11
[3,5,2,1,4] => 7
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 11
[3,5,4,1,2] => 9
[3,5,4,2,1] => 9
[4,1,2,3,5] => 5
[4,1,2,5,3] => 7
[4,1,3,2,5] => 7
[4,1,3,5,2] => 9
[4,1,5,2,3] => 9
[4,1,5,3,2] => 9
[4,2,1,3,5] => 5
[4,2,1,5,3] => 7
[4,2,3,1,5] => 7
[4,2,3,5,1] => 11
[4,2,5,1,3] => 9
[4,2,5,3,1] => 9
[4,3,1,2,5] => 5
[4,3,1,5,2] => 9
[4,3,2,1,5] => 5
[4,3,2,5,1] => 11
[4,3,5,1,2] => 9
[4,3,5,2,1] => 9
[4,5,1,2,3] => 7
[4,5,1,3,2] => 9
[4,5,2,1,3] => 7
[4,5,2,3,1] => 9
[4,5,3,1,2] => 7
[4,5,3,2,1] => 7
[5,1,2,3,4] => 5
[5,1,2,4,3] => 7
[5,1,3,2,4] => 7
[5,1,3,4,2] => 9
[5,1,4,2,3] => 9
[5,1,4,3,2] => 9
[5,2,1,3,4] => 5
[5,2,1,4,3] => 7
[5,2,3,1,4] => 7
[5,2,3,4,1] => 9
[5,2,4,1,3] => 7
[5,2,4,3,1] => 9
[5,3,1,2,4] => 5
[5,3,1,4,2] => 7
[5,3,2,1,4] => 5
[5,3,2,4,1] => 9
[5,3,4,1,2] => 7
[5,3,4,2,1] => 7
[5,4,1,2,3] => 5
[5,4,1,3,2] => 7
[5,4,2,1,3] => 5
[5,4,2,3,1] => 7
[5,4,3,1,2] => 5
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 8
[1,2,3,5,4,6] => 8
[1,2,3,5,6,4] => 10
[1,2,3,6,4,5] => 10
[1,2,3,6,5,4] => 10
[1,2,4,3,5,6] => 8
[1,2,4,3,6,5] => 10
[1,2,4,5,3,6] => 10
[1,2,4,5,6,3] => 12
[1,2,4,6,3,5] => 10
[1,2,4,6,5,3] => 12
[1,2,5,3,4,6] => 10
[1,2,5,3,6,4] => 12
[1,2,5,4,3,6] => 10
[1,2,5,4,6,3] => 14
[1,2,5,6,3,4] => 12
[1,2,5,6,4,3] => 12
[1,2,6,3,4,5] => 12
[1,2,6,3,5,4] => 14
[1,2,6,4,3,5] => 12
[1,2,6,4,5,3] => 14
[1,2,6,5,3,4] => 12
[1,2,6,5,4,3] => 12
[1,3,2,4,5,6] => 8
[1,3,2,4,6,5] => 10
[1,3,2,5,4,6] => 10
[1,3,2,5,6,4] => 12
[1,3,2,6,4,5] => 12
[1,3,2,6,5,4] => 12
[1,3,4,2,5,6] => 10
[1,3,4,2,6,5] => 12
[1,3,4,5,2,6] => 12
[1,3,4,5,6,2] => 14
[1,3,4,6,2,5] => 12
[1,3,4,6,5,2] => 14
[1,3,5,2,4,6] => 10
[1,3,5,2,6,4] => 14
[1,3,5,4,2,6] => 12
[1,3,5,4,6,2] => 16
[1,3,5,6,2,4] => 12
[1,3,5,6,4,2] => 14
[1,3,6,2,4,5] => 12
[1,3,6,2,5,4] => 14
[1,3,6,4,2,5] => 12
[1,3,6,4,5,2] => 16
[1,3,6,5,2,4] => 12
[1,3,6,5,4,2] => 14
[1,4,2,3,5,6] => 10
[1,4,2,3,6,5] => 12
[1,4,2,5,3,6] => 12
[1,4,2,5,6,3] => 14
[1,4,2,6,3,5] => 14
[1,4,2,6,5,3] => 14
[1,4,3,2,5,6] => 10
[1,4,3,2,6,5] => 12
[1,4,3,5,2,6] => 14
[1,4,3,5,6,2] => 16
[1,4,3,6,2,5] => 14
[1,4,3,6,5,2] => 16
[1,4,5,2,3,6] => 12
[1,4,5,2,6,3] => 16
[1,4,5,3,2,6] => 12
[1,4,5,3,6,2] => 18
[1,4,5,6,2,3] => 14
[1,4,5,6,3,2] => 14
[1,4,6,2,3,5] => 12
[1,4,6,2,5,3] => 16
[1,4,6,3,2,5] => 12
[1,4,6,3,5,2] => 16
[1,4,6,5,2,3] => 14
[1,4,6,5,3,2] => 14
[1,5,2,3,4,6] => 12
[1,5,2,3,6,4] => 14
[1,5,2,4,3,6] => 14
[1,5,2,4,6,3] => 16
[1,5,2,6,3,4] => 16
[1,5,2,6,4,3] => 16
[1,5,3,2,4,6] => 12
[1,5,3,2,6,4] => 14
[1,5,3,4,2,6] => 14
[1,5,3,4,6,2] => 18
[1,5,3,6,2,4] => 16
[1,5,3,6,4,2] => 16
[1,5,4,2,3,6] => 12
[1,5,4,2,6,3] => 16
[1,5,4,3,2,6] => 12
[1,5,4,3,6,2] => 18
[1,5,4,6,2,3] => 16
[1,5,4,6,3,2] => 16
[1,5,6,2,3,4] => 14
[1,5,6,2,4,3] => 16
[1,5,6,3,2,4] => 14
[1,5,6,3,4,2] => 16
[1,5,6,4,2,3] => 14
[1,5,6,4,3,2] => 14
[1,6,2,3,4,5] => 14
[1,6,2,3,5,4] => 16
[1,6,2,4,3,5] => 16
[1,6,2,4,5,3] => 18
[1,6,2,5,3,4] => 18
[1,6,2,5,4,3] => 18
[1,6,3,2,4,5] => 14
[1,6,3,2,5,4] => 16
[1,6,3,4,2,5] => 16
[1,6,3,4,5,2] => 18
[1,6,3,5,2,4] => 16
[1,6,3,5,4,2] => 18
[1,6,4,2,3,5] => 14
[1,6,4,2,5,3] => 16
[1,6,4,3,2,5] => 14
[1,6,4,3,5,2] => 18
[1,6,4,5,2,3] => 16
[1,6,4,5,3,2] => 16
[1,6,5,2,3,4] => 14
[1,6,5,2,4,3] => 16
[1,6,5,3,2,4] => 14
[1,6,5,3,4,2] => 16
[1,6,5,4,2,3] => 14
[1,6,5,4,3,2] => 14
[2,1,3,4,5,6] => 6
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 8
[2,1,3,5,6,4] => 10
[2,1,3,6,4,5] => 10
[2,1,3,6,5,4] => 10
[2,1,4,3,5,6] => 8
[2,1,4,3,6,5] => 10
[2,1,4,5,3,6] => 10
[2,1,4,5,6,3] => 12
[2,1,4,6,3,5] => 10
[2,1,4,6,5,3] => 12
[2,1,5,3,4,6] => 10
[2,1,5,3,6,4] => 12
[2,1,5,4,3,6] => 10
[2,1,5,4,6,3] => 14
[2,1,5,6,3,4] => 12
[2,1,5,6,4,3] => 12
[2,1,6,3,4,5] => 12
[2,1,6,3,5,4] => 14
[2,1,6,4,3,5] => 12
[2,1,6,4,5,3] => 14
[2,1,6,5,3,4] => 12
[2,1,6,5,4,3] => 12
[2,3,1,4,5,6] => 8
[2,3,1,4,6,5] => 10
[2,3,1,5,4,6] => 10
[2,3,1,5,6,4] => 12
[2,3,1,6,4,5] => 12
[2,3,1,6,5,4] => 12
[2,3,4,1,5,6] => 10
[2,3,4,1,6,5] => 12
[2,3,4,5,1,6] => 12
[2,3,4,5,6,1] => 14
[2,3,4,6,1,5] => 12
[2,3,4,6,5,1] => 14
[2,3,5,1,4,6] => 10
[2,3,5,1,6,4] => 14
[2,3,5,4,1,6] => 12
[2,3,5,4,6,1] => 16
[2,3,5,6,1,4] => 12
[2,3,5,6,4,1] => 14
[2,3,6,1,4,5] => 12
[2,3,6,1,5,4] => 14
[2,3,6,4,1,5] => 12
[2,3,6,4,5,1] => 16
[2,3,6,5,1,4] => 12
[2,3,6,5,4,1] => 14
[2,4,1,3,5,6] => 8
[2,4,1,3,6,5] => 10
[2,4,1,5,3,6] => 12
[2,4,1,5,6,3] => 14
[2,4,1,6,3,5] => 14
[2,4,1,6,5,3] => 14
[2,4,3,1,5,6] => 10
[2,4,3,1,6,5] => 12
[2,4,3,5,1,6] => 14
[2,4,3,5,6,1] => 16
[2,4,3,6,1,5] => 14
[2,4,3,6,5,1] => 16
[2,4,5,1,3,6] => 10
[2,4,5,1,6,3] => 16
[2,4,5,3,1,6] => 12
[2,4,5,3,6,1] => 18
[2,4,5,6,1,3] => 12
[2,4,5,6,3,1] => 14
[2,4,6,1,3,5] => 10
[2,4,6,1,5,3] => 16
[2,4,6,3,1,5] => 12
[2,4,6,3,5,1] => 16
[2,4,6,5,1,3] => 12
[2,4,6,5,3,1] => 14
[2,5,1,3,4,6] => 10
[2,5,1,3,6,4] => 12
[2,5,1,4,3,6] => 12
[2,5,1,4,6,3] => 14
[2,5,1,6,3,4] => 16
[2,5,1,6,4,3] => 16
[2,5,3,1,4,6] => 10
[2,5,3,1,6,4] => 14
[2,5,3,4,1,6] => 14
[2,5,3,4,6,1] => 18
[2,5,3,6,1,4] => 14
[2,5,3,6,4,1] => 16
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 16
[2,5,4,3,1,6] => 12
[2,5,4,3,6,1] => 18
[2,5,4,6,1,3] => 14
[2,5,4,6,3,1] => 16
[2,5,6,1,3,4] => 12
[2,5,6,1,4,3] => 14
[2,5,6,3,1,4] => 12
[2,5,6,3,4,1] => 16
[2,5,6,4,1,3] => 12
[2,5,6,4,3,1] => 14
[2,6,1,3,4,5] => 12
[2,6,1,3,5,4] => 14
[2,6,1,4,3,5] => 14
[2,6,1,4,5,3] => 16
[2,6,1,5,3,4] => 16
[2,6,1,5,4,3] => 16
[2,6,3,1,4,5] => 12
[2,6,3,1,5,4] => 14
[2,6,3,4,1,5] => 14
[2,6,3,4,5,1] => 18
[2,6,3,5,1,4] => 14
[2,6,3,5,4,1] => 18
[2,6,4,1,3,5] => 12
[2,6,4,1,5,3] => 14
[2,6,4,3,1,5] => 12
[2,6,4,3,5,1] => 18
[2,6,4,5,1,3] => 14
[2,6,4,5,3,1] => 16
[2,6,5,1,3,4] => 12
[2,6,5,1,4,3] => 14
[2,6,5,3,1,4] => 12
[2,6,5,3,4,1] => 16
[2,6,5,4,1,3] => 12
[2,6,5,4,3,1] => 14
[3,1,2,4,5,6] => 6
[3,1,2,4,6,5] => 8
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 10
[3,1,2,6,4,5] => 10
[3,1,2,6,5,4] => 10
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 10
[3,1,4,5,2,6] => 10
[3,1,4,5,6,2] => 12
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 12
[3,1,5,2,4,6] => 10
[3,1,5,2,6,4] => 12
[3,1,5,4,2,6] => 10
[3,1,5,4,6,2] => 14
[3,1,5,6,2,4] => 12
[3,1,5,6,4,2] => 12
[3,1,6,2,4,5] => 12
[3,1,6,2,5,4] => 14
[3,1,6,4,2,5] => 12
[3,1,6,4,5,2] => 14
[3,1,6,5,2,4] => 12
[3,1,6,5,4,2] => 12
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 8
[3,2,1,5,4,6] => 8
[3,2,1,5,6,4] => 10
[3,2,1,6,4,5] => 10
[3,2,1,6,5,4] => 10
[3,2,4,1,5,6] => 10
[3,2,4,1,6,5] => 12
[3,2,4,5,1,6] => 12
[3,2,4,5,6,1] => 14
[3,2,4,6,1,5] => 12
[3,2,4,6,5,1] => 14
[3,2,5,1,4,6] => 10
[3,2,5,1,6,4] => 14
[3,2,5,4,1,6] => 12
[3,2,5,4,6,1] => 16
[3,2,5,6,1,4] => 12
[3,2,5,6,4,1] => 14
[3,2,6,1,4,5] => 12
[3,2,6,1,5,4] => 14
[3,2,6,4,1,5] => 12
[3,2,6,4,5,1] => 16
[3,2,6,5,1,4] => 12
[3,2,6,5,4,1] => 14
[3,4,1,2,5,6] => 8
[3,4,1,2,6,5] => 10
[3,4,1,5,2,6] => 12
[3,4,1,5,6,2] => 14
[3,4,1,6,2,5] => 14
[3,4,1,6,5,2] => 14
[3,4,2,1,5,6] => 8
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 14
[3,4,2,5,6,1] => 16
[3,4,2,6,1,5] => 14
[3,4,2,6,5,1] => 16
[3,4,5,1,2,6] => 10
[3,4,5,1,6,2] => 16
[3,4,5,2,1,6] => 10
[3,4,5,2,6,1] => 18
[3,4,5,6,1,2] => 12
[3,4,5,6,2,1] => 12
[3,4,6,1,2,5] => 10
[3,4,6,1,5,2] => 16
[3,4,6,2,1,5] => 10
[3,4,6,2,5,1] => 16
[3,4,6,5,1,2] => 12
[3,4,6,5,2,1] => 12
[3,5,1,2,4,6] => 8
[3,5,1,2,6,4] => 12
[3,5,1,4,2,6] => 12
[3,5,1,4,6,2] => 14
[3,5,1,6,2,4] => 14
[3,5,1,6,4,2] => 16
[3,5,2,1,4,6] => 8
[3,5,2,1,6,4] => 12
[3,5,2,4,1,6] => 12
[3,5,2,4,6,1] => 16
[3,5,2,6,1,4] => 14
[3,5,2,6,4,1] => 16
[3,5,4,1,2,6] => 10
[3,5,4,1,6,2] => 16
[3,5,4,2,1,6] => 10
[3,5,4,2,6,1] => 18
[3,5,4,6,1,2] => 14
[3,5,4,6,2,1] => 14
[3,5,6,1,2,4] => 10
[3,5,6,1,4,2] => 14
[3,5,6,2,1,4] => 10
[3,5,6,2,4,1] => 14
[3,5,6,4,1,2] => 12
[3,5,6,4,2,1] => 12
[3,6,1,2,4,5] => 10
[3,6,1,2,5,4] => 12
[3,6,1,4,2,5] => 12
[3,6,1,4,5,2] => 16
[3,6,1,5,2,4] => 14
[3,6,1,5,4,2] => 16
[3,6,2,1,4,5] => 10
[3,6,2,1,5,4] => 12
[3,6,2,4,1,5] => 12
[3,6,2,4,5,1] => 16
[3,6,2,5,1,4] => 12
[3,6,2,5,4,1] => 16
[3,6,4,1,2,5] => 10
[3,6,4,1,5,2] => 14
[3,6,4,2,1,5] => 10
[3,6,4,2,5,1] => 16
[3,6,4,5,1,2] => 14
[3,6,4,5,2,1] => 14
[3,6,5,1,2,4] => 10
[3,6,5,1,4,2] => 14
[3,6,5,2,1,4] => 10
[3,6,5,2,4,1] => 14
[3,6,5,4,1,2] => 12
[3,6,5,4,2,1] => 12
[4,1,2,3,5,6] => 6
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 8
[4,1,2,5,6,3] => 10
[4,1,2,6,3,5] => 10
[4,1,2,6,5,3] => 10
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 10
[4,1,3,5,2,6] => 10
[4,1,3,5,6,2] => 12
[4,1,3,6,2,5] => 10
[4,1,3,6,5,2] => 12
[4,1,5,2,3,6] => 10
[4,1,5,2,6,3] => 12
[4,1,5,3,2,6] => 10
[4,1,5,3,6,2] => 14
[4,1,5,6,2,3] => 12
[4,1,5,6,3,2] => 12
[4,1,6,2,3,5] => 12
[4,1,6,2,5,3] => 14
[4,1,6,3,2,5] => 12
[4,1,6,3,5,2] => 14
[4,1,6,5,2,3] => 12
[4,1,6,5,3,2] => 12
[4,2,1,3,5,6] => 6
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 8
[4,2,1,5,6,3] => 10
[4,2,1,6,3,5] => 10
[4,2,1,6,5,3] => 10
[4,2,3,1,5,6] => 8
[4,2,3,1,6,5] => 10
[4,2,3,5,1,6] => 12
[4,2,3,5,6,1] => 14
[4,2,3,6,1,5] => 12
[4,2,3,6,5,1] => 14
[4,2,5,1,3,6] => 10
[4,2,5,1,6,3] => 14
[4,2,5,3,1,6] => 10
[4,2,5,3,6,1] => 16
[4,2,5,6,1,3] => 12
[4,2,5,6,3,1] => 12
[4,2,6,1,3,5] => 12
[4,2,6,1,5,3] => 14
[4,2,6,3,1,5] => 10
[4,2,6,3,5,1] => 16
[4,2,6,5,1,3] => 12
[4,2,6,5,3,1] => 12
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 10
[4,3,1,5,6,2] => 12
[4,3,1,6,2,5] => 12
[4,3,1,6,5,2] => 12
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 8
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 14
[4,3,2,6,1,5] => 12
[4,3,2,6,5,1] => 14
[4,3,5,1,2,6] => 10
[4,3,5,1,6,2] => 16
[4,3,5,2,1,6] => 10
[4,3,5,2,6,1] => 18
[4,3,5,6,1,2] => 12
[4,3,5,6,2,1] => 12
[4,3,6,1,2,5] => 10
[4,3,6,1,5,2] => 16
[4,3,6,2,1,5] => 10
[4,3,6,2,5,1] => 16
[4,3,6,5,1,2] => 12
[4,3,6,5,2,1] => 12
[4,5,1,2,3,6] => 8
[4,5,1,2,6,3] => 12
[4,5,1,3,2,6] => 10
[4,5,1,3,6,2] => 14
[4,5,1,6,2,3] => 14
[4,5,1,6,3,2] => 14
[4,5,2,1,3,6] => 8
[4,5,2,1,6,3] => 12
[4,5,2,3,1,6] => 10
[4,5,2,3,6,1] => 16
[4,5,2,6,1,3] => 14
[4,5,2,6,3,1] => 14
[4,5,3,1,2,6] => 8
[4,5,3,1,6,2] => 14
[4,5,3,2,1,6] => 8
[4,5,3,2,6,1] => 16
[4,5,3,6,1,2] => 14
[4,5,3,6,2,1] => 14
[4,5,6,1,2,3] => 10
[4,5,6,1,3,2] => 12
[4,5,6,2,1,3] => 10
[4,5,6,2,3,1] => 12
[4,5,6,3,1,2] => 10
[4,5,6,3,2,1] => 10
[4,6,1,2,3,5] => 8
[4,6,1,2,5,3] => 12
[4,6,1,3,2,5] => 10
[4,6,1,3,5,2] => 14
[4,6,1,5,2,3] => 14
[4,6,1,5,3,2] => 14
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 12
[4,6,2,3,1,5] => 10
[4,6,2,3,5,1] => 14
[4,6,2,5,1,3] => 12
[4,6,2,5,3,1] => 14
[4,6,3,1,2,5] => 8
[4,6,3,1,5,2] => 12
[4,6,3,2,1,5] => 8
[4,6,3,2,5,1] => 14
[4,6,3,5,1,2] => 12
[4,6,3,5,2,1] => 12
[4,6,5,1,2,3] => 10
[4,6,5,1,3,2] => 12
[4,6,5,2,1,3] => 10
[4,6,5,2,3,1] => 12
[4,6,5,3,1,2] => 10
[4,6,5,3,2,1] => 10
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 8
[5,1,2,4,3,6] => 8
[5,1,2,4,6,3] => 10
[5,1,2,6,3,4] => 10
[5,1,2,6,4,3] => 10
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 10
[5,1,3,4,2,6] => 10
[5,1,3,4,6,2] => 12
[5,1,3,6,2,4] => 10
[5,1,3,6,4,2] => 12
[5,1,4,2,3,6] => 10
[5,1,4,2,6,3] => 12
[5,1,4,3,2,6] => 10
[5,1,4,3,6,2] => 14
[5,1,4,6,2,3] => 12
[5,1,4,6,3,2] => 12
[5,1,6,2,3,4] => 12
[5,1,6,2,4,3] => 14
[5,1,6,3,2,4] => 12
[5,1,6,3,4,2] => 14
[5,1,6,4,2,3] => 12
[5,1,6,4,3,2] => 12
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 8
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 10
[5,2,1,6,3,4] => 10
[5,2,1,6,4,3] => 10
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 10
[5,2,3,4,1,6] => 10
[5,2,3,4,6,1] => 14
[5,2,3,6,1,4] => 12
[5,2,3,6,4,1] => 12
[5,2,4,1,3,6] => 8
[5,2,4,1,6,3] => 12
[5,2,4,3,1,6] => 10
[5,2,4,3,6,1] => 16
[5,2,4,6,1,3] => 12
[5,2,4,6,3,1] => 12
[5,2,6,1,3,4] => 12
[5,2,6,1,4,3] => 14
[5,2,6,3,1,4] => 10
[5,2,6,3,4,1] => 14
[5,2,6,4,1,3] => 10
[5,2,6,4,3,1] => 12
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 8
[5,3,1,4,6,2] => 12
[5,3,1,6,2,4] => 12
[5,3,1,6,4,2] => 10
[5,3,2,1,4,6] => 6
[5,3,2,1,6,4] => 8
[5,3,2,4,1,6] => 10
[5,3,2,4,6,1] => 14
[5,3,2,6,1,4] => 12
[5,3,2,6,4,1] => 12
[5,3,4,1,2,6] => 8
[5,3,4,1,6,2] => 14
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 16
[5,3,4,6,1,2] => 12
[5,3,4,6,2,1] => 12
[5,3,6,1,2,4] => 10
[5,3,6,1,4,2] => 14
[5,3,6,2,1,4] => 10
[5,3,6,2,4,1] => 14
[5,3,6,4,1,2] => 10
[5,3,6,4,2,1] => 10
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 10
[5,4,1,3,2,6] => 8
[5,4,1,3,6,2] => 12
[5,4,1,6,2,3] => 12
[5,4,1,6,3,2] => 12
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 10
[5,4,2,3,1,6] => 8
[5,4,2,3,6,1] => 14
[5,4,2,6,1,3] => 12
[5,4,2,6,3,1] => 12
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 12
[5,4,3,2,1,6] => 6
[5,4,3,2,6,1] => 14
[5,4,3,6,1,2] => 12
[5,4,3,6,2,1] => 12
[5,4,6,1,2,3] => 10
[5,4,6,1,3,2] => 12
[5,4,6,2,1,3] => 10
[5,4,6,2,3,1] => 12
[5,4,6,3,1,2] => 10
[5,4,6,3,2,1] => 10
[5,6,1,2,3,4] => 8
[5,6,1,2,4,3] => 10
[5,6,1,3,2,4] => 10
[5,6,1,3,4,2] => 12
[5,6,1,4,2,3] => 12
[5,6,1,4,3,2] => 12
[5,6,2,1,3,4] => 8
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 10
[5,6,2,3,4,1] => 12
[5,6,2,4,1,3] => 10
[5,6,2,4,3,1] => 12
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 10
[5,6,3,2,1,4] => 8
[5,6,3,2,4,1] => 12
[5,6,3,4,1,2] => 10
[5,6,3,4,2,1] => 10
[5,6,4,1,2,3] => 8
[5,6,4,1,3,2] => 10
[5,6,4,2,1,3] => 8
[5,6,4,2,3,1] => 10
[5,6,4,3,1,2] => 8
[5,6,4,3,2,1] => 8
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 8
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 10
[6,1,2,5,3,4] => 10
[6,1,2,5,4,3] => 10
[6,1,3,2,4,5] => 8
[6,1,3,2,5,4] => 10
[6,1,3,4,2,5] => 10
[6,1,3,4,5,2] => 12
[6,1,3,5,2,4] => 10
[6,1,3,5,4,2] => 12
[6,1,4,2,3,5] => 10
[6,1,4,2,5,3] => 12
[6,1,4,3,2,5] => 10
[6,1,4,3,5,2] => 14
[6,1,4,5,2,3] => 12
[6,1,4,5,3,2] => 12
[6,1,5,2,3,4] => 12
[6,1,5,2,4,3] => 14
[6,1,5,3,2,4] => 12
[6,1,5,3,4,2] => 14
[6,1,5,4,2,3] => 12
[6,1,5,4,3,2] => 12
[6,2,1,3,4,5] => 6
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 8
[6,2,1,4,5,3] => 10
[6,2,1,5,3,4] => 10
[6,2,1,5,4,3] => 10
[6,2,3,1,4,5] => 8
[6,2,3,1,5,4] => 10
[6,2,3,4,1,5] => 10
[6,2,3,4,5,1] => 12
[6,2,3,5,1,4] => 10
[6,2,3,5,4,1] => 12
[6,2,4,1,3,5] => 8
[6,2,4,1,5,3] => 12
[6,2,4,3,1,5] => 10
[6,2,4,3,5,1] => 14
[6,2,4,5,1,3] => 10
[6,2,4,5,3,1] => 12
[6,2,5,1,3,4] => 10
[6,2,5,1,4,3] => 12
[6,2,5,3,1,4] => 10
[6,2,5,3,4,1] => 14
[6,2,5,4,1,3] => 10
[6,2,5,4,3,1] => 12
[6,3,1,2,4,5] => 6
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 8
[6,3,1,4,5,2] => 10
[6,3,1,5,2,4] => 10
[6,3,1,5,4,2] => 10
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 8
[6,3,2,4,1,5] => 10
[6,3,2,4,5,1] => 12
[6,3,2,5,1,4] => 10
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 8
[6,3,4,1,5,2] => 12
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 14
[6,3,4,5,1,2] => 10
[6,3,4,5,2,1] => 10
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 12
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 12
[6,3,5,4,1,2] => 10
[6,3,5,4,2,1] => 10
[6,4,1,2,3,5] => 6
[6,4,1,2,5,3] => 8
[6,4,1,3,2,5] => 8
[6,4,1,3,5,2] => 10
[6,4,1,5,2,3] => 10
[6,4,1,5,3,2] => 10
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 8
[6,4,2,3,1,5] => 8
[6,4,2,3,5,1] => 12
[6,4,2,5,1,3] => 10
[6,4,2,5,3,1] => 10
[6,4,3,1,2,5] => 6
[6,4,3,1,5,2] => 10
[6,4,3,2,1,5] => 6
[6,4,3,2,5,1] => 12
[6,4,3,5,1,2] => 10
[6,4,3,5,2,1] => 10
[6,4,5,1,2,3] => 8
[6,4,5,1,3,2] => 10
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 10
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 8
[6,5,1,2,3,4] => 6
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 8
[6,5,1,3,4,2] => 10
[6,5,1,4,2,3] => 10
[6,5,1,4,3,2] => 10
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 8
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 10
[6,5,2,4,1,3] => 8
[6,5,2,4,3,1] => 10
[6,5,3,1,2,4] => 6
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 6
[6,5,3,2,4,1] => 10
[6,5,3,4,1,2] => 8
[6,5,3,4,2,1] => 8
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 8
[6,5,4,2,1,3] => 6
[6,5,4,2,3,1] => 8
[6,5,4,3,1,2] => 6
[6,5,4,3,2,1] => 6
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 9
[1,2,3,4,6,5,7] => 9
[1,2,3,4,6,7,5] => 11
[1,2,3,4,7,5,6] => 11
[1,2,3,4,7,6,5] => 11
[1,2,3,5,4,6,7] => 9
[1,2,3,5,4,7,6] => 11
[1,2,3,5,6,4,7] => 11
[1,2,3,5,6,7,4] => 13
[1,2,3,5,7,4,6] => 11
[1,2,3,5,7,6,4] => 13
[1,2,3,6,4,5,7] => 11
[1,2,3,6,4,7,5] => 13
[1,2,3,6,5,4,7] => 11
[1,2,3,6,5,7,4] => 15
[1,2,3,6,7,4,5] => 13
[1,2,3,6,7,5,4] => 13
[1,2,3,7,4,5,6] => 13
[1,2,3,7,4,6,5] => 15
[1,2,3,7,5,4,6] => 13
[1,2,3,7,5,6,4] => 15
[1,2,3,7,6,4,5] => 13
[1,2,3,7,6,5,4] => 13
[1,2,4,3,5,6,7] => 9
[1,2,4,3,5,7,6] => 11
[1,2,4,3,6,5,7] => 11
[1,2,4,3,6,7,5] => 13
[1,2,4,3,7,5,6] => 13
[1,2,4,3,7,6,5] => 13
[1,2,4,5,3,6,7] => 11
[1,2,4,5,3,7,6] => 13
[1,2,4,5,6,3,7] => 13
[1,2,4,5,6,7,3] => 15
[1,2,4,5,7,3,6] => 13
[1,2,4,5,7,6,3] => 15
[1,2,4,6,3,5,7] => 11
[1,2,4,6,3,7,5] => 15
[1,2,4,6,5,3,7] => 13
[1,2,4,6,5,7,3] => 17
[1,2,4,6,7,3,5] => 13
[1,2,4,6,7,5,3] => 15
[1,2,4,7,3,5,6] => 13
[1,2,4,7,3,6,5] => 15
[1,2,4,7,5,3,6] => 13
[1,2,4,7,5,6,3] => 17
[1,2,4,7,6,3,5] => 13
[1,2,4,7,6,5,3] => 15
[1,2,5,3,4,6,7] => 11
[1,2,5,3,4,7,6] => 13
[1,2,5,3,6,4,7] => 13
[1,2,5,3,6,7,4] => 15
[1,2,5,3,7,4,6] => 15
[1,2,5,3,7,6,4] => 15
[1,2,5,4,3,6,7] => 11
[1,2,5,4,3,7,6] => 13
[1,2,5,4,6,3,7] => 15
[1,2,5,4,6,7,3] => 17
[1,2,5,4,7,3,6] => 15
[1,2,5,4,7,6,3] => 17
[1,2,5,6,3,4,7] => 13
[1,2,5,6,3,7,4] => 17
[1,2,5,6,4,3,7] => 13
[1,2,5,6,4,7,3] => 19
[1,2,5,6,7,3,4] => 15
[1,2,5,6,7,4,3] => 15
[1,2,5,7,3,4,6] => 13
[1,2,5,7,3,6,4] => 17
[1,2,5,7,4,3,6] => 13
[1,2,5,7,4,6,3] => 17
[1,2,5,7,6,3,4] => 15
[1,2,5,7,6,4,3] => 15
[1,2,6,3,4,5,7] => 13
[1,2,6,3,4,7,5] => 15
[1,2,6,3,5,4,7] => 15
[1,2,6,3,5,7,4] => 17
[1,2,6,3,7,4,5] => 17
[1,2,6,3,7,5,4] => 17
[1,2,6,4,3,5,7] => 13
[1,2,6,4,3,7,5] => 15
[1,2,6,4,5,3,7] => 15
[1,2,6,4,5,7,3] => 19
[1,2,6,4,7,3,5] => 17
[1,2,6,4,7,5,3] => 17
[1,2,6,5,3,4,7] => 13
[1,2,6,5,3,7,4] => 17
[1,2,6,5,4,3,7] => 13
[1,2,6,5,4,7,3] => 19
[1,2,6,5,7,3,4] => 17
[1,2,6,5,7,4,3] => 17
[1,2,6,7,3,4,5] => 15
[1,2,6,7,3,5,4] => 17
[1,2,6,7,4,3,5] => 15
[1,2,6,7,4,5,3] => 17
[1,2,6,7,5,3,4] => 15
[1,2,6,7,5,4,3] => 15
[1,2,7,3,4,5,6] => 15
[1,2,7,3,4,6,5] => 17
[1,2,7,3,5,4,6] => 17
[1,2,7,3,5,6,4] => 19
[1,2,7,3,6,4,5] => 19
[1,2,7,3,6,5,4] => 19
[1,2,7,4,3,5,6] => 15
[1,2,7,4,3,6,5] => 17
[1,2,7,4,5,3,6] => 17
[1,2,7,4,5,6,3] => 19
[1,2,7,4,6,3,5] => 17
[1,2,7,4,6,5,3] => 19
[1,2,7,5,3,4,6] => 15
[1,2,7,5,3,6,4] => 17
[1,2,7,5,4,3,6] => 15
[1,2,7,5,4,6,3] => 19
[1,2,7,5,6,3,4] => 17
[1,2,7,5,6,4,3] => 17
[1,2,7,6,3,4,5] => 15
[1,2,7,6,3,5,4] => 17
[1,2,7,6,4,3,5] => 15
[1,2,7,6,4,5,3] => 17
[1,2,7,6,5,3,4] => 15
[1,2,7,6,5,4,3] => 15
[1,3,2,4,5,6,7] => 9
[1,3,2,4,5,7,6] => 11
[1,3,2,4,6,5,7] => 11
[1,3,2,4,6,7,5] => 13
[1,3,2,4,7,5,6] => 13
[1,3,2,4,7,6,5] => 13
[1,3,2,5,4,6,7] => 11
[1,3,2,5,4,7,6] => 13
[1,3,2,5,6,4,7] => 13
[1,3,2,5,6,7,4] => 15
[1,3,2,5,7,4,6] => 13
[1,3,2,5,7,6,4] => 15
[1,3,2,6,4,5,7] => 13
[1,3,2,6,4,7,5] => 15
[1,3,2,6,5,4,7] => 13
[1,3,2,6,5,7,4] => 17
[1,3,2,6,7,4,5] => 15
[1,3,2,6,7,5,4] => 15
[1,3,2,7,4,5,6] => 15
[1,3,2,7,4,6,5] => 17
[1,3,2,7,5,4,6] => 15
[1,3,2,7,5,6,4] => 17
[1,3,2,7,6,4,5] => 15
[1,3,2,7,6,5,4] => 15
[1,3,4,2,5,6,7] => 11
[1,3,4,2,5,7,6] => 13
[1,3,4,2,6,5,7] => 13
[1,3,4,2,6,7,5] => 15
[1,3,4,2,7,5,6] => 15
[1,3,4,2,7,6,5] => 15
[1,3,4,5,2,6,7] => 13
[1,3,4,5,2,7,6] => 15
[1,3,4,5,6,2,7] => 15
[1,3,4,5,6,7,2] => 17
[1,3,4,5,7,2,6] => 15
[1,3,4,5,7,6,2] => 17
[1,3,4,6,2,5,7] => 13
[1,3,4,6,2,7,5] => 17
[1,3,4,6,5,2,7] => 15
[1,3,4,6,5,7,2] => 19
[1,3,4,6,7,2,5] => 15
[1,3,4,6,7,5,2] => 17
[1,3,4,7,2,5,6] => 15
[1,3,4,7,2,6,5] => 17
[1,3,4,7,5,2,6] => 15
[1,3,4,7,5,6,2] => 19
[1,3,4,7,6,2,5] => 15
[1,3,4,7,6,5,2] => 17
[1,3,5,2,4,6,7] => 11
[1,3,5,2,4,7,6] => 13
[1,3,5,2,6,4,7] => 15
[1,3,5,2,6,7,4] => 17
[1,3,5,2,7,4,6] => 17
[1,3,5,2,7,6,4] => 17
[1,3,5,4,2,6,7] => 13
[1,3,5,4,2,7,6] => 15
[1,3,5,4,6,2,7] => 17
[1,3,5,4,6,7,2] => 19
[1,3,5,4,7,2,6] => 17
[1,3,5,4,7,6,2] => 19
[1,3,5,6,2,4,7] => 13
[1,3,5,6,2,7,4] => 19
[1,3,5,6,4,2,7] => 15
[1,3,5,6,4,7,2] => 21
[1,3,5,6,7,2,4] => 15
[1,3,5,6,7,4,2] => 17
[1,3,5,7,2,4,6] => 13
[1,3,5,7,2,6,4] => 19
[1,3,5,7,4,2,6] => 15
[1,3,5,7,4,6,2] => 19
[1,3,5,7,6,2,4] => 15
[1,3,5,7,6,4,2] => 17
[1,3,6,2,4,5,7] => 13
[1,3,6,2,4,7,5] => 15
[1,3,6,2,5,4,7] => 15
[1,3,6,2,5,7,4] => 17
[1,3,6,2,7,4,5] => 19
[1,3,6,2,7,5,4] => 19
[1,3,6,4,2,5,7] => 13
[1,3,6,4,2,7,5] => 17
[1,3,6,4,5,2,7] => 17
[1,3,6,4,5,7,2] => 21
[1,3,6,4,7,2,5] => 17
[1,3,6,4,7,5,2] => 19
[1,3,6,5,2,4,7] => 13
[1,3,6,5,2,7,4] => 19
[1,3,6,5,4,2,7] => 15
[1,3,6,5,4,7,2] => 21
[1,3,6,5,7,2,4] => 17
[1,3,6,5,7,4,2] => 19
[1,3,6,7,2,4,5] => 15
[1,3,6,7,2,5,4] => 17
[1,3,6,7,4,2,5] => 15
[1,3,6,7,4,5,2] => 19
[1,3,6,7,5,2,4] => 15
[1,3,6,7,5,4,2] => 17
[1,3,7,2,4,5,6] => 15
[1,3,7,2,4,6,5] => 17
[1,3,7,2,5,4,6] => 17
[1,3,7,2,5,6,4] => 19
[1,3,7,2,6,4,5] => 19
[1,3,7,2,6,5,4] => 19
[1,3,7,4,2,5,6] => 15
[1,3,7,4,2,6,5] => 17
[1,3,7,4,5,2,6] => 17
[1,3,7,4,5,6,2] => 21
[1,3,7,4,6,2,5] => 17
[1,3,7,4,6,5,2] => 21
[1,3,7,5,2,4,6] => 15
[1,3,7,5,2,6,4] => 17
[1,3,7,5,4,2,6] => 15
[1,3,7,5,4,6,2] => 21
[1,3,7,5,6,2,4] => 17
[1,3,7,5,6,4,2] => 19
[1,3,7,6,2,4,5] => 15
[1,3,7,6,2,5,4] => 17
[1,3,7,6,4,2,5] => 15
[1,3,7,6,4,5,2] => 19
[1,3,7,6,5,2,4] => 15
[1,3,7,6,5,4,2] => 17
[1,4,2,3,5,6,7] => 11
[1,4,2,3,5,7,6] => 13
[1,4,2,3,6,5,7] => 13
[1,4,2,3,6,7,5] => 15
[1,4,2,3,7,5,6] => 15
[1,4,2,3,7,6,5] => 15
[1,4,2,5,3,6,7] => 13
[1,4,2,5,3,7,6] => 15
[1,4,2,5,6,3,7] => 15
[1,4,2,5,6,7,3] => 17
[1,4,2,5,7,3,6] => 15
[1,4,2,5,7,6,3] => 17
[1,4,2,6,3,5,7] => 15
[1,4,2,6,3,7,5] => 17
[1,4,2,6,5,3,7] => 15
[1,4,2,6,5,7,3] => 19
[1,4,2,6,7,3,5] => 17
[1,4,2,6,7,5,3] => 17
[1,4,2,7,3,5,6] => 17
[1,4,2,7,3,6,5] => 19
[1,4,2,7,5,3,6] => 17
[1,4,2,7,5,6,3] => 19
[1,4,2,7,6,3,5] => 17
[1,4,2,7,6,5,3] => 17
[1,4,3,2,5,6,7] => 11
[1,4,3,2,5,7,6] => 13
[1,4,3,2,6,5,7] => 13
[1,4,3,2,6,7,5] => 15
[1,4,3,2,7,5,6] => 15
[1,4,3,2,7,6,5] => 15
[1,4,3,5,2,6,7] => 15
[1,4,3,5,2,7,6] => 17
[1,4,3,5,6,2,7] => 17
[1,4,3,5,6,7,2] => 19
[1,4,3,5,7,2,6] => 17
[1,4,3,5,7,6,2] => 19
[1,4,3,6,2,5,7] => 15
[1,4,3,6,2,7,5] => 19
[1,4,3,6,5,2,7] => 17
[1,4,3,6,5,7,2] => 21
[1,4,3,6,7,2,5] => 17
[1,4,3,6,7,5,2] => 19
[1,4,3,7,2,5,6] => 17
[1,4,3,7,2,6,5] => 19
[1,4,3,7,5,2,6] => 17
[1,4,3,7,5,6,2] => 21
[1,4,3,7,6,2,5] => 17
[1,4,3,7,6,5,2] => 19
[1,4,5,2,3,6,7] => 13
[1,4,5,2,3,7,6] => 15
[1,4,5,2,6,3,7] => 17
[1,4,5,2,6,7,3] => 19
[1,4,5,2,7,3,6] => 19
[1,4,5,2,7,6,3] => 19
[1,4,5,3,2,6,7] => 13
[1,4,5,3,2,7,6] => 15
[1,4,5,3,6,2,7] => 19
[1,4,5,3,6,7,2] => 21
[1,4,5,3,7,2,6] => 19
[1,4,5,3,7,6,2] => 21
[1,4,5,6,2,3,7] => 15
[1,4,5,6,2,7,3] => 21
[1,4,5,6,3,2,7] => 15
[1,4,5,6,3,7,2] => 23
[1,4,5,6,7,2,3] => 17
[1,4,5,6,7,3,2] => 17
[1,4,5,7,2,3,6] => 15
[1,4,5,7,2,6,3] => 21
[1,4,5,7,3,2,6] => 15
[1,4,5,7,3,6,2] => 21
[1,4,5,7,6,2,3] => 17
[1,4,5,7,6,3,2] => 17
[1,4,6,2,3,5,7] => 13
[1,4,6,2,3,7,5] => 17
[1,4,6,2,5,3,7] => 17
[1,4,6,2,5,7,3] => 19
[1,4,6,2,7,3,5] => 19
[1,4,6,2,7,5,3] => 21
[1,4,6,3,2,5,7] => 13
[1,4,6,3,2,7,5] => 17
[1,4,6,3,5,2,7] => 17
[1,4,6,3,5,7,2] => 21
[1,4,6,3,7,2,5] => 19
[1,4,6,3,7,5,2] => 21
[1,4,6,5,2,3,7] => 15
[1,4,6,5,2,7,3] => 21
[1,4,6,5,3,2,7] => 15
[1,4,6,5,3,7,2] => 23
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Description
The number of inversions of the cyclic embedding of a permutation.
The cyclic embedding of a permutation $\pi$ of length $n$ is given by the permutation of length $n+1$ represented in cycle notation by $(\pi_1,\ldots,\pi_n,n+1)$.
This reflects in particular the fact that the number of long cycles of length $n+1$ equals $n!$.
This statistic counts the number of inversions of this embedding, see [1]. As shown in [2], the sum of this statistic on all permutations of length $n$ equals $n!\cdot(3n-1)/12$.
References
[1] The number of inversions over all n-permutations consisting only of a single cycle. OEIS:A227404
[2] Palcoux, S. Examples of integer sequences coincidences MathOverflow:289976
Code
def statistic(pi):
    n = len(pi)+Integer(1)
    pi = tuple(list(pi)+[n])
    return Permutation(pi).number_of_inversions()
Created
Jan 05, 2018 at 15:58 by Christian Stump
Updated
Jan 05, 2018 at 18:38 by Christian Stump