edit this statistic or download as text // json
Identifier
Values
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 4
[3,1,2] => 4
[3,2,1] => 4
[1,2,3,4] => 0
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 4
[2,1,3,4] => 2
[2,1,4,3] => 4
[2,3,1,4] => 4
[2,3,4,1] => 6
[2,4,1,3] => 6
[2,4,3,1] => 6
[3,1,2,4] => 4
[3,1,4,2] => 6
[3,2,1,4] => 4
[3,2,4,1] => 6
[3,4,1,2] => 8
[3,4,2,1] => 8
[4,1,2,3] => 6
[4,1,3,2] => 6
[4,2,1,3] => 6
[4,2,3,1] => 6
[4,3,1,2] => 8
[4,3,2,1] => 8
[1,2,3,4,5] => 0
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 4
[1,3,2,4,5] => 2
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 6
[1,3,5,2,4] => 6
[1,3,5,4,2] => 6
[1,4,2,3,5] => 4
[1,4,2,5,3] => 6
[1,4,3,2,5] => 4
[1,4,3,5,2] => 6
[1,4,5,2,3] => 8
[1,4,5,3,2] => 8
[1,5,2,3,4] => 6
[1,5,2,4,3] => 6
[1,5,3,2,4] => 6
[1,5,3,4,2] => 6
[1,5,4,2,3] => 8
[1,5,4,3,2] => 8
[2,1,3,4,5] => 2
[2,1,3,5,4] => 4
[2,1,4,3,5] => 4
[2,1,4,5,3] => 6
[2,1,5,3,4] => 6
[2,1,5,4,3] => 6
[2,3,1,4,5] => 4
[2,3,1,5,4] => 6
[2,3,4,1,5] => 6
[2,3,4,5,1] => 8
[2,3,5,1,4] => 8
[2,3,5,4,1] => 8
[2,4,1,3,5] => 6
[2,4,1,5,3] => 8
[2,4,3,1,5] => 6
[2,4,3,5,1] => 8
[2,4,5,1,3] => 10
[2,4,5,3,1] => 10
[2,5,1,3,4] => 8
[2,5,1,4,3] => 8
[2,5,3,1,4] => 8
[2,5,3,4,1] => 8
[2,5,4,1,3] => 10
[2,5,4,3,1] => 10
[3,1,2,4,5] => 4
[3,1,2,5,4] => 6
[3,1,4,2,5] => 6
[3,1,4,5,2] => 8
[3,1,5,2,4] => 8
[3,1,5,4,2] => 8
[3,2,1,4,5] => 4
[3,2,1,5,4] => 6
[3,2,4,1,5] => 6
[3,2,4,5,1] => 8
[3,2,5,1,4] => 8
[3,2,5,4,1] => 8
[3,4,1,2,5] => 8
[3,4,1,5,2] => 10
[3,4,2,1,5] => 8
[3,4,2,5,1] => 10
[3,4,5,1,2] => 12
[3,4,5,2,1] => 12
[3,5,1,2,4] => 10
[3,5,1,4,2] => 10
[3,5,2,1,4] => 10
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 10
[3,5,4,1,2] => 12
[3,5,4,2,1] => 12
[4,1,2,3,5] => 6
[4,1,2,5,3] => 8
[4,1,3,2,5] => 6
[4,1,3,5,2] => 8
[4,1,5,2,3] => 10
[4,1,5,3,2] => 10
[4,2,1,3,5] => 6
[4,2,1,5,3] => 8
[4,2,3,1,5] => 6
[4,2,3,5,1] => 8
[4,2,5,1,3] => 10
[4,2,5,3,1] => 10
[4,3,1,2,5] => 8
[4,3,1,5,2] => 10
[4,3,2,1,5] => 8
[4,3,2,5,1] => 10
[4,3,5,1,2] => 12
[4,3,5,2,1] => 12
[4,5,1,2,3] => 12
[4,5,1,3,2] => 12
[4,5,2,1,3] => 12
[4,5,2,3,1] => 12
[4,5,3,1,2] => 12
[4,5,3,2,1] => 12
[5,1,2,3,4] => 8
[5,1,2,4,3] => 8
[5,1,3,2,4] => 8
[5,1,3,4,2] => 8
[5,1,4,2,3] => 10
[5,1,4,3,2] => 10
[5,2,1,3,4] => 8
[5,2,1,4,3] => 8
[5,2,3,1,4] => 8
[5,2,3,4,1] => 8
[5,2,4,1,3] => 10
[5,2,4,3,1] => 10
[5,3,1,2,4] => 10
[5,3,1,4,2] => 10
[5,3,2,1,4] => 10
[5,3,2,4,1] => 10
[5,3,4,1,2] => 12
[5,3,4,2,1] => 12
[5,4,1,2,3] => 12
[5,4,1,3,2] => 12
[5,4,2,1,3] => 12
[5,4,2,3,1] => 12
[5,4,3,1,2] => 12
[5,4,3,2,1] => 12
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 2
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 4
[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] => 4
[1,2,4,5,6,3] => 6
[1,2,4,6,3,5] => 6
[1,2,4,6,5,3] => 6
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 6
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 6
[1,2,5,6,3,4] => 8
[1,2,5,6,4,3] => 8
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 6
[1,2,6,4,3,5] => 6
[1,2,6,4,5,3] => 6
[1,2,6,5,3,4] => 8
[1,2,6,5,4,3] => 8
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 6
[1,3,2,6,4,5] => 6
[1,3,2,6,5,4] => 6
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 6
[1,3,4,5,2,6] => 6
[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] => 6
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 10
[1,3,5,6,4,2] => 10
[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] => 10
[1,3,6,5,4,2] => 10
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 6
[1,4,2,5,3,6] => 6
[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] => 6
[1,4,3,5,2,6] => 6
[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] => 8
[1,4,5,2,6,3] => 10
[1,4,5,3,2,6] => 8
[1,4,5,3,6,2] => 10
[1,4,5,6,2,3] => 12
[1,4,5,6,3,2] => 12
[1,4,6,2,3,5] => 10
[1,4,6,2,5,3] => 10
[1,4,6,3,2,5] => 10
[1,4,6,3,5,2] => 10
[1,4,6,5,2,3] => 12
[1,4,6,5,3,2] => 12
[1,5,2,3,4,6] => 6
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 6
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 10
[1,5,2,6,4,3] => 10
[1,5,3,2,4,6] => 6
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 10
[1,5,3,6,4,2] => 10
[1,5,4,2,3,6] => 8
[1,5,4,2,6,3] => 10
[1,5,4,3,2,6] => 8
[1,5,4,3,6,2] => 10
[1,5,4,6,2,3] => 12
[1,5,4,6,3,2] => 12
[1,5,6,2,3,4] => 12
[1,5,6,2,4,3] => 12
[1,5,6,3,2,4] => 12
[1,5,6,3,4,2] => 12
[1,5,6,4,2,3] => 12
[1,5,6,4,3,2] => 12
[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] => 10
[1,6,2,5,4,3] => 10
[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] => 8
[1,6,3,5,2,4] => 10
[1,6,3,5,4,2] => 10
[1,6,4,2,3,5] => 10
[1,6,4,2,5,3] => 10
[1,6,4,3,2,5] => 10
[1,6,4,3,5,2] => 10
[1,6,4,5,2,3] => 12
[1,6,4,5,3,2] => 12
[1,6,5,2,3,4] => 12
[1,6,5,2,4,3] => 12
[1,6,5,3,2,4] => 12
[1,6,5,3,4,2] => 12
[1,6,5,4,2,3] => 12
[1,6,5,4,3,2] => 12
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 6
[2,1,3,6,4,5] => 6
[2,1,3,6,5,4] => 6
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => 6
[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] => 6
[2,1,5,3,6,4] => 8
[2,1,5,4,3,6] => 6
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 10
[2,1,5,6,4,3] => 10
[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] => 8
[2,1,6,5,3,4] => 10
[2,1,6,5,4,3] => 10
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 6
[2,3,1,5,4,6] => 6
[2,3,1,5,6,4] => 8
[2,3,1,6,4,5] => 8
[2,3,1,6,5,4] => 8
[2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 8
[2,3,4,5,6,1] => 10
[2,3,4,6,1,5] => 10
[2,3,4,6,5,1] => 10
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 10
[2,3,5,4,1,6] => 8
[2,3,5,4,6,1] => 10
[2,3,5,6,1,4] => 12
[2,3,5,6,4,1] => 12
[2,3,6,1,4,5] => 10
[2,3,6,1,5,4] => 10
[2,3,6,4,1,5] => 10
[2,3,6,4,5,1] => 10
[2,3,6,5,1,4] => 12
[2,3,6,5,4,1] => 12
[2,4,1,3,5,6] => 6
[2,4,1,3,6,5] => 8
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 10
[2,4,1,6,3,5] => 10
[2,4,1,6,5,3] => 10
[2,4,3,1,5,6] => 6
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 8
[2,4,3,5,6,1] => 10
[2,4,3,6,1,5] => 10
[2,4,3,6,5,1] => 10
[2,4,5,1,3,6] => 10
[2,4,5,1,6,3] => 12
[2,4,5,3,1,6] => 10
[2,4,5,3,6,1] => 12
[2,4,5,6,1,3] => 14
[2,4,5,6,3,1] => 14
[2,4,6,1,3,5] => 12
[2,4,6,1,5,3] => 12
[2,4,6,3,1,5] => 12
[2,4,6,3,5,1] => 12
[2,4,6,5,1,3] => 14
[2,4,6,5,3,1] => 14
[2,5,1,3,4,6] => 8
[2,5,1,3,6,4] => 10
[2,5,1,4,3,6] => 8
[2,5,1,4,6,3] => 10
[2,5,1,6,3,4] => 12
[2,5,1,6,4,3] => 12
[2,5,3,1,4,6] => 8
[2,5,3,1,6,4] => 10
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 10
[2,5,3,6,1,4] => 12
[2,5,3,6,4,1] => 12
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 12
[2,5,4,3,1,6] => 10
[2,5,4,3,6,1] => 12
[2,5,4,6,1,3] => 14
[2,5,4,6,3,1] => 14
[2,5,6,1,3,4] => 14
[2,5,6,1,4,3] => 14
[2,5,6,3,1,4] => 14
[2,5,6,3,4,1] => 14
[2,5,6,4,1,3] => 14
[2,5,6,4,3,1] => 14
[2,6,1,3,4,5] => 10
[2,6,1,3,5,4] => 10
[2,6,1,4,3,5] => 10
[2,6,1,4,5,3] => 10
[2,6,1,5,3,4] => 12
[2,6,1,5,4,3] => 12
[2,6,3,1,4,5] => 10
[2,6,3,1,5,4] => 10
[2,6,3,4,1,5] => 10
[2,6,3,4,5,1] => 10
[2,6,3,5,1,4] => 12
[2,6,3,5,4,1] => 12
[2,6,4,1,3,5] => 12
[2,6,4,1,5,3] => 12
[2,6,4,3,1,5] => 12
[2,6,4,3,5,1] => 12
[2,6,4,5,1,3] => 14
[2,6,4,5,3,1] => 14
[2,6,5,1,3,4] => 14
[2,6,5,1,4,3] => 14
[2,6,5,3,1,4] => 14
[2,6,5,3,4,1] => 14
[2,6,5,4,1,3] => 14
[2,6,5,4,3,1] => 14
[3,1,2,4,5,6] => 4
[3,1,2,4,6,5] => 6
[3,1,2,5,4,6] => 6
[3,1,2,5,6,4] => 8
[3,1,2,6,4,5] => 8
[3,1,2,6,5,4] => 8
[3,1,4,2,5,6] => 6
[3,1,4,2,6,5] => 8
[3,1,4,5,2,6] => 8
[3,1,4,5,6,2] => 10
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 10
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 10
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 10
[3,1,5,6,2,4] => 12
[3,1,5,6,4,2] => 12
[3,1,6,2,4,5] => 10
[3,1,6,2,5,4] => 10
[3,1,6,4,2,5] => 10
[3,1,6,4,5,2] => 10
[3,1,6,5,2,4] => 12
[3,1,6,5,4,2] => 12
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 6
[3,2,1,5,4,6] => 6
[3,2,1,5,6,4] => 8
[3,2,1,6,4,5] => 8
[3,2,1,6,5,4] => 8
[3,2,4,1,5,6] => 6
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 10
[3,2,4,6,1,5] => 10
[3,2,4,6,5,1] => 10
[3,2,5,1,4,6] => 8
[3,2,5,1,6,4] => 10
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 10
[3,2,5,6,1,4] => 12
[3,2,5,6,4,1] => 12
[3,2,6,1,4,5] => 10
[3,2,6,1,5,4] => 10
[3,2,6,4,1,5] => 10
[3,2,6,4,5,1] => 10
[3,2,6,5,1,4] => 12
[3,2,6,5,4,1] => 12
[3,4,1,2,5,6] => 8
[3,4,1,2,6,5] => 10
[3,4,1,5,2,6] => 10
[3,4,1,5,6,2] => 12
[3,4,1,6,2,5] => 12
[3,4,1,6,5,2] => 12
[3,4,2,1,5,6] => 8
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 10
[3,4,2,5,6,1] => 12
[3,4,2,6,1,5] => 12
[3,4,2,6,5,1] => 12
[3,4,5,1,2,6] => 12
[3,4,5,1,6,2] => 14
[3,4,5,2,1,6] => 12
[3,4,5,2,6,1] => 14
[3,4,5,6,1,2] => 16
[3,4,5,6,2,1] => 16
[3,4,6,1,2,5] => 14
[3,4,6,1,5,2] => 14
[3,4,6,2,1,5] => 14
[3,4,6,2,5,1] => 14
[3,4,6,5,1,2] => 16
[3,4,6,5,2,1] => 16
[3,5,1,2,4,6] => 10
[3,5,1,2,6,4] => 12
[3,5,1,4,2,6] => 10
[3,5,1,4,6,2] => 12
[3,5,1,6,2,4] => 14
[3,5,1,6,4,2] => 14
[3,5,2,1,4,6] => 10
[3,5,2,1,6,4] => 12
[3,5,2,4,1,6] => 10
[3,5,2,4,6,1] => 12
[3,5,2,6,1,4] => 14
[3,5,2,6,4,1] => 14
[3,5,4,1,2,6] => 12
[3,5,4,1,6,2] => 14
[3,5,4,2,1,6] => 12
[3,5,4,2,6,1] => 14
[3,5,4,6,1,2] => 16
[3,5,4,6,2,1] => 16
[3,5,6,1,2,4] => 16
[3,5,6,1,4,2] => 16
[3,5,6,2,1,4] => 16
[3,5,6,2,4,1] => 16
[3,5,6,4,1,2] => 16
[3,5,6,4,2,1] => 16
[3,6,1,2,4,5] => 12
[3,6,1,2,5,4] => 12
[3,6,1,4,2,5] => 12
[3,6,1,4,5,2] => 12
[3,6,1,5,2,4] => 14
[3,6,1,5,4,2] => 14
[3,6,2,1,4,5] => 12
[3,6,2,1,5,4] => 12
[3,6,2,4,1,5] => 12
[3,6,2,4,5,1] => 12
[3,6,2,5,1,4] => 14
[3,6,2,5,4,1] => 14
[3,6,4,1,2,5] => 14
[3,6,4,1,5,2] => 14
[3,6,4,2,1,5] => 14
[3,6,4,2,5,1] => 14
[3,6,4,5,1,2] => 16
[3,6,4,5,2,1] => 16
[3,6,5,1,2,4] => 16
[3,6,5,1,4,2] => 16
[3,6,5,2,1,4] => 16
[3,6,5,2,4,1] => 16
[3,6,5,4,1,2] => 16
[3,6,5,4,2,1] => 16
[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] => 6
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 8
[4,1,3,5,6,2] => 10
[4,1,3,6,2,5] => 10
[4,1,3,6,5,2] => 10
[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] => 12
[4,1,5,6,2,3] => 14
[4,1,5,6,3,2] => 14
[4,1,6,2,3,5] => 12
[4,1,6,2,5,3] => 12
[4,1,6,3,2,5] => 12
[4,1,6,3,5,2] => 12
[4,1,6,5,2,3] => 14
[4,1,6,5,3,2] => 14
[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] => 6
[4,2,3,1,6,5] => 8
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 10
[4,2,3,6,1,5] => 10
[4,2,3,6,5,1] => 10
[4,2,5,1,3,6] => 10
[4,2,5,1,6,3] => 12
[4,2,5,3,1,6] => 10
[4,2,5,3,6,1] => 12
[4,2,5,6,1,3] => 14
[4,2,5,6,3,1] => 14
[4,2,6,1,3,5] => 12
[4,2,6,1,5,3] => 12
[4,2,6,3,1,5] => 12
[4,2,6,3,5,1] => 12
[4,2,6,5,1,3] => 14
[4,2,6,5,3,1] => 14
[4,3,1,2,5,6] => 8
[4,3,1,2,6,5] => 10
[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] => 8
[4,3,2,1,6,5] => 10
[4,3,2,5,1,6] => 10
[4,3,2,5,6,1] => 12
[4,3,2,6,1,5] => 12
[4,3,2,6,5,1] => 12
[4,3,5,1,2,6] => 12
[4,3,5,1,6,2] => 14
[4,3,5,2,1,6] => 12
[4,3,5,2,6,1] => 14
[4,3,5,6,1,2] => 16
[4,3,5,6,2,1] => 16
[4,3,6,1,2,5] => 14
[4,3,6,1,5,2] => 14
[4,3,6,2,1,5] => 14
[4,3,6,2,5,1] => 14
[4,3,6,5,1,2] => 16
[4,3,6,5,2,1] => 16
[4,5,1,2,3,6] => 12
[4,5,1,2,6,3] => 14
[4,5,1,3,2,6] => 12
[4,5,1,3,6,2] => 14
[4,5,1,6,2,3] => 16
[4,5,1,6,3,2] => 16
[4,5,2,1,3,6] => 12
[4,5,2,1,6,3] => 14
[4,5,2,3,1,6] => 12
[4,5,2,3,6,1] => 14
[4,5,2,6,1,3] => 16
[4,5,2,6,3,1] => 16
[4,5,3,1,2,6] => 12
[4,5,3,1,6,2] => 14
[4,5,3,2,1,6] => 12
[4,5,3,2,6,1] => 14
[4,5,3,6,1,2] => 16
[4,5,3,6,2,1] => 16
[4,5,6,1,2,3] => 18
[4,5,6,1,3,2] => 18
[4,5,6,2,1,3] => 18
[4,5,6,2,3,1] => 18
[4,5,6,3,1,2] => 18
[4,5,6,3,2,1] => 18
[4,6,1,2,3,5] => 14
[4,6,1,2,5,3] => 14
[4,6,1,3,2,5] => 14
[4,6,1,3,5,2] => 14
[4,6,1,5,2,3] => 16
[4,6,1,5,3,2] => 16
[4,6,2,1,3,5] => 14
[4,6,2,1,5,3] => 14
[4,6,2,3,1,5] => 14
[4,6,2,3,5,1] => 14
[4,6,2,5,1,3] => 16
[4,6,2,5,3,1] => 16
[4,6,3,1,2,5] => 14
[4,6,3,1,5,2] => 14
[4,6,3,2,1,5] => 14
[4,6,3,2,5,1] => 14
[4,6,3,5,1,2] => 16
[4,6,3,5,2,1] => 16
[4,6,5,1,2,3] => 18
[4,6,5,1,3,2] => 18
[4,6,5,2,1,3] => 18
[4,6,5,2,3,1] => 18
[4,6,5,3,1,2] => 18
[4,6,5,3,2,1] => 18
[5,1,2,3,4,6] => 8
[5,1,2,3,6,4] => 10
[5,1,2,4,3,6] => 8
[5,1,2,4,6,3] => 10
[5,1,2,6,3,4] => 12
[5,1,2,6,4,3] => 12
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 10
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 10
[5,1,3,6,2,4] => 12
[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] => 12
[5,1,4,6,2,3] => 14
[5,1,4,6,3,2] => 14
[5,1,6,2,3,4] => 14
[5,1,6,2,4,3] => 14
[5,1,6,3,2,4] => 14
[5,1,6,3,4,2] => 14
[5,1,6,4,2,3] => 14
[5,1,6,4,3,2] => 14
[5,2,1,3,4,6] => 8
[5,2,1,3,6,4] => 10
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 10
[5,2,1,6,3,4] => 12
[5,2,1,6,4,3] => 12
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 10
[5,2,3,4,1,6] => 8
[5,2,3,4,6,1] => 10
[5,2,3,6,1,4] => 12
[5,2,3,6,4,1] => 12
[5,2,4,1,3,6] => 10
[5,2,4,1,6,3] => 12
[5,2,4,3,1,6] => 10
[5,2,4,3,6,1] => 12
[5,2,4,6,1,3] => 14
[5,2,4,6,3,1] => 14
[5,2,6,1,3,4] => 14
[5,2,6,1,4,3] => 14
[5,2,6,3,1,4] => 14
[5,2,6,3,4,1] => 14
[5,2,6,4,1,3] => 14
[5,2,6,4,3,1] => 14
[5,3,1,2,4,6] => 10
[5,3,1,2,6,4] => 12
[5,3,1,4,2,6] => 10
[5,3,1,4,6,2] => 12
[5,3,1,6,2,4] => 14
[5,3,1,6,4,2] => 14
[5,3,2,1,4,6] => 10
[5,3,2,1,6,4] => 12
[5,3,2,4,1,6] => 10
[5,3,2,4,6,1] => 12
[5,3,2,6,1,4] => 14
[5,3,2,6,4,1] => 14
[5,3,4,1,2,6] => 12
[5,3,4,1,6,2] => 14
[5,3,4,2,1,6] => 12
[5,3,4,2,6,1] => 14
[5,3,4,6,1,2] => 16
[5,3,4,6,2,1] => 16
[5,3,6,1,2,4] => 16
[5,3,6,1,4,2] => 16
[5,3,6,2,1,4] => 16
[5,3,6,2,4,1] => 16
[5,3,6,4,1,2] => 16
[5,3,6,4,2,1] => 16
[5,4,1,2,3,6] => 12
[5,4,1,2,6,3] => 14
[5,4,1,3,2,6] => 12
[5,4,1,3,6,2] => 14
[5,4,1,6,2,3] => 16
[5,4,1,6,3,2] => 16
[5,4,2,1,3,6] => 12
[5,4,2,1,6,3] => 14
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 14
[5,4,2,6,1,3] => 16
[5,4,2,6,3,1] => 16
[5,4,3,1,2,6] => 12
[5,4,3,1,6,2] => 14
[5,4,3,2,1,6] => 12
[5,4,3,2,6,1] => 14
[5,4,3,6,1,2] => 16
[5,4,3,6,2,1] => 16
[5,4,6,1,2,3] => 18
[5,4,6,1,3,2] => 18
[5,4,6,2,1,3] => 18
[5,4,6,2,3,1] => 18
[5,4,6,3,1,2] => 18
[5,4,6,3,2,1] => 18
[5,6,1,2,3,4] => 16
[5,6,1,2,4,3] => 16
[5,6,1,3,2,4] => 16
[5,6,1,3,4,2] => 16
[5,6,1,4,2,3] => 16
[5,6,1,4,3,2] => 16
[5,6,2,1,3,4] => 16
[5,6,2,1,4,3] => 16
[5,6,2,3,1,4] => 16
[5,6,2,3,4,1] => 16
[5,6,2,4,1,3] => 16
[5,6,2,4,3,1] => 16
[5,6,3,1,2,4] => 16
[5,6,3,1,4,2] => 16
[5,6,3,2,1,4] => 16
[5,6,3,2,4,1] => 16
[5,6,3,4,1,2] => 16
[5,6,3,4,2,1] => 16
[5,6,4,1,2,3] => 18
[5,6,4,1,3,2] => 18
[5,6,4,2,1,3] => 18
[5,6,4,2,3,1] => 18
[5,6,4,3,1,2] => 18
[5,6,4,3,2,1] => 18
[6,1,2,3,4,5] => 10
[6,1,2,3,5,4] => 10
[6,1,2,4,3,5] => 10
[6,1,2,4,5,3] => 10
[6,1,2,5,3,4] => 12
[6,1,2,5,4,3] => 12
[6,1,3,2,4,5] => 10
[6,1,3,2,5,4] => 10
[6,1,3,4,2,5] => 10
[6,1,3,4,5,2] => 10
[6,1,3,5,2,4] => 12
[6,1,3,5,4,2] => 12
[6,1,4,2,3,5] => 12
[6,1,4,2,5,3] => 12
[6,1,4,3,2,5] => 12
[6,1,4,3,5,2] => 12
[6,1,4,5,2,3] => 14
[6,1,4,5,3,2] => 14
[6,1,5,2,3,4] => 14
[6,1,5,2,4,3] => 14
[6,1,5,3,2,4] => 14
[6,1,5,3,4,2] => 14
[6,1,5,4,2,3] => 14
[6,1,5,4,3,2] => 14
[6,2,1,3,4,5] => 10
[6,2,1,3,5,4] => 10
[6,2,1,4,3,5] => 10
[6,2,1,4,5,3] => 10
[6,2,1,5,3,4] => 12
[6,2,1,5,4,3] => 12
[6,2,3,1,4,5] => 10
[6,2,3,1,5,4] => 10
[6,2,3,4,1,5] => 10
[6,2,3,4,5,1] => 10
[6,2,3,5,1,4] => 12
[6,2,3,5,4,1] => 12
[6,2,4,1,3,5] => 12
[6,2,4,1,5,3] => 12
[6,2,4,3,1,5] => 12
[6,2,4,3,5,1] => 12
[6,2,4,5,1,3] => 14
[6,2,4,5,3,1] => 14
[6,2,5,1,3,4] => 14
[6,2,5,1,4,3] => 14
[6,2,5,3,1,4] => 14
[6,2,5,3,4,1] => 14
[6,2,5,4,1,3] => 14
[6,2,5,4,3,1] => 14
[6,3,1,2,4,5] => 12
[6,3,1,2,5,4] => 12
[6,3,1,4,2,5] => 12
[6,3,1,4,5,2] => 12
[6,3,1,5,2,4] => 14
[6,3,1,5,4,2] => 14
[6,3,2,1,4,5] => 12
[6,3,2,1,5,4] => 12
[6,3,2,4,1,5] => 12
[6,3,2,4,5,1] => 12
[6,3,2,5,1,4] => 14
[6,3,2,5,4,1] => 14
[6,3,4,1,2,5] => 14
[6,3,4,1,5,2] => 14
[6,3,4,2,1,5] => 14
[6,3,4,2,5,1] => 14
[6,3,4,5,1,2] => 16
[6,3,4,5,2,1] => 16
[6,3,5,1,2,4] => 16
[6,3,5,1,4,2] => 16
[6,3,5,2,1,4] => 16
[6,3,5,2,4,1] => 16
[6,3,5,4,1,2] => 16
[6,3,5,4,2,1] => 16
[6,4,1,2,3,5] => 14
[6,4,1,2,5,3] => 14
[6,4,1,3,2,5] => 14
[6,4,1,3,5,2] => 14
[6,4,1,5,2,3] => 16
[6,4,1,5,3,2] => 16
[6,4,2,1,3,5] => 14
[6,4,2,1,5,3] => 14
[6,4,2,3,1,5] => 14
[6,4,2,3,5,1] => 14
[6,4,2,5,1,3] => 16
[6,4,2,5,3,1] => 16
[6,4,3,1,2,5] => 14
[6,4,3,1,5,2] => 14
[6,4,3,2,1,5] => 14
[6,4,3,2,5,1] => 14
[6,4,3,5,1,2] => 16
[6,4,3,5,2,1] => 16
[6,4,5,1,2,3] => 18
[6,4,5,1,3,2] => 18
[6,4,5,2,1,3] => 18
[6,4,5,2,3,1] => 18
[6,4,5,3,1,2] => 18
[6,4,5,3,2,1] => 18
[6,5,1,2,3,4] => 16
[6,5,1,2,4,3] => 16
[6,5,1,3,2,4] => 16
[6,5,1,3,4,2] => 16
[6,5,1,4,2,3] => 16
[6,5,1,4,3,2] => 16
[6,5,2,1,3,4] => 16
[6,5,2,1,4,3] => 16
[6,5,2,3,1,4] => 16
[6,5,2,3,4,1] => 16
[6,5,2,4,1,3] => 16
[6,5,2,4,3,1] => 16
[6,5,3,1,2,4] => 16
[6,5,3,1,4,2] => 16
[6,5,3,2,1,4] => 16
[6,5,3,2,4,1] => 16
[6,5,3,4,1,2] => 16
[6,5,3,4,2,1] => 16
[6,5,4,1,2,3] => 18
[6,5,4,1,3,2] => 18
[6,5,4,2,1,3] => 18
[6,5,4,2,3,1] => 18
[6,5,4,3,1,2] => 18
[6,5,4,3,2,1] => 18
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 2
[1,2,3,4,6,5,7] => 2
[1,2,3,4,6,7,5] => 4
[1,2,3,4,7,5,6] => 4
[1,2,3,4,7,6,5] => 4
[1,2,3,5,4,6,7] => 2
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 4
[1,2,3,5,6,7,4] => 6
[1,2,3,5,7,4,6] => 6
[1,2,3,5,7,6,4] => 6
[1,2,3,6,4,5,7] => 4
[1,2,3,6,4,7,5] => 6
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 6
[1,2,3,6,7,4,5] => 8
[1,2,3,6,7,5,4] => 8
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 6
[1,2,3,7,5,4,6] => 6
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 8
[1,2,3,7,6,5,4] => 8
[1,2,4,3,5,6,7] => 2
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 6
[1,2,4,3,7,5,6] => 6
[1,2,4,3,7,6,5] => 6
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 6
[1,2,4,5,6,3,7] => 6
[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] => 6
[1,2,4,6,3,7,5] => 8
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 8
[1,2,4,6,7,3,5] => 10
[1,2,4,6,7,5,3] => 10
[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] => 10
[1,2,4,7,6,5,3] => 10
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 6
[1,2,5,3,6,4,7] => 6
[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] => 4
[1,2,5,4,3,7,6] => 6
[1,2,5,4,6,3,7] => 6
[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] => 8
[1,2,5,6,3,7,4] => 10
[1,2,5,6,4,3,7] => 8
[1,2,5,6,4,7,3] => 10
[1,2,5,6,7,3,4] => 12
[1,2,5,6,7,4,3] => 12
[1,2,5,7,3,4,6] => 10
[1,2,5,7,3,6,4] => 10
[1,2,5,7,4,3,6] => 10
[1,2,5,7,4,6,3] => 10
[1,2,5,7,6,3,4] => 12
[1,2,5,7,6,4,3] => 12
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 8
[1,2,6,3,5,4,7] => 6
[1,2,6,3,5,7,4] => 8
[1,2,6,3,7,4,5] => 10
[1,2,6,3,7,5,4] => 10
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 8
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 8
[1,2,6,4,7,3,5] => 10
[1,2,6,4,7,5,3] => 10
[1,2,6,5,3,4,7] => 8
[1,2,6,5,3,7,4] => 10
[1,2,6,5,4,3,7] => 8
[1,2,6,5,4,7,3] => 10
[1,2,6,5,7,3,4] => 12
[1,2,6,5,7,4,3] => 12
[1,2,6,7,3,4,5] => 12
[1,2,6,7,3,5,4] => 12
[1,2,6,7,4,3,5] => 12
[1,2,6,7,4,5,3] => 12
[1,2,6,7,5,3,4] => 12
[1,2,6,7,5,4,3] => 12
[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] => 10
[1,2,7,3,6,5,4] => 10
[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] => 8
[1,2,7,4,6,3,5] => 10
[1,2,7,4,6,5,3] => 10
[1,2,7,5,3,4,6] => 10
[1,2,7,5,3,6,4] => 10
[1,2,7,5,4,3,6] => 10
[1,2,7,5,4,6,3] => 10
[1,2,7,5,6,3,4] => 12
[1,2,7,5,6,4,3] => 12
[1,2,7,6,3,4,5] => 12
[1,2,7,6,3,5,4] => 12
[1,2,7,6,4,3,5] => 12
[1,2,7,6,4,5,3] => 12
[1,2,7,6,5,3,4] => 12
[1,2,7,6,5,4,3] => 12
[1,3,2,4,5,6,7] => 2
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 4
[1,3,2,4,6,7,5] => 6
[1,3,2,4,7,5,6] => 6
[1,3,2,4,7,6,5] => 6
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 6
[1,3,2,5,6,4,7] => 6
[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] => 6
[1,3,2,6,4,7,5] => 8
[1,3,2,6,5,4,7] => 6
[1,3,2,6,5,7,4] => 8
[1,3,2,6,7,4,5] => 10
[1,3,2,6,7,5,4] => 10
[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] => 8
[1,3,2,7,6,4,5] => 10
[1,3,2,7,6,5,4] => 10
[1,3,4,2,5,6,7] => 4
[1,3,4,2,5,7,6] => 6
[1,3,4,2,6,5,7] => 6
[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] => 6
[1,3,4,5,2,7,6] => 8
[1,3,4,5,6,2,7] => 8
[1,3,4,5,6,7,2] => 10
[1,3,4,5,7,2,6] => 10
[1,3,4,5,7,6,2] => 10
[1,3,4,6,2,5,7] => 8
[1,3,4,6,2,7,5] => 10
[1,3,4,6,5,2,7] => 8
[1,3,4,6,5,7,2] => 10
[1,3,4,6,7,2,5] => 12
[1,3,4,6,7,5,2] => 12
[1,3,4,7,2,5,6] => 10
[1,3,4,7,2,6,5] => 10
[1,3,4,7,5,2,6] => 10
[1,3,4,7,5,6,2] => 10
[1,3,4,7,6,2,5] => 12
[1,3,4,7,6,5,2] => 12
[1,3,5,2,4,6,7] => 6
[1,3,5,2,4,7,6] => 8
[1,3,5,2,6,4,7] => 8
[1,3,5,2,6,7,4] => 10
[1,3,5,2,7,4,6] => 10
[1,3,5,2,7,6,4] => 10
[1,3,5,4,2,6,7] => 6
[1,3,5,4,2,7,6] => 8
[1,3,5,4,6,2,7] => 8
[1,3,5,4,6,7,2] => 10
[1,3,5,4,7,2,6] => 10
[1,3,5,4,7,6,2] => 10
[1,3,5,6,2,4,7] => 10
[1,3,5,6,2,7,4] => 12
[1,3,5,6,4,2,7] => 10
[1,3,5,6,4,7,2] => 12
[1,3,5,6,7,2,4] => 14
[1,3,5,6,7,4,2] => 14
[1,3,5,7,2,4,6] => 12
[1,3,5,7,2,6,4] => 12
[1,3,5,7,4,2,6] => 12
[1,3,5,7,4,6,2] => 12
[1,3,5,7,6,2,4] => 14
[1,3,5,7,6,4,2] => 14
[1,3,6,2,4,5,7] => 8
[1,3,6,2,4,7,5] => 10
[1,3,6,2,5,4,7] => 8
[1,3,6,2,5,7,4] => 10
[1,3,6,2,7,4,5] => 12
[1,3,6,2,7,5,4] => 12
[1,3,6,4,2,5,7] => 8
[1,3,6,4,2,7,5] => 10
[1,3,6,4,5,2,7] => 8
[1,3,6,4,5,7,2] => 10
[1,3,6,4,7,2,5] => 12
[1,3,6,4,7,5,2] => 12
[1,3,6,5,2,4,7] => 10
[1,3,6,5,2,7,4] => 12
[1,3,6,5,4,2,7] => 10
[1,3,6,5,4,7,2] => 12
[1,3,6,5,7,2,4] => 14
[1,3,6,5,7,4,2] => 14
[1,3,6,7,2,4,5] => 14
[1,3,6,7,2,5,4] => 14
[1,3,6,7,4,2,5] => 14
[1,3,6,7,4,5,2] => 14
[1,3,6,7,5,2,4] => 14
[1,3,6,7,5,4,2] => 14
[1,3,7,2,4,5,6] => 10
[1,3,7,2,4,6,5] => 10
[1,3,7,2,5,4,6] => 10
[1,3,7,2,5,6,4] => 10
[1,3,7,2,6,4,5] => 12
[1,3,7,2,6,5,4] => 12
[1,3,7,4,2,5,6] => 10
[1,3,7,4,2,6,5] => 10
[1,3,7,4,5,2,6] => 10
[1,3,7,4,5,6,2] => 10
[1,3,7,4,6,2,5] => 12
[1,3,7,4,6,5,2] => 12
[1,3,7,5,2,4,6] => 12
[1,3,7,5,2,6,4] => 12
[1,3,7,5,4,2,6] => 12
[1,3,7,5,4,6,2] => 12
[1,3,7,5,6,2,4] => 14
[1,3,7,5,6,4,2] => 14
[1,3,7,6,2,4,5] => 14
[1,3,7,6,2,5,4] => 14
[1,3,7,6,4,2,5] => 14
[1,3,7,6,4,5,2] => 14
[1,3,7,6,5,2,4] => 14
[1,3,7,6,5,4,2] => 14
[1,4,2,3,5,6,7] => 4
[1,4,2,3,5,7,6] => 6
[1,4,2,3,6,5,7] => 6
[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] => 6
[1,4,2,5,3,7,6] => 8
[1,4,2,5,6,3,7] => 8
[1,4,2,5,6,7,3] => 10
[1,4,2,5,7,3,6] => 10
[1,4,2,5,7,6,3] => 10
[1,4,2,6,3,5,7] => 8
[1,4,2,6,3,7,5] => 10
[1,4,2,6,5,3,7] => 8
[1,4,2,6,5,7,3] => 10
[1,4,2,6,7,3,5] => 12
[1,4,2,6,7,5,3] => 12
[1,4,2,7,3,5,6] => 10
[1,4,2,7,3,6,5] => 10
[1,4,2,7,5,3,6] => 10
[1,4,2,7,5,6,3] => 10
[1,4,2,7,6,3,5] => 12
[1,4,2,7,6,5,3] => 12
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 6
[1,4,3,2,6,5,7] => 6
[1,4,3,2,6,7,5] => 8
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 8
[1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => 8
[1,4,3,5,6,2,7] => 8
[1,4,3,5,6,7,2] => 10
[1,4,3,5,7,2,6] => 10
[1,4,3,5,7,6,2] => 10
[1,4,3,6,2,5,7] => 8
[1,4,3,6,2,7,5] => 10
[1,4,3,6,5,2,7] => 8
[1,4,3,6,5,7,2] => 10
[1,4,3,6,7,2,5] => 12
[1,4,3,6,7,5,2] => 12
[1,4,3,7,2,5,6] => 10
[1,4,3,7,2,6,5] => 10
[1,4,3,7,5,2,6] => 10
[1,4,3,7,5,6,2] => 10
[1,4,3,7,6,2,5] => 12
[1,4,3,7,6,5,2] => 12
[1,4,5,2,3,6,7] => 8
[1,4,5,2,3,7,6] => 10
[1,4,5,2,6,3,7] => 10
[1,4,5,2,6,7,3] => 12
[1,4,5,2,7,3,6] => 12
[1,4,5,2,7,6,3] => 12
[1,4,5,3,2,6,7] => 8
[1,4,5,3,2,7,6] => 10
[1,4,5,3,6,2,7] => 10
[1,4,5,3,6,7,2] => 12
[1,4,5,3,7,2,6] => 12
[1,4,5,3,7,6,2] => 12
[1,4,5,6,2,3,7] => 12
[1,4,5,6,2,7,3] => 14
[1,4,5,6,3,2,7] => 12
[1,4,5,6,3,7,2] => 14
[1,4,5,6,7,2,3] => 16
[1,4,5,6,7,3,2] => 16
[1,4,5,7,2,3,6] => 14
[1,4,5,7,2,6,3] => 14
[1,4,5,7,3,2,6] => 14
[1,4,5,7,3,6,2] => 14
[1,4,5,7,6,2,3] => 16
[1,4,5,7,6,3,2] => 16
[1,4,6,2,3,5,7] => 10
[1,4,6,2,3,7,5] => 12
[1,4,6,2,5,3,7] => 10
[1,4,6,2,5,7,3] => 12
[1,4,6,2,7,3,5] => 14
[1,4,6,2,7,5,3] => 14
[1,4,6,3,2,5,7] => 10
[1,4,6,3,2,7,5] => 12
[1,4,6,3,5,2,7] => 10
[1,4,6,3,5,7,2] => 12
[1,4,6,3,7,2,5] => 14
[1,4,6,3,7,5,2] => 14
[1,4,6,5,2,3,7] => 12
[1,4,6,5,2,7,3] => 14
[1,4,6,5,3,2,7] => 12
[1,4,6,5,3,7,2] => 14
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Description
The total displacement of a permutation.
This is, for a permutation $\pi$ of $n$, given by $\sum_{i = 1}^n | \pi(i) - i |.$
This is twice the statistic St000029The depth of a permutation. and can be found in [3, Problem 5.1.1.28] and also in [1, 2].
References
[1] Chatterjee, S., Diaconis, P. A central limit theorem for a new statistic on permutations arXiv:1608.01666
[2] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray MathSciNet:0652736
[3] Knuth, D. E. The art of computer programming. Vol. 3 MathSciNet:3077154
Code
def statistic(pi):
    return sum( abs(pi(i) - i) for i in [ 1 .. len(pi) ] )
Created
May 31, 2017 at 10:42 by Christian Stump
Updated
May 31, 2017 at 13:53 by Christian Stump