edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 1
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 4
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 4
[2,4,3,1] => 4
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 5
[3,2,4,1] => 5
[3,4,1,2] => 2
[3,4,2,1] => 5
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 4
[4,2,3,1] => 4
[4,3,1,2] => 3
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 2
[1,2,4,5,3] => 2
[1,2,5,3,4] => 1
[1,2,5,4,3] => 3
[1,3,2,4,5] => 3
[1,3,2,5,4] => 4
[1,3,4,2,5] => 3
[1,3,4,5,2] => 3
[1,3,5,2,4] => 4
[1,3,5,4,2] => 4
[1,4,2,3,5] => 2
[1,4,2,5,3] => 2
[1,4,3,2,5] => 5
[1,4,3,5,2] => 5
[1,4,5,2,3] => 2
[1,4,5,3,2] => 5
[1,5,2,3,4] => 1
[1,5,2,4,3] => 3
[1,5,3,2,4] => 4
[1,5,3,4,2] => 4
[1,5,4,2,3] => 3
[1,5,4,3,2] => 6
[2,1,3,4,5] => 4
[2,1,3,5,4] => 5
[2,1,4,3,5] => 6
[2,1,4,5,3] => 6
[2,1,5,3,4] => 5
[2,1,5,4,3] => 7
[2,3,1,4,5] => 4
[2,3,1,5,4] => 5
[2,3,4,1,5] => 4
[2,3,4,5,1] => 4
[2,3,5,1,4] => 5
[2,3,5,4,1] => 5
[2,4,1,3,5] => 6
[2,4,1,5,3] => 6
[2,4,3,1,5] => 6
[2,4,3,5,1] => 6
[2,4,5,1,3] => 6
[2,4,5,3,1] => 6
[2,5,1,3,4] => 5
[2,5,1,4,3] => 7
[2,5,3,1,4] => 5
[2,5,3,4,1] => 5
[2,5,4,1,3] => 7
[2,5,4,3,1] => 7
[3,1,2,4,5] => 3
[3,1,2,5,4] => 4
[3,1,4,2,5] => 3
[3,1,4,5,2] => 3
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 7
[3,2,1,5,4] => 8
[3,2,4,1,5] => 7
[3,2,4,5,1] => 7
[3,2,5,1,4] => 8
[3,2,5,4,1] => 8
[3,4,1,2,5] => 3
[3,4,1,5,2] => 3
[3,4,2,1,5] => 7
[3,4,2,5,1] => 7
[3,4,5,1,2] => 3
[3,4,5,2,1] => 7
[3,5,1,2,4] => 4
[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] => 4
[3,5,4,2,1] => 8
[4,1,2,3,5] => 2
[4,1,2,5,3] => 2
[4,1,3,2,5] => 5
[4,1,3,5,2] => 5
[4,1,5,2,3] => 2
[4,1,5,3,2] => 5
[4,2,1,3,5] => 6
[4,2,1,5,3] => 6
[4,2,3,1,5] => 6
[4,2,3,5,1] => 6
[4,2,5,1,3] => 6
[4,2,5,3,1] => 6
[4,3,1,2,5] => 5
[4,3,1,5,2] => 5
[4,3,2,1,5] => 9
[4,3,2,5,1] => 9
[4,3,5,1,2] => 5
[4,3,5,2,1] => 9
[4,5,1,2,3] => 2
[4,5,1,3,2] => 5
[4,5,2,1,3] => 6
[4,5,2,3,1] => 6
[4,5,3,1,2] => 5
[4,5,3,2,1] => 9
[5,1,2,3,4] => 1
[5,1,2,4,3] => 3
[5,1,3,2,4] => 4
[5,1,3,4,2] => 4
[5,1,4,2,3] => 3
[5,1,4,3,2] => 6
[5,2,1,3,4] => 5
[5,2,1,4,3] => 7
[5,2,3,1,4] => 5
[5,2,3,4,1] => 5
[5,2,4,1,3] => 7
[5,2,4,3,1] => 7
[5,3,1,2,4] => 4
[5,3,1,4,2] => 4
[5,3,2,1,4] => 8
[5,3,2,4,1] => 8
[5,3,4,1,2] => 4
[5,3,4,2,1] => 8
[5,4,1,2,3] => 3
[5,4,1,3,2] => 6
[5,4,2,1,3] => 7
[5,4,2,3,1] => 7
[5,4,3,1,2] => 6
[5,4,3,2,1] => 10
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 3
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 2
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 5
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 5
[1,2,6,3,4,5] => 1
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 4
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 4
[1,3,2,4,6,5] => 5
[1,3,2,5,4,6] => 6
[1,3,2,5,6,4] => 6
[1,3,2,6,4,5] => 5
[1,3,2,6,5,4] => 7
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 5
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 5
[1,3,4,6,5,2] => 5
[1,3,5,2,4,6] => 6
[1,3,5,2,6,4] => 6
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 6
[1,3,5,6,2,4] => 6
[1,3,5,6,4,2] => 6
[1,3,6,2,4,5] => 5
[1,3,6,2,5,4] => 7
[1,3,6,4,2,5] => 5
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 7
[1,3,6,5,4,2] => 7
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 3
[1,4,2,6,3,5] => 4
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 7
[1,4,3,2,6,5] => 8
[1,4,3,5,2,6] => 7
[1,4,3,5,6,2] => 7
[1,4,3,6,2,5] => 8
[1,4,3,6,5,2] => 8
[1,4,5,2,3,6] => 3
[1,4,5,2,6,3] => 3
[1,4,5,3,2,6] => 7
[1,4,5,3,6,2] => 7
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 7
[1,4,6,2,3,5] => 4
[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] => 4
[1,4,6,5,3,2] => 8
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 5
[1,5,2,4,6,3] => 5
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 5
[1,5,3,2,4,6] => 6
[1,5,3,2,6,4] => 6
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 6
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 6
[1,5,4,2,3,6] => 5
[1,5,4,2,6,3] => 5
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 9
[1,5,4,6,2,3] => 5
[1,5,4,6,3,2] => 9
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 5
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 5
[1,5,6,4,3,2] => 9
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 4
[1,6,2,5,3,4] => 3
[1,6,2,5,4,3] => 6
[1,6,3,2,4,5] => 5
[1,6,3,2,5,4] => 7
[1,6,3,4,2,5] => 5
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 7
[1,6,3,5,4,2] => 7
[1,6,4,2,3,5] => 4
[1,6,4,2,5,3] => 4
[1,6,4,3,2,5] => 8
[1,6,4,3,5,2] => 8
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 3
[1,6,5,2,4,3] => 6
[1,6,5,3,2,4] => 7
[1,6,5,3,4,2] => 7
[1,6,5,4,2,3] => 6
[1,6,5,4,3,2] => 10
[2,1,3,4,5,6] => 5
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 7
[2,1,3,5,6,4] => 7
[2,1,3,6,4,5] => 6
[2,1,3,6,5,4] => 8
[2,1,4,3,5,6] => 8
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 8
[2,1,4,6,3,5] => 9
[2,1,4,6,5,3] => 9
[2,1,5,3,4,6] => 7
[2,1,5,3,6,4] => 7
[2,1,5,4,3,6] => 10
[2,1,5,4,6,3] => 10
[2,1,5,6,3,4] => 7
[2,1,5,6,4,3] => 10
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 9
[2,1,6,4,5,3] => 9
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 11
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 6
[2,3,1,5,4,6] => 7
[2,3,1,5,6,4] => 7
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 8
[2,3,4,1,5,6] => 5
[2,3,4,1,6,5] => 6
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 6
[2,3,4,6,5,1] => 6
[2,3,5,1,4,6] => 7
[2,3,5,1,6,4] => 7
[2,3,5,4,1,6] => 7
[2,3,5,4,6,1] => 7
[2,3,5,6,1,4] => 7
[2,3,5,6,4,1] => 7
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 8
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 6
[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] => 9
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 8
[2,4,1,6,3,5] => 9
[2,4,1,6,5,3] => 9
[2,4,3,1,5,6] => 8
[2,4,3,1,6,5] => 9
[2,4,3,5,1,6] => 8
[2,4,3,5,6,1] => 8
[2,4,3,6,1,5] => 9
[2,4,3,6,5,1] => 9
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 8
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 8
[2,4,6,1,3,5] => 9
[2,4,6,1,5,3] => 9
[2,4,6,3,1,5] => 9
[2,4,6,3,5,1] => 9
[2,4,6,5,1,3] => 9
[2,4,6,5,3,1] => 9
[2,5,1,3,4,6] => 7
[2,5,1,3,6,4] => 7
[2,5,1,4,3,6] => 10
[2,5,1,4,6,3] => 10
[2,5,1,6,3,4] => 7
[2,5,1,6,4,3] => 10
[2,5,3,1,4,6] => 7
[2,5,3,1,6,4] => 7
[2,5,3,4,1,6] => 7
[2,5,3,4,6,1] => 7
[2,5,3,6,1,4] => 7
[2,5,3,6,4,1] => 7
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 10
[2,5,4,3,1,6] => 10
[2,5,4,3,6,1] => 10
[2,5,4,6,1,3] => 10
[2,5,4,6,3,1] => 10
[2,5,6,1,3,4] => 7
[2,5,6,1,4,3] => 10
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 7
[2,5,6,4,1,3] => 10
[2,5,6,4,3,1] => 10
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 8
[2,6,1,4,3,5] => 9
[2,6,1,4,5,3] => 9
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 11
[2,6,3,1,4,5] => 6
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 6
[2,6,3,5,1,4] => 8
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 9
[2,6,4,1,5,3] => 9
[2,6,4,3,1,5] => 9
[2,6,4,3,5,1] => 9
[2,6,4,5,1,3] => 9
[2,6,4,5,3,1] => 9
[2,6,5,1,3,4] => 8
[2,6,5,1,4,3] => 11
[2,6,5,3,1,4] => 8
[2,6,5,3,4,1] => 8
[2,6,5,4,1,3] => 11
[2,6,5,4,3,1] => 11
[3,1,2,4,5,6] => 4
[3,1,2,4,6,5] => 5
[3,1,2,5,4,6] => 6
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 7
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 5
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 6
[3,1,5,2,6,4] => 6
[3,1,5,4,2,6] => 6
[3,1,5,4,6,2] => 6
[3,1,5,6,2,4] => 6
[3,1,5,6,4,2] => 6
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 7
[3,1,6,4,2,5] => 5
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 7
[3,1,6,5,4,2] => 7
[3,2,1,4,5,6] => 9
[3,2,1,4,6,5] => 10
[3,2,1,5,4,6] => 11
[3,2,1,5,6,4] => 11
[3,2,1,6,4,5] => 10
[3,2,1,6,5,4] => 12
[3,2,4,1,5,6] => 9
[3,2,4,1,6,5] => 10
[3,2,4,5,1,6] => 9
[3,2,4,5,6,1] => 9
[3,2,4,6,1,5] => 10
[3,2,4,6,5,1] => 10
[3,2,5,1,4,6] => 11
[3,2,5,1,6,4] => 11
[3,2,5,4,1,6] => 11
[3,2,5,4,6,1] => 11
[3,2,5,6,1,4] => 11
[3,2,5,6,4,1] => 11
[3,2,6,1,4,5] => 10
[3,2,6,1,5,4] => 12
[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] => 4
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 4
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 5
[3,4,1,6,5,2] => 5
[3,4,2,1,5,6] => 9
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 9
[3,4,2,5,6,1] => 9
[3,4,2,6,1,5] => 10
[3,4,2,6,5,1] => 10
[3,4,5,1,2,6] => 4
[3,4,5,1,6,2] => 4
[3,4,5,2,1,6] => 9
[3,4,5,2,6,1] => 9
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 9
[3,4,6,1,2,5] => 5
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 10
[3,4,6,2,5,1] => 10
[3,4,6,5,1,2] => 5
[3,4,6,5,2,1] => 10
[3,5,1,2,4,6] => 6
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 6
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 6
[3,5,2,1,4,6] => 11
[3,5,2,1,6,4] => 11
[3,5,2,4,1,6] => 11
[3,5,2,4,6,1] => 11
[3,5,2,6,1,4] => 11
[3,5,2,6,4,1] => 11
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 6
[3,5,4,2,1,6] => 11
[3,5,4,2,6,1] => 11
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 11
[3,5,6,1,2,4] => 6
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 11
[3,5,6,2,4,1] => 11
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 11
[3,6,1,2,4,5] => 5
[3,6,1,2,5,4] => 7
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 5
[3,6,1,5,2,4] => 7
[3,6,1,5,4,2] => 7
[3,6,2,1,4,5] => 10
[3,6,2,1,5,4] => 12
[3,6,2,4,1,5] => 10
[3,6,2,4,5,1] => 10
[3,6,2,5,1,4] => 12
[3,6,2,5,4,1] => 12
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 5
[3,6,4,2,1,5] => 10
[3,6,4,2,5,1] => 10
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 10
[3,6,5,1,2,4] => 7
[3,6,5,1,4,2] => 7
[3,6,5,2,1,4] => 12
[3,6,5,2,4,1] => 12
[3,6,5,4,1,2] => 7
[3,6,5,4,2,1] => 12
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 4
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 7
[4,1,3,5,6,2] => 7
[4,1,3,6,2,5] => 8
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 3
[4,1,5,3,2,6] => 7
[4,1,5,3,6,2] => 7
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 7
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 4
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 8
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 8
[4,2,1,3,5,6] => 8
[4,2,1,3,6,5] => 9
[4,2,1,5,3,6] => 8
[4,2,1,5,6,3] => 8
[4,2,1,6,3,5] => 9
[4,2,1,6,5,3] => 9
[4,2,3,1,5,6] => 8
[4,2,3,1,6,5] => 9
[4,2,3,5,1,6] => 8
[4,2,3,5,6,1] => 8
[4,2,3,6,1,5] => 9
[4,2,3,6,5,1] => 9
[4,2,5,1,3,6] => 8
[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] => 9
[4,2,6,1,5,3] => 9
[4,2,6,3,1,5] => 9
[4,2,6,3,5,1] => 9
[4,2,6,5,1,3] => 9
[4,2,6,5,3,1] => 9
[4,3,1,2,5,6] => 7
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 7
[4,3,1,5,6,2] => 7
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 8
[4,3,2,1,5,6] => 12
[4,3,2,1,6,5] => 13
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 12
[4,3,2,6,1,5] => 13
[4,3,2,6,5,1] => 13
[4,3,5,1,2,6] => 7
[4,3,5,1,6,2] => 7
[4,3,5,2,1,6] => 12
[4,3,5,2,6,1] => 12
[4,3,5,6,1,2] => 7
[4,3,5,6,2,1] => 12
[4,3,6,1,2,5] => 8
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 13
[4,3,6,2,5,1] => 13
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 13
[4,5,1,2,3,6] => 3
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 7
[4,5,1,3,6,2] => 7
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 7
[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] => 7
[4,5,3,1,6,2] => 7
[4,5,3,2,1,6] => 12
[4,5,3,2,6,1] => 12
[4,5,3,6,1,2] => 7
[4,5,3,6,2,1] => 12
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 7
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 12
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 4
[4,6,1,3,2,5] => 8
[4,6,1,3,5,2] => 8
[4,6,1,5,2,3] => 4
[4,6,1,5,3,2] => 8
[4,6,2,1,3,5] => 9
[4,6,2,1,5,3] => 9
[4,6,2,3,1,5] => 9
[4,6,2,3,5,1] => 9
[4,6,2,5,1,3] => 9
[4,6,2,5,3,1] => 9
[4,6,3,1,2,5] => 8
[4,6,3,1,5,2] => 8
[4,6,3,2,1,5] => 13
[4,6,3,2,5,1] => 13
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 13
[4,6,5,1,2,3] => 4
[4,6,5,1,3,2] => 8
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 9
[4,6,5,3,1,2] => 8
[4,6,5,3,2,1] => 13
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 2
[5,1,2,4,3,6] => 5
[5,1,2,4,6,3] => 5
[5,1,2,6,3,4] => 2
[5,1,2,6,4,3] => 5
[5,1,3,2,4,6] => 6
[5,1,3,2,6,4] => 6
[5,1,3,4,2,6] => 6
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 5
[5,1,4,2,6,3] => 5
[5,1,4,3,2,6] => 9
[5,1,4,3,6,2] => 9
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 9
[5,1,6,2,3,4] => 2
[5,1,6,2,4,3] => 5
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 5
[5,1,6,4,3,2] => 9
[5,2,1,3,4,6] => 7
[5,2,1,3,6,4] => 7
[5,2,1,4,3,6] => 10
[5,2,1,4,6,3] => 10
[5,2,1,6,3,4] => 7
[5,2,1,6,4,3] => 10
[5,2,3,1,4,6] => 7
[5,2,3,1,6,4] => 7
[5,2,3,4,1,6] => 7
[5,2,3,4,6,1] => 7
[5,2,3,6,1,4] => 7
[5,2,3,6,4,1] => 7
[5,2,4,1,3,6] => 10
[5,2,4,1,6,3] => 10
[5,2,4,3,1,6] => 10
[5,2,4,3,6,1] => 10
[5,2,4,6,1,3] => 10
[5,2,4,6,3,1] => 10
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 10
[5,2,6,3,1,4] => 7
[5,2,6,3,4,1] => 7
[5,2,6,4,1,3] => 10
[5,2,6,4,3,1] => 10
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 6
[5,3,1,4,2,6] => 6
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 6
[5,3,2,1,4,6] => 11
[5,3,2,1,6,4] => 11
[5,3,2,4,1,6] => 11
[5,3,2,4,6,1] => 11
[5,3,2,6,1,4] => 11
[5,3,2,6,4,1] => 11
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 11
[5,3,4,2,6,1] => 11
[5,3,4,6,1,2] => 6
[5,3,4,6,2,1] => 11
[5,3,6,1,2,4] => 6
[5,3,6,1,4,2] => 6
[5,3,6,2,1,4] => 11
[5,3,6,2,4,1] => 11
[5,3,6,4,1,2] => 6
[5,3,6,4,2,1] => 11
[5,4,1,2,3,6] => 5
[5,4,1,2,6,3] => 5
[5,4,1,3,2,6] => 9
[5,4,1,3,6,2] => 9
[5,4,1,6,2,3] => 5
[5,4,1,6,3,2] => 9
[5,4,2,1,3,6] => 10
[5,4,2,1,6,3] => 10
[5,4,2,3,1,6] => 10
[5,4,2,3,6,1] => 10
[5,4,2,6,1,3] => 10
[5,4,2,6,3,1] => 10
[5,4,3,1,2,6] => 9
[5,4,3,1,6,2] => 9
[5,4,3,2,1,6] => 14
[5,4,3,2,6,1] => 14
[5,4,3,6,1,2] => 9
[5,4,3,6,2,1] => 14
[5,4,6,1,2,3] => 5
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 10
[5,4,6,2,3,1] => 10
[5,4,6,3,1,2] => 9
[5,4,6,3,2,1] => 14
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 5
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 6
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 9
[5,6,2,1,3,4] => 7
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 7
[5,6,2,3,4,1] => 7
[5,6,2,4,1,3] => 10
[5,6,2,4,3,1] => 10
[5,6,3,1,2,4] => 6
[5,6,3,1,4,2] => 6
[5,6,3,2,1,4] => 11
[5,6,3,2,4,1] => 11
[5,6,3,4,1,2] => 6
[5,6,3,4,2,1] => 11
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 9
[5,6,4,2,1,3] => 10
[5,6,4,2,3,1] => 10
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 14
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 3
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 6
[6,1,3,2,4,5] => 5
[6,1,3,2,5,4] => 7
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 5
[6,1,3,5,2,4] => 7
[6,1,3,5,4,2] => 7
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 4
[6,1,4,3,2,5] => 8
[6,1,4,3,5,2] => 8
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 8
[6,1,5,2,3,4] => 3
[6,1,5,2,4,3] => 6
[6,1,5,3,2,4] => 7
[6,1,5,3,4,2] => 7
[6,1,5,4,2,3] => 6
[6,1,5,4,3,2] => 10
[6,2,1,3,4,5] => 6
[6,2,1,3,5,4] => 8
[6,2,1,4,3,5] => 9
[6,2,1,4,5,3] => 9
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 11
[6,2,3,1,4,5] => 6
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 6
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 8
[6,2,3,5,4,1] => 8
[6,2,4,1,3,5] => 9
[6,2,4,1,5,3] => 9
[6,2,4,3,1,5] => 9
[6,2,4,3,5,1] => 9
[6,2,4,5,1,3] => 9
[6,2,4,5,3,1] => 9
[6,2,5,1,3,4] => 8
[6,2,5,1,4,3] => 11
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 8
[6,2,5,4,1,3] => 11
[6,2,5,4,3,1] => 11
[6,3,1,2,4,5] => 5
[6,3,1,2,5,4] => 7
[6,3,1,4,2,5] => 5
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 7
[6,3,2,1,4,5] => 10
[6,3,2,1,5,4] => 12
[6,3,2,4,1,5] => 10
[6,3,2,4,5,1] => 10
[6,3,2,5,1,4] => 12
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 5
[6,3,4,2,1,5] => 10
[6,3,4,2,5,1] => 10
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 10
[6,3,5,1,2,4] => 7
[6,3,5,1,4,2] => 7
[6,3,5,2,1,4] => 12
[6,3,5,2,4,1] => 12
[6,3,5,4,1,2] => 7
[6,3,5,4,2,1] => 12
[6,4,1,2,3,5] => 4
[6,4,1,2,5,3] => 4
[6,4,1,3,2,5] => 8
[6,4,1,3,5,2] => 8
[6,4,1,5,2,3] => 4
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 9
[6,4,2,1,5,3] => 9
[6,4,2,3,1,5] => 9
[6,4,2,3,5,1] => 9
[6,4,2,5,1,3] => 9
[6,4,2,5,3,1] => 9
[6,4,3,1,2,5] => 8
[6,4,3,1,5,2] => 8
[6,4,3,2,1,5] => 13
[6,4,3,2,5,1] => 13
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 13
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 8
[6,4,5,2,1,3] => 9
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 13
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 6
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 7
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 10
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 11
[6,5,2,4,3,1] => 11
[6,5,3,1,2,4] => 7
[6,5,3,1,4,2] => 7
[6,5,3,2,1,4] => 12
[6,5,3,2,4,1] => 12
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 12
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 10
[6,5,4,2,1,3] => 11
[6,5,4,2,3,1] => 11
[6,5,4,3,1,2] => 10
[6,5,4,3,2,1] => 15
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 2
[1,2,3,4,6,7,5] => 2
[1,2,3,4,7,5,6] => 1
[1,2,3,4,7,6,5] => 3
[1,2,3,5,4,6,7] => 3
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 3
[1,2,3,5,6,7,4] => 3
[1,2,3,5,7,4,6] => 4
[1,2,3,5,7,6,4] => 4
[1,2,3,6,4,5,7] => 2
[1,2,3,6,4,7,5] => 2
[1,2,3,6,5,4,7] => 5
[1,2,3,6,5,7,4] => 5
[1,2,3,6,7,4,5] => 2
[1,2,3,6,7,5,4] => 5
[1,2,3,7,4,5,6] => 1
[1,2,3,7,4,6,5] => 3
[1,2,3,7,5,4,6] => 4
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 3
[1,2,3,7,6,5,4] => 6
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 5
[1,2,4,3,6,5,7] => 6
[1,2,4,3,6,7,5] => 6
[1,2,4,3,7,5,6] => 5
[1,2,4,3,7,6,5] => 7
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 5
[1,2,4,5,6,3,7] => 4
[1,2,4,5,6,7,3] => 4
[1,2,4,5,7,3,6] => 5
[1,2,4,5,7,6,3] => 5
[1,2,4,6,3,5,7] => 6
[1,2,4,6,3,7,5] => 6
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 6
[1,2,4,6,7,3,5] => 6
[1,2,4,6,7,5,3] => 6
[1,2,4,7,3,5,6] => 5
[1,2,4,7,3,6,5] => 7
[1,2,4,7,5,3,6] => 5
[1,2,4,7,5,6,3] => 5
[1,2,4,7,6,3,5] => 7
[1,2,4,7,6,5,3] => 7
[1,2,5,3,4,6,7] => 3
[1,2,5,3,4,7,6] => 4
[1,2,5,3,6,4,7] => 3
[1,2,5,3,6,7,4] => 3
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 4
[1,2,5,4,3,6,7] => 7
[1,2,5,4,3,7,6] => 8
[1,2,5,4,6,3,7] => 7
[1,2,5,4,6,7,3] => 7
[1,2,5,4,7,3,6] => 8
[1,2,5,4,7,6,3] => 8
[1,2,5,6,3,4,7] => 3
[1,2,5,6,3,7,4] => 3
[1,2,5,6,4,3,7] => 7
[1,2,5,6,4,7,3] => 7
[1,2,5,6,7,3,4] => 3
[1,2,5,6,7,4,3] => 7
[1,2,5,7,3,4,6] => 4
[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] => 4
[1,2,5,7,6,4,3] => 8
[1,2,6,3,4,5,7] => 2
[1,2,6,3,4,7,5] => 2
[1,2,6,3,5,4,7] => 5
[1,2,6,3,5,7,4] => 5
[1,2,6,3,7,4,5] => 2
[1,2,6,3,7,5,4] => 5
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 6
[1,2,6,4,7,3,5] => 6
[1,2,6,4,7,5,3] => 6
[1,2,6,5,3,4,7] => 5
[1,2,6,5,3,7,4] => 5
[1,2,6,5,4,3,7] => 9
[1,2,6,5,4,7,3] => 9
[1,2,6,5,7,3,4] => 5
[1,2,6,5,7,4,3] => 9
[1,2,6,7,3,4,5] => 2
[1,2,6,7,3,5,4] => 5
[1,2,6,7,4,3,5] => 6
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 5
[1,2,6,7,5,4,3] => 9
[1,2,7,3,4,5,6] => 1
[1,2,7,3,4,6,5] => 3
[1,2,7,3,5,4,6] => 4
[1,2,7,3,5,6,4] => 4
[1,2,7,3,6,4,5] => 3
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 5
[1,2,7,4,3,6,5] => 7
[1,2,7,4,5,3,6] => 5
[1,2,7,4,5,6,3] => 5
[1,2,7,4,6,3,5] => 7
[1,2,7,4,6,5,3] => 7
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 4
[1,2,7,5,4,3,6] => 8
[1,2,7,5,4,6,3] => 8
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 8
[1,2,7,6,3,4,5] => 3
[1,2,7,6,3,5,4] => 6
[1,2,7,6,4,3,5] => 7
[1,2,7,6,4,5,3] => 7
[1,2,7,6,5,3,4] => 6
[1,2,7,6,5,4,3] => 10
[1,3,2,4,5,6,7] => 5
[1,3,2,4,5,7,6] => 6
[1,3,2,4,6,5,7] => 7
[1,3,2,4,6,7,5] => 7
[1,3,2,4,7,5,6] => 6
[1,3,2,4,7,6,5] => 8
[1,3,2,5,4,6,7] => 8
[1,3,2,5,4,7,6] => 9
[1,3,2,5,6,4,7] => 8
[1,3,2,5,6,7,4] => 8
[1,3,2,5,7,4,6] => 9
[1,3,2,5,7,6,4] => 9
[1,3,2,6,4,5,7] => 7
[1,3,2,6,4,7,5] => 7
[1,3,2,6,5,4,7] => 10
[1,3,2,6,5,7,4] => 10
[1,3,2,6,7,4,5] => 7
[1,3,2,6,7,5,4] => 10
[1,3,2,7,4,5,6] => 6
[1,3,2,7,4,6,5] => 8
[1,3,2,7,5,4,6] => 9
[1,3,2,7,5,6,4] => 9
[1,3,2,7,6,4,5] => 8
[1,3,2,7,6,5,4] => 11
[1,3,4,2,5,6,7] => 5
[1,3,4,2,5,7,6] => 6
[1,3,4,2,6,5,7] => 7
[1,3,4,2,6,7,5] => 7
[1,3,4,2,7,5,6] => 6
[1,3,4,2,7,6,5] => 8
[1,3,4,5,2,6,7] => 5
[1,3,4,5,2,7,6] => 6
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 5
[1,3,4,5,7,2,6] => 6
[1,3,4,5,7,6,2] => 6
[1,3,4,6,2,5,7] => 7
[1,3,4,6,2,7,5] => 7
[1,3,4,6,5,2,7] => 7
[1,3,4,6,5,7,2] => 7
[1,3,4,6,7,2,5] => 7
[1,3,4,6,7,5,2] => 7
[1,3,4,7,2,5,6] => 6
[1,3,4,7,2,6,5] => 8
[1,3,4,7,5,2,6] => 6
[1,3,4,7,5,6,2] => 6
[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] => 9
[1,3,5,2,6,4,7] => 8
[1,3,5,2,6,7,4] => 8
[1,3,5,2,7,4,6] => 9
[1,3,5,2,7,6,4] => 9
[1,3,5,4,2,6,7] => 8
[1,3,5,4,2,7,6] => 9
[1,3,5,4,6,2,7] => 8
[1,3,5,4,6,7,2] => 8
[1,3,5,4,7,2,6] => 9
[1,3,5,4,7,6,2] => 9
[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] => 9
[1,3,5,7,2,6,4] => 9
[1,3,5,7,4,2,6] => 9
[1,3,5,7,4,6,2] => 9
[1,3,5,7,6,2,4] => 9
[1,3,5,7,6,4,2] => 9
[1,3,6,2,4,5,7] => 7
[1,3,6,2,4,7,5] => 7
[1,3,6,2,5,4,7] => 10
[1,3,6,2,5,7,4] => 10
[1,3,6,2,7,4,5] => 7
[1,3,6,2,7,5,4] => 10
[1,3,6,4,2,5,7] => 7
[1,3,6,4,2,7,5] => 7
[1,3,6,4,5,2,7] => 7
[1,3,6,4,5,7,2] => 7
[1,3,6,4,7,2,5] => 7
[1,3,6,4,7,5,2] => 7
[1,3,6,5,2,4,7] => 10
[1,3,6,5,2,7,4] => 10
[1,3,6,5,4,2,7] => 10
[1,3,6,5,4,7,2] => 10
[1,3,6,5,7,2,4] => 10
[1,3,6,5,7,4,2] => 10
[1,3,6,7,2,4,5] => 7
[1,3,6,7,2,5,4] => 10
[1,3,6,7,4,2,5] => 7
[1,3,6,7,4,5,2] => 7
[1,3,6,7,5,2,4] => 10
[1,3,6,7,5,4,2] => 10
[1,3,7,2,4,5,6] => 6
[1,3,7,2,4,6,5] => 8
[1,3,7,2,5,4,6] => 9
[1,3,7,2,5,6,4] => 9
[1,3,7,2,6,4,5] => 8
[1,3,7,2,6,5,4] => 11
[1,3,7,4,2,5,6] => 6
[1,3,7,4,2,6,5] => 8
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 6
[1,3,7,4,6,2,5] => 8
[1,3,7,4,6,5,2] => 8
[1,3,7,5,2,4,6] => 9
[1,3,7,5,2,6,4] => 9
[1,3,7,5,4,2,6] => 9
[1,3,7,5,4,6,2] => 9
[1,3,7,5,6,2,4] => 9
[1,3,7,5,6,4,2] => 9
[1,3,7,6,2,4,5] => 8
[1,3,7,6,2,5,4] => 11
[1,3,7,6,4,2,5] => 8
[1,3,7,6,4,5,2] => 8
[1,3,7,6,5,2,4] => 11
[1,3,7,6,5,4,2] => 11
[1,4,2,3,5,6,7] => 4
[1,4,2,3,5,7,6] => 5
[1,4,2,3,6,5,7] => 6
[1,4,2,3,6,7,5] => 6
[1,4,2,3,7,5,6] => 5
[1,4,2,3,7,6,5] => 7
[1,4,2,5,3,6,7] => 4
[1,4,2,5,3,7,6] => 5
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 4
[1,4,2,5,7,3,6] => 5
[1,4,2,5,7,6,3] => 5
[1,4,2,6,3,5,7] => 6
[1,4,2,6,3,7,5] => 6
[1,4,2,6,5,3,7] => 6
[1,4,2,6,5,7,3] => 6
[1,4,2,6,7,3,5] => 6
[1,4,2,6,7,5,3] => 6
[1,4,2,7,3,5,6] => 5
[1,4,2,7,3,6,5] => 7
[1,4,2,7,5,3,6] => 5
[1,4,2,7,5,6,3] => 5
[1,4,2,7,6,3,5] => 7
[1,4,2,7,6,5,3] => 7
[1,4,3,2,5,6,7] => 9
[1,4,3,2,5,7,6] => 10
[1,4,3,2,6,5,7] => 11
[1,4,3,2,6,7,5] => 11
[1,4,3,2,7,5,6] => 10
[1,4,3,2,7,6,5] => 12
[1,4,3,5,2,6,7] => 9
[1,4,3,5,2,7,6] => 10
[1,4,3,5,6,2,7] => 9
[1,4,3,5,6,7,2] => 9
[1,4,3,5,7,2,6] => 10
[1,4,3,5,7,6,2] => 10
[1,4,3,6,2,5,7] => 11
[1,4,3,6,2,7,5] => 11
[1,4,3,6,5,2,7] => 11
[1,4,3,6,5,7,2] => 11
[1,4,3,6,7,2,5] => 11
[1,4,3,6,7,5,2] => 11
[1,4,3,7,2,5,6] => 10
[1,4,3,7,2,6,5] => 12
[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] => 4
[1,4,5,2,3,7,6] => 5
[1,4,5,2,6,3,7] => 4
[1,4,5,2,6,7,3] => 4
[1,4,5,2,7,3,6] => 5
[1,4,5,2,7,6,3] => 5
[1,4,5,3,2,6,7] => 9
[1,4,5,3,2,7,6] => 10
[1,4,5,3,6,2,7] => 9
[1,4,5,3,6,7,2] => 9
[1,4,5,3,7,2,6] => 10
[1,4,5,3,7,6,2] => 10
[1,4,5,6,2,3,7] => 4
[1,4,5,6,2,7,3] => 4
[1,4,5,6,3,2,7] => 9
[1,4,5,6,3,7,2] => 9
[1,4,5,6,7,2,3] => 4
[1,4,5,6,7,3,2] => 9
[1,4,5,7,2,3,6] => 5
[1,4,5,7,2,6,3] => 5
[1,4,5,7,3,2,6] => 10
[1,4,5,7,3,6,2] => 10
[1,4,5,7,6,2,3] => 5
[1,4,5,7,6,3,2] => 10
[1,4,6,2,3,5,7] => 6
[1,4,6,2,3,7,5] => 6
[1,4,6,2,5,3,7] => 6
[1,4,6,2,5,7,3] => 6
[1,4,6,2,7,3,5] => 6
[1,4,6,2,7,5,3] => 6
[1,4,6,3,2,5,7] => 11
[1,4,6,3,2,7,5] => 11
[1,4,6,3,5,2,7] => 11
[1,4,6,3,5,7,2] => 11
[1,4,6,3,7,2,5] => 11
[1,4,6,3,7,5,2] => 11
[1,4,6,5,2,3,7] => 6
[1,4,6,5,2,7,3] => 6
[1,4,6,5,3,2,7] => 11
[1,4,6,5,3,7,2] => 11
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Description
The disorder of a permutation.
Consider a permutation $\pi = [\pi_1,\ldots,\pi_n]$ and cyclically scanning $\pi$ from left to right and remove the elements $1$ through $n$ on this order one after the other. The disorder of $\pi$ is defined to be the number of times a position was not removed in this process.
For example, the disorder of $[3,5,2,1,4]$ is $8$ since on the first scan, 3,5,2 and 4 are not removed, on the second, 3,5 and 4, and on the third and last scan, 5 is once again not removed.
References
[1] Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product_i=0..n-1 (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). OEIS:A008302
Code
def statistic(pi):
    i = 1
    pos = 0
    count = 0
    while i < len(pi):
        if pi[pos] == i:
            i += 1
        elif pi[pos] > i:
            count += 1
        pos = (pos+1)%len(pi)
    return count
Created
Mar 15, 2016 at 22:34 by Christian Stump
Updated
May 10, 2019 at 17:35 by Henning Ulfarsson