edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 2
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 0
[3,1,2,4] => 0
[3,1,4,2] => 1
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 1
[4,3,2,1] => 2
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 0
[1,3,2,5,4] => 2
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 0
[1,4,2,3,5] => 0
[1,4,2,5,3] => 1
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 0
[1,4,5,3,2] => 1
[1,5,2,3,4] => 0
[1,5,2,4,3] => 0
[1,5,3,2,4] => 0
[1,5,3,4,2] => 0
[1,5,4,2,3] => 1
[1,5,4,3,2] => 2
[2,1,3,4,5] => 0
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 2
[2,3,1,4,5] => 0
[2,3,1,5,4] => 3
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 2
[2,3,5,4,1] => 0
[2,4,1,3,5] => 1
[2,4,1,5,3] => 2
[2,4,3,1,5] => 0
[2,4,3,5,1] => 0
[2,4,5,1,3] => 1
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,4,3] => 1
[2,5,3,1,4] => 1
[2,5,3,4,1] => 0
[2,5,4,1,3] => 2
[2,5,4,3,1] => 3
[3,1,2,4,5] => 0
[3,1,2,5,4] => 3
[3,1,4,2,5] => 1
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,4,2] => 1
[3,2,1,4,5] => 0
[3,2,1,5,4] => 2
[3,2,4,1,5] => 0
[3,2,4,5,1] => 0
[3,2,5,1,4] => 1
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 2
[3,4,5,1,2] => 0
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 0
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 2
[3,5,2,4,1] => 1
[3,5,4,1,2] => 1
[3,5,4,2,1] => 2
[4,1,2,3,5] => 0
[4,1,2,5,3] => 2
[4,1,3,2,5] => 0
[4,1,3,5,2] => 1
[4,1,5,2,3] => 1
[4,1,5,3,2] => 2
[4,2,1,3,5] => 0
[4,2,1,5,3] => 1
[4,2,3,1,5] => 0
[4,2,3,5,1] => 0
[4,2,5,1,3] => 0
[4,2,5,3,1] => 1
[4,3,1,2,5] => 1
[4,3,1,5,2] => 2
[4,3,2,1,5] => 2
[4,3,2,5,1] => 3
[4,3,5,1,2] => 1
[4,3,5,2,1] => 2
[4,5,1,2,3] => 0
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 2
[4,5,3,1,2] => 0
[4,5,3,2,1] => 1
[5,1,2,3,4] => 0
[5,1,2,4,3] => 0
[5,1,3,2,4] => 0
[5,1,3,4,2] => 0
[5,1,4,2,3] => 2
[5,1,4,3,2] => 3
[5,2,1,3,4] => 0
[5,2,1,4,3] => 0
[5,2,3,1,4] => 0
[5,2,3,4,1] => 0
[5,2,4,1,3] => 1
[5,2,4,3,1] => 2
[5,3,1,2,4] => 2
[5,3,1,4,2] => 1
[5,3,2,1,4] => 3
[5,3,2,4,1] => 2
[5,3,4,1,2] => 2
[5,3,4,2,1] => 3
[5,4,1,2,3] => 1
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 3
[5,4,3,1,2] => 1
[5,4,3,2,1] => 2
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 0
[1,2,3,5,4,6] => 0
[1,2,3,5,6,4] => 0
[1,2,3,6,4,5] => 0
[1,2,3,6,5,4] => 0
[1,2,4,3,5,6] => 0
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 0
[1,2,4,5,6,3] => 0
[1,2,4,6,3,5] => 1
[1,2,4,6,5,3] => 0
[1,2,5,3,4,6] => 0
[1,2,5,3,6,4] => 1
[1,2,5,4,3,6] => 0
[1,2,5,4,6,3] => 0
[1,2,5,6,3,4] => 0
[1,2,5,6,4,3] => 1
[1,2,6,3,4,5] => 0
[1,2,6,3,5,4] => 0
[1,2,6,4,3,5] => 0
[1,2,6,4,5,3] => 0
[1,2,6,5,3,4] => 1
[1,2,6,5,4,3] => 2
[1,3,2,4,5,6] => 0
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => 0
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 0
[1,3,4,5,6,2] => 0
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 0
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 0
[1,3,5,4,6,2] => 0
[1,3,5,6,2,4] => 1
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 1
[1,3,6,4,2,5] => 1
[1,3,6,4,5,2] => 0
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 0
[1,4,2,3,6,5] => 3
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 1
[1,4,3,2,5,6] => 0
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 0
[1,4,3,5,6,2] => 0
[1,4,3,6,2,5] => 1
[1,4,3,6,5,2] => 0
[1,4,5,2,3,6] => 0
[1,4,5,2,6,3] => 1
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 0
[1,4,5,6,3,2] => 1
[1,4,6,2,3,5] => 1
[1,4,6,2,5,3] => 0
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 1
[1,4,6,5,2,3] => 1
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 0
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 0
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 1
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 0
[1,5,3,2,6,4] => 1
[1,5,3,4,2,6] => 0
[1,5,3,4,6,2] => 0
[1,5,3,6,2,4] => 0
[1,5,3,6,4,2] => 1
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 2
[1,5,4,3,6,2] => 3
[1,5,4,6,2,3] => 1
[1,5,4,6,3,2] => 2
[1,5,6,2,3,4] => 0
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 0
[1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => 0
[1,6,2,3,5,4] => 0
[1,6,2,4,3,5] => 0
[1,6,2,4,5,3] => 0
[1,6,2,5,3,4] => 2
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 0
[1,6,3,2,5,4] => 0
[1,6,3,4,2,5] => 0
[1,6,3,4,5,2] => 0
[1,6,3,5,2,4] => 1
[1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 1
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 1
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 2
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 3
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 5
[2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => 3
[2,1,5,6,3,4] => 4
[2,1,5,6,4,3] => 5
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 3
[2,1,6,4,3,5] => 3
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 5
[2,1,6,5,4,3] => 6
[2,3,1,4,5,6] => 0
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 5
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 0
[2,3,4,1,6,5] => 4
[2,3,4,5,1,6] => 0
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 0
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 3
[2,3,5,4,1,6] => 0
[2,3,5,4,6,1] => 0
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 3
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 0
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 4
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 5
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 0
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 0
[2,4,3,5,6,1] => 0
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 0
[2,4,5,1,3,6] => 1
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 3
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 1
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 2
[2,4,6,5,3,1] => 3
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 1
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 3
[2,5,1,6,4,3] => 4
[2,5,3,1,4,6] => 1
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 0
[2,5,3,4,6,1] => 0
[2,5,3,6,1,4] => 1
[2,5,3,6,4,1] => 2
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 3
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 4
[2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => 3
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 3
[2,5,6,3,1,4] => 3
[2,5,6,3,4,1] => 4
[2,5,6,4,1,3] => 1
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 3
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 1
[2,6,1,5,3,4] => 4
[2,6,1,5,4,3] => 5
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 1
[2,6,3,4,1,5] => 1
[2,6,3,4,5,1] => 0
[2,6,3,5,1,4] => 2
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 4
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 5
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 3
[2,6,5,1,4,3] => 4
[2,6,5,3,1,4] => 4
[2,6,5,3,4,1] => 5
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 3
[3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => 3
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 5
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 5
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 4
[3,1,5,4,2,6] => 1
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 4
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 1
[3,1,6,5,2,4] => 4
[3,1,6,5,4,2] => 5
[3,2,1,4,5,6] => 0
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 0
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 0
[3,2,4,5,6,1] => 0
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 0
[3,2,5,1,4,6] => 1
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 0
[3,2,5,4,6,1] => 0
[3,2,5,6,1,4] => 1
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 2
[3,2,6,1,5,4] => 1
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 0
[3,2,6,5,1,4] => 2
[3,2,6,5,4,1] => 3
[3,4,1,2,5,6] => 0
[3,4,1,2,6,5] => 4
[3,4,1,5,2,6] => 1
[3,4,1,5,6,2] => 2
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 1
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 5
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 0
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 2
[3,4,5,6,1,2] => 0
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 2
[3,4,6,1,5,2] => 0
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 1
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 2
[3,5,1,2,4,6] => 1
[3,5,1,2,6,4] => 3
[3,5,1,4,2,6] => 0
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 3
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 1
[3,5,2,4,6,1] => 2
[3,5,2,6,1,4] => 3
[3,5,2,6,4,1] => 4
[3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 3
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 2
[3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 2
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 0
[3,5,6,4,2,1] => 1
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 0
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 5
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 4
[3,6,4,2,5,1] => 2
[3,6,4,5,1,2] => 2
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 2
[3,6,5,1,4,2] => 3
[3,6,5,2,1,4] => 3
[3,6,5,2,4,1] => 4
[3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 0
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 3
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 0
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 1
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 1
[4,1,5,2,3,6] => 1
[4,1,5,2,6,3] => 3
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 2
[4,1,5,6,3,2] => 3
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 3
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 0
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 1
[4,2,1,5,6,3] => 2
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 0
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 0
[4,2,3,5,6,1] => 0
[4,2,3,6,1,5] => 1
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 0
[4,2,5,1,6,3] => 1
[4,2,5,3,1,6] => 1
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 0
[4,2,5,6,3,1] => 1
[4,2,6,1,3,5] => 1
[4,2,6,1,5,3] => 0
[4,2,6,3,1,5] => 2
[4,2,6,3,5,1] => 1
[4,2,6,5,1,3] => 1
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 5
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 4
[4,3,1,6,5,2] => 2
[4,3,2,1,5,6] => 2
[4,3,2,1,6,5] => 6
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 4
[4,3,2,6,1,5] => 5
[4,3,2,6,5,1] => 3
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => 2
[4,3,5,2,6,1] => 3
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 2
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 1
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 2
[4,3,6,5,2,1] => 3
[4,5,1,2,3,6] => 0
[4,5,1,2,6,3] => 2
[4,5,1,3,2,6] => 1
[4,5,1,3,6,2] => 3
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 2
[4,5,2,1,3,6] => 1
[4,5,2,1,6,3] => 3
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 4
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 3
[4,5,3,1,2,6] => 0
[4,5,3,1,6,2] => 1
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 0
[4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => 0
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 2
[4,5,6,3,1,2] => 2
[4,5,6,3,2,1] => 3
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 0
[4,6,1,3,2,5] => 2
[4,6,1,3,5,2] => 1
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 3
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 1
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 3
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 1
[4,6,3,1,5,2] => 0
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 1
[4,6,3,5,1,2] => 1
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 3
[4,6,5,3,2,1] => 4
[5,1,2,3,4,6] => 0
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 0
[5,1,2,4,6,3] => 2
[5,1,2,6,3,4] => 2
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 0
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 0
[5,1,3,4,6,2] => 1
[5,1,3,6,2,4] => 1
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 2
[5,1,4,2,6,3] => 4
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 5
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 4
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 2
[5,1,6,3,2,4] => 2
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 1
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 0
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 0
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 1
[5,2,1,6,4,3] => 2
[5,2,3,1,4,6] => 0
[5,2,3,1,6,4] => 1
[5,2,3,4,1,6] => 0
[5,2,3,4,6,1] => 0
[5,2,3,6,1,4] => 0
[5,2,3,6,4,1] => 1
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 1
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 0
[5,2,6,1,4,3] => 1
[5,2,6,3,1,4] => 1
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 1
[5,3,1,2,4,6] => 2
[5,3,1,2,6,4] => 4
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 2
[5,3,1,6,2,4] => 3
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 5
[5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => 3
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 5
[5,3,4,1,2,6] => 2
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 3
[5,3,4,2,6,1] => 4
[5,3,4,6,1,2] => 2
[5,3,4,6,2,1] => 3
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 3
[5,3,6,2,1,4] => 3
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 1
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 2
[5,4,1,3,6,2] => 4
[5,4,1,6,2,3] => 2
[5,4,1,6,3,2] => 3
[5,4,2,1,3,6] => 2
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 5
[5,4,2,6,1,3] => 3
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 2
[5,4,3,2,6,1] => 3
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 2
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 2
[5,4,6,2,3,1] => 3
[5,4,6,3,1,2] => 3
[5,4,6,3,2,1] => 4
[5,6,1,2,3,4] => 0
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 2
[5,6,1,4,2,3] => 0
[5,6,1,4,3,2] => 1
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 2
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 1
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 0
[5,6,3,1,4,2] => 1
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 0
[5,6,3,4,2,1] => 1
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 3
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 4
[5,6,4,3,2,1] => 5
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 0
[6,1,2,4,3,5] => 0
[6,1,2,4,5,3] => 0
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 4
[6,1,3,2,4,5] => 0
[6,1,3,2,5,4] => 0
[6,1,3,4,2,5] => 0
[6,1,3,4,5,2] => 0
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 3
[6,1,4,2,3,5] => 3
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 4
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 5
[6,1,5,2,3,4] => 2
[6,1,5,2,4,3] => 3
[6,1,5,3,2,4] => 3
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 2
[6,1,5,4,3,2] => 3
[6,2,1,3,4,5] => 0
[6,2,1,3,5,4] => 0
[6,2,1,4,3,5] => 0
[6,2,1,4,5,3] => 0
[6,2,1,5,3,4] => 2
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 0
[6,2,3,1,5,4] => 0
[6,2,3,4,1,5] => 0
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 2
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 1
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 2
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 4
[6,3,1,5,4,2] => 5
[6,3,2,1,4,5] => 4
[6,3,2,1,5,4] => 3
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 2
[6,3,2,5,1,4] => 5
[6,3,2,5,4,1] => 6
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 5
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 3
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 3
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 5
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 2
[6,4,1,2,5,3] => 1
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 2
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 3
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 4
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 4
[6,4,2,5,3,1] => 5
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 3
[6,4,3,2,5,1] => 2
[6,4,3,5,1,2] => 2
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 2
[6,4,5,1,3,2] => 3
[6,4,5,2,1,3] => 3
[6,4,5,2,3,1] => 4
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 5
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 2
[6,5,1,3,2,4] => 2
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 2
[6,5,2,1,3,4] => 2
[6,5,2,1,4,3] => 3
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 1
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 2
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => 4
[6,5,4,2,1,3] => 4
[6,5,4,2,3,1] => 5
[6,5,4,3,1,2] => 5
[6,5,4,3,2,1] => 6
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 0
[1,2,3,4,6,5,7] => 0
[1,2,3,4,6,7,5] => 0
[1,2,3,4,7,5,6] => 0
[1,2,3,4,7,6,5] => 0
[1,2,3,5,4,6,7] => 0
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 0
[1,2,3,5,6,7,4] => 0
[1,2,3,5,7,4,6] => 1
[1,2,3,5,7,6,4] => 0
[1,2,3,6,4,5,7] => 0
[1,2,3,6,4,7,5] => 1
[1,2,3,6,5,4,7] => 0
[1,2,3,6,5,7,4] => 0
[1,2,3,6,7,4,5] => 0
[1,2,3,6,7,5,4] => 1
[1,2,3,7,4,5,6] => 0
[1,2,3,7,4,6,5] => 0
[1,2,3,7,5,4,6] => 0
[1,2,3,7,5,6,4] => 0
[1,2,3,7,6,4,5] => 1
[1,2,3,7,6,5,4] => 2
[1,2,4,3,5,6,7] => 0
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 3
[1,2,4,3,7,5,6] => 3
[1,2,4,3,7,6,5] => 2
[1,2,4,5,3,6,7] => 0
[1,2,4,5,3,7,6] => 3
[1,2,4,5,6,3,7] => 0
[1,2,4,5,6,7,3] => 0
[1,2,4,5,7,3,6] => 2
[1,2,4,5,7,6,3] => 0
[1,2,4,6,3,5,7] => 1
[1,2,4,6,3,7,5] => 2
[1,2,4,6,5,3,7] => 0
[1,2,4,6,5,7,3] => 0
[1,2,4,6,7,3,5] => 1
[1,2,4,6,7,5,3] => 2
[1,2,4,7,3,5,6] => 2
[1,2,4,7,3,6,5] => 1
[1,2,4,7,5,3,6] => 1
[1,2,4,7,5,6,3] => 0
[1,2,4,7,6,3,5] => 2
[1,2,4,7,6,5,3] => 3
[1,2,5,3,4,6,7] => 0
[1,2,5,3,4,7,6] => 3
[1,2,5,3,6,4,7] => 1
[1,2,5,3,6,7,4] => 2
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 1
[1,2,5,4,3,6,7] => 0
[1,2,5,4,3,7,6] => 2
[1,2,5,4,6,3,7] => 0
[1,2,5,4,6,7,3] => 0
[1,2,5,4,7,3,6] => 1
[1,2,5,4,7,6,3] => 0
[1,2,5,6,3,4,7] => 0
[1,2,5,6,3,7,4] => 1
[1,2,5,6,4,3,7] => 1
[1,2,5,6,4,7,3] => 2
[1,2,5,6,7,3,4] => 0
[1,2,5,6,7,4,3] => 1
[1,2,5,7,3,4,6] => 1
[1,2,5,7,3,6,4] => 0
[1,2,5,7,4,3,6] => 2
[1,2,5,7,4,6,3] => 1
[1,2,5,7,6,3,4] => 1
[1,2,5,7,6,4,3] => 2
[1,2,6,3,4,5,7] => 0
[1,2,6,3,4,7,5] => 2
[1,2,6,3,5,4,7] => 0
[1,2,6,3,5,7,4] => 1
[1,2,6,3,7,4,5] => 1
[1,2,6,3,7,5,4] => 2
[1,2,6,4,3,5,7] => 0
[1,2,6,4,3,7,5] => 1
[1,2,6,4,5,3,7] => 0
[1,2,6,4,5,7,3] => 0
[1,2,6,4,7,3,5] => 0
[1,2,6,4,7,5,3] => 1
[1,2,6,5,3,4,7] => 1
[1,2,6,5,3,7,4] => 2
[1,2,6,5,4,3,7] => 2
[1,2,6,5,4,7,3] => 3
[1,2,6,5,7,3,4] => 1
[1,2,6,5,7,4,3] => 2
[1,2,6,7,3,4,5] => 0
[1,2,6,7,3,5,4] => 1
[1,2,6,7,4,3,5] => 1
[1,2,6,7,4,5,3] => 2
[1,2,6,7,5,3,4] => 0
[1,2,6,7,5,4,3] => 1
[1,2,7,3,4,5,6] => 0
[1,2,7,3,4,6,5] => 0
[1,2,7,3,5,4,6] => 0
[1,2,7,3,5,6,4] => 0
[1,2,7,3,6,4,5] => 2
[1,2,7,3,6,5,4] => 3
[1,2,7,4,3,5,6] => 0
[1,2,7,4,3,6,5] => 0
[1,2,7,4,5,3,6] => 0
[1,2,7,4,5,6,3] => 0
[1,2,7,4,6,3,5] => 1
[1,2,7,4,6,5,3] => 2
[1,2,7,5,3,4,6] => 2
[1,2,7,5,3,6,4] => 1
[1,2,7,5,4,3,6] => 3
[1,2,7,5,4,6,3] => 2
[1,2,7,5,6,3,4] => 2
[1,2,7,5,6,4,3] => 3
[1,2,7,6,3,4,5] => 1
[1,2,7,6,3,5,4] => 2
[1,2,7,6,4,3,5] => 2
[1,2,7,6,4,5,3] => 3
[1,2,7,6,5,3,4] => 1
[1,2,7,6,5,4,3] => 2
[1,3,2,4,5,6,7] => 0
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 3
[1,3,2,4,7,5,6] => 3
[1,3,2,4,7,6,5] => 2
[1,3,2,5,4,6,7] => 2
[1,3,2,5,4,7,6] => 6
[1,3,2,5,6,4,7] => 3
[1,3,2,5,6,7,4] => 4
[1,3,2,5,7,4,6] => 5
[1,3,2,5,7,6,4] => 3
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 5
[1,3,2,6,5,4,7] => 2
[1,3,2,6,5,7,4] => 3
[1,3,2,6,7,4,5] => 4
[1,3,2,6,7,5,4] => 5
[1,3,2,7,4,5,6] => 4
[1,3,2,7,4,6,5] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 2
[1,3,2,7,6,4,5] => 5
[1,3,2,7,6,5,4] => 6
[1,3,4,2,5,6,7] => 0
[1,3,4,2,5,7,6] => 3
[1,3,4,2,6,5,7] => 3
[1,3,4,2,6,7,5] => 4
[1,3,4,2,7,5,6] => 5
[1,3,4,2,7,6,5] => 3
[1,3,4,5,2,6,7] => 0
[1,3,4,5,2,7,6] => 4
[1,3,4,5,6,2,7] => 0
[1,3,4,5,6,7,2] => 0
[1,3,4,5,7,2,6] => 3
[1,3,4,5,7,6,2] => 0
[1,3,4,6,2,5,7] => 2
[1,3,4,6,2,7,5] => 3
[1,3,4,6,5,2,7] => 0
[1,3,4,6,5,7,2] => 0
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 3
[1,3,4,7,2,5,6] => 4
[1,3,4,7,2,6,5] => 2
[1,3,4,7,5,2,6] => 2
[1,3,4,7,5,6,2] => 0
[1,3,4,7,6,2,5] => 3
[1,3,4,7,6,5,2] => 4
[1,3,5,2,4,6,7] => 1
[1,3,5,2,4,7,6] => 5
[1,3,5,2,6,4,7] => 2
[1,3,5,2,6,7,4] => 3
[1,3,5,2,7,4,6] => 4
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 0
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 0
[1,3,5,4,6,7,2] => 0
[1,3,5,4,7,2,6] => 2
[1,3,5,4,7,6,2] => 0
[1,3,5,6,2,4,7] => 1
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 2
[1,3,5,6,4,7,2] => 3
[1,3,5,6,7,2,4] => 1
[1,3,5,6,7,4,2] => 2
[1,3,5,7,2,4,6] => 3
[1,3,5,7,2,6,4] => 1
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 2
[1,3,5,7,6,2,4] => 2
[1,3,5,7,6,4,2] => 3
[1,3,6,2,4,5,7] => 2
[1,3,6,2,4,7,5] => 4
[1,3,6,2,5,4,7] => 1
[1,3,6,2,5,7,4] => 2
[1,3,6,2,7,4,5] => 3
[1,3,6,2,7,5,4] => 4
[1,3,6,4,2,5,7] => 1
[1,3,6,4,2,7,5] => 2
[1,3,6,4,5,2,7] => 0
[1,3,6,4,5,7,2] => 0
[1,3,6,4,7,2,5] => 1
[1,3,6,4,7,5,2] => 2
[1,3,6,5,2,4,7] => 2
[1,3,6,5,2,7,4] => 3
[1,3,6,5,4,2,7] => 3
[1,3,6,5,4,7,2] => 4
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 3
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 3
[1,3,6,7,4,2,5] => 3
[1,3,6,7,4,5,2] => 4
[1,3,6,7,5,2,4] => 1
[1,3,6,7,5,4,2] => 2
[1,3,7,2,4,5,6] => 3
[1,3,7,2,4,6,5] => 2
[1,3,7,2,5,4,6] => 2
[1,3,7,2,5,6,4] => 1
[1,3,7,2,6,4,5] => 4
[1,3,7,2,6,5,4] => 5
[1,3,7,4,2,5,6] => 2
[1,3,7,4,2,6,5] => 1
[1,3,7,4,5,2,6] => 1
[1,3,7,4,5,6,2] => 0
[1,3,7,4,6,2,5] => 2
[1,3,7,4,6,5,2] => 3
[1,3,7,5,2,4,6] => 4
[1,3,7,5,2,6,4] => 2
[1,3,7,5,4,2,6] => 5
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 4
[1,3,7,6,2,4,5] => 3
[1,3,7,6,2,5,4] => 4
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 5
[1,3,7,6,5,2,4] => 2
[1,3,7,6,5,4,2] => 3
[1,4,2,3,5,6,7] => 0
[1,4,2,3,5,7,6] => 3
[1,4,2,3,6,5,7] => 3
[1,4,2,3,6,7,5] => 5
[1,4,2,3,7,5,6] => 4
[1,4,2,3,7,6,5] => 3
[1,4,2,5,3,6,7] => 1
[1,4,2,5,3,7,6] => 5
[1,4,2,5,6,3,7] => 2
[1,4,2,5,6,7,3] => 3
[1,4,2,5,7,3,6] => 4
[1,4,2,5,7,6,3] => 2
[1,4,2,6,3,5,7] => 2
[1,4,2,6,3,7,5] => 4
[1,4,2,6,5,3,7] => 1
[1,4,2,6,5,7,3] => 2
[1,4,2,6,7,3,5] => 3
[1,4,2,6,7,5,3] => 4
[1,4,2,7,3,5,6] => 3
[1,4,2,7,3,6,5] => 2
[1,4,2,7,5,3,6] => 2
[1,4,2,7,5,6,3] => 1
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 5
[1,4,3,2,5,6,7] => 0
[1,4,3,2,5,7,6] => 2
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 3
[1,4,3,2,7,5,6] => 3
[1,4,3,2,7,6,5] => 2
[1,4,3,5,2,6,7] => 0
[1,4,3,5,2,7,6] => 3
[1,4,3,5,6,2,7] => 0
[1,4,3,5,6,7,2] => 0
[1,4,3,5,7,2,6] => 2
[1,4,3,5,7,6,2] => 0
[1,4,3,6,2,5,7] => 1
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 0
[1,4,3,6,5,7,2] => 0
[1,4,3,6,7,2,5] => 1
[1,4,3,6,7,5,2] => 2
[1,4,3,7,2,5,6] => 2
[1,4,3,7,2,6,5] => 1
[1,4,3,7,5,2,6] => 1
[1,4,3,7,5,6,2] => 0
[1,4,3,7,6,2,5] => 2
[1,4,3,7,6,5,2] => 3
[1,4,5,2,3,6,7] => 0
[1,4,5,2,3,7,6] => 4
[1,4,5,2,6,3,7] => 1
[1,4,5,2,6,7,3] => 2
[1,4,5,2,7,3,6] => 3
[1,4,5,2,7,6,3] => 1
[1,4,5,3,2,6,7] => 1
[1,4,5,3,2,7,6] => 5
[1,4,5,3,6,2,7] => 2
[1,4,5,3,6,7,2] => 3
[1,4,5,3,7,2,6] => 4
[1,4,5,3,7,6,2] => 2
[1,4,5,6,2,3,7] => 0
[1,4,5,6,2,7,3] => 1
[1,4,5,6,3,2,7] => 1
[1,4,5,6,3,7,2] => 2
[1,4,5,6,7,2,3] => 0
[1,4,5,6,7,3,2] => 1
[1,4,5,7,2,3,6] => 2
[1,4,5,7,2,6,3] => 0
[1,4,5,7,3,2,6] => 3
[1,4,5,7,3,6,2] => 1
[1,4,5,7,6,2,3] => 1
[1,4,5,7,6,3,2] => 2
[1,4,6,2,3,5,7] => 1
[1,4,6,2,3,7,5] => 3
[1,4,6,2,5,3,7] => 0
[1,4,6,2,5,7,3] => 1
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 3
[1,4,6,3,2,5,7] => 2
[1,4,6,3,2,7,5] => 4
[1,4,6,3,5,2,7] => 1
[1,4,6,3,5,7,2] => 2
[1,4,6,3,7,2,5] => 3
[1,4,6,3,7,5,2] => 4
[1,4,6,5,2,3,7] => 1
[1,4,6,5,2,7,3] => 2
[1,4,6,5,3,2,7] => 2
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Description
The number of cyclic alignments of a permutation.
The pair $(i,j)$ is a cyclic alignment of a permutation $\pi$ if $i, j, \pi(j), \pi(i)$ are cyclically ordered and all distinct, see Section 5 of [1]
References
[1] Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
Code
def in_cyclic_order(i, j, k, l):
    return (i < j < k < l or
            j < k < l < i or
            k < l < i < j or
            l < i < j < k)

def statistic(pi):
    """
    sage: statistic(Permutation([7,6,2,1,9,5,4,3,8]))
    9

    sage: statistic(Permutation([5,4,1,6,3,2]))
    3

    sage: statistic(Permutation([4,5,6,7,8,1,2,3]))
    0
    """
    n = len(pi)
    a = 0
    for i, pi_i in enumerate(pi, 1):
        for j, pi_j in enumerate(pi, 1):
            if in_cyclic_order(i, j, pi_j, pi_i):
                a += 1
    return a
Created
May 09, 2020 at 22:00 by Martin Rubey
Updated
May 09, 2020 at 22:00 by Martin Rubey