edit this statistic or download as text // json
Identifier
Values
[1,2] => 2
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 4
[1,2,4,3] => 1
[1,3,2,4] => 2
[1,3,4,2] => 1
[1,4,2,3] => 2
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 0
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 2
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 5
[1,2,3,5,4] => 1
[1,2,4,3,5] => 2
[1,2,4,5,3] => 1
[1,2,5,3,4] => 2
[1,2,5,4,3] => 0
[1,3,2,4,5] => 3
[1,3,2,5,4] => 1
[1,3,4,2,5] => 2
[1,3,4,5,2] => 1
[1,3,5,2,4] => 2
[1,3,5,4,2] => 0
[1,4,2,3,5] => 3
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 2
[1,4,5,3,2] => 0
[1,5,2,3,4] => 3
[1,5,2,4,3] => 1
[1,5,3,2,4] => 1
[1,5,3,4,2] => 1
[1,5,4,2,3] => 0
[1,5,4,3,2] => 0
[2,1,3,4,5] => 3
[2,1,3,5,4] => 1
[2,1,4,3,5] => 2
[2,1,4,5,3] => 1
[2,1,5,3,4] => 2
[2,1,5,4,3] => 0
[2,3,1,4,5] => 3
[2,3,1,5,4] => 1
[2,3,4,1,5] => 2
[2,3,4,5,1] => 1
[2,3,5,1,4] => 2
[2,3,5,4,1] => 0
[2,4,1,3,5] => 3
[2,4,1,5,3] => 1
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 2
[2,4,5,3,1] => 0
[2,5,1,3,4] => 3
[2,5,1,4,3] => 1
[2,5,3,1,4] => 1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,4,5] => 2
[3,1,2,5,4] => 1
[3,1,4,2,5] => 2
[3,1,4,5,2] => 1
[3,1,5,2,4] => 2
[3,1,5,4,2] => 0
[3,2,1,4,5] => 2
[3,2,1,5,4] => 1
[3,2,4,1,5] => 2
[3,2,4,5,1] => 1
[3,2,5,1,4] => 2
[3,2,5,4,1] => 0
[3,4,1,2,5] => 3
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 2
[3,4,5,2,1] => 0
[3,5,1,2,4] => 3
[3,5,1,4,2] => 1
[3,5,2,1,4] => 1
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 1
[3,5,4,1,2] => 0
[3,5,4,2,1] => 0
[4,1,2,3,5] => 1
[4,1,2,5,3] => 1
[4,1,3,2,5] => 1
[4,1,3,5,2] => 1
[4,1,5,2,3] => 2
[4,1,5,3,2] => 0
[4,2,1,3,5] => 1
[4,2,1,5,3] => 1
[4,2,3,1,5] => 1
[4,2,3,5,1] => 1
[4,2,5,1,3] => 2
[4,2,5,3,1] => 0
[4,3,1,2,5] => 1
[4,3,1,5,2] => 1
[4,3,2,1,5] => 1
[4,3,2,5,1] => 1
[4,3,5,1,2] => 2
[4,3,5,2,1] => 0
[4,5,1,2,3] => 3
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 0
[4,5,3,2,1] => 0
[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] => 0
[5,1,4,3,2] => 0
[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] => 0
[5,2,4,3,1] => 0
[5,3,1,2,4] => 0
[5,3,1,4,2] => 0
[5,3,2,1,4] => 0
[5,3,2,4,1] => 0
[5,3,4,1,2] => 0
[5,3,4,2,1] => 0
[5,4,1,2,3] => 0
[5,4,1,3,2] => 0
[5,4,2,1,3] => 0
[5,4,2,3,1] => 0
[5,4,3,1,2] => 0
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => 2
[1,2,3,6,5,4] => 0
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => 2
[1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 0
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 1
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 0
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 1
[1,2,6,4,5,3] => 1
[1,2,6,5,3,4] => 0
[1,2,6,5,4,3] => 0
[1,3,2,4,5,6] => 4
[1,3,2,4,6,5] => 1
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 0
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 1
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 0
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 1
[1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 0
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 1
[1,3,6,4,2,5] => 1
[1,3,6,4,5,2] => 1
[1,3,6,5,2,4] => 0
[1,3,6,5,4,2] => 0
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => 2
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 0
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 1
[1,4,3,5,2,6] => 2
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 0
[1,4,5,2,3,6] => 3
[1,4,5,2,6,3] => 1
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 1
[1,4,5,6,2,3] => 2
[1,4,5,6,3,2] => 0
[1,4,6,2,3,5] => 3
[1,4,6,2,5,3] => 1
[1,4,6,3,2,5] => 1
[1,4,6,3,5,2] => 1
[1,4,6,5,2,3] => 0
[1,4,6,5,3,2] => 0
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 2
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 0
[1,5,3,2,4,6] => 2
[1,5,3,2,6,4] => 1
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => 2
[1,5,3,6,4,2] => 0
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 1
[1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => 2
[1,5,4,6,3,2] => 0
[1,5,6,2,3,4] => 3
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => 1
[1,5,6,4,2,3] => 0
[1,5,6,4,3,2] => 0
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 2
[1,6,2,4,5,3] => 1
[1,6,2,5,3,4] => 2
[1,6,2,5,4,3] => 0
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 1
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => 2
[1,6,3,5,4,2] => 0
[1,6,4,2,3,5] => 1
[1,6,4,2,5,3] => 1
[1,6,4,3,2,5] => 1
[1,6,4,3,5,2] => 1
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 0
[1,6,5,2,3,4] => 0
[1,6,5,2,4,3] => 0
[1,6,5,3,2,4] => 0
[1,6,5,3,4,2] => 0
[1,6,5,4,2,3] => 0
[1,6,5,4,3,2] => 0
[2,1,3,4,5,6] => 4
[2,1,3,4,6,5] => 1
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 1
[2,1,3,6,4,5] => 2
[2,1,3,6,5,4] => 0
[2,1,4,3,5,6] => 3
[2,1,4,3,6,5] => 1
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 1
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 0
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 1
[2,1,5,4,3,6] => 1
[2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 0
[2,1,6,3,4,5] => 3
[2,1,6,3,5,4] => 1
[2,1,6,4,3,5] => 1
[2,1,6,4,5,3] => 1
[2,1,6,5,3,4] => 0
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 1
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 1
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 0
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 1
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 2
[2,3,4,6,5,1] => 0
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 0
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 1
[2,3,6,4,1,5] => 1
[2,3,6,4,5,1] => 1
[2,3,6,5,1,4] => 0
[2,3,6,5,4,1] => 0
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 0
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => 2
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 0
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 1
[2,4,5,3,1,6] => 1
[2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 0
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 1
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 1
[2,4,6,5,1,3] => 0
[2,4,6,5,3,1] => 0
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 1
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 0
[2,5,3,1,4,6] => 2
[2,5,3,1,6,4] => 1
[2,5,3,4,1,6] => 2
[2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => 0
[2,5,4,1,3,6] => 1
[2,5,4,1,6,3] => 1
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => 0
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 1
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 1
[2,5,6,4,1,3] => 0
[2,5,6,4,3,1] => 0
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 1
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 0
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 1
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 2
[2,6,3,5,4,1] => 0
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 1
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 1
[2,6,4,5,1,3] => 2
[2,6,4,5,3,1] => 0
[2,6,5,1,3,4] => 0
[2,6,5,1,4,3] => 0
[2,6,5,3,1,4] => 0
[2,6,5,3,4,1] => 0
[2,6,5,4,1,3] => 0
[2,6,5,4,3,1] => 0
[3,1,2,4,5,6] => 3
[3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => 2
[3,1,2,5,6,4] => 1
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 0
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 1
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 2
[3,1,4,6,5,2] => 0
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 1
[3,1,5,4,6,2] => 1
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 0
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 1
[3,1,6,4,2,5] => 1
[3,1,6,4,5,2] => 1
[3,1,6,5,2,4] => 0
[3,1,6,5,4,2] => 0
[3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => 2
[3,2,1,6,5,4] => 0
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 1
[3,2,4,5,1,6] => 2
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 0
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 1
[3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => 2
[3,2,5,6,4,1] => 0
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 1
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 1
[3,2,6,5,1,4] => 0
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 1
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 0
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 0
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => 0
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 1
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 1
[3,4,6,5,1,2] => 0
[3,4,6,5,2,1] => 0
[3,5,1,2,4,6] => 4
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 2
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 0
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 1
[3,5,2,4,1,6] => 2
[3,5,2,4,6,1] => 1
[3,5,2,6,1,4] => 2
[3,5,2,6,4,1] => 0
[3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 2
[3,5,4,6,2,1] => 0
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 1
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 1
[3,5,6,4,1,2] => 0
[3,5,6,4,2,1] => 0
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 1
[3,6,1,5,2,4] => 2
[3,6,1,5,4,2] => 0
[3,6,2,1,4,5] => 2
[3,6,2,1,5,4] => 1
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 2
[3,6,2,5,4,1] => 0
[3,6,4,1,2,5] => 1
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 1
[3,6,4,2,5,1] => 1
[3,6,4,5,1,2] => 2
[3,6,4,5,2,1] => 0
[3,6,5,1,2,4] => 0
[3,6,5,1,4,2] => 0
[3,6,5,2,1,4] => 0
[3,6,5,2,4,1] => 0
[3,6,5,4,1,2] => 0
[3,6,5,4,2,1] => 0
[4,1,2,3,5,6] => 2
[4,1,2,3,6,5] => 1
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 1
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 0
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 1
[4,1,3,5,2,6] => 2
[4,1,3,5,6,2] => 1
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 0
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 1
[4,1,5,3,6,2] => 1
[4,1,5,6,2,3] => 2
[4,1,5,6,3,2] => 0
[4,1,6,2,3,5] => 3
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 1
[4,1,6,3,5,2] => 1
[4,1,6,5,2,3] => 0
[4,1,6,5,3,2] => 0
[4,2,1,3,5,6] => 2
[4,2,1,3,6,5] => 1
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 1
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 0
[4,2,3,1,5,6] => 2
[4,2,3,1,6,5] => 1
[4,2,3,5,1,6] => 2
[4,2,3,5,6,1] => 1
[4,2,3,6,1,5] => 2
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 1
[4,2,5,3,1,6] => 1
[4,2,5,3,6,1] => 1
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 0
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 1
[4,2,6,3,1,5] => 1
[4,2,6,3,5,1] => 1
[4,2,6,5,1,3] => 0
[4,2,6,5,3,1] => 0
[4,3,1,2,5,6] => 2
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 0
[4,3,2,1,5,6] => 2
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 2
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 2
[4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 2
[4,3,5,6,2,1] => 0
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 1
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 1
[4,3,6,5,1,2] => 0
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 4
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 1
[4,5,1,6,2,3] => 2
[4,5,1,6,3,2] => 0
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 1
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 1
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 0
[4,5,3,1,2,6] => 1
[4,5,3,1,6,2] => 1
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 0
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 0
[4,5,6,3,2,1] => 0
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 1
[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] => 0
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 1
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 1
[4,6,2,5,1,3] => 2
[4,6,2,5,3,1] => 0
[4,6,3,1,2,5] => 1
[4,6,3,1,5,2] => 1
[4,6,3,2,1,5] => 1
[4,6,3,2,5,1] => 1
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 0
[4,6,5,1,2,3] => 0
[4,6,5,1,3,2] => 0
[4,6,5,2,1,3] => 0
[4,6,5,2,3,1] => 0
[4,6,5,3,1,2] => 0
[4,6,5,3,2,1] => 0
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 1
[5,1,2,4,3,6] => 1
[5,1,2,4,6,3] => 1
[5,1,2,6,3,4] => 2
[5,1,2,6,4,3] => 0
[5,1,3,2,4,6] => 1
[5,1,3,2,6,4] => 1
[5,1,3,4,2,6] => 1
[5,1,3,4,6,2] => 1
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 0
[5,1,4,2,3,6] => 1
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 1
[5,1,4,3,6,2] => 1
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 0
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 1
[5,1,6,4,2,3] => 0
[5,1,6,4,3,2] => 0
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 1
[5,2,1,4,3,6] => 1
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 2
[5,2,1,6,4,3] => 0
[5,2,3,1,4,6] => 1
[5,2,3,1,6,4] => 1
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => 0
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 1
[5,2,4,3,1,6] => 1
[5,2,4,3,6,1] => 1
[5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => 0
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 1
[5,2,6,3,1,4] => 1
[5,2,6,3,4,1] => 1
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 0
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 1
[5,3,1,6,2,4] => 2
[5,3,1,6,4,2] => 0
[5,3,2,1,4,6] => 1
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 0
[5,3,4,1,2,6] => 1
[5,3,4,1,6,2] => 1
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 1
[5,3,4,6,1,2] => 2
[5,3,4,6,2,1] => 0
[5,3,6,1,2,4] => 3
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 1
[5,3,6,2,4,1] => 1
[5,3,6,4,1,2] => 0
[5,3,6,4,2,1] => 0
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 1
[5,4,1,6,2,3] => 2
[5,4,1,6,3,2] => 0
[5,4,2,1,3,6] => 1
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 0
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => 0
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 0
[5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 1
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 0
[5,6,2,1,3,4] => 2
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 2
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 0
[5,6,3,1,2,4] => 1
[5,6,3,1,4,2] => 1
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 1
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 0
[5,6,4,1,2,3] => 0
[5,6,4,1,3,2] => 0
[5,6,4,2,1,3] => 0
[5,6,4,2,3,1] => 0
[5,6,4,3,1,2] => 0
[5,6,4,3,2,1] => 0
[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] => 0
[6,1,2,5,4,3] => 0
[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] => 0
[6,1,3,5,4,2] => 0
[6,1,4,2,3,5] => 0
[6,1,4,2,5,3] => 0
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 0
[6,1,4,5,2,3] => 0
[6,1,4,5,3,2] => 0
[6,1,5,2,3,4] => 0
[6,1,5,2,4,3] => 0
[6,1,5,3,2,4] => 0
[6,1,5,3,4,2] => 0
[6,1,5,4,2,3] => 0
[6,1,5,4,3,2] => 0
[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] => 0
[6,2,1,5,4,3] => 0
[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] => 0
[6,2,3,5,4,1] => 0
[6,2,4,1,3,5] => 0
[6,2,4,1,5,3] => 0
[6,2,4,3,1,5] => 0
[6,2,4,3,5,1] => 0
[6,2,4,5,1,3] => 0
[6,2,4,5,3,1] => 0
[6,2,5,1,3,4] => 0
[6,2,5,1,4,3] => 0
[6,2,5,3,1,4] => 0
[6,2,5,3,4,1] => 0
[6,2,5,4,1,3] => 0
[6,2,5,4,3,1] => 0
[6,3,1,2,4,5] => 0
[6,3,1,2,5,4] => 0
[6,3,1,4,2,5] => 0
[6,3,1,4,5,2] => 0
[6,3,1,5,2,4] => 0
[6,3,1,5,4,2] => 0
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 0
[6,3,2,4,5,1] => 0
[6,3,2,5,1,4] => 0
[6,3,2,5,4,1] => 0
[6,3,4,1,2,5] => 0
[6,3,4,1,5,2] => 0
[6,3,4,2,1,5] => 0
[6,3,4,2,5,1] => 0
[6,3,4,5,1,2] => 0
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 0
[6,3,5,1,4,2] => 0
[6,3,5,2,1,4] => 0
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 0
[6,3,5,4,2,1] => 0
[6,4,1,2,3,5] => 0
[6,4,1,2,5,3] => 0
[6,4,1,3,2,5] => 0
[6,4,1,3,5,2] => 0
[6,4,1,5,2,3] => 0
[6,4,1,5,3,2] => 0
[6,4,2,1,3,5] => 0
[6,4,2,1,5,3] => 0
[6,4,2,3,1,5] => 0
[6,4,2,3,5,1] => 0
[6,4,2,5,1,3] => 0
[6,4,2,5,3,1] => 0
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 0
[6,4,3,2,1,5] => 0
[6,4,3,2,5,1] => 0
[6,4,3,5,1,2] => 0
[6,4,3,5,2,1] => 0
[6,4,5,1,2,3] => 0
[6,4,5,1,3,2] => 0
[6,4,5,2,1,3] => 0
[6,4,5,2,3,1] => 0
[6,4,5,3,1,2] => 0
[6,4,5,3,2,1] => 0
[6,5,1,2,3,4] => 0
[6,5,1,2,4,3] => 0
[6,5,1,3,2,4] => 0
[6,5,1,3,4,2] => 0
[6,5,1,4,2,3] => 0
[6,5,1,4,3,2] => 0
[6,5,2,1,3,4] => 0
[6,5,2,1,4,3] => 0
[6,5,2,3,1,4] => 0
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 0
[6,5,2,4,3,1] => 0
[6,5,3,1,2,4] => 0
[6,5,3,1,4,2] => 0
[6,5,3,2,1,4] => 0
[6,5,3,2,4,1] => 0
[6,5,3,4,1,2] => 0
[6,5,3,4,2,1] => 0
[6,5,4,1,2,3] => 0
[6,5,4,1,3,2] => 0
[6,5,4,2,1,3] => 0
[6,5,4,2,3,1] => 0
[6,5,4,3,1,2] => 0
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 2
[1,2,3,4,6,7,5] => 1
[1,2,3,4,7,5,6] => 2
[1,2,3,4,7,6,5] => 0
[1,2,3,5,4,6,7] => 3
[1,2,3,5,4,7,6] => 1
[1,2,3,5,6,4,7] => 2
[1,2,3,5,6,7,4] => 1
[1,2,3,5,7,4,6] => 2
[1,2,3,5,7,6,4] => 0
[1,2,3,6,4,5,7] => 3
[1,2,3,6,4,7,5] => 1
[1,2,3,6,5,4,7] => 1
[1,2,3,6,5,7,4] => 1
[1,2,3,6,7,4,5] => 2
[1,2,3,6,7,5,4] => 0
[1,2,3,7,4,5,6] => 3
[1,2,3,7,4,6,5] => 1
[1,2,3,7,5,4,6] => 1
[1,2,3,7,5,6,4] => 1
[1,2,3,7,6,4,5] => 0
[1,2,3,7,6,5,4] => 0
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 1
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 1
[1,2,4,3,7,5,6] => 2
[1,2,4,3,7,6,5] => 0
[1,2,4,5,3,6,7] => 3
[1,2,4,5,3,7,6] => 1
[1,2,4,5,6,3,7] => 2
[1,2,4,5,6,7,3] => 1
[1,2,4,5,7,3,6] => 2
[1,2,4,5,7,6,3] => 0
[1,2,4,6,3,5,7] => 3
[1,2,4,6,3,7,5] => 1
[1,2,4,6,5,3,7] => 1
[1,2,4,6,5,7,3] => 1
[1,2,4,6,7,3,5] => 2
[1,2,4,6,7,5,3] => 0
[1,2,4,7,3,5,6] => 3
[1,2,4,7,3,6,5] => 1
[1,2,4,7,5,3,6] => 1
[1,2,4,7,5,6,3] => 1
[1,2,4,7,6,3,5] => 0
[1,2,4,7,6,5,3] => 0
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 1
[1,2,5,3,6,4,7] => 2
[1,2,5,3,6,7,4] => 1
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 0
[1,2,5,4,3,6,7] => 2
[1,2,5,4,3,7,6] => 1
[1,2,5,4,6,3,7] => 2
[1,2,5,4,6,7,3] => 1
[1,2,5,4,7,3,6] => 2
[1,2,5,4,7,6,3] => 0
[1,2,5,6,3,4,7] => 3
[1,2,5,6,3,7,4] => 1
[1,2,5,6,4,3,7] => 1
[1,2,5,6,4,7,3] => 1
[1,2,5,6,7,3,4] => 2
[1,2,5,6,7,4,3] => 0
[1,2,5,7,3,4,6] => 3
[1,2,5,7,3,6,4] => 1
[1,2,5,7,4,3,6] => 1
[1,2,5,7,4,6,3] => 1
[1,2,5,7,6,3,4] => 0
[1,2,5,7,6,4,3] => 0
[1,2,6,3,4,5,7] => 4
[1,2,6,3,4,7,5] => 1
[1,2,6,3,5,4,7] => 2
[1,2,6,3,5,7,4] => 1
[1,2,6,3,7,4,5] => 2
[1,2,6,3,7,5,4] => 0
[1,2,6,4,3,5,7] => 2
[1,2,6,4,3,7,5] => 1
[1,2,6,4,5,3,7] => 2
[1,2,6,4,5,7,3] => 1
[1,2,6,4,7,3,5] => 2
[1,2,6,4,7,5,3] => 0
[1,2,6,5,3,4,7] => 1
[1,2,6,5,3,7,4] => 1
[1,2,6,5,4,3,7] => 1
[1,2,6,5,4,7,3] => 1
[1,2,6,5,7,3,4] => 2
[1,2,6,5,7,4,3] => 0
[1,2,6,7,3,4,5] => 3
[1,2,6,7,3,5,4] => 1
[1,2,6,7,4,3,5] => 1
[1,2,6,7,4,5,3] => 1
[1,2,6,7,5,3,4] => 0
[1,2,6,7,5,4,3] => 0
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 1
[1,2,7,3,5,4,6] => 2
[1,2,7,3,5,6,4] => 1
[1,2,7,3,6,4,5] => 2
[1,2,7,3,6,5,4] => 0
[1,2,7,4,3,5,6] => 2
[1,2,7,4,3,6,5] => 1
[1,2,7,4,5,3,6] => 2
[1,2,7,4,5,6,3] => 1
[1,2,7,4,6,3,5] => 2
[1,2,7,4,6,5,3] => 0
[1,2,7,5,3,4,6] => 1
[1,2,7,5,3,6,4] => 1
[1,2,7,5,4,3,6] => 1
[1,2,7,5,4,6,3] => 1
[1,2,7,5,6,3,4] => 2
[1,2,7,5,6,4,3] => 0
[1,2,7,6,3,4,5] => 0
[1,2,7,6,3,5,4] => 0
[1,2,7,6,4,3,5] => 0
[1,2,7,6,4,5,3] => 0
[1,2,7,6,5,3,4] => 0
[1,2,7,6,5,4,3] => 0
[1,3,2,4,5,6,7] => 5
[1,3,2,4,5,7,6] => 1
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 1
[1,3,2,4,7,5,6] => 2
[1,3,2,4,7,6,5] => 0
[1,3,2,5,4,6,7] => 3
[1,3,2,5,4,7,6] => 1
[1,3,2,5,6,4,7] => 2
[1,3,2,5,6,7,4] => 1
[1,3,2,5,7,4,6] => 2
[1,3,2,5,7,6,4] => 0
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 1
[1,3,2,6,5,4,7] => 1
[1,3,2,6,5,7,4] => 1
[1,3,2,6,7,4,5] => 2
[1,3,2,6,7,5,4] => 0
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 1
[1,3,2,7,5,4,6] => 1
[1,3,2,7,5,6,4] => 1
[1,3,2,7,6,4,5] => 0
[1,3,2,7,6,5,4] => 0
[1,3,4,2,5,6,7] => 4
[1,3,4,2,5,7,6] => 1
[1,3,4,2,6,5,7] => 2
[1,3,4,2,6,7,5] => 1
[1,3,4,2,7,5,6] => 2
[1,3,4,2,7,6,5] => 0
[1,3,4,5,2,6,7] => 3
[1,3,4,5,2,7,6] => 1
[1,3,4,5,6,2,7] => 2
[1,3,4,5,6,7,2] => 1
[1,3,4,5,7,2,6] => 2
[1,3,4,5,7,6,2] => 0
[1,3,4,6,2,5,7] => 3
[1,3,4,6,2,7,5] => 1
[1,3,4,6,5,2,7] => 1
[1,3,4,6,5,7,2] => 1
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 0
[1,3,4,7,2,5,6] => 3
[1,3,4,7,2,6,5] => 1
[1,3,4,7,5,2,6] => 1
[1,3,4,7,5,6,2] => 1
[1,3,4,7,6,2,5] => 0
[1,3,4,7,6,5,2] => 0
[1,3,5,2,4,6,7] => 4
[1,3,5,2,4,7,6] => 1
[1,3,5,2,6,4,7] => 2
[1,3,5,2,6,7,4] => 1
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 0
[1,3,5,4,2,6,7] => 2
[1,3,5,4,2,7,6] => 1
[1,3,5,4,6,2,7] => 2
[1,3,5,4,6,7,2] => 1
[1,3,5,4,7,2,6] => 2
[1,3,5,4,7,6,2] => 0
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 1
[1,3,5,6,4,2,7] => 1
[1,3,5,6,4,7,2] => 1
[1,3,5,6,7,2,4] => 2
[1,3,5,6,7,4,2] => 0
[1,3,5,7,2,4,6] => 3
[1,3,5,7,2,6,4] => 1
[1,3,5,7,4,2,6] => 1
[1,3,5,7,4,6,2] => 1
[1,3,5,7,6,2,4] => 0
[1,3,5,7,6,4,2] => 0
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 1
[1,3,6,2,5,4,7] => 2
[1,3,6,2,5,7,4] => 1
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 0
[1,3,6,4,2,5,7] => 2
[1,3,6,4,2,7,5] => 1
[1,3,6,4,5,2,7] => 2
[1,3,6,4,5,7,2] => 1
[1,3,6,4,7,2,5] => 2
[1,3,6,4,7,5,2] => 0
[1,3,6,5,2,4,7] => 1
[1,3,6,5,2,7,4] => 1
[1,3,6,5,4,2,7] => 1
[1,3,6,5,4,7,2] => 1
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 0
[1,3,6,7,2,4,5] => 3
[1,3,6,7,2,5,4] => 1
[1,3,6,7,4,2,5] => 1
[1,3,6,7,4,5,2] => 1
[1,3,6,7,5,2,4] => 0
[1,3,6,7,5,4,2] => 0
[1,3,7,2,4,5,6] => 4
[1,3,7,2,4,6,5] => 1
[1,3,7,2,5,4,6] => 2
[1,3,7,2,5,6,4] => 1
[1,3,7,2,6,4,5] => 2
[1,3,7,2,6,5,4] => 0
[1,3,7,4,2,5,6] => 2
[1,3,7,4,2,6,5] => 1
[1,3,7,4,5,2,6] => 2
[1,3,7,4,5,6,2] => 1
[1,3,7,4,6,2,5] => 2
[1,3,7,4,6,5,2] => 0
[1,3,7,5,2,4,6] => 1
[1,3,7,5,2,6,4] => 1
[1,3,7,5,4,2,6] => 1
[1,3,7,5,4,6,2] => 1
[1,3,7,5,6,2,4] => 2
[1,3,7,5,6,4,2] => 0
[1,3,7,6,2,4,5] => 0
[1,3,7,6,2,5,4] => 0
[1,3,7,6,4,2,5] => 0
[1,3,7,6,4,5,2] => 0
[1,3,7,6,5,2,4] => 0
[1,3,7,6,5,4,2] => 0
[1,4,2,3,5,6,7] => 5
[1,4,2,3,5,7,6] => 1
[1,4,2,3,6,5,7] => 2
[1,4,2,3,6,7,5] => 1
[1,4,2,3,7,5,6] => 2
[1,4,2,3,7,6,5] => 0
[1,4,2,5,3,6,7] => 3
[1,4,2,5,3,7,6] => 1
[1,4,2,5,6,3,7] => 2
[1,4,2,5,6,7,3] => 1
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 0
[1,4,2,6,3,5,7] => 3
[1,4,2,6,3,7,5] => 1
[1,4,2,6,5,3,7] => 1
[1,4,2,6,5,7,3] => 1
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 0
[1,4,2,7,3,5,6] => 3
[1,4,2,7,3,6,5] => 1
[1,4,2,7,5,3,6] => 1
[1,4,2,7,5,6,3] => 1
[1,4,2,7,6,3,5] => 0
[1,4,2,7,6,5,3] => 0
[1,4,3,2,5,6,7] => 3
[1,4,3,2,5,7,6] => 1
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 2
[1,4,3,2,7,6,5] => 0
[1,4,3,5,2,6,7] => 3
[1,4,3,5,2,7,6] => 1
[1,4,3,5,6,2,7] => 2
[1,4,3,5,6,7,2] => 1
[1,4,3,5,7,2,6] => 2
[1,4,3,5,7,6,2] => 0
[1,4,3,6,2,5,7] => 3
[1,4,3,6,2,7,5] => 1
[1,4,3,6,5,2,7] => 1
[1,4,3,6,5,7,2] => 1
[1,4,3,6,7,2,5] => 2
[1,4,3,6,7,5,2] => 0
[1,4,3,7,2,5,6] => 3
[1,4,3,7,2,6,5] => 1
[1,4,3,7,5,2,6] => 1
[1,4,3,7,5,6,2] => 1
[1,4,3,7,6,2,5] => 0
[1,4,3,7,6,5,2] => 0
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 1
[1,4,5,2,6,3,7] => 2
[1,4,5,2,6,7,3] => 1
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 0
[1,4,5,3,2,6,7] => 2
[1,4,5,3,2,7,6] => 1
[1,4,5,3,6,2,7] => 2
[1,4,5,3,6,7,2] => 1
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 0
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 1
[1,4,5,6,3,2,7] => 1
[1,4,5,6,3,7,2] => 1
[1,4,5,6,7,2,3] => 2
[1,4,5,6,7,3,2] => 0
[1,4,5,7,2,3,6] => 3
[1,4,5,7,2,6,3] => 1
[1,4,5,7,3,2,6] => 1
[1,4,5,7,3,6,2] => 1
[1,4,5,7,6,2,3] => 0
[1,4,5,7,6,3,2] => 0
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 1
[1,4,6,2,5,3,7] => 2
[1,4,6,2,5,7,3] => 1
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 0
[1,4,6,3,2,5,7] => 2
[1,4,6,3,2,7,5] => 1
[1,4,6,3,5,2,7] => 2
[1,4,6,3,5,7,2] => 1
[1,4,6,3,7,2,5] => 2
[1,4,6,3,7,5,2] => 0
[1,4,6,5,2,3,7] => 1
[1,4,6,5,2,7,3] => 1
[1,4,6,5,3,2,7] => 1
[1,4,6,5,3,7,2] => 1
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Description
The rix statistic of a permutation.
This statistic is defined recursively as follows: $rix([]) = 0$, and if $w_i = \max\{w_1, w_2,\dots, w_k\}$, then
$rix(w) := 0$ if $i = 1 < k$,
$rix(w) := 1 + rix(w_1,w_2,\dots,w_{k−1})$ if $i = k$ and
$rix(w) := rix(w_{i+1},w_{i+2},\dots,w_k)$ if $1 < i < k$.
References
[1] Lin, Z., Zeng, J. The γ-positivity of basic Eulerian polynomials via group actions arXiv:1411.3397
Code
def statistic(w):
    """
    sage: statistic([1])
    1
    sage: statistic([2,9,1,7,5,3,4,6,8])
    2

    """
    if len(w) == 0:
        return 0
    k = len(w)
    i = w.index(max(w)) + 1
    if i == 1 < k:
        return 0
    elif i == k:
        return 1 + statistic(w[:-1])
    elif 1 < i < k:
        return statistic(w[i:])
    raise ValueError
Created
Apr 07, 2016 at 11:45 by Martin Rubey
Updated
Apr 07, 2016 at 11:45 by Martin Rubey