edit this statistic or download as text // json
Identifier
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 2
[2,4,1,3] => 1
[2,4,3,1] => 3
[3,1,2,4] => 1
[3,1,4,2] => 3
[3,2,1,4] => 2
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 3
[4,1,2,3] => 2
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 1
[1,2,5,3,4] => 1
[1,2,5,4,3] => 2
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 1
[1,3,4,5,2] => 2
[1,3,5,2,4] => 1
[1,3,5,4,2] => 3
[1,4,2,3,5] => 1
[1,4,2,5,3] => 3
[1,4,3,2,5] => 2
[1,4,3,5,2] => 3
[1,4,5,2,3] => 2
[1,4,5,3,2] => 3
[1,5,2,3,4] => 2
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 3
[1,5,4,3,2] => 4
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 3
[2,3,1,4,5] => 1
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 2
[2,3,5,4,1] => 3
[2,4,1,3,5] => 1
[2,4,1,5,3] => 3
[2,4,3,1,5] => 3
[2,4,3,5,1] => 3
[2,4,5,1,3] => 3
[2,4,5,3,1] => 3
[2,5,1,3,4] => 2
[2,5,1,4,3] => 3
[2,5,3,1,4] => 4
[2,5,3,4,1] => 3
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 1
[3,1,2,5,4] => 2
[3,1,4,2,5] => 3
[3,1,4,5,2] => 2
[3,1,5,2,4] => 3
[3,1,5,4,2] => 3
[3,2,1,4,5] => 2
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 4
[3,4,1,2,5] => 2
[3,4,1,5,2] => 3
[3,4,2,1,5] => 3
[3,4,2,5,1] => 3
[3,4,5,1,2] => 3
[3,4,5,2,1] => 4
[3,5,1,2,4] => 3
[3,5,1,4,2] => 3
[3,5,2,1,4] => 4
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 3
[3,5,4,1,2] => 4
[3,5,4,2,1] => 5
[4,1,2,3,5] => 2
[4,1,2,5,3] => 2
[4,1,3,2,5] => 3
[4,1,3,5,2] => 2
[4,1,5,2,3] => 3
[4,1,5,3,2] => 4
[4,2,1,3,5] => 3
[4,2,1,5,3] => 3
[4,2,3,1,5] => 3
[4,2,3,5,1] => 3
[4,2,5,1,3] => 3
[4,2,5,3,1] => 5
[4,3,1,2,5] => 3
[4,3,1,5,2] => 4
[4,3,2,1,5] => 4
[4,3,2,5,1] => 4
[4,3,5,1,2] => 4
[4,3,5,2,1] => 5
[4,5,1,2,3] => 3
[4,5,1,3,2] => 4
[4,5,2,1,3] => 4
[4,5,2,3,1] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 5
[5,1,2,3,4] => 2
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 4
[5,2,1,3,4] => 3
[5,2,1,4,3] => 4
[5,2,3,1,4] => 3
[5,2,3,4,1] => 4
[5,2,4,1,3] => 3
[5,2,4,3,1] => 5
[5,3,1,2,4] => 3
[5,3,1,4,2] => 5
[5,3,2,1,4] => 4
[5,3,2,4,1] => 5
[5,3,4,1,2] => 4
[5,3,4,2,1] => 5
[5,4,1,2,3] => 4
[5,4,1,3,2] => 5
[5,4,2,1,3] => 5
[5,4,2,3,1] => 5
[5,4,3,1,2] => 5
[5,4,3,2,1] => 6
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => 2
[1,2,4,6,3,5] => 1
[1,2,4,6,5,3] => 3
[1,2,5,3,4,6] => 1
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 2
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 3
[1,2,6,3,4,5] => 2
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 2
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 2
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 3
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 3
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 3
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 4
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 2
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 3
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 3
[1,4,5,3,2,6] => 3
[1,4,5,3,6,2] => 3
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 4
[1,4,6,2,3,5] => 3
[1,4,6,2,5,3] => 3
[1,4,6,3,2,5] => 4
[1,4,6,3,5,2] => 3
[1,4,6,5,2,3] => 4
[1,4,6,5,3,2] => 5
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 2
[1,5,2,6,3,4] => 3
[1,5,2,6,4,3] => 4
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 3
[1,5,3,4,6,2] => 3
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 5
[1,5,4,2,3,6] => 3
[1,5,4,2,6,3] => 4
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 4
[1,5,4,6,2,3] => 4
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 3
[1,5,6,2,4,3] => 4
[1,5,6,3,2,4] => 4
[1,5,6,3,4,2] => 4
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 5
[1,6,2,3,4,5] => 2
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 3
[1,6,2,5,3,4] => 3
[1,6,2,5,4,3] => 4
[1,6,3,2,4,5] => 3
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 4
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 5
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 5
[1,6,4,3,2,5] => 4
[1,6,4,3,5,2] => 5
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 4
[1,6,5,2,4,3] => 5
[1,6,5,3,2,4] => 5
[1,6,5,3,4,2] => 5
[1,6,5,4,2,3] => 5
[1,6,5,4,3,2] => 6
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 2
[2,1,3,6,4,5] => 2
[2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 3
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 2
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 3
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 3
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 5
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 2
[2,3,4,1,6,5] => 3
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 3
[2,3,4,6,1,5] => 2
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 4
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 4
[2,3,5,6,1,4] => 3
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 4
[2,3,6,4,1,5] => 4
[2,3,6,4,5,1] => 4
[2,3,6,5,1,4] => 4
[2,3,6,5,4,1] => 5
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 3
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 3
[2,4,1,6,5,3] => 3
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 4
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 5
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 4
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 5
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 4
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 4
[2,4,6,5,1,3] => 4
[2,4,6,5,3,1] => 6
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 2
[2,5,1,4,3,6] => 3
[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] => 4
[2,5,3,1,6,4] => 4
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 6
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 4
[2,5,4,6,3,1] => 6
[2,5,6,1,3,4] => 4
[2,5,6,1,4,3] => 5
[2,5,6,3,1,4] => 4
[2,5,6,3,4,1] => 5
[2,5,6,4,1,3] => 4
[2,5,6,4,3,1] => 6
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 3
[2,6,1,5,4,3] => 4
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 5
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 6
[2,6,4,1,3,5] => 4
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 4
[2,6,4,5,3,1] => 6
[2,6,5,1,3,4] => 5
[2,6,5,1,4,3] => 6
[2,6,5,3,1,4] => 5
[2,6,5,3,4,1] => 6
[2,6,5,4,1,3] => 5
[2,6,5,4,3,1] => 7
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 2
[3,1,2,5,4,6] => 2
[3,1,2,5,6,4] => 2
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 2
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 5
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 5
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 5
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 4
[3,1,6,5,4,2] => 6
[3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 4
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 4
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 5
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 5
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 5
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 5
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 5
[3,2,6,5,1,4] => 5
[3,2,6,5,4,1] => 6
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 3
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 4
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 3
[3,4,2,6,5,1] => 5
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 5
[3,4,5,2,1,6] => 4
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 5
[3,4,6,1,2,5] => 4
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 5
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 5
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 3
[3,5,1,2,6,4] => 3
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 3
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 5
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 3
[3,5,2,6,4,1] => 6
[3,5,4,1,2,6] => 4
[3,5,4,1,6,2] => 6
[3,5,4,2,1,6] => 5
[3,5,4,2,6,1] => 6
[3,5,4,6,1,2] => 5
[3,5,4,6,2,1] => 6
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 6
[3,5,6,2,1,4] => 5
[3,5,6,2,4,1] => 6
[3,5,6,4,1,2] => 5
[3,5,6,4,2,1] => 6
[3,6,1,2,4,5] => 3
[3,6,1,2,5,4] => 4
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 5
[3,6,2,1,4,5] => 4
[3,6,2,1,5,4] => 5
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 5
[3,6,2,5,1,4] => 3
[3,6,2,5,4,1] => 6
[3,6,4,1,2,5] => 4
[3,6,4,1,5,2] => 7
[3,6,4,2,1,5] => 5
[3,6,4,2,5,1] => 7
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 6
[3,6,5,1,2,4] => 5
[3,6,5,1,4,2] => 7
[3,6,5,2,1,4] => 6
[3,6,5,2,4,1] => 7
[3,6,5,4,1,2] => 6
[3,6,5,4,2,1] => 7
[4,1,2,3,5,6] => 2
[4,1,2,3,6,5] => 3
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 4
[4,1,3,5,2,6] => 2
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 5
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 4
[4,1,5,3,6,2] => 6
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 5
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 5
[4,1,6,5,3,2] => 6
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 3
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 5
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 6
[4,2,6,5,3,1] => 6
[4,3,1,2,5,6] => 3
[4,3,1,2,6,5] => 4
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 4
[4,3,1,6,5,2] => 5
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 5
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 5
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 6
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 6
[4,3,5,2,1,6] => 5
[4,3,5,2,6,1] => 6
[4,3,5,6,1,2] => 5
[4,3,5,6,2,1] => 6
[4,3,6,1,2,5] => 5
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 6
[4,3,6,2,5,1] => 6
[4,3,6,5,1,2] => 6
[4,3,6,5,2,1] => 7
[4,5,1,2,3,6] => 3
[4,5,1,2,6,3] => 4
[4,5,1,3,2,6] => 4
[4,5,1,3,6,2] => 4
[4,5,1,6,2,3] => 4
[4,5,1,6,3,2] => 5
[4,5,2,1,3,6] => 4
[4,5,2,1,6,3] => 5
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 5
[4,5,2,6,1,3] => 4
[4,5,2,6,3,1] => 6
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 6
[4,5,3,2,1,6] => 5
[4,5,3,2,6,1] => 6
[4,5,3,6,1,2] => 5
[4,5,3,6,2,1] => 6
[4,5,6,1,2,3] => 5
[4,5,6,1,3,2] => 6
[4,5,6,2,1,3] => 6
[4,5,6,2,3,1] => 6
[4,5,6,3,1,2] => 6
[4,5,6,3,2,1] => 7
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 5
[4,6,1,3,2,5] => 4
[4,6,1,3,5,2] => 5
[4,6,1,5,2,3] => 4
[4,6,1,5,3,2] => 5
[4,6,2,1,3,5] => 4
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 4
[4,6,2,3,5,1] => 6
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 6
[4,6,3,1,2,5] => 4
[4,6,3,1,5,2] => 7
[4,6,3,2,1,5] => 5
[4,6,3,2,5,1] => 7
[4,6,3,5,1,2] => 5
[4,6,3,5,2,1] => 6
[4,6,5,1,2,3] => 6
[4,6,5,1,3,2] => 7
[4,6,5,2,1,3] => 7
[4,6,5,2,3,1] => 7
[4,6,5,3,1,2] => 7
[4,6,5,3,2,1] => 8
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 4
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 4
[5,1,2,6,3,4] => 3
[5,1,2,6,4,3] => 4
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 5
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 5
[5,1,3,6,2,4] => 3
[5,1,3,6,4,2] => 5
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 4
[5,1,4,3,6,2] => 6
[5,1,4,6,2,3] => 4
[5,1,4,6,3,2] => 5
[5,1,6,2,3,4] => 5
[5,1,6,2,4,3] => 6
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 6
[5,1,6,4,3,2] => 7
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 4
[5,2,1,6,4,3] => 5
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 5
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 5
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 5
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 5
[5,2,6,1,3,4] => 5
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 7
[5,2,6,3,4,1] => 6
[5,2,6,4,1,3] => 7
[5,2,6,4,3,1] => 7
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 5
[5,3,1,4,2,6] => 5
[5,3,1,4,6,2] => 5
[5,3,1,6,2,4] => 5
[5,3,1,6,4,2] => 5
[5,3,2,1,4,6] => 4
[5,3,2,1,6,4] => 6
[5,3,2,4,1,6] => 5
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 5
[5,3,2,6,4,1] => 6
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 5
[5,3,4,2,6,1] => 6
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 6
[5,3,6,1,2,4] => 6
[5,3,6,1,4,2] => 6
[5,3,6,2,1,4] => 7
[5,3,6,2,4,1] => 6
[5,3,6,4,1,2] => 7
[5,3,6,4,2,1] => 8
[5,4,1,2,3,6] => 4
[5,4,1,2,6,3] => 5
[5,4,1,3,2,6] => 5
[5,4,1,3,6,2] => 5
[5,4,1,6,2,3] => 5
[5,4,1,6,3,2] => 6
[5,4,2,1,3,6] => 5
[5,4,2,1,6,3] => 6
[5,4,2,3,1,6] => 5
[5,4,2,3,6,1] => 6
[5,4,2,6,1,3] => 5
[5,4,2,6,3,1] => 7
[5,4,3,1,2,6] => 5
[5,4,3,1,6,2] => 7
[5,4,3,2,1,6] => 6
[5,4,3,2,6,1] => 7
[5,4,3,6,1,2] => 6
[5,4,3,6,2,1] => 7
[5,4,6,1,2,3] => 6
[5,4,6,1,3,2] => 7
[5,4,6,2,1,3] => 7
[5,4,6,2,3,1] => 7
[5,4,6,3,1,2] => 7
[5,4,6,3,2,1] => 8
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 5
[5,6,1,3,2,4] => 5
[5,6,1,3,4,2] => 5
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 6
[5,6,2,1,3,4] => 5
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 5
[5,6,2,3,4,1] => 6
[5,6,2,4,1,3] => 5
[5,6,2,4,3,1] => 7
[5,6,3,1,2,4] => 5
[5,6,3,1,4,2] => 7
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 7
[5,6,3,4,1,2] => 6
[5,6,3,4,2,1] => 7
[5,6,4,1,2,3] => 6
[5,6,4,1,3,2] => 7
[5,6,4,2,1,3] => 7
[5,6,4,2,3,1] => 7
[5,6,4,3,1,2] => 7
[5,6,4,3,2,1] => 8
[6,1,2,3,4,5] => 3
[6,1,2,3,5,4] => 4
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 5
[6,1,3,2,4,5] => 4
[6,1,3,2,5,4] => 5
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 5
[6,1,3,5,2,4] => 4
[6,1,3,5,4,2] => 6
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 6
[6,1,5,2,3,4] => 5
[6,1,5,2,4,3] => 6
[6,1,5,3,2,4] => 6
[6,1,5,3,4,2] => 6
[6,1,5,4,2,3] => 6
[6,1,5,4,3,2] => 7
[6,2,1,3,4,5] => 4
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 5
[6,2,1,4,5,3] => 5
[6,2,1,5,3,4] => 5
[6,2,1,5,4,3] => 6
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 5
[6,2,3,4,1,5] => 5
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 6
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 6
[6,2,4,5,1,3] => 6
[6,2,4,5,3,1] => 6
[6,2,5,1,3,4] => 5
[6,2,5,1,4,3] => 6
[6,2,5,3,1,4] => 7
[6,2,5,3,4,1] => 6
[6,2,5,4,1,3] => 7
[6,2,5,4,3,1] => 7
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 5
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 6
[6,3,2,1,4,5] => 5
[6,3,2,1,5,4] => 6
[6,3,2,4,1,5] => 6
[6,3,2,4,5,1] => 6
[6,3,2,5,1,4] => 6
[6,3,2,5,4,1] => 7
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 6
[6,3,4,2,1,5] => 6
[6,3,4,2,5,1] => 6
[6,3,4,5,1,2] => 6
[6,3,4,5,2,1] => 7
[6,3,5,1,2,4] => 6
[6,3,5,1,4,2] => 6
[6,3,5,2,1,4] => 7
[6,3,5,2,4,1] => 6
[6,3,5,4,1,2] => 7
[6,3,5,4,2,1] => 8
[6,4,1,2,3,5] => 5
[6,4,1,2,5,3] => 5
[6,4,1,3,2,5] => 6
[6,4,1,3,5,2] => 5
[6,4,1,5,2,3] => 6
[6,4,1,5,3,2] => 7
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 6
[6,4,2,3,1,5] => 6
[6,4,2,3,5,1] => 6
[6,4,2,5,1,3] => 6
[6,4,2,5,3,1] => 8
[6,4,3,1,2,5] => 6
[6,4,3,1,5,2] => 7
[6,4,3,2,1,5] => 7
[6,4,3,2,5,1] => 7
[6,4,3,5,1,2] => 7
[6,4,3,5,2,1] => 8
[6,4,5,1,2,3] => 6
[6,4,5,1,3,2] => 7
[6,4,5,2,1,3] => 7
[6,4,5,2,3,1] => 7
[6,4,5,3,1,2] => 7
[6,4,5,3,2,1] => 8
[6,5,1,2,3,4] => 5
[6,5,1,2,4,3] => 6
[6,5,1,3,2,4] => 6
[6,5,1,3,4,2] => 6
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 7
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 7
[6,5,2,3,1,4] => 6
[6,5,2,3,4,1] => 7
[6,5,2,4,1,3] => 6
[6,5,2,4,3,1] => 8
[6,5,3,1,2,4] => 6
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 7
[6,5,3,2,4,1] => 8
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 8
[6,5,4,1,2,3] => 7
[6,5,4,1,3,2] => 8
[6,5,4,2,1,3] => 8
[6,5,4,2,3,1] => 8
[6,5,4,3,1,2] => 8
[6,5,4,3,2,1] => 9
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 1
[1,2,3,4,6,7,5] => 1
[1,2,3,4,7,5,6] => 1
[1,2,3,4,7,6,5] => 2
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 1
[1,2,3,5,6,7,4] => 2
[1,2,3,5,7,4,6] => 1
[1,2,3,5,7,6,4] => 3
[1,2,3,6,4,5,7] => 1
[1,2,3,6,4,7,5] => 3
[1,2,3,6,5,4,7] => 2
[1,2,3,6,5,7,4] => 3
[1,2,3,6,7,4,5] => 2
[1,2,3,6,7,5,4] => 3
[1,2,3,7,4,5,6] => 2
[1,2,3,7,4,6,5] => 3
[1,2,3,7,5,4,6] => 3
[1,2,3,7,5,6,4] => 3
[1,2,3,7,6,4,5] => 3
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 2
[1,2,4,3,6,7,5] => 2
[1,2,4,3,7,5,6] => 2
[1,2,4,3,7,6,5] => 3
[1,2,4,5,3,6,7] => 1
[1,2,4,5,3,7,6] => 2
[1,2,4,5,6,3,7] => 2
[1,2,4,5,6,7,3] => 2
[1,2,4,5,7,3,6] => 2
[1,2,4,5,7,6,3] => 3
[1,2,4,6,3,5,7] => 1
[1,2,4,6,3,7,5] => 3
[1,2,4,6,5,3,7] => 3
[1,2,4,6,5,7,3] => 3
[1,2,4,6,7,3,5] => 3
[1,2,4,6,7,5,3] => 3
[1,2,4,7,3,5,6] => 2
[1,2,4,7,3,6,5] => 3
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 3
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 1
[1,2,5,3,4,7,6] => 2
[1,2,5,3,6,4,7] => 3
[1,2,5,3,6,7,4] => 2
[1,2,5,3,7,4,6] => 3
[1,2,5,3,7,6,4] => 3
[1,2,5,4,3,6,7] => 2
[1,2,5,4,3,7,6] => 3
[1,2,5,4,6,3,7] => 3
[1,2,5,4,6,7,3] => 3
[1,2,5,4,7,3,6] => 3
[1,2,5,4,7,6,3] => 4
[1,2,5,6,3,4,7] => 2
[1,2,5,6,3,7,4] => 3
[1,2,5,6,4,3,7] => 3
[1,2,5,6,4,7,3] => 3
[1,2,5,6,7,3,4] => 3
[1,2,5,6,7,4,3] => 4
[1,2,5,7,3,4,6] => 3
[1,2,5,7,3,6,4] => 3
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 3
[1,2,5,7,6,3,4] => 4
[1,2,5,7,6,4,3] => 5
[1,2,6,3,4,5,7] => 2
[1,2,6,3,4,7,5] => 2
[1,2,6,3,5,4,7] => 3
[1,2,6,3,5,7,4] => 2
[1,2,6,3,7,4,5] => 3
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 3
[1,2,6,4,3,7,5] => 3
[1,2,6,4,5,3,7] => 3
[1,2,6,4,5,7,3] => 3
[1,2,6,4,7,3,5] => 3
[1,2,6,4,7,5,3] => 5
[1,2,6,5,3,4,7] => 3
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 4
[1,2,6,5,7,3,4] => 4
[1,2,6,5,7,4,3] => 5
[1,2,6,7,3,4,5] => 3
[1,2,6,7,3,5,4] => 4
[1,2,6,7,4,3,5] => 4
[1,2,6,7,4,5,3] => 4
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 5
[1,2,7,3,4,5,6] => 2
[1,2,7,3,4,6,5] => 3
[1,2,7,3,5,4,6] => 3
[1,2,7,3,5,6,4] => 3
[1,2,7,3,6,4,5] => 3
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 3
[1,2,7,4,3,6,5] => 4
[1,2,7,4,5,3,6] => 3
[1,2,7,4,5,6,3] => 4
[1,2,7,4,6,3,5] => 3
[1,2,7,4,6,5,3] => 5
[1,2,7,5,3,4,6] => 3
[1,2,7,5,3,6,4] => 5
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 5
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 5
[1,2,7,6,3,4,5] => 4
[1,2,7,6,3,5,4] => 5
[1,2,7,6,4,3,5] => 5
[1,2,7,6,4,5,3] => 5
[1,2,7,6,5,3,4] => 5
[1,2,7,6,5,4,3] => 6
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 2
[1,3,2,4,7,5,6] => 2
[1,3,2,4,7,6,5] => 3
[1,3,2,5,4,6,7] => 2
[1,3,2,5,4,7,6] => 3
[1,3,2,5,6,4,7] => 2
[1,3,2,5,6,7,4] => 3
[1,3,2,5,7,4,6] => 2
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 2
[1,3,2,6,4,7,5] => 4
[1,3,2,6,5,4,7] => 3
[1,3,2,6,5,7,4] => 4
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 4
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 4
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 4
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 5
[1,3,4,2,5,6,7] => 1
[1,3,4,2,5,7,6] => 2
[1,3,4,2,6,5,7] => 2
[1,3,4,2,6,7,5] => 2
[1,3,4,2,7,5,6] => 2
[1,3,4,2,7,6,5] => 3
[1,3,4,5,2,6,7] => 2
[1,3,4,5,2,7,6] => 3
[1,3,4,5,6,2,7] => 2
[1,3,4,5,6,7,2] => 3
[1,3,4,5,7,2,6] => 2
[1,3,4,5,7,6,2] => 4
[1,3,4,6,2,5,7] => 2
[1,3,4,6,2,7,5] => 4
[1,3,4,6,5,2,7] => 3
[1,3,4,6,5,7,2] => 4
[1,3,4,6,7,2,5] => 3
[1,3,4,6,7,5,2] => 4
[1,3,4,7,2,5,6] => 3
[1,3,4,7,2,6,5] => 4
[1,3,4,7,5,2,6] => 4
[1,3,4,7,5,6,2] => 4
[1,3,4,7,6,2,5] => 4
[1,3,4,7,6,5,2] => 5
[1,3,5,2,4,6,7] => 1
[1,3,5,2,4,7,6] => 2
[1,3,5,2,6,4,7] => 3
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 3
[1,3,5,2,7,6,4] => 3
[1,3,5,4,2,6,7] => 3
[1,3,5,4,2,7,6] => 4
[1,3,5,4,6,2,7] => 3
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 3
[1,3,5,4,7,6,2] => 5
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 4
[1,3,5,6,4,2,7] => 3
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 5
[1,3,5,7,2,4,6] => 4
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 4
[1,3,5,7,6,2,4] => 4
[1,3,5,7,6,4,2] => 6
[1,3,6,2,4,5,7] => 2
[1,3,6,2,4,7,5] => 2
[1,3,6,2,5,4,7] => 3
[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] => 4
[1,3,6,4,2,7,5] => 4
[1,3,6,4,5,2,7] => 3
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 3
[1,3,6,4,7,5,2] => 6
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 5
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 5
[1,3,6,5,7,2,4] => 4
[1,3,6,5,7,4,2] => 6
[1,3,6,7,2,4,5] => 4
[1,3,6,7,2,5,4] => 5
[1,3,6,7,4,2,5] => 4
[1,3,6,7,4,5,2] => 5
[1,3,6,7,5,2,4] => 4
[1,3,6,7,5,4,2] => 6
[1,3,7,2,4,5,6] => 2
[1,3,7,2,4,6,5] => 3
[1,3,7,2,5,4,6] => 3
[1,3,7,2,5,6,4] => 3
[1,3,7,2,6,4,5] => 3
[1,3,7,2,6,5,4] => 4
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 5
[1,3,7,4,5,2,6] => 3
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 3
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 4
[1,3,7,5,2,6,4] => 6
[1,3,7,5,4,2,6] => 4
[1,3,7,5,4,6,2] => 6
[1,3,7,5,6,2,4] => 4
[1,3,7,5,6,4,2] => 6
[1,3,7,6,2,4,5] => 5
[1,3,7,6,2,5,4] => 6
[1,3,7,6,4,2,5] => 5
[1,3,7,6,4,5,2] => 6
[1,3,7,6,5,2,4] => 5
[1,3,7,6,5,4,2] => 7
[1,4,2,3,5,6,7] => 1
[1,4,2,3,5,7,6] => 2
[1,4,2,3,6,5,7] => 2
[1,4,2,3,6,7,5] => 2
[1,4,2,3,7,5,6] => 2
[1,4,2,3,7,6,5] => 3
[1,4,2,5,3,6,7] => 3
[1,4,2,5,3,7,6] => 4
[1,4,2,5,6,3,7] => 2
[1,4,2,5,6,7,3] => 4
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 5
[1,4,2,6,3,5,7] => 3
[1,4,2,6,3,7,5] => 5
[1,4,2,6,5,3,7] => 3
[1,4,2,6,5,7,3] => 5
[1,4,2,6,7,3,5] => 3
[1,4,2,6,7,5,3] => 5
[1,4,2,7,3,5,6] => 4
[1,4,2,7,3,6,5] => 5
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 5
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 6
[1,4,3,2,5,6,7] => 2
[1,4,3,2,5,7,6] => 3
[1,4,3,2,6,5,7] => 3
[1,4,3,2,6,7,5] => 3
[1,4,3,2,7,5,6] => 3
[1,4,3,2,7,6,5] => 4
[1,4,3,5,2,6,7] => 3
[1,4,3,5,2,7,6] => 4
[1,4,3,5,6,2,7] => 3
[1,4,3,5,6,7,2] => 4
[1,4,3,5,7,2,6] => 3
[1,4,3,5,7,6,2] => 5
[1,4,3,6,2,5,7] => 3
[1,4,3,6,2,7,5] => 5
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 5
[1,4,3,6,7,2,5] => 4
[1,4,3,6,7,5,2] => 5
[1,4,3,7,2,5,6] => 4
[1,4,3,7,2,6,5] => 5
[1,4,3,7,5,2,6] => 5
[1,4,3,7,5,6,2] => 5
[1,4,3,7,6,2,5] => 5
[1,4,3,7,6,5,2] => 6
[1,4,5,2,3,6,7] => 2
[1,4,5,2,3,7,6] => 3
[1,4,5,2,6,3,7] => 3
[1,4,5,2,6,7,3] => 3
[1,4,5,2,7,3,6] => 3
[1,4,5,2,7,6,3] => 4
[1,4,5,3,2,6,7] => 3
[1,4,5,3,2,7,6] => 4
[1,4,5,3,6,2,7] => 3
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 3
[1,4,5,3,7,6,2] => 5
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 5
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 5
[1,4,5,6,7,2,3] => 4
[1,4,5,6,7,3,2] => 5
[1,4,5,7,2,3,6] => 4
[1,4,5,7,2,6,3] => 5
[1,4,5,7,3,2,6] => 5
[1,4,5,7,3,6,2] => 5
[1,4,5,7,6,2,3] => 5
[1,4,5,7,6,3,2] => 6
[1,4,6,2,3,5,7] => 3
[1,4,6,2,3,7,5] => 3
[1,4,6,2,5,3,7] => 3
[1,4,6,2,5,7,3] => 3
[1,4,6,2,7,3,5] => 3
[1,4,6,2,7,5,3] => 5
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 4
[1,4,6,3,5,2,7] => 3
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 3
[1,4,6,3,7,5,2] => 6
[1,4,6,5,2,3,7] => 4
[1,4,6,5,2,7,3] => 6
[1,4,6,5,3,2,7] => 5
[1,4,6,5,3,7,2] => 6
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Description
The number of odd inversions of a permutation.
An inversion $i < j$ of a permutation is odd if $i \not\equiv j\ (\operatorname{mod} 2)$. See St000538The number of even inversions of a permutation. for even inversions.
References
[1] Klopsch, B., Voll, C. Igusa-type functions associated to finite formed spaces and their functional equations MathSciNet:2500892 arXiv:math/0603565
[2] Brenti, F., Carnevale, A. Odd length for even hyperoctahedral groups and signed generating functions arXiv:1606.01751
[3] Brenti, F., Carnevale, A. Odd length in Weyl groups arXiv:1709.03320
Code
def statistic(pi):
    return sum(1 for i,j in pi.inversions() if is_odd(j-i))
Created
Jun 22, 2016 at 12:32 by Christian Stump
Updated
Nov 06, 2017 at 21:57 by Martin Rubey