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] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[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] => 1
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 0
[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] => 1
[1,3,2,4,5] => 1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 1
[1,3,4,5,2] => 1
[1,3,5,2,4] => 2
[1,3,5,4,2] => 2
[1,4,2,3,5] => 1
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 1
[1,4,5,3,2] => 1
[1,5,2,3,4] => 1
[1,5,2,4,3] => 1
[1,5,3,2,4] => 2
[1,5,3,4,2] => 2
[1,5,4,2,3] => 1
[1,5,4,3,2] => 1
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 1
[2,1,4,5,3] => 1
[2,1,5,3,4] => 2
[2,1,5,4,3] => 1
[2,3,1,4,5] => 1
[2,3,1,5,4] => 2
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 2
[2,3,5,4,1] => 1
[2,4,1,3,5] => 2
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 2
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,4,3] => 1
[2,5,3,1,4] => 2
[2,5,3,4,1] => 1
[2,5,4,1,3] => 1
[2,5,4,3,1] => 1
[3,1,2,4,5] => 1
[3,1,2,5,4] => 1
[3,1,4,2,5] => 1
[3,1,4,5,2] => 1
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 1
[3,2,5,4,1] => 1
[3,4,1,2,5] => 1
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 2
[3,5,1,4,2] => 2
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 1
[3,5,2,4,1] => 1
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 1
[4,1,2,5,3] => 1
[4,1,3,2,5] => 1
[4,1,3,5,2] => 2
[4,1,5,2,3] => 1
[4,1,5,3,2] => 2
[4,2,1,3,5] => 2
[4,2,1,5,3] => 2
[4,2,3,1,5] => 2
[4,2,3,5,1] => 2
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 1
[4,3,1,5,2] => 2
[4,3,2,1,5] => 1
[4,3,2,5,1] => 1
[4,3,5,1,2] => 2
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 2
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 2
[4,5,3,2,1] => 1
[5,1,2,3,4] => 1
[5,1,2,4,3] => 1
[5,1,3,2,4] => 2
[5,1,3,4,2] => 2
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 1
[5,2,1,4,3] => 1
[5,2,3,1,4] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 1
[5,2,4,3,1] => 1
[5,3,1,2,4] => 2
[5,3,1,4,2] => 2
[5,3,2,1,4] => 1
[5,3,2,4,1] => 1
[5,3,4,1,2] => 1
[5,3,4,2,1] => 1
[5,4,1,2,3] => 1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 1
[5,4,3,1,2] => 1
[5,4,3,2,1] => 0
[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] => 1
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 2
[1,2,5,3,4,6] => 1
[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] => 1
[1,2,5,6,4,3] => 1
[1,2,6,3,4,5] => 1
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 2
[1,2,6,4,5,3] => 2
[1,2,6,5,3,4] => 1
[1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 2
[1,3,5,2,4,6] => 2
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 2
[1,3,5,4,6,2] => 2
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 2
[1,3,6,4,5,2] => 2
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 1
[1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 2
[1,4,5,2,3,6] => 1
[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] => 1
[1,4,5,6,3,2] => 1
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 2
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 2
[1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 1
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 1
[1,5,2,4,6,3] => 2
[1,5,2,6,3,4] => 1
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 2
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 2
[1,5,3,6,2,4] => 2
[1,5,3,6,4,2] => 2
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 2
[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] => 1
[1,5,6,2,3,4] => 1
[1,5,6,2,4,3] => 2
[1,5,6,3,2,4] => 2
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 2
[1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 2
[1,6,2,4,5,3] => 2
[1,6,2,5,3,4] => 1
[1,6,2,5,4,3] => 1
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 2
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 2
[1,6,3,5,2,4] => 2
[1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 2
[1,6,4,3,2,5] => 2
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 2
[1,6,5,2,3,4] => 1
[1,6,5,2,4,3] => 1
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 1
[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] => 2
[2,1,4,3,5,6] => 1
[2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => 1
[2,1,4,5,6,3] => 1
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 2
[2,1,5,3,6,4] => 2
[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] => 1
[2,1,6,3,4,5] => 2
[2,1,6,3,5,4] => 2
[2,1,6,4,3,5] => 2
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 2
[2,1,6,5,4,3] => 1
[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] => 2
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 2
[2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 2
[2,3,5,4,6,1] => 2
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 2
[2,3,6,1,4,5] => 2
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 1
[2,3,6,5,1,4] => 2
[2,3,6,5,4,1] => 1
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 2
[2,4,3,5,6,1] => 2
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 2
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 2
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => 2
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 2
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 2
[2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 2
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 2
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 2
[2,5,3,4,6,1] => 2
[2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => 2
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 2
[2,5,4,3,6,1] => 2
[2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => 2
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 2
[2,5,6,3,1,4] => 2
[2,5,6,3,4,1] => 2
[2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 2
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 2
[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] => 1
[2,6,4,1,3,5] => 2
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => 2
[2,6,4,5,3,1] => 2
[2,6,5,1,3,4] => 2
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 2
[3,1,2,5,4,6] => 1
[3,1,2,5,6,4] => 1
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 1
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 1
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 2
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 2
[3,1,6,2,4,5] => 2
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 2
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 2
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => 2
[3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 2
[3,2,5,1,4,6] => 2
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => 2
[3,2,5,6,1,4] => 2
[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] => 2
[3,2,6,4,5,1] => 2
[3,2,6,5,1,4] => 1
[3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 1
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 2
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 1
[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] => 1
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 2
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 2
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 2
[3,5,1,4,6,2] => 2
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 2
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 2
[3,5,2,4,6,1] => 2
[3,5,2,6,1,4] => 2
[3,5,2,6,4,1] => 2
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 2
[3,5,4,6,2,1] => 2
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 2
[3,5,6,2,4,1] => 2
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 2
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 2
[3,6,1,5,2,4] => 2
[3,6,1,5,4,2] => 2
[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] => 2
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 1
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => 2
[3,6,4,2,5,1] => 2
[3,6,4,5,1,2] => 1
[3,6,4,5,2,1] => 1
[3,6,5,1,2,4] => 2
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 1
[3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => 1
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 1
[4,1,2,5,3,6] => 1
[4,1,2,5,6,3] => 1
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 1
[4,1,3,5,2,6] => 2
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 1
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 2
[4,1,5,6,2,3] => 1
[4,1,5,6,3,2] => 2
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 2
[4,1,6,5,3,2] => 2
[4,2,1,3,5,6] => 2
[4,2,1,3,6,5] => 2
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 2
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 2
[4,2,3,1,5,6] => 2
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 2
[4,2,3,5,6,1] => 2
[4,2,3,6,1,5] => 2
[4,2,3,6,5,1] => 2
[4,2,5,1,3,6] => 2
[4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => 2
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 2
[4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => 2
[4,2,6,3,5,1] => 2
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 2
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 2
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => 2
[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] => 1
[4,3,6,1,2,5] => 2
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 1
[4,3,6,5,1,2] => 2
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 1
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 2
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 2
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 2
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 2
[4,5,3,1,6,2] => 2
[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] => 1
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 2
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 2
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 2
[4,6,2,5,3,1] => 2
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 2
[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] => 1
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 2
[4,6,5,3,2,1] => 1
[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] => 2
[5,1,2,6,3,4] => 1
[5,1,2,6,4,3] => 2
[5,1,3,2,4,6] => 2
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 2
[5,1,3,4,6,2] => 2
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 1
[5,1,4,2,6,3] => 2
[5,1,4,3,2,6] => 1
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 2
[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] => 2
[5,1,6,4,2,3] => 2
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 2
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 2
[5,2,1,4,6,3] => 2
[5,2,1,6,3,4] => 2
[5,2,1,6,4,3] => 2
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 2
[5,2,3,4,1,6] => 2
[5,2,3,4,6,1] => 2
[5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => 2
[5,2,4,1,3,6] => 2
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 2
[5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 2
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 2
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 2
[5,3,1,2,6,4] => 2
[5,3,1,4,2,6] => 2
[5,3,1,4,6,2] => 2
[5,3,1,6,2,4] => 2
[5,3,1,6,4,2] => 2
[5,3,2,1,4,6] => 2
[5,3,2,1,6,4] => 2
[5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => 2
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 2
[5,3,4,1,6,2] => 2
[5,3,4,2,1,6] => 2
[5,3,4,2,6,1] => 2
[5,3,4,6,1,2] => 2
[5,3,4,6,2,1] => 2
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 2
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 2
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 2
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 2
[5,4,1,6,2,3] => 2
[5,4,1,6,3,2] => 2
[5,4,2,1,3,6] => 2
[5,4,2,1,6,3] => 2
[5,4,2,3,1,6] => 2
[5,4,2,3,6,1] => 2
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 2
[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] => 1
[5,4,6,1,2,3] => 2
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 2
[5,4,6,2,3,1] => 2
[5,4,6,3,1,2] => 2
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 2
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 2
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 2
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[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] => 1
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 2
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 1
[6,1,2,4,3,5] => 2
[6,1,2,4,5,3] => 2
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 1
[6,1,3,2,4,5] => 2
[6,1,3,2,5,4] => 2
[6,1,3,4,2,5] => 2
[6,1,3,4,5,2] => 2
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 2
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 2
[6,1,4,3,5,2] => 2
[6,1,4,5,2,3] => 2
[6,1,4,5,3,2] => 2
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 2
[6,1,5,3,4,2] => 2
[6,1,5,4,2,3] => 1
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 2
[6,2,1,4,3,5] => 2
[6,2,1,4,5,3] => 2
[6,2,1,5,3,4] => 2
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 2
[6,2,3,5,4,1] => 1
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 2
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 1
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 1
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 1
[6,3,1,2,4,5] => 2
[6,3,1,2,5,4] => 2
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 2
[6,3,1,5,2,4] => 2
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 2
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 1
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 1
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 2
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 2
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 2
[6,4,1,3,5,2] => 2
[6,4,1,5,2,3] => 2
[6,4,1,5,3,2] => 2
[6,4,2,1,3,5] => 2
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 2
[6,4,2,3,5,1] => 2
[6,4,2,5,1,3] => 2
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 1
[6,4,3,5,1,2] => 2
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 2
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 1
[6,4,5,3,1,2] => 2
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 2
[6,5,1,3,4,2] => 2
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 2
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 1
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
[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] => 1
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 1
[1,2,3,5,6,4,7] => 1
[1,2,3,5,6,7,4] => 1
[1,2,3,5,7,4,6] => 2
[1,2,3,5,7,6,4] => 2
[1,2,3,6,4,5,7] => 1
[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] => 1
[1,2,3,6,7,5,4] => 1
[1,2,3,7,4,5,6] => 1
[1,2,3,7,4,6,5] => 1
[1,2,3,7,5,4,6] => 2
[1,2,3,7,5,6,4] => 2
[1,2,3,7,6,4,5] => 1
[1,2,3,7,6,5,4] => 1
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 1
[1,2,4,3,6,7,5] => 1
[1,2,4,3,7,5,6] => 2
[1,2,4,3,7,6,5] => 1
[1,2,4,5,3,6,7] => 1
[1,2,4,5,3,7,6] => 2
[1,2,4,5,6,3,7] => 1
[1,2,4,5,6,7,3] => 1
[1,2,4,5,7,3,6] => 2
[1,2,4,5,7,6,3] => 2
[1,2,4,6,3,5,7] => 2
[1,2,4,6,3,7,5] => 2
[1,2,4,6,5,3,7] => 2
[1,2,4,6,5,7,3] => 2
[1,2,4,6,7,3,5] => 2
[1,2,4,6,7,5,3] => 2
[1,2,4,7,3,5,6] => 2
[1,2,4,7,3,6,5] => 2
[1,2,4,7,5,3,6] => 2
[1,2,4,7,5,6,3] => 2
[1,2,4,7,6,3,5] => 2
[1,2,4,7,6,5,3] => 2
[1,2,5,3,4,6,7] => 1
[1,2,5,3,4,7,6] => 1
[1,2,5,3,6,4,7] => 1
[1,2,5,3,6,7,4] => 1
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 2
[1,2,5,4,3,6,7] => 1
[1,2,5,4,3,7,6] => 1
[1,2,5,4,6,3,7] => 1
[1,2,5,4,6,7,3] => 1
[1,2,5,4,7,3,6] => 2
[1,2,5,4,7,6,3] => 2
[1,2,5,6,3,4,7] => 1
[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] => 1
[1,2,5,6,7,4,3] => 1
[1,2,5,7,3,4,6] => 2
[1,2,5,7,3,6,4] => 2
[1,2,5,7,4,3,6] => 2
[1,2,5,7,4,6,3] => 2
[1,2,5,7,6,3,4] => 2
[1,2,5,7,6,4,3] => 2
[1,2,6,3,4,5,7] => 1
[1,2,6,3,4,7,5] => 1
[1,2,6,3,5,4,7] => 1
[1,2,6,3,5,7,4] => 2
[1,2,6,3,7,4,5] => 1
[1,2,6,3,7,5,4] => 2
[1,2,6,4,3,5,7] => 2
[1,2,6,4,3,7,5] => 2
[1,2,6,4,5,3,7] => 2
[1,2,6,4,5,7,3] => 2
[1,2,6,4,7,3,5] => 2
[1,2,6,4,7,5,3] => 2
[1,2,6,5,3,4,7] => 1
[1,2,6,5,3,7,4] => 2
[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] => 1
[1,2,6,7,3,4,5] => 1
[1,2,6,7,3,5,4] => 2
[1,2,6,7,4,3,5] => 2
[1,2,6,7,4,5,3] => 2
[1,2,6,7,5,3,4] => 2
[1,2,6,7,5,4,3] => 1
[1,2,7,3,4,5,6] => 1
[1,2,7,3,4,6,5] => 1
[1,2,7,3,5,4,6] => 2
[1,2,7,3,5,6,4] => 2
[1,2,7,3,6,4,5] => 1
[1,2,7,3,6,5,4] => 1
[1,2,7,4,3,5,6] => 2
[1,2,7,4,3,6,5] => 2
[1,2,7,4,5,3,6] => 2
[1,2,7,4,5,6,3] => 2
[1,2,7,4,6,3,5] => 2
[1,2,7,4,6,5,3] => 2
[1,2,7,5,3,4,6] => 2
[1,2,7,5,3,6,4] => 2
[1,2,7,5,4,3,6] => 2
[1,2,7,5,4,6,3] => 2
[1,2,7,5,6,3,4] => 2
[1,2,7,5,6,4,3] => 2
[1,2,7,6,3,4,5] => 1
[1,2,7,6,3,5,4] => 1
[1,2,7,6,4,3,5] => 2
[1,2,7,6,4,5,3] => 2
[1,2,7,6,5,3,4] => 1
[1,2,7,6,5,4,3] => 1
[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] => 2
[1,3,2,5,4,6,7] => 1
[1,3,2,5,4,7,6] => 2
[1,3,2,5,6,4,7] => 1
[1,3,2,5,6,7,4] => 1
[1,3,2,5,7,4,6] => 2
[1,3,2,5,7,6,4] => 2
[1,3,2,6,4,5,7] => 2
[1,3,2,6,4,7,5] => 2
[1,3,2,6,5,4,7] => 1
[1,3,2,6,5,7,4] => 2
[1,3,2,6,7,4,5] => 2
[1,3,2,6,7,5,4] => 2
[1,3,2,7,4,5,6] => 2
[1,3,2,7,4,6,5] => 2
[1,3,2,7,5,4,6] => 2
[1,3,2,7,5,6,4] => 2
[1,3,2,7,6,4,5] => 2
[1,3,2,7,6,5,4] => 1
[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] => 2
[1,3,4,5,2,6,7] => 1
[1,3,4,5,2,7,6] => 2
[1,3,4,5,6,2,7] => 1
[1,3,4,5,6,7,2] => 1
[1,3,4,5,7,2,6] => 2
[1,3,4,5,7,6,2] => 2
[1,3,4,6,2,5,7] => 2
[1,3,4,6,2,7,5] => 2
[1,3,4,6,5,2,7] => 2
[1,3,4,6,5,7,2] => 2
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 2
[1,3,4,7,2,6,5] => 2
[1,3,4,7,5,2,6] => 2
[1,3,4,7,5,6,2] => 2
[1,3,4,7,6,2,5] => 2
[1,3,4,7,6,5,2] => 2
[1,3,5,2,4,6,7] => 2
[1,3,5,2,4,7,6] => 2
[1,3,5,2,6,4,7] => 2
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 2
[1,3,5,4,2,7,6] => 2
[1,3,5,4,6,2,7] => 2
[1,3,5,4,6,7,2] => 2
[1,3,5,4,7,2,6] => 2
[1,3,5,4,7,6,2] => 2
[1,3,5,6,2,4,7] => 2
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 2
[1,3,5,6,4,7,2] => 2
[1,3,5,6,7,2,4] => 2
[1,3,5,6,7,4,2] => 2
[1,3,5,7,2,4,6] => 3
[1,3,5,7,2,6,4] => 3
[1,3,5,7,4,2,6] => 3
[1,3,5,7,4,6,2] => 3
[1,3,5,7,6,2,4] => 3
[1,3,5,7,6,4,2] => 3
[1,3,6,2,4,5,7] => 2
[1,3,6,2,4,7,5] => 2
[1,3,6,2,5,4,7] => 2
[1,3,6,2,5,7,4] => 2
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 2
[1,3,6,4,2,5,7] => 2
[1,3,6,4,2,7,5] => 2
[1,3,6,4,5,2,7] => 2
[1,3,6,4,5,7,2] => 2
[1,3,6,4,7,2,5] => 2
[1,3,6,4,7,5,2] => 2
[1,3,6,5,2,4,7] => 2
[1,3,6,5,2,7,4] => 2
[1,3,6,5,4,2,7] => 2
[1,3,6,5,4,7,2] => 2
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 2
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 2
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 2
[1,3,6,7,5,2,4] => 2
[1,3,6,7,5,4,2] => 2
[1,3,7,2,4,5,6] => 2
[1,3,7,2,4,6,5] => 2
[1,3,7,2,5,4,6] => 2
[1,3,7,2,5,6,4] => 2
[1,3,7,2,6,4,5] => 2
[1,3,7,2,6,5,4] => 2
[1,3,7,4,2,5,6] => 2
[1,3,7,4,2,6,5] => 2
[1,3,7,4,5,2,6] => 2
[1,3,7,4,5,6,2] => 2
[1,3,7,4,6,2,5] => 2
[1,3,7,4,6,5,2] => 2
[1,3,7,5,2,4,6] => 3
[1,3,7,5,2,6,4] => 3
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 3
[1,3,7,6,2,4,5] => 2
[1,3,7,6,2,5,4] => 2
[1,3,7,6,4,2,5] => 2
[1,3,7,6,4,5,2] => 2
[1,3,7,6,5,2,4] => 2
[1,3,7,6,5,4,2] => 2
[1,4,2,3,5,6,7] => 1
[1,4,2,3,5,7,6] => 2
[1,4,2,3,6,5,7] => 1
[1,4,2,3,6,7,5] => 1
[1,4,2,3,7,5,6] => 2
[1,4,2,3,7,6,5] => 1
[1,4,2,5,3,6,7] => 1
[1,4,2,5,3,7,6] => 2
[1,4,2,5,6,3,7] => 1
[1,4,2,5,6,7,3] => 1
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 2
[1,4,2,6,3,5,7] => 2
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 2
[1,4,2,6,5,7,3] => 2
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 2
[1,4,2,7,3,5,6] => 2
[1,4,2,7,3,6,5] => 2
[1,4,2,7,5,3,6] => 2
[1,4,2,7,5,6,3] => 2
[1,4,2,7,6,3,5] => 2
[1,4,2,7,6,5,3] => 2
[1,4,3,2,5,6,7] => 1
[1,4,3,2,5,7,6] => 2
[1,4,3,2,6,5,7] => 1
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 2
[1,4,3,2,7,6,5] => 1
[1,4,3,5,2,6,7] => 1
[1,4,3,5,2,7,6] => 2
[1,4,3,5,6,2,7] => 1
[1,4,3,5,6,7,2] => 1
[1,4,3,5,7,2,6] => 2
[1,4,3,5,7,6,2] => 2
[1,4,3,6,2,5,7] => 2
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 2
[1,4,3,6,5,7,2] => 2
[1,4,3,6,7,2,5] => 2
[1,4,3,6,7,5,2] => 2
[1,4,3,7,2,5,6] => 2
[1,4,3,7,2,6,5] => 2
[1,4,3,7,5,2,6] => 2
[1,4,3,7,5,6,2] => 2
[1,4,3,7,6,2,5] => 2
[1,4,3,7,6,5,2] => 2
[1,4,5,2,3,6,7] => 1
[1,4,5,2,3,7,6] => 2
[1,4,5,2,6,3,7] => 1
[1,4,5,2,6,7,3] => 1
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 2
[1,4,5,3,2,6,7] => 1
[1,4,5,3,2,7,6] => 2
[1,4,5,3,6,2,7] => 1
[1,4,5,3,6,7,2] => 1
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 2
[1,4,5,6,2,3,7] => 1
[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] => 1
[1,4,5,6,7,3,2] => 1
[1,4,5,7,2,3,6] => 2
[1,4,5,7,2,6,3] => 2
[1,4,5,7,3,2,6] => 2
[1,4,5,7,3,6,2] => 2
[1,4,5,7,6,2,3] => 2
[1,4,5,7,6,3,2] => 2
[1,4,6,2,3,5,7] => 2
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 2
[1,4,6,2,5,7,3] => 2
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 2
[1,4,6,3,2,5,7] => 2
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 2
[1,4,6,3,5,7,2] => 2
[1,4,6,3,7,2,5] => 2
[1,4,6,3,7,5,2] => 2
[1,4,6,5,2,3,7] => 2
[1,4,6,5,2,7,3] => 2
[1,4,6,5,3,2,7] => 2
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Description
The holeyness of a permutation.
For $S\subset [n]:=\{1,2,\dots,n\}$ let $\delta(S)$ be the number of elements $m\in S$ such that $m+1\notin S$.
For a permutation $\pi$ of $[n]$ the holeyness of $\pi$ is $$\max_{S\subset [n]} (\delta(\pi(S))-\delta(S)).$$
References
[1] Helfgott, H. A. How rare are unholey permutations? MathOverflow:340179
Code
def delta(S): return sum(1 for m in S if m + 1 not in S)

def statistic(pi):
    n = len(pi)
    m = 0
    for S in subsets(range(1, n+1)):
        h_pi = delta([pi(s) for s in S])
        h_S = delta(S)
        m = max(m, h_pi-h_S)

    return m
Created
Sep 09, 2019 at 07:41 by Martin Rubey
Updated
Sep 09, 2019 at 07:41 by Martin Rubey