edit this statistic or download as text // json
Identifier
Values
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 3
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 3
[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] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 3
[1,2,5,4,3] => 3
[1,3,2,4,5] => 3
[1,3,2,5,4] => 4
[1,3,4,2,5] => 3
[1,3,4,5,2] => 4
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 4
[1,4,3,2,5] => 3
[1,4,3,5,2] => 3
[1,4,5,2,3] => 3
[1,4,5,3,2] => 3
[1,5,2,3,4] => 3
[1,5,2,4,3] => 4
[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] => 4
[2,1,3,5,4] => 3
[2,1,4,3,5] => 4
[2,1,4,5,3] => 3
[2,1,5,3,4] => 3
[2,1,5,4,3] => 3
[2,3,1,4,5] => 3
[2,3,1,5,4] => 3
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 3
[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] => 3
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 4
[3,1,2,4,5] => 4
[3,1,2,5,4] => 3
[3,1,4,2,5] => 4
[3,1,4,5,2] => 3
[3,1,5,2,4] => 3
[3,1,5,4,2] => 3
[3,2,1,4,5] => 3
[3,2,1,5,4] => 3
[3,2,4,1,5] => 4
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 3
[3,4,1,2,5] => 3
[3,4,1,5,2] => 3
[3,4,2,1,5] => 3
[3,4,2,5,1] => 4
[3,4,5,1,2] => 3
[3,4,5,2,1] => 3
[3,5,1,2,4] => 3
[3,5,1,4,2] => 3
[3,5,2,1,4] => 3
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 4
[3,5,4,1,2] => 3
[3,5,4,2,1] => 4
[4,1,2,3,5] => 4
[4,1,2,5,3] => 3
[4,1,3,2,5] => 3
[4,1,3,5,2] => 3
[4,1,5,2,3] => 3
[4,1,5,3,2] => 3
[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] => 3
[4,3,1,2,5] => 3
[4,3,1,5,2] => 3
[4,3,2,1,5] => 4
[4,3,2,5,1] => 3
[4,3,5,1,2] => 3
[4,3,5,2,1] => 3
[4,5,1,2,3] => 3
[4,5,1,3,2] => 3
[4,5,2,1,3] => 3
[4,5,2,3,1] => 4
[4,5,3,1,2] => 3
[4,5,3,2,1] => 4
[5,1,2,3,4] => 4
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 3
[5,1,4,2,3] => 4
[5,1,4,3,2] => 3
[5,2,1,3,4] => 3
[5,2,1,4,3] => 3
[5,2,3,1,4] => 3
[5,2,3,4,1] => 3
[5,2,4,1,3] => 4
[5,2,4,3,1] => 3
[5,3,1,2,4] => 3
[5,3,1,4,2] => 3
[5,3,2,1,4] => 4
[5,3,2,4,1] => 3
[5,3,4,1,2] => 4
[5,3,4,2,1] => 3
[5,4,1,2,3] => 3
[5,4,1,3,2] => 3
[5,4,2,1,3] => 4
[5,4,2,3,1] => 3
[5,4,3,1,2] => 4
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 4
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 4
[1,2,5,4,3,6] => 3
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 4
[1,2,6,3,5,4] => 4
[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] => 4
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 5
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 4
[1,3,2,6,5,4] => 4
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 4
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 4
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 4
[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] => 4
[1,3,5,6,4,2] => 4
[1,3,6,2,4,5] => 4
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 3
[1,4,2,6,3,5] => 4
[1,4,2,6,5,3] => 4
[1,4,3,2,5,6] => 3
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 4
[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] => 4
[1,4,5,2,6,3] => 3
[1,4,5,3,2,6] => 3
[1,4,5,3,6,2] => 4
[1,4,5,6,2,3] => 4
[1,4,5,6,3,2] => 4
[1,4,6,2,3,5] => 4
[1,4,6,2,5,3] => 3
[1,4,6,3,2,5] => 3
[1,4,6,3,5,2] => 4
[1,4,6,5,2,3] => 3
[1,4,6,5,3,2] => 4
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 4
[1,5,2,4,3,6] => 4
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 4
[1,5,2,6,4,3] => 4
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 4
[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] => 4
[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] => 3
[1,5,4,6,2,3] => 3
[1,5,4,6,3,2] => 3
[1,5,6,2,3,4] => 4
[1,5,6,2,4,3] => 3
[1,5,6,3,2,4] => 3
[1,5,6,3,4,2] => 4
[1,5,6,4,2,3] => 3
[1,5,6,4,3,2] => 4
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 3
[1,6,2,5,3,4] => 5
[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] => 3
[1,6,3,5,2,4] => 4
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 4
[1,6,4,3,2,5] => 4
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 3
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 4
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 4
[1,6,5,4,3,2] => 5
[2,1,3,4,5,6] => 5
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 4
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 5
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 3
[2,1,4,6,5,3] => 3
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 3
[2,1,5,6,4,3] => 3
[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] => 3
[2,1,6,5,3,4] => 3
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 3
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 4
[2,3,4,1,6,5] => 3
[2,3,4,5,1,6] => 4
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 4
[2,3,5,1,6,4] => 3
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 3
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 4
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 3
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 4
[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] => 4
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 4
[2,4,5,1,6,3] => 3
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 3
[2,4,6,3,1,5] => 3
[2,4,6,3,5,1] => 4
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 3
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 4
[2,5,1,6,3,4] => 3
[2,5,1,6,4,3] => 3
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 4
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 3
[2,5,4,1,6,3] => 4
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 3
[2,5,4,6,1,3] => 3
[2,5,4,6,3,1] => 3
[2,5,6,1,3,4] => 4
[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] => 3
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 4
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 4
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 4
[2,6,3,5,4,1] => 4
[2,6,4,1,3,5] => 3
[2,6,4,1,5,3] => 4
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 4
[2,6,4,5,3,1] => 3
[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] => 3
[2,6,5,4,1,3] => 4
[2,6,5,4,3,1] => 5
[3,1,2,4,5,6] => 5
[3,1,2,4,6,5] => 4
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 3
[3,1,4,6,5,2] => 3
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 5
[3,1,5,4,2,6] => 4
[3,1,5,4,6,2] => 4
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 3
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 4
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 3
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 4
[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] => 4
[3,2,4,1,6,5] => 4
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 4
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 4
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 4
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 3
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 4
[3,2,6,4,5,1] => 3
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 4
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 3
[3,4,1,5,2,6] => 4
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 3
[3,4,2,5,1,6] => 5
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 4
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 4
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 4
[3,4,6,1,2,5] => 4
[3,4,6,1,5,2] => 3
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 4
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 4
[3,5,1,2,4,6] => 4
[3,5,1,2,6,4] => 3
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 4
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 3
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 3
[3,5,2,4,1,6] => 4
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 4
[3,5,2,6,4,1] => 3
[3,5,4,1,2,6] => 3
[3,5,4,1,6,2] => 4
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 3
[3,5,4,6,1,2] => 3
[3,5,4,6,2,1] => 3
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 3
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 4
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 3
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 4
[3,6,1,5,4,2] => 3
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 3
[3,6,2,4,1,5] => 4
[3,6,2,4,5,1] => 4
[3,6,2,5,1,4] => 5
[3,6,2,5,4,1] => 3
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 4
[3,6,4,2,1,5] => 4
[3,6,4,2,5,1] => 3
[3,6,4,5,1,2] => 4
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 3
[3,6,5,1,4,2] => 4
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 3
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 5
[4,1,2,3,5,6] => 5
[4,1,2,3,6,5] => 4
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 4
[4,1,2,6,5,3] => 3
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 4
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 4
[4,1,3,6,5,2] => 3
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 5
[4,1,5,3,2,6] => 4
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 3
[4,1,6,2,3,5] => 3
[4,1,6,2,5,3] => 4
[4,1,6,3,2,5] => 4
[4,1,6,3,5,2] => 3
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 4
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 3
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 3
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 4
[4,2,5,3,1,6] => 4
[4,2,5,3,6,1] => 4
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 3
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 4
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 3
[4,2,6,5,3,1] => 4
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 3
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 3
[4,3,1,6,5,2] => 4
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 3
[4,3,2,6,1,5] => 3
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 4
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 3
[4,3,5,6,2,1] => 3
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 3
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 4
[4,3,6,5,1,2] => 3
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 4
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 3
[4,5,1,3,6,2] => 4
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 3
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 3
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 4
[4,5,2,6,1,3] => 4
[4,5,2,6,3,1] => 3
[4,5,3,1,2,6] => 3
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 4
[4,5,3,2,6,1] => 4
[4,5,3,6,1,2] => 4
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 4
[4,5,6,1,3,2] => 3
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 3
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 4
[4,6,1,5,2,3] => 4
[4,6,1,5,3,2] => 3
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 3
[4,6,2,3,1,5] => 4
[4,6,2,3,5,1] => 4
[4,6,2,5,1,3] => 5
[4,6,2,5,3,1] => 3
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 3
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 4
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 5
[5,1,2,3,4,6] => 5
[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] => 4
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 4
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 4
[5,1,3,6,4,2] => 3
[5,1,4,2,3,6] => 4
[5,1,4,2,6,3] => 4
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 3
[5,1,4,6,2,3] => 4
[5,1,4,6,3,2] => 3
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 4
[5,1,6,3,2,4] => 4
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 3
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 3
[5,2,1,6,3,4] => 3
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 4
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 4
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 4
[5,2,4,6,3,1] => 3
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 3
[5,2,6,3,1,4] => 4
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 4
[5,3,1,4,6,2] => 3
[5,3,1,6,2,4] => 3
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 4
[5,3,2,1,6,4] => 4
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 3
[5,3,2,6,1,4] => 3
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 4
[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] => 4
[5,3,4,6,2,1] => 3
[5,3,6,1,2,4] => 3
[5,3,6,1,4,2] => 3
[5,3,6,2,1,4] => 4
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 3
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 4
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 3
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 4
[5,4,2,1,3,6] => 4
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 3
[5,4,2,6,1,3] => 3
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 4
[5,4,3,1,6,2] => 4
[5,4,3,2,1,6] => 5
[5,4,3,2,6,1] => 4
[5,4,3,6,1,2] => 3
[5,4,3,6,2,1] => 4
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 3
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 3
[5,4,6,3,2,1] => 4
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 3
[5,6,1,3,2,4] => 3
[5,6,1,3,4,2] => 4
[5,6,1,4,2,3] => 4
[5,6,1,4,3,2] => 3
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 3
[5,6,2,3,1,4] => 4
[5,6,2,3,4,1] => 4
[5,6,2,4,1,3] => 4
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 3
[5,6,3,2,1,4] => 4
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 5
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 4
[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] => 5
[6,1,2,3,5,4] => 4
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 4
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 4
[6,1,3,5,2,4] => 4
[6,1,3,5,4,2] => 3
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 4
[6,1,4,3,2,5] => 3
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 3
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 5
[6,1,5,3,2,4] => 3
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 4
[6,1,5,4,3,2] => 4
[6,2,1,3,4,5] => 4
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 3
[6,2,1,5,3,4] => 3
[6,2,1,5,4,3] => 4
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 4
[6,2,3,5,1,4] => 4
[6,2,3,5,4,1] => 3
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 3
[6,2,4,5,1,3] => 4
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 4
[6,2,5,1,4,3] => 4
[6,2,5,3,1,4] => 3
[6,2,5,3,4,1] => 4
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 4
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 3
[6,3,1,5,4,2] => 4
[6,3,2,1,4,5] => 4
[6,3,2,1,5,4] => 4
[6,3,2,4,1,5] => 4
[6,3,2,4,5,1] => 3
[6,3,2,5,1,4] => 3
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 3
[6,3,4,2,1,5] => 3
[6,3,4,2,5,1] => 4
[6,3,4,5,1,2] => 4
[6,3,4,5,2,1] => 3
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 3
[6,3,5,2,4,1] => 5
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 4
[6,4,1,2,3,5] => 4
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 3
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 4
[6,4,2,1,3,5] => 4
[6,4,2,1,5,3] => 4
[6,4,2,3,1,5] => 3
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 3
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 4
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 4
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 4
[6,4,5,2,1,3] => 3
[6,4,5,2,3,1] => 5
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 4
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 4
[6,5,1,4,3,2] => 4
[6,5,2,1,3,4] => 4
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 3
[6,5,2,4,1,3] => 4
[6,5,2,4,3,1] => 4
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 5
[6,5,3,2,4,1] => 4
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 4
[6,5,4,2,1,3] => 5
[6,5,4,2,3,1] => 4
[6,5,4,3,1,2] => 5
[6,5,4,3,2,1] => 6
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 5
[1,2,3,4,6,7,5] => 6
[1,2,3,4,7,5,6] => 5
[1,2,3,4,7,6,5] => 5
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 4
[1,2,3,5,6,4,7] => 5
[1,2,3,5,6,7,4] => 6
[1,2,3,5,7,4,6] => 5
[1,2,3,5,7,6,4] => 5
[1,2,3,6,4,5,7] => 4
[1,2,3,6,4,7,5] => 4
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 4
[1,2,3,6,7,4,5] => 5
[1,2,3,6,7,5,4] => 5
[1,2,3,7,4,5,6] => 4
[1,2,3,7,4,6,5] => 4
[1,2,3,7,5,4,6] => 4
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 4
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 5
[1,2,4,3,6,5,7] => 5
[1,2,4,3,6,7,5] => 4
[1,2,4,3,7,5,6] => 4
[1,2,4,3,7,6,5] => 4
[1,2,4,5,3,6,7] => 4
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 5
[1,2,4,5,6,7,3] => 6
[1,2,4,5,7,3,6] => 5
[1,2,4,5,7,6,3] => 5
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 4
[1,2,4,6,5,3,7] => 4
[1,2,4,6,5,7,3] => 4
[1,2,4,6,7,3,5] => 5
[1,2,4,6,7,5,3] => 5
[1,2,4,7,3,5,6] => 4
[1,2,4,7,3,6,5] => 4
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 4
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 5
[1,2,5,3,6,4,7] => 5
[1,2,5,3,6,7,4] => 4
[1,2,5,3,7,4,6] => 4
[1,2,5,3,7,6,4] => 4
[1,2,5,4,3,6,7] => 4
[1,2,5,4,3,7,6] => 4
[1,2,5,4,6,3,7] => 4
[1,2,5,4,6,7,3] => 4
[1,2,5,4,7,3,6] => 3
[1,2,5,4,7,6,3] => 4
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 4
[1,2,5,6,4,3,7] => 4
[1,2,5,6,4,7,3] => 4
[1,2,5,6,7,3,4] => 5
[1,2,5,6,7,4,3] => 5
[1,2,5,7,3,4,6] => 4
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 4
[1,2,5,7,6,3,4] => 4
[1,2,5,7,6,4,3] => 4
[1,2,6,3,4,5,7] => 4
[1,2,6,3,4,7,5] => 5
[1,2,6,3,5,4,7] => 4
[1,2,6,3,5,7,4] => 4
[1,2,6,3,7,4,5] => 4
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 4
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 3
[1,2,6,4,5,7,3] => 4
[1,2,6,4,7,3,5] => 3
[1,2,6,4,7,5,3] => 4
[1,2,6,5,3,4,7] => 4
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 3
[1,2,6,5,7,3,4] => 3
[1,2,6,5,7,4,3] => 3
[1,2,6,7,3,4,5] => 4
[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] => 4
[1,2,7,3,4,5,6] => 4
[1,2,7,3,4,6,5] => 5
[1,2,7,3,5,4,6] => 4
[1,2,7,3,5,6,4] => 4
[1,2,7,3,6,4,5] => 5
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 4
[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] => 4
[1,2,7,4,6,5,3] => 4
[1,2,7,5,3,4,6] => 4
[1,2,7,5,3,6,4] => 4
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 3
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 3
[1,2,7,6,3,4,5] => 4
[1,2,7,6,3,5,4] => 4
[1,2,7,6,4,3,5] => 4
[1,2,7,6,4,5,3] => 3
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 5
[1,3,2,4,5,6,7] => 5
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 5
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 4
[1,3,2,5,4,6,7] => 5
[1,3,2,5,4,7,6] => 6
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 4
[1,3,2,5,7,4,6] => 3
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 5
[1,3,2,6,5,4,7] => 4
[1,3,2,6,5,7,4] => 5
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 4
[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] => 4
[1,3,4,2,5,6,7] => 4
[1,3,4,2,5,7,6] => 4
[1,3,4,2,6,5,7] => 4
[1,3,4,2,6,7,5] => 5
[1,3,4,2,7,5,6] => 3
[1,3,4,2,7,6,5] => 3
[1,3,4,5,2,6,7] => 4
[1,3,4,5,2,7,6] => 4
[1,3,4,5,6,2,7] => 5
[1,3,4,5,6,7,2] => 6
[1,3,4,5,7,2,6] => 5
[1,3,4,5,7,6,2] => 5
[1,3,4,6,2,5,7] => 4
[1,3,4,6,2,7,5] => 4
[1,3,4,6,5,2,7] => 4
[1,3,4,6,5,7,2] => 4
[1,3,4,6,7,2,5] => 5
[1,3,4,6,7,5,2] => 5
[1,3,4,7,2,5,6] => 4
[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] => 4
[1,3,5,2,4,6,7] => 4
[1,3,5,2,4,7,6] => 4
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 5
[1,3,5,2,7,4,6] => 3
[1,3,5,2,7,6,4] => 3
[1,3,5,4,2,6,7] => 4
[1,3,5,4,2,7,6] => 4
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 3
[1,3,5,4,7,6,2] => 4
[1,3,5,6,2,4,7] => 4
[1,3,5,6,2,7,4] => 4
[1,3,5,6,4,2,7] => 4
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 5
[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] => 4
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 4
[1,3,6,2,5,4,7] => 3
[1,3,6,2,5,7,4] => 5
[1,3,6,2,7,4,5] => 3
[1,3,6,2,7,5,4] => 3
[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] => 4
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 4
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 3
[1,3,6,5,7,2,4] => 3
[1,3,6,5,7,4,2] => 3
[1,3,6,7,2,4,5] => 4
[1,3,6,7,2,5,4] => 4
[1,3,6,7,4,2,5] => 4
[1,3,6,7,4,5,2] => 4
[1,3,6,7,5,2,4] => 4
[1,3,6,7,5,4,2] => 4
[1,3,7,2,4,5,6] => 4
[1,3,7,2,4,6,5] => 4
[1,3,7,2,5,4,6] => 3
[1,3,7,2,5,6,4] => 5
[1,3,7,2,6,4,5] => 4
[1,3,7,2,6,5,4] => 3
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 4
[1,3,7,4,5,2,6] => 3
[1,3,7,4,5,6,2] => 4
[1,3,7,4,6,2,5] => 4
[1,3,7,4,6,5,2] => 4
[1,3,7,5,2,4,6] => 4
[1,3,7,5,2,6,4] => 4
[1,3,7,5,4,2,6] => 4
[1,3,7,5,4,6,2] => 3
[1,3,7,5,6,2,4] => 4
[1,3,7,5,6,4,2] => 3
[1,3,7,6,2,4,5] => 4
[1,3,7,6,2,5,4] => 4
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 3
[1,3,7,6,5,2,4] => 4
[1,3,7,6,5,4,2] => 5
[1,4,2,3,5,6,7] => 5
[1,4,2,3,5,7,6] => 4
[1,4,2,3,6,5,7] => 4
[1,4,2,3,6,7,5] => 4
[1,4,2,3,7,5,6] => 5
[1,4,2,3,7,6,5] => 4
[1,4,2,5,3,6,7] => 5
[1,4,2,5,3,7,6] => 5
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 4
[1,4,2,5,7,3,6] => 3
[1,4,2,5,7,6,3] => 4
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 6
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 5
[1,4,2,6,7,3,5] => 3
[1,4,2,6,7,5,3] => 3
[1,4,2,7,3,5,6] => 4
[1,4,2,7,3,6,5] => 4
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 4
[1,4,2,7,6,3,5] => 4
[1,4,2,7,6,5,3] => 4
[1,4,3,2,5,6,7] => 4
[1,4,3,2,5,7,6] => 4
[1,4,3,2,6,5,7] => 4
[1,4,3,2,6,7,5] => 3
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 5
[1,4,3,5,2,6,7] => 4
[1,4,3,5,2,7,6] => 4
[1,4,3,5,6,2,7] => 4
[1,4,3,5,6,7,2] => 4
[1,4,3,5,7,2,6] => 3
[1,4,3,5,7,6,2] => 4
[1,4,3,6,2,5,7] => 3
[1,4,3,6,2,7,5] => 4
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 5
[1,4,3,6,7,2,5] => 3
[1,4,3,6,7,5,2] => 3
[1,4,3,7,2,5,6] => 3
[1,4,3,7,2,6,5] => 4
[1,4,3,7,5,2,6] => 4
[1,4,3,7,5,6,2] => 4
[1,4,3,7,6,2,5] => 4
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 4
[1,4,5,2,6,3,7] => 4
[1,4,5,2,6,7,3] => 5
[1,4,5,2,7,3,6] => 3
[1,4,5,2,7,6,3] => 3
[1,4,5,3,2,6,7] => 4
[1,4,5,3,2,7,6] => 3
[1,4,5,3,6,2,7] => 5
[1,4,5,3,6,7,2] => 4
[1,4,5,3,7,2,6] => 4
[1,4,5,3,7,6,2] => 3
[1,4,5,6,2,3,7] => 4
[1,4,5,6,2,7,3] => 4
[1,4,5,6,3,2,7] => 4
[1,4,5,6,3,7,2] => 4
[1,4,5,6,7,2,3] => 5
[1,4,5,6,7,3,2] => 5
[1,4,5,7,2,3,6] => 4
[1,4,5,7,2,6,3] => 4
[1,4,5,7,3,2,6] => 4
[1,4,5,7,3,6,2] => 4
[1,4,5,7,6,2,3] => 4
[1,4,5,7,6,3,2] => 4
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 4
[1,4,6,2,5,3,7] => 3
[1,4,6,2,5,7,3] => 5
[1,4,6,2,7,3,5] => 3
[1,4,6,2,7,5,3] => 3
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 3
[1,4,6,3,5,2,7] => 4
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 4
[1,4,6,3,7,5,2] => 3
[1,4,6,5,2,3,7] => 4
[1,4,6,5,2,7,3] => 4
[1,4,6,5,3,2,7] => 4
[1,4,6,5,3,7,2] => 3
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The minimal number with no two order isomorphic substrings of this length in a permutation.
For example, the length $3$ substrings of the permutation $12435$ are $124$, $243$ and $435$, whereas its length $2$ substrings are $12$, $24$, $43$ and $35$.
No two sequences among $124$, $243$ and $435$ are order isomorphic, but $12$ and $24$ are, so the statistic on $12435$ is $3$.
This is inspired by St000922The minimal number such that all substrings of this length are unique..
Code
def statistic(w):
    from sage.combinat.permutation import to_standard
    for k in range(1,len(w)+1):
        S = []
        for i in range(len(w)-k+1):
            s = to_standard(w[i:i+k])
            if s in S:
                break
            else:
                S.append(s)
        else:
            return k
Created
Aug 03, 2017 at 00:22 by Martin Rubey
Updated
Aug 03, 2017 at 08:49 by Martin Rubey