edit this statistic or download as text // json
Identifier
Values
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 3
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 4
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 3
[1,4,3,2] => 4
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 3
[2,3,4,1] => 4
[2,4,1,3] => 4
[2,4,3,1] => 4
[3,1,2,4] => 4
[3,1,4,2] => 4
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 4
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 4
[4,2,3,1] => 3
[4,3,1,2] => 2
[4,3,2,1] => 4
[1,2,3,4,5] => 5
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 5
[1,2,5,3,4] => 4
[1,2,5,4,3] => 5
[1,3,2,4,5] => 3
[1,3,2,5,4] => 3
[1,3,4,2,5] => 4
[1,3,4,5,2] => 5
[1,3,5,2,4] => 5
[1,3,5,4,2] => 5
[1,4,2,3,5] => 5
[1,4,2,5,3] => 5
[1,4,3,2,5] => 4
[1,4,3,5,2] => 4
[1,4,5,2,3] => 3
[1,4,5,3,2] => 5
[1,5,2,3,4] => 4
[1,5,2,4,3] => 4
[1,5,3,2,4] => 5
[1,5,3,4,2] => 4
[1,5,4,2,3] => 3
[1,5,4,3,2] => 5
[2,1,3,4,5] => 2
[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] => 2
[2,3,1,4,5] => 3
[2,3,1,5,4] => 3
[2,3,4,1,5] => 4
[2,3,4,5,1] => 5
[2,3,5,1,4] => 5
[2,3,5,4,1] => 5
[2,4,1,3,5] => 4
[2,4,1,5,3] => 4
[2,4,3,1,5] => 4
[2,4,3,5,1] => 4
[2,4,5,1,3] => 5
[2,4,5,3,1] => 5
[2,5,1,3,4] => 5
[2,5,1,4,3] => 5
[2,5,3,1,4] => 5
[2,5,3,4,1] => 4
[2,5,4,1,3] => 5
[2,5,4,3,1] => 5
[3,1,2,4,5] => 5
[3,1,2,5,4] => 5
[3,1,4,2,5] => 4
[3,1,4,5,2] => 5
[3,1,5,2,4] => 4
[3,1,5,4,2] => 5
[3,2,1,4,5] => 3
[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] => 3
[3,4,1,2,5] => 5
[3,4,1,5,2] => 5
[3,4,2,1,5] => 4
[3,4,2,5,1] => 4
[3,4,5,1,2] => 2
[3,4,5,2,1] => 5
[3,5,1,2,4] => 4
[3,5,1,4,2] => 4
[3,5,2,1,4] => 5
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 5
[3,5,4,1,2] => 2
[3,5,4,2,1] => 5
[4,1,2,3,5] => 5
[4,1,2,5,3] => 5
[4,1,3,2,5] => 3
[4,1,3,5,2] => 5
[4,1,5,2,3] => 3
[4,1,5,3,2] => 5
[4,2,1,3,5] => 4
[4,2,1,5,3] => 4
[4,2,3,1,5] => 3
[4,2,3,5,1] => 5
[4,2,5,1,3] => 4
[4,2,5,3,1] => 5
[4,3,1,2,5] => 5
[4,3,1,5,2] => 5
[4,3,2,1,5] => 4
[4,3,2,5,1] => 4
[4,3,5,1,2] => 2
[4,3,5,2,1] => 4
[4,5,1,2,3] => 3
[4,5,1,3,2] => 3
[4,5,2,1,3] => 5
[4,5,2,3,1] => 3
[4,5,3,1,2] => 2
[4,5,3,2,1] => 5
[5,1,2,3,4] => 4
[5,1,2,4,3] => 4
[5,1,3,2,4] => 3
[5,1,3,4,2] => 4
[5,1,4,2,3] => 3
[5,1,4,3,2] => 4
[5,2,1,3,4] => 5
[5,2,1,4,3] => 5
[5,2,3,1,4] => 3
[5,2,3,4,1] => 4
[5,2,4,1,3] => 4
[5,2,4,3,1] => 4
[5,3,1,2,4] => 4
[5,3,1,4,2] => 4
[5,3,2,1,4] => 5
[5,3,2,4,1] => 5
[5,3,4,1,2] => 2
[5,3,4,2,1] => 4
[5,4,1,2,3] => 3
[5,4,1,3,2] => 3
[5,4,2,1,3] => 5
[5,4,2,3,1] => 3
[5,4,3,1,2] => 2
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 6
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 6
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 4
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 5
[1,2,4,5,6,3] => 6
[1,2,4,6,3,5] => 6
[1,2,4,6,5,3] => 6
[1,2,5,3,4,6] => 6
[1,2,5,3,6,4] => 6
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 5
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 6
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 5
[1,2,6,4,3,5] => 6
[1,2,6,4,5,3] => 5
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 3
[1,3,2,4,6,5] => 3
[1,3,2,5,4,6] => 3
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 4
[1,3,4,5,2,6] => 5
[1,3,4,5,6,2] => 6
[1,3,4,6,2,5] => 6
[1,3,4,6,5,2] => 6
[1,3,5,2,4,6] => 5
[1,3,5,2,6,4] => 5
[1,3,5,4,2,6] => 5
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 6
[1,3,5,6,4,2] => 6
[1,3,6,2,4,5] => 6
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 6
[1,3,6,5,4,2] => 6
[1,4,2,3,5,6] => 6
[1,4,2,3,6,5] => 6
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 6
[1,4,2,6,3,5] => 5
[1,4,2,6,5,3] => 6
[1,4,3,2,5,6] => 4
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 4
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 4
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 6
[1,4,5,2,6,3] => 6
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 6
[1,4,6,2,3,5] => 5
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 6
[1,4,6,5,2,3] => 3
[1,4,6,5,3,2] => 6
[1,5,2,3,4,6] => 6
[1,5,2,3,6,4] => 6
[1,5,2,4,3,6] => 4
[1,5,2,4,6,3] => 6
[1,5,2,6,3,4] => 4
[1,5,2,6,4,3] => 6
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 5
[1,5,3,4,2,6] => 4
[1,5,3,4,6,2] => 6
[1,5,3,6,2,4] => 5
[1,5,3,6,4,2] => 6
[1,5,4,2,3,6] => 6
[1,5,4,2,6,3] => 6
[1,5,4,3,2,6] => 5
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 3
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 4
[1,5,6,2,4,3] => 4
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 4
[1,5,6,4,2,3] => 3
[1,5,6,4,3,2] => 6
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 5
[1,6,2,4,3,5] => 4
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 4
[1,6,2,5,4,3] => 5
[1,6,3,2,4,5] => 6
[1,6,3,2,5,4] => 6
[1,6,3,4,2,5] => 4
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 5
[1,6,3,5,4,2] => 5
[1,6,4,2,3,5] => 5
[1,6,4,2,5,3] => 5
[1,6,4,3,2,5] => 6
[1,6,4,3,5,2] => 6
[1,6,4,5,2,3] => 3
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 4
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 6
[1,6,5,3,4,2] => 4
[1,6,5,4,2,3] => 3
[1,6,5,4,3,2] => 6
[2,1,3,4,5,6] => 2
[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] => 2
[2,1,4,3,6,5] => 2
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 2
[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] => 2
[2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 2
[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] => 2
[2,3,1,4,5,6] => 3
[2,3,1,4,6,5] => 3
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 3
[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] => 4
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 6
[2,3,4,6,1,5] => 6
[2,3,4,6,5,1] => 6
[2,3,5,1,4,6] => 5
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 5
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 6
[2,3,5,6,4,1] => 6
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 6
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 5
[2,3,6,5,1,4] => 6
[2,3,6,5,4,1] => 6
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 4
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 4
[2,4,3,1,5,6] => 4
[2,4,3,1,6,5] => 4
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 4
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 5
[2,4,5,1,6,3] => 5
[2,4,5,3,1,6] => 5
[2,4,5,3,6,1] => 5
[2,4,5,6,1,3] => 6
[2,4,5,6,3,1] => 6
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 6
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 6
[2,4,6,5,3,1] => 6
[2,5,1,3,4,6] => 5
[2,5,1,3,6,4] => 5
[2,5,1,4,3,6] => 5
[2,5,1,4,6,3] => 5
[2,5,1,6,3,4] => 5
[2,5,1,6,4,3] => 5
[2,5,3,1,4,6] => 5
[2,5,3,1,6,4] => 5
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 6
[2,5,3,6,1,4] => 5
[2,5,3,6,4,1] => 6
[2,5,4,1,3,6] => 5
[2,5,4,1,6,3] => 5
[2,5,4,3,1,6] => 5
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 5
[2,5,4,6,3,1] => 5
[2,5,6,1,3,4] => 6
[2,5,6,1,4,3] => 6
[2,5,6,3,1,4] => 6
[2,5,6,3,4,1] => 4
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 6
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 6
[2,6,1,4,3,5] => 6
[2,6,1,4,5,3] => 6
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 6
[2,6,3,1,4,5] => 6
[2,6,3,1,5,4] => 6
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 5
[2,6,3,5,1,4] => 5
[2,6,3,5,4,1] => 5
[2,6,4,1,3,5] => 6
[2,6,4,1,5,3] => 6
[2,6,4,3,1,5] => 6
[2,6,4,3,5,1] => 6
[2,6,4,5,1,3] => 5
[2,6,4,5,3,1] => 5
[2,6,5,1,3,4] => 6
[2,6,5,1,4,3] => 6
[2,6,5,3,1,4] => 6
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 6
[2,6,5,4,3,1] => 6
[3,1,2,4,5,6] => 6
[3,1,2,4,6,5] => 6
[3,1,2,5,4,6] => 5
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 6
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 5
[3,1,4,5,6,2] => 6
[3,1,4,6,2,5] => 6
[3,1,4,6,5,2] => 6
[3,1,5,2,4,6] => 6
[3,1,5,2,6,4] => 6
[3,1,5,4,2,6] => 5
[3,1,5,4,6,2] => 5
[3,1,5,6,2,4] => 4
[3,1,5,6,4,2] => 6
[3,1,6,2,4,5] => 5
[3,1,6,2,5,4] => 5
[3,1,6,4,2,5] => 6
[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] => 3
[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] => 3
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[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] => 3
[3,2,5,4,1,6] => 3
[3,2,5,4,6,1] => 3
[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] => 3
[3,2,6,4,5,1] => 3
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 3
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 6
[3,4,1,5,2,6] => 5
[3,4,1,5,6,2] => 6
[3,4,1,6,2,5] => 5
[3,4,1,6,5,2] => 6
[3,4,2,1,5,6] => 4
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 4
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 4
[3,4,5,1,2,6] => 6
[3,4,5,1,6,2] => 6
[3,4,5,2,1,6] => 5
[3,4,5,2,6,1] => 5
[3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => 6
[3,4,6,1,2,5] => 5
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 6
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 2
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 6
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 6
[3,5,1,6,2,4] => 4
[3,5,1,6,4,2] => 6
[3,5,2,1,4,6] => 5
[3,5,2,1,6,4] => 5
[3,5,2,4,1,6] => 5
[3,5,2,4,6,1] => 5
[3,5,2,6,1,4] => 5
[3,5,2,6,4,1] => 5
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 6
[3,5,4,2,1,6] => 5
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 2
[3,5,4,6,2,1] => 5
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 4
[3,5,6,2,1,4] => 6
[3,5,6,2,4,1] => 6
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 6
[3,6,1,2,4,5] => 5
[3,6,1,2,5,4] => 5
[3,6,1,4,2,5] => 4
[3,6,1,4,5,2] => 5
[3,6,1,5,2,4] => 4
[3,6,1,5,4,2] => 5
[3,6,2,1,4,5] => 6
[3,6,2,1,5,4] => 6
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 6
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 6
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 5
[3,6,4,2,1,5] => 6
[3,6,4,2,5,1] => 6
[3,6,4,5,1,2] => 2
[3,6,4,5,2,1] => 5
[3,6,5,1,2,4] => 4
[3,6,5,1,4,2] => 4
[3,6,5,2,1,4] => 6
[3,6,5,2,4,1] => 6
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 6
[4,1,2,3,5,6] => 6
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 5
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 6
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 5
[4,1,3,5,6,2] => 6
[4,1,3,6,2,5] => 6
[4,1,3,6,5,2] => 6
[4,1,5,2,3,6] => 6
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 5
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 6
[4,1,6,2,3,5] => 5
[4,1,6,2,5,3] => 5
[4,1,6,3,2,5] => 6
[4,1,6,3,5,2] => 5
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 6
[4,2,1,3,5,6] => 4
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 4
[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] => 5
[4,2,3,5,6,1] => 6
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 6
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 4
[4,2,5,3,1,6] => 5
[4,2,5,3,6,1] => 5
[4,2,5,6,1,3] => 4
[4,2,5,6,3,1] => 6
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 5
[4,2,6,5,1,3] => 4
[4,2,6,5,3,1] => 6
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 6
[4,3,1,5,2,6] => 5
[4,3,1,5,6,2] => 6
[4,3,1,6,2,5] => 5
[4,3,1,6,5,2] => 6
[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] => 4
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 6
[4,3,5,1,6,2] => 6
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 4
[4,3,5,6,1,2] => 2
[4,3,5,6,2,1] => 4
[4,3,6,1,2,5] => 5
[4,3,6,1,5,2] => 5
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 4
[4,3,6,5,1,2] => 2
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 6
[4,5,1,2,6,3] => 6
[4,5,1,3,2,6] => 3
[4,5,1,3,6,2] => 6
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 6
[4,5,2,1,3,6] => 5
[4,5,2,1,6,3] => 5
[4,5,2,3,1,6] => 3
[4,5,2,3,6,1] => 6
[4,5,2,6,1,3] => 5
[4,5,2,6,3,1] => 6
[4,5,3,1,2,6] => 6
[4,5,3,1,6,2] => 6
[4,5,3,2,1,6] => 5
[4,5,3,2,6,1] => 5
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 5
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 3
[4,5,6,2,1,3] => 6
[4,5,6,2,3,1] => 3
[4,5,6,3,1,2] => 2
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 5
[4,6,1,2,5,3] => 5
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 5
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 5
[4,6,2,1,3,5] => 6
[4,6,2,1,5,3] => 6
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 5
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 5
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 5
[4,6,3,2,1,5] => 6
[4,6,3,2,5,1] => 6
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 6
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 3
[4,6,5,2,1,3] => 6
[4,6,5,2,3,1] => 3
[4,6,5,3,1,2] => 2
[4,6,5,3,2,1] => 6
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 6
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 3
[5,1,3,4,2,6] => 4
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 6
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 4
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 6
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 4
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 4
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 6
[5,2,1,3,4,6] => 5
[5,2,1,3,6,4] => 5
[5,2,1,4,3,6] => 5
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 5
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 4
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 6
[5,2,4,1,3,6] => 4
[5,2,4,1,6,3] => 4
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 4
[5,2,4,6,1,3] => 6
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 5
[5,2,6,1,4,3] => 5
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 4
[5,2,6,4,1,3] => 6
[5,2,6,4,3,1] => 6
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 6
[5,3,1,4,2,6] => 4
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 4
[5,3,1,6,4,2] => 6
[5,3,2,1,4,6] => 5
[5,3,2,1,6,4] => 5
[5,3,2,4,1,6] => 5
[5,3,2,4,6,1] => 5
[5,3,2,6,1,4] => 5
[5,3,2,6,4,1] => 5
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 4
[5,3,4,6,1,2] => 2
[5,3,4,6,2,1] => 6
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 5
[5,3,6,2,4,1] => 5
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 6
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 6
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 6
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 6
[5,4,2,1,3,6] => 5
[5,4,2,1,6,3] => 5
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 6
[5,4,2,6,1,3] => 5
[5,4,2,6,3,1] => 6
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 6
[5,4,3,2,1,6] => 5
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => 5
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 3
[5,4,6,2,1,3] => 5
[5,4,6,2,3,1] => 3
[5,4,6,3,1,2] => 2
[5,4,6,3,2,1] => 5
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 4
[5,6,1,3,2,4] => 3
[5,6,1,3,4,2] => 4
[5,6,1,4,2,3] => 3
[5,6,1,4,3,2] => 4
[5,6,2,1,3,4] => 6
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 4
[5,6,2,4,1,3] => 4
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 4
[5,6,3,1,4,2] => 4
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 6
[5,6,3,4,1,2] => 2
[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] => 6
[5,6,4,2,3,1] => 3
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 6
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 5
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 5
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 5
[6,1,3,5,2,4] => 5
[6,1,3,5,4,2] => 5
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 5
[6,1,4,3,2,5] => 4
[6,1,4,3,5,2] => 4
[6,1,4,5,2,3] => 3
[6,1,4,5,3,2] => 5
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 4
[6,1,5,3,2,4] => 5
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 3
[6,1,5,4,3,2] => 5
[6,2,1,3,4,5] => 6
[6,2,1,3,5,4] => 6
[6,2,1,4,3,5] => 6
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 6
[6,2,1,5,4,3] => 6
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 4
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 5
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 4
[6,2,4,3,1,5] => 4
[6,2,4,3,5,1] => 4
[6,2,4,5,1,3] => 5
[6,2,4,5,3,1] => 5
[6,2,5,1,3,4] => 5
[6,2,5,1,4,3] => 5
[6,2,5,3,1,4] => 5
[6,2,5,3,4,1] => 4
[6,2,5,4,1,3] => 5
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 5
[6,3,1,2,5,4] => 5
[6,3,1,4,2,5] => 4
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 4
[6,3,1,5,4,2] => 5
[6,3,2,1,4,5] => 6
[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] => 6
[6,3,4,1,2,5] => 5
[6,3,4,1,5,2] => 5
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 4
[6,3,4,5,1,2] => 2
[6,3,4,5,2,1] => 5
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 5
[6,3,5,2,4,1] => 5
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 5
[6,4,1,2,3,5] => 5
[6,4,1,2,5,3] => 5
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 5
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 5
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 6
[6,4,2,3,1,5] => 3
[6,4,2,3,5,1] => 5
[6,4,2,5,1,3] => 6
[6,4,2,5,3,1] => 5
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 5
[6,4,3,2,1,5] => 6
[6,4,3,2,5,1] => 6
[6,4,3,5,1,2] => 2
[6,4,3,5,2,1] => 6
[6,4,5,1,2,3] => 3
[6,4,5,1,3,2] => 3
[6,4,5,2,1,3] => 5
[6,4,5,2,3,1] => 3
[6,4,5,3,1,2] => 2
[6,4,5,3,2,1] => 5
[6,5,1,2,3,4] => 4
[6,5,1,2,4,3] => 4
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 4
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 6
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 4
[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] => 6
[6,5,3,2,4,1] => 6
[6,5,3,4,1,2] => 2
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => 3
[6,5,4,2,1,3] => 6
[6,5,4,2,3,1] => 3
[6,5,4,3,1,2] => 2
[6,5,4,3,2,1] => 6
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 7
[1,2,3,4,6,5,7] => 6
[1,2,3,4,6,7,5] => 7
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 7
[1,2,3,5,4,6,7] => 5
[1,2,3,5,4,7,6] => 5
[1,2,3,5,6,4,7] => 6
[1,2,3,5,6,7,4] => 7
[1,2,3,5,7,4,6] => 7
[1,2,3,5,7,6,4] => 7
[1,2,3,6,4,5,7] => 7
[1,2,3,6,4,7,5] => 7
[1,2,3,6,5,4,7] => 6
[1,2,3,6,5,7,4] => 6
[1,2,3,6,7,4,5] => 5
[1,2,3,6,7,5,4] => 7
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 6
[1,2,3,7,5,4,6] => 7
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 5
[1,2,3,7,6,5,4] => 7
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[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] => 5
[1,2,4,5,3,7,6] => 5
[1,2,4,5,6,3,7] => 6
[1,2,4,5,6,7,3] => 7
[1,2,4,5,7,3,6] => 7
[1,2,4,5,7,6,3] => 7
[1,2,4,6,3,5,7] => 6
[1,2,4,6,3,7,5] => 6
[1,2,4,6,5,3,7] => 6
[1,2,4,6,5,7,3] => 6
[1,2,4,6,7,3,5] => 7
[1,2,4,6,7,5,3] => 7
[1,2,4,7,3,5,6] => 7
[1,2,4,7,3,6,5] => 7
[1,2,4,7,5,3,6] => 7
[1,2,4,7,5,6,3] => 6
[1,2,4,7,6,3,5] => 7
[1,2,4,7,6,5,3] => 7
[1,2,5,3,4,6,7] => 7
[1,2,5,3,4,7,6] => 7
[1,2,5,3,6,4,7] => 6
[1,2,5,3,6,7,4] => 7
[1,2,5,3,7,4,6] => 6
[1,2,5,3,7,6,4] => 7
[1,2,5,4,3,6,7] => 5
[1,2,5,4,3,7,6] => 5
[1,2,5,4,6,3,7] => 5
[1,2,5,4,6,7,3] => 5
[1,2,5,4,7,3,6] => 5
[1,2,5,4,7,6,3] => 5
[1,2,5,6,3,4,7] => 7
[1,2,5,6,3,7,4] => 7
[1,2,5,6,4,3,7] => 6
[1,2,5,6,4,7,3] => 6
[1,2,5,6,7,3,4] => 4
[1,2,5,6,7,4,3] => 7
[1,2,5,7,3,4,6] => 6
[1,2,5,7,3,6,4] => 6
[1,2,5,7,4,3,6] => 7
[1,2,5,7,4,6,3] => 7
[1,2,5,7,6,3,4] => 4
[1,2,5,7,6,4,3] => 7
[1,2,6,3,4,5,7] => 7
[1,2,6,3,4,7,5] => 7
[1,2,6,3,5,4,7] => 5
[1,2,6,3,5,7,4] => 7
[1,2,6,3,7,4,5] => 5
[1,2,6,3,7,5,4] => 7
[1,2,6,4,3,5,7] => 6
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 5
[1,2,6,4,5,7,3] => 7
[1,2,6,4,7,3,5] => 6
[1,2,6,4,7,5,3] => 7
[1,2,6,5,3,4,7] => 7
[1,2,6,5,3,7,4] => 7
[1,2,6,5,4,3,7] => 6
[1,2,6,5,4,7,3] => 6
[1,2,6,5,7,3,4] => 4
[1,2,6,5,7,4,3] => 6
[1,2,6,7,3,4,5] => 5
[1,2,6,7,3,5,4] => 5
[1,2,6,7,4,3,5] => 7
[1,2,6,7,4,5,3] => 5
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 7
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 6
[1,2,7,3,5,4,6] => 5
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 5
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 7
[1,2,7,4,3,6,5] => 7
[1,2,7,4,5,3,6] => 5
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 6
[1,2,7,4,6,5,3] => 6
[1,2,7,5,3,4,6] => 6
[1,2,7,5,3,6,4] => 6
[1,2,7,5,4,3,6] => 7
[1,2,7,5,4,6,3] => 7
[1,2,7,5,6,3,4] => 4
[1,2,7,5,6,4,3] => 6
[1,2,7,6,3,4,5] => 5
[1,2,7,6,3,5,4] => 5
[1,2,7,6,4,3,5] => 7
[1,2,7,6,4,5,3] => 5
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 7
[1,3,2,4,5,6,7] => 3
[1,3,2,4,5,7,6] => 3
[1,3,2,4,6,5,7] => 3
[1,3,2,4,6,7,5] => 3
[1,3,2,4,7,5,6] => 3
[1,3,2,4,7,6,5] => 3
[1,3,2,5,4,6,7] => 3
[1,3,2,5,4,7,6] => 3
[1,3,2,5,6,4,7] => 3
[1,3,2,5,6,7,4] => 3
[1,3,2,5,7,4,6] => 3
[1,3,2,5,7,6,4] => 3
[1,3,2,6,4,5,7] => 3
[1,3,2,6,4,7,5] => 3
[1,3,2,6,5,4,7] => 3
[1,3,2,6,5,7,4] => 3
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 3
[1,3,2,7,6,4,5] => 3
[1,3,2,7,6,5,4] => 3
[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] => 4
[1,3,4,2,7,5,6] => 4
[1,3,4,2,7,6,5] => 4
[1,3,4,5,2,6,7] => 5
[1,3,4,5,2,7,6] => 5
[1,3,4,5,6,2,7] => 6
[1,3,4,5,6,7,2] => 7
[1,3,4,5,7,2,6] => 7
[1,3,4,5,7,6,2] => 7
[1,3,4,6,2,5,7] => 6
[1,3,4,6,2,7,5] => 6
[1,3,4,6,5,2,7] => 6
[1,3,4,6,5,7,2] => 6
[1,3,4,6,7,2,5] => 7
[1,3,4,6,7,5,2] => 7
[1,3,4,7,2,5,6] => 7
[1,3,4,7,2,6,5] => 7
[1,3,4,7,5,2,6] => 7
[1,3,4,7,5,6,2] => 6
[1,3,4,7,6,2,5] => 7
[1,3,4,7,6,5,2] => 7
[1,3,5,2,4,6,7] => 5
[1,3,5,2,4,7,6] => 5
[1,3,5,2,6,4,7] => 5
[1,3,5,2,6,7,4] => 5
[1,3,5,2,7,4,6] => 5
[1,3,5,2,7,6,4] => 5
[1,3,5,4,2,6,7] => 5
[1,3,5,4,2,7,6] => 5
[1,3,5,4,6,2,7] => 5
[1,3,5,4,6,7,2] => 5
[1,3,5,4,7,2,6] => 5
[1,3,5,4,7,6,2] => 5
[1,3,5,6,2,4,7] => 6
[1,3,5,6,2,7,4] => 6
[1,3,5,6,4,2,7] => 6
[1,3,5,6,4,7,2] => 6
[1,3,5,6,7,2,4] => 7
[1,3,5,6,7,4,2] => 7
[1,3,5,7,2,4,6] => 7
[1,3,5,7,2,6,4] => 7
[1,3,5,7,4,2,6] => 7
[1,3,5,7,4,6,2] => 7
[1,3,5,7,6,2,4] => 7
[1,3,5,7,6,4,2] => 7
[1,3,6,2,4,5,7] => 6
[1,3,6,2,4,7,5] => 6
[1,3,6,2,5,4,7] => 6
[1,3,6,2,5,7,4] => 6
[1,3,6,2,7,4,5] => 6
[1,3,6,2,7,5,4] => 6
[1,3,6,4,2,5,7] => 6
[1,3,6,4,2,7,5] => 6
[1,3,6,4,5,2,7] => 5
[1,3,6,4,5,7,2] => 7
[1,3,6,4,7,2,5] => 6
[1,3,6,4,7,5,2] => 7
[1,3,6,5,2,4,7] => 6
[1,3,6,5,2,7,4] => 6
[1,3,6,5,4,2,7] => 6
[1,3,6,5,4,7,2] => 6
[1,3,6,5,7,2,4] => 6
[1,3,6,5,7,4,2] => 6
[1,3,6,7,2,4,5] => 7
[1,3,6,7,2,5,4] => 7
[1,3,6,7,4,2,5] => 7
[1,3,6,7,4,5,2] => 5
[1,3,6,7,5,2,4] => 7
[1,3,6,7,5,4,2] => 7
[1,3,7,2,4,5,6] => 7
[1,3,7,2,4,6,5] => 7
[1,3,7,2,5,4,6] => 7
[1,3,7,2,5,6,4] => 7
[1,3,7,2,6,4,5] => 7
[1,3,7,2,6,5,4] => 7
[1,3,7,4,2,5,6] => 7
[1,3,7,4,2,6,5] => 7
[1,3,7,4,5,2,6] => 5
[1,3,7,4,5,6,2] => 6
[1,3,7,4,6,2,5] => 6
[1,3,7,4,6,5,2] => 6
[1,3,7,5,2,4,6] => 7
[1,3,7,5,2,6,4] => 7
[1,3,7,5,4,2,6] => 7
[1,3,7,5,4,6,2] => 7
[1,3,7,5,6,2,4] => 6
[1,3,7,5,6,4,2] => 6
[1,3,7,6,2,4,5] => 7
[1,3,7,6,2,5,4] => 7
[1,3,7,6,4,2,5] => 7
[1,3,7,6,4,5,2] => 5
[1,3,7,6,5,2,4] => 7
[1,3,7,6,5,4,2] => 7
[1,4,2,3,5,6,7] => 7
[1,4,2,3,5,7,6] => 7
[1,4,2,3,6,5,7] => 6
[1,4,2,3,6,7,5] => 7
[1,4,2,3,7,5,6] => 6
[1,4,2,3,7,6,5] => 7
[1,4,2,5,3,6,7] => 5
[1,4,2,5,3,7,6] => 5
[1,4,2,5,6,3,7] => 6
[1,4,2,5,6,7,3] => 7
[1,4,2,5,7,3,6] => 7
[1,4,2,5,7,6,3] => 7
[1,4,2,6,3,5,7] => 7
[1,4,2,6,3,7,5] => 7
[1,4,2,6,5,3,7] => 6
[1,4,2,6,5,7,3] => 6
[1,4,2,6,7,3,5] => 5
[1,4,2,6,7,5,3] => 7
[1,4,2,7,3,5,6] => 6
[1,4,2,7,3,6,5] => 6
[1,4,2,7,5,3,6] => 7
[1,4,2,7,5,6,3] => 6
[1,4,2,7,6,3,5] => 5
[1,4,2,7,6,5,3] => 7
[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] => 4
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 4
[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] => 4
[1,4,3,5,7,6,2] => 4
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 4
[1,4,3,6,5,2,7] => 4
[1,4,3,6,5,7,2] => 4
[1,4,3,6,7,2,5] => 4
[1,4,3,6,7,5,2] => 4
[1,4,3,7,2,5,6] => 4
[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] => 7
[1,4,5,2,3,7,6] => 7
[1,4,5,2,6,3,7] => 6
[1,4,5,2,6,7,3] => 7
[1,4,5,2,7,3,6] => 6
[1,4,5,2,7,6,3] => 7
[1,4,5,3,2,6,7] => 5
[1,4,5,3,2,7,6] => 5
[1,4,5,3,6,2,7] => 5
[1,4,5,3,6,7,2] => 5
[1,4,5,3,7,2,6] => 5
[1,4,5,3,7,6,2] => 5
[1,4,5,6,2,3,7] => 7
[1,4,5,6,2,7,3] => 7
[1,4,5,6,3,2,7] => 6
[1,4,5,6,3,7,2] => 6
[1,4,5,6,7,2,3] => 3
[1,4,5,6,7,3,2] => 7
[1,4,5,7,2,3,6] => 6
[1,4,5,7,2,6,3] => 6
[1,4,5,7,3,2,6] => 7
[1,4,5,7,3,6,2] => 7
[1,4,5,7,6,2,3] => 3
[1,4,5,7,6,3,2] => 7
[1,4,6,2,3,5,7] => 7
[1,4,6,2,3,7,5] => 7
[1,4,6,2,5,3,7] => 5
[1,4,6,2,5,7,3] => 7
[1,4,6,2,7,3,5] => 5
[1,4,6,2,7,5,3] => 7
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 6
[1,4,6,3,5,2,7] => 6
[1,4,6,3,5,7,2] => 6
[1,4,6,3,7,2,5] => 6
[1,4,6,3,7,5,2] => 6
[1,4,6,5,2,3,7] => 7
[1,4,6,5,2,7,3] => 7
[1,4,6,5,3,2,7] => 6
[1,4,6,5,3,7,2] => 6
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Description
The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation.
Associate an increasing binary tree to the permutation using Mp00061to increasing tree. Then follow the path starting at the root which always selects the child with the smaller label. This statistic is the label of the leaf in the path, see [1].
Han [2] showed that this statistic is (up to a shift) equidistributed on zigzag permutations (permutations $\pi$ such that $\pi(1) < \pi(2) > \pi(3) \cdots$) with the greater neighbor of the maximum (St000060The greater neighbor of the maximum.), see also [3].
References
[1] Poupard, C. Deux propriétés des arbres binaires ordonnés stricts MathSciNet:1005843
[2] https://www.emis.de/journals/SLC/wpapers/s74vortrag/han.pdf
[3] Foata, D., Han, G.-N. Finite difference calculus for alternating permutations MathSciNet:3173528 arXiv:1304.2483
Code
def statistic(pi):
    pi = list(pi)
    if len(pi) == 1:
        return pi[0]
    else:
        a = min(pi)
        j = pi.index(a)
        b = min( x for x in pi if x != a )
        if pi.index(b) < j:
            return statistic(pi[:j])
        else:
            return statistic(pi[j+1:])
Created
Mar 28, 2017 at 11:20 by Christian Stump
Updated
Mar 28, 2017 at 11:47 by Christian Stump