edit this statistic or download as text // json
Identifier
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 3
[1,4,3,2] => 5
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 2
[2,4,3,1] => 4
[3,1,2,4] => 2
[3,1,4,2] => 4
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 5
[4,2,1,3] => 4
[4,2,3,1] => 4
[4,3,1,2] => 5
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 3
[1,2,5,3,4] => 4
[1,2,5,4,3] => 7
[1,3,2,4,5] => 2
[1,3,2,5,4] => 6
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 3
[1,3,5,4,2] => 6
[1,4,2,3,5] => 3
[1,4,2,5,3] => 6
[1,4,3,2,5] => 5
[1,4,3,5,2] => 5
[1,4,5,2,3] => 3
[1,4,5,3,2] => 5
[1,5,2,3,4] => 4
[1,5,2,4,3] => 7
[1,5,3,2,4] => 6
[1,5,3,4,2] => 6
[1,5,4,2,3] => 7
[1,5,4,3,2] => 9
[2,1,3,4,5] => 1
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 4
[2,1,5,3,4] => 5
[2,1,5,4,3] => 8
[2,3,1,4,5] => 1
[2,3,1,5,4] => 5
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 2
[2,3,5,4,1] => 5
[2,4,1,3,5] => 2
[2,4,1,5,3] => 5
[2,4,3,1,5] => 4
[2,4,3,5,1] => 4
[2,4,5,1,3] => 2
[2,4,5,3,1] => 4
[2,5,1,3,4] => 3
[2,5,1,4,3] => 6
[2,5,3,1,4] => 5
[2,5,3,4,1] => 5
[2,5,4,1,3] => 6
[2,5,4,3,1] => 8
[3,1,2,4,5] => 2
[3,1,2,5,4] => 6
[3,1,4,2,5] => 4
[3,1,4,5,2] => 4
[3,1,5,2,4] => 5
[3,1,5,4,2] => 8
[3,2,1,4,5] => 3
[3,2,1,5,4] => 7
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 7
[3,4,1,2,5] => 2
[3,4,1,5,2] => 4
[3,4,2,1,5] => 3
[3,4,2,5,1] => 3
[3,4,5,1,2] => 2
[3,4,5,2,1] => 3
[3,5,1,2,4] => 3
[3,5,1,4,2] => 5
[3,5,2,1,4] => 4
>>> Load all 1200 entries. <<<
[3,5,2,4,1] => 4
[3,5,4,1,2] => 6
[3,5,4,2,1] => 7
[4,1,2,3,5] => 3
[4,1,2,5,3] => 6
[4,1,3,2,5] => 5
[4,1,3,5,2] => 5
[4,1,5,2,3] => 6
[4,1,5,3,2] => 8
[4,2,1,3,5] => 4
[4,2,1,5,3] => 7
[4,2,3,1,5] => 4
[4,2,3,5,1] => 4
[4,2,5,1,3] => 5
[4,2,5,3,1] => 7
[4,3,1,2,5] => 5
[4,3,1,5,2] => 7
[4,3,2,1,5] => 6
[4,3,2,5,1] => 6
[4,3,5,1,2] => 5
[4,3,5,2,1] => 6
[4,5,1,2,3] => 3
[4,5,1,3,2] => 5
[4,5,2,1,3] => 4
[4,5,2,3,1] => 4
[4,5,3,1,2] => 5
[4,5,3,2,1] => 6
[5,1,2,3,4] => 4
[5,1,2,4,3] => 7
[5,1,3,2,4] => 6
[5,1,3,4,2] => 6
[5,1,4,2,3] => 7
[5,1,4,3,2] => 9
[5,2,1,3,4] => 5
[5,2,1,4,3] => 8
[5,2,3,1,4] => 5
[5,2,3,4,1] => 5
[5,2,4,1,3] => 6
[5,2,4,3,1] => 8
[5,3,1,2,4] => 6
[5,3,1,4,2] => 8
[5,3,2,1,4] => 7
[5,3,2,4,1] => 7
[5,3,4,1,2] => 6
[5,3,4,2,1] => 7
[5,4,1,2,3] => 7
[5,4,1,3,2] => 9
[5,4,2,1,3] => 8
[5,4,2,3,1] => 8
[5,4,3,1,2] => 9
[5,4,3,2,1] => 10
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 9
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 7
[1,2,5,4,6,3] => 7
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 7
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 9
[1,2,6,4,3,5] => 8
[1,2,6,4,5,3] => 8
[1,2,6,5,3,4] => 9
[1,2,6,5,4,3] => 12
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 7
[1,3,2,5,4,6] => 6
[1,3,2,5,6,4] => 6
[1,3,2,6,4,5] => 7
[1,3,2,6,5,4] => 11
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 7
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 2
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 7
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 7
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 6
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 6
[1,3,6,2,4,5] => 4
[1,3,6,2,5,4] => 8
[1,3,6,4,2,5] => 7
[1,3,6,4,5,2] => 7
[1,3,6,5,2,4] => 8
[1,3,6,5,4,2] => 11
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 6
[1,4,2,5,6,3] => 6
[1,4,2,6,3,5] => 7
[1,4,2,6,5,3] => 11
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 10
[1,4,3,5,2,6] => 5
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 10
[1,4,5,2,3,6] => 3
[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] => 5
[1,4,6,2,3,5] => 4
[1,4,6,2,5,3] => 7
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 6
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 10
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 7
[1,5,2,4,6,3] => 7
[1,5,2,6,3,4] => 8
[1,5,2,6,4,3] => 11
[1,5,3,2,4,6] => 6
[1,5,3,2,6,4] => 10
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 6
[1,5,3,6,2,4] => 7
[1,5,3,6,4,2] => 10
[1,5,4,2,3,6] => 7
[1,5,4,2,6,3] => 10
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 9
[1,5,4,6,2,3] => 7
[1,5,4,6,3,2] => 9
[1,5,6,2,3,4] => 4
[1,5,6,2,4,3] => 7
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 7
[1,5,6,4,3,2] => 9
[1,6,2,3,4,5] => 5
[1,6,2,3,5,4] => 9
[1,6,2,4,3,5] => 8
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 9
[1,6,2,5,4,3] => 12
[1,6,3,2,4,5] => 7
[1,6,3,2,5,4] => 11
[1,6,3,4,2,5] => 7
[1,6,3,4,5,2] => 7
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 11
[1,6,4,2,3,5] => 8
[1,6,4,2,5,3] => 11
[1,6,4,3,2,5] => 10
[1,6,4,3,5,2] => 10
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 10
[1,6,5,2,3,4] => 9
[1,6,5,2,4,3] => 12
[1,6,5,3,2,4] => 11
[1,6,5,3,4,2] => 11
[1,6,5,4,2,3] => 12
[1,6,5,4,3,2] => 14
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 5
[2,1,3,5,6,4] => 5
[2,1,3,6,4,5] => 6
[2,1,3,6,5,4] => 10
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 9
[2,1,5,3,4,6] => 5
[2,1,5,3,6,4] => 9
[2,1,5,4,3,6] => 8
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 10
[2,1,6,4,3,5] => 9
[2,1,6,4,5,3] => 9
[2,1,6,5,3,4] => 10
[2,1,6,5,4,3] => 13
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 6
[2,3,1,5,4,6] => 5
[2,3,1,5,6,4] => 5
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 10
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 6
[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] => 6
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 6
[2,3,5,4,1,6] => 5
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 5
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 7
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 6
[2,3,6,5,1,4] => 7
[2,3,6,5,4,1] => 10
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 7
[2,4,1,5,3,6] => 5
[2,4,1,5,6,3] => 5
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 10
[2,4,3,1,5,6] => 4
[2,4,3,1,6,5] => 9
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 9
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 5
[2,4,5,3,1,6] => 4
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 6
[2,4,6,3,1,5] => 5
[2,4,6,3,5,1] => 5
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 9
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 7
[2,5,1,4,3,6] => 6
[2,5,1,4,6,3] => 6
[2,5,1,6,3,4] => 7
[2,5,1,6,4,3] => 10
[2,5,3,1,4,6] => 5
[2,5,3,1,6,4] => 9
[2,5,3,4,1,6] => 5
[2,5,3,4,6,1] => 5
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 9
[2,5,4,1,3,6] => 6
[2,5,4,1,6,3] => 9
[2,5,4,3,1,6] => 8
[2,5,4,3,6,1] => 8
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 8
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 6
[2,5,6,3,1,4] => 5
[2,5,6,3,4,1] => 5
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 8
[2,6,1,4,3,5] => 7
[2,6,1,4,5,3] => 7
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 11
[2,6,3,1,4,5] => 6
[2,6,3,1,5,4] => 10
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 6
[2,6,3,5,1,4] => 7
[2,6,3,5,4,1] => 10
[2,6,4,1,3,5] => 7
[2,6,4,1,5,3] => 10
[2,6,4,3,1,5] => 9
[2,6,4,3,5,1] => 9
[2,6,4,5,1,3] => 7
[2,6,4,5,3,1] => 9
[2,6,5,1,3,4] => 8
[2,6,5,1,4,3] => 11
[2,6,5,3,1,4] => 10
[2,6,5,3,4,1] => 10
[2,6,5,4,1,3] => 11
[2,6,5,4,3,1] => 13
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 7
[3,1,2,5,4,6] => 6
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 7
[3,1,2,6,5,4] => 11
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 9
[3,1,4,5,2,6] => 4
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 9
[3,1,5,2,4,6] => 5
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 8
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 6
[3,1,6,2,5,4] => 10
[3,1,6,4,2,5] => 9
[3,1,6,4,5,2] => 9
[3,1,6,5,2,4] => 10
[3,1,6,5,4,2] => 13
[3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => 8
[3,2,1,5,4,6] => 7
[3,2,1,5,6,4] => 7
[3,2,1,6,4,5] => 8
[3,2,1,6,5,4] => 12
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 4
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 7
[3,2,5,4,6,1] => 7
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 7
[3,2,6,1,4,5] => 5
[3,2,6,1,5,4] => 9
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 8
[3,2,6,5,1,4] => 9
[3,2,6,5,4,1] => 12
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 7
[3,4,1,5,2,6] => 4
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 5
[3,4,1,6,5,2] => 9
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 8
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 4
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => 3
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 4
[3,4,6,2,5,1] => 4
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 3
[3,5,1,2,6,4] => 7
[3,5,1,4,2,6] => 5
[3,5,1,4,6,2] => 5
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 9
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 4
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 5
[3,5,2,6,4,1] => 8
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 8
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 7
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 7
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 5
[3,5,6,2,1,4] => 4
[3,5,6,2,4,1] => 4
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 7
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 6
[3,6,1,5,2,4] => 7
[3,6,1,5,4,2] => 10
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 9
[3,6,2,4,1,5] => 5
[3,6,2,4,5,1] => 5
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 9
[3,6,4,1,2,5] => 7
[3,6,4,1,5,2] => 9
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 7
[3,6,4,5,2,1] => 8
[3,6,5,1,2,4] => 8
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 9
[3,6,5,4,1,2] => 11
[3,6,5,4,2,1] => 12
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 6
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 7
[4,1,2,6,5,3] => 11
[4,1,3,2,5,6] => 5
[4,1,3,2,6,5] => 10
[4,1,3,5,2,6] => 5
[4,1,3,5,6,2] => 5
[4,1,3,6,2,5] => 6
[4,1,3,6,5,2] => 10
[4,1,5,2,3,6] => 6
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 8
[4,1,5,6,2,3] => 6
[4,1,5,6,3,2] => 8
[4,1,6,2,3,5] => 7
[4,1,6,2,5,3] => 10
[4,1,6,3,2,5] => 9
[4,1,6,3,5,2] => 9
[4,1,6,5,2,3] => 11
[4,1,6,5,3,2] => 13
[4,2,1,3,5,6] => 4
[4,2,1,3,6,5] => 9
[4,2,1,5,3,6] => 7
[4,2,1,5,6,3] => 7
[4,2,1,6,3,5] => 8
[4,2,1,6,5,3] => 12
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 9
[4,2,3,5,1,6] => 4
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 5
[4,2,3,6,5,1] => 9
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 8
[4,2,5,3,1,6] => 7
[4,2,5,3,6,1] => 7
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 7
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 9
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 8
[4,2,6,5,1,3] => 10
[4,2,6,5,3,1] => 12
[4,3,1,2,5,6] => 5
[4,3,1,2,6,5] => 10
[4,3,1,5,2,6] => 7
[4,3,1,5,6,2] => 7
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 12
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 11
[4,3,2,5,1,6] => 6
[4,3,2,5,6,1] => 6
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 11
[4,3,5,1,2,6] => 5
[4,3,5,1,6,2] => 7
[4,3,5,2,1,6] => 6
[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] => 6
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 7
[4,3,6,2,5,1] => 7
[4,3,6,5,1,2] => 10
[4,3,6,5,2,1] => 11
[4,5,1,2,3,6] => 3
[4,5,1,2,6,3] => 6
[4,5,1,3,2,6] => 5
[4,5,1,3,6,2] => 5
[4,5,1,6,2,3] => 6
[4,5,1,6,3,2] => 8
[4,5,2,1,3,6] => 4
[4,5,2,1,6,3] => 7
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 4
[4,5,2,6,1,3] => 5
[4,5,2,6,3,1] => 7
[4,5,3,1,2,6] => 5
[4,5,3,1,6,2] => 7
[4,5,3,2,1,6] => 6
[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] => 3
[4,5,6,1,3,2] => 5
[4,5,6,2,1,3] => 4
[4,5,6,2,3,1] => 4
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 7
[4,6,1,5,3,2] => 9
[4,6,2,1,3,5] => 5
[4,6,2,1,5,3] => 8
[4,6,2,3,1,5] => 5
[4,6,2,3,5,1] => 5
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 6
[4,6,3,1,5,2] => 8
[4,6,3,2,1,5] => 7
[4,6,3,2,5,1] => 7
[4,6,3,5,1,2] => 6
[4,6,3,5,2,1] => 7
[4,6,5,1,2,3] => 8
[4,6,5,1,3,2] => 10
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 9
[4,6,5,3,1,2] => 10
[4,6,5,3,2,1] => 11
[5,1,2,3,4,6] => 4
[5,1,2,3,6,4] => 8
[5,1,2,4,3,6] => 7
[5,1,2,4,6,3] => 7
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 11
[5,1,3,2,4,6] => 6
[5,1,3,2,6,4] => 10
[5,1,3,4,2,6] => 6
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 7
[5,1,3,6,4,2] => 10
[5,1,4,2,3,6] => 7
[5,1,4,2,6,3] => 10
[5,1,4,3,2,6] => 9
[5,1,4,3,6,2] => 9
[5,1,4,6,2,3] => 7
[5,1,4,6,3,2] => 9
[5,1,6,2,3,4] => 8
[5,1,6,2,4,3] => 11
[5,1,6,3,2,4] => 10
[5,1,6,3,4,2] => 10
[5,1,6,4,2,3] => 11
[5,1,6,4,3,2] => 13
[5,2,1,3,4,6] => 5
[5,2,1,3,6,4] => 9
[5,2,1,4,3,6] => 8
[5,2,1,4,6,3] => 8
[5,2,1,6,3,4] => 9
[5,2,1,6,4,3] => 12
[5,2,3,1,4,6] => 5
[5,2,3,1,6,4] => 9
[5,2,3,4,1,6] => 5
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 9
[5,2,4,1,3,6] => 6
[5,2,4,1,6,3] => 9
[5,2,4,3,1,6] => 8
[5,2,4,3,6,1] => 8
[5,2,4,6,1,3] => 6
[5,2,4,6,3,1] => 8
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 10
[5,2,6,3,1,4] => 9
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 10
[5,2,6,4,3,1] => 12
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 10
[5,3,1,4,2,6] => 8
[5,3,1,4,6,2] => 8
[5,3,1,6,2,4] => 9
[5,3,1,6,4,2] => 12
[5,3,2,1,4,6] => 7
[5,3,2,1,6,4] => 11
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 7
[5,3,2,6,1,4] => 8
[5,3,2,6,4,1] => 11
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 8
[5,3,4,2,1,6] => 7
[5,3,4,2,6,1] => 7
[5,3,4,6,1,2] => 6
[5,3,4,6,2,1] => 7
[5,3,6,1,2,4] => 7
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 8
[5,3,6,4,1,2] => 10
[5,3,6,4,2,1] => 11
[5,4,1,2,3,6] => 7
[5,4,1,2,6,3] => 10
[5,4,1,3,2,6] => 9
[5,4,1,3,6,2] => 9
[5,4,1,6,2,3] => 10
[5,4,1,6,3,2] => 12
[5,4,2,1,3,6] => 8
[5,4,2,1,6,3] => 11
[5,4,2,3,1,6] => 8
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 9
[5,4,2,6,3,1] => 11
[5,4,3,1,2,6] => 9
[5,4,3,1,6,2] => 11
[5,4,3,2,1,6] => 10
[5,4,3,2,6,1] => 10
[5,4,3,6,1,2] => 9
[5,4,3,6,2,1] => 10
[5,4,6,1,2,3] => 7
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 8
[5,4,6,2,3,1] => 8
[5,4,6,3,1,2] => 9
[5,4,6,3,2,1] => 10
[5,6,1,2,3,4] => 4
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 6
[5,6,1,4,2,3] => 7
[5,6,1,4,3,2] => 9
[5,6,2,1,3,4] => 5
[5,6,2,1,4,3] => 8
[5,6,2,3,1,4] => 5
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 6
[5,6,2,4,3,1] => 8
[5,6,3,1,2,4] => 6
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 7
[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] => 7
[5,6,4,1,3,2] => 9
[5,6,4,2,1,3] => 8
[5,6,4,2,3,1] => 8
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 10
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 9
[6,1,2,4,3,5] => 8
[6,1,2,4,5,3] => 8
[6,1,2,5,3,4] => 9
[6,1,2,5,4,3] => 12
[6,1,3,2,4,5] => 7
[6,1,3,2,5,4] => 11
[6,1,3,4,2,5] => 7
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 11
[6,1,4,2,3,5] => 8
[6,1,4,2,5,3] => 11
[6,1,4,3,2,5] => 10
[6,1,4,3,5,2] => 10
[6,1,4,5,2,3] => 8
[6,1,4,5,3,2] => 10
[6,1,5,2,3,4] => 9
[6,1,5,2,4,3] => 12
[6,1,5,3,2,4] => 11
[6,1,5,3,4,2] => 11
[6,1,5,4,2,3] => 12
[6,1,5,4,3,2] => 14
[6,2,1,3,4,5] => 6
[6,2,1,3,5,4] => 10
[6,2,1,4,3,5] => 9
[6,2,1,4,5,3] => 9
[6,2,1,5,3,4] => 10
[6,2,1,5,4,3] => 13
[6,2,3,1,4,5] => 6
[6,2,3,1,5,4] => 10
[6,2,3,4,1,5] => 6
[6,2,3,4,5,1] => 6
[6,2,3,5,1,4] => 7
[6,2,3,5,4,1] => 10
[6,2,4,1,3,5] => 7
[6,2,4,1,5,3] => 10
[6,2,4,3,1,5] => 9
[6,2,4,3,5,1] => 9
[6,2,4,5,1,3] => 7
[6,2,4,5,3,1] => 9
[6,2,5,1,3,4] => 8
[6,2,5,1,4,3] => 11
[6,2,5,3,1,4] => 10
[6,2,5,3,4,1] => 10
[6,2,5,4,1,3] => 11
[6,2,5,4,3,1] => 13
[6,3,1,2,4,5] => 7
[6,3,1,2,5,4] => 11
[6,3,1,4,2,5] => 9
[6,3,1,4,5,2] => 9
[6,3,1,5,2,4] => 10
[6,3,1,5,4,2] => 13
[6,3,2,1,4,5] => 8
[6,3,2,1,5,4] => 12
[6,3,2,4,1,5] => 8
[6,3,2,4,5,1] => 8
[6,3,2,5,1,4] => 9
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 7
[6,3,4,1,5,2] => 9
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 7
[6,3,4,5,2,1] => 8
[6,3,5,1,2,4] => 8
[6,3,5,1,4,2] => 10
[6,3,5,2,1,4] => 9
[6,3,5,2,4,1] => 9
[6,3,5,4,1,2] => 11
[6,3,5,4,2,1] => 12
[6,4,1,2,3,5] => 8
[6,4,1,2,5,3] => 11
[6,4,1,3,2,5] => 10
[6,4,1,3,5,2] => 10
[6,4,1,5,2,3] => 11
[6,4,1,5,3,2] => 13
[6,4,2,1,3,5] => 9
[6,4,2,1,5,3] => 12
[6,4,2,3,1,5] => 9
[6,4,2,3,5,1] => 9
[6,4,2,5,1,3] => 10
[6,4,2,5,3,1] => 12
[6,4,3,1,2,5] => 10
[6,4,3,1,5,2] => 12
[6,4,3,2,1,5] => 11
[6,4,3,2,5,1] => 11
[6,4,3,5,1,2] => 10
[6,4,3,5,2,1] => 11
[6,4,5,1,2,3] => 8
[6,4,5,1,3,2] => 10
[6,4,5,2,1,3] => 9
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 10
[6,4,5,3,2,1] => 11
[6,5,1,2,3,4] => 9
[6,5,1,2,4,3] => 12
[6,5,1,3,2,4] => 11
[6,5,1,3,4,2] => 11
[6,5,1,4,2,3] => 12
[6,5,1,4,3,2] => 14
[6,5,2,1,3,4] => 10
[6,5,2,1,4,3] => 13
[6,5,2,3,1,4] => 10
[6,5,2,3,4,1] => 10
[6,5,2,4,1,3] => 11
[6,5,2,4,3,1] => 13
[6,5,3,1,2,4] => 11
[6,5,3,1,4,2] => 13
[6,5,3,2,1,4] => 12
[6,5,3,2,4,1] => 12
[6,5,3,4,1,2] => 11
[6,5,3,4,2,1] => 12
[6,5,4,1,2,3] => 12
[6,5,4,1,3,2] => 14
[6,5,4,2,1,3] => 13
[6,5,4,2,3,1] => 13
[6,5,4,3,1,2] => 14
[6,5,4,3,2,1] => 15
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 5
[1,2,3,4,6,7,5] => 5
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 11
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 10
[1,2,3,5,6,4,7] => 4
[1,2,3,5,6,7,4] => 4
[1,2,3,5,7,4,6] => 5
[1,2,3,5,7,6,4] => 10
[1,2,3,6,4,5,7] => 5
[1,2,3,6,4,7,5] => 10
[1,2,3,6,5,4,7] => 9
[1,2,3,6,5,7,4] => 9
[1,2,3,6,7,4,5] => 5
[1,2,3,6,7,5,4] => 9
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 11
[1,2,3,7,5,4,6] => 10
[1,2,3,7,5,6,4] => 10
[1,2,3,7,6,4,5] => 11
[1,2,3,7,6,5,4] => 15
[1,2,4,3,5,6,7] => 3
[1,2,4,3,5,7,6] => 9
[1,2,4,3,6,5,7] => 8
[1,2,4,3,6,7,5] => 8
[1,2,4,3,7,5,6] => 9
[1,2,4,3,7,6,5] => 14
[1,2,4,5,3,6,7] => 3
[1,2,4,5,3,7,6] => 9
[1,2,4,5,6,3,7] => 3
[1,2,4,5,6,7,3] => 3
[1,2,4,5,7,3,6] => 4
[1,2,4,5,7,6,3] => 9
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 9
[1,2,4,6,5,3,7] => 8
[1,2,4,6,5,7,3] => 8
[1,2,4,6,7,3,5] => 4
[1,2,4,6,7,5,3] => 8
[1,2,4,7,3,5,6] => 5
[1,2,4,7,3,6,5] => 10
[1,2,4,7,5,3,6] => 9
[1,2,4,7,5,6,3] => 9
[1,2,4,7,6,3,5] => 10
[1,2,4,7,6,5,3] => 14
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 10
[1,2,5,3,6,4,7] => 8
[1,2,5,3,6,7,4] => 8
[1,2,5,3,7,4,6] => 9
[1,2,5,3,7,6,4] => 14
[1,2,5,4,3,6,7] => 7
[1,2,5,4,3,7,6] => 13
[1,2,5,4,6,3,7] => 7
[1,2,5,4,6,7,3] => 7
[1,2,5,4,7,3,6] => 8
[1,2,5,4,7,6,3] => 13
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 8
[1,2,5,6,4,3,7] => 7
[1,2,5,6,4,7,3] => 7
[1,2,5,6,7,3,4] => 4
[1,2,5,6,7,4,3] => 7
[1,2,5,7,3,4,6] => 5
[1,2,5,7,3,6,4] => 9
[1,2,5,7,4,3,6] => 8
[1,2,5,7,4,6,3] => 8
[1,2,5,7,6,3,4] => 10
[1,2,5,7,6,4,3] => 13
[1,2,6,3,4,5,7] => 5
[1,2,6,3,4,7,5] => 10
[1,2,6,3,5,4,7] => 9
[1,2,6,3,5,7,4] => 9
[1,2,6,3,7,4,5] => 10
[1,2,6,3,7,5,4] => 14
[1,2,6,4,3,5,7] => 8
[1,2,6,4,3,7,5] => 13
[1,2,6,4,5,3,7] => 8
[1,2,6,4,5,7,3] => 8
[1,2,6,4,7,3,5] => 9
[1,2,6,4,7,5,3] => 13
[1,2,6,5,3,4,7] => 9
[1,2,6,5,3,7,4] => 13
[1,2,6,5,4,3,7] => 12
[1,2,6,5,4,7,3] => 12
[1,2,6,5,7,3,4] => 9
[1,2,6,5,7,4,3] => 12
[1,2,6,7,3,4,5] => 5
[1,2,6,7,3,5,4] => 9
[1,2,6,7,4,3,5] => 8
[1,2,6,7,4,5,3] => 8
[1,2,6,7,5,3,4] => 9
[1,2,6,7,5,4,3] => 12
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 11
[1,2,7,3,5,4,6] => 10
[1,2,7,3,5,6,4] => 10
[1,2,7,3,6,4,5] => 11
[1,2,7,3,6,5,4] => 15
[1,2,7,4,3,5,6] => 9
[1,2,7,4,3,6,5] => 14
[1,2,7,4,5,3,6] => 9
[1,2,7,4,5,6,3] => 9
[1,2,7,4,6,3,5] => 10
[1,2,7,4,6,5,3] => 14
[1,2,7,5,3,4,6] => 10
[1,2,7,5,3,6,4] => 14
[1,2,7,5,4,3,6] => 13
[1,2,7,5,4,6,3] => 13
[1,2,7,5,6,3,4] => 10
[1,2,7,5,6,4,3] => 13
[1,2,7,6,3,4,5] => 11
[1,2,7,6,3,5,4] => 15
[1,2,7,6,4,3,5] => 14
[1,2,7,6,4,5,3] => 14
[1,2,7,6,5,3,4] => 15
[1,2,7,6,5,4,3] => 18
[1,3,2,4,5,6,7] => 2
[1,3,2,4,5,7,6] => 8
[1,3,2,4,6,5,7] => 7
[1,3,2,4,6,7,5] => 7
[1,3,2,4,7,5,6] => 8
[1,3,2,4,7,6,5] => 13
[1,3,2,5,4,6,7] => 6
[1,3,2,5,4,7,6] => 12
[1,3,2,5,6,4,7] => 6
[1,3,2,5,6,7,4] => 6
[1,3,2,5,7,4,6] => 7
[1,3,2,5,7,6,4] => 12
[1,3,2,6,4,5,7] => 7
[1,3,2,6,4,7,5] => 12
[1,3,2,6,5,4,7] => 11
[1,3,2,6,5,7,4] => 11
[1,3,2,6,7,4,5] => 7
[1,3,2,6,7,5,4] => 11
[1,3,2,7,4,5,6] => 8
[1,3,2,7,4,6,5] => 13
[1,3,2,7,5,4,6] => 12
[1,3,2,7,5,6,4] => 12
[1,3,2,7,6,4,5] => 13
[1,3,2,7,6,5,4] => 17
[1,3,4,2,5,6,7] => 2
[1,3,4,2,5,7,6] => 8
[1,3,4,2,6,5,7] => 7
[1,3,4,2,6,7,5] => 7
[1,3,4,2,7,5,6] => 8
[1,3,4,2,7,6,5] => 13
[1,3,4,5,2,6,7] => 2
[1,3,4,5,2,7,6] => 8
[1,3,4,5,6,2,7] => 2
[1,3,4,5,6,7,2] => 2
[1,3,4,5,7,2,6] => 3
[1,3,4,5,7,6,2] => 8
[1,3,4,6,2,5,7] => 3
[1,3,4,6,2,7,5] => 8
[1,3,4,6,5,2,7] => 7
[1,3,4,6,5,7,2] => 7
[1,3,4,6,7,2,5] => 3
[1,3,4,6,7,5,2] => 7
[1,3,4,7,2,5,6] => 4
[1,3,4,7,2,6,5] => 9
[1,3,4,7,5,2,6] => 8
[1,3,4,7,5,6,2] => 8
[1,3,4,7,6,2,5] => 9
[1,3,4,7,6,5,2] => 13
[1,3,5,2,4,6,7] => 3
[1,3,5,2,4,7,6] => 9
[1,3,5,2,6,4,7] => 7
[1,3,5,2,6,7,4] => 7
[1,3,5,2,7,4,6] => 8
[1,3,5,2,7,6,4] => 13
[1,3,5,4,2,6,7] => 6
[1,3,5,4,2,7,6] => 12
[1,3,5,4,6,2,7] => 6
[1,3,5,4,6,7,2] => 6
[1,3,5,4,7,2,6] => 7
[1,3,5,4,7,6,2] => 12
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 7
[1,3,5,6,4,2,7] => 6
[1,3,5,6,4,7,2] => 6
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 6
[1,3,5,7,2,4,6] => 4
[1,3,5,7,2,6,4] => 8
[1,3,5,7,4,2,6] => 7
[1,3,5,7,4,6,2] => 7
[1,3,5,7,6,2,4] => 9
[1,3,5,7,6,4,2] => 12
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 9
[1,3,6,2,5,4,7] => 8
[1,3,6,2,5,7,4] => 8
[1,3,6,2,7,4,5] => 9
[1,3,6,2,7,5,4] => 13
[1,3,6,4,2,5,7] => 7
[1,3,6,4,2,7,5] => 12
[1,3,6,4,5,2,7] => 7
[1,3,6,4,5,7,2] => 7
[1,3,6,4,7,2,5] => 8
[1,3,6,4,7,5,2] => 12
[1,3,6,5,2,4,7] => 8
[1,3,6,5,2,7,4] => 12
[1,3,6,5,4,2,7] => 11
[1,3,6,5,4,7,2] => 11
[1,3,6,5,7,2,4] => 8
[1,3,6,5,7,4,2] => 11
[1,3,6,7,2,4,5] => 4
[1,3,6,7,2,5,4] => 8
[1,3,6,7,4,2,5] => 7
[1,3,6,7,4,5,2] => 7
[1,3,6,7,5,2,4] => 8
[1,3,6,7,5,4,2] => 11
[1,3,7,2,4,5,6] => 5
[1,3,7,2,4,6,5] => 10
[1,3,7,2,5,4,6] => 9
[1,3,7,2,5,6,4] => 9
[1,3,7,2,6,4,5] => 10
[1,3,7,2,6,5,4] => 14
[1,3,7,4,2,5,6] => 8
[1,3,7,4,2,6,5] => 13
[1,3,7,4,5,2,6] => 8
[1,3,7,4,5,6,2] => 8
[1,3,7,4,6,2,5] => 9
[1,3,7,4,6,5,2] => 13
[1,3,7,5,2,4,6] => 9
[1,3,7,5,2,6,4] => 13
[1,3,7,5,4,2,6] => 12
[1,3,7,5,4,6,2] => 12
[1,3,7,5,6,2,4] => 9
[1,3,7,5,6,4,2] => 12
[1,3,7,6,2,4,5] => 10
[1,3,7,6,2,5,4] => 14
[1,3,7,6,4,2,5] => 13
[1,3,7,6,4,5,2] => 13
[1,3,7,6,5,2,4] => 14
[1,3,7,6,5,4,2] => 17
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 9
[1,4,2,3,6,5,7] => 8
[1,4,2,3,6,7,5] => 8
[1,4,2,3,7,5,6] => 9
[1,4,2,3,7,6,5] => 14
[1,4,2,5,3,6,7] => 6
[1,4,2,5,3,7,6] => 12
[1,4,2,5,6,3,7] => 6
[1,4,2,5,6,7,3] => 6
[1,4,2,5,7,3,6] => 7
[1,4,2,5,7,6,3] => 12
[1,4,2,6,3,5,7] => 7
[1,4,2,6,3,7,5] => 12
[1,4,2,6,5,3,7] => 11
[1,4,2,6,5,7,3] => 11
[1,4,2,6,7,3,5] => 7
[1,4,2,6,7,5,3] => 11
[1,4,2,7,3,5,6] => 8
[1,4,2,7,3,6,5] => 13
[1,4,2,7,5,3,6] => 12
[1,4,2,7,5,6,3] => 12
[1,4,2,7,6,3,5] => 13
[1,4,2,7,6,5,3] => 17
[1,4,3,2,5,6,7] => 5
[1,4,3,2,5,7,6] => 11
[1,4,3,2,6,5,7] => 10
[1,4,3,2,6,7,5] => 10
[1,4,3,2,7,5,6] => 11
[1,4,3,2,7,6,5] => 16
[1,4,3,5,2,6,7] => 5
[1,4,3,5,2,7,6] => 11
[1,4,3,5,6,2,7] => 5
[1,4,3,5,6,7,2] => 5
[1,4,3,5,7,2,6] => 6
[1,4,3,5,7,6,2] => 11
[1,4,3,6,2,5,7] => 6
[1,4,3,6,2,7,5] => 11
[1,4,3,6,5,2,7] => 10
[1,4,3,6,5,7,2] => 10
[1,4,3,6,7,2,5] => 6
[1,4,3,6,7,5,2] => 10
[1,4,3,7,2,5,6] => 7
[1,4,3,7,2,6,5] => 12
[1,4,3,7,5,2,6] => 11
[1,4,3,7,5,6,2] => 11
[1,4,3,7,6,2,5] => 12
[1,4,3,7,6,5,2] => 16
[1,4,5,2,3,6,7] => 3
[1,4,5,2,3,7,6] => 9
[1,4,5,2,6,3,7] => 6
[1,4,5,2,6,7,3] => 6
[1,4,5,2,7,3,6] => 7
[1,4,5,2,7,6,3] => 12
[1,4,5,3,2,6,7] => 5
[1,4,5,3,2,7,6] => 11
[1,4,5,3,6,2,7] => 5
[1,4,5,3,6,7,2] => 5
[1,4,5,3,7,2,6] => 6
[1,4,5,3,7,6,2] => 11
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 6
[1,4,5,6,3,2,7] => 5
[1,4,5,6,3,7,2] => 5
[1,4,5,6,7,2,3] => 3
[1,4,5,6,7,3,2] => 5
[1,4,5,7,2,3,6] => 4
[1,4,5,7,2,6,3] => 7
[1,4,5,7,3,2,6] => 6
[1,4,5,7,3,6,2] => 6
[1,4,5,7,6,2,3] => 9
[1,4,5,7,6,3,2] => 11
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 9
[1,4,6,2,5,3,7] => 7
[1,4,6,2,5,7,3] => 7
[1,4,6,2,7,3,5] => 8
[1,4,6,2,7,5,3] => 12
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 11
[1,4,6,3,5,2,7] => 6
[1,4,6,3,5,7,2] => 6
[1,4,6,3,7,2,5] => 7
[1,4,6,3,7,5,2] => 11
[1,4,6,5,2,3,7] => 8
[1,4,6,5,2,7,3] => 11
[1,4,6,5,3,2,7] => 10
[1,4,6,5,3,7,2] => 10
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Description
The makl of a permutation.
According to [1], this is the sum of the number of occurrences of the vincular patterns $(1\underline{32})$, $(\underline{31}2)$, $(\underline{32}1)$ and $(\underline{21})$, where matches of the underlined letters must be adjacent.
References
[1] Amini, N. Equidistributions of Mahonian statistics over pattern avoiding permutations arXiv:1705.05298
Code
def statistic(pi):
    patterns = [([1,3,2],[2]), ([3,1,2],[1]), ([3,2,1],[1]), ([2,1],[1])]
    return sum(vincular_occurrences(pi, p, c) for p, c in patterns)

def vincular_occurrences(perm, pat, columns):
    n = len(pat)
    R = [(c, i) for c in columns for i in range(n+1)]
    return mesh_pattern_occurrences(perm, pat, R=R)

def G(w):
    return [ (x+1,y) for (x,y) in enumerate(w) ]

def mesh_pattern_occurrences(perm, pat, R=[]):
    occs = 0
    k = len(pat)
    n = len(perm)
    pat = G(pat)
    perm = G(perm)
    for H in Subsets(perm, k):
        H = sorted(H)
        X = dict(G(sorted(i for (i,_) in H)))
        Y = dict(G(sorted(j for (_,j) in H)))
        if H == [ (X[i], Y[j]) for (i,j) in pat ]:
            X[0], X[k+1] = 0, n+1
            Y[0], Y[k+1] = 0, n+1
            shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
                      for (i,j) in R
                      for (x,y) in perm
                      )
            if not any(shady):
                occs = occs + 1
    return occs
Created
May 16, 2017 at 16:57 by Martin Rubey
Updated
Jan 10, 2018 at 20:36 by Martin Rubey