edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 3
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 5
[1,4,2,3] => 3
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 3
[2,3,4,1] => 6
[2,4,1,3] => 4
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 5
[3,2,1,4] => 1
[3,2,4,1] => 4
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 1
[4,3,1,2] => 5
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 7
[1,2,5,3,4] => 4
[1,2,5,4,3] => 3
[1,3,2,4,5] => 2
[1,3,2,5,4] => 6
[1,3,4,2,5] => 5
[1,3,4,5,2] => 9
[1,3,5,2,4] => 6
[1,3,5,4,2] => 5
[1,4,2,3,5] => 3
[1,4,2,5,3] => 7
[1,4,3,2,5] => 2
[1,4,3,5,2] => 6
[1,4,5,2,3] => 6
[1,4,5,3,2] => 5
[1,5,2,3,4] => 4
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 2
[1,5,4,2,3] => 7
[1,5,4,3,2] => 6
[2,1,3,4,5] => 1
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 8
[2,1,5,3,4] => 5
[2,1,5,4,3] => 4
[2,3,1,4,5] => 3
[2,3,1,5,4] => 7
[2,3,4,1,5] => 6
[2,3,4,5,1] => 10
[2,3,5,1,4] => 7
[2,3,5,4,1] => 6
[2,4,1,3,5] => 4
[2,4,1,5,3] => 8
[2,4,3,1,5] => 3
[2,4,3,5,1] => 7
[2,4,5,1,3] => 7
[2,4,5,3,1] => 6
[2,5,1,3,4] => 5
[2,5,1,4,3] => 4
[2,5,3,1,4] => 4
[2,5,3,4,1] => 3
[2,5,4,1,3] => 8
[2,5,4,3,1] => 7
[3,1,2,4,5] => 2
[3,1,2,5,4] => 6
[3,1,4,2,5] => 5
[3,1,4,5,2] => 9
[3,1,5,2,4] => 6
[3,1,5,4,2] => 5
[3,2,1,4,5] => 1
[3,2,1,5,4] => 5
[3,2,4,1,5] => 4
[3,2,4,5,1] => 8
[3,2,5,1,4] => 5
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 8
[3,4,2,1,5] => 3
[3,4,2,5,1] => 7
[3,4,5,1,2] => 7
[3,4,5,2,1] => 6
[3,5,1,2,4] => 5
[3,5,1,4,2] => 4
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 4
[3,5,2,4,1] => 3
[3,5,4,1,2] => 8
[3,5,4,2,1] => 7
[4,1,2,3,5] => 3
[4,1,2,5,3] => 7
[4,1,3,2,5] => 2
[4,1,3,5,2] => 6
[4,1,5,2,3] => 6
[4,1,5,3,2] => 5
[4,2,1,3,5] => 2
[4,2,1,5,3] => 6
[4,2,3,1,5] => 1
[4,2,3,5,1] => 5
[4,2,5,1,3] => 5
[4,2,5,3,1] => 4
[4,3,1,2,5] => 5
[4,3,1,5,2] => 9
[4,3,2,1,5] => 4
[4,3,2,5,1] => 8
[4,3,5,1,2] => 8
[4,3,5,2,1] => 7
[4,5,1,2,3] => 6
[4,5,1,3,2] => 5
[4,5,2,1,3] => 5
[4,5,2,3,1] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 3
[5,1,2,3,4] => 4
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 2
[5,1,4,2,3] => 7
[5,1,4,3,2] => 6
[5,2,1,3,4] => 3
[5,2,1,4,3] => 2
[5,2,3,1,4] => 2
[5,2,3,4,1] => 1
[5,2,4,1,3] => 6
[5,2,4,3,1] => 5
[5,3,1,2,4] => 6
[5,3,1,4,2] => 5
[5,3,2,1,4] => 5
[5,3,2,4,1] => 4
[5,3,4,1,2] => 9
[5,3,4,2,1] => 8
[5,4,1,2,3] => 7
[5,4,1,3,2] => 6
[5,4,2,1,3] => 6
[5,4,2,3,1] => 5
[5,4,3,1,2] => 5
[5,4,3,2,1] => 4
[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] => 9
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 7
[1,2,4,5,6,3] => 12
[1,2,4,6,3,5] => 8
[1,2,4,6,5,3] => 7
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 9
[1,2,5,4,3,6] => 3
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 8
[1,2,5,6,4,3] => 7
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 4
[1,2,6,4,3,5] => 4
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 9
[1,2,6,5,4,3] => 8
[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] => 11
[1,3,2,6,4,5] => 7
[1,3,2,6,5,4] => 6
[1,3,4,2,5,6] => 5
[1,3,4,2,6,5] => 10
[1,3,4,5,2,6] => 9
[1,3,4,5,6,2] => 14
[1,3,4,6,2,5] => 10
[1,3,4,6,5,2] => 9
[1,3,5,2,4,6] => 6
[1,3,5,2,6,4] => 11
[1,3,5,4,2,6] => 5
[1,3,5,4,6,2] => 10
[1,3,5,6,2,4] => 10
[1,3,5,6,4,2] => 9
[1,3,6,2,4,5] => 7
[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] => 11
[1,3,6,5,4,2] => 10
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 7
[1,4,2,5,6,3] => 12
[1,4,2,6,3,5] => 8
[1,4,2,6,5,3] => 7
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 7
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 11
[1,4,3,6,2,5] => 7
[1,4,3,6,5,2] => 6
[1,4,5,2,3,6] => 6
[1,4,5,2,6,3] => 11
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 10
[1,4,5,6,2,3] => 10
[1,4,5,6,3,2] => 9
[1,4,6,2,3,5] => 7
[1,4,6,2,5,3] => 6
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 11
[1,4,6,5,3,2] => 10
[1,5,2,3,4,6] => 4
[1,5,2,3,6,4] => 9
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 8
[1,5,2,6,4,3] => 7
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 7
[1,5,3,6,2,4] => 7
[1,5,3,6,4,2] => 6
[1,5,4,2,3,6] => 7
[1,5,4,2,6,3] => 12
[1,5,4,3,2,6] => 6
[1,5,4,3,6,2] => 11
[1,5,4,6,2,3] => 11
[1,5,4,6,3,2] => 10
[1,5,6,2,3,4] => 8
[1,5,6,2,4,3] => 7
[1,5,6,3,2,4] => 7
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 6
[1,5,6,4,3,2] => 5
[1,6,2,3,4,5] => 5
[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] => 9
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 4
[1,6,3,2,5,4] => 3
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 2
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 7
[1,6,4,2,3,5] => 8
[1,6,4,2,5,3] => 7
[1,6,4,3,2,5] => 7
[1,6,4,3,5,2] => 6
[1,6,4,5,2,3] => 12
[1,6,4,5,3,2] => 11
[1,6,5,2,3,4] => 9
[1,6,5,2,4,3] => 8
[1,6,5,3,2,4] => 8
[1,6,5,3,4,2] => 7
[1,6,5,4,2,3] => 7
[1,6,5,4,3,2] => 6
[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] => 10
[2,1,3,6,4,5] => 6
[2,1,3,6,5,4] => 5
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 13
[2,1,4,6,3,5] => 9
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 5
[2,1,5,3,6,4] => 10
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 9
[2,1,5,6,3,4] => 9
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 5
[2,1,6,4,3,5] => 5
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 10
[2,1,6,5,4,3] => 9
[2,3,1,4,5,6] => 3
[2,3,1,4,6,5] => 8
[2,3,1,5,4,6] => 7
[2,3,1,5,6,4] => 12
[2,3,1,6,4,5] => 8
[2,3,1,6,5,4] => 7
[2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => 11
[2,3,4,5,1,6] => 10
[2,3,4,5,6,1] => 15
[2,3,4,6,1,5] => 11
[2,3,4,6,5,1] => 10
[2,3,5,1,4,6] => 7
[2,3,5,1,6,4] => 12
[2,3,5,4,1,6] => 6
[2,3,5,4,6,1] => 11
[2,3,5,6,1,4] => 11
[2,3,5,6,4,1] => 10
[2,3,6,1,4,5] => 8
[2,3,6,1,5,4] => 7
[2,3,6,4,1,5] => 7
[2,3,6,4,5,1] => 6
[2,3,6,5,1,4] => 12
[2,3,6,5,4,1] => 11
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 9
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 13
[2,4,1,6,3,5] => 9
[2,4,1,6,5,3] => 8
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 7
[2,4,3,5,6,1] => 12
[2,4,3,6,1,5] => 8
[2,4,3,6,5,1] => 7
[2,4,5,1,3,6] => 7
[2,4,5,1,6,3] => 12
[2,4,5,3,1,6] => 6
[2,4,5,3,6,1] => 11
[2,4,5,6,1,3] => 11
[2,4,5,6,3,1] => 10
[2,4,6,1,3,5] => 8
[2,4,6,1,5,3] => 7
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 6
[2,4,6,5,1,3] => 12
[2,4,6,5,3,1] => 11
[2,5,1,3,4,6] => 5
[2,5,1,3,6,4] => 10
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 9
[2,5,1,6,3,4] => 9
[2,5,1,6,4,3] => 8
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 9
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 8
[2,5,3,6,1,4] => 8
[2,5,3,6,4,1] => 7
[2,5,4,1,3,6] => 8
[2,5,4,1,6,3] => 13
[2,5,4,3,1,6] => 7
[2,5,4,3,6,1] => 12
[2,5,4,6,1,3] => 12
[2,5,4,6,3,1] => 11
[2,5,6,1,3,4] => 9
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 7
[2,5,6,4,1,3] => 7
[2,5,6,4,3,1] => 6
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 5
[2,6,1,4,3,5] => 5
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 10
[2,6,1,5,4,3] => 9
[2,6,3,1,4,5] => 5
[2,6,3,1,5,4] => 4
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 9
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 9
[2,6,4,1,5,3] => 8
[2,6,4,3,1,5] => 8
[2,6,4,3,5,1] => 7
[2,6,4,5,1,3] => 13
[2,6,4,5,3,1] => 12
[2,6,5,1,3,4] => 10
[2,6,5,1,4,3] => 9
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 8
[2,6,5,4,1,3] => 8
[2,6,5,4,3,1] => 7
[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] => 11
[3,1,2,6,4,5] => 7
[3,1,2,6,5,4] => 6
[3,1,4,2,5,6] => 5
[3,1,4,2,6,5] => 10
[3,1,4,5,2,6] => 9
[3,1,4,5,6,2] => 14
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 9
[3,1,5,2,4,6] => 6
[3,1,5,2,6,4] => 11
[3,1,5,4,2,6] => 5
[3,1,5,4,6,2] => 10
[3,1,5,6,2,4] => 10
[3,1,5,6,4,2] => 9
[3,1,6,2,4,5] => 7
[3,1,6,2,5,4] => 6
[3,1,6,4,2,5] => 6
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 11
[3,1,6,5,4,2] => 10
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 6
[3,2,1,5,4,6] => 5
[3,2,1,5,6,4] => 10
[3,2,1,6,4,5] => 6
[3,2,1,6,5,4] => 5
[3,2,4,1,5,6] => 4
[3,2,4,1,6,5] => 9
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 13
[3,2,4,6,1,5] => 9
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 5
[3,2,5,1,6,4] => 10
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 9
[3,2,5,6,1,4] => 9
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 6
[3,2,6,1,5,4] => 5
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 10
[3,2,6,5,4,1] => 9
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 9
[3,4,1,5,2,6] => 8
[3,4,1,5,6,2] => 13
[3,4,1,6,2,5] => 9
[3,4,1,6,5,2] => 8
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 7
[3,4,2,5,6,1] => 12
[3,4,2,6,1,5] => 8
[3,4,2,6,5,1] => 7
[3,4,5,1,2,6] => 7
[3,4,5,1,6,2] => 12
[3,4,5,2,1,6] => 6
[3,4,5,2,6,1] => 11
[3,4,5,6,1,2] => 11
[3,4,5,6,2,1] => 10
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 6
[3,4,6,5,1,2] => 12
[3,4,6,5,2,1] => 11
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 10
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 9
[3,5,1,6,2,4] => 9
[3,5,1,6,4,2] => 8
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 9
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 8
[3,5,2,6,1,4] => 8
[3,5,2,6,4,1] => 7
[3,5,4,1,2,6] => 8
[3,5,4,1,6,2] => 13
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 12
[3,5,4,6,1,2] => 12
[3,5,4,6,2,1] => 11
[3,5,6,1,2,4] => 9
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 7
[3,5,6,4,1,2] => 7
[3,5,6,4,2,1] => 6
[3,6,1,2,4,5] => 6
[3,6,1,2,5,4] => 5
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 4
[3,6,1,5,2,4] => 10
[3,6,1,5,4,2] => 9
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 4
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 9
[3,6,2,5,4,1] => 8
[3,6,4,1,2,5] => 9
[3,6,4,1,5,2] => 8
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 7
[3,6,4,5,1,2] => 13
[3,6,4,5,2,1] => 12
[3,6,5,1,2,4] => 10
[3,6,5,1,4,2] => 9
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 8
[3,6,5,4,2,1] => 7
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 8
[4,1,2,5,3,6] => 7
[4,1,2,5,6,3] => 12
[4,1,2,6,3,5] => 8
[4,1,2,6,5,3] => 7
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 7
[4,1,3,5,2,6] => 6
[4,1,3,5,6,2] => 11
[4,1,3,6,2,5] => 7
[4,1,3,6,5,2] => 6
[4,1,5,2,3,6] => 6
[4,1,5,2,6,3] => 11
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 10
[4,1,5,6,2,3] => 10
[4,1,5,6,3,2] => 9
[4,1,6,2,3,5] => 7
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 6
[4,1,6,3,5,2] => 5
[4,1,6,5,2,3] => 11
[4,1,6,5,3,2] => 10
[4,2,1,3,5,6] => 2
[4,2,1,3,6,5] => 7
[4,2,1,5,3,6] => 6
[4,2,1,5,6,3] => 11
[4,2,1,6,3,5] => 7
[4,2,1,6,5,3] => 6
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 5
[4,2,3,5,6,1] => 10
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 5
[4,2,5,1,6,3] => 10
[4,2,5,3,1,6] => 4
[4,2,5,3,6,1] => 9
[4,2,5,6,1,3] => 9
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 5
[4,2,6,3,1,5] => 5
[4,2,6,3,5,1] => 4
[4,2,6,5,1,3] => 10
[4,2,6,5,3,1] => 9
[4,3,1,2,5,6] => 5
[4,3,1,2,6,5] => 10
[4,3,1,5,2,6] => 9
[4,3,1,5,6,2] => 14
[4,3,1,6,2,5] => 10
[4,3,1,6,5,2] => 9
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 9
[4,3,2,5,1,6] => 8
[4,3,2,5,6,1] => 13
[4,3,2,6,1,5] => 9
[4,3,2,6,5,1] => 8
[4,3,5,1,2,6] => 8
[4,3,5,1,6,2] => 13
[4,3,5,2,1,6] => 7
[4,3,5,2,6,1] => 12
[4,3,5,6,1,2] => 12
[4,3,5,6,2,1] => 11
[4,3,6,1,2,5] => 9
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 7
[4,3,6,5,1,2] => 13
[4,3,6,5,2,1] => 12
[4,5,1,2,3,6] => 6
[4,5,1,2,6,3] => 11
[4,5,1,3,2,6] => 5
[4,5,1,3,6,2] => 10
[4,5,1,6,2,3] => 10
[4,5,1,6,3,2] => 9
[4,5,2,1,3,6] => 5
[4,5,2,1,6,3] => 10
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 9
[4,5,2,6,1,3] => 9
[4,5,2,6,3,1] => 8
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 9
[4,5,3,2,1,6] => 3
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 7
[4,5,6,1,2,3] => 9
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 7
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 7
[4,6,1,2,5,3] => 6
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 5
[4,6,1,5,2,3] => 11
[4,6,1,5,3,2] => 10
[4,6,2,1,3,5] => 6
[4,6,2,1,5,3] => 5
[4,6,2,3,1,5] => 5
[4,6,2,3,5,1] => 4
[4,6,2,5,1,3] => 10
[4,6,2,5,3,1] => 9
[4,6,3,1,2,5] => 5
[4,6,3,1,5,2] => 4
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 3
[4,6,3,5,1,2] => 9
[4,6,3,5,2,1] => 8
[4,6,5,1,2,3] => 10
[4,6,5,1,3,2] => 9
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 8
[4,6,5,3,1,2] => 8
[4,6,5,3,2,1] => 7
[5,1,2,3,4,6] => 4
[5,1,2,3,6,4] => 9
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 8
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 7
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 2
[5,1,3,4,6,2] => 7
[5,1,3,6,2,4] => 7
[5,1,3,6,4,2] => 6
[5,1,4,2,3,6] => 7
[5,1,4,2,6,3] => 12
[5,1,4,3,2,6] => 6
[5,1,4,3,6,2] => 11
[5,1,4,6,2,3] => 11
[5,1,4,6,3,2] => 10
[5,1,6,2,3,4] => 8
[5,1,6,2,4,3] => 7
[5,1,6,3,2,4] => 7
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 6
[5,1,6,4,3,2] => 5
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 8
[5,2,1,4,3,6] => 2
[5,2,1,4,6,3] => 7
[5,2,1,6,3,4] => 7
[5,2,1,6,4,3] => 6
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 7
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 5
[5,2,4,1,3,6] => 6
[5,2,4,1,6,3] => 11
[5,2,4,3,1,6] => 5
[5,2,4,3,6,1] => 10
[5,2,4,6,1,3] => 10
[5,2,4,6,3,1] => 9
[5,2,6,1,3,4] => 7
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 5
[5,2,6,4,1,3] => 5
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 11
[5,3,1,4,2,6] => 5
[5,3,1,4,6,2] => 10
[5,3,1,6,2,4] => 10
[5,3,1,6,4,2] => 9
[5,3,2,1,4,6] => 5
[5,3,2,1,6,4] => 10
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 9
[5,3,2,6,1,4] => 9
[5,3,2,6,4,1] => 8
[5,3,4,1,2,6] => 9
[5,3,4,1,6,2] => 14
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 13
[5,3,4,6,1,2] => 13
[5,3,4,6,2,1] => 12
[5,3,6,1,2,4] => 10
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 9
[5,3,6,2,4,1] => 8
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 7
[5,4,1,2,3,6] => 7
[5,4,1,2,6,3] => 12
[5,4,1,3,2,6] => 6
[5,4,1,3,6,2] => 11
[5,4,1,6,2,3] => 11
[5,4,1,6,3,2] => 10
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 11
[5,4,2,3,1,6] => 5
[5,4,2,3,6,1] => 10
[5,4,2,6,1,3] => 10
[5,4,2,6,3,1] => 9
[5,4,3,1,2,6] => 5
[5,4,3,1,6,2] => 10
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 9
[5,4,3,6,1,2] => 9
[5,4,3,6,2,1] => 8
[5,4,6,1,2,3] => 10
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 9
[5,4,6,2,3,1] => 8
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 7
[5,6,1,2,3,4] => 8
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 7
[5,6,1,3,4,2] => 6
[5,6,1,4,2,3] => 6
[5,6,1,4,3,2] => 5
[5,6,2,1,3,4] => 7
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 6
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 5
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 6
[5,6,3,1,4,2] => 5
[5,6,3,2,1,4] => 5
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 4
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 11
[5,6,4,1,3,2] => 10
[5,6,4,2,1,3] => 10
[5,6,4,2,3,1] => 9
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 8
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 4
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 9
[6,1,2,5,4,3] => 8
[6,1,3,2,4,5] => 4
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 2
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 7
[6,1,4,2,3,5] => 8
[6,1,4,2,5,3] => 7
[6,1,4,3,2,5] => 7
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 12
[6,1,4,5,3,2] => 11
[6,1,5,2,3,4] => 9
[6,1,5,2,4,3] => 8
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 7
[6,1,5,4,2,3] => 7
[6,1,5,4,3,2] => 6
[6,2,1,3,4,5] => 4
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 3
[6,2,1,4,5,3] => 2
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 7
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 2
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 7
[6,2,3,5,4,1] => 6
[6,2,4,1,3,5] => 7
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 5
[6,2,4,5,1,3] => 11
[6,2,4,5,3,1] => 10
[6,2,5,1,3,4] => 8
[6,2,5,1,4,3] => 7
[6,2,5,3,1,4] => 7
[6,2,5,3,4,1] => 6
[6,2,5,4,1,3] => 6
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 7
[6,3,1,2,5,4] => 6
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 11
[6,3,1,5,4,2] => 10
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 5
[6,3,2,4,1,5] => 5
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 10
[6,3,2,5,4,1] => 9
[6,3,4,1,2,5] => 10
[6,3,4,1,5,2] => 9
[6,3,4,2,1,5] => 9
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 14
[6,3,4,5,2,1] => 13
[6,3,5,1,2,4] => 11
[6,3,5,1,4,2] => 10
[6,3,5,2,1,4] => 10
[6,3,5,2,4,1] => 9
[6,3,5,4,1,2] => 9
[6,3,5,4,2,1] => 8
[6,4,1,2,3,5] => 8
[6,4,1,2,5,3] => 7
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 6
[6,4,1,5,2,3] => 12
[6,4,1,5,3,2] => 11
[6,4,2,1,3,5] => 7
[6,4,2,1,5,3] => 6
[6,4,2,3,1,5] => 6
[6,4,2,3,5,1] => 5
[6,4,2,5,1,3] => 11
[6,4,2,5,3,1] => 10
[6,4,3,1,2,5] => 6
[6,4,3,1,5,2] => 5
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 10
[6,4,3,5,2,1] => 9
[6,4,5,1,2,3] => 11
[6,4,5,1,3,2] => 10
[6,4,5,2,1,3] => 10
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 9
[6,4,5,3,2,1] => 8
[6,5,1,2,3,4] => 9
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 8
[6,5,1,3,4,2] => 7
[6,5,1,4,2,3] => 7
[6,5,1,4,3,2] => 6
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 7
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 6
[6,5,2,4,1,3] => 6
[6,5,2,4,3,1] => 5
[6,5,3,1,2,4] => 7
[6,5,3,1,4,2] => 6
[6,5,3,2,1,4] => 6
[6,5,3,2,4,1] => 5
[6,5,3,4,1,2] => 5
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 12
[6,5,4,1,3,2] => 11
[6,5,4,2,1,3] => 11
[6,5,4,2,3,1] => 10
[6,5,4,3,1,2] => 10
[6,5,4,3,2,1] => 9
[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] => 11
[1,2,3,4,7,5,6] => 6
[1,2,3,4,7,6,5] => 5
[1,2,3,5,4,6,7] => 4
[1,2,3,5,4,7,6] => 10
[1,2,3,5,6,4,7] => 9
[1,2,3,5,6,7,4] => 15
[1,2,3,5,7,4,6] => 10
[1,2,3,5,7,6,4] => 9
[1,2,3,6,4,5,7] => 5
[1,2,3,6,4,7,5] => 11
[1,2,3,6,5,4,7] => 4
[1,2,3,6,5,7,4] => 10
[1,2,3,6,7,4,5] => 10
[1,2,3,6,7,5,4] => 9
[1,2,3,7,4,5,6] => 6
[1,2,3,7,4,6,5] => 5
[1,2,3,7,5,4,6] => 5
[1,2,3,7,5,6,4] => 4
[1,2,3,7,6,4,5] => 11
[1,2,3,7,6,5,4] => 10
[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] => 14
[1,2,4,3,7,5,6] => 9
[1,2,4,3,7,6,5] => 8
[1,2,4,5,3,6,7] => 7
[1,2,4,5,3,7,6] => 13
[1,2,4,5,6,3,7] => 12
[1,2,4,5,6,7,3] => 18
[1,2,4,5,7,3,6] => 13
[1,2,4,5,7,6,3] => 12
[1,2,4,6,3,5,7] => 8
[1,2,4,6,3,7,5] => 14
[1,2,4,6,5,3,7] => 7
[1,2,4,6,5,7,3] => 13
[1,2,4,6,7,3,5] => 13
[1,2,4,6,7,5,3] => 12
[1,2,4,7,3,5,6] => 9
[1,2,4,7,3,6,5] => 8
[1,2,4,7,5,3,6] => 8
[1,2,4,7,5,6,3] => 7
[1,2,4,7,6,3,5] => 14
[1,2,4,7,6,5,3] => 13
[1,2,5,3,4,6,7] => 4
[1,2,5,3,4,7,6] => 10
[1,2,5,3,6,4,7] => 9
[1,2,5,3,6,7,4] => 15
[1,2,5,3,7,4,6] => 10
[1,2,5,3,7,6,4] => 9
[1,2,5,4,3,6,7] => 3
[1,2,5,4,3,7,6] => 9
[1,2,5,4,6,3,7] => 8
[1,2,5,4,6,7,3] => 14
[1,2,5,4,7,3,6] => 9
[1,2,5,4,7,6,3] => 8
[1,2,5,6,3,4,7] => 8
[1,2,5,6,3,7,4] => 14
[1,2,5,6,4,3,7] => 7
[1,2,5,6,4,7,3] => 13
[1,2,5,6,7,3,4] => 13
[1,2,5,6,7,4,3] => 12
[1,2,5,7,3,4,6] => 9
[1,2,5,7,3,6,4] => 8
[1,2,5,7,4,3,6] => 8
[1,2,5,7,4,6,3] => 7
[1,2,5,7,6,3,4] => 14
[1,2,5,7,6,4,3] => 13
[1,2,6,3,4,5,7] => 5
[1,2,6,3,4,7,5] => 11
[1,2,6,3,5,4,7] => 4
[1,2,6,3,5,7,4] => 10
[1,2,6,3,7,4,5] => 10
[1,2,6,3,7,5,4] => 9
[1,2,6,4,3,5,7] => 4
[1,2,6,4,3,7,5] => 10
[1,2,6,4,5,3,7] => 3
[1,2,6,4,5,7,3] => 9
[1,2,6,4,7,3,5] => 9
[1,2,6,4,7,5,3] => 8
[1,2,6,5,3,4,7] => 9
[1,2,6,5,3,7,4] => 15
[1,2,6,5,4,3,7] => 8
[1,2,6,5,4,7,3] => 14
[1,2,6,5,7,3,4] => 14
[1,2,6,5,7,4,3] => 13
[1,2,6,7,3,4,5] => 10
[1,2,6,7,3,5,4] => 9
[1,2,6,7,4,3,5] => 9
[1,2,6,7,4,5,3] => 8
[1,2,6,7,5,3,4] => 8
[1,2,6,7,5,4,3] => 7
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 5
[1,2,7,3,5,4,6] => 5
[1,2,7,3,5,6,4] => 4
[1,2,7,3,6,4,5] => 11
[1,2,7,3,6,5,4] => 10
[1,2,7,4,3,5,6] => 5
[1,2,7,4,3,6,5] => 4
[1,2,7,4,5,3,6] => 4
[1,2,7,4,5,6,3] => 3
[1,2,7,4,6,3,5] => 10
[1,2,7,4,6,5,3] => 9
[1,2,7,5,3,4,6] => 10
[1,2,7,5,3,6,4] => 9
[1,2,7,5,4,3,6] => 9
[1,2,7,5,4,6,3] => 8
[1,2,7,5,6,3,4] => 15
[1,2,7,5,6,4,3] => 14
[1,2,7,6,3,4,5] => 11
[1,2,7,6,3,5,4] => 10
[1,2,7,6,4,3,5] => 10
[1,2,7,6,4,5,3] => 9
[1,2,7,6,5,3,4] => 9
[1,2,7,6,5,4,3] => 8
[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] => 13
[1,3,2,4,7,5,6] => 8
[1,3,2,4,7,6,5] => 7
[1,3,2,5,4,6,7] => 6
[1,3,2,5,4,7,6] => 12
[1,3,2,5,6,4,7] => 11
[1,3,2,5,6,7,4] => 17
[1,3,2,5,7,4,6] => 12
[1,3,2,5,7,6,4] => 11
[1,3,2,6,4,5,7] => 7
[1,3,2,6,4,7,5] => 13
[1,3,2,6,5,4,7] => 6
[1,3,2,6,5,7,4] => 12
[1,3,2,6,7,4,5] => 12
[1,3,2,6,7,5,4] => 11
[1,3,2,7,4,5,6] => 8
[1,3,2,7,4,6,5] => 7
[1,3,2,7,5,4,6] => 7
[1,3,2,7,5,6,4] => 6
[1,3,2,7,6,4,5] => 13
[1,3,2,7,6,5,4] => 12
[1,3,4,2,5,6,7] => 5
[1,3,4,2,5,7,6] => 11
[1,3,4,2,6,5,7] => 10
[1,3,4,2,6,7,5] => 16
[1,3,4,2,7,5,6] => 11
[1,3,4,2,7,6,5] => 10
[1,3,4,5,2,6,7] => 9
[1,3,4,5,2,7,6] => 15
[1,3,4,5,6,2,7] => 14
[1,3,4,5,6,7,2] => 20
[1,3,4,5,7,2,6] => 15
[1,3,4,5,7,6,2] => 14
[1,3,4,6,2,5,7] => 10
[1,3,4,6,2,7,5] => 16
[1,3,4,6,5,2,7] => 9
[1,3,4,6,5,7,2] => 15
[1,3,4,6,7,2,5] => 15
[1,3,4,6,7,5,2] => 14
[1,3,4,7,2,5,6] => 11
[1,3,4,7,2,6,5] => 10
[1,3,4,7,5,2,6] => 10
[1,3,4,7,5,6,2] => 9
[1,3,4,7,6,2,5] => 16
[1,3,4,7,6,5,2] => 15
[1,3,5,2,4,6,7] => 6
[1,3,5,2,4,7,6] => 12
[1,3,5,2,6,4,7] => 11
[1,3,5,2,6,7,4] => 17
[1,3,5,2,7,4,6] => 12
[1,3,5,2,7,6,4] => 11
[1,3,5,4,2,6,7] => 5
[1,3,5,4,2,7,6] => 11
[1,3,5,4,6,2,7] => 10
[1,3,5,4,6,7,2] => 16
[1,3,5,4,7,2,6] => 11
[1,3,5,4,7,6,2] => 10
[1,3,5,6,2,4,7] => 10
[1,3,5,6,2,7,4] => 16
[1,3,5,6,4,2,7] => 9
[1,3,5,6,4,7,2] => 15
[1,3,5,6,7,2,4] => 15
[1,3,5,6,7,4,2] => 14
[1,3,5,7,2,4,6] => 11
[1,3,5,7,2,6,4] => 10
[1,3,5,7,4,2,6] => 10
[1,3,5,7,4,6,2] => 9
[1,3,5,7,6,2,4] => 16
[1,3,5,7,6,4,2] => 15
[1,3,6,2,4,5,7] => 7
[1,3,6,2,4,7,5] => 13
[1,3,6,2,5,4,7] => 6
[1,3,6,2,5,7,4] => 12
[1,3,6,2,7,4,5] => 12
[1,3,6,2,7,5,4] => 11
[1,3,6,4,2,5,7] => 6
[1,3,6,4,2,7,5] => 12
[1,3,6,4,5,2,7] => 5
[1,3,6,4,5,7,2] => 11
[1,3,6,4,7,2,5] => 11
[1,3,6,4,7,5,2] => 10
[1,3,6,5,2,4,7] => 11
[1,3,6,5,2,7,4] => 17
[1,3,6,5,4,2,7] => 10
[1,3,6,5,4,7,2] => 16
[1,3,6,5,7,2,4] => 16
[1,3,6,5,7,4,2] => 15
[1,3,6,7,2,4,5] => 12
[1,3,6,7,2,5,4] => 11
[1,3,6,7,4,2,5] => 11
[1,3,6,7,4,5,2] => 10
[1,3,6,7,5,2,4] => 10
[1,3,6,7,5,4,2] => 9
[1,3,7,2,4,5,6] => 8
[1,3,7,2,4,6,5] => 7
[1,3,7,2,5,4,6] => 7
[1,3,7,2,5,6,4] => 6
[1,3,7,2,6,4,5] => 13
[1,3,7,2,6,5,4] => 12
[1,3,7,4,2,5,6] => 7
[1,3,7,4,2,6,5] => 6
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 12
[1,3,7,4,6,5,2] => 11
[1,3,7,5,2,4,6] => 12
[1,3,7,5,2,6,4] => 11
[1,3,7,5,4,2,6] => 11
[1,3,7,5,4,6,2] => 10
[1,3,7,5,6,2,4] => 17
[1,3,7,5,6,4,2] => 16
[1,3,7,6,2,4,5] => 13
[1,3,7,6,2,5,4] => 12
[1,3,7,6,4,2,5] => 12
[1,3,7,6,4,5,2] => 11
[1,3,7,6,5,2,4] => 11
[1,3,7,6,5,4,2] => 10
[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] => 14
[1,4,2,3,7,5,6] => 9
[1,4,2,3,7,6,5] => 8
[1,4,2,5,3,6,7] => 7
[1,4,2,5,3,7,6] => 13
[1,4,2,5,6,3,7] => 12
[1,4,2,5,6,7,3] => 18
[1,4,2,5,7,3,6] => 13
[1,4,2,5,7,6,3] => 12
[1,4,2,6,3,5,7] => 8
[1,4,2,6,3,7,5] => 14
[1,4,2,6,5,3,7] => 7
[1,4,2,6,5,7,3] => 13
[1,4,2,6,7,3,5] => 13
[1,4,2,6,7,5,3] => 12
[1,4,2,7,3,5,6] => 9
[1,4,2,7,3,6,5] => 8
[1,4,2,7,5,3,6] => 8
[1,4,2,7,5,6,3] => 7
[1,4,2,7,6,3,5] => 14
[1,4,2,7,6,5,3] => 13
[1,4,3,2,5,6,7] => 2
[1,4,3,2,5,7,6] => 8
[1,4,3,2,6,5,7] => 7
[1,4,3,2,6,7,5] => 13
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 7
[1,4,3,5,2,6,7] => 6
[1,4,3,5,2,7,6] => 12
[1,4,3,5,6,2,7] => 11
[1,4,3,5,6,7,2] => 17
[1,4,3,5,7,2,6] => 12
[1,4,3,5,7,6,2] => 11
[1,4,3,6,2,5,7] => 7
[1,4,3,6,2,7,5] => 13
[1,4,3,6,5,2,7] => 6
[1,4,3,6,5,7,2] => 12
[1,4,3,6,7,2,5] => 12
[1,4,3,6,7,5,2] => 11
[1,4,3,7,2,5,6] => 8
[1,4,3,7,2,6,5] => 7
[1,4,3,7,5,2,6] => 7
[1,4,3,7,5,6,2] => 6
[1,4,3,7,6,2,5] => 13
[1,4,3,7,6,5,2] => 12
[1,4,5,2,3,6,7] => 6
[1,4,5,2,3,7,6] => 12
[1,4,5,2,6,3,7] => 11
[1,4,5,2,6,7,3] => 17
[1,4,5,2,7,3,6] => 12
[1,4,5,2,7,6,3] => 11
[1,4,5,3,2,6,7] => 5
[1,4,5,3,2,7,6] => 11
[1,4,5,3,6,2,7] => 10
[1,4,5,3,6,7,2] => 16
[1,4,5,3,7,2,6] => 11
[1,4,5,3,7,6,2] => 10
[1,4,5,6,2,3,7] => 10
[1,4,5,6,2,7,3] => 16
[1,4,5,6,3,2,7] => 9
[1,4,5,6,3,7,2] => 15
[1,4,5,6,7,2,3] => 15
[1,4,5,6,7,3,2] => 14
[1,4,5,7,2,3,6] => 11
[1,4,5,7,2,6,3] => 10
[1,4,5,7,3,2,6] => 10
[1,4,5,7,3,6,2] => 9
[1,4,5,7,6,2,3] => 16
[1,4,5,7,6,3,2] => 15
[1,4,6,2,3,5,7] => 7
[1,4,6,2,3,7,5] => 13
[1,4,6,2,5,3,7] => 6
[1,4,6,2,5,7,3] => 12
[1,4,6,2,7,3,5] => 12
[1,4,6,2,7,5,3] => 11
[1,4,6,3,2,5,7] => 6
[1,4,6,3,2,7,5] => 12
[1,4,6,3,5,2,7] => 5
[1,4,6,3,5,7,2] => 11
[1,4,6,3,7,2,5] => 11
[1,4,6,3,7,5,2] => 10
[1,4,6,5,2,3,7] => 11
[1,4,6,5,2,7,3] => 17
[1,4,6,5,3,2,7] => 10
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
Haglund's hag of a permutation.
Let $edif$ be the sum of the differences of exceedence tops and bottoms, let $\pi_E$ the subsequence of exceedence tops and let $\pi_N$ be the subsequence of non-exceedence tops. Finally, let $L$ be the number of pairs of indices $k < i$ such that $\pi_k \leq i < \pi_i$.
Then $hag(\pi) = edif + inv(\pi_E) - inv(\pi_N) + L$, where $inv$ denotes the number of inversions of a word.
References
[1] Wilson, M. C. An interesting new Mahonian permutation statistic MathSciNet:2745700
Code
def statistic(pi):
    standard = sage.combinat.permutation.to_standard
    pi_E = standard([pi_i for i, pi_i in enumerate(pi, 1) if i < pi_i])
    pi_N = standard([pi_i for i, pi_i in enumerate(pi, 1) if i >= pi_i])
    edif = sum(pi_i - i for i, pi_i in enumerate(pi, 1) if i < pi_i)
    L = sum(sum(1 for k in range(1, i) if pi(k) <= i)
            for i, pi_i in enumerate(pi, 1) if i < pi_i)
    return edif + pi_E.number_of_inversions() - pi_N.number_of_inversions() + L
Created
Jan 18, 2021 at 19:10 by Martin Rubey
Updated
Jan 18, 2021 at 19:10 by Martin Rubey