edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 4
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 10
[1,2,4,3] => 9
[1,3,2,4] => 9
[1,3,4,2] => 7
[1,4,2,3] => 7
[1,4,3,2] => 6
[2,1,3,4] => 9
[2,1,4,3] => 8
[2,3,1,4] => 7
[2,3,4,1] => 4
[2,4,1,3] => 5
[2,4,3,1] => 3
[3,1,2,4] => 7
[3,1,4,2] => 5
[3,2,1,4] => 6
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 1
[4,1,2,3] => 4
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 20
[1,2,3,5,4] => 19
[1,2,4,3,5] => 19
[1,2,4,5,3] => 17
[1,2,5,3,4] => 17
[1,2,5,4,3] => 16
[1,3,2,4,5] => 19
[1,3,2,5,4] => 18
[1,3,4,2,5] => 17
[1,3,4,5,2] => 14
[1,3,5,2,4] => 15
[1,3,5,4,2] => 13
[1,4,2,3,5] => 17
[1,4,2,5,3] => 15
[1,4,3,2,5] => 16
[1,4,3,5,2] => 13
[1,4,5,2,3] => 12
[1,4,5,3,2] => 11
[1,5,2,3,4] => 14
[1,5,2,4,3] => 13
[1,5,3,2,4] => 13
[1,5,3,4,2] => 11
[1,5,4,2,3] => 11
[1,5,4,3,2] => 10
[2,1,3,4,5] => 19
[2,1,3,5,4] => 18
[2,1,4,3,5] => 18
[2,1,4,5,3] => 16
[2,1,5,3,4] => 16
[2,1,5,4,3] => 15
[2,3,1,4,5] => 17
[2,3,1,5,4] => 16
[2,3,4,1,5] => 14
[2,3,4,5,1] => 10
[2,3,5,1,4] => 12
[2,3,5,4,1] => 9
[2,4,1,3,5] => 15
[2,4,1,5,3] => 13
[2,4,3,1,5] => 13
[2,4,3,5,1] => 9
[2,4,5,1,3] => 9
[2,4,5,3,1] => 7
[2,5,1,3,4] => 12
[2,5,1,4,3] => 11
[2,5,3,1,4] => 10
[2,5,3,4,1] => 7
[2,5,4,1,3] => 8
[2,5,4,3,1] => 6
[3,1,2,4,5] => 17
[3,1,2,5,4] => 16
[3,1,4,2,5] => 15
[3,1,4,5,2] => 12
[3,1,5,2,4] => 13
[3,1,5,4,2] => 11
[3,2,1,4,5] => 16
[3,2,1,5,4] => 15
[3,2,4,1,5] => 13
[3,2,4,5,1] => 9
[3,2,5,1,4] => 11
[3,2,5,4,1] => 8
[3,4,1,2,5] => 12
[3,4,1,5,2] => 9
[3,4,2,1,5] => 11
[3,4,2,5,1] => 7
[3,4,5,1,2] => 5
[3,4,5,2,1] => 4
[3,5,1,2,4] => 9
[3,5,1,4,2] => 7
>>> Load all 1201 entries. <<<
[3,5,2,1,4] => 8
[3,5,2,4,1] => 5
[3,5,4,1,2] => 4
[3,5,4,2,1] => 3
[4,1,2,3,5] => 14
[4,1,2,5,3] => 12
[4,1,3,2,5] => 13
[4,1,3,5,2] => 10
[4,1,5,2,3] => 9
[4,1,5,3,2] => 8
[4,2,1,3,5] => 13
[4,2,1,5,3] => 11
[4,2,3,1,5] => 11
[4,2,3,5,1] => 7
[4,2,5,1,3] => 7
[4,2,5,3,1] => 5
[4,3,1,2,5] => 11
[4,3,1,5,2] => 8
[4,3,2,1,5] => 10
[4,3,2,5,1] => 6
[4,3,5,1,2] => 4
[4,3,5,2,1] => 3
[4,5,1,2,3] => 5
[4,5,1,3,2] => 4
[4,5,2,1,3] => 4
[4,5,2,3,1] => 2
[4,5,3,1,2] => 2
[4,5,3,2,1] => 1
[5,1,2,3,4] => 10
[5,1,2,4,3] => 9
[5,1,3,2,4] => 9
[5,1,3,4,2] => 7
[5,1,4,2,3] => 7
[5,1,4,3,2] => 6
[5,2,1,3,4] => 9
[5,2,1,4,3] => 8
[5,2,3,1,4] => 7
[5,2,3,4,1] => 4
[5,2,4,1,3] => 5
[5,2,4,3,1] => 3
[5,3,1,2,4] => 7
[5,3,1,4,2] => 5
[5,3,2,1,4] => 6
[5,3,2,4,1] => 3
[5,3,4,1,2] => 2
[5,3,4,2,1] => 1
[5,4,1,2,3] => 4
[5,4,1,3,2] => 3
[5,4,2,1,3] => 3
[5,4,2,3,1] => 1
[5,4,3,1,2] => 1
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 35
[1,2,3,4,6,5] => 34
[1,2,3,5,4,6] => 34
[1,2,3,5,6,4] => 32
[1,2,3,6,4,5] => 32
[1,2,3,6,5,4] => 31
[1,2,4,3,5,6] => 34
[1,2,4,3,6,5] => 33
[1,2,4,5,3,6] => 32
[1,2,4,5,6,3] => 29
[1,2,4,6,3,5] => 30
[1,2,4,6,5,3] => 28
[1,2,5,3,4,6] => 32
[1,2,5,3,6,4] => 30
[1,2,5,4,3,6] => 31
[1,2,5,4,6,3] => 28
[1,2,5,6,3,4] => 27
[1,2,5,6,4,3] => 26
[1,2,6,3,4,5] => 29
[1,2,6,3,5,4] => 28
[1,2,6,4,3,5] => 28
[1,2,6,4,5,3] => 26
[1,2,6,5,3,4] => 26
[1,2,6,5,4,3] => 25
[1,3,2,4,5,6] => 34
[1,3,2,4,6,5] => 33
[1,3,2,5,4,6] => 33
[1,3,2,5,6,4] => 31
[1,3,2,6,4,5] => 31
[1,3,2,6,5,4] => 30
[1,3,4,2,5,6] => 32
[1,3,4,2,6,5] => 31
[1,3,4,5,2,6] => 29
[1,3,4,5,6,2] => 25
[1,3,4,6,2,5] => 27
[1,3,4,6,5,2] => 24
[1,3,5,2,4,6] => 30
[1,3,5,2,6,4] => 28
[1,3,5,4,2,6] => 28
[1,3,5,4,6,2] => 24
[1,3,5,6,2,4] => 24
[1,3,5,6,4,2] => 22
[1,3,6,2,4,5] => 27
[1,3,6,2,5,4] => 26
[1,3,6,4,2,5] => 25
[1,3,6,4,5,2] => 22
[1,3,6,5,2,4] => 23
[1,3,6,5,4,2] => 21
[1,4,2,3,5,6] => 32
[1,4,2,3,6,5] => 31
[1,4,2,5,3,6] => 30
[1,4,2,5,6,3] => 27
[1,4,2,6,3,5] => 28
[1,4,2,6,5,3] => 26
[1,4,3,2,5,6] => 31
[1,4,3,2,6,5] => 30
[1,4,3,5,2,6] => 28
[1,4,3,5,6,2] => 24
[1,4,3,6,2,5] => 26
[1,4,3,6,5,2] => 23
[1,4,5,2,3,6] => 27
[1,4,5,2,6,3] => 24
[1,4,5,3,2,6] => 26
[1,4,5,3,6,2] => 22
[1,4,5,6,2,3] => 20
[1,4,5,6,3,2] => 19
[1,4,6,2,3,5] => 24
[1,4,6,2,5,3] => 22
[1,4,6,3,2,5] => 23
[1,4,6,3,5,2] => 20
[1,4,6,5,2,3] => 19
[1,4,6,5,3,2] => 18
[1,5,2,3,4,6] => 29
[1,5,2,3,6,4] => 27
[1,5,2,4,3,6] => 28
[1,5,2,4,6,3] => 25
[1,5,2,6,3,4] => 24
[1,5,2,6,4,3] => 23
[1,5,3,2,4,6] => 28
[1,5,3,2,6,4] => 26
[1,5,3,4,2,6] => 26
[1,5,3,4,6,2] => 22
[1,5,3,6,2,4] => 22
[1,5,3,6,4,2] => 20
[1,5,4,2,3,6] => 26
[1,5,4,2,6,3] => 23
[1,5,4,3,2,6] => 25
[1,5,4,3,6,2] => 21
[1,5,4,6,2,3] => 19
[1,5,4,6,3,2] => 18
[1,5,6,2,3,4] => 20
[1,5,6,2,4,3] => 19
[1,5,6,3,2,4] => 19
[1,5,6,3,4,2] => 17
[1,5,6,4,2,3] => 17
[1,5,6,4,3,2] => 16
[1,6,2,3,4,5] => 25
[1,6,2,3,5,4] => 24
[1,6,2,4,3,5] => 24
[1,6,2,4,5,3] => 22
[1,6,2,5,3,4] => 22
[1,6,2,5,4,3] => 21
[1,6,3,2,4,5] => 24
[1,6,3,2,5,4] => 23
[1,6,3,4,2,5] => 22
[1,6,3,4,5,2] => 19
[1,6,3,5,2,4] => 20
[1,6,3,5,4,2] => 18
[1,6,4,2,3,5] => 22
[1,6,4,2,5,3] => 20
[1,6,4,3,2,5] => 21
[1,6,4,3,5,2] => 18
[1,6,4,5,2,3] => 17
[1,6,4,5,3,2] => 16
[1,6,5,2,3,4] => 19
[1,6,5,2,4,3] => 18
[1,6,5,3,2,4] => 18
[1,6,5,3,4,2] => 16
[1,6,5,4,2,3] => 16
[1,6,5,4,3,2] => 15
[2,1,3,4,5,6] => 34
[2,1,3,4,6,5] => 33
[2,1,3,5,4,6] => 33
[2,1,3,5,6,4] => 31
[2,1,3,6,4,5] => 31
[2,1,3,6,5,4] => 30
[2,1,4,3,5,6] => 33
[2,1,4,3,6,5] => 32
[2,1,4,5,3,6] => 31
[2,1,4,5,6,3] => 28
[2,1,4,6,3,5] => 29
[2,1,4,6,5,3] => 27
[2,1,5,3,4,6] => 31
[2,1,5,3,6,4] => 29
[2,1,5,4,3,6] => 30
[2,1,5,4,6,3] => 27
[2,1,5,6,3,4] => 26
[2,1,5,6,4,3] => 25
[2,1,6,3,4,5] => 28
[2,1,6,3,5,4] => 27
[2,1,6,4,3,5] => 27
[2,1,6,4,5,3] => 25
[2,1,6,5,3,4] => 25
[2,1,6,5,4,3] => 24
[2,3,1,4,5,6] => 32
[2,3,1,4,6,5] => 31
[2,3,1,5,4,6] => 31
[2,3,1,5,6,4] => 29
[2,3,1,6,4,5] => 29
[2,3,1,6,5,4] => 28
[2,3,4,1,5,6] => 29
[2,3,4,1,6,5] => 28
[2,3,4,5,1,6] => 25
[2,3,4,5,6,1] => 20
[2,3,4,6,1,5] => 23
[2,3,4,6,5,1] => 19
[2,3,5,1,4,6] => 27
[2,3,5,1,6,4] => 25
[2,3,5,4,1,6] => 24
[2,3,5,4,6,1] => 19
[2,3,5,6,1,4] => 20
[2,3,5,6,4,1] => 17
[2,3,6,1,4,5] => 24
[2,3,6,1,5,4] => 23
[2,3,6,4,1,5] => 21
[2,3,6,4,5,1] => 17
[2,3,6,5,1,4] => 19
[2,3,6,5,4,1] => 16
[2,4,1,3,5,6] => 30
[2,4,1,3,6,5] => 29
[2,4,1,5,3,6] => 28
[2,4,1,5,6,3] => 25
[2,4,1,6,3,5] => 26
[2,4,1,6,5,3] => 24
[2,4,3,1,5,6] => 28
[2,4,3,1,6,5] => 27
[2,4,3,5,1,6] => 24
[2,4,3,5,6,1] => 19
[2,4,3,6,1,5] => 22
[2,4,3,6,5,1] => 18
[2,4,5,1,3,6] => 24
[2,4,5,1,6,3] => 21
[2,4,5,3,1,6] => 22
[2,4,5,3,6,1] => 17
[2,4,5,6,1,3] => 16
[2,4,5,6,3,1] => 14
[2,4,6,1,3,5] => 21
[2,4,6,1,5,3] => 19
[2,4,6,3,1,5] => 19
[2,4,6,3,5,1] => 15
[2,4,6,5,1,3] => 15
[2,4,6,5,3,1] => 13
[2,5,1,3,4,6] => 27
[2,5,1,3,6,4] => 25
[2,5,1,4,3,6] => 26
[2,5,1,4,6,3] => 23
[2,5,1,6,3,4] => 22
[2,5,1,6,4,3] => 21
[2,5,3,1,4,6] => 25
[2,5,3,1,6,4] => 23
[2,5,3,4,1,6] => 22
[2,5,3,4,6,1] => 17
[2,5,3,6,1,4] => 18
[2,5,3,6,4,1] => 15
[2,5,4,1,3,6] => 23
[2,5,4,1,6,3] => 20
[2,5,4,3,1,6] => 21
[2,5,4,3,6,1] => 16
[2,5,4,6,1,3] => 15
[2,5,4,6,3,1] => 13
[2,5,6,1,3,4] => 17
[2,5,6,1,4,3] => 16
[2,5,6,3,1,4] => 15
[2,5,6,3,4,1] => 12
[2,5,6,4,1,3] => 13
[2,5,6,4,3,1] => 11
[2,6,1,3,4,5] => 23
[2,6,1,3,5,4] => 22
[2,6,1,4,3,5] => 22
[2,6,1,4,5,3] => 20
[2,6,1,5,3,4] => 20
[2,6,1,5,4,3] => 19
[2,6,3,1,4,5] => 21
[2,6,3,1,5,4] => 20
[2,6,3,4,1,5] => 18
[2,6,3,4,5,1] => 14
[2,6,3,5,1,4] => 16
[2,6,3,5,4,1] => 13
[2,6,4,1,3,5] => 19
[2,6,4,1,5,3] => 17
[2,6,4,3,1,5] => 17
[2,6,4,3,5,1] => 13
[2,6,4,5,1,3] => 13
[2,6,4,5,3,1] => 11
[2,6,5,1,3,4] => 16
[2,6,5,1,4,3] => 15
[2,6,5,3,1,4] => 14
[2,6,5,3,4,1] => 11
[2,6,5,4,1,3] => 12
[2,6,5,4,3,1] => 10
[3,1,2,4,5,6] => 32
[3,1,2,4,6,5] => 31
[3,1,2,5,4,6] => 31
[3,1,2,5,6,4] => 29
[3,1,2,6,4,5] => 29
[3,1,2,6,5,4] => 28
[3,1,4,2,5,6] => 30
[3,1,4,2,6,5] => 29
[3,1,4,5,2,6] => 27
[3,1,4,5,6,2] => 23
[3,1,4,6,2,5] => 25
[3,1,4,6,5,2] => 22
[3,1,5,2,4,6] => 28
[3,1,5,2,6,4] => 26
[3,1,5,4,2,6] => 26
[3,1,5,4,6,2] => 22
[3,1,5,6,2,4] => 22
[3,1,5,6,4,2] => 20
[3,1,6,2,4,5] => 25
[3,1,6,2,5,4] => 24
[3,1,6,4,2,5] => 23
[3,1,6,4,5,2] => 20
[3,1,6,5,2,4] => 21
[3,1,6,5,4,2] => 19
[3,2,1,4,5,6] => 31
[3,2,1,4,6,5] => 30
[3,2,1,5,4,6] => 30
[3,2,1,5,6,4] => 28
[3,2,1,6,4,5] => 28
[3,2,1,6,5,4] => 27
[3,2,4,1,5,6] => 28
[3,2,4,1,6,5] => 27
[3,2,4,5,1,6] => 24
[3,2,4,5,6,1] => 19
[3,2,4,6,1,5] => 22
[3,2,4,6,5,1] => 18
[3,2,5,1,4,6] => 26
[3,2,5,1,6,4] => 24
[3,2,5,4,1,6] => 23
[3,2,5,4,6,1] => 18
[3,2,5,6,1,4] => 19
[3,2,5,6,4,1] => 16
[3,2,6,1,4,5] => 23
[3,2,6,1,5,4] => 22
[3,2,6,4,1,5] => 20
[3,2,6,4,5,1] => 16
[3,2,6,5,1,4] => 18
[3,2,6,5,4,1] => 15
[3,4,1,2,5,6] => 27
[3,4,1,2,6,5] => 26
[3,4,1,5,2,6] => 24
[3,4,1,5,6,2] => 20
[3,4,1,6,2,5] => 22
[3,4,1,6,5,2] => 19
[3,4,2,1,5,6] => 26
[3,4,2,1,6,5] => 25
[3,4,2,5,1,6] => 22
[3,4,2,5,6,1] => 17
[3,4,2,6,1,5] => 20
[3,4,2,6,5,1] => 16
[3,4,5,1,2,6] => 20
[3,4,5,1,6,2] => 16
[3,4,5,2,1,6] => 19
[3,4,5,2,6,1] => 14
[3,4,5,6,1,2] => 11
[3,4,5,6,2,1] => 10
[3,4,6,1,2,5] => 17
[3,4,6,1,5,2] => 14
[3,4,6,2,1,5] => 16
[3,4,6,2,5,1] => 12
[3,4,6,5,1,2] => 10
[3,4,6,5,2,1] => 9
[3,5,1,2,4,6] => 24
[3,5,1,2,6,4] => 22
[3,5,1,4,2,6] => 22
[3,5,1,4,6,2] => 18
[3,5,1,6,2,4] => 18
[3,5,1,6,4,2] => 16
[3,5,2,1,4,6] => 23
[3,5,2,1,6,4] => 21
[3,5,2,4,1,6] => 20
[3,5,2,4,6,1] => 15
[3,5,2,6,1,4] => 16
[3,5,2,6,4,1] => 13
[3,5,4,1,2,6] => 19
[3,5,4,1,6,2] => 15
[3,5,4,2,1,6] => 18
[3,5,4,2,6,1] => 13
[3,5,4,6,1,2] => 10
[3,5,4,6,2,1] => 9
[3,5,6,1,2,4] => 13
[3,5,6,1,4,2] => 11
[3,5,6,2,1,4] => 12
[3,5,6,2,4,1] => 9
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 7
[3,6,1,2,4,5] => 20
[3,6,1,2,5,4] => 19
[3,6,1,4,2,5] => 18
[3,6,1,4,5,2] => 15
[3,6,1,5,2,4] => 16
[3,6,1,5,4,2] => 14
[3,6,2,1,4,5] => 19
[3,6,2,1,5,4] => 18
[3,6,2,4,1,5] => 16
[3,6,2,4,5,1] => 12
[3,6,2,5,1,4] => 14
[3,6,2,5,4,1] => 11
[3,6,4,1,2,5] => 15
[3,6,4,1,5,2] => 12
[3,6,4,2,1,5] => 14
[3,6,4,2,5,1] => 10
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 7
[3,6,5,1,2,4] => 12
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 11
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 7
[3,6,5,4,2,1] => 6
[4,1,2,3,5,6] => 29
[4,1,2,3,6,5] => 28
[4,1,2,5,3,6] => 27
[4,1,2,5,6,3] => 24
[4,1,2,6,3,5] => 25
[4,1,2,6,5,3] => 23
[4,1,3,2,5,6] => 28
[4,1,3,2,6,5] => 27
[4,1,3,5,2,6] => 25
[4,1,3,5,6,2] => 21
[4,1,3,6,2,5] => 23
[4,1,3,6,5,2] => 20
[4,1,5,2,3,6] => 24
[4,1,5,2,6,3] => 21
[4,1,5,3,2,6] => 23
[4,1,5,3,6,2] => 19
[4,1,5,6,2,3] => 17
[4,1,5,6,3,2] => 16
[4,1,6,2,3,5] => 21
[4,1,6,2,5,3] => 19
[4,1,6,3,2,5] => 20
[4,1,6,3,5,2] => 17
[4,1,6,5,2,3] => 16
[4,1,6,5,3,2] => 15
[4,2,1,3,5,6] => 28
[4,2,1,3,6,5] => 27
[4,2,1,5,3,6] => 26
[4,2,1,5,6,3] => 23
[4,2,1,6,3,5] => 24
[4,2,1,6,5,3] => 22
[4,2,3,1,5,6] => 26
[4,2,3,1,6,5] => 25
[4,2,3,5,1,6] => 22
[4,2,3,5,6,1] => 17
[4,2,3,6,1,5] => 20
[4,2,3,6,5,1] => 16
[4,2,5,1,3,6] => 22
[4,2,5,1,6,3] => 19
[4,2,5,3,1,6] => 20
[4,2,5,3,6,1] => 15
[4,2,5,6,1,3] => 14
[4,2,5,6,3,1] => 12
[4,2,6,1,3,5] => 19
[4,2,6,1,5,3] => 17
[4,2,6,3,1,5] => 17
[4,2,6,3,5,1] => 13
[4,2,6,5,1,3] => 13
[4,2,6,5,3,1] => 11
[4,3,1,2,5,6] => 26
[4,3,1,2,6,5] => 25
[4,3,1,5,2,6] => 23
[4,3,1,5,6,2] => 19
[4,3,1,6,2,5] => 21
[4,3,1,6,5,2] => 18
[4,3,2,1,5,6] => 25
[4,3,2,1,6,5] => 24
[4,3,2,5,1,6] => 21
[4,3,2,5,6,1] => 16
[4,3,2,6,1,5] => 19
[4,3,2,6,5,1] => 15
[4,3,5,1,2,6] => 19
[4,3,5,1,6,2] => 15
[4,3,5,2,1,6] => 18
[4,3,5,2,6,1] => 13
[4,3,5,6,1,2] => 10
[4,3,5,6,2,1] => 9
[4,3,6,1,2,5] => 16
[4,3,6,1,5,2] => 13
[4,3,6,2,1,5] => 15
[4,3,6,2,5,1] => 11
[4,3,6,5,1,2] => 9
[4,3,6,5,2,1] => 8
[4,5,1,2,3,6] => 20
[4,5,1,2,6,3] => 17
[4,5,1,3,2,6] => 19
[4,5,1,3,6,2] => 15
[4,5,1,6,2,3] => 13
[4,5,1,6,3,2] => 12
[4,5,2,1,3,6] => 19
[4,5,2,1,6,3] => 16
[4,5,2,3,1,6] => 17
[4,5,2,3,6,1] => 12
[4,5,2,6,1,3] => 11
[4,5,2,6,3,1] => 9
[4,5,3,1,2,6] => 17
[4,5,3,1,6,2] => 13
[4,5,3,2,1,6] => 16
[4,5,3,2,6,1] => 11
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 7
[4,5,6,1,2,3] => 8
[4,5,6,1,3,2] => 7
[4,5,6,2,1,3] => 7
[4,5,6,2,3,1] => 5
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 16
[4,6,1,2,5,3] => 14
[4,6,1,3,2,5] => 15
[4,6,1,3,5,2] => 12
[4,6,1,5,2,3] => 11
[4,6,1,5,3,2] => 10
[4,6,2,1,3,5] => 15
[4,6,2,1,5,3] => 13
[4,6,2,3,1,5] => 13
[4,6,2,3,5,1] => 9
[4,6,2,5,1,3] => 9
[4,6,2,5,3,1] => 7
[4,6,3,1,2,5] => 13
[4,6,3,1,5,2] => 10
[4,6,3,2,1,5] => 12
[4,6,3,2,5,1] => 8
[4,6,3,5,1,2] => 6
[4,6,3,5,2,1] => 5
[4,6,5,1,2,3] => 7
[4,6,5,1,3,2] => 6
[4,6,5,2,1,3] => 6
[4,6,5,2,3,1] => 4
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 3
[5,1,2,3,4,6] => 25
[5,1,2,3,6,4] => 23
[5,1,2,4,3,6] => 24
[5,1,2,4,6,3] => 21
[5,1,2,6,3,4] => 20
[5,1,2,6,4,3] => 19
[5,1,3,2,4,6] => 24
[5,1,3,2,6,4] => 22
[5,1,3,4,2,6] => 22
[5,1,3,4,6,2] => 18
[5,1,3,6,2,4] => 18
[5,1,3,6,4,2] => 16
[5,1,4,2,3,6] => 22
[5,1,4,2,6,3] => 19
[5,1,4,3,2,6] => 21
[5,1,4,3,6,2] => 17
[5,1,4,6,2,3] => 15
[5,1,4,6,3,2] => 14
[5,1,6,2,3,4] => 16
[5,1,6,2,4,3] => 15
[5,1,6,3,2,4] => 15
[5,1,6,3,4,2] => 13
[5,1,6,4,2,3] => 13
[5,1,6,4,3,2] => 12
[5,2,1,3,4,6] => 24
[5,2,1,3,6,4] => 22
[5,2,1,4,3,6] => 23
[5,2,1,4,6,3] => 20
[5,2,1,6,3,4] => 19
[5,2,1,6,4,3] => 18
[5,2,3,1,4,6] => 22
[5,2,3,1,6,4] => 20
[5,2,3,4,1,6] => 19
[5,2,3,4,6,1] => 14
[5,2,3,6,1,4] => 15
[5,2,3,6,4,1] => 12
[5,2,4,1,3,6] => 20
[5,2,4,1,6,3] => 17
[5,2,4,3,1,6] => 18
[5,2,4,3,6,1] => 13
[5,2,4,6,1,3] => 12
[5,2,4,6,3,1] => 10
[5,2,6,1,3,4] => 14
[5,2,6,1,4,3] => 13
[5,2,6,3,1,4] => 12
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 10
[5,2,6,4,3,1] => 8
[5,3,1,2,4,6] => 22
[5,3,1,2,6,4] => 20
[5,3,1,4,2,6] => 20
[5,3,1,4,6,2] => 16
[5,3,1,6,2,4] => 16
[5,3,1,6,4,2] => 14
[5,3,2,1,4,6] => 21
[5,3,2,1,6,4] => 19
[5,3,2,4,1,6] => 18
[5,3,2,4,6,1] => 13
[5,3,2,6,1,4] => 14
[5,3,2,6,4,1] => 11
[5,3,4,1,2,6] => 17
[5,3,4,1,6,2] => 13
[5,3,4,2,1,6] => 16
[5,3,4,2,6,1] => 11
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 7
[5,3,6,1,2,4] => 11
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 10
[5,3,6,2,4,1] => 7
[5,3,6,4,1,2] => 6
[5,3,6,4,2,1] => 5
[5,4,1,2,3,6] => 19
[5,4,1,2,6,3] => 16
[5,4,1,3,2,6] => 18
[5,4,1,3,6,2] => 14
[5,4,1,6,2,3] => 12
[5,4,1,6,3,2] => 11
[5,4,2,1,3,6] => 18
[5,4,2,1,6,3] => 15
[5,4,2,3,1,6] => 16
[5,4,2,3,6,1] => 11
[5,4,2,6,1,3] => 10
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 16
[5,4,3,1,6,2] => 12
[5,4,3,2,1,6] => 15
[5,4,3,2,6,1] => 10
[5,4,3,6,1,2] => 7
[5,4,3,6,2,1] => 6
[5,4,6,1,2,3] => 7
[5,4,6,1,3,2] => 6
[5,4,6,2,1,3] => 6
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 4
[5,4,6,3,2,1] => 3
[5,6,1,2,3,4] => 11
[5,6,1,2,4,3] => 10
[5,6,1,3,2,4] => 10
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 7
[5,6,2,1,3,4] => 10
[5,6,2,1,4,3] => 9
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 6
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 6
[5,6,3,2,1,4] => 7
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 2
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 4
[5,6,4,2,1,3] => 4
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 20
[6,1,2,3,5,4] => 19
[6,1,2,4,3,5] => 19
[6,1,2,4,5,3] => 17
[6,1,2,5,3,4] => 17
[6,1,2,5,4,3] => 16
[6,1,3,2,4,5] => 19
[6,1,3,2,5,4] => 18
[6,1,3,4,2,5] => 17
[6,1,3,4,5,2] => 14
[6,1,3,5,2,4] => 15
[6,1,3,5,4,2] => 13
[6,1,4,2,3,5] => 17
[6,1,4,2,5,3] => 15
[6,1,4,3,2,5] => 16
[6,1,4,3,5,2] => 13
[6,1,4,5,2,3] => 12
[6,1,4,5,3,2] => 11
[6,1,5,2,3,4] => 14
[6,1,5,2,4,3] => 13
[6,1,5,3,2,4] => 13
[6,1,5,3,4,2] => 11
[6,1,5,4,2,3] => 11
[6,1,5,4,3,2] => 10
[6,2,1,3,4,5] => 19
[6,2,1,3,5,4] => 18
[6,2,1,4,3,5] => 18
[6,2,1,4,5,3] => 16
[6,2,1,5,3,4] => 16
[6,2,1,5,4,3] => 15
[6,2,3,1,4,5] => 17
[6,2,3,1,5,4] => 16
[6,2,3,4,1,5] => 14
[6,2,3,4,5,1] => 10
[6,2,3,5,1,4] => 12
[6,2,3,5,4,1] => 9
[6,2,4,1,3,5] => 15
[6,2,4,1,5,3] => 13
[6,2,4,3,1,5] => 13
[6,2,4,3,5,1] => 9
[6,2,4,5,1,3] => 9
[6,2,4,5,3,1] => 7
[6,2,5,1,3,4] => 12
[6,2,5,1,4,3] => 11
[6,2,5,3,1,4] => 10
[6,2,5,3,4,1] => 7
[6,2,5,4,1,3] => 8
[6,2,5,4,3,1] => 6
[6,3,1,2,4,5] => 17
[6,3,1,2,5,4] => 16
[6,3,1,4,2,5] => 15
[6,3,1,4,5,2] => 12
[6,3,1,5,2,4] => 13
[6,3,1,5,4,2] => 11
[6,3,2,1,4,5] => 16
[6,3,2,1,5,4] => 15
[6,3,2,4,1,5] => 13
[6,3,2,4,5,1] => 9
[6,3,2,5,1,4] => 11
[6,3,2,5,4,1] => 8
[6,3,4,1,2,5] => 12
[6,3,4,1,5,2] => 9
[6,3,4,2,1,5] => 11
[6,3,4,2,5,1] => 7
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 9
[6,3,5,1,4,2] => 7
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 5
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 14
[6,4,1,2,5,3] => 12
[6,4,1,3,2,5] => 13
[6,4,1,3,5,2] => 10
[6,4,1,5,2,3] => 9
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 13
[6,4,2,1,5,3] => 11
[6,4,2,3,1,5] => 11
[6,4,2,3,5,1] => 7
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 5
[6,4,3,1,2,5] => 11
[6,4,3,1,5,2] => 8
[6,4,3,2,1,5] => 10
[6,4,3,2,5,1] => 6
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 5
[6,4,5,1,3,2] => 4
[6,4,5,2,1,3] => 4
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 2
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 10
[6,5,1,2,4,3] => 9
[6,5,1,3,2,4] => 9
[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] => 9
[6,5,2,1,4,3] => 8
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 5
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 7
[6,5,3,1,4,2] => 5
[6,5,3,2,1,4] => 6
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 2
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 3
[6,5,4,2,1,3] => 3
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 56
[1,2,3,4,5,7,6] => 55
[1,2,3,4,6,5,7] => 55
[1,2,3,4,6,7,5] => 53
[1,2,3,4,7,5,6] => 53
[1,2,3,4,7,6,5] => 52
[1,2,3,5,4,6,7] => 55
[1,2,3,5,4,7,6] => 54
[1,2,3,5,6,4,7] => 53
[1,2,3,5,6,7,4] => 50
[1,2,3,5,7,4,6] => 51
[1,2,3,5,7,6,4] => 49
[1,2,3,6,4,5,7] => 53
[1,2,3,6,4,7,5] => 51
[1,2,3,6,5,4,7] => 52
[1,2,3,6,5,7,4] => 49
[1,2,3,6,7,4,5] => 48
[1,2,3,6,7,5,4] => 47
[1,2,3,7,4,5,6] => 50
[1,2,3,7,4,6,5] => 49
[1,2,3,7,5,4,6] => 49
[1,2,3,7,5,6,4] => 47
[1,2,3,7,6,4,5] => 47
[1,2,3,7,6,5,4] => 46
[1,2,4,3,5,6,7] => 55
[1,2,4,3,5,7,6] => 54
[1,2,4,3,6,5,7] => 54
[1,2,4,3,6,7,5] => 52
[1,2,4,3,7,5,6] => 52
[1,2,4,3,7,6,5] => 51
[1,2,4,5,3,6,7] => 53
[1,2,4,5,3,7,6] => 52
[1,2,4,5,6,3,7] => 50
[1,2,4,5,6,7,3] => 46
[1,2,4,5,7,3,6] => 48
[1,2,4,5,7,6,3] => 45
[1,2,4,6,3,5,7] => 51
[1,2,4,6,3,7,5] => 49
[1,2,4,6,5,3,7] => 49
[1,2,4,6,5,7,3] => 45
[1,2,4,6,7,3,5] => 45
[1,2,4,6,7,5,3] => 43
[1,2,4,7,3,5,6] => 48
[1,2,4,7,3,6,5] => 47
[1,2,4,7,5,3,6] => 46
[1,2,4,7,5,6,3] => 43
[1,2,4,7,6,3,5] => 44
[1,2,4,7,6,5,3] => 42
[1,2,5,3,4,6,7] => 53
[1,2,5,3,4,7,6] => 52
[1,2,5,3,6,4,7] => 51
[1,2,5,3,6,7,4] => 48
[1,2,5,3,7,4,6] => 49
[1,2,5,3,7,6,4] => 47
[1,2,5,4,3,6,7] => 52
[1,2,5,4,3,7,6] => 51
[1,2,5,4,6,3,7] => 49
[1,2,5,4,6,7,3] => 45
[1,2,5,4,7,3,6] => 47
[1,2,5,4,7,6,3] => 44
[1,2,5,6,3,4,7] => 48
[1,2,5,6,3,7,4] => 45
[1,2,5,6,4,3,7] => 47
[1,2,5,6,4,7,3] => 43
[1,2,5,6,7,3,4] => 41
[1,2,5,6,7,4,3] => 40
[1,2,5,7,3,4,6] => 45
[1,2,5,7,3,6,4] => 43
[1,2,5,7,4,3,6] => 44
[1,2,5,7,4,6,3] => 41
[1,2,5,7,6,3,4] => 40
[1,2,5,7,6,4,3] => 39
[1,2,6,3,4,5,7] => 50
[1,2,6,3,4,7,5] => 48
[1,2,6,3,5,4,7] => 49
[1,2,6,3,5,7,4] => 46
[1,2,6,3,7,4,5] => 45
[1,2,6,3,7,5,4] => 44
[1,2,6,4,3,5,7] => 49
[1,2,6,4,3,7,5] => 47
[1,2,6,4,5,3,7] => 47
[1,2,6,4,5,7,3] => 43
[1,2,6,4,7,3,5] => 43
[1,2,6,4,7,5,3] => 41
[1,2,6,5,3,4,7] => 47
[1,2,6,5,3,7,4] => 44
[1,2,6,5,4,3,7] => 46
[1,2,6,5,4,7,3] => 42
[1,2,6,5,7,3,4] => 40
[1,2,6,5,7,4,3] => 39
[1,2,6,7,3,4,5] => 41
[1,2,6,7,3,5,4] => 40
[1,2,6,7,4,3,5] => 40
[1,2,6,7,4,5,3] => 38
[1,2,6,7,5,3,4] => 38
[1,2,6,7,5,4,3] => 37
[1,2,7,3,4,5,6] => 46
[1,2,7,3,4,6,5] => 45
[1,2,7,3,5,4,6] => 45
[1,2,7,3,5,6,4] => 43
[1,2,7,3,6,4,5] => 43
[1,2,7,3,6,5,4] => 42
[1,2,7,4,3,5,6] => 45
[1,2,7,4,3,6,5] => 44
[1,2,7,4,5,3,6] => 43
[1,2,7,4,5,6,3] => 40
[1,2,7,4,6,3,5] => 41
[1,2,7,4,6,5,3] => 39
[1,2,7,5,3,4,6] => 43
[1,2,7,5,3,6,4] => 41
[1,2,7,5,4,3,6] => 42
[1,2,7,5,4,6,3] => 39
[1,2,7,5,6,3,4] => 38
[1,2,7,5,6,4,3] => 37
[1,2,7,6,3,4,5] => 40
[1,2,7,6,3,5,4] => 39
[1,2,7,6,4,3,5] => 39
[1,2,7,6,4,5,3] => 37
[1,2,7,6,5,3,4] => 37
[1,2,7,6,5,4,3] => 36
[1,3,2,4,5,6,7] => 55
[1,3,2,4,5,7,6] => 54
[1,3,2,4,6,5,7] => 54
[1,3,2,4,6,7,5] => 52
[1,3,2,4,7,5,6] => 52
[1,3,2,4,7,6,5] => 51
[1,3,2,5,4,6,7] => 54
[1,3,2,5,4,7,6] => 53
[1,3,2,5,6,4,7] => 52
[1,3,2,5,6,7,4] => 49
[1,3,2,5,7,4,6] => 50
[1,3,2,5,7,6,4] => 48
[1,3,2,6,4,5,7] => 52
[1,3,2,6,4,7,5] => 50
[1,3,2,6,5,4,7] => 51
[1,3,2,6,5,7,4] => 48
[1,3,2,6,7,4,5] => 47
[1,3,2,6,7,5,4] => 46
[1,3,2,7,4,5,6] => 49
[1,3,2,7,4,6,5] => 48
[1,3,2,7,5,4,6] => 48
[1,3,2,7,5,6,4] => 46
[1,3,2,7,6,4,5] => 46
[1,3,2,7,6,5,4] => 45
[1,3,4,2,5,6,7] => 53
[1,3,4,2,5,7,6] => 52
[1,3,4,2,6,5,7] => 52
[1,3,4,2,6,7,5] => 50
[1,3,4,2,7,5,6] => 50
[1,3,4,2,7,6,5] => 49
[1,3,4,5,2,6,7] => 50
[1,3,4,5,2,7,6] => 49
[1,3,4,5,6,2,7] => 46
[1,3,4,5,6,7,2] => 41
[1,3,4,5,7,2,6] => 44
[1,3,4,5,7,6,2] => 40
[1,3,4,6,2,5,7] => 48
[1,3,4,6,2,7,5] => 46
[1,3,4,6,5,2,7] => 45
[1,3,4,6,5,7,2] => 40
[1,3,4,6,7,2,5] => 41
[1,3,4,6,7,5,2] => 38
[1,3,4,7,2,5,6] => 45
[1,3,4,7,2,6,5] => 44
[1,3,4,7,5,2,6] => 42
[1,3,4,7,5,6,2] => 38
[1,3,4,7,6,2,5] => 40
[1,3,4,7,6,5,2] => 37
[1,3,5,2,4,6,7] => 51
[1,3,5,2,4,7,6] => 50
[1,3,5,2,6,4,7] => 49
[1,3,5,2,6,7,4] => 46
[1,3,5,2,7,4,6] => 47
[1,3,5,2,7,6,4] => 45
[1,3,5,4,2,6,7] => 49
[1,3,5,4,2,7,6] => 48
[1,3,5,4,6,2,7] => 45
[1,3,5,4,6,7,2] => 40
[1,3,5,4,7,2,6] => 43
[1,3,5,4,7,6,2] => 39
[1,3,5,6,2,4,7] => 45
[1,3,5,6,2,7,4] => 42
[1,3,5,6,4,2,7] => 43
[1,3,5,6,4,7,2] => 38
[1,3,5,6,7,2,4] => 37
[1,3,5,6,7,4,2] => 35
[1,3,5,7,2,4,6] => 42
[1,3,5,7,2,6,4] => 40
[1,3,5,7,4,2,6] => 40
[1,3,5,7,4,6,2] => 36
[1,3,5,7,6,2,4] => 36
[1,3,5,7,6,4,2] => 34
[1,3,6,2,4,5,7] => 48
[1,3,6,2,4,7,5] => 46
[1,3,6,2,5,4,7] => 47
[1,3,6,2,5,7,4] => 44
[1,3,6,2,7,4,5] => 43
[1,3,6,2,7,5,4] => 42
[1,3,6,4,2,5,7] => 46
[1,3,6,4,2,7,5] => 44
[1,3,6,4,5,2,7] => 43
[1,3,6,4,5,7,2] => 38
[1,3,6,4,7,2,5] => 39
[1,3,6,4,7,5,2] => 36
[1,3,6,5,2,4,7] => 44
[1,3,6,5,2,7,4] => 41
[1,3,6,5,4,2,7] => 42
[1,3,6,5,4,7,2] => 37
[1,3,6,5,7,2,4] => 36
[1,3,6,5,7,4,2] => 34
[1,3,6,7,2,4,5] => 38
[1,3,6,7,2,5,4] => 37
[1,3,6,7,4,2,5] => 36
[1,3,6,7,4,5,2] => 33
[1,3,6,7,5,2,4] => 34
[1,3,6,7,5,4,2] => 32
[1,3,7,2,4,5,6] => 44
[1,3,7,2,4,6,5] => 43
[1,3,7,2,5,4,6] => 43
[1,3,7,2,5,6,4] => 41
[1,3,7,2,6,4,5] => 41
[1,3,7,2,6,5,4] => 40
[1,3,7,4,2,5,6] => 42
[1,3,7,4,2,6,5] => 41
[1,3,7,4,5,2,6] => 39
[1,3,7,4,5,6,2] => 35
[1,3,7,4,6,2,5] => 37
[1,3,7,4,6,5,2] => 34
[1,3,7,5,2,4,6] => 40
[1,3,7,5,2,6,4] => 38
[1,3,7,5,4,2,6] => 38
[1,3,7,5,4,6,2] => 34
[1,3,7,5,6,2,4] => 34
[1,3,7,5,6,4,2] => 32
[1,3,7,6,2,4,5] => 37
[1,3,7,6,2,5,4] => 36
[1,3,7,6,4,2,5] => 35
[1,3,7,6,4,5,2] => 32
[1,3,7,6,5,2,4] => 33
[1,3,7,6,5,4,2] => 31
[1,4,2,3,5,6,7] => 53
[1,4,2,3,5,7,6] => 52
[1,4,2,3,6,5,7] => 52
[1,4,2,3,6,7,5] => 50
[1,4,2,3,7,5,6] => 50
[1,4,2,3,7,6,5] => 49
[1,4,2,5,3,6,7] => 51
[1,4,2,5,3,7,6] => 50
[1,4,2,5,6,3,7] => 48
[1,4,2,5,6,7,3] => 44
[1,4,2,5,7,3,6] => 46
[1,4,2,5,7,6,3] => 43
[1,4,2,6,3,5,7] => 49
[1,4,2,6,3,7,5] => 47
[1,4,2,6,5,3,7] => 47
[1,4,2,6,5,7,3] => 43
[1,4,2,6,7,3,5] => 43
[1,4,2,6,7,5,3] => 41
[1,4,2,7,3,5,6] => 46
[1,4,2,7,3,6,5] => 45
[1,4,2,7,5,3,6] => 44
[1,4,2,7,5,6,3] => 41
[1,4,2,7,6,3,5] => 42
[1,4,2,7,6,5,3] => 40
[1,4,3,2,5,6,7] => 52
[1,4,3,2,5,7,6] => 51
[1,4,3,2,6,5,7] => 51
[1,4,3,2,6,7,5] => 49
[1,4,3,2,7,5,6] => 49
[1,4,3,2,7,6,5] => 48
[1,4,3,5,2,6,7] => 49
[1,4,3,5,2,7,6] => 48
[1,4,3,5,6,2,7] => 45
[1,4,3,5,6,7,2] => 40
[1,4,3,5,7,2,6] => 43
[1,4,3,5,7,6,2] => 39
[1,4,3,6,2,5,7] => 47
[1,4,3,6,2,7,5] => 45
[1,4,3,6,5,2,7] => 44
[1,4,3,6,5,7,2] => 39
[1,4,3,6,7,2,5] => 40
[1,4,3,6,7,5,2] => 37
[1,4,3,7,2,5,6] => 44
[1,4,3,7,2,6,5] => 43
[1,4,3,7,5,2,6] => 41
[1,4,3,7,5,6,2] => 37
[1,4,3,7,6,2,5] => 39
[1,4,3,7,6,5,2] => 36
[1,4,5,2,3,6,7] => 48
[1,4,5,2,3,7,6] => 47
[1,4,5,2,6,3,7] => 45
[1,4,5,2,6,7,3] => 41
[1,4,5,2,7,3,6] => 43
[1,4,5,2,7,6,3] => 40
[1,4,5,3,2,6,7] => 47
[1,4,5,3,2,7,6] => 46
[1,4,5,3,6,2,7] => 43
[1,4,5,3,6,7,2] => 38
[1,4,5,3,7,2,6] => 41
[1,4,5,3,7,6,2] => 37
[1,4,5,6,2,3,7] => 41
[1,4,5,6,2,7,3] => 37
[1,4,5,6,3,2,7] => 40
[1,4,5,6,3,7,2] => 35
[1,4,5,6,7,2,3] => 32
[1,4,5,6,7,3,2] => 31
[1,4,5,7,2,3,6] => 38
[1,4,5,7,2,6,3] => 35
[1,4,5,7,3,2,6] => 37
[1,4,5,7,3,6,2] => 33
[1,4,5,7,6,2,3] => 31
[1,4,5,7,6,3,2] => 30
[1,4,6,2,3,5,7] => 45
[1,4,6,2,3,7,5] => 43
[1,4,6,2,5,3,7] => 43
[1,4,6,2,5,7,3] => 39
[1,4,6,2,7,3,5] => 39
[1,4,6,2,7,5,3] => 37
[1,4,6,3,2,5,7] => 44
[1,4,6,3,2,7,5] => 42
[1,4,6,3,5,2,7] => 41
[1,4,6,3,5,7,2] => 36
[1,4,6,3,7,2,5] => 37
[1,4,6,3,7,5,2] => 34
[1,4,6,5,2,3,7] => 40
[1,4,6,5,2,7,3] => 36
[1,4,6,5,3,2,7] => 39
[1,4,6,5,3,7,2] => 34
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Description
The non-inversion sum of a permutation.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
References
[1] Sack, J., Úlfarsson, H. Refined inversion statistics on permutations MathSciNet:2880660 arXiv:1106.1995
[2] The inversion sum of a permutation. St000055
Code
def statistic(pi):
        return sum( inv[1]-inv[0] for inv in pi.noninversions(2) )
Created
Dec 23, 2015 at 08:49 by Christian Stump
Updated
Sep 29, 2022 at 19:06 by Will Dowling