Processing math: 100%

edit this statistic or download as text // json
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 1
[3,1,2,4] => 0
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 1
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 1
[1,3,2,5,4] => 1
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 0
[1,3,5,4,2] => 1
[1,4,2,3,5] => 0
[1,4,2,5,3] => 0
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 0
[1,4,5,3,2] => 0
[1,5,2,3,4] => 0
[1,5,2,4,3] => 1
[1,5,3,2,4] => 0
[1,5,3,4,2] => 0
[1,5,4,2,3] => 0
[1,5,4,3,2] => 0
[2,1,3,4,5] => 0
[2,1,3,5,4] => 1
[2,1,4,3,5] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,4,3] => 0
[2,3,1,4,5] => 0
[2,3,1,5,4] => 0
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,4,1] => 1
[2,4,1,3,5] => 0
[2,4,1,5,3] => 0
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 0
[2,4,5,3,1] => 0
[2,5,1,3,4] => 0
[2,5,1,4,3] => 0
[2,5,3,1,4] => 0
[2,5,3,4,1] => 0
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,4,5] => 0
[3,1,2,5,4] => 0
[3,1,4,2,5] => 0
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,4,2] => 0
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 0
[3,2,4,5,1] => 0
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 0
[3,4,2,1,5] => 0
[3,4,2,5,1] => 0
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 0
[3,5,1,4,2] => 0
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 0
[3,5,2,4,1] => 0
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 0
[4,1,2,5,3] => 0
[4,1,3,2,5] => 1
[4,1,3,5,2] => 0
[4,1,5,2,3] => 0
[4,1,5,3,2] => 0
[4,2,1,3,5] => 0
[4,2,1,5,3] => 0
[4,2,3,1,5] => 0
[4,2,3,5,1] => 0
[4,2,5,1,3] => 0
[4,2,5,3,1] => 0
[4,3,1,2,5] => 0
[4,3,1,5,2] => 0
[4,3,2,1,5] => 0
[4,3,2,5,1] => 0
[4,3,5,1,2] => 0
[4,3,5,2,1] => 0
[4,5,1,2,3] => 0
[4,5,1,3,2] => 1
[4,5,2,1,3] => 0
[4,5,2,3,1] => 0
[4,5,3,1,2] => 0
[4,5,3,2,1] => 0
[5,1,2,3,4] => 0
[5,1,2,4,3] => 1
[5,1,3,2,4] => 1
[5,1,3,4,2] => 0
[5,1,4,2,3] => 0
[5,1,4,3,2] => 0
[5,2,1,3,4] => 0
[5,2,1,4,3] => 0
[5,2,3,1,4] => 0
[5,2,3,4,1] => 0
[5,2,4,1,3] => 0
[5,2,4,3,1] => 1
[5,3,1,2,4] => 0
[5,3,1,4,2] => 0
[5,3,2,1,4] => 0
[5,3,2,4,1] => 0
[5,3,4,1,2] => 0
[5,3,4,2,1] => 0
[5,4,1,2,3] => 0
[5,4,1,3,2] => 1
[5,4,2,1,3] => 0
[5,4,2,3,1] => 0
[5,4,3,1,2] => 0
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 0
[1,2,3,6,4,5] => 0
[1,2,3,6,5,4] => 0
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 1
[1,2,4,5,3,6] => 0
[1,2,4,5,6,3] => 0
[1,2,4,6,3,5] => 0
[1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => 0
[1,2,5,3,6,4] => 0
[1,2,5,4,3,6] => 0
[1,2,5,4,6,3] => 0
[1,2,5,6,3,4] => 0
[1,2,5,6,4,3] => 0
[1,2,6,3,4,5] => 0
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 0
[1,2,6,4,5,3] => 0
[1,2,6,5,3,4] => 0
[1,2,6,5,4,3] => 0
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 0
[1,3,4,2,6,5] => 0
[1,3,4,5,2,6] => 0
[1,3,4,5,6,2] => 0
[1,3,4,6,2,5] => 0
[1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => 0
[1,3,5,2,6,4] => 0
[1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => 0
[1,3,5,6,4,2] => 0
[1,3,6,2,4,5] => 0
[1,3,6,2,5,4] => 0
[1,3,6,4,2,5] => 0
[1,3,6,4,5,2] => 0
[1,3,6,5,2,4] => 0
[1,3,6,5,4,2] => 0
[1,4,2,3,5,6] => 0
[1,4,2,3,6,5] => 0
[1,4,2,5,3,6] => 0
[1,4,2,5,6,3] => 0
[1,4,2,6,3,5] => 0
[1,4,2,6,5,3] => 0
[1,4,3,2,5,6] => 0
[1,4,3,2,6,5] => 0
[1,4,3,5,2,6] => 0
[1,4,3,5,6,2] => 0
[1,4,3,6,2,5] => 0
[1,4,3,6,5,2] => 0
[1,4,5,2,3,6] => 0
[1,4,5,2,6,3] => 0
[1,4,5,3,2,6] => 0
[1,4,5,3,6,2] => 0
[1,4,5,6,2,3] => 0
[1,4,5,6,3,2] => 0
[1,4,6,2,3,5] => 0
[1,4,6,2,5,3] => 0
[1,4,6,3,2,5] => 0
[1,4,6,3,5,2] => 0
[1,4,6,5,2,3] => 1
[1,4,6,5,3,2] => 1
[1,5,2,3,4,6] => 0
[1,5,2,3,6,4] => 0
[1,5,2,4,3,6] => 1
[1,5,2,4,6,3] => 0
[1,5,2,6,3,4] => 0
[1,5,2,6,4,3] => 0
[1,5,3,2,4,6] => 0
[1,5,3,2,6,4] => 0
[1,5,3,4,2,6] => 0
[1,5,3,4,6,2] => 0
[1,5,3,6,2,4] => 0
[1,5,3,6,4,2] => 0
[1,5,4,2,3,6] => 0
[1,5,4,2,6,3] => 0
[1,5,4,3,2,6] => 0
[1,5,4,3,6,2] => 0
[1,5,4,6,2,3] => 0
[1,5,4,6,3,2] => 0
[1,5,6,2,3,4] => 0
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 0
[1,5,6,3,4,2] => 0
[1,5,6,4,2,3] => 0
[1,5,6,4,3,2] => 0
[1,6,2,3,4,5] => 0
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 1
[1,6,2,4,5,3] => 0
[1,6,2,5,3,4] => 0
[1,6,2,5,4,3] => 0
[1,6,3,2,4,5] => 0
[1,6,3,2,5,4] => 0
[1,6,3,4,2,5] => 0
[1,6,3,4,5,2] => 0
[1,6,3,5,2,4] => 0
[1,6,3,5,4,2] => 1
[1,6,4,2,3,5] => 0
[1,6,4,2,5,3] => 0
[1,6,4,3,2,5] => 0
[1,6,4,3,5,2] => 0
[1,6,4,5,2,3] => 0
[1,6,4,5,3,2] => 0
[1,6,5,2,3,4] => 0
[1,6,5,2,4,3] => 1
[1,6,5,3,2,4] => 0
[1,6,5,3,4,2] => 0
[1,6,5,4,2,3] => 0
[1,6,5,4,3,2] => 0
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 1
[2,1,3,5,4,6] => 1
[2,1,3,5,6,4] => 0
[2,1,3,6,4,5] => 0
[2,1,3,6,5,4] => 0
[2,1,4,3,5,6] => 0
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 0
[2,1,4,5,6,3] => 0
[2,1,4,6,3,5] => 0
[2,1,4,6,5,3] => 1
[2,1,5,3,4,6] => 0
[2,1,5,3,6,4] => 0
[2,1,5,4,3,6] => 0
[2,1,5,4,6,3] => 0
[2,1,5,6,3,4] => 0
[2,1,5,6,4,3] => 0
[2,1,6,3,4,5] => 0
[2,1,6,3,5,4] => 1
[2,1,6,4,3,5] => 0
[2,1,6,4,5,3] => 0
[2,1,6,5,3,4] => 0
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 0
[2,3,1,4,6,5] => 1
[2,3,1,5,4,6] => 0
[2,3,1,5,6,4] => 0
[2,3,1,6,4,5] => 0
[2,3,1,6,5,4] => 0
[2,3,4,1,5,6] => 0
[2,3,4,1,6,5] => 0
[2,3,4,5,1,6] => 0
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 0
[2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => 0
[2,3,5,1,6,4] => 0
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 0
[2,3,5,6,4,1] => 0
[2,3,6,1,4,5] => 0
[2,3,6,1,5,4] => 0
[2,3,6,4,1,5] => 0
[2,3,6,4,5,1] => 0
[2,3,6,5,1,4] => 0
[2,3,6,5,4,1] => 0
[2,4,1,3,5,6] => 0
[2,4,1,3,6,5] => 0
[2,4,1,5,3,6] => 0
[2,4,1,5,6,3] => 0
[2,4,1,6,3,5] => 0
[2,4,1,6,5,3] => 0
[2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => 0
[2,4,5,1,6,3] => 0
[2,4,5,3,1,6] => 0
[2,4,5,3,6,1] => 0
[2,4,5,6,1,3] => 0
[2,4,5,6,3,1] => 0
[2,4,6,1,3,5] => 0
[2,4,6,1,5,3] => 0
[2,4,6,3,1,5] => 0
[2,4,6,3,5,1] => 0
[2,4,6,5,1,3] => 1
[2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => 0
[2,5,1,3,6,4] => 0
[2,5,1,4,3,6] => 0
[2,5,1,4,6,3] => 0
[2,5,1,6,3,4] => 0
[2,5,1,6,4,3] => 0
[2,5,3,1,4,6] => 0
[2,5,3,1,6,4] => 0
[2,5,3,4,1,6] => 0
[2,5,3,4,6,1] => 0
[2,5,3,6,1,4] => 0
[2,5,3,6,4,1] => 0
[2,5,4,1,3,6] => 0
[2,5,4,1,6,3] => 0
[2,5,4,3,1,6] => 0
[2,5,4,3,6,1] => 0
[2,5,4,6,1,3] => 0
[2,5,4,6,3,1] => 0
[2,5,6,1,3,4] => 0
[2,5,6,1,4,3] => 0
[2,5,6,3,1,4] => 0
[2,5,6,3,4,1] => 0
[2,5,6,4,1,3] => 0
[2,5,6,4,3,1] => 0
[2,6,1,3,4,5] => 0
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 0
[2,6,1,4,5,3] => 0
[2,6,1,5,3,4] => 0
[2,6,1,5,4,3] => 0
[2,6,3,1,4,5] => 0
[2,6,3,1,5,4] => 0
[2,6,3,4,1,5] => 0
[2,6,3,4,5,1] => 0
[2,6,3,5,1,4] => 0
[2,6,3,5,4,1] => 1
[2,6,4,1,3,5] => 0
[2,6,4,1,5,3] => 0
[2,6,4,3,1,5] => 0
[2,6,4,3,5,1] => 0
[2,6,4,5,1,3] => 0
[2,6,4,5,3,1] => 0
[2,6,5,1,3,4] => 0
[2,6,5,1,4,3] => 0
[2,6,5,3,1,4] => 0
[2,6,5,3,4,1] => 0
[2,6,5,4,1,3] => 0
[2,6,5,4,3,1] => 0
[3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => 0
[3,1,2,5,6,4] => 0
[3,1,2,6,4,5] => 0
[3,1,2,6,5,4] => 0
[3,1,4,2,5,6] => 0
[3,1,4,2,6,5] => 0
[3,1,4,5,2,6] => 0
[3,1,4,5,6,2] => 0
[3,1,4,6,2,5] => 0
[3,1,4,6,5,2] => 1
[3,1,5,2,4,6] => 0
[3,1,5,2,6,4] => 0
[3,1,5,4,2,6] => 0
[3,1,5,4,6,2] => 0
[3,1,5,6,2,4] => 0
[3,1,5,6,4,2] => 0
[3,1,6,2,4,5] => 0
[3,1,6,2,5,4] => 0
[3,1,6,4,2,5] => 0
[3,1,6,4,5,2] => 0
[3,1,6,5,2,4] => 0
[3,1,6,5,4,2] => 0
[3,2,1,4,5,6] => 0
[3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => 0
[3,2,1,5,6,4] => 0
[3,2,1,6,4,5] => 0
[3,2,1,6,5,4] => 0
[3,2,4,1,5,6] => 0
[3,2,4,1,6,5] => 0
[3,2,4,5,1,6] => 0
[3,2,4,5,6,1] => 0
[3,2,4,6,1,5] => 0
[3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => 0
[3,2,5,1,6,4] => 0
[3,2,5,4,1,6] => 0
[3,2,5,4,6,1] => 0
[3,2,5,6,1,4] => 0
[3,2,5,6,4,1] => 0
[3,2,6,1,4,5] => 0
[3,2,6,1,5,4] => 0
[3,2,6,4,1,5] => 0
[3,2,6,4,5,1] => 0
[3,2,6,5,1,4] => 0
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 0
[3,4,1,2,6,5] => 0
[3,4,1,5,2,6] => 0
[3,4,1,5,6,2] => 0
[3,4,1,6,2,5] => 0
[3,4,1,6,5,2] => 0
[3,4,2,1,5,6] => 0
[3,4,2,1,6,5] => 0
[3,4,2,5,1,6] => 0
[3,4,2,5,6,1] => 0
[3,4,2,6,1,5] => 0
[3,4,2,6,5,1] => 0
[3,4,5,1,2,6] => 0
[3,4,5,1,6,2] => 0
[3,4,5,2,1,6] => 0
[3,4,5,2,6,1] => 0
[3,4,5,6,1,2] => 0
[3,4,5,6,2,1] => 0
[3,4,6,1,2,5] => 0
[3,4,6,1,5,2] => 0
[3,4,6,2,1,5] => 0
[3,4,6,2,5,1] => 0
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 0
[3,5,1,2,6,4] => 0
[3,5,1,4,2,6] => 0
[3,5,1,4,6,2] => 0
[3,5,1,6,2,4] => 0
[3,5,1,6,4,2] => 0
[3,5,2,1,4,6] => 0
[3,5,2,1,6,4] => 0
[3,5,2,4,1,6] => 0
[3,5,2,4,6,1] => 0
[3,5,2,6,1,4] => 0
[3,5,2,6,4,1] => 0
[3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 0
[3,5,6,1,4,2] => 0
[3,5,6,2,1,4] => 0
[3,5,6,2,4,1] => 0
[3,5,6,4,1,2] => 0
[3,5,6,4,2,1] => 0
[3,6,1,2,4,5] => 0
[3,6,1,2,5,4] => 0
[3,6,1,4,2,5] => 0
[3,6,1,4,5,2] => 0
[3,6,1,5,2,4] => 0
[3,6,1,5,4,2] => 0
[3,6,2,1,4,5] => 0
[3,6,2,1,5,4] => 0
[3,6,2,4,1,5] => 0
[3,6,2,4,5,1] => 0
[3,6,2,5,1,4] => 0
[3,6,2,5,4,1] => 0
[3,6,4,1,2,5] => 0
[3,6,4,1,5,2] => 0
[3,6,4,2,1,5] => 0
[3,6,4,2,5,1] => 0
[3,6,4,5,1,2] => 0
[3,6,4,5,2,1] => 0
[3,6,5,1,2,4] => 0
[3,6,5,1,4,2] => 0
[3,6,5,2,1,4] => 0
[3,6,5,2,4,1] => 0
[3,6,5,4,1,2] => 0
[3,6,5,4,2,1] => 0
[4,1,2,3,5,6] => 0
[4,1,2,3,6,5] => 0
[4,1,2,5,3,6] => 0
[4,1,2,5,6,3] => 0
[4,1,2,6,3,5] => 0
[4,1,2,6,5,3] => 0
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 1
[4,1,3,5,2,6] => 0
[4,1,3,5,6,2] => 0
[4,1,3,6,2,5] => 0
[4,1,3,6,5,2] => 0
[4,1,5,2,3,6] => 0
[4,1,5,2,6,3] => 0
[4,1,5,3,2,6] => 0
[4,1,5,3,6,2] => 0
[4,1,5,6,2,3] => 0
[4,1,5,6,3,2] => 0
[4,1,6,2,3,5] => 0
[4,1,6,2,5,3] => 0
[4,1,6,3,2,5] => 0
[4,1,6,3,5,2] => 0
[4,1,6,5,2,3] => 0
[4,1,6,5,3,2] => 0
[4,2,1,3,5,6] => 0
[4,2,1,3,6,5] => 0
[4,2,1,5,3,6] => 0
[4,2,1,5,6,3] => 0
[4,2,1,6,3,5] => 0
[4,2,1,6,5,3] => 0
[4,2,3,1,5,6] => 0
[4,2,3,1,6,5] => 0
[4,2,3,5,1,6] => 0
[4,2,3,5,6,1] => 0
[4,2,3,6,1,5] => 0
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 0
[4,2,5,1,6,3] => 0
[4,2,5,3,1,6] => 0
[4,2,5,3,6,1] => 0
[4,2,5,6,1,3] => 0
[4,2,5,6,3,1] => 0
[4,2,6,1,3,5] => 0
[4,2,6,1,5,3] => 0
[4,2,6,3,1,5] => 0
[4,2,6,3,5,1] => 0
[4,2,6,5,1,3] => 0
[4,2,6,5,3,1] => 0
[4,3,1,2,5,6] => 0
[4,3,1,2,6,5] => 0
[4,3,1,5,2,6] => 0
[4,3,1,5,6,2] => 0
[4,3,1,6,2,5] => 0
[4,3,1,6,5,2] => 0
[4,3,2,1,5,6] => 0
[4,3,2,1,6,5] => 0
[4,3,2,5,1,6] => 0
[4,3,2,5,6,1] => 0
[4,3,2,6,1,5] => 0
[4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => 0
[4,3,5,1,6,2] => 0
[4,3,5,2,1,6] => 0
[4,3,5,2,6,1] => 0
[4,3,5,6,1,2] => 0
[4,3,5,6,2,1] => 0
[4,3,6,1,2,5] => 0
[4,3,6,1,5,2] => 0
[4,3,6,2,1,5] => 0
[4,3,6,2,5,1] => 0
[4,3,6,5,1,2] => 0
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 0
[4,5,1,2,6,3] => 0
[4,5,1,3,2,6] => 1
[4,5,1,3,6,2] => 0
[4,5,1,6,2,3] => 0
[4,5,1,6,3,2] => 0
[4,5,2,1,3,6] => 0
[4,5,2,1,6,3] => 0
[4,5,2,3,1,6] => 0
[4,5,2,3,6,1] => 0
[4,5,2,6,1,3] => 0
[4,5,2,6,3,1] => 0
[4,5,3,1,2,6] => 0
[4,5,3,1,6,2] => 0
[4,5,3,2,1,6] => 0
[4,5,3,2,6,1] => 0
[4,5,3,6,1,2] => 0
[4,5,3,6,2,1] => 0
[4,5,6,1,2,3] => 0
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 0
[4,5,6,2,3,1] => 0
[4,5,6,3,1,2] => 0
[4,5,6,3,2,1] => 0
[4,6,1,2,3,5] => 0
[4,6,1,2,5,3] => 0
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 0
[4,6,1,5,2,3] => 0
[4,6,1,5,3,2] => 0
[4,6,2,1,3,5] => 0
[4,6,2,1,5,3] => 0
[4,6,2,3,1,5] => 0
[4,6,2,3,5,1] => 0
[4,6,2,5,1,3] => 0
[4,6,2,5,3,1] => 0
[4,6,3,1,2,5] => 0
[4,6,3,1,5,2] => 0
[4,6,3,2,1,5] => 0
[4,6,3,2,5,1] => 0
[4,6,3,5,1,2] => 0
[4,6,3,5,2,1] => 0
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 0
[5,1,2,3,6,4] => 0
[5,1,2,4,3,6] => 1
[5,1,2,4,6,3] => 0
[5,1,2,6,3,4] => 0
[5,1,2,6,4,3] => 0
[5,1,3,2,4,6] => 1
[5,1,3,2,6,4] => 1
[5,1,3,4,2,6] => 0
[5,1,3,4,6,2] => 0
[5,1,3,6,2,4] => 0
[5,1,3,6,4,2] => 0
[5,1,4,2,3,6] => 0
[5,1,4,2,6,3] => 0
[5,1,4,3,2,6] => 0
[5,1,4,3,6,2] => 0
[5,1,4,6,2,3] => 0
[5,1,4,6,3,2] => 0
[5,1,6,2,3,4] => 0
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 0
[5,1,6,3,4,2] => 0
[5,1,6,4,2,3] => 0
[5,1,6,4,3,2] => 0
[5,2,1,3,4,6] => 0
[5,2,1,3,6,4] => 0
[5,2,1,4,3,6] => 0
[5,2,1,4,6,3] => 0
[5,2,1,6,3,4] => 0
[5,2,1,6,4,3] => 0
[5,2,3,1,4,6] => 0
[5,2,3,1,6,4] => 0
[5,2,3,4,1,6] => 0
[5,2,3,4,6,1] => 0
[5,2,3,6,1,4] => 0
[5,2,3,6,4,1] => 0
[5,2,4,1,3,6] => 0
[5,2,4,1,6,3] => 0
[5,2,4,3,1,6] => 1
[5,2,4,3,6,1] => 1
[5,2,4,6,1,3] => 0
[5,2,4,6,3,1] => 0
[5,2,6,1,3,4] => 0
[5,2,6,1,4,3] => 0
[5,2,6,3,1,4] => 0
[5,2,6,3,4,1] => 0
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 0
[5,3,1,2,4,6] => 0
[5,3,1,2,6,4] => 0
[5,3,1,4,2,6] => 0
[5,3,1,4,6,2] => 0
[5,3,1,6,2,4] => 0
[5,3,1,6,4,2] => 0
[5,3,2,1,4,6] => 0
[5,3,2,1,6,4] => 0
[5,3,2,4,1,6] => 0
[5,3,2,4,6,1] => 0
[5,3,2,6,1,4] => 0
[5,3,2,6,4,1] => 0
[5,3,4,1,2,6] => 0
[5,3,4,1,6,2] => 0
[5,3,4,2,1,6] => 0
[5,3,4,2,6,1] => 0
[5,3,4,6,1,2] => 0
[5,3,4,6,2,1] => 0
[5,3,6,1,2,4] => 0
[5,3,6,1,4,2] => 0
[5,3,6,2,1,4] => 0
[5,3,6,2,4,1] => 0
[5,3,6,4,1,2] => 0
[5,3,6,4,2,1] => 0
[5,4,1,2,3,6] => 0
[5,4,1,2,6,3] => 0
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 0
[5,4,1,6,2,3] => 0
[5,4,1,6,3,2] => 0
[5,4,2,1,3,6] => 0
[5,4,2,1,6,3] => 0
[5,4,2,3,1,6] => 0
[5,4,2,3,6,1] => 0
[5,4,2,6,1,3] => 0
[5,4,2,6,3,1] => 0
[5,4,3,1,2,6] => 0
[5,4,3,1,6,2] => 0
[5,4,3,2,1,6] => 0
[5,4,3,2,6,1] => 0
[5,4,3,6,1,2] => 0
[5,4,3,6,2,1] => 0
[5,4,6,1,2,3] => 0
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 0
[5,4,6,2,3,1] => 0
[5,4,6,3,1,2] => 0
[5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => 0
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 0
[5,6,1,4,2,3] => 0
[5,6,1,4,3,2] => 0
[5,6,2,1,3,4] => 0
[5,6,2,1,4,3] => 0
[5,6,2,3,1,4] => 0
[5,6,2,3,4,1] => 0
[5,6,2,4,1,3] => 0
[5,6,2,4,3,1] => 1
[5,6,3,1,2,4] => 0
[5,6,3,1,4,2] => 0
[5,6,3,2,1,4] => 0
[5,6,3,2,4,1] => 0
[5,6,3,4,1,2] => 0
[5,6,3,4,2,1] => 0
[5,6,4,1,2,3] => 0
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 0
[5,6,4,2,3,1] => 0
[5,6,4,3,1,2] => 0
[5,6,4,3,2,1] => 0
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 1
[6,1,2,4,3,5] => 1
[6,1,2,4,5,3] => 0
[6,1,2,5,3,4] => 0
[6,1,2,5,4,3] => 0
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 1
[6,1,3,4,2,5] => 0
[6,1,3,4,5,2] => 0
[6,1,3,5,2,4] => 0
[6,1,3,5,4,2] => 1
[6,1,4,2,3,5] => 0
[6,1,4,2,5,3] => 0
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 0
[6,1,4,5,2,3] => 0
[6,1,4,5,3,2] => 0
[6,1,5,2,3,4] => 0
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 0
[6,1,5,3,4,2] => 0
[6,1,5,4,2,3] => 0
[6,1,5,4,3,2] => 0
[6,2,1,3,4,5] => 0
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 0
[6,2,1,4,5,3] => 0
[6,2,1,5,3,4] => 0
[6,2,1,5,4,3] => 0
[6,2,3,1,4,5] => 0
[6,2,3,1,5,4] => 0
[6,2,3,4,1,5] => 0
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 0
[6,2,3,5,4,1] => 1
[6,2,4,1,3,5] => 0
[6,2,4,1,5,3] => 0
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 1
[6,2,4,5,1,3] => 0
[6,2,4,5,3,1] => 0
[6,2,5,1,3,4] => 0
[6,2,5,1,4,3] => 0
[6,2,5,3,1,4] => 0
[6,2,5,3,4,1] => 0
[6,2,5,4,1,3] => 0
[6,2,5,4,3,1] => 0
[6,3,1,2,4,5] => 0
[6,3,1,2,5,4] => 0
[6,3,1,4,2,5] => 0
[6,3,1,4,5,2] => 0
[6,3,1,5,2,4] => 0
[6,3,1,5,4,2] => 0
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 0
[6,3,2,4,5,1] => 0
[6,3,2,5,1,4] => 0
[6,3,2,5,4,1] => 0
[6,3,4,1,2,5] => 0
[6,3,4,1,5,2] => 0
[6,3,4,2,1,5] => 0
[6,3,4,2,5,1] => 0
[6,3,4,5,1,2] => 0
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 0
[6,3,5,1,4,2] => 0
[6,3,5,2,1,4] => 0
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 0
[6,4,1,2,5,3] => 0
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 0
[6,4,1,5,2,3] => 0
[6,4,1,5,3,2] => 0
[6,4,2,1,3,5] => 0
[6,4,2,1,5,3] => 0
[6,4,2,3,1,5] => 0
[6,4,2,3,5,1] => 0
[6,4,2,5,1,3] => 0
[6,4,2,5,3,1] => 0
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 0
[6,4,3,2,1,5] => 0
[6,4,3,2,5,1] => 0
[6,4,3,5,1,2] => 0
[6,4,3,5,2,1] => 0
[6,4,5,1,2,3] => 0
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 0
[6,4,5,2,3,1] => 0
[6,4,5,3,1,2] => 0
[6,4,5,3,2,1] => 0
[6,5,1,2,3,4] => 0
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 0
[6,5,1,4,2,3] => 0
[6,5,1,4,3,2] => 0
[6,5,2,1,3,4] => 0
[6,5,2,1,4,3] => 0
[6,5,2,3,1,4] => 0
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 0
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 0
[6,5,3,1,4,2] => 0
[6,5,3,2,1,4] => 0
[6,5,3,2,4,1] => 0
[6,5,3,4,1,2] => 0
[6,5,3,4,2,1] => 0
[6,5,4,1,2,3] => 0
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 0
[6,5,4,2,3,1] => 0
[6,5,4,3,1,2] => 0
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 1
[1,2,3,4,6,5,7] => 1
[1,2,3,4,6,7,5] => 0
[1,2,3,4,7,5,6] => 0
[1,2,3,4,7,6,5] => 0
[1,2,3,5,4,6,7] => 1
[1,2,3,5,4,7,6] => 1
[1,2,3,5,6,4,7] => 0
[1,2,3,5,6,7,4] => 0
[1,2,3,5,7,4,6] => 0
[1,2,3,5,7,6,4] => 1
[1,2,3,6,4,5,7] => 0
[1,2,3,6,4,7,5] => 0
[1,2,3,6,5,4,7] => 0
[1,2,3,6,5,7,4] => 0
[1,2,3,6,7,4,5] => 0
[1,2,3,6,7,5,4] => 0
[1,2,3,7,4,5,6] => 0
[1,2,3,7,4,6,5] => 1
[1,2,3,7,5,4,6] => 0
[1,2,3,7,5,6,4] => 0
[1,2,3,7,6,4,5] => 0
[1,2,3,7,6,5,4] => 0
[1,2,4,3,5,6,7] => 1
[1,2,4,3,5,7,6] => 2
[1,2,4,3,6,5,7] => 1
[1,2,4,3,6,7,5] => 1
[1,2,4,3,7,5,6] => 1
[1,2,4,3,7,6,5] => 1
[1,2,4,5,3,6,7] => 0
[1,2,4,5,3,7,6] => 0
[1,2,4,5,6,3,7] => 0
[1,2,4,5,6,7,3] => 0
[1,2,4,5,7,3,6] => 0
[1,2,4,5,7,6,3] => 1
[1,2,4,6,3,5,7] => 0
[1,2,4,6,3,7,5] => 0
[1,2,4,6,5,3,7] => 1
[1,2,4,6,5,7,3] => 1
[1,2,4,6,7,3,5] => 0
[1,2,4,6,7,5,3] => 0
[1,2,4,7,3,5,6] => 0
[1,2,4,7,3,6,5] => 0
[1,2,4,7,5,3,6] => 0
[1,2,4,7,5,6,3] => 0
[1,2,4,7,6,3,5] => 0
[1,2,4,7,6,5,3] => 0
[1,2,5,3,4,6,7] => 0
[1,2,5,3,4,7,6] => 0
[1,2,5,3,6,4,7] => 0
[1,2,5,3,6,7,4] => 0
[1,2,5,3,7,4,6] => 0
[1,2,5,3,7,6,4] => 0
[1,2,5,4,3,6,7] => 0
[1,2,5,4,3,7,6] => 0
[1,2,5,4,6,3,7] => 0
[1,2,5,4,6,7,3] => 0
[1,2,5,4,7,3,6] => 0
[1,2,5,4,7,6,3] => 0
[1,2,5,6,3,4,7] => 0
[1,2,5,6,3,7,4] => 0
[1,2,5,6,4,3,7] => 0
[1,2,5,6,4,7,3] => 0
[1,2,5,6,7,3,4] => 0
[1,2,5,6,7,4,3] => 0
[1,2,5,7,3,4,6] => 0
[1,2,5,7,3,6,4] => 0
[1,2,5,7,4,3,6] => 0
[1,2,5,7,4,6,3] => 0
[1,2,5,7,6,3,4] => 1
[1,2,5,7,6,4,3] => 1
[1,2,6,3,4,5,7] => 0
[1,2,6,3,4,7,5] => 0
[1,2,6,3,5,4,7] => 1
[1,2,6,3,5,7,4] => 0
[1,2,6,3,7,4,5] => 0
[1,2,6,3,7,5,4] => 0
[1,2,6,4,3,5,7] => 0
[1,2,6,4,3,7,5] => 0
[1,2,6,4,5,3,7] => 0
[1,2,6,4,5,7,3] => 0
[1,2,6,4,7,3,5] => 0
[1,2,6,4,7,5,3] => 0
[1,2,6,5,3,4,7] => 0
[1,2,6,5,3,7,4] => 0
[1,2,6,5,4,3,7] => 0
[1,2,6,5,4,7,3] => 0
[1,2,6,5,7,3,4] => 0
[1,2,6,5,7,4,3] => 0
[1,2,6,7,3,4,5] => 0
[1,2,6,7,3,5,4] => 1
[1,2,6,7,4,3,5] => 0
[1,2,6,7,4,5,3] => 0
[1,2,6,7,5,3,4] => 0
[1,2,6,7,5,4,3] => 0
[1,2,7,3,4,5,6] => 0
[1,2,7,3,4,6,5] => 1
[1,2,7,3,5,4,6] => 1
[1,2,7,3,5,6,4] => 0
[1,2,7,3,6,4,5] => 0
[1,2,7,3,6,5,4] => 0
[1,2,7,4,3,5,6] => 0
[1,2,7,4,3,6,5] => 0
[1,2,7,4,5,3,6] => 0
[1,2,7,4,5,6,3] => 0
[1,2,7,4,6,3,5] => 0
[1,2,7,4,6,5,3] => 1
[1,2,7,5,3,4,6] => 0
[1,2,7,5,3,6,4] => 0
[1,2,7,5,4,3,6] => 0
[1,2,7,5,4,6,3] => 0
[1,2,7,5,6,3,4] => 0
[1,2,7,5,6,4,3] => 0
[1,2,7,6,3,4,5] => 0
[1,2,7,6,3,5,4] => 1
[1,2,7,6,4,3,5] => 0
[1,2,7,6,4,5,3] => 0
[1,2,7,6,5,3,4] => 0
[1,2,7,6,5,4,3] => 0
[1,3,2,4,5,6,7] => 1
[1,3,2,4,5,7,6] => 2
[1,3,2,4,6,5,7] => 2
[1,3,2,4,6,7,5] => 1
[1,3,2,4,7,5,6] => 1
[1,3,2,4,7,6,5] => 1
[1,3,2,5,4,6,7] => 1
[1,3,2,5,4,7,6] => 1
[1,3,2,5,6,4,7] => 1
[1,3,2,5,6,7,4] => 1
[1,3,2,5,7,4,6] => 1
[1,3,2,5,7,6,4] => 2
[1,3,2,6,4,5,7] => 1
[1,3,2,6,4,7,5] => 1
[1,3,2,6,5,4,7] => 1
[1,3,2,6,5,7,4] => 1
[1,3,2,6,7,4,5] => 1
[1,3,2,6,7,5,4] => 1
[1,3,2,7,4,5,6] => 1
[1,3,2,7,4,6,5] => 2
[1,3,2,7,5,4,6] => 1
[1,3,2,7,5,6,4] => 1
[1,3,2,7,6,4,5] => 1
[1,3,2,7,6,5,4] => 1
[1,3,4,2,5,6,7] => 0
[1,3,4,2,5,7,6] => 1
[1,3,4,2,6,5,7] => 0
[1,3,4,2,6,7,5] => 0
[1,3,4,2,7,5,6] => 0
[1,3,4,2,7,6,5] => 0
[1,3,4,5,2,6,7] => 0
[1,3,4,5,2,7,6] => 0
[1,3,4,5,6,2,7] => 0
[1,3,4,5,6,7,2] => 0
[1,3,4,5,7,2,6] => 0
[1,3,4,5,7,6,2] => 1
[1,3,4,6,2,5,7] => 0
[1,3,4,6,2,7,5] => 0
[1,3,4,6,5,2,7] => 1
[1,3,4,6,5,7,2] => 1
[1,3,4,6,7,2,5] => 0
[1,3,4,6,7,5,2] => 0
[1,3,4,7,2,5,6] => 0
[1,3,4,7,2,6,5] => 0
[1,3,4,7,5,2,6] => 0
[1,3,4,7,5,6,2] => 0
[1,3,4,7,6,2,5] => 0
[1,3,4,7,6,5,2] => 0
[1,3,5,2,4,6,7] => 0
[1,3,5,2,4,7,6] => 0
[1,3,5,2,6,4,7] => 0
[1,3,5,2,6,7,4] => 0
[1,3,5,2,7,4,6] => 0
[1,3,5,2,7,6,4] => 0
[1,3,5,4,2,6,7] => 1
[1,3,5,4,2,7,6] => 1
[1,3,5,4,6,2,7] => 1
[1,3,5,4,6,7,2] => 1
[1,3,5,4,7,2,6] => 1
[1,3,5,4,7,6,2] => 1
[1,3,5,6,2,4,7] => 0
[1,3,5,6,2,7,4] => 0
[1,3,5,6,4,2,7] => 0
[1,3,5,6,4,7,2] => 0
[1,3,5,6,7,2,4] => 0
[1,3,5,6,7,4,2] => 0
[1,3,5,7,2,4,6] => 0
[1,3,5,7,2,6,4] => 0
[1,3,5,7,4,2,6] => 0
[1,3,5,7,4,6,2] => 0
[1,3,5,7,6,2,4] => 1
[1,3,5,7,6,4,2] => 1
[1,3,6,2,4,5,7] => 0
[1,3,6,2,4,7,5] => 0
[1,3,6,2,5,4,7] => 0
[1,3,6,2,5,7,4] => 0
[1,3,6,2,7,4,5] => 0
[1,3,6,2,7,5,4] => 0
[1,3,6,4,2,5,7] => 0
[1,3,6,4,2,7,5] => 0
[1,3,6,4,5,2,7] => 0
[1,3,6,4,5,7,2] => 0
[1,3,6,4,7,2,5] => 0
[1,3,6,4,7,5,2] => 0
[1,3,6,5,2,4,7] => 0
[1,3,6,5,2,7,4] => 0
[1,3,6,5,4,2,7] => 0
[1,3,6,5,4,7,2] => 0
[1,3,6,5,7,2,4] => 0
[1,3,6,5,7,4,2] => 0
[1,3,6,7,2,4,5] => 0
[1,3,6,7,2,5,4] => 0
[1,3,6,7,4,2,5] => 0
[1,3,6,7,4,5,2] => 0
[1,3,6,7,5,2,4] => 0
[1,3,6,7,5,4,2] => 0
[1,3,7,2,4,5,6] => 0
[1,3,7,2,4,6,5] => 1
[1,3,7,2,5,4,6] => 0
[1,3,7,2,5,6,4] => 0
[1,3,7,2,6,4,5] => 0
[1,3,7,2,6,5,4] => 0
[1,3,7,4,2,5,6] => 0
[1,3,7,4,2,6,5] => 0
[1,3,7,4,5,2,6] => 0
[1,3,7,4,5,6,2] => 0
[1,3,7,4,6,2,5] => 0
[1,3,7,4,6,5,2] => 1
[1,3,7,5,2,4,6] => 0
[1,3,7,5,2,6,4] => 0
[1,3,7,5,4,2,6] => 0
[1,3,7,5,4,6,2] => 0
[1,3,7,5,6,2,4] => 0
[1,3,7,5,6,4,2] => 0
[1,3,7,6,2,4,5] => 0
[1,3,7,6,2,5,4] => 0
[1,3,7,6,4,2,5] => 0
[1,3,7,6,4,5,2] => 0
[1,3,7,6,5,2,4] => 0
[1,3,7,6,5,4,2] => 0
[1,4,2,3,5,6,7] => 0
[1,4,2,3,5,7,6] => 1
[1,4,2,3,6,5,7] => 0
[1,4,2,3,6,7,5] => 0
[1,4,2,3,7,5,6] => 0
[1,4,2,3,7,6,5] => 0
[1,4,2,5,3,6,7] => 0
[1,4,2,5,3,7,6] => 0
[1,4,2,5,6,3,7] => 0
[1,4,2,5,6,7,3] => 0
[1,4,2,5,7,3,6] => 0
[1,4,2,5,7,6,3] => 1
[1,4,2,6,3,5,7] => 0
[1,4,2,6,3,7,5] => 0
[1,4,2,6,5,3,7] => 0
[1,4,2,6,5,7,3] => 0
[1,4,2,6,7,3,5] => 0
[1,4,2,6,7,5,3] => 0
[1,4,2,7,3,5,6] => 0
[1,4,2,7,3,6,5] => 0
[1,4,2,7,5,3,6] => 0
[1,4,2,7,5,6,3] => 0
[1,4,2,7,6,3,5] => 0
[1,4,2,7,6,5,3] => 0
[1,4,3,2,5,6,7] => 0
[1,4,3,2,5,7,6] => 1
[1,4,3,2,6,5,7] => 0
[1,4,3,2,6,7,5] => 0
[1,4,3,2,7,5,6] => 0
[1,4,3,2,7,6,5] => 0
[1,4,3,5,2,6,7] => 0
[1,4,3,5,2,7,6] => 0
[1,4,3,5,6,2,7] => 0
[1,4,3,5,6,7,2] => 0
[1,4,3,5,7,2,6] => 0
[1,4,3,5,7,6,2] => 1
[1,4,3,6,2,5,7] => 0
[1,4,3,6,2,7,5] => 0
[1,4,3,6,5,2,7] => 0
[1,4,3,6,5,7,2] => 0
[1,4,3,6,7,2,5] => 0
[1,4,3,6,7,5,2] => 0
[1,4,3,7,2,5,6] => 0
[1,4,3,7,2,6,5] => 0
[1,4,3,7,5,2,6] => 0
[1,4,3,7,5,6,2] => 0
[1,4,3,7,6,2,5] => 0
[1,4,3,7,6,5,2] => 0
[1,4,5,2,3,6,7] => 0
[1,4,5,2,3,7,6] => 0
[1,4,5,2,6,3,7] => 0
[1,4,5,2,6,7,3] => 0
[1,4,5,2,7,3,6] => 0
[1,4,5,2,7,6,3] => 0
[1,4,5,3,2,6,7] => 0
[1,4,5,3,2,7,6] => 0
[1,4,5,3,6,2,7] => 0
[1,4,5,3,6,7,2] => 0
[1,4,5,3,7,2,6] => 0
[1,4,5,3,7,6,2] => 0
[1,4,5,6,2,3,7] => 0
[1,4,5,6,2,7,3] => 0
[1,4,5,6,3,2,7] => 0
[1,4,5,6,3,7,2] => 0
[1,4,5,6,7,2,3] => 0
[1,4,5,6,7,3,2] => 0
[1,4,5,7,2,3,6] => 0
[1,4,5,7,2,6,3] => 0
[1,4,5,7,3,2,6] => 0
[1,4,5,7,3,6,2] => 0
[1,4,5,7,6,2,3] => 1
[1,4,5,7,6,3,2] => 1
[1,4,6,2,3,5,7] => 0
[1,4,6,2,3,7,5] => 0
[1,4,6,2,5,3,7] => 0
[1,4,6,2,5,7,3] => 0
[1,4,6,2,7,3,5] => 0
[1,4,6,2,7,5,3] => 0
[1,4,6,3,2,5,7] => 0
[1,4,6,3,2,7,5] => 0
[1,4,6,3,5,2,7] => 0
[1,4,6,3,5,7,2] => 0
[1,4,6,3,7,2,5] => 0
[1,4,6,3,7,5,2] => 0
[1,4,6,5,2,3,7] => 1
[1,4,6,5,2,7,3] => 1
[1,4,6,5,3,2,7] => 1
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Description
The number of occurrences of the Hertzsprung pattern 132 in a permutation.
A Hertzsprung occurrence of the pattern τ=(τ1,…,τk) in a permutation π is a factor πi,πi+1,…,πi+k−1 of π such that πi+j−1−τj is constant for 1≤j≤k.
References
[1] Myers, A. N. Counting permutations by their rigid patterns MathSciNet:1917026
[2] Claesson, A. From Hertzsprung's problem to pattern-rewriting systems arXiv:2012.15309
Code
def hertzsprung_occurrences(pi, tau):
    k = len(tau)
    c = 0
    for i in range(len(pi)-len(tau)+1):
        d = pi[i] - tau[0]
        if all(pi[i+j] - tau[j] == d for j in range(1, k)):
            c += 1
    return c

def statistic(pi):
    return hertzsprung_occurrences(pi, [1,3,2])
Created
Jan 01, 2021 at 13:15 by Martin Rubey
Updated
May 02, 2021 at 22:02 by Martin Rubey