- FindStat

edit this statistic or download as text // json

Identifier

St001377: Permutations ⟶ ℤ

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]=>-1
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>1
[1,4,2,3]=>0
[1,4,3,2]=>2
[2,1,3,4]=>0
[2,1,4,3]=>2
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>-1
[2,4,3,1]=>1
[3,1,2,4]=>-1
[3,1,4,2]=>1
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>-2
[3,4,2,1]=>0
[4,1,2,3]=>-2
[4,1,3,2]=>0
[4,2,1,3]=>-1
[4,2,3,1]=>-1
[4,3,1,2]=>-2
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>3
[1,2,4,3,5]=>2
[1,2,4,5,3]=>2
[1,2,5,3,4]=>1
[1,2,5,4,3]=>4
[1,3,2,4,5]=>1
[1,3,2,5,4]=>4
[1,3,4,2,5]=>1
[1,3,4,5,2]=>1
[1,3,5,2,4]=>0
[1,3,5,4,2]=>3
[1,4,2,3,5]=>0
[1,4,2,5,3]=>3
[1,4,3,2,5]=>2
[1,4,3,5,2]=>2
[1,4,5,2,3]=>-1
[1,4,5,3,2]=>2
[1,5,2,3,4]=>-1
[1,5,2,4,3]=>2
[1,5,3,2,4]=>1
[1,5,3,4,2]=>1
[1,5,4,2,3]=>0
[1,5,4,3,2]=>3
[2,1,3,4,5]=>0
[2,1,3,5,4]=>3
[2,1,4,3,5]=>2
[2,1,4,5,3]=>2
[2,1,5,3,4]=>1
[2,1,5,4,3]=>4
[2,3,1,4,5]=>0
[2,3,1,5,4]=>3
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>-1
[2,3,5,4,1]=>2
[2,4,1,3,5]=>-1
[2,4,1,5,3]=>2
[2,4,3,1,5]=>1
[2,4,3,5,1]=>1
[2,4,5,1,3]=>-2
[2,4,5,3,1]=>1
[2,5,1,3,4]=>-2
[2,5,1,4,3]=>1
[2,5,3,1,4]=>0
[2,5,3,4,1]=>0
[2,5,4,1,3]=>-1
[2,5,4,3,1]=>2
[3,1,2,4,5]=>-1
[3,1,2,5,4]=>2
[3,1,4,2,5]=>1
[3,1,4,5,2]=>1
[3,1,5,2,4]=>0
[3,1,5,4,2]=>3
[3,2,1,4,5]=>0
[3,2,1,5,4]=>3
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>-1
[3,2,5,4,1]=>2
[3,4,1,2,5]=>-2
[3,4,1,5,2]=>1
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>-3
[3,4,5,2,1]=>0
[3,5,1,2,4]=>-3
[3,5,1,4,2]=>0
[3,5,2,1,4]=>-1
[3,5,2,4,1]=>-1
[3,5,4,1,2]=>-2
[3,5,4,2,1]=>1
[4,1,2,3,5]=>-2
[4,1,2,5,3]=>1
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>-1
[4,1,5,3,2]=>2
[4,2,1,3,5]=>-1
[4,2,1,5,3]=>2
[4,2,3,1,5]=>-1
[4,2,3,5,1]=>-1
[4,2,5,1,3]=>-2
[4,2,5,3,1]=>1
[4,3,1,2,5]=>-2
[4,3,1,5,2]=>1
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>-3
[4,3,5,2,1]=>0
[4,5,1,2,3]=>-4
[4,5,1,3,2]=>-1
[4,5,2,1,3]=>-2
[4,5,2,3,1]=>-2
[4,5,3,1,2]=>-3
[4,5,3,2,1]=>0
[5,1,2,3,4]=>-3
[5,1,2,4,3]=>0
[5,1,3,2,4]=>-1
[5,1,3,4,2]=>-1
[5,1,4,2,3]=>-2
[5,1,4,3,2]=>1
[5,2,1,3,4]=>-2
[5,2,1,4,3]=>1
[5,2,3,1,4]=>-2
[5,2,3,4,1]=>-2
[5,2,4,1,3]=>-3
[5,2,4,3,1]=>0
[5,3,1,2,4]=>-3
[5,3,1,4,2]=>0
[5,3,2,1,4]=>-1
[5,3,2,4,1]=>-1
[5,3,4,1,2]=>-4
[5,3,4,2,1]=>-1
[5,4,1,2,3]=>-4
[5,4,1,3,2]=>-1
[5,4,2,1,3]=>-2
[5,4,2,3,1]=>-2
[5,4,3,1,2]=>-3
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>4
[1,2,3,5,4,6]=>3
[1,2,3,5,6,4]=>3
[1,2,3,6,4,5]=>2
[1,2,3,6,5,4]=>6
[1,2,4,3,5,6]=>2
[1,2,4,3,6,5]=>6
[1,2,4,5,3,6]=>2
[1,2,4,5,6,3]=>2
[1,2,4,6,3,5]=>1
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>1
[1,2,5,3,6,4]=>5
[1,2,5,4,3,6]=>4
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>4
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>4
[1,2,6,4,3,5]=>3
[1,2,6,4,5,3]=>3
[1,2,6,5,3,4]=>2
[1,2,6,5,4,3]=>6
[1,3,2,4,5,6]=>1
[1,3,2,4,6,5]=>5
[1,3,2,5,4,6]=>4
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>3
[1,3,2,6,5,4]=>7
[1,3,4,2,5,6]=>1
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>1
[1,3,4,5,6,2]=>1
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>3
[1,3,5,4,6,2]=>3
[1,3,5,6,2,4]=>-1
[1,3,5,6,4,2]=>3
[1,3,6,2,4,5]=>-1
[1,3,6,2,5,4]=>3
[1,3,6,4,2,5]=>2
[1,3,6,4,5,2]=>2
[1,3,6,5,2,4]=>1
[1,3,6,5,4,2]=>5
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>4
[1,4,2,5,3,6]=>3
[1,4,2,5,6,3]=>3
[1,4,2,6,3,5]=>2
[1,4,2,6,5,3]=>6
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>6
[1,4,3,5,2,6]=>2
[1,4,3,5,6,2]=>2
[1,4,3,6,2,5]=>1
[1,4,3,6,5,2]=>5
[1,4,5,2,3,6]=>-1
[1,4,5,2,6,3]=>3
[1,4,5,3,2,6]=>2
[1,4,5,3,6,2]=>2
[1,4,5,6,2,3]=>-2
[1,4,5,6,3,2]=>2
[1,4,6,2,3,5]=>-2
[1,4,6,2,5,3]=>2
[1,4,6,3,2,5]=>1
[1,4,6,3,5,2]=>1
[1,4,6,5,2,3]=>0
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>-1
[1,5,2,3,6,4]=>3
[1,5,2,4,3,6]=>2
[1,5,2,4,6,3]=>2
[1,5,2,6,3,4]=>1
[1,5,2,6,4,3]=>5
[1,5,3,2,4,6]=>1
[1,5,3,2,6,4]=>5
[1,5,3,4,2,6]=>1
[1,5,3,4,6,2]=>1
[1,5,3,6,2,4]=>0
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>0
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>3
[1,5,4,3,6,2]=>3
[1,5,4,6,2,3]=>-1
[1,5,4,6,3,2]=>3
[1,5,6,2,3,4]=>-3
[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]=>-1
[1,5,6,4,3,2]=>3
[1,6,2,3,4,5]=>-2
[1,6,2,3,5,4]=>2
[1,6,2,4,3,5]=>1
[1,6,2,4,5,3]=>1
[1,6,2,5,3,4]=>0
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>0
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>-1
[1,6,3,5,4,2]=>3
[1,6,4,2,3,5]=>-1
[1,6,4,2,5,3]=>3
[1,6,4,3,2,5]=>2
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>-2
[1,6,4,5,3,2]=>2
[1,6,5,2,3,4]=>-2
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>1
[1,6,5,3,4,2]=>1
[1,6,5,4,2,3]=>0
[1,6,5,4,3,2]=>4
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>4
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>2
[2,1,3,6,5,4]=>6
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>6
[2,1,4,5,3,6]=>2
[2,1,4,5,6,3]=>2
[2,1,4,6,3,5]=>1
[2,1,4,6,5,3]=>5
[2,1,5,3,4,6]=>1
[2,1,5,3,6,4]=>5
[2,1,5,4,3,6]=>4
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>3
[2,1,6,4,5,3]=>3
[2,1,6,5,3,4]=>2
[2,1,6,5,4,3]=>6
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>3
[2,3,1,5,6,4]=>3
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>6
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>-1
[2,3,4,6,5,1]=>3
[2,3,5,1,4,6]=>-1
[2,3,5,1,6,4]=>3
[2,3,5,4,1,6]=>2
[2,3,5,4,6,1]=>2
[2,3,5,6,1,4]=>-2
[2,3,5,6,4,1]=>2
[2,3,6,1,4,5]=>-2
[2,3,6,1,5,4]=>2
[2,3,6,4,1,5]=>1
[2,3,6,4,5,1]=>1
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>-1
[2,4,1,3,6,5]=>3
[2,4,1,5,3,6]=>2
[2,4,1,5,6,3]=>2
[2,4,1,6,3,5]=>1
[2,4,1,6,5,3]=>5
[2,4,3,1,5,6]=>1
[2,4,3,1,6,5]=>5
[2,4,3,5,1,6]=>1
[2,4,3,5,6,1]=>1
[2,4,3,6,1,5]=>0
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>-2
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>1
[2,4,5,3,6,1]=>1
[2,4,5,6,1,3]=>-3
[2,4,5,6,3,1]=>1
[2,4,6,1,3,5]=>-3
[2,4,6,1,5,3]=>1
[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]=>3
[2,5,1,3,4,6]=>-2
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>1
[2,5,1,4,6,3]=>1
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>4
[2,5,3,1,4,6]=>0
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>-1
[2,5,3,6,4,1]=>3
[2,5,4,1,3,6]=>-1
[2,5,4,1,6,3]=>3
[2,5,4,3,1,6]=>2
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>-2
[2,5,4,6,3,1]=>2
[2,5,6,1,3,4]=>-4
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>-1
[2,5,6,3,4,1]=>-1
[2,5,6,4,1,3]=>-2
[2,5,6,4,3,1]=>2
[2,6,1,3,4,5]=>-3
[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]=>-1
[2,6,1,5,4,3]=>3
[2,6,3,1,4,5]=>-1
[2,6,3,1,5,4]=>3
[2,6,3,4,1,5]=>-1
[2,6,3,4,5,1]=>-1
[2,6,3,5,1,4]=>-2
[2,6,3,5,4,1]=>2
[2,6,4,1,3,5]=>-2
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>1
[2,6,4,3,5,1]=>1
[2,6,4,5,1,3]=>-3
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>-3
[2,6,5,1,4,3]=>1
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>-1
[2,6,5,4,3,1]=>3
[3,1,2,4,5,6]=>-1
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>2
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>1
[3,1,2,6,5,4]=>5
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>5
[3,1,4,5,2,6]=>1
[3,1,4,5,6,2]=>1
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>4
[3,1,5,4,2,6]=>3
[3,1,5,4,6,2]=>3
[3,1,5,6,2,4]=>-1
[3,1,5,6,4,2]=>3
[3,1,6,2,4,5]=>-1
[3,1,6,2,5,4]=>3
[3,1,6,4,2,5]=>2
[3,1,6,4,5,2]=>2
[3,1,6,5,2,4]=>1
[3,1,6,5,4,2]=>5
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>4
[3,2,1,5,4,6]=>3
[3,2,1,5,6,4]=>3
[3,2,1,6,4,5]=>2
[3,2,1,6,5,4]=>6
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>4
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>-1
[3,2,4,6,5,1]=>3
[3,2,5,1,4,6]=>-1
[3,2,5,1,6,4]=>3
[3,2,5,4,1,6]=>2
[3,2,5,4,6,1]=>2
[3,2,5,6,1,4]=>-2
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>-2
[3,2,6,1,5,4]=>2
[3,2,6,4,1,5]=>1
[3,2,6,4,5,1]=>1
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>-2
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>1
[3,4,1,5,6,2]=>1
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>-1
[3,4,2,6,5,1]=>3
[3,4,5,1,2,6]=>-3
[3,4,5,1,6,2]=>1
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>-4
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>-4
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>-1
[3,4,6,2,5,1]=>-1
[3,4,6,5,1,2]=>-2
[3,4,6,5,2,1]=>2
[3,5,1,2,4,6]=>-3
[3,5,1,2,6,4]=>1
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>-1
[3,5,1,6,4,2]=>3
[3,5,2,1,4,6]=>-1
[3,5,2,1,6,4]=>3
[3,5,2,4,1,6]=>-1
[3,5,2,4,6,1]=>-1
[3,5,2,6,1,4]=>-2
[3,5,2,6,4,1]=>2
[3,5,4,1,2,6]=>-2
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>-3
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>-5
[3,5,6,1,4,2]=>-1
[3,5,6,2,1,4]=>-2
[3,5,6,2,4,1]=>-2
[3,5,6,4,1,2]=>-3
[3,5,6,4,2,1]=>1
[3,6,1,2,4,5]=>-4
[3,6,1,2,5,4]=>0
[3,6,1,4,2,5]=>-1
[3,6,1,4,5,2]=>-1
[3,6,1,5,2,4]=>-2
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>-2
[3,6,2,1,5,4]=>2
[3,6,2,4,1,5]=>-2
[3,6,2,4,5,1]=>-2
[3,6,2,5,1,4]=>-3
[3,6,2,5,4,1]=>1
[3,6,4,1,2,5]=>-3
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>0
[3,6,4,2,5,1]=>0
[3,6,4,5,1,2]=>-4
[3,6,4,5,2,1]=>0
[3,6,5,1,2,4]=>-4
[3,6,5,1,4,2]=>0
[3,6,5,2,1,4]=>-1
[3,6,5,2,4,1]=>-1
[3,6,5,4,1,2]=>-2
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>-2
[4,1,2,3,6,5]=>2
[4,1,2,5,3,6]=>1
[4,1,2,5,6,3]=>1
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>4
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>0
[4,1,3,5,6,2]=>0
[4,1,3,6,2,5]=>-1
[4,1,3,6,5,2]=>3
[4,1,5,2,3,6]=>-1
[4,1,5,2,6,3]=>3
[4,1,5,3,2,6]=>2
[4,1,5,3,6,2]=>2
[4,1,5,6,2,3]=>-2
[4,1,5,6,3,2]=>2
[4,1,6,2,3,5]=>-2
[4,1,6,2,5,3]=>2
[4,1,6,3,2,5]=>1
[4,1,6,3,5,2]=>1
[4,1,6,5,2,3]=>0
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>-1
[4,2,1,3,6,5]=>3
[4,2,1,5,3,6]=>2
[4,2,1,5,6,3]=>2
[4,2,1,6,3,5]=>1
[4,2,1,6,5,3]=>5
[4,2,3,1,5,6]=>-1
[4,2,3,1,6,5]=>3
[4,2,3,5,1,6]=>-1
[4,2,3,5,6,1]=>-1
[4,2,3,6,1,5]=>-2
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>-2
[4,2,5,1,6,3]=>2
[4,2,5,3,1,6]=>1
[4,2,5,3,6,1]=>1
[4,2,5,6,1,3]=>-3
[4,2,5,6,3,1]=>1
[4,2,6,1,3,5]=>-3
[4,2,6,1,5,3]=>1
[4,2,6,3,1,5]=>0
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>-1
[4,2,6,5,3,1]=>3
[4,3,1,2,5,6]=>-2
[4,3,1,2,6,5]=>2
[4,3,1,5,2,6]=>1
[4,3,1,5,6,2]=>1
[4,3,1,6,2,5]=>0
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>4
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>-1
[4,3,2,6,5,1]=>3
[4,3,5,1,2,6]=>-3
[4,3,5,1,6,2]=>1
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>-4
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>-4
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>-1
[4,3,6,2,5,1]=>-1
[4,3,6,5,1,2]=>-2
[4,3,6,5,2,1]=>2
[4,5,1,2,3,6]=>-4
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>-1
[4,5,1,3,6,2]=>-1
[4,5,1,6,2,3]=>-2
[4,5,1,6,3,2]=>2
[4,5,2,1,3,6]=>-2
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>-2
[4,5,2,3,6,1]=>-2
[4,5,2,6,1,3]=>-3
[4,5,2,6,3,1]=>1
[4,5,3,1,2,6]=>-3
[4,5,3,1,6,2]=>1
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>-4
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>-6
[4,5,6,1,3,2]=>-2
[4,5,6,2,1,3]=>-3
[4,5,6,2,3,1]=>-3
[4,5,6,3,1,2]=>-4
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>-5
[4,6,1,2,5,3]=>-1
[4,6,1,3,2,5]=>-2
[4,6,1,3,5,2]=>-2
[4,6,1,5,2,3]=>-3
[4,6,1,5,3,2]=>1
[4,6,2,1,3,5]=>-3
[4,6,2,1,5,3]=>1
[4,6,2,3,1,5]=>-3
[4,6,2,3,5,1]=>-3
[4,6,2,5,1,3]=>-4
[4,6,2,5,3,1]=>0
[4,6,3,1,2,5]=>-4
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>-1
[4,6,3,2,5,1]=>-1
[4,6,3,5,1,2]=>-5
[4,6,3,5,2,1]=>-1
[4,6,5,1,2,3]=>-5
[4,6,5,1,3,2]=>-1
[4,6,5,2,1,3]=>-2
[4,6,5,2,3,1]=>-2
[4,6,5,3,1,2]=>-3
[4,6,5,3,2,1]=>1
[5,1,2,3,4,6]=>-3
[5,1,2,3,6,4]=>1
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>-1
[5,1,2,6,4,3]=>3
[5,1,3,2,4,6]=>-1
[5,1,3,2,6,4]=>3
[5,1,3,4,2,6]=>-1
[5,1,3,4,6,2]=>-1
[5,1,3,6,2,4]=>-2
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>-2
[5,1,4,2,6,3]=>2
[5,1,4,3,2,6]=>1
[5,1,4,3,6,2]=>1
[5,1,4,6,2,3]=>-3
[5,1,4,6,3,2]=>1
[5,1,6,2,3,4]=>-3
[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]=>-1
[5,1,6,4,3,2]=>3
[5,2,1,3,4,6]=>-2
[5,2,1,3,6,4]=>2
[5,2,1,4,3,6]=>1
[5,2,1,4,6,3]=>1
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>-2
[5,2,3,1,6,4]=>2
[5,2,3,4,1,6]=>-2
[5,2,3,4,6,1]=>-2
[5,2,3,6,1,4]=>-3
[5,2,3,6,4,1]=>1
[5,2,4,1,3,6]=>-3
[5,2,4,1,6,3]=>1
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>-4
[5,2,4,6,3,1]=>0
[5,2,6,1,3,4]=>-4
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>-1
[5,2,6,3,4,1]=>-1
[5,2,6,4,1,3]=>-2
[5,2,6,4,3,1]=>2
[5,3,1,2,4,6]=>-3
[5,3,1,2,6,4]=>1
[5,3,1,4,2,6]=>0
[5,3,1,4,6,2]=>0
[5,3,1,6,2,4]=>-1
[5,3,1,6,4,2]=>3
[5,3,2,1,4,6]=>-1
[5,3,2,1,6,4]=>3
[5,3,2,4,1,6]=>-1
[5,3,2,4,6,1]=>-1
[5,3,2,6,1,4]=>-2
[5,3,2,6,4,1]=>2
[5,3,4,1,2,6]=>-4
[5,3,4,1,6,2]=>0
[5,3,4,2,1,6]=>-1
[5,3,4,2,6,1]=>-1
[5,3,4,6,1,2]=>-5
[5,3,4,6,2,1]=>-1
[5,3,6,1,2,4]=>-5
[5,3,6,1,4,2]=>-1
[5,3,6,2,1,4]=>-2
[5,3,6,2,4,1]=>-2
[5,3,6,4,1,2]=>-3
[5,3,6,4,2,1]=>1
[5,4,1,2,3,6]=>-4
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>-1
[5,4,1,3,6,2]=>-1
[5,4,1,6,2,3]=>-2
[5,4,1,6,3,2]=>2
[5,4,2,1,3,6]=>-2
[5,4,2,1,6,3]=>2
[5,4,2,3,1,6]=>-2
[5,4,2,3,6,1]=>-2
[5,4,2,6,1,3]=>-3
[5,4,2,6,3,1]=>1
[5,4,3,1,2,6]=>-3
[5,4,3,1,6,2]=>1
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>-4
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>-6
[5,4,6,1,3,2]=>-2
[5,4,6,2,1,3]=>-3
[5,4,6,2,3,1]=>-3
[5,4,6,3,1,2]=>-4
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>-6
[5,6,1,2,4,3]=>-2
[5,6,1,3,2,4]=>-3
[5,6,1,3,4,2]=>-3
[5,6,1,4,2,3]=>-4
[5,6,1,4,3,2]=>0
[5,6,2,1,3,4]=>-4
[5,6,2,1,4,3]=>0
[5,6,2,3,1,4]=>-4
[5,6,2,3,4,1]=>-4
[5,6,2,4,1,3]=>-5
[5,6,2,4,3,1]=>-1
[5,6,3,1,2,4]=>-5
[5,6,3,1,4,2]=>-1
[5,6,3,2,1,4]=>-2
[5,6,3,2,4,1]=>-2
[5,6,3,4,1,2]=>-6
[5,6,3,4,2,1]=>-2
[5,6,4,1,2,3]=>-6
[5,6,4,1,3,2]=>-2
[5,6,4,2,1,3]=>-3
[5,6,4,2,3,1]=>-3
[5,6,4,3,1,2]=>-4
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>-4
[6,1,2,3,5,4]=>0
[6,1,2,4,3,5]=>-1
[6,1,2,4,5,3]=>-1
[6,1,2,5,3,4]=>-2
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>-2
[6,1,3,2,5,4]=>2
[6,1,3,4,2,5]=>-2
[6,1,3,4,5,2]=>-2
[6,1,3,5,2,4]=>-3
[6,1,3,5,4,2]=>1
[6,1,4,2,3,5]=>-3
[6,1,4,2,5,3]=>1
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>-4
[6,1,4,5,3,2]=>0
[6,1,5,2,3,4]=>-4
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>-1
[6,1,5,3,4,2]=>-1
[6,1,5,4,2,3]=>-2
[6,1,5,4,3,2]=>2
[6,2,1,3,4,5]=>-3
[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]=>-1
[6,2,1,5,4,3]=>3
[6,2,3,1,4,5]=>-3
[6,2,3,1,5,4]=>1
[6,2,3,4,1,5]=>-3
[6,2,3,4,5,1]=>-3
[6,2,3,5,1,4]=>-4
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>-4
[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]=>-5
[6,2,4,5,3,1]=>-1
[6,2,5,1,3,4]=>-5
[6,2,5,1,4,3]=>-1
[6,2,5,3,1,4]=>-2
[6,2,5,3,4,1]=>-2
[6,2,5,4,1,3]=>-3
[6,2,5,4,3,1]=>1
[6,3,1,2,4,5]=>-4
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>-1
[6,3,1,4,5,2]=>-1
[6,3,1,5,2,4]=>-2
[6,3,1,5,4,2]=>2
[6,3,2,1,4,5]=>-2
[6,3,2,1,5,4]=>2
[6,3,2,4,1,5]=>-2
[6,3,2,4,5,1]=>-2
[6,3,2,5,1,4]=>-3
[6,3,2,5,4,1]=>1
[6,3,4,1,2,5]=>-5
[6,3,4,1,5,2]=>-1
[6,3,4,2,1,5]=>-2
[6,3,4,2,5,1]=>-2
[6,3,4,5,1,2]=>-6
[6,3,4,5,2,1]=>-2
[6,3,5,1,2,4]=>-6
[6,3,5,1,4,2]=>-2
[6,3,5,2,1,4]=>-3
[6,3,5,2,4,1]=>-3
[6,3,5,4,1,2]=>-4
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>-5
[6,4,1,2,5,3]=>-1
[6,4,1,3,2,5]=>-2
[6,4,1,3,5,2]=>-2
[6,4,1,5,2,3]=>-3
[6,4,1,5,3,2]=>1
[6,4,2,1,3,5]=>-3
[6,4,2,1,5,3]=>1
[6,4,2,3,1,5]=>-3
[6,4,2,3,5,1]=>-3
[6,4,2,5,1,3]=>-4
[6,4,2,5,3,1]=>0
[6,4,3,1,2,5]=>-4
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>-1
[6,4,3,2,5,1]=>-1
[6,4,3,5,1,2]=>-5
[6,4,3,5,2,1]=>-1
[6,4,5,1,2,3]=>-7
[6,4,5,1,3,2]=>-3
[6,4,5,2,1,3]=>-4
[6,4,5,2,3,1]=>-4
[6,4,5,3,1,2]=>-5
[6,4,5,3,2,1]=>-1
[6,5,1,2,3,4]=>-6
[6,5,1,2,4,3]=>-2
[6,5,1,3,2,4]=>-3
[6,5,1,3,4,2]=>-3
[6,5,1,4,2,3]=>-4
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>-4
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>-4
[6,5,2,3,4,1]=>-4
[6,5,2,4,1,3]=>-5
[6,5,2,4,3,1]=>-1
[6,5,3,1,2,4]=>-5
[6,5,3,1,4,2]=>-1
[6,5,3,2,1,4]=>-2
[6,5,3,2,4,1]=>-2
[6,5,3,4,1,2]=>-6
[6,5,3,4,2,1]=>-2
[6,5,4,1,2,3]=>-6
[6,5,4,1,3,2]=>-2
[6,5,4,2,1,3]=>-3
[6,5,4,2,3,1]=>-3
[6,5,4,3,1,2]=>-4
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>5
[1,2,3,4,6,5,7]=>4
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>3
[1,2,3,4,7,6,5]=>8
[1,2,3,5,4,6,7]=>3
[1,2,3,5,4,7,6]=>8
[1,2,3,5,6,4,7]=>3
[1,2,3,5,6,7,4]=>3
[1,2,3,5,7,4,6]=>2
[1,2,3,5,7,6,4]=>7
[1,2,3,6,4,5,7]=>2
[1,2,3,6,4,7,5]=>7
[1,2,3,6,5,4,7]=>6
[1,2,3,6,5,7,4]=>6
[1,2,3,6,7,4,5]=>1
[1,2,3,6,7,5,4]=>6
[1,2,3,7,4,5,6]=>1
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>5
[1,2,3,7,5,6,4]=>5
[1,2,3,7,6,4,5]=>4
[1,2,3,7,6,5,4]=>9
[1,2,4,3,5,6,7]=>2
[1,2,4,3,5,7,6]=>7
[1,2,4,3,6,5,7]=>6
[1,2,4,3,6,7,5]=>6
[1,2,4,3,7,5,6]=>5
[1,2,4,3,7,6,5]=>10
[1,2,4,5,3,6,7]=>2
[1,2,4,5,3,7,6]=>7
[1,2,4,5,6,3,7]=>2
[1,2,4,5,6,7,3]=>2
[1,2,4,5,7,3,6]=>1
[1,2,4,5,7,6,3]=>6
[1,2,4,6,3,5,7]=>1
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>5
[1,2,4,6,5,7,3]=>5
[1,2,4,6,7,3,5]=>0
[1,2,4,6,7,5,3]=>5
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>5
[1,2,4,7,5,3,6]=>4
[1,2,4,7,5,6,3]=>4
[1,2,4,7,6,3,5]=>3
[1,2,4,7,6,5,3]=>8
[1,2,5,3,4,6,7]=>1
[1,2,5,3,4,7,6]=>6
[1,2,5,3,6,4,7]=>5
[1,2,5,3,6,7,4]=>5
[1,2,5,3,7,4,6]=>4
[1,2,5,3,7,6,4]=>9
[1,2,5,4,3,6,7]=>4
[1,2,5,4,3,7,6]=>9
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>3
[1,2,5,4,7,6,3]=>8
[1,2,5,6,3,4,7]=>0
[1,2,5,6,3,7,4]=>5
[1,2,5,6,4,3,7]=>4
[1,2,5,6,4,7,3]=>4
[1,2,5,6,7,3,4]=>-1
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>-1
[1,2,5,7,3,6,4]=>4
[1,2,5,7,4,3,6]=>3
[1,2,5,7,4,6,3]=>3
[1,2,5,7,6,3,4]=>2
[1,2,5,7,6,4,3]=>7
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>5
[1,2,6,3,5,4,7]=>4
[1,2,6,3,5,7,4]=>4
[1,2,6,3,7,4,5]=>3
[1,2,6,3,7,5,4]=>8
[1,2,6,4,3,5,7]=>3
[1,2,6,4,3,7,5]=>8
[1,2,6,4,5,3,7]=>3
[1,2,6,4,5,7,3]=>3
[1,2,6,4,7,3,5]=>2
[1,2,6,4,7,5,3]=>7
[1,2,6,5,3,4,7]=>2
[1,2,6,5,3,7,4]=>7
[1,2,6,5,4,3,7]=>6
[1,2,6,5,4,7,3]=>6
[1,2,6,5,7,3,4]=>1
[1,2,6,5,7,4,3]=>6
[1,2,6,7,3,4,5]=>-2
[1,2,6,7,3,5,4]=>3
[1,2,6,7,4,3,5]=>2
[1,2,6,7,4,5,3]=>2
[1,2,6,7,5,3,4]=>1
[1,2,6,7,5,4,3]=>6
[1,2,7,3,4,5,6]=>-1
[1,2,7,3,4,6,5]=>4
[1,2,7,3,5,4,6]=>3
[1,2,7,3,5,6,4]=>3
[1,2,7,3,6,4,5]=>2
[1,2,7,3,6,5,4]=>7
[1,2,7,4,3,5,6]=>2
[1,2,7,4,3,6,5]=>7
[1,2,7,4,5,3,6]=>2
[1,2,7,4,5,6,3]=>2
[1,2,7,4,6,3,5]=>1
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>1
[1,2,7,5,3,6,4]=>6
[1,2,7,5,4,3,6]=>5
[1,2,7,5,4,6,3]=>5
[1,2,7,5,6,3,4]=>0
[1,2,7,5,6,4,3]=>5
[1,2,7,6,3,4,5]=>0
[1,2,7,6,3,5,4]=>5
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>4
[1,2,7,6,5,3,4]=>3
[1,2,7,6,5,4,3]=>8
[1,3,2,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>6
[1,3,2,4,6,5,7]=>5
[1,3,2,4,6,7,5]=>5
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>9
[1,3,2,5,4,6,7]=>4
[1,3,2,5,4,7,6]=>9
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>3
[1,3,2,5,7,6,4]=>8
[1,3,2,6,4,5,7]=>3
[1,3,2,6,4,7,5]=>8
[1,3,2,6,5,4,7]=>7
[1,3,2,6,5,7,4]=>7
[1,3,2,6,7,4,5]=>2
[1,3,2,6,7,5,4]=>7
[1,3,2,7,4,5,6]=>2
[1,3,2,7,4,6,5]=>7
[1,3,2,7,5,4,6]=>6
[1,3,2,7,5,6,4]=>6
[1,3,2,7,6,4,5]=>5
[1,3,2,7,6,5,4]=>10
[1,3,4,2,5,6,7]=>1
[1,3,4,2,5,7,6]=>6
[1,3,4,2,6,5,7]=>5
[1,3,4,2,6,7,5]=>5
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>9
[1,3,4,5,2,6,7]=>1
[1,3,4,5,2,7,6]=>6
[1,3,4,5,6,2,7]=>1
[1,3,4,5,6,7,2]=>1
[1,3,4,5,7,2,6]=>0
[1,3,4,5,7,6,2]=>5
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>5
[1,3,4,6,5,2,7]=>4
[1,3,4,6,5,7,2]=>4
[1,3,4,6,7,2,5]=>-1
[1,3,4,6,7,5,2]=>4
[1,3,4,7,2,5,6]=>-1
[1,3,4,7,2,6,5]=>4
[1,3,4,7,5,2,6]=>3
[1,3,4,7,5,6,2]=>3
[1,3,4,7,6,2,5]=>2
[1,3,4,7,6,5,2]=>7
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>5
[1,3,5,2,6,4,7]=>4
[1,3,5,2,6,7,4]=>4
[1,3,5,2,7,4,6]=>3
[1,3,5,2,7,6,4]=>8
[1,3,5,4,2,6,7]=>3
[1,3,5,4,2,7,6]=>8
[1,3,5,4,6,2,7]=>3
[1,3,5,4,6,7,2]=>3
[1,3,5,4,7,2,6]=>2
[1,3,5,4,7,6,2]=>7
[1,3,5,6,2,4,7]=>-1
[1,3,5,6,2,7,4]=>4
[1,3,5,6,4,2,7]=>3
[1,3,5,6,4,7,2]=>3
[1,3,5,6,7,2,4]=>-2
[1,3,5,6,7,4,2]=>3
[1,3,5,7,2,4,6]=>-2
[1,3,5,7,2,6,4]=>3
[1,3,5,7,4,2,6]=>2
[1,3,5,7,4,6,2]=>2
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>6
[1,3,6,2,4,5,7]=>-1
[1,3,6,2,4,7,5]=>4
[1,3,6,2,5,4,7]=>3
[1,3,6,2,5,7,4]=>3
[1,3,6,2,7,4,5]=>2
[1,3,6,2,7,5,4]=>7
[1,3,6,4,2,5,7]=>2
[1,3,6,4,2,7,5]=>7
[1,3,6,4,5,2,7]=>2
[1,3,6,4,5,7,2]=>2
[1,3,6,4,7,2,5]=>1
[1,3,6,4,7,5,2]=>6
[1,3,6,5,2,4,7]=>1
[1,3,6,5,2,7,4]=>6
[1,3,6,5,4,2,7]=>5
[1,3,6,5,4,7,2]=>5
[1,3,6,5,7,2,4]=>0
[1,3,6,5,7,4,2]=>5
[1,3,6,7,2,4,5]=>-3
[1,3,6,7,2,5,4]=>2
[1,3,6,7,4,2,5]=>1
[1,3,6,7,4,5,2]=>1
[1,3,6,7,5,2,4]=>0
[1,3,6,7,5,4,2]=>5
[1,3,7,2,4,5,6]=>-2
[1,3,7,2,4,6,5]=>3
[1,3,7,2,5,4,6]=>2
[1,3,7,2,5,6,4]=>2
[1,3,7,2,6,4,5]=>1
[1,3,7,2,6,5,4]=>6
[1,3,7,4,2,5,6]=>1
[1,3,7,4,2,6,5]=>6
[1,3,7,4,5,2,6]=>1
[1,3,7,4,5,6,2]=>1
[1,3,7,4,6,2,5]=>0
[1,3,7,4,6,5,2]=>5
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>5
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>4
[1,3,7,5,6,2,4]=>-1
[1,3,7,5,6,4,2]=>4
[1,3,7,6,2,4,5]=>-1
[1,3,7,6,2,5,4]=>4
[1,3,7,6,4,2,5]=>3
[1,3,7,6,4,5,2]=>3
[1,3,7,6,5,2,4]=>2
[1,3,7,6,5,4,2]=>7
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>5
[1,4,2,3,6,5,7]=>4
[1,4,2,3,6,7,5]=>4
[1,4,2,3,7,5,6]=>3
[1,4,2,3,7,6,5]=>8
[1,4,2,5,3,6,7]=>3
[1,4,2,5,3,7,6]=>8
[1,4,2,5,6,3,7]=>3
[1,4,2,5,6,7,3]=>3
[1,4,2,5,7,3,6]=>2
[1,4,2,5,7,6,3]=>7
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>7
[1,4,2,6,5,3,7]=>6
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>1
[1,4,2,6,7,5,3]=>6
[1,4,2,7,3,5,6]=>1
[1,4,2,7,3,6,5]=>6
[1,4,2,7,5,3,6]=>5
[1,4,2,7,5,6,3]=>5
[1,4,2,7,6,3,5]=>4
[1,4,2,7,6,5,3]=>9
[1,4,3,2,5,6,7]=>2
[1,4,3,2,5,7,6]=>7
[1,4,3,2,6,5,7]=>6
[1,4,3,2,6,7,5]=>6
[1,4,3,2,7,5,6]=>5
[1,4,3,2,7,6,5]=>10
[1,4,3,5,2,6,7]=>2
[1,4,3,5,2,7,6]=>7
[1,4,3,5,6,2,7]=>2
[1,4,3,5,6,7,2]=>2
[1,4,3,5,7,2,6]=>1
[1,4,3,5,7,6,2]=>6
[1,4,3,6,2,5,7]=>1
[1,4,3,6,2,7,5]=>6
[1,4,3,6,5,2,7]=>5
[1,4,3,6,5,7,2]=>5
[1,4,3,6,7,2,5]=>0
[1,4,3,6,7,5,2]=>5
[1,4,3,7,2,5,6]=>0
[1,4,3,7,2,6,5]=>5
[1,4,3,7,5,2,6]=>4
[1,4,3,7,5,6,2]=>4
[1,4,3,7,6,2,5]=>3
[1,4,3,7,6,5,2]=>8
[1,4,5,2,3,6,7]=>-1
[1,4,5,2,3,7,6]=>4
[1,4,5,2,6,3,7]=>3
[1,4,5,2,6,7,3]=>3
[1,4,5,2,7,3,6]=>2
[1,4,5,2,7,6,3]=>7
[1,4,5,3,2,6,7]=>2
[1,4,5,3,2,7,6]=>7
[1,4,5,3,6,2,7]=>2
[1,4,5,3,6,7,2]=>2
[1,4,5,3,7,2,6]=>1
[1,4,5,3,7,6,2]=>6
[1,4,5,6,2,3,7]=>-2
[1,4,5,6,2,7,3]=>3
[1,4,5,6,3,2,7]=>2
[1,4,5,6,3,7,2]=>2
[1,4,5,6,7,2,3]=>-3
[1,4,5,6,7,3,2]=>2
[1,4,5,7,2,3,6]=>-3
[1,4,5,7,2,6,3]=>2
[1,4,5,7,3,2,6]=>1
[1,4,5,7,3,6,2]=>1
[1,4,5,7,6,2,3]=>0
[1,4,5,7,6,3,2]=>5
[1,4,6,2,3,5,7]=>-2
[1,4,6,2,3,7,5]=>3
[1,4,6,2,5,3,7]=>2
[1,4,6,2,5,7,3]=>2
[1,4,6,2,7,3,5]=>1
[1,4,6,2,7,5,3]=>6
[1,4,6,3,2,5,7]=>1
[1,4,6,3,2,7,5]=>6
[1,4,6,3,5,2,7]=>1
[1,4,6,3,5,7,2]=>1
[1,4,6,3,7,2,5]=>0
[1,4,6,3,7,5,2]=>5
[1,4,6,5,2,3,7]=>0
[1,4,6,5,2,7,3]=>5
[1,4,6,5,3,2,7]=>4
                    

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Description

The major index minus the number of inversions of a permutation.
This is, the difference between St000004The major index of a permutation. and St000018The number of inversions of a permutation..

References

[1] Wachs, M. L. An involution for signed Eulerian numbers MathSciNet:1158780

Code

def statistic(pi):
    return pi.major_index() - pi.number_of_inversions()

Created

Mar 30, 2019 at 08:56 by Christian Stump

Updated

Mar 30, 2019 at 08:56 by Christian Stump