- FindStat

edit this statistic or download as text // json

Identifier

St001332: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1]=>0
[1,2]=>1
[2,1]=>0
[1,2,3]=>2
[1,3,2]=>2
[2,1,3]=>0
[2,3,1]=>2
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>3
[1,2,4,3]=>3
[1,3,2,4]=>3
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>0
[2,3,1,4]=>3
[2,3,4,1]=>3
[2,4,1,3]=>3
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>3
[3,4,2,1]=>2
[4,1,2,3]=>1
[4,1,3,2]=>0
[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]=>4
[1,2,3,5,4]=>4
[1,2,4,3,5]=>4
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>4
[1,3,2,4,5]=>4
[1,3,2,5,4]=>4
[1,3,4,2,5]=>4
[1,3,4,5,2]=>4
[1,3,5,2,4]=>4
[1,3,5,4,2]=>4
[1,4,2,3,5]=>4
[1,4,2,5,3]=>4
[1,4,3,2,5]=>2
[1,4,3,5,2]=>4
[1,4,5,2,3]=>4
[1,4,5,3,2]=>4
[1,5,2,3,4]=>4
[1,5,2,4,3]=>4
[1,5,3,2,4]=>2
[1,5,3,4,2]=>4
[1,5,4,2,3]=>2
[1,5,4,3,2]=>2
[2,1,3,4,5]=>2
[2,1,3,5,4]=>2
[2,1,4,3,5]=>0
[2,1,4,5,3]=>2
[2,1,5,3,4]=>0
[2,1,5,4,3]=>0
[2,3,1,4,5]=>4
[2,3,1,5,4]=>4
[2,3,4,1,5]=>4
[2,3,4,5,1]=>4
[2,3,5,1,4]=>4
[2,3,5,4,1]=>4
[2,4,1,3,5]=>4
[2,4,1,5,3]=>4
[2,4,3,1,5]=>2
[2,4,3,5,1]=>4
[2,4,5,1,3]=>4
[2,4,5,3,1]=>4
[2,5,1,3,4]=>4
[2,5,1,4,3]=>4
[2,5,3,1,4]=>2
[2,5,3,4,1]=>4
[2,5,4,1,3]=>2
[2,5,4,3,1]=>2
[3,1,2,4,5]=>2
[3,1,2,5,4]=>2
[3,1,4,2,5]=>0
[3,1,4,5,2]=>2
[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]=>2
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>4
[3,4,1,5,2]=>4
[3,4,2,1,5]=>2
[3,4,2,5,1]=>4
[3,4,5,1,2]=>4
[3,4,5,2,1]=>4
[3,5,1,2,4]=>4
[3,5,1,4,2]=>4
[3,5,2,1,4]=>2
[3,5,2,4,1]=>4
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>2
[4,1,2,5,3]=>2
[4,1,3,2,5]=>0
[4,1,3,5,2]=>2
[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]=>2
[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]=>4
[4,5,1,3,2]=>4
[4,5,2,1,3]=>2
[4,5,2,3,1]=>4
[4,5,3,1,2]=>2
[4,5,3,2,1]=>2
[5,1,2,3,4]=>2
[5,1,2,4,3]=>2
[5,1,3,2,4]=>0
[5,1,3,4,2]=>2
[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]=>2
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[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]=>0
[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]=>5
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>5
[1,2,3,5,6,4]=>5
[1,2,3,6,4,5]=>5
[1,2,3,6,5,4]=>5
[1,2,4,3,5,6]=>5
[1,2,4,3,6,5]=>5
[1,2,4,5,3,6]=>5
[1,2,4,5,6,3]=>5
[1,2,4,6,3,5]=>5
[1,2,4,6,5,3]=>5
[1,2,5,3,4,6]=>5
[1,2,5,3,6,4]=>5
[1,2,5,4,3,6]=>5
[1,2,5,4,6,3]=>5
[1,2,5,6,3,4]=>5
[1,2,5,6,4,3]=>5
[1,2,6,3,4,5]=>5
[1,2,6,3,5,4]=>5
[1,2,6,4,3,5]=>5
[1,2,6,4,5,3]=>5
[1,2,6,5,3,4]=>5
[1,2,6,5,4,3]=>4
[1,3,2,4,5,6]=>5
[1,3,2,4,6,5]=>5
[1,3,2,5,4,6]=>5
[1,3,2,5,6,4]=>5
[1,3,2,6,4,5]=>5
[1,3,2,6,5,4]=>4
[1,3,4,2,5,6]=>5
[1,3,4,2,6,5]=>5
[1,3,4,5,2,6]=>5
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>5
[1,3,4,6,5,2]=>5
[1,3,5,2,4,6]=>5
[1,3,5,2,6,4]=>5
[1,3,5,4,2,6]=>5
[1,3,5,4,6,2]=>5
[1,3,5,6,2,4]=>5
[1,3,5,6,4,2]=>5
[1,3,6,2,4,5]=>5
[1,3,6,2,5,4]=>5
[1,3,6,4,2,5]=>5
[1,3,6,4,5,2]=>5
[1,3,6,5,2,4]=>5
[1,3,6,5,4,2]=>4
[1,4,2,3,5,6]=>5
[1,4,2,3,6,5]=>5
[1,4,2,5,3,6]=>5
[1,4,2,5,6,3]=>5
[1,4,2,6,3,5]=>5
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>3
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>5
[1,4,3,5,6,2]=>5
[1,4,3,6,2,5]=>5
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>5
[1,4,5,2,6,3]=>5
[1,4,5,3,2,6]=>5
[1,4,5,3,6,2]=>5
[1,4,5,6,2,3]=>5
[1,4,5,6,3,2]=>5
[1,4,6,2,3,5]=>5
[1,4,6,2,5,3]=>5
[1,4,6,3,2,5]=>5
[1,4,6,3,5,2]=>5
[1,4,6,5,2,3]=>5
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>5
[1,5,2,3,6,4]=>5
[1,5,2,4,3,6]=>5
[1,5,2,4,6,3]=>5
[1,5,2,6,3,4]=>5
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>3
[1,5,3,2,6,4]=>2
[1,5,3,4,2,6]=>5
[1,5,3,4,6,2]=>5
[1,5,3,6,2,4]=>5
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>3
[1,5,4,2,6,3]=>2
[1,5,4,3,2,6]=>2
[1,5,4,3,6,2]=>2
[1,5,4,6,2,3]=>5
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>5
[1,5,6,2,4,3]=>5
[1,5,6,3,2,4]=>5
[1,5,6,3,4,2]=>5
[1,5,6,4,2,3]=>5
[1,5,6,4,3,2]=>4
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>5
[1,6,2,4,3,5]=>5
[1,6,2,4,5,3]=>5
[1,6,2,5,3,4]=>5
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>3
[1,6,3,2,5,4]=>2
[1,6,3,4,2,5]=>5
[1,6,3,4,5,2]=>5
[1,6,3,5,2,4]=>5
[1,6,3,5,4,2]=>4
[1,6,4,2,3,5]=>3
[1,6,4,2,5,3]=>2
[1,6,4,3,2,5]=>2
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>5
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>3
[1,6,5,2,4,3]=>2
[1,6,5,3,2,4]=>2
[1,6,5,3,4,2]=>2
[1,6,5,4,2,3]=>2
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>3
[2,1,3,4,6,5]=>3
[2,1,3,5,4,6]=>3
[2,1,3,5,6,4]=>3
[2,1,3,6,4,5]=>3
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>1
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>3
[2,1,4,5,6,3]=>3
[2,1,4,6,3,5]=>3
[2,1,4,6,5,3]=>2
[2,1,5,3,4,6]=>1
[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]=>3
[2,1,5,6,4,3]=>2
[2,1,6,3,4,5]=>1
[2,1,6,3,5,4]=>0
[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]=>5
[2,3,1,4,6,5]=>5
[2,3,1,5,4,6]=>5
[2,3,1,5,6,4]=>5
[2,3,1,6,4,5]=>5
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>5
[2,3,4,1,6,5]=>5
[2,3,4,5,1,6]=>5
[2,3,4,5,6,1]=>5
[2,3,4,6,1,5]=>5
[2,3,4,6,5,1]=>5
[2,3,5,1,4,6]=>5
[2,3,5,1,6,4]=>5
[2,3,5,4,1,6]=>5
[2,3,5,4,6,1]=>5
[2,3,5,6,1,4]=>5
[2,3,5,6,4,1]=>5
[2,3,6,1,4,5]=>5
[2,3,6,1,5,4]=>5
[2,3,6,4,1,5]=>5
[2,3,6,4,5,1]=>5
[2,3,6,5,1,4]=>5
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>5
[2,4,1,3,6,5]=>5
[2,4,1,5,3,6]=>5
[2,4,1,5,6,3]=>5
[2,4,1,6,3,5]=>5
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>3
[2,4,3,1,6,5]=>2
[2,4,3,5,1,6]=>5
[2,4,3,5,6,1]=>5
[2,4,3,6,1,5]=>5
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>5
[2,4,5,1,6,3]=>5
[2,4,5,3,1,6]=>5
[2,4,5,3,6,1]=>5
[2,4,5,6,1,3]=>5
[2,4,5,6,3,1]=>5
[2,4,6,1,3,5]=>5
[2,4,6,1,5,3]=>5
[2,4,6,3,1,5]=>5
[2,4,6,3,5,1]=>5
[2,4,6,5,1,3]=>5
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>5
[2,5,1,3,6,4]=>5
[2,5,1,4,3,6]=>5
[2,5,1,4,6,3]=>5
[2,5,1,6,3,4]=>5
[2,5,1,6,4,3]=>4
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>2
[2,5,3,4,1,6]=>5
[2,5,3,4,6,1]=>5
[2,5,3,6,1,4]=>5
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>3
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>2
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>5
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>5
[2,5,6,1,4,3]=>5
[2,5,6,3,1,4]=>5
[2,5,6,3,4,1]=>5
[2,5,6,4,1,3]=>5
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>5
[2,6,1,3,5,4]=>5
[2,6,1,4,3,5]=>5
[2,6,1,4,5,3]=>5
[2,6,1,5,3,4]=>5
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>3
[2,6,3,1,5,4]=>2
[2,6,3,4,1,5]=>5
[2,6,3,4,5,1]=>5
[2,6,3,5,1,4]=>5
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>3
[2,6,4,1,5,3]=>2
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>2
[2,6,4,5,1,3]=>5
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>3
[2,6,5,1,4,3]=>2
[2,6,5,3,1,4]=>2
[2,6,5,3,4,1]=>2
[2,6,5,4,1,3]=>2
[2,6,5,4,3,1]=>2
[3,1,2,4,5,6]=>3
[3,1,2,4,6,5]=>3
[3,1,2,5,4,6]=>3
[3,1,2,5,6,4]=>3
[3,1,2,6,4,5]=>3
[3,1,2,6,5,4]=>2
[3,1,4,2,5,6]=>1
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>3
[3,1,4,5,6,2]=>3
[3,1,4,6,2,5]=>3
[3,1,4,6,5,2]=>2
[3,1,5,2,4,6]=>1
[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]=>3
[3,1,5,6,4,2]=>2
[3,1,6,2,4,5]=>1
[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]=>1
[3,2,1,4,6,5]=>0
[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]=>1
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>3
[3,2,4,5,6,1]=>3
[3,2,4,6,1,5]=>3
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>1
[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]=>3
[3,2,5,6,4,1]=>2
[3,2,6,1,4,5]=>1
[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]=>5
[3,4,1,2,6,5]=>5
[3,4,1,5,2,6]=>5
[3,4,1,5,6,2]=>5
[3,4,1,6,2,5]=>5
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>3
[3,4,2,1,6,5]=>2
[3,4,2,5,1,6]=>5
[3,4,2,5,6,1]=>5
[3,4,2,6,1,5]=>5
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>5
[3,4,5,1,6,2]=>5
[3,4,5,2,1,6]=>5
[3,4,5,2,6,1]=>5
[3,4,5,6,1,2]=>5
[3,4,5,6,2,1]=>5
[3,4,6,1,2,5]=>5
[3,4,6,1,5,2]=>5
[3,4,6,2,1,5]=>5
[3,4,6,2,5,1]=>5
[3,4,6,5,1,2]=>5
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>5
[3,5,1,2,6,4]=>5
[3,5,1,4,2,6]=>5
[3,5,1,4,6,2]=>5
[3,5,1,6,2,4]=>5
[3,5,1,6,4,2]=>4
[3,5,2,1,4,6]=>3
[3,5,2,1,6,4]=>2
[3,5,2,4,1,6]=>5
[3,5,2,4,6,1]=>5
[3,5,2,6,1,4]=>5
[3,5,2,6,4,1]=>4
[3,5,4,1,2,6]=>3
[3,5,4,1,6,2]=>2
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>5
[3,5,4,6,2,1]=>4
[3,5,6,1,2,4]=>5
[3,5,6,1,4,2]=>5
[3,5,6,2,1,4]=>5
[3,5,6,2,4,1]=>5
[3,5,6,4,1,2]=>5
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>5
[3,6,1,2,5,4]=>5
[3,6,1,4,2,5]=>5
[3,6,1,4,5,2]=>5
[3,6,1,5,2,4]=>5
[3,6,1,5,4,2]=>4
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>2
[3,6,2,4,1,5]=>5
[3,6,2,4,5,1]=>5
[3,6,2,5,1,4]=>5
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>2
[3,6,4,2,1,5]=>2
[3,6,4,2,5,1]=>2
[3,6,4,5,1,2]=>5
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>3
[3,6,5,1,4,2]=>2
[3,6,5,2,1,4]=>2
[3,6,5,2,4,1]=>2
[3,6,5,4,1,2]=>2
[3,6,5,4,2,1]=>2
[4,1,2,3,5,6]=>3
[4,1,2,3,6,5]=>3
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>3
[4,1,2,6,3,5]=>3
[4,1,2,6,5,3]=>2
[4,1,3,2,5,6]=>1
[4,1,3,2,6,5]=>0
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>3
[4,1,3,6,2,5]=>3
[4,1,3,6,5,2]=>2
[4,1,5,2,3,6]=>1
[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]=>3
[4,1,5,6,3,2]=>2
[4,1,6,2,3,5]=>1
[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]=>1
[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]=>1
[4,2,3,1,6,5]=>0
[4,2,3,5,1,6]=>3
[4,2,3,5,6,1]=>3
[4,2,3,6,1,5]=>3
[4,2,3,6,5,1]=>2
[4,2,5,1,3,6]=>1
[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]=>3
[4,2,5,6,3,1]=>2
[4,2,6,1,3,5]=>1
[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]=>1
[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]=>1
[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]=>3
[4,3,5,6,2,1]=>2
[4,3,6,1,2,5]=>1
[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]=>5
[4,5,1,2,6,3]=>5
[4,5,1,3,2,6]=>5
[4,5,1,3,6,2]=>5
[4,5,1,6,2,3]=>5
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>3
[4,5,2,1,6,3]=>2
[4,5,2,3,1,6]=>5
[4,5,2,3,6,1]=>5
[4,5,2,6,1,3]=>5
[4,5,2,6,3,1]=>4
[4,5,3,1,2,6]=>3
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>2
[4,5,3,2,6,1]=>2
[4,5,3,6,1,2]=>5
[4,5,3,6,2,1]=>4
[4,5,6,1,2,3]=>5
[4,5,6,1,3,2]=>5
[4,5,6,2,1,3]=>5
[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]=>5
[4,6,1,2,5,3]=>5
[4,6,1,3,2,5]=>5
[4,6,1,3,5,2]=>5
[4,6,1,5,2,3]=>5
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>3
[4,6,2,1,5,3]=>2
[4,6,2,3,1,5]=>5
[4,6,2,3,5,1]=>5
[4,6,2,5,1,3]=>5
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>3
[4,6,3,1,5,2]=>2
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>5
[4,6,3,5,2,1]=>4
[4,6,5,1,2,3]=>3
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>2
[4,6,5,3,1,2]=>2
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>3
[5,1,2,3,6,4]=>3
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>3
[5,1,2,6,3,4]=>3
[5,1,2,6,4,3]=>2
[5,1,3,2,4,6]=>1
[5,1,3,2,6,4]=>0
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>3
[5,1,3,6,2,4]=>3
[5,1,3,6,4,2]=>2
[5,1,4,2,3,6]=>1
[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]=>3
[5,1,4,6,3,2]=>2
[5,1,6,2,3,4]=>1
[5,1,6,2,4,3]=>0
[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]=>1
[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]=>1
[5,2,3,1,6,4]=>0
[5,2,3,4,1,6]=>3
[5,2,3,4,6,1]=>3
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>2
[5,2,4,1,3,6]=>1
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>2
[5,2,6,1,3,4]=>1
[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]=>1
[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]=>1
[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]=>3
[5,3,4,6,2,1]=>2
[5,3,6,1,2,4]=>1
[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]=>1
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>0
[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]=>1
[5,4,6,1,3,2]=>0
[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]=>5
[5,6,1,2,4,3]=>5
[5,6,1,3,2,4]=>5
[5,6,1,3,4,2]=>5
[5,6,1,4,2,3]=>5
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>3
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>5
[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]=>3
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>2
[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>5
[5,6,3,4,2,1]=>4
[5,6,4,1,2,3]=>3
[5,6,4,1,3,2]=>2
[5,6,4,2,1,3]=>2
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>2
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>3
[6,1,2,3,5,4]=>3
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>3
[6,1,2,5,3,4]=>3
[6,1,2,5,4,3]=>2
[6,1,3,2,4,5]=>1
[6,1,3,2,5,4]=>0
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>3
[6,1,3,5,2,4]=>3
[6,1,3,5,4,2]=>2
[6,1,4,2,3,5]=>1
[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]=>3
[6,1,4,5,3,2]=>2
[6,1,5,2,3,4]=>1
[6,1,5,2,4,3]=>0
[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]=>1
[6,2,1,3,5,4]=>0
[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]=>1
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>3
[6,2,3,4,5,1]=>3
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>1
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>2
[6,2,5,1,3,4]=>1
[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]=>1
[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]=>1
[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]=>3
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>1
[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]=>0
[6,3,5,4,2,1]=>0
[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[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]=>1
[6,4,5,1,3,2]=>0
[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]=>1
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[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]=>0
[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]=>0
[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]=>6
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>6
[1,2,3,4,6,7,5]=>6
[1,2,3,4,7,5,6]=>6
[1,2,3,4,7,6,5]=>6
[1,2,3,5,4,6,7]=>6
[1,2,3,5,4,7,6]=>6
[1,2,3,5,6,4,7]=>6
[1,2,3,5,6,7,4]=>6
[1,2,3,5,7,4,6]=>6
[1,2,3,5,7,6,4]=>6
[1,2,3,6,4,5,7]=>6
[1,2,3,6,4,7,5]=>6
[1,2,3,6,5,4,7]=>6
[1,2,3,6,5,7,4]=>6
[1,2,3,6,7,4,5]=>6
[1,2,3,6,7,5,4]=>6
[1,2,3,7,4,5,6]=>6
[1,2,3,7,4,6,5]=>6
[1,2,3,7,5,4,6]=>6
[1,2,3,7,5,6,4]=>6
[1,2,3,7,6,4,5]=>6
[1,2,3,7,6,5,4]=>6
[1,2,4,3,5,6,7]=>6
[1,2,4,3,5,7,6]=>6
[1,2,4,3,6,5,7]=>6
[1,2,4,3,6,7,5]=>6
[1,2,4,3,7,5,6]=>6
[1,2,4,3,7,6,5]=>6
[1,2,4,5,3,6,7]=>6
[1,2,4,5,3,7,6]=>6
[1,2,4,5,6,3,7]=>6
[1,2,4,5,6,7,3]=>6
[1,2,4,5,7,3,6]=>6
[1,2,4,5,7,6,3]=>6
[1,2,4,6,3,5,7]=>6
[1,2,4,6,3,7,5]=>6
[1,2,4,6,5,3,7]=>6
[1,2,4,6,5,7,3]=>6
[1,2,4,6,7,3,5]=>6
[1,2,4,6,7,5,3]=>6
[1,2,4,7,3,5,6]=>6
[1,2,4,7,3,6,5]=>6
[1,2,4,7,5,3,6]=>6
[1,2,4,7,5,6,3]=>6
[1,2,4,7,6,3,5]=>6
[1,2,4,7,6,5,3]=>6
[1,2,5,3,4,6,7]=>6
[1,2,5,3,4,7,6]=>6
[1,2,5,3,6,4,7]=>6
[1,2,5,3,6,7,4]=>6
[1,2,5,3,7,4,6]=>6
[1,2,5,3,7,6,4]=>6
[1,2,5,4,3,6,7]=>6
[1,2,5,4,3,7,6]=>6
[1,2,5,4,6,3,7]=>6
[1,2,5,4,6,7,3]=>6
[1,2,5,4,7,3,6]=>6
[1,2,5,4,7,6,3]=>6
[1,2,5,6,3,4,7]=>6
[1,2,5,6,3,7,4]=>6
[1,2,5,6,4,3,7]=>6
[1,2,5,6,4,7,3]=>6
[1,2,5,6,7,3,4]=>6
[1,2,5,6,7,4,3]=>6
[1,2,5,7,3,4,6]=>6
[1,2,5,7,3,6,4]=>6
[1,2,5,7,4,3,6]=>6
[1,2,5,7,4,6,3]=>6
[1,2,5,7,6,3,4]=>6
[1,2,5,7,6,4,3]=>6
[1,2,6,3,4,5,7]=>6
[1,2,6,3,4,7,5]=>6
[1,2,6,3,5,4,7]=>6
[1,2,6,3,5,7,4]=>6
[1,2,6,3,7,4,5]=>6
[1,2,6,3,7,5,4]=>6
[1,2,6,4,3,5,7]=>6
[1,2,6,4,3,7,5]=>6
[1,2,6,4,5,3,7]=>6
[1,2,6,4,5,7,3]=>6
[1,2,6,4,7,3,5]=>6
[1,2,6,4,7,5,3]=>6
[1,2,6,5,3,4,7]=>6
[1,2,6,5,3,7,4]=>6
[1,2,6,5,4,3,7]=>4
[1,2,6,5,4,7,3]=>6
[1,2,6,5,7,3,4]=>6
[1,2,6,5,7,4,3]=>6
[1,2,6,7,3,4,5]=>6
[1,2,6,7,3,5,4]=>6
[1,2,6,7,4,3,5]=>6
[1,2,6,7,4,5,3]=>6
[1,2,6,7,5,3,4]=>6
[1,2,6,7,5,4,3]=>6
[1,2,7,3,4,5,6]=>6
[1,2,7,3,4,6,5]=>6
[1,2,7,3,5,4,6]=>6
[1,2,7,3,5,6,4]=>6
[1,2,7,3,6,4,5]=>6
[1,2,7,3,6,5,4]=>6
[1,2,7,4,3,5,6]=>6
[1,2,7,4,3,6,5]=>6
[1,2,7,4,5,3,6]=>6
[1,2,7,4,5,6,3]=>6
[1,2,7,4,6,3,5]=>6
[1,2,7,4,6,5,3]=>6
[1,2,7,5,3,4,6]=>6
[1,2,7,5,3,6,4]=>6
[1,2,7,5,4,3,6]=>4
[1,2,7,5,4,6,3]=>6
[1,2,7,5,6,3,4]=>6
[1,2,7,5,6,4,3]=>6
[1,2,7,6,3,4,5]=>6
[1,2,7,6,3,5,4]=>6
[1,2,7,6,4,3,5]=>4
[1,2,7,6,4,5,3]=>6
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>4
[1,3,2,4,5,6,7]=>6
[1,3,2,4,5,7,6]=>6
[1,3,2,4,6,5,7]=>6
[1,3,2,4,6,7,5]=>6
[1,3,2,4,7,5,6]=>6
[1,3,2,4,7,6,5]=>6
[1,3,2,5,4,6,7]=>6
[1,3,2,5,4,7,6]=>6
[1,3,2,5,6,4,7]=>6
[1,3,2,5,6,7,4]=>6
[1,3,2,5,7,4,6]=>6
[1,3,2,5,7,6,4]=>6
[1,3,2,6,4,5,7]=>6
[1,3,2,6,4,7,5]=>6
[1,3,2,6,5,4,7]=>4
[1,3,2,6,5,7,4]=>6
[1,3,2,6,7,4,5]=>6
[1,3,2,6,7,5,4]=>6
[1,3,2,7,4,5,6]=>6
[1,3,2,7,4,6,5]=>6
[1,3,2,7,5,4,6]=>4
[1,3,2,7,5,6,4]=>6
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>4
[1,3,4,2,5,6,7]=>6
[1,3,4,2,5,7,6]=>6
[1,3,4,2,6,5,7]=>6
[1,3,4,2,6,7,5]=>6
[1,3,4,2,7,5,6]=>6
[1,3,4,2,7,6,5]=>6
[1,3,4,5,2,6,7]=>6
[1,3,4,5,2,7,6]=>6
[1,3,4,5,6,2,7]=>6
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>6
[1,3,4,5,7,6,2]=>6
[1,3,4,6,2,5,7]=>6
[1,3,4,6,2,7,5]=>6
[1,3,4,6,5,2,7]=>6
[1,3,4,6,5,7,2]=>6
[1,3,4,6,7,2,5]=>6
[1,3,4,6,7,5,2]=>6
[1,3,4,7,2,5,6]=>6
[1,3,4,7,2,6,5]=>6
[1,3,4,7,5,2,6]=>6
[1,3,4,7,5,6,2]=>6
[1,3,4,7,6,2,5]=>6
[1,3,4,7,6,5,2]=>6
[1,3,5,2,4,6,7]=>6
[1,3,5,2,4,7,6]=>6
[1,3,5,2,6,4,7]=>6
[1,3,5,2,6,7,4]=>6
[1,3,5,2,7,4,6]=>6
[1,3,5,2,7,6,4]=>6
[1,3,5,4,2,6,7]=>6
[1,3,5,4,2,7,6]=>6
[1,3,5,4,6,2,7]=>6
[1,3,5,4,6,7,2]=>6
[1,3,5,4,7,2,6]=>6
[1,3,5,4,7,6,2]=>6
[1,3,5,6,2,4,7]=>6
[1,3,5,6,2,7,4]=>6
[1,3,5,6,4,2,7]=>6
[1,3,5,6,4,7,2]=>6
[1,3,5,6,7,2,4]=>6
[1,3,5,6,7,4,2]=>6
[1,3,5,7,2,4,6]=>6
[1,3,5,7,2,6,4]=>6
[1,3,5,7,4,2,6]=>6
[1,3,5,7,4,6,2]=>6
[1,3,5,7,6,2,4]=>6
[1,3,5,7,6,4,2]=>6
[1,3,6,2,4,5,7]=>6
[1,3,6,2,4,7,5]=>6
[1,3,6,2,5,4,7]=>6
[1,3,6,2,5,7,4]=>6
[1,3,6,2,7,4,5]=>6
[1,3,6,2,7,5,4]=>6
[1,3,6,4,2,5,7]=>6
[1,3,6,4,2,7,5]=>6
[1,3,6,4,5,2,7]=>6
[1,3,6,4,5,7,2]=>6
[1,3,6,4,7,2,5]=>6
[1,3,6,4,7,5,2]=>6
[1,3,6,5,2,4,7]=>6
[1,3,6,5,2,7,4]=>6
[1,3,6,5,4,2,7]=>4
[1,3,6,5,4,7,2]=>6
[1,3,6,5,7,2,4]=>6
[1,3,6,5,7,4,2]=>6
[1,3,6,7,2,4,5]=>6
[1,3,6,7,2,5,4]=>6
[1,3,6,7,4,2,5]=>6
[1,3,6,7,4,5,2]=>6
[1,3,6,7,5,2,4]=>6
[1,3,6,7,5,4,2]=>6
[1,3,7,2,4,5,6]=>6
[1,3,7,2,4,6,5]=>6
[1,3,7,2,5,4,6]=>6
[1,3,7,2,5,6,4]=>6
[1,3,7,2,6,4,5]=>6
[1,3,7,2,6,5,4]=>6
[1,3,7,4,2,5,6]=>6
[1,3,7,4,2,6,5]=>6
[1,3,7,4,5,2,6]=>6
[1,3,7,4,5,6,2]=>6
[1,3,7,4,6,2,5]=>6
[1,3,7,4,6,5,2]=>6
[1,3,7,5,2,4,6]=>6
[1,3,7,5,2,6,4]=>6
[1,3,7,5,4,2,6]=>4
[1,3,7,5,4,6,2]=>6
[1,3,7,5,6,2,4]=>6
[1,3,7,5,6,4,2]=>6
[1,3,7,6,2,4,5]=>6
[1,3,7,6,2,5,4]=>6
[1,3,7,6,4,2,5]=>4
[1,3,7,6,4,5,2]=>6
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>4
[1,4,2,3,5,6,7]=>6
[1,4,2,3,5,7,6]=>6
[1,4,2,3,6,5,7]=>6
[1,4,2,3,6,7,5]=>6
[1,4,2,3,7,5,6]=>6
[1,4,2,3,7,6,5]=>6
[1,4,2,5,3,6,7]=>6
[1,4,2,5,3,7,6]=>6
[1,4,2,5,6,3,7]=>6
[1,4,2,5,6,7,3]=>6
[1,4,2,5,7,3,6]=>6
[1,4,2,5,7,6,3]=>6
[1,4,2,6,3,5,7]=>6
[1,4,2,6,3,7,5]=>6
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>6
[1,4,2,6,7,3,5]=>6
[1,4,2,6,7,5,3]=>6
[1,4,2,7,3,5,6]=>6
[1,4,2,7,3,6,5]=>6
[1,4,2,7,5,3,6]=>4
[1,4,2,7,5,6,3]=>6
[1,4,2,7,6,3,5]=>4
[1,4,2,7,6,5,3]=>4
[1,4,3,2,5,6,7]=>4
[1,4,3,2,5,7,6]=>4
[1,4,3,2,6,5,7]=>2
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>2
[1,4,3,2,7,6,5]=>2
[1,4,3,5,2,6,7]=>6
[1,4,3,5,2,7,6]=>6
[1,4,3,5,6,2,7]=>6
[1,4,3,5,6,7,2]=>6
[1,4,3,5,7,2,6]=>6
[1,4,3,5,7,6,2]=>6
[1,4,3,6,2,5,7]=>6
[1,4,3,6,2,7,5]=>6
[1,4,3,6,5,2,7]=>4
[1,4,3,6,5,7,2]=>6
[1,4,3,6,7,2,5]=>6
[1,4,3,6,7,5,2]=>6
[1,4,3,7,2,5,6]=>6
[1,4,3,7,2,6,5]=>6
[1,4,3,7,5,2,6]=>4
[1,4,3,7,5,6,2]=>6
[1,4,3,7,6,2,5]=>4
[1,4,3,7,6,5,2]=>4
[1,4,5,2,3,6,7]=>6
[1,4,5,2,3,7,6]=>6
[1,4,5,2,6,3,7]=>6
[1,4,5,2,6,7,3]=>6
[1,4,5,2,7,3,6]=>6
[1,4,5,2,7,6,3]=>6
[1,4,5,3,2,6,7]=>6
[1,4,5,3,2,7,6]=>6
[1,4,5,3,6,2,7]=>6
[1,4,5,3,6,7,2]=>6
[1,4,5,3,7,2,6]=>6
[1,4,5,3,7,6,2]=>6
[1,4,5,6,2,3,7]=>6
[1,4,5,6,2,7,3]=>6
[1,4,5,6,3,2,7]=>6
[1,4,5,6,3,7,2]=>6
[1,4,5,6,7,2,3]=>6
[1,4,5,6,7,3,2]=>6
[1,4,5,7,2,3,6]=>6
[1,4,5,7,2,6,3]=>6
[1,4,5,7,3,2,6]=>6
[1,4,5,7,3,6,2]=>6
[1,4,5,7,6,2,3]=>6
[1,4,5,7,6,3,2]=>6
[1,4,6,2,3,5,7]=>6
[1,4,6,2,3,7,5]=>6
[1,4,6,2,5,3,7]=>6
[1,4,6,2,5,7,3]=>6
[1,4,6,2,7,3,5]=>6
[1,4,6,2,7,5,3]=>6
[1,4,6,3,2,5,7]=>6
[1,4,6,3,2,7,5]=>6
[1,4,6,3,5,2,7]=>6
[1,4,6,3,5,7,2]=>6
[1,4,6,3,7,2,5]=>6
[1,4,6,3,7,5,2]=>6
[1,4,6,5,2,3,7]=>6
[1,4,6,5,2,7,3]=>6
[1,4,6,5,3,2,7]=>4
                    

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Description

The number of steps on the non-negative side of the walk associated with the permutation.
Consider the walk taking an up step for each ascent, and a down step for each descent of the permutation. Then this statistic is the number of steps that begin and end at non-negative height.

References

[1] Bernardi, O., Duplantier, B., Nadeau, P. A Bijection between well-labelled positive paths and matchings arXiv:0903.5379

Code

def signature(pi):
    return [1 if pi[i] < pi[i+1] else -1 for i in range(len(pi)-1)]

def walk(pi):
    x = signature(pi)
    return [sum(x[:k]) for k in range(len(pi))]

def statistic(pi):
    w = walk(pi)
    return sum(1 for i in range(len(pi)-1) if w[i] >= 0 and w[i+1] >= 0)

Created

Dec 21, 2018 at 18:50 by Martin Rubey

Updated

Dec 17, 2021 at 19:21 by Nadia Lafreniere