- FindStat

edit this statistic or download as text // json

Identifier

St000923: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The minimal number with no two order isomorphic substrings of this length in a permutation.
For example, the length $3$ substrings of the permutation $12435$ are $124$, $243$ and $435$, whereas its length $2$ substrings are $12$, $24$, $43$ and $35$.
No two sequences among $124$, $243$ and $435$ are order isomorphic, but $12$ and $24$ are, so the statistic on $12435$ is $3$.
This is inspired by St000922The minimal number such that all substrings of this length are unique..

Code

def statistic(w):
    from sage.combinat.permutation import to_standard
    for k in range(1,len(w)+1):
        S = []
        for i in range(len(w)-k+1):
            s = to_standard(w[i:i+k])
            if s in S:
                break
            else:
                S.append(s)
        else:
            return k

Created

Aug 03, 2017 at 00:22 by Martin Rubey

Updated

Aug 03, 2017 at 08:49 by Martin Rubey