- FindStat

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Identifier

St000542: Permutations ⟶ ℤ (values match St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right.)

Values

=>
                            
                            
                            
                            

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

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Description

The number of left-to-right-minima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a left-to-right-minimum if there does not exist a j < i such that $\sigma_j < \sigma_i$.

Code

def statistic(pi):
    pi = list(pi)
    i = len(pi)+1; count = 0
    for j in range(len(pi)):
        if pi[j] < i:
            i = pi[j] 
            count += 1
    return count

Created

Jun 28, 2016 at 17:09 by Christian Stump

Updated

Mar 18, 2019 at 11:16 by Henning Ulfarsson