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Identifier

St001427: Signed permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

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

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Description

The number of descents of a signed permutation.
A descent of a signed permutation $\sigma$ of length $n$ is an index $0 \leq i < n$ such that $\sigma(i) > \sigma(i+1)$, setting $\sigma(0) = 0$.

Code

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

Created

Jun 21, 2019 at 13:52 by Christian Stump

Updated

Jun 30, 2023 at 14:25 by Martin Rubey