- FindStat

edit this statistic or download as text // json

Identifier

St000402: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>2
[1,3,2,4]=>1
[1,3,4,2]=>4
[1,4,2,3]=>4
[1,4,3,2]=>2
[2,1,3,4]=>2
[2,1,4,3]=>1
[2,3,1,4]=>4
[2,3,4,1]=>2
[2,4,1,3]=>1
[2,4,3,1]=>4
[3,1,2,4]=>4
[3,1,4,2]=>1
[3,2,1,4]=>2
[3,2,4,1]=>4
[3,4,1,2]=>1
[3,4,2,1]=>2
[4,1,2,3]=>2
[4,1,3,2]=>4
[4,2,1,3]=>4
[4,2,3,1]=>1
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>2
[1,2,4,3,5]=>2
[1,2,4,5,3]=>4
[1,2,5,3,4]=>4
[1,2,5,4,3]=>2
[1,3,2,4,5]=>2
[1,3,2,5,4]=>2
[1,3,4,2,5]=>2
[1,3,4,5,2]=>4
[1,3,5,2,4]=>4
[1,3,5,4,2]=>4
[1,4,2,3,5]=>2
[1,4,2,5,3]=>4
[1,4,3,2,5]=>1
[1,4,3,5,2]=>4
[1,4,5,2,3]=>2
[1,4,5,3,2]=>4
[1,5,2,3,4]=>4
[1,5,2,4,3]=>4
[1,5,3,2,4]=>4
[1,5,3,4,2]=>2
[1,5,4,2,3]=>4
[1,5,4,3,2]=>2
[2,1,3,4,5]=>2
[2,1,3,5,4]=>1
[2,1,4,3,5]=>2
[2,1,4,5,3]=>4
[2,1,5,3,4]=>4
[2,1,5,4,3]=>2
[2,3,1,4,5]=>4
[2,3,1,5,4]=>4
[2,3,4,1,5]=>4
[2,3,4,5,1]=>2
[2,3,5,1,4]=>4
[2,3,5,4,1]=>4
[2,4,1,3,5]=>4
[2,4,1,5,3]=>2
[2,4,3,1,5]=>4
[2,4,3,5,1]=>2
[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]=>1
[2,5,3,4,1]=>4
[2,5,4,1,3]=>4
[2,5,4,3,1]=>4
[3,1,2,4,5]=>4
[3,1,2,5,4]=>4
[3,1,4,2,5]=>4
[3,1,4,5,2]=>4
[3,1,5,2,4]=>2
[3,1,5,4,2]=>4
[3,2,1,4,5]=>2
[3,2,1,5,4]=>2
[3,2,4,1,5]=>4
[3,2,4,5,1]=>4
[3,2,5,1,4]=>4
[3,2,5,4,1]=>2
[3,4,1,2,5]=>2
[3,4,1,5,2]=>4
[3,4,2,1,5]=>4
[3,4,2,5,1]=>4
[3,4,5,1,2]=>2
[3,4,5,2,1]=>2
[3,5,1,2,4]=>4
[3,5,1,4,2]=>2
[3,5,2,1,4]=>4
[3,5,2,4,1]=>4
[3,5,4,1,2]=>4
[3,5,4,2,1]=>4
[4,1,2,3,5]=>4
[4,1,2,5,3]=>4
[4,1,3,2,5]=>4
[4,1,3,5,2]=>1
[4,1,5,2,3]=>4
[4,1,5,3,2]=>4
[4,2,1,3,5]=>4
[4,2,1,5,3]=>4
[4,2,3,1,5]=>2
[4,2,3,5,1]=>4
[4,2,5,1,3]=>2
[4,2,5,3,1]=>4
[4,3,1,2,5]=>4
[4,3,1,5,2]=>4
[4,3,2,1,5]=>2
[4,3,2,5,1]=>4
[4,3,5,1,2]=>4
[4,3,5,2,1]=>4
[4,5,1,2,3]=>2
[4,5,1,3,2]=>4
[4,5,2,1,3]=>4
[4,5,2,3,1]=>2
[4,5,3,1,2]=>1
[4,5,3,2,1]=>2
[5,1,2,3,4]=>2
[5,1,2,4,3]=>4
[5,1,3,2,4]=>2
[5,1,3,4,2]=>4
[5,1,4,2,3]=>4
[5,1,4,3,2]=>4
[5,2,1,3,4]=>4
[5,2,1,4,3]=>2
[5,2,3,1,4]=>4
[5,2,3,4,1]=>1
[5,2,4,1,3]=>4
[5,2,4,3,1]=>2
[5,3,1,2,4]=>4
[5,3,1,4,2]=>4
[5,3,2,1,4]=>4
[5,3,2,4,1]=>2
[5,3,4,1,2]=>2
[5,3,4,2,1]=>2
[5,4,1,2,3]=>2
[5,4,1,3,2]=>4
[5,4,2,1,3]=>4
[5,4,2,3,1]=>2
[5,4,3,1,2]=>2
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>2
[1,2,3,5,4,6]=>2
[1,2,3,5,6,4]=>4
[1,2,3,6,4,5]=>4
[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]=>4
[1,2,4,5,6,3]=>4
[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]=>2
[1,2,5,4,6,3]=>4
[1,2,5,6,3,4]=>2
[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]=>4
[1,2,6,4,5,3]=>2
[1,2,6,5,3,4]=>4
[1,2,6,5,4,3]=>2
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>2
[1,3,2,5,4,6]=>1
[1,3,2,5,6,4]=>4
[1,3,2,6,4,5]=>4
[1,3,2,6,5,4]=>2
[1,3,4,2,5,6]=>4
[1,3,4,2,6,5]=>4
[1,3,4,5,2,6]=>2
[1,3,4,5,6,2]=>4
[1,3,4,6,2,5]=>4
[1,3,4,6,5,2]=>4
[1,3,5,2,4,6]=>2
[1,3,5,2,6,4]=>4
[1,3,5,4,2,6]=>4
[1,3,5,4,6,2]=>4
[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]=>4
[1,3,6,4,2,5]=>4
[1,3,6,4,5,2]=>4
[1,3,6,5,2,4]=>4
[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]=>2
[1,4,2,5,6,3]=>4
[1,4,2,6,3,5]=>4
[1,4,2,6,5,3]=>4
[1,4,3,2,5,6]=>2
[1,4,3,2,6,5]=>2
[1,4,3,5,2,6]=>4
[1,4,3,5,6,2]=>4
[1,4,3,6,2,5]=>4
[1,4,3,6,5,2]=>4
[1,4,5,2,3,6]=>1
[1,4,5,2,6,3]=>4
[1,4,5,3,2,6]=>2
[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]=>2
[1,4,6,3,2,5]=>4
[1,4,6,3,5,2]=>4
[1,4,6,5,2,3]=>4
[1,4,6,5,3,2]=>4
[1,5,2,3,4,6]=>2
[1,5,2,3,6,4]=>4
[1,5,2,4,3,6]=>4
[1,5,2,4,6,3]=>4
[1,5,2,6,3,4]=>4
[1,5,2,6,4,3]=>4
[1,5,3,2,4,6]=>4
[1,5,3,2,6,4]=>4
[1,5,3,4,2,6]=>1
[1,5,3,4,6,2]=>4
[1,5,3,6,2,4]=>2
[1,5,3,6,4,2]=>4
[1,5,4,2,3,6]=>2
[1,5,4,2,6,3]=>4
[1,5,4,3,2,6]=>1
[1,5,4,3,6,2]=>4
[1,5,4,6,2,3]=>4
[1,5,4,6,3,2]=>4
[1,5,6,2,3,4]=>4
[1,5,6,2,4,3]=>4
[1,5,6,3,2,4]=>4
[1,5,6,3,4,2]=>4
[1,5,6,4,2,3]=>2
[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]=>4
[1,6,2,5,3,4]=>4
[1,6,2,5,4,3]=>4
[1,6,3,2,4,5]=>4
[1,6,3,2,5,4]=>4
[1,6,3,4,2,5]=>4
[1,6,3,4,5,2]=>2
[1,6,3,5,2,4]=>4
[1,6,3,5,4,2]=>2
[1,6,4,2,3,5]=>4
[1,6,4,2,5,3]=>4
[1,6,4,3,2,5]=>4
[1,6,4,3,5,2]=>2
[1,6,4,5,2,3]=>4
[1,6,4,5,3,2]=>4
[1,6,5,2,3,4]=>4
[1,6,5,2,4,3]=>4
[1,6,5,3,2,4]=>4
[1,6,5,3,4,2]=>4
[1,6,5,4,2,3]=>4
[1,6,5,4,3,2]=>2
[2,1,3,4,5,6]=>2
[2,1,3,4,6,5]=>1
[2,1,3,5,4,6]=>2
[2,1,3,5,6,4]=>4
[2,1,3,6,4,5]=>4
[2,1,3,6,5,4]=>2
[2,1,4,3,5,6]=>2
[2,1,4,3,6,5]=>1
[2,1,4,5,3,6]=>4
[2,1,4,5,6,3]=>4
[2,1,4,6,3,5]=>4
[2,1,4,6,5,3]=>4
[2,1,5,3,4,6]=>4
[2,1,5,3,6,4]=>4
[2,1,5,4,3,6]=>2
[2,1,5,4,6,3]=>4
[2,1,5,6,3,4]=>2
[2,1,5,6,4,3]=>4
[2,1,6,3,4,5]=>4
[2,1,6,3,5,4]=>4
[2,1,6,4,3,5]=>4
[2,1,6,4,5,3]=>2
[2,1,6,5,3,4]=>4
[2,1,6,5,4,3]=>2
[2,3,1,4,5,6]=>4
[2,3,1,4,6,5]=>4
[2,3,1,5,4,6]=>4
[2,3,1,5,6,4]=>2
[2,3,1,6,4,5]=>2
[2,3,1,6,5,4]=>4
[2,3,4,1,5,6]=>4
[2,3,4,1,6,5]=>4
[2,3,4,5,1,6]=>4
[2,3,4,5,6,1]=>2
[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]=>4
[2,3,5,4,1,6]=>4
[2,3,5,4,6,1]=>4
[2,3,5,6,1,4]=>4
[2,3,5,6,4,1]=>4
[2,3,6,1,4,5]=>2
[2,3,6,1,5,4]=>4
[2,3,6,4,1,5]=>4
[2,3,6,4,5,1]=>4
[2,3,6,5,1,4]=>4
[2,3,6,5,4,1]=>4
[2,4,1,3,5,6]=>4
[2,4,1,3,6,5]=>4
[2,4,1,5,3,6]=>4
[2,4,1,5,6,3]=>4
[2,4,1,6,3,5]=>2
[2,4,1,6,5,3]=>4
[2,4,3,1,5,6]=>4
[2,4,3,1,6,5]=>4
[2,4,3,5,1,6]=>4
[2,4,3,5,6,1]=>4
[2,4,3,6,1,5]=>4
[2,4,3,6,5,1]=>4
[2,4,5,1,3,6]=>4
[2,4,5,1,6,3]=>2
[2,4,5,3,1,6]=>4
[2,4,5,3,6,1]=>2
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>2
[2,4,6,1,5,3]=>4
[2,4,6,3,1,5]=>4
[2,4,6,3,5,1]=>4
[2,4,6,5,1,3]=>4
[2,4,6,5,3,1]=>4
[2,5,1,3,4,6]=>4
[2,5,1,3,6,4]=>2
[2,5,1,4,3,6]=>4
[2,5,1,4,6,3]=>4
[2,5,1,6,3,4]=>4
[2,5,1,6,4,3]=>4
[2,5,3,1,4,6]=>4
[2,5,3,1,6,4]=>4
[2,5,3,4,1,6]=>4
[2,5,3,4,6,1]=>2
[2,5,3,6,1,4]=>4
[2,5,3,6,4,1]=>4
[2,5,4,1,3,6]=>4
[2,5,4,1,6,3]=>2
[2,5,4,3,1,6]=>4
[2,5,4,3,6,1]=>2
[2,5,4,6,1,3]=>4
[2,5,4,6,3,1]=>4
[2,5,6,1,3,4]=>4
[2,5,6,1,4,3]=>4
[2,5,6,3,1,4]=>4
[2,5,6,3,4,1]=>4
[2,5,6,4,1,3]=>4
[2,5,6,4,3,1]=>4
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>4
[2,6,1,4,3,5]=>4
[2,6,1,4,5,3]=>4
[2,6,1,5,3,4]=>4
[2,6,1,5,4,3]=>4
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>4
[2,6,3,4,1,5]=>2
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>4
[2,6,3,5,4,1]=>4
[2,6,4,1,3,5]=>4
[2,6,4,1,5,3]=>4
[2,6,4,3,1,5]=>2
[2,6,4,3,5,1]=>4
[2,6,4,5,1,3]=>4
[2,6,4,5,3,1]=>4
[2,6,5,1,3,4]=>4
[2,6,5,1,4,3]=>4
[2,6,5,3,1,4]=>4
[2,6,5,3,4,1]=>4
[2,6,5,4,1,3]=>4
[2,6,5,4,3,1]=>4
[3,1,2,4,5,6]=>4
[3,1,2,4,6,5]=>4
[3,1,2,5,4,6]=>4
[3,1,2,5,6,4]=>2
[3,1,2,6,4,5]=>2
[3,1,2,6,5,4]=>4
[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]=>2
[3,1,4,6,5,2]=>4
[3,1,5,2,4,6]=>4
[3,1,5,2,6,4]=>2
[3,1,5,4,2,6]=>4
[3,1,5,4,6,2]=>4
[3,1,5,6,2,4]=>4
[3,1,5,6,4,2]=>4
[3,1,6,2,4,5]=>4
[3,1,6,2,5,4]=>4
[3,1,6,4,2,5]=>4
[3,1,6,4,5,2]=>4
[3,1,6,5,2,4]=>4
[3,1,6,5,4,2]=>4
[3,2,1,4,5,6]=>2
[3,2,1,4,6,5]=>2
[3,2,1,5,4,6]=>2
[3,2,1,5,6,4]=>4
[3,2,1,6,4,5]=>4
[3,2,1,6,5,4]=>1
[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]=>4
[3,2,4,6,5,1]=>2
[3,2,5,1,4,6]=>4
[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]=>4
[3,2,5,6,4,1]=>4
[3,2,6,1,4,5]=>4
[3,2,6,1,5,4]=>2
[3,2,6,4,1,5]=>4
[3,2,6,4,5,1]=>4
[3,2,6,5,1,4]=>4
[3,2,6,5,4,1]=>4
[3,4,1,2,5,6]=>2
[3,4,1,2,6,5]=>2
[3,4,1,5,2,6]=>4
[3,4,1,5,6,2]=>4
[3,4,1,6,2,5]=>4
[3,4,1,6,5,2]=>4
[3,4,2,1,5,6]=>4
[3,4,2,1,6,5]=>4
[3,4,2,5,1,6]=>4
[3,4,2,5,6,1]=>4
[3,4,2,6,1,5]=>4
[3,4,2,6,5,1]=>4
[3,4,5,1,2,6]=>4
[3,4,5,1,6,2]=>4
[3,4,5,2,1,6]=>4
[3,4,5,2,6,1]=>4
[3,4,5,6,1,2]=>2
[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>4
[3,4,6,1,5,2]=>4
[3,4,6,2,1,5]=>4
[3,4,6,2,5,1]=>4
[3,4,6,5,1,2]=>4
[3,4,6,5,2,1]=>4
[3,5,1,2,4,6]=>4
[3,5,1,2,6,4]=>4
[3,5,1,4,2,6]=>2
[3,5,1,4,6,2]=>4
[3,5,1,6,2,4]=>1
[3,5,1,6,4,2]=>4
[3,5,2,1,4,6]=>4
[3,5,2,1,6,4]=>4
[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]=>2
[3,5,4,1,2,6]=>4
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>4
[3,5,4,2,6,1]=>4
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>2
[3,5,6,1,4,2]=>4
[3,5,6,2,1,4]=>4
[3,5,6,2,4,1]=>4
[3,5,6,4,1,2]=>4
[3,5,6,4,2,1]=>4
[3,6,1,2,4,5]=>4
[3,6,1,2,5,4]=>4
[3,6,1,4,2,5]=>4
[3,6,1,4,5,2]=>2
[3,6,1,5,2,4]=>4
[3,6,1,5,4,2]=>2
[3,6,2,1,4,5]=>4
[3,6,2,1,5,4]=>4
[3,6,2,4,1,5]=>4
[3,6,2,4,5,1]=>4
[3,6,2,5,1,4]=>2
[3,6,2,5,4,1]=>4
[3,6,4,1,2,5]=>4
[3,6,4,1,5,2]=>4
[3,6,4,2,1,5]=>4
[3,6,4,2,5,1]=>4
[3,6,4,5,1,2]=>4
[3,6,4,5,2,1]=>4
[3,6,5,1,2,4]=>4
[3,6,5,1,4,2]=>4
[3,6,5,2,1,4]=>2
[3,6,5,2,4,1]=>4
[3,6,5,4,1,2]=>4
[3,6,5,4,2,1]=>4
[4,1,2,3,5,6]=>4
[4,1,2,3,6,5]=>4
[4,1,2,5,3,6]=>4
[4,1,2,5,6,3]=>2
[4,1,2,6,3,5]=>4
[4,1,2,6,5,3]=>4
[4,1,3,2,5,6]=>4
[4,1,3,2,6,5]=>4
[4,1,3,5,2,6]=>4
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>4
[4,1,3,6,5,2]=>4
[4,1,5,2,3,6]=>4
[4,1,5,2,6,3]=>2
[4,1,5,3,2,6]=>4
[4,1,5,3,6,2]=>4
[4,1,5,6,2,3]=>4
[4,1,5,6,3,2]=>4
[4,1,6,2,3,5]=>2
[4,1,6,2,5,3]=>4
[4,1,6,3,2,5]=>2
[4,1,6,3,5,2]=>4
[4,1,6,5,2,3]=>4
[4,1,6,5,3,2]=>4
[4,2,1,3,5,6]=>4
[4,2,1,3,6,5]=>4
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>4
[4,2,1,6,3,5]=>4
[4,2,1,6,5,3]=>2
[4,2,3,1,5,6]=>2
[4,2,3,1,6,5]=>2
[4,2,3,5,1,6]=>4
[4,2,3,5,6,1]=>4
[4,2,3,6,1,5]=>4
[4,2,3,6,5,1]=>4
[4,2,5,1,3,6]=>2
[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]=>4
[4,2,5,6,3,1]=>4
[4,2,6,1,3,5]=>4
[4,2,6,1,5,3]=>1
[4,2,6,3,1,5]=>4
[4,2,6,3,5,1]=>2
[4,2,6,5,1,3]=>4
[4,2,6,5,3,1]=>4
[4,3,1,2,5,6]=>4
[4,3,1,2,6,5]=>4
[4,3,1,5,2,6]=>4
[4,3,1,5,6,2]=>4
[4,3,1,6,2,5]=>4
[4,3,1,6,5,2]=>4
[4,3,2,1,5,6]=>2
[4,3,2,1,6,5]=>2
[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]=>4
[4,3,5,1,6,2]=>4
[4,3,5,2,1,6]=>4
[4,3,5,2,6,1]=>4
[4,3,5,6,1,2]=>4
[4,3,5,6,2,1]=>4
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>4
[4,3,6,2,1,5]=>4
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>2
[4,3,6,5,2,1]=>2
[4,5,1,2,3,6]=>4
[4,5,1,2,6,3]=>4
[4,5,1,3,2,6]=>4
[4,5,1,3,6,2]=>4
[4,5,1,6,2,3]=>2
[4,5,1,6,3,2]=>4
[4,5,2,1,3,6]=>4
[4,5,2,1,6,3]=>4
[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]=>4
[4,5,3,1,2,6]=>2
[4,5,3,1,6,2]=>4
[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]=>1
[4,5,6,1,3,2]=>4
[4,5,6,2,1,3]=>4
[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>2
[4,6,1,2,3,5]=>4
[4,6,1,2,5,3]=>4
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>4
[4,6,1,5,2,3]=>4
[4,6,1,5,3,2]=>4
[4,6,2,1,3,5]=>4
[4,6,2,1,5,3]=>4
[4,6,2,3,1,5]=>4
[4,6,2,3,5,1]=>4
[4,6,2,5,1,3]=>2
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>4
[4,6,3,1,5,2]=>2
[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]=>4
[4,6,5,1,3,2]=>2
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>4
[4,6,5,3,1,2]=>4
[4,6,5,3,2,1]=>4
[5,1,2,3,4,6]=>4
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>4
[5,1,2,4,6,3]=>4
[5,1,2,6,3,4]=>4
[5,1,2,6,4,3]=>4
[5,1,3,2,4,6]=>4
[5,1,3,2,6,4]=>4
[5,1,3,4,2,6]=>4
[5,1,3,4,6,2]=>2
[5,1,3,6,2,4]=>4
[5,1,3,6,4,2]=>4
[5,1,4,2,3,6]=>4
[5,1,4,2,6,3]=>4
[5,1,4,3,2,6]=>4
[5,1,4,3,6,2]=>2
[5,1,4,6,2,3]=>4
[5,1,4,6,3,2]=>4
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>4
[5,1,6,3,2,4]=>4
[5,1,6,3,4,2]=>4
[5,1,6,4,2,3]=>4
[5,1,6,4,3,2]=>4
[5,2,1,3,4,6]=>4
[5,2,1,3,6,4]=>4
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>4
[5,2,1,6,3,4]=>4
[5,2,1,6,4,3]=>4
[5,2,3,1,4,6]=>4
[5,2,3,1,6,4]=>4
[5,2,3,4,1,6]=>2
[5,2,3,4,6,1]=>4
[5,2,3,6,1,4]=>2
[5,2,3,6,4,1]=>4
[5,2,4,1,3,6]=>4
[5,2,4,1,6,3]=>4
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>4
[5,2,4,6,1,3]=>4
[5,2,4,6,3,1]=>4
[5,2,6,1,3,4]=>4
[5,2,6,1,4,3]=>4
[5,2,6,3,1,4]=>4
[5,2,6,3,4,1]=>4
[5,2,6,4,1,3]=>2
[5,2,6,4,3,1]=>4
[5,3,1,2,4,6]=>4
[5,3,1,2,6,4]=>4
[5,3,1,4,2,6]=>4
[5,3,1,4,6,2]=>4
[5,3,1,6,2,4]=>4
[5,3,1,6,4,2]=>2
[5,3,2,1,4,6]=>4
[5,3,2,1,6,4]=>4
[5,3,2,4,1,6]=>2
[5,3,2,4,6,1]=>4
[5,3,2,6,1,4]=>2
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>4
[5,3,4,1,6,2]=>4
[5,3,4,2,1,6]=>4
[5,3,4,2,6,1]=>4
[5,3,4,6,1,2]=>4
[5,3,4,6,2,1]=>4
[5,3,6,1,2,4]=>4
[5,3,6,1,4,2]=>2
[5,3,6,2,1,4]=>4
[5,3,6,2,4,1]=>4
[5,3,6,4,1,2]=>4
[5,3,6,4,2,1]=>4
[5,4,1,2,3,6]=>4
[5,4,1,2,6,3]=>4
[5,4,1,3,2,6]=>4
[5,4,1,3,6,2]=>4
[5,4,1,6,2,3]=>4
[5,4,1,6,3,2]=>2
[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]=>2
[5,4,3,2,6,1]=>4
[5,4,3,6,1,2]=>4
[5,4,3,6,2,1]=>4
[5,4,6,1,2,3]=>4
[5,4,6,1,3,2]=>2
[5,4,6,2,1,3]=>2
[5,4,6,2,3,1]=>4
[5,4,6,3,1,2]=>4
[5,4,6,3,2,1]=>4
[5,6,1,2,3,4]=>2
[5,6,1,2,4,3]=>4
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>4
[5,6,1,4,2,3]=>4
[5,6,1,4,3,2]=>4
[5,6,2,1,3,4]=>4
[5,6,2,1,4,3]=>2
[5,6,2,3,1,4]=>4
[5,6,2,3,4,1]=>2
[5,6,2,4,1,3]=>4
[5,6,2,4,3,1]=>4
[5,6,3,1,2,4]=>4
[5,6,3,1,4,2]=>4
[5,6,3,2,1,4]=>4
[5,6,3,2,4,1]=>4
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>2
[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>4
[5,6,4,2,1,3]=>4
[5,6,4,2,3,1]=>2
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>2
[6,1,2,3,4,5]=>2
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>4
[6,1,2,4,5,3]=>4
[6,1,2,5,3,4]=>4
[6,1,2,5,4,3]=>4
[6,1,3,2,4,5]=>4
[6,1,3,2,5,4]=>4
[6,1,3,4,2,5]=>2
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>4
[6,1,3,5,4,2]=>4
[6,1,4,2,3,5]=>2
[6,1,4,2,5,3]=>4
[6,1,4,3,2,5]=>2
[6,1,4,3,5,2]=>4
[6,1,4,5,2,3]=>4
[6,1,4,5,3,2]=>4
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>4
[6,1,5,3,2,4]=>4
[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]=>2
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>4
[6,2,1,5,3,4]=>4
[6,2,1,5,4,3]=>4
[6,2,3,1,4,5]=>4
[6,2,3,1,5,4]=>4
[6,2,3,4,1,5]=>4
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>4
[6,2,3,5,4,1]=>2
[6,2,4,1,3,5]=>4
[6,2,4,1,5,3]=>2
[6,2,4,3,1,5]=>4
[6,2,4,3,5,1]=>1
[6,2,4,5,1,3]=>4
[6,2,4,5,3,1]=>4
[6,2,5,1,3,4]=>4
[6,2,5,1,4,3]=>4
[6,2,5,3,1,4]=>4
[6,2,5,3,4,1]=>4
[6,2,5,4,1,3]=>4
[6,2,5,4,3,1]=>2
[6,3,1,2,4,5]=>4
[6,3,1,2,5,4]=>4
[6,3,1,4,2,5]=>4
[6,3,1,4,5,2]=>4
[6,3,1,5,2,4]=>2
[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]=>2
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>1
[6,3,4,1,2,5]=>4
[6,3,4,1,5,2]=>4
[6,3,4,2,1,5]=>4
[6,3,4,2,5,1]=>4
[6,3,4,5,1,2]=>2
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>4
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>4
[6,3,5,2,4,1]=>2
[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]=>4
[6,4,1,3,2,5]=>4
[6,4,1,3,5,2]=>4
[6,4,1,5,2,3]=>4
[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]=>4
[6,4,2,3,5,1]=>4
[6,4,2,5,1,3]=>4
[6,4,2,5,3,1]=>2
[6,4,3,1,2,5]=>4
[6,4,3,1,5,2]=>4
[6,4,3,2,1,5]=>4
[6,4,3,2,5,1]=>2
[6,4,3,5,1,2]=>4
[6,4,3,5,2,1]=>4
[6,4,5,1,2,3]=>2
[6,4,5,1,3,2]=>4
[6,4,5,2,1,3]=>4
[6,4,5,2,3,1]=>1
[6,4,5,3,1,2]=>2
[6,4,5,3,2,1]=>2
[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>4
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>4
[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]=>2
[6,5,2,3,1,4]=>4
[6,5,2,3,4,1]=>2
[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]=>4
[6,5,3,2,4,1]=>4
[6,5,3,4,1,2]=>2
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>2
[6,5,4,1,3,2]=>4
[6,5,4,2,1,3]=>4
[6,5,4,2,3,1]=>2
[6,5,4,3,1,2]=>2
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>2
[1,2,3,4,6,5,7]=>2
[1,2,3,4,6,7,5]=>4
[1,2,3,4,7,5,6]=>4
[1,2,3,4,7,6,5]=>2
[1,2,3,5,4,6,7]=>2
[1,2,3,5,4,7,6]=>2
[1,2,3,5,6,4,7]=>4
[1,2,3,5,6,7,4]=>4
[1,2,3,5,7,4,6]=>4
[1,2,3,5,7,6,4]=>4
[1,2,3,6,4,5,7]=>4
[1,2,3,6,4,7,5]=>4
[1,2,3,6,5,4,7]=>2
[1,2,3,6,5,7,4]=>4
[1,2,3,6,7,4,5]=>2
[1,2,3,6,7,5,4]=>4
[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]=>2
[1,2,3,7,6,4,5]=>4
[1,2,3,7,6,5,4]=>2
[1,2,4,3,5,6,7]=>2
[1,2,4,3,5,7,6]=>2
[1,2,4,3,6,5,7]=>2
[1,2,4,3,6,7,5]=>4
[1,2,4,3,7,5,6]=>4
[1,2,4,3,7,6,5]=>2
[1,2,4,5,3,6,7]=>2
[1,2,4,5,3,7,6]=>4
[1,2,4,5,6,3,7]=>4
[1,2,4,5,6,7,3]=>4
[1,2,4,5,7,3,6]=>4
[1,2,4,5,7,6,3]=>4
[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]=>4
[1,2,4,6,7,5,3]=>4
[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]=>2
[1,2,5,3,4,7,6]=>4
[1,2,5,3,6,4,7]=>4
[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]=>1
[1,2,5,4,3,7,6]=>2
[1,2,5,4,6,3,7]=>4
[1,2,5,4,6,7,3]=>4
[1,2,5,4,7,3,6]=>4
[1,2,5,4,7,6,3]=>4
[1,2,5,6,3,4,7]=>2
[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]=>4
[1,2,5,6,7,4,3]=>4
[1,2,5,7,3,4,6]=>4
[1,2,5,7,3,6,4]=>2
[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]=>4
[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]=>2
[1,2,6,4,5,7,3]=>4
[1,2,6,4,7,3,5]=>2
[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]=>2
[1,2,6,5,4,7,3]=>4
[1,2,6,5,7,3,4]=>4
[1,2,6,5,7,4,3]=>4
[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]=>2
[1,2,6,7,5,4,3]=>4
[1,2,7,3,4,5,6]=>4
[1,2,7,3,4,6,5]=>4
[1,2,7,3,5,4,6]=>4
[1,2,7,3,5,6,4]=>4
[1,2,7,3,6,4,5]=>4
[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]=>4
[1,2,7,4,5,6,3]=>2
[1,2,7,4,6,3,5]=>4
[1,2,7,4,6,5,3]=>2
[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]=>2
[1,2,7,5,6,3,4]=>4
[1,2,7,5,6,4,3]=>4
[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]=>4
[1,2,7,6,5,3,4]=>4
[1,2,7,6,5,4,3]=>2
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>2
[1,3,2,4,6,5,7]=>1
[1,3,2,4,6,7,5]=>4
[1,3,2,4,7,5,6]=>4
[1,3,2,4,7,6,5]=>2
[1,3,2,5,4,6,7]=>2
[1,3,2,5,4,7,6]=>2
[1,3,2,5,6,4,7]=>4
[1,3,2,5,6,7,4]=>4
[1,3,2,5,7,4,6]=>4
[1,3,2,5,7,6,4]=>4
[1,3,2,6,4,5,7]=>4
[1,3,2,6,4,7,5]=>4
[1,3,2,6,5,4,7]=>2
[1,3,2,6,5,7,4]=>4
[1,3,2,6,7,4,5]=>2
[1,3,2,6,7,5,4]=>4
[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]=>2
[1,3,2,7,6,4,5]=>4
[1,3,2,7,6,5,4]=>2
[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]=>4
[1,3,4,2,7,5,6]=>4
[1,3,4,2,7,6,5]=>4
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>4
[1,3,4,5,6,2,7]=>2
[1,3,4,5,6,7,2]=>4
[1,3,4,5,7,2,6]=>4
[1,3,4,5,7,6,2]=>4
[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]=>4
[1,3,4,6,7,5,2]=>4
[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]=>2
[1,3,5,2,6,7,4]=>4
[1,3,5,2,7,4,6]=>4
[1,3,5,2,7,6,4]=>4
[1,3,5,4,2,6,7]=>4
[1,3,5,4,2,7,6]=>4
[1,3,5,4,6,2,7]=>2
[1,3,5,4,6,7,2]=>4
[1,3,5,4,7,2,6]=>4
[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]=>4
[1,3,5,6,7,4,2]=>4
[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]=>4
[1,3,6,2,5,7,4]=>4
[1,3,6,2,7,4,5]=>4
[1,3,6,2,7,5,4]=>4
[1,3,6,4,2,5,7]=>2
[1,3,6,4,2,7,5]=>4
[1,3,6,4,5,2,7]=>4
[1,3,6,4,5,7,2]=>4
[1,3,6,4,7,2,5]=>4
[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]=>4
[1,3,6,5,7,2,4]=>4
[1,3,6,5,7,4,2]=>4
[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]=>4
[1,3,7,2,5,6,4]=>4
[1,3,7,2,6,4,5]=>4
[1,3,7,2,6,5,4]=>4
[1,3,7,4,2,5,6]=>4
[1,3,7,4,2,6,5]=>4
[1,3,7,4,5,2,6]=>4
[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]=>4
[1,3,7,5,6,2,4]=>4
[1,3,7,5,6,4,2]=>4
[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]=>4
[1,3,7,6,5,2,4]=>4
[1,3,7,6,5,4,2]=>4
[1,4,2,3,5,6,7]=>4
[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]=>4
[1,4,2,3,7,6,5]=>4
[1,4,2,5,3,6,7]=>4
[1,4,2,5,3,7,6]=>4
[1,4,2,5,6,3,7]=>4
[1,4,2,5,6,7,3]=>4
[1,4,2,5,7,3,6]=>4
[1,4,2,5,7,6,3]=>4
[1,4,2,6,3,5,7]=>2
[1,4,2,6,3,7,5]=>4
[1,4,2,6,5,3,7]=>4
[1,4,2,6,5,7,3]=>4
[1,4,2,6,7,3,5]=>4
[1,4,2,6,7,5,3]=>4
[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]=>2
[1,4,3,2,5,7,6]=>2
[1,4,3,2,6,5,7]=>2
[1,4,3,2,6,7,5]=>4
[1,4,3,2,7,5,6]=>4
[1,4,3,2,7,6,5]=>2
[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]=>4
[1,4,3,5,7,6,2]=>4
[1,4,3,6,2,5,7]=>4
[1,4,3,6,2,7,5]=>4
[1,4,3,6,5,2,7]=>2
[1,4,3,6,5,7,2]=>4
[1,4,3,6,7,2,5]=>4
[1,4,3,6,7,5,2]=>4
[1,4,3,7,2,5,6]=>4
[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]=>2
[1,4,5,2,3,7,6]=>2
[1,4,5,2,6,3,7]=>4
[1,4,5,2,6,7,3]=>4
[1,4,5,2,7,3,6]=>4
[1,4,5,2,7,6,3]=>4
[1,4,5,3,2,6,7]=>4
[1,4,5,3,2,7,6]=>4
[1,4,5,3,6,2,7]=>4
[1,4,5,3,6,7,2]=>4
[1,4,5,3,7,2,6]=>4
[1,4,5,3,7,6,2]=>4
[1,4,5,6,2,3,7]=>2
[1,4,5,6,2,7,3]=>4
[1,4,5,6,3,2,7]=>2
[1,4,5,6,3,7,2]=>4
[1,4,5,6,7,2,3]=>4
[1,4,5,6,7,3,2]=>4
[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]=>2
[1,4,6,2,5,7,3]=>4
[1,4,6,2,7,3,5]=>2
[1,4,6,2,7,5,3]=>4
[1,4,6,3,2,5,7]=>4
[1,4,6,3,2,7,5]=>4
[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]=>4
[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]=>4
[1,4,6,7,2,3,5]=>4
[1,4,6,7,5,3,2]=>4
[1,4,7,2,3,5,6]=>4
[1,4,7,6,5,3,2]=>4
[1,5,2,3,4,7,6]=>4
[1,5,2,7,3,4,6]=>4
[1,5,4,7,6,3,2]=>4
[1,5,6,2,7,3,4]=>4
[1,5,6,4,7,3,2]=>4
[1,5,6,7,2,3,4]=>2
[1,5,6,7,4,3,2]=>4
[1,5,7,2,3,4,6]=>4
[1,5,7,6,4,3,2]=>4
[1,6,2,3,4,7,5]=>4
[1,6,2,3,7,4,5]=>4
[1,6,2,7,3,4,5]=>4
[1,6,5,4,3,7,2]=>4
[1,6,5,4,7,3,2]=>4
[1,6,5,7,4,3,2]=>4
[1,6,7,2,3,4,5]=>4
[1,6,7,5,4,3,2]=>4
[1,7,2,3,4,5,6]=>4
[1,7,3,5,6,4,2]=>4
[1,7,3,6,5,4,2]=>2
[1,7,4,3,6,5,2]=>2
[1,7,4,5,3,6,2]=>4
[1,7,4,5,6,3,2]=>4
[1,7,4,6,5,3,2]=>4
[1,7,5,4,3,6,2]=>2
[1,7,5,4,6,3,2]=>4
[1,7,6,4,5,3,2]=>2
[1,7,6,5,4,3,2]=>2
[2,1,3,4,5,6,7]=>2
[2,1,3,4,7,5,6]=>4
[2,1,3,7,4,5,6]=>4
[2,1,6,3,4,5,7]=>4
[2,1,7,3,4,5,6]=>4
[2,1,7,6,5,4,3]=>2
[2,3,1,4,5,6,7]=>4
[2,3,4,1,5,6,7]=>4
[2,3,4,1,5,7,6]=>4
[2,3,4,5,1,6,7]=>4
[2,3,4,5,1,7,6]=>4
[2,3,4,5,6,1,7]=>4
[2,3,4,5,6,7,1]=>2
[2,3,4,5,7,1,6]=>4
[2,3,4,6,1,7,5]=>4
[2,3,4,6,7,1,5]=>4
[2,3,4,7,1,5,6]=>4
[2,3,5,6,7,1,4]=>4
[2,4,1,3,5,6,7]=>4
[2,5,1,3,4,6,7]=>4
[2,5,7,1,3,4,6]=>4
[2,6,1,3,4,5,7]=>4
[2,6,1,7,3,4,5]=>4
[2,6,5,4,3,1,7]=>4
[2,6,7,1,3,4,5]=>4
[2,7,1,3,4,5,6]=>4
[3,1,2,4,5,6,7]=>4
[3,1,2,4,5,7,6]=>4
[3,2,1,4,5,6,7]=>2
[3,2,4,5,6,7,1]=>4
[3,4,1,2,5,6,7]=>2
[3,4,2,5,6,7,1]=>4
[3,4,5,2,6,7,1]=>4
[3,4,5,6,2,7,1]=>4
[3,4,5,6,7,1,2]=>2
[3,5,6,1,2,4,7]=>4
[3,5,6,4,2,1,7]=>4
[3,6,1,2,4,5,7]=>4
[3,6,5,4,2,1,7]=>4
[4,1,2,3,5,6,7]=>4
[4,1,2,3,5,7,6]=>4
[4,1,6,2,3,5,7]=>4
[4,2,3,5,6,7,1]=>4
[4,2,5,1,3,6,7]=>2
[4,3,2,1,5,6,7]=>2
[4,3,2,5,6,7,1]=>4
[4,3,5,2,6,7,1]=>4
[4,3,6,5,2,1,7]=>4
[4,5,1,6,2,3,7]=>4
[4,5,2,3,6,7,1]=>4
[4,5,3,6,2,1,7]=>4
[4,5,6,1,2,3,7]=>2
[4,5,6,3,2,1,7]=>4
[4,6,1,2,3,5,7]=>4
[4,6,1,2,3,7,5]=>4
[4,6,5,3,2,1,7]=>4
[5,1,2,3,4,6,7]=>4
[5,1,2,3,4,7,6]=>4
[5,1,2,3,6,4,7]=>4
[5,1,2,3,6,7,4]=>4
[5,1,2,3,7,4,6]=>4
[5,1,2,6,3,4,7]=>4
[5,1,6,2,3,4,7]=>4
[5,1,6,2,3,7,4]=>4
[5,2,3,4,6,7,1]=>4
[5,2,6,7,1,3,4]=>2
[5,3,2,4,6,7,1]=>4
[5,3,2,6,1,4,7]=>2
[5,4,3,2,1,6,7]=>2
[5,4,3,2,1,7,6]=>2
[5,4,3,2,6,1,7]=>4
[5,4,3,6,2,1,7]=>4
[5,4,6,3,2,1,7]=>4
[5,6,1,2,3,4,7]=>4
[5,6,1,2,3,7,4]=>4
[5,6,3,4,1,2,7]=>2
[5,6,4,3,2,1,7]=>4
[5,6,7,1,2,3,4]=>2
[6,1,2,3,4,5,7]=>4
[6,1,2,3,4,7,5]=>4
[6,1,2,3,7,4,5]=>4
[6,1,2,7,3,4,5]=>4
[6,2,3,4,5,7,1]=>4
[6,2,4,5,3,1,7]=>4
[6,2,5,4,3,1,7]=>2
[6,3,2,5,4,1,7]=>2
[6,3,4,2,5,1,7]=>4
[6,3,4,5,2,1,7]=>4
[6,3,5,4,2,1,7]=>4
[6,4,3,2,5,1,7]=>2
[6,4,3,2,7,1,5]=>2
[6,4,3,5,2,1,7]=>4
[6,4,7,2,5,1,3]=>2
[6,5,3,4,2,1,7]=>2
[6,5,4,3,2,1,7]=>2
[6,7,1,2,3,4,5]=>2
[6,7,4,5,1,2,3]=>2
[7,1,2,3,4,5,6]=>2
[7,2,1,3,4,5,6]=>4
[7,2,3,1,4,5,6]=>4
[7,2,3,4,1,5,6]=>4
[7,2,3,4,5,1,6]=>4
[7,3,1,2,4,5,6]=>4
[7,3,2,1,4,5,6]=>4
[7,3,2,4,1,5,6]=>4
[7,3,4,1,2,5,6]=>4
[7,4,1,2,3,5,6]=>4
[7,4,2,1,3,5,6]=>4
[7,4,5,6,1,2,3]=>2
[7,5,1,2,3,4,6]=>4
[7,5,6,1,2,3,4]=>2
[7,5,6,3,4,1,2]=>2
[7,6,1,2,3,4,5]=>2
[7,6,4,5,1,2,3]=>2
[7,6,5,1,2,3,4]=>2
[7,6,5,3,4,1,2]=>2
[7,6,5,4,1,2,3]=>2
[7,6,5,4,3,1,2]=>2
[7,6,5,4,3,2,1]=>1
[8,7,6,5,4,3,2,1]=>1
[7,6,8,5,4,3,2,1]=>4
[7,8,5,6,4,3,2,1]=>2
[7,8,6,4,5,3,2,1]=>2
[8,6,7,4,5,3,2,1]=>2
[7,6,5,4,8,3,2,1]=>4
[6,5,7,4,8,3,2,1]=>4
[7,8,6,5,3,4,2,1]=>2
[8,6,7,5,3,4,2,1]=>2
[8,7,5,6,3,4,2,1]=>1
[6,7,8,3,4,5,2,1]=>2
[7,8,6,5,4,2,3,1]=>2
[8,6,7,5,4,2,3,1]=>1
[8,7,5,6,4,2,3,1]=>2
[8,7,6,4,5,2,3,1]=>2
[8,6,5,7,3,2,4,1]=>2
[6,7,8,5,2,3,4,1]=>2
[8,5,6,7,2,3,4,1]=>1
[7,8,3,2,4,5,6,1]=>4
[7,6,5,4,3,2,8,1]=>4
[6,5,7,4,3,2,8,1]=>4
[6,5,4,3,7,2,8,1]=>4
[5,4,6,3,7,2,8,1]=>4
[3,4,5,2,6,7,8,1]=>4
[5,2,3,4,6,7,8,1]=>4
[4,3,2,5,6,7,8,1]=>4
[3,4,2,5,6,7,8,1]=>4
[4,2,3,5,6,7,8,1]=>4
[3,2,4,5,6,7,8,1]=>4
[2,3,4,5,6,7,8,1]=>2
[8,7,6,5,4,3,1,2]=>2
[7,8,6,5,4,3,1,2]=>1
[8,6,7,5,4,3,1,2]=>2
[8,7,5,6,4,3,1,2]=>2
[8,7,6,4,5,3,1,2]=>2
[8,7,6,5,3,4,1,2]=>2
[8,7,5,6,3,4,1,2]=>2
[7,8,5,6,3,4,1,2]=>1
[5,6,7,8,3,4,1,2]=>2
[7,8,3,4,5,6,1,2]=>1
[3,4,5,6,7,8,1,2]=>2
[8,7,6,5,4,2,1,3]=>4
[7,6,8,5,4,2,1,3]=>2
[8,7,6,5,4,1,2,3]=>2
[6,7,8,5,4,1,2,3]=>1
[8,5,6,7,4,1,2,3]=>2
[8,7,6,4,5,1,2,3]=>2
[8,6,7,4,5,1,2,3]=>2
[8,7,4,5,6,1,2,3]=>2
[7,8,4,5,6,1,2,3]=>2
[7,6,5,8,3,2,1,4]=>2
[7,5,6,8,2,3,1,4]=>2
[6,7,5,8,3,1,2,4]=>2
[6,5,7,8,2,1,3,4]=>2
[8,7,6,5,1,2,3,4]=>2
[8,7,5,6,1,2,3,4]=>2
[7,8,5,6,1,2,3,4]=>2
[8,5,6,7,1,2,3,4]=>2
[5,6,7,8,1,2,3,4]=>1
[8,7,6,4,3,2,1,5]=>4
[8,7,6,4,2,1,3,5]=>4
[8,7,6,1,2,3,4,5]=>2
[8,6,7,1,2,3,4,5]=>2
[6,7,8,1,2,3,4,5]=>2
[7,8,5,4,2,1,3,6]=>4
[7,8,5,4,1,2,3,6]=>4
[8,7,1,2,3,4,5,6]=>2
[7,8,1,2,3,4,5,6]=>2
[8,6,5,4,3,2,1,7]=>4
[8,6,5,4,3,1,2,7]=>4
[8,5,6,3,4,1,2,7]=>4
[8,6,5,4,2,1,3,7]=>4
[8,6,4,3,2,1,5,7]=>4
[8,6,4,2,1,3,5,7]=>4
[8,2,3,4,1,5,6,7]=>4
[8,4,1,2,3,5,6,7]=>4
[8,3,2,1,4,5,6,7]=>4
[8,2,3,1,4,5,6,7]=>4
[8,3,1,2,4,5,6,7]=>4
[8,2,1,3,4,5,6,7]=>4
[8,1,2,3,4,5,6,7]=>2
[7,6,5,4,3,2,1,8]=>2
[6,7,5,4,3,2,1,8]=>4
[6,5,7,4,3,2,1,8]=>4
[5,6,7,4,3,2,1,8]=>4
[7,6,4,5,3,2,1,8]=>4
[6,5,4,7,3,2,1,8]=>4
[7,5,6,3,4,2,1,8]=>4
[7,6,4,3,5,2,1,8]=>2
[7,6,3,4,5,2,1,8]=>2
[7,5,4,3,6,2,1,8]=>4
[6,7,5,4,2,3,1,8]=>4
[6,5,7,3,2,4,1,8]=>4
[5,6,7,2,3,4,1,8]=>4
[2,3,4,5,6,7,1,8]=>4
[5,6,7,1,2,3,4,8]=>4
[6,7,1,2,3,4,5,8]=>4
[7,1,2,3,4,5,6,8]=>4
[6,5,4,3,2,1,7,8]=>2
[2,3,4,5,6,1,7,8]=>4
[5,6,3,4,1,2,7,8]=>2
[4,5,6,1,2,3,7,8]=>2
[6,1,2,3,4,5,7,8]=>4
[5,4,3,2,1,6,7,8]=>2
[2,3,4,5,1,6,7,8]=>4
[5,1,2,3,4,6,7,8]=>4
[4,3,2,1,5,6,7,8]=>2
[3,4,1,2,5,6,7,8]=>2
[3,2,1,4,5,6,7,8]=>2
[2,1,3,4,5,6,7,8]=>2
[1,2,3,4,5,6,7,8]=>1
[6,5,8,7,4,3,2,1]=>2
[3,5,8,7,6,4,2,1]=>4
[4,3,6,5,8,7,2,1]=>2
[2,6,8,7,5,4,3,1]=>4
[2,3,5,6,8,7,4,1]=>4
[3,2,6,5,4,8,7,1]=>2
[4,3,6,5,7,2,8,1]=>4
[3,2,6,5,7,4,8,1]=>4
[4,3,5,2,7,6,8,1]=>4
[3,2,5,4,7,6,8,1]=>4
[1,8,7,6,5,4,3,2]=>2
[1,7,8,6,5,4,3,2]=>4
[1,6,8,7,5,4,3,2]=>4
[1,7,6,8,5,4,3,2]=>4
[1,6,7,8,5,4,3,2]=>4
[1,5,8,7,6,4,3,2]=>4
[1,7,6,5,8,4,3,2]=>4
[1,3,5,7,8,6,4,2]=>4
[1,4,3,8,7,6,5,2]=>4
[1,6,5,4,3,8,7,2]=>4
[1,4,3,6,5,8,7,2]=>4
[2,1,8,7,6,5,4,3]=>2
[2,1,6,5,7,4,8,3]=>4
[2,1,5,4,7,6,8,3]=>4
[1,2,6,7,8,5,4,3]=>4
[3,2,1,8,7,6,5,4]=>2
[3,2,1,6,5,8,7,4]=>4
[1,2,3,5,6,7,8,4]=>4
[4,3,2,1,8,7,6,5]=>1
[3,4,2,1,7,8,6,5]=>2
[2,4,3,1,6,8,7,5]=>4
[2,4,3,1,7,6,8,5]=>2
[3,2,4,1,6,8,7,5]=>2
[3,2,4,1,7,6,8,5]=>4
[2,3,4,1,6,7,8,5]=>2
[2,1,4,3,8,7,6,5]=>2
[2,1,4,3,6,8,7,5]=>4
[2,1,4,3,7,6,8,5]=>4
[5,4,3,2,1,8,7,6]=>2
[3,2,5,4,1,8,7,6]=>4
[3,2,1,4,5,8,7,6]=>1
[2,3,1,4,5,7,8,6]=>2
[6,5,4,3,2,1,8,7]=>2
[4,3,5,2,6,1,8,7]=>4
[3,2,5,4,6,1,8,7]=>4
[2,3,4,5,6,1,8,7]=>4
[2,1,6,5,4,3,8,7]=>1
[2,1,4,6,5,3,8,7]=>4
[2,1,5,4,6,3,8,7]=>4
[4,3,2,1,6,5,8,7]=>2
[2,4,3,1,6,5,8,7]=>4
[3,2,4,1,6,5,8,7]=>4
[2,1,4,3,6,5,8,7]=>1
[2,1,3,4,5,6,8,7]=>1
[1,2,3,4,5,6,8,7]=>2
[5,7,6,4,3,2,1,8]=>4
[4,7,6,5,3,2,1,8]=>4
[3,2,7,6,5,4,1,8]=>4
[5,4,3,2,7,6,1,8]=>4
[3,2,5,4,7,6,1,8]=>4
[1,4,3,2,7,6,5,8]=>1
[1,3,4,2,6,7,5,8]=>2
[1,3,2,5,4,7,6,8]=>1
[1,2,3,5,4,7,6,8]=>2
[1,3,2,4,5,7,6,8]=>1
[1,2,3,4,5,7,6,8]=>2
[1,2,4,3,6,5,7,8]=>1
[1,3,2,5,4,6,7,8]=>2
[1,2,3,5,4,6,7,8]=>1
[1,3,2,4,5,6,7,8]=>2
[1,8,4,7,6,5,3,2]=>4
[1,8,5,4,7,6,3,2]=>4
[1,8,7,4,5,6,3,2]=>2
[1,8,7,4,6,5,3,2]=>2
[1,8,6,5,4,7,3,2]=>4
[1,8,7,5,4,6,3,2]=>2
[1,8,7,5,6,4,3,2]=>4
[2,1,4,5,8,6,7,3]=>4
[2,1,8,5,4,7,6,3]=>2
[2,3,4,8,5,6,7,1]=>4
[2,3,6,4,5,1,8,7]=>4
[2,3,7,4,5,6,8,1]=>4
[2,8,4,3,5,7,6,1]=>4
[4,2,3,1,8,6,7,5]=>1
[8,2,7,4,6,5,3,1]=>2
[4,3,2,7,5,6,8,1]=>4
[4,3,2,8,5,7,6,1]=>4
[6,3,2,5,4,1,8,7]=>2
[8,3,2,5,4,7,6,1]=>1
[8,3,2,7,6,5,4,1]=>2
[8,3,7,4,6,5,2,1]=>4
[7,3,6,5,4,2,1,8]=>4
[7,4,3,6,5,2,1,8]=>4
[7,6,3,5,4,2,1,8]=>2
[8,5,4,3,2,7,6,1]=>2
[8,7,4,3,6,5,2,1]=>1
[2,4,6,8,1,3,5,7]=>2
[2,4,6,1,7,3,8,5]=>2
[2,1,4,3,7,5,8,6]=>4
[2,4,1,3,7,5,8,6]=>2
[2,1,4,3,7,8,5,6]=>2
[2,4,7,8,1,3,5,6]=>4
[2,1,4,3,8,5,6,7]=>4
[2,4,5,6,7,1,8,3]=>2
[2,1,5,3,6,4,8,7]=>2
[2,1,5,6,3,4,8,7]=>1
[2,5,6,8,1,3,4,7]=>2
[2,1,5,3,7,4,8,6]=>4
[2,5,1,7,3,4,8,6]=>2
[2,1,5,7,3,8,4,6]=>2
[2,5,7,8,1,3,4,6]=>4
[2,3,5,6,1,7,8,4]=>2
[2,1,6,3,7,4,8,5]=>4
[2,6,7,1,3,4,8,5]=>2
[2,1,6,7,8,3,4,5]=>2
[2,6,7,8,1,3,4,5]=>4
[2,1,6,3,4,7,8,5]=>4
[2,1,6,3,4,5,8,7]=>2
[2,6,1,3,4,5,7,8]=>4
[2,7,8,1,3,4,5,6]=>4
[2,7,1,3,4,5,6,8]=>4
[2,3,4,5,7,8,1,6]=>4
[2,1,8,3,4,5,6,7]=>4
[2,8,1,3,4,5,6,7]=>4
[2,1,3,8,4,5,6,7]=>4
[2,3,4,5,6,8,1,7]=>4
[3,1,4,2,6,5,8,7]=>4
[3,4,1,2,6,5,8,7]=>2
[3,1,4,2,6,8,5,7]=>2
[3,4,6,8,1,2,5,7]=>4
[3,1,4,2,7,5,8,6]=>2
[3,4,1,2,7,8,5,6]=>1
[3,4,7,8,1,2,5,6]=>2
[3,1,5,2,6,4,8,7]=>4
[3,5,1,6,2,4,8,7]=>2
[3,1,5,6,2,8,4,7]=>2
[3,5,6,8,1,2,4,7]=>4
[3,1,5,2,7,4,8,6]=>2
[3,5,1,7,2,8,4,6]=>1
[3,5,7,8,1,2,4,6]=>2
[1,3,2,5,4,8,6,7]=>4
[1,3,5,8,2,4,6,7]=>4
[1,3,5,6,2,7,4,8]=>2
[3,1,6,2,7,4,8,5]=>4
[3,6,7,1,2,8,4,5]=>2
[3,6,1,7,8,2,4,5]=>2
[3,6,7,8,1,2,4,5]=>4
[1,3,2,6,4,7,5,8]=>4
[3,1,2,6,7,4,8,5]=>4
[1,3,2,6,4,8,5,7]=>4
[1,3,2,6,4,5,7,8]=>4
[1,3,2,7,4,8,5,6]=>4
[1,3,2,7,4,5,6,8]=>4
[1,3,2,8,4,5,6,7]=>4
[3,1,2,4,5,8,6,7]=>2
[1,3,2,4,5,8,6,7]=>4
[4,1,5,2,6,3,8,7]=>4
[4,5,6,1,2,3,8,7]=>2
[4,1,5,6,8,2,3,7]=>2
[4,5,6,8,1,2,3,7]=>4
[4,1,5,2,7,3,8,6]=>4
[4,1,5,2,7,8,3,6]=>4
[4,5,7,1,2,8,3,6]=>2
[4,5,1,7,8,2,3,6]=>2
[4,5,7,8,1,2,3,6]=>4
[1,4,2,5,3,7,6,8]=>4
[1,4,2,5,3,8,6,7]=>4
[1,4,2,5,3,6,7,8]=>4
[1,4,5,6,7,2,3,8]=>2
[4,1,6,2,7,3,8,5]=>2
[4,6,7,1,8,2,3,5]=>1
[4,6,7,8,1,2,3,5]=>2
[1,4,2,6,3,7,5,8]=>2
[1,4,2,6,7,8,3,5]=>4
[1,4,2,6,3,8,5,7]=>4
[4,1,2,3,6,5,8,7]=>4
[1,4,2,6,3,5,7,8]=>4
[1,4,2,7,3,8,5,6]=>4
[4,7,1,2,3,5,6,8]=>4
[1,4,2,7,3,5,6,8]=>4
[1,4,2,3,7,5,6,8]=>2
[1,4,2,3,5,7,6,8]=>4
[1,4,2,8,3,5,6,7]=>4
[4,1,2,3,8,5,6,7]=>2
[1,4,2,3,5,8,6,7]=>4
[1,4,2,3,5,6,7,8]=>4
[5,1,6,2,7,3,8,4]=>2
[1,5,2,6,3,7,4,8]=>2
[1,5,2,6,3,8,4,7]=>4
[1,5,2,6,3,4,7,8]=>4
[1,2,5,6,3,4,7,8]=>1
[1,5,2,7,3,8,4,6]=>4
[5,7,1,2,3,4,6,8]=>4
[1,5,2,7,3,4,6,8]=>2
[1,5,2,3,4,7,6,8]=>4
[5,1,2,8,3,4,6,7]=>2
[1,5,2,8,3,4,6,7]=>4
[1,5,8,2,3,4,6,7]=>4
[1,5,2,3,4,8,6,7]=>4
[1,2,3,5,4,8,6,7]=>4
[5,1,2,3,4,6,8,7]=>4
[1,5,2,3,4,6,7,8]=>4
[1,6,2,7,3,8,4,5]=>4
[1,6,7,8,2,3,4,5]=>4
[6,7,1,2,3,4,8,5]=>4
[6,1,7,2,3,4,5,8]=>4
[6,1,2,7,3,4,5,8]=>4
[1,6,2,7,3,4,5,8]=>4
[1,6,7,2,3,4,5,8]=>2
[1,6,2,3,4,7,5,8]=>4
[1,2,3,6,4,7,5,8]=>4
[6,1,8,2,3,4,5,7]=>2
[1,6,2,8,3,4,5,7]=>4
[1,6,8,2,3,4,5,7]=>4
[1,6,2,3,4,8,5,7]=>4
[1,2,3,6,4,8,5,7]=>4
[6,1,2,3,4,5,8,7]=>4
[1,6,2,3,4,5,7,8]=>4
[1,2,3,6,4,5,7,8]=>4
[1,7,2,8,3,4,5,6]=>4
[1,7,8,2,3,4,5,6]=>4
[1,7,2,3,8,4,5,6]=>4
[7,1,2,3,4,8,5,6]=>4
[1,7,2,3,4,8,5,6]=>4
[1,2,3,7,4,8,5,6]=>4
[7,1,2,3,4,5,8,6]=>4
[1,7,2,3,4,5,8,6]=>4
[1,2,7,3,4,5,8,6]=>4
[1,7,2,3,4,5,6,8]=>2
[1,2,3,7,4,5,6,8]=>4
[1,8,2,3,4,5,6,7]=>4
[1,2,3,8,4,5,6,7]=>4
[1,2,3,4,5,8,6,7]=>4
[5,3,2,6,1,4,8,7]=>2
[7,3,2,5,4,8,1,6]=>2
[8,4,5,2,3,7,6,1]=>2
[7,4,5,2,3,8,1,6]=>2
[6,4,5,2,3,1,8,7]=>2
[5,4,6,2,1,3,8,7]=>2
[3,6,1,5,4,2,8,7]=>2
[4,6,5,1,3,2,8,7]=>2
[5,6,4,3,1,2,8,7]=>2
[7,5,4,3,2,8,1,6]=>2
[8,6,4,3,7,2,5,1]=>2
[7,6,4,3,8,2,1,5]=>2
[6,7,4,3,8,1,2,5]=>2
[5,7,4,3,1,8,2,6]=>2
[4,7,5,1,3,8,2,6]=>2
[3,7,1,5,4,8,2,6]=>1
[2,1,7,5,4,8,3,6]=>2
[3,8,1,5,4,7,6,2]=>2
[4,8,5,1,3,7,6,2]=>2
[5,8,4,3,1,7,6,2]=>2
[6,8,4,3,7,1,5,2]=>2
[7,8,4,3,6,5,1,2]=>1
[6,8,5,7,3,1,4,2]=>2
[5,8,6,7,1,3,4,2]=>2
[4,8,6,1,7,3,5,2]=>2
[3,8,1,6,7,4,5,2]=>2
[2,1,8,6,7,4,5,3]=>2
[2,1,7,6,8,4,3,5]=>2
[3,7,1,6,8,4,2,5]=>2
[4,7,6,1,8,3,2,5]=>1
[5,7,6,8,1,3,2,4]=>1
[5,4,7,2,1,8,3,6]=>2
[6,4,7,2,8,1,3,5]=>2
[7,4,6,2,8,3,1,5]=>2
[8,4,6,2,7,3,5,1]=>1
[8,3,2,6,7,4,5,1]=>2
[7,3,2,6,8,4,1,5]=>2
[6,3,2,7,8,1,4,5]=>2
[5,3,2,7,1,8,4,6]=>2
[4,3,2,1,7,8,5,6]=>2
[3,4,1,2,8,7,6,5]=>2
[5,3,2,8,1,7,6,4]=>1
[6,3,2,8,7,1,5,4]=>2
[7,3,2,8,6,5,1,4]=>2
[8,4,7,2,6,5,3,1]=>2
[7,4,8,2,6,5,1,3]=>2
[6,4,8,2,7,1,5,3]=>1
[5,4,8,2,1,7,6,3]=>2
[4,5,8,1,2,7,6,3]=>2
[3,5,1,8,2,7,6,4]=>2
[2,1,5,8,3,7,6,4]=>2
[2,1,6,8,7,3,5,4]=>2
[3,6,1,8,7,2,5,4]=>2
[4,6,8,1,7,2,5,3]=>2
[5,6,8,7,1,2,4,3]=>2
[6,5,8,7,2,1,4,3]=>1
[7,5,8,6,2,4,1,3]=>2
[8,5,7,6,2,4,3,1]=>2
[5,7,8,6,1,4,2,3]=>2
[4,7,8,1,6,5,2,3]=>2
[3,7,1,8,6,5,2,4]=>2
[2,1,7,8,6,5,3,4]=>2
[3,8,1,7,6,5,4,2]=>2
[4,8,7,1,6,5,3,2]=>2
[5,8,7,6,1,4,3,2]=>2
[6,8,7,5,4,1,3,2]=>2
[4,2,5,1,3,6,7,8]=>2
[5,2,6,7,1,3,4,8]=>2
[3,2,7,8,1,4,5,6]=>4
[5,3,2,6,1,4,7,8]=>2
[7,4,3,8,1,2,5,6]=>4
[4,7,3,6,8,1,2,5]=>4
[6,7,3,4,8,1,2,5]=>2
[5,4,2,7,8,1,3,6]=>4
[6,4,7,2,5,1,3,8]=>2
[6,4,3,2,7,1,5,8]=>2
[5,4,3,2,8,1,6,7]=>4
[7,5,3,8,2,6,1,4]=>2
[8,5,4,7,2,6,1,3]=>4
[8,5,4,7,3,6,1,2]=>4
[8,1,2,7,6,3,4,5]=>4
[8,1,4,2,6,3,5,7]=>2
[8,3,1,2,4,7,5,6]=>2
[8,3,1,5,6,2,4,7]=>4
[6,3,8,1,2,7,4,5]=>2
[7,8,4,1,6,2,3,5]=>2
[8,3,4,1,6,7,2,5]=>2
[2,7,6,5,1,3,8,4]=>2
[8,3,6,5,1,7,2,4]=>2
[4,6,7,3,8,5,1,2]=>2
[3,5,2,7,1,8,6,4]=>2
[4,6,7,2,8,1,5,3]=>2
[5,6,7,8,2,1,4,3]=>2
[6,5,8,7,3,4,1,2]=>2
[3,6,7,4,5,8,1,2]=>2
[2,6,7,4,5,1,8,3]=>2
[1,6,7,4,5,2,3,8]=>1
[1,5,4,7,6,2,3,8]=>2
[2,5,4,7,6,1,8,3]=>2
[3,5,4,7,6,8,1,2]=>2
[4,5,3,7,8,6,1,2]=>2
[5,4,3,8,7,6,1,2]=>2
[6,4,8,3,7,5,1,2]=>2
[6,3,8,4,5,7,1,2]=>2
[5,3,4,8,6,7,1,2]=>2
[4,3,5,6,8,7,1,2]=>2
[3,2,5,6,1,8,7,4]=>2
[4,2,5,6,8,1,7,3]=>2
[5,2,4,8,6,1,7,3]=>2
[6,2,8,4,5,1,7,3]=>1
[7,8,2,4,5,1,6,3]=>2
[7,8,1,4,5,2,3,6]=>2
[6,1,8,4,5,2,3,7]=>2
[5,1,4,8,6,2,3,7]=>2
[4,1,3,2,8,6,5,7]=>2
[5,1,3,8,2,6,4,7]=>2
[6,1,8,3,2,5,4,7]=>2
[7,8,1,3,2,5,4,6]=>2
[7,8,2,3,1,5,6,4]=>2
[6,2,8,3,1,5,7,4]=>2
[5,2,3,8,1,6,7,4]=>1
[6,3,8,2,1,7,5,4]=>2
[7,8,3,2,1,6,5,4]=>2
[7,8,4,2,6,1,5,3]=>2
[5,4,2,8,7,1,6,3]=>2
[4,5,2,7,8,1,6,3]=>2
[2,5,3,7,1,6,8,4]=>2
[1,5,3,7,2,6,4,8]=>1
[1,6,7,3,2,5,4,8]=>2
[2,6,7,3,1,5,8,4]=>2
[3,6,7,2,1,8,5,4]=>2
[7,8,5,6,2,1,4,3]=>2
[6,5,8,7,1,2,3,4]=>2
[5,4,1,8,7,2,3,6]=>2
[6,4,8,1,7,2,3,5]=>2
[7,8,3,1,2,6,4,5]=>2
[5,3,1,8,2,7,4,6]=>2
[4,3,1,2,8,7,5,6]=>2
[4,2,1,3,8,5,7,6]=>2
[5,2,1,8,3,4,7,6]=>2
[6,2,8,1,3,4,7,5]=>2
[7,8,2,1,3,4,6,5]=>2
[6,3,1,5,2,4,8,7]=>4
[2,1,8,5,3,7,4,6]=>4
[8,2,6,1,4,3,7,5]=>2
[4,7,1,5,8,3,2,6]=>2
[8,6,1,3,4,2,5,7]=>4
[8,1,2,4,5,6,3,7]=>4
[8,2,5,1,3,6,4,7]=>4
[4,1,5,3,7,2,8,6]=>4
[5,2,7,1,3,8,4,6]=>4
[5,3,1,7,8,2,4,6]=>4
[1,7,3,4,2,5,8,6]=>4
[4,7,2,1,3,5,8,6]=>4
[4,5,2,3,7,6,1,8]=>4
[6,4,3,7,2,5,1,8]=>4
[8,4,3,6,5,1,2,7]=>4
[1,5,6,3,4,8,7,2]=>4
[4,6,2,7,3,5,1,8]=>4
[3,2,6,7,4,5,1,8]=>4
[4,7,2,6,5,3,1,8]=>4
[5,7,6,2,4,3,1,8]=>4
[1,7,5,4,8,3,6,2]=>4
[8,7,5,4,1,3,2,6]=>4
[6,8,5,4,2,1,3,7]=>4
[5,8,6,2,4,1,3,7]=>4
[4,8,2,6,5,1,3,7]=>4
[3,2,8,6,5,1,4,7]=>4
[4,1,2,6,5,8,7,3]=>4
[5,1,6,2,4,8,7,3]=>4
[6,1,5,4,2,8,7,3]=>4
[7,1,5,4,8,2,6,3]=>4
[8,1,5,4,7,6,2,3]=>4
[1,8,6,7,4,5,3,2]=>4
[8,1,6,7,4,5,2,3]=>4
[7,1,6,8,4,2,5,3]=>4
[6,1,7,8,2,4,5,3]=>4
[5,1,7,2,8,4,6,3]=>4
[4,1,2,7,8,5,6,3]=>4
[3,2,1,7,8,5,6,4]=>4
[3,2,8,7,1,5,4,6]=>4
[4,8,2,7,1,5,3,6]=>4
[5,8,7,2,1,4,3,6]=>4
[6,8,7,1,2,4,3,5]=>4
[7,8,6,1,4,2,3,5]=>2
[8,7,6,1,4,3,2,5]=>2
[1,7,6,8,4,3,5,2]=>4
[1,6,7,8,3,4,5,2]=>4
[8,6,7,1,3,4,2,5]=>2
[7,6,8,1,3,2,4,5]=>4
[5,7,8,2,1,3,4,6]=>4
[4,7,2,8,1,3,5,6]=>4
[3,2,6,8,4,1,5,7]=>4
[4,6,2,8,3,1,5,7]=>4
[5,6,8,2,3,1,4,7]=>4
[6,5,8,3,2,1,4,7]=>4
[7,5,8,3,1,2,4,6]=>4
[8,5,7,3,1,4,2,6]=>4
[1,5,7,3,8,4,6,2]=>4
[1,4,3,7,8,5,6,2]=>4
[8,4,3,7,1,5,2,6]=>4
[6,4,3,8,2,1,5,7]=>4
[4,5,2,3,8,1,6,7]=>4
[3,2,5,4,8,1,6,7]=>4
[4,5,2,3,1,8,7,6]=>4
[6,4,3,1,2,8,7,5]=>4
[7,4,3,1,8,2,6,5]=>4
[8,4,3,1,7,6,2,5]=>2
[1,5,8,3,7,6,4,2]=>4
[8,5,1,3,7,6,2,4]=>4
[7,5,1,3,8,2,6,4]=>4
[6,5,1,3,2,8,7,4]=>4
[5,6,1,2,3,8,7,4]=>4
[4,6,2,1,3,8,7,5]=>4
[3,2,6,1,4,8,7,5]=>2
[3,2,7,1,8,4,6,5]=>4
[4,7,2,1,8,3,6,5]=>2
[5,7,1,2,8,3,6,4]=>4
[6,7,1,8,2,3,5,4]=>4
[7,6,1,8,3,2,5,4]=>4
[8,6,1,7,3,5,2,4]=>4
[1,6,8,7,3,5,4,2]=>4
[1,7,8,6,5,3,4,2]=>4
[8,7,1,6,5,3,2,4]=>4
[7,8,1,6,5,2,3,4]=>4
[6,8,1,7,2,5,3,4]=>4
[5,8,1,2,7,6,3,4]=>4
[4,8,2,1,7,6,3,5]=>4
[3,2,8,1,7,6,4,5]=>4
[4,1,2,8,7,6,5,3]=>4
[5,1,8,2,7,6,4,3]=>4
[6,1,8,7,2,5,4,3]=>4
[7,1,8,6,5,2,4,3]=>4
[8,1,7,6,5,4,2,3]=>4
[1,4,3,8,7,5,6,2]=>4
[4,1,2,8,7,5,6,3]=>4
[3,2,5,1,6,4,8,7]=>4
[3,2,5,4,7,1,8,6]=>4
[4,2,5,3,7,6,8,1]=>4
[4,2,5,3,7,1,8,6]=>4
[4,2,5,3,6,1,8,7]=>4
[4,2,5,1,6,3,8,7]=>4
[3,1,5,4,6,2,8,7]=>4
[4,1,5,3,6,2,8,7]=>4
[4,3,5,1,6,2,8,7]=>4
[4,3,5,2,7,1,8,6]=>4
[4,3,6,2,7,5,8,1]=>4
[4,3,6,2,7,1,8,5]=>4
[4,3,6,1,7,2,8,5]=>4
[4,3,5,1,7,2,8,6]=>4
[3,1,5,4,7,2,8,6]=>4
[2,1,5,4,7,3,8,6]=>4
[3,1,5,4,7,6,8,2]=>4
[4,1,5,3,7,6,8,2]=>4
[4,3,5,1,7,6,8,2]=>4
[4,3,6,1,7,5,8,2]=>4
[4,3,6,5,7,1,8,2]=>4
[5,3,6,4,7,2,8,1]=>4
[5,3,6,4,7,1,8,2]=>4
[5,3,6,1,7,4,8,2]=>4
[5,1,6,3,7,4,8,2]=>4
[4,1,6,3,7,5,8,2]=>4
[3,1,6,4,7,5,8,2]=>4
[2,1,6,4,7,5,8,3]=>4
[2,1,6,4,7,3,8,5]=>4
[3,1,6,4,7,2,8,5]=>4
[4,1,6,3,7,2,8,5]=>4
[5,1,6,3,7,2,8,4]=>4
[5,3,6,1,7,2,8,4]=>4
[5,3,6,2,7,1,8,4]=>4
[5,3,6,2,7,4,8,1]=>4
[5,2,6,3,7,4,8,1]=>4
[5,2,6,3,7,1,8,4]=>4
[5,2,6,1,7,3,8,4]=>4
[4,2,5,1,7,3,8,6]=>4
[4,2,6,1,7,3,8,5]=>4
[4,2,6,3,7,1,8,5]=>4
[4,2,6,3,7,5,8,1]=>4
[3,2,6,4,7,5,8,1]=>4
[3,2,6,4,7,1,8,5]=>4
[3,2,6,1,7,4,8,5]=>4
[3,2,5,1,7,4,8,6]=>4
[3,2,4,1,7,5,8,6]=>4
[3,1,4,2,7,6,8,5]=>4
[3,2,5,1,7,6,8,4]=>4
[3,2,6,1,7,5,8,4]=>4
[3,2,6,5,7,1,8,4]=>4
[4,2,6,5,7,3,8,1]=>4
[4,2,6,5,7,1,8,3]=>4
[4,2,6,1,7,5,8,3]=>4
[4,2,5,1,7,6,8,3]=>4
[4,1,5,2,7,6,8,3]=>4
[3,1,5,2,7,6,8,4]=>4
[2,1,5,3,7,6,8,4]=>4
[2,1,6,3,7,5,8,4]=>4
[3,1,6,2,7,5,8,4]=>4
[4,1,6,2,7,5,8,3]=>4
[5,1,6,2,7,4,8,3]=>4
[5,2,6,1,7,4,8,3]=>4
[5,2,6,4,7,1,8,3]=>4
[5,2,6,4,7,3,8,1]=>4
[5,4,6,2,7,3,8,1]=>4
[5,4,6,2,7,1,8,3]=>4
[5,4,6,1,7,2,8,3]=>4
[5,1,6,4,7,2,8,3]=>4
[4,1,6,5,7,2,8,3]=>4
[3,1,6,5,7,2,8,4]=>4
[2,1,6,5,7,3,8,4]=>4
[3,1,6,5,7,4,8,2]=>4
[4,1,6,5,7,3,8,2]=>4
[5,1,6,4,7,3,8,2]=>4
[5,4,6,1,7,3,8,2]=>4
[5,4,6,3,7,1,8,2]=>4
[8,3,5,2,1,6,4,7]=>4
[8,6,3,5,2,4,1,7]=>4
[3,7,5,2,4,1,8,6]=>4
[8,3,7,5,2,4,6,1]=>4
[8,2,4,5,7,3,6,1]=>4
[2,4,5,7,3,1,8,6]=>4
[8,2,4,6,5,3,1,7]=>4
[8,2,5,4,6,1,3,7]=>4
[8,6,3,5,1,4,2,7]=>4
[8,6,1,4,5,3,2,7]=>4
[8,1,5,6,4,3,2,7]=>2
[5,7,4,3,2,1,8,6]=>4
[8,5,7,4,3,2,6,1]=>4
[4,6,8,3,2,7,5,1]=>4
[4,7,6,3,2,8,1,5]=>4
[1,4,6,7,3,2,8,5]=>4
[5,4,7,3,1,8,2,6]=>4
[1,7,4,5,3,2,8,6]=>4
[3,7,5,1,4,2,8,6]=>4
[5,7,4,2,1,3,8,6]=>4
[8,5,7,4,2,1,6,3]=>4
[8,3,7,5,1,4,6,2]=>4
[8,4,1,7,5,3,6,2]=>4
[4,6,3,8,7,1,5,2]=>4
[1,7,4,8,6,3,5,2]=>4
[8,4,7,6,3,5,2,1]=>4
[3,6,5,8,7,4,1,2]=>4
[3,1,5,8,6,7,4,2]=>4
[4,8,1,6,7,3,5,2]=>4
[3,6,4,1,8,7,5,2]=>4
[8,2,6,1,4,7,5,3]=>4
[2,7,6,8,1,4,3,5]=>4
[3,7,1,6,4,8,2,5]=>4
[1,7,3,5,6,8,2,4]=>4
[1,3,6,7,5,8,2,4]=>4
[3,7,6,5,8,2,1,4]=>4
[3,6,8,5,7,2,4,1]=>4
[2,3,5,7,6,8,1,4]=>4
[2,1,6,5,7,8,3,4]=>4
[4,2,7,6,8,3,1,5]=>4
[4,2,6,8,7,3,5,1]=>4
[3,8,2,4,6,7,5,1]=>4
[3,7,2,6,4,8,1,5]=>4
[3,2,6,1,4,7,8,5]=>4
[5,3,7,2,1,8,4,6]=>4
[4,7,3,2,1,5,8,6]=>4
[8,7,6,1,3,4,2,5]=>2
[8,5,7,3,2,1,6,4]=>4
[8,3,6,7,2,1,5,4]=>4
[3,7,8,6,2,1,5,4]=>4
[8,7,6,3,5,2,4,1]=>4
[2,7,4,8,1,6,5,3]=>4
[4,6,8,2,1,7,5,3]=>4
[8,4,1,5,7,2,6,3]=>4
[8,5,3,7,1,6,2,4]=>2
[8,5,7,2,1,3,6,4]=>4
[8,2,6,7,1,3,5,4]=>4
[8,3,6,1,7,5,2,4]=>4
[4,6,1,8,7,2,5,3]=>4
[8,1,2,5,6,7,4,3]=>4
[8,2,6,5,7,4,1,3]=>4
[2,1,7,8,5,6,4,3]=>4
[8,2,5,7,6,4,3,1]=>4
[2,7,6,8,5,4,1,3]=>4
[1,7,2,5,8,6,4,3]=>4
[1,7,4,8,2,6,5,3]=>4
[3,7,8,1,6,5,2,4]=>4
[2,7,8,6,1,3,5,4]=>4
[8,7,6,3,5,1,4,2]=>4
[8,4,7,6,5,1,3,2]=>4
[8,7,1,5,6,4,3,2]=>4
[8,1,6,7,5,4,3,2]=>4
[5,4,3,6,1,2,8,7]=>4
[2,7,6,4,5,8,1,3]=>4
[5,7,3,6,1,8,2,4]=>4
[2,1,7,6,5,8,3,4]=>4
[6,4,3,5,8,1,7,2]=>4
[7,3,5,4,8,6,1,2]=>4
[5,4,3,2,7,1,8,6]=>4
[4,3,6,2,8,7,5,1]=>2
[4,3,7,6,2,1,8,5]=>4
[6,4,3,1,7,2,8,5]=>4
[4,3,7,1,8,6,5,2]=>4
[5,3,8,7,6,4,2,1]=>4
[7,5,3,1,8,6,4,2]=>2
[1,8,6,5,3,7,4,2]=>4
[6,1,7,5,3,2,8,4]=>4
[7,6,5,3,2,1,8,4]=>4
[6,5,3,2,8,7,4,1]=>4
[5,2,6,3,8,7,4,1]=>4
[5,2,7,6,3,1,8,4]=>4
[6,5,2,1,7,3,8,4]=>4
[5,2,7,1,8,6,4,3]=>4
[6,2,8,7,5,4,3,1]=>4
[7,6,2,1,8,5,4,3]=>4
[6,1,7,2,8,5,4,3]=>4
[7,1,8,6,5,4,3,2]=>4
[4,5,2,6,3,1,8,7]=>4
[6,5,2,1,4,3,8,7]=>4
[6,5,2,7,4,8,3,1]=>4
[8,5,2,7,4,1,6,3]=>2
[8,3,7,5,2,1,6,4]=>4
[6,3,7,5,2,8,4,1]=>4
[3,1,6,5,4,2,8,7]=>4
[5,6,3,2,4,1,8,7]=>4
[3,6,2,4,1,5,8,7]=>4
[2,6,1,3,5,4,8,7]=>4
[6,7,2,3,4,8,5,1]=>4
[8,7,2,3,4,1,6,5]=>4
[5,1,7,3,8,4,6,2]=>4
[2,5,7,3,8,6,4,1]=>4
[7,6,1,3,5,8,4,2]=>4
[3,6,7,4,1,8,5,2]=>4
[5,6,3,7,4,8,1,2]=>4
[2,1,6,7,4,8,5,3]=>4
[2,1,8,7,4,3,6,5]=>4
[5,8,3,7,4,2,6,1]=>4
[3,8,7,4,1,2,6,5]=>4
[7,8,1,3,5,2,6,4]=>4
[5,8,7,3,2,6,1,4]=>4
[2,8,6,3,1,5,7,4]=>4
[8,1,6,3,2,5,4,7]=>2
[2,8,4,1,6,3,7,5]=>4
[4,8,1,2,7,6,3,5]=>4
[3,8,4,2,5,7,1,6]=>4
[6,8,3,5,2,7,4,1]=>4
[2,1,5,3,8,7,6,4]=>4
[6,5,3,2,8,7,1,4]=>4
[7,5,2,4,8,1,6,3]=>4
[3,4,2,8,5,7,6,1]=>4
[2,4,1,8,7,6,5,3]=>4
[8,4,2,1,7,5,3,6]=>4
[4,3,1,8,6,7,5,2]=>4
[3,1,4,8,6,5,7,2]=>4
[7,1,6,5,4,8,2,3]=>4
[3,7,5,6,8,4,2,1]=>4
[5,7,1,6,8,2,4,3]=>4
[8,6,2,5,1,7,4,3]=>4
[5,6,2,1,8,7,3,4]=>1
[4,6,2,5,8,3,7,1]=>4
[7,5,2,6,3,8,1,4]=>4
[4,1,2,3,6,8,7,5]=>4
[2,4,3,1,8,5,6,7]=>4
[7,5,2,8,3,4,6,1]=>4
[5,6,2,8,4,3,1,7]=>4
[4,7,2,8,1,5,3,6]=>4
[8,7,2,1,4,5,6,3]=>4
[3,6,8,7,1,5,4,2]=>4
[5,7,8,6,3,4,1,2]=>4
[7,1,8,5,4,3,6,2]=>4
[2,7,8,4,5,3,6,1]=>4
[5,7,3,8,1,4,6,2]=>4
[2,1,7,8,5,4,6,3]=>4
[2,1,5,8,4,6,3,7]=>4
[6,5,3,8,4,1,2,7]=>4
[7,5,8,4,3,6,2,1]=>4
[2,4,8,3,5,6,1,7]=>4
[4,1,8,3,6,5,2,7]=>4
[3,4,8,1,7,2,5,6]=>4
[8,4,1,3,7,2,6,5]=>4
[3,1,8,2,4,7,6,5]=>4
[2,3,8,1,4,6,7,5]=>4
[4,3,8,2,5,1,7,6]=>4
[6,3,8,4,2,5,7,1]=>4
[7,4,3,8,2,5,1,6]=>4
[2,1,4,8,3,5,7,6]=>4
[6,8,2,4,3,5,1,7]=>4
[4,8,2,3,5,1,6,7]=>4
[3,8,2,1,4,6,5,7]=>4
[2,8,1,3,4,5,7,6]=>4
[7,1,6,8,4,3,2,5]=>4
[7,1,6,5,8,3,2,4]=>4
[3,7,6,1,4,8,2,5]=>2
[2,7,8,4,1,6,5,3]=>4
[3,6,4,5,7,2,8,1]=>4
[1,8,2,7,3,4,5,6]=>4
[3,2,1,5,8,4,6,7]=>4
[5,4,3,2,1,8,6,7]=>4
[1,8,2,4,3,5,6,7]=>4
[1,7,2,4,3,5,6,8]=>4
[1,6,2,4,3,5,7,8]=>4
[1,5,2,4,3,6,7,8]=>4
[1,6,2,5,3,4,7,8]=>4
[1,7,2,5,3,4,6,8]=>2
[1,8,2,5,3,4,6,7]=>4
[1,8,2,6,3,4,5,7]=>4
[1,7,2,6,3,4,5,8]=>4
[1,8,2,7,3,5,4,6]=>4
[1,7,2,8,3,5,4,6]=>4
[1,6,2,8,3,5,4,7]=>4
[1,5,2,8,3,6,4,7]=>4
[1,4,2,8,3,6,5,7]=>4
[1,3,2,8,4,6,5,7]=>4
[1,2,3,8,4,6,5,7]=>4
[1,2,3,7,4,6,5,8]=>4
[1,3,2,7,4,6,5,8]=>4
[1,4,2,7,3,6,5,8]=>4
[1,5,2,7,3,6,4,8]=>4
[1,6,2,7,3,5,4,8]=>4
[1,7,2,6,3,5,4,8]=>4
[1,8,2,6,3,5,4,7]=>4
[1,8,2,5,3,6,4,7]=>4
[1,7,2,5,3,6,4,8]=>4
[1,6,2,5,3,7,4,8]=>4
[1,5,2,4,3,7,6,8]=>4
[1,6,2,4,3,7,5,8]=>4
[1,7,2,4,3,6,5,8]=>4
[1,8,2,4,3,6,5,7]=>4
[1,8,2,3,4,6,5,7]=>4
[1,7,2,3,4,6,5,8]=>4
[1,8,2,3,4,7,5,6]=>4
[1,8,2,4,3,7,5,6]=>4
[1,7,2,4,3,8,5,6]=>4
[1,6,2,4,3,8,5,7]=>4
[1,5,2,4,3,8,6,7]=>4
[1,6,2,5,3,8,4,7]=>4
[1,7,2,5,3,8,4,6]=>4
[1,8,2,5,3,7,4,6]=>4
[1,8,2,6,3,7,4,5]=>4
[1,7,2,6,3,8,4,5]=>4
[1,2,3,8,4,7,5,6]=>4
[1,3,2,8,4,7,5,6]=>4
[1,4,2,8,3,7,5,6]=>4
[1,5,2,8,3,7,4,6]=>4
[1,6,2,8,3,7,4,5]=>4
[1,7,2,8,3,6,4,5]=>4
[1,8,2,7,3,6,4,5]=>4
[6,7,8,1,4,3,2,5]=>2
[2,8,4,1,6,7,5,3]=>4
[4,8,5,7,1,6,2,3]=>4
[8,7,6,5,2,1,4,3]=>2
[8,3,1,5,4,7,2,6]=>2
[8,7,6,5,1,4,2,3]=>4
[7,5,1,3,8,4,2,6]=>4
[7,6,1,4,8,3,2,5]=>4
[7,1,3,5,8,2,4,6]=>4
[7,5,3,6,4,2,8,1]=>4
[8,2,6,3,4,7,5,1]=>4
[7,2,6,3,5,4,8,1]=>4
[6,2,7,4,3,5,8,1]=>4
[3,7,6,4,5,2,8,1]=>4
[2,7,6,5,3,4,8,1]=>2
[8,6,5,4,2,7,3,1]=>4
[6,5,8,4,2,7,3,1]=>4
[1,8,6,3,7,5,2,4]=>4
[8,7,5,2,6,4,3,1]=>4
[8,7,1,6,2,5,4,3]=>4
[1,7,2,8,5,3,4,6]=>4
[7,6,1,8,4,3,2,5]=>4
[8,6,1,7,4,2,5,3]=>4
[8,1,2,7,3,4,6,5]=>4
[7,1,2,8,3,5,4,6]=>4
[8,2,6,1,7,3,5,4]=>4
[4,7,5,6,8,3,2,1]=>2
[8,6,4,7,5,3,2,1]=>4
[5,4,8,1,7,2,6,3]=>4
[2,3,8,7,4,5,6,1]=>4
[7,2,8,6,4,3,5,1]=>4
[8,2,7,6,3,5,4,1]=>4
[8,1,7,6,5,2,4,3]=>4
[7,1,8,6,5,3,2,4]=>4
[1,2,8,7,6,3,4,5]=>4
[3,8,7,6,4,5,2,1]=>4
[2,8,7,6,5,3,4,1]=>4
[1,8,7,6,5,4,2,3]=>4
[3,8,6,7,1,5,2,4]=>4
[5,4,7,1,3,8,2,6]=>4
[5,6,2,1,4,8,3,7]=>4
[2,1,8,4,7,5,6,3]=>4
[4,1,3,2,8,5,6,7]=>4
[3,2,1,4,8,5,6,7]=>4
[1,8,4,2,5,3,6,7]=>4
[8,1,5,3,2,4,6,7]=>4
[3,8,1,5,2,4,6,7]=>4
[1,6,7,2,8,4,3,5]=>4
[6,7,1,4,2,8,3,5]=>4
[6,3,7,1,4,8,2,5]=>4
[3,7,8,1,5,2,4,6]=>4
[7,1,2,8,5,3,4,6]=>4
[1,7,2,8,4,5,3,6]=>4
[1,2,7,5,8,3,4,6]=>4
[2,8,1,7,4,3,6,5]=>4
[4,2,6,5,8,3,7,1]=>2
[5,2,4,7,3,6,8,1]=>4
[5,1,2,4,8,3,6,7]=>4
[4,3,6,1,5,8,2,7]=>4
[2,6,1,4,5,8,3,7]=>2
[2,5,3,4,1,8,6,7]=>4
[4,3,5,2,1,8,6,7]=>4
[3,1,6,7,5,8,2,4]=>4
[2,8,1,7,5,6,3,4]=>4
[5,3,6,8,4,7,2,1]=>2
[3,7,2,5,4,8,6,1]=>2
[8,4,2,5,7,3,6,1]=>2
[4,7,2,5,8,3,6,1]=>2
[5,2,6,8,4,3,7,1]=>2
[3,1,6,5,4,8,2,7]=>2
[4,1,6,5,8,3,2,7]=>2
[5,1,6,8,4,3,2,7]=>2
[8,5,4,7,6,3,2,1]=>2
[5,7,1,8,4,3,2,6]=>2
[2,7,1,5,4,3,8,6]=>2
[8,2,1,5,4,3,7,6]=>2
[8,4,1,5,7,3,2,6]=>2
[8,5,6,7,1,3,2,4]=>2
[8,4,6,1,7,3,2,5]=>2
[8,3,6,1,4,7,2,5]=>2
[2,7,6,1,4,3,8,5]=>2
[6,7,8,5,1,3,2,4]=>2
[5,7,6,8,2,3,4,1]=>2
[5,7,2,8,4,3,6,1]=>2
[6,7,8,2,4,3,5,1]=>2
[4,7,6,2,8,3,5,1]=>2
[8,3,6,2,4,7,5,1]=>2
[3,7,6,2,4,8,5,1]=>2
[5,7,3,8,4,6,2,1]=>2
[4,7,3,5,8,6,2,1]=>2
[8,7,2,1,4,3,6,5]=>2
[8,7,3,1,4,6,2,5]=>2
[8,7,6,3,2,5,4,1]=>2
[8,7,3,5,1,6,2,4]=>2
[8,7,2,5,1,3,6,4]=>2
[8,2,6,5,1,3,7,4]=>2
[8,4,6,5,7,1,2,3]=>2
[5,7,6,8,4,1,2,3]=>2
[4,7,6,5,8,1,2,3]=>2
[3,7,6,5,1,8,2,4]=>2
[2,6,5,7,3,4,8,1]=>4
[1,6,4,7,5,8,2,3]=>4
[8,5,3,6,2,7,4,1]=>4
[1,3,7,4,6,8,2,5]=>4
[4,7,5,6,3,2,8,1]=>4
[1,7,6,5,4,8,2,3]=>4
[8,1,6,5,7,2,4,3]=>4
[1,2,7,6,8,3,4,5]=>4
[6,1,7,5,3,8,2,4]=>4
[2,1,7,5,6,8,3,4]=>4
[5,4,1,7,6,8,2,3]=>4
[4,8,5,6,2,7,3,1]=>4
[3,8,6,4,2,7,5,1]=>4
[7,8,5,2,4,6,3,1]=>4
[2,8,6,3,7,4,5,1]=>4
[7,8,1,6,2,4,5,3]=>4
[6,8,1,4,7,2,5,3]=>4
[3,8,4,1,7,2,6,5]=>4
[5,4,7,1,8,3,2,6]=>4
[3,7,4,1,8,5,2,6]=>2
[6,7,1,4,8,3,2,5]=>4
[2,7,1,8,4,5,3,6]=>4
[6,1,2,8,4,3,5,7]=>4
[6,5,1,4,3,8,2,7]=>4
[1,6,2,5,8,3,4,7]=>4
[8,5,1,3,7,2,6,4]=>4
[8,4,2,1,7,3,6,5]=>2
[7,4,2,1,8,5,3,6]=>4
[1,5,4,2,8,3,6,7]=>4
[6,4,3,1,5,8,2,7]=>4
[3,7,6,8,4,5,2,1]=>4
[2,7,6,8,5,3,4,1]=>4
[1,7,6,8,5,4,2,3]=>4
[1,4,8,6,7,5,2,3]=>4
[2,4,8,6,7,3,5,1]=>4
[7,3,8,5,4,6,2,1]=>4
[3,4,8,5,6,7,2,1]=>4
[6,3,5,8,4,7,2,1]=>4
[5,4,3,8,6,7,2,1]=>4
[5,4,2,8,7,3,6,1]=>2
[6,2,5,8,7,3,4,1]=>4
[3,2,8,5,7,4,6,1]=>4
[1,3,8,7,5,6,2,4]=>4
[2,1,8,7,4,6,3,5]=>4
[3,1,8,5,7,6,2,4]=>4
[6,1,5,8,7,4,2,3]=>4
[5,4,1,8,7,6,2,3]=>4
[5,8,6,7,4,3,2,1]=>4
[4,8,7,5,6,3,2,1]=>4
[2,8,3,1,5,4,6,7]=>4
[2,5,3,4,7,1,8,6]=>4
[2,4,8,3,5,7,6,1]=>4
[4,2,5,3,1,8,6,7]=>4
[4,2,1,8,5,3,6,7]=>4
[5,4,1,3,8,2,6,7]=>4
[5,1,4,8,3,2,6,7]=>4
[1,5,8,4,3,2,6,7]=>4
[1,8,5,4,3,2,6,7]=>4
[1,7,4,3,8,5,2,6]=>4
[1,5,7,3,8,4,2,6]=>4
[5,1,4,7,8,3,2,6]=>4
[4,8,1,5,7,3,6,2]=>4
[8,1,5,3,7,4,6,2]=>4
[3,8,4,7,6,5,2,1]=>4
[1,6,8,5,3,7,4,2]=>4
[6,8,1,7,4,3,5,2]=>4
[6,4,8,1,7,3,5,2]=>4
[6,4,8,7,1,5,2,3]=>4
[7,6,4,1,3,8,2,5]=>4
[1,7,5,6,3,2,8,4]=>4
[4,2,1,7,8,5,3,6]=>4
[2,7,4,6,3,1,8,5]=>4
[2,6,8,4,3,7,5,1]=>4
[6,2,4,8,3,7,5,1]=>4
[7,2,6,3,4,1,8,5]=>4
[2,6,7,3,1,4,8,5]=>4
[2,7,1,8,3,5,4,6]=>4
[2,1,7,3,5,8,4,6]=>4
[8,7,1,3,6,2,4,5]=>4
[8,2,1,7,3,5,6,4]=>4
[7,8,2,6,3,1,5,4]=>4
[8,7,2,6,3,5,4,1]=>4
[1,2,8,7,4,5,6,3]=>4
[8,3,7,1,5,6,2,4]=>4
[8,6,1,2,7,5,3,4]=>4
[8,1,6,2,7,4,5,3]=>4
[1,8,5,2,6,7,4,3]=>4
[5,2,1,8,6,7,4,3]=>4
[2,8,5,7,6,4,3,1]=>4
[1,7,8,5,2,6,4,3]=>4
[7,8,1,6,4,2,5,3]=>4
[7,8,6,1,5,3,2,4]=>4
[7,3,8,6,1,5,2,4]=>4
[8,7,6,1,5,3,4,2]=>4
[8,7,1,6,4,5,3,2]=>4
[8,1,7,5,6,4,3,2]=>4
[1,8,6,7,5,4,3,2]=>4
[9,1,2,3,4,5,6,7,8]=>2
[8,1,2,3,4,5,6,9,7]=>4
[2,9,1,3,4,5,6,7,8]=>4
[9,3,1,2,4,5,6,7,8]=>4
[8,9,1,2,3,4,5,6,7]=>2
[9,7,8,1,2,3,4,5,6]=>2
[2,3,4,5,6,7,9,1,8]=>4
[2,3,4,5,6,7,8,9,1]=>2
[2,3,4,5,6,7,8,1,9]=>4
[2,3,4,5,6,7,1,8,9]=>4
[1,2,3,4,5,6,7,9,8]=>2
[2,1,3,4,5,6,7,8,9]=>2
[1,8,2,3,4,5,6,9,7]=>4
[7,1,2,3,4,5,6,9,8]=>4
[2,1,9,3,4,5,6,7,8]=>4
[2,8,1,3,4,5,6,7,9]=>4
[1,2,3,4,5,6,7,8,9]=>1
[3,2,4,5,6,7,8,9,1]=>4
[9,8,7,6,5,4,3,2,1]=>1
[8,7,6,5,4,3,2,1,9]=>2
[1,9,8,7,6,5,4,3,2]=>2
[8,7,6,4,5,3,2,1,9]=>2
[1,9,8,7,5,6,4,3,2]=>2
[8,7,5,4,6,3,2,1,9]=>4
[8,7,4,6,5,3,2,1,9]=>4
[1,9,8,6,5,7,4,3,2]=>4
[1,9,8,5,7,6,4,3,2]=>4
[9,2,1,3,4,5,6,7,8]=>4
[9,2,3,1,4,5,6,7,8]=>4
[4,2,3,5,6,7,8,9,1]=>4
[3,4,2,5,6,7,8,9,1]=>4
[9,8,1,2,3,4,5,6,7]=>2
[7,8,9,1,2,3,4,5,6]=>2
[9,8,7,1,2,3,4,5,6]=>2
[6,7,8,9,1,2,3,4,5]=>2
[9,6,7,8,1,2,3,4,5]=>2
[8,9,6,7,1,2,3,4,5]=>2
[9,8,6,7,1,2,3,4,5]=>2
[9,8,7,6,1,2,3,4,5]=>2
[9,5,6,7,8,1,2,3,4]=>2
[8,9,5,6,7,1,2,3,4]=>2
[9,8,5,6,7,1,2,3,4]=>2
[9,7,8,5,6,1,2,3,4]=>2
[9,8,7,5,6,1,2,3,4]=>2
[9,8,7,6,5,1,2,3,4]=>2
[7,8,9,4,5,6,1,2,3]=>1
[9,7,8,4,5,6,1,2,3]=>2
[9,8,7,4,5,6,1,2,3]=>2
[8,9,6,7,4,5,1,2,3]=>2
[9,8,6,7,4,5,1,2,3]=>2
[9,8,7,6,4,5,1,2,3]=>2
[9,8,7,6,5,4,1,2,3]=>2
[9,7,8,5,6,3,4,1,2]=>2
[9,8,7,5,6,3,4,1,2]=>2
[9,8,7,6,5,3,4,1,2]=>2
[9,8,7,6,5,4,3,1,2]=>2
[7,8,6,5,4,3,2,1,9]=>4
[1,8,9,7,6,5,4,3,2]=>4
[7,6,8,5,4,3,2,1,9]=>4
[6,8,7,5,4,3,2,1,9]=>4
[1,8,7,9,6,5,4,3,2]=>4
[1,7,9,8,6,5,4,3,2]=>4
[8,1,2,3,4,5,6,7,9]=>4
[1,9,2,3,4,5,6,7,8]=>4
[7,8,1,2,3,4,5,6,9]=>4
[1,8,9,2,3,4,5,6,7]=>4
[7,1,8,2,3,4,5,6,9]=>4
[6,8,1,2,3,4,5,7,9]=>4
[1,8,2,9,3,4,5,6,7]=>4
[1,7,9,2,3,4,5,6,8]=>4
[7,1,2,3,4,5,6,8,9]=>4
[3,4,1,2,5,6,7,8,9]=>2
[3,2,1,4,5,6,7,8,9]=>2
[4,5,6,1,2,3,7,8,9]=>2
[4,2,5,1,3,6,7,8,9]=>2
[4,3,2,1,5,6,7,8,9]=>2
[5,6,7,8,1,2,3,4,9]=>2
[5,2,6,7,1,3,4,8,9]=>2
[5,6,3,4,1,2,7,8,9]=>2
[5,3,2,6,1,4,7,8,9]=>2
[5,4,3,2,1,6,7,8,9]=>2
[6,2,7,8,9,1,3,4,5]=>2
[6,7,3,4,8,1,2,5,9]=>2
[6,3,2,7,8,1,4,5,9]=>2
[6,4,7,2,5,1,3,8,9]=>2
[6,4,3,2,7,1,5,8,9]=>2
[6,5,4,3,2,1,7,8,9]=>2
[7,4,8,2,5,9,1,3,6]=>2
[7,4,3,2,8,9,1,5,6]=>2
[7,8,5,6,3,4,1,2,9]=>2
[7,5,3,8,2,6,1,4,9]=>2
[7,5,4,3,2,8,1,6,9]=>2
[7,6,5,4,3,2,1,8,9]=>2
[8,6,9,4,7,2,5,1,3]=>2
[8,6,4,3,9,2,7,1,5]=>2
[8,6,5,4,3,2,9,1,7]=>2
[2,1,4,3,6,5,8,7,10,9]=>1
[4,3,2,1,6,5,8,7,10,9]=>2
[6,3,2,5,4,1,8,7,10,9]=>2
[8,3,2,5,4,7,6,1,10,9]=>2
[10,3,2,5,4,7,6,9,8,1]=>1
[2,1,6,5,4,3,8,7,10,9]=>2
[6,5,4,3,2,1,8,7,10,9]=>2
[8,5,4,3,2,7,6,1,10,9]=>2
[10,5,4,3,2,7,6,9,8,1]=>2
[2,1,8,5,4,7,6,3,10,9]=>1
[8,7,4,3,6,5,2,1,10,9]=>2
[10,7,4,3,6,5,2,9,8,1]=>2
[2,1,10,5,4,7,6,9,8,3]=>2
[10,9,4,3,6,5,8,7,2,1]=>1
[8,9,5,6,3,4,10,1,2,7]=>2
[2,1,4,3,8,7,6,5,10,9]=>2
[4,3,2,1,8,7,6,5,10,9]=>2
[8,3,2,7,6,5,4,1,10,9]=>2
[10,3,2,7,6,5,4,9,8,1]=>1
[2,1,8,7,6,5,4,3,10,9]=>1
[8,7,6,5,4,3,2,1,10,9]=>2
[9,7,6,5,4,3,2,10,1,8]=>2
[10,7,6,5,4,3,2,9,8,1]=>2
[2,1,10,7,6,5,4,9,8,3]=>2
[10,9,6,5,4,3,8,7,2,1]=>2
[2,1,4,3,10,7,6,9,8,5]=>2
[4,3,2,1,10,7,6,9,8,5]=>2
[10,3,2,9,6,5,8,7,4,1]=>2
[2,1,10,9,6,5,8,7,4,3]=>2
[10,9,8,5,4,7,6,3,2,1]=>1
[6,7,8,9,10,1,2,3,4,5]=>1
[7,3,2,8,9,10,1,4,5,6]=>2
[8,5,4,3,2,9,10,1,6,7]=>2
[2,1,4,3,6,5,10,9,8,7]=>2
[4,3,2,1,6,5,10,9,8,7]=>1
[6,3,2,5,4,1,10,9,8,7]=>2
[10,3,2,5,4,9,8,7,6,1]=>2
[2,1,6,5,4,3,10,9,8,7]=>2
[6,5,4,3,2,1,10,9,8,7]=>2
[10,5,4,3,2,9,8,7,6,1]=>1
[2,1,10,5,4,9,8,7,6,3]=>2
[10,9,4,3,8,7,6,5,2,1]=>2
[9,7,5,10,3,8,2,6,1,4]=>2
[2,1,4,3,10,9,8,7,6,5]=>2
[4,3,2,1,10,9,8,7,6,5]=>2
[10,3,2,9,8,7,6,5,4,1]=>2
[2,1,10,9,8,7,6,5,4,3]=>2
[10,9,8,7,6,5,4,3,2,1]=>1
[2,3,4,5,6,7,8,9,10,1]=>2
[2,3,4,5,6,7,8,9,1,10]=>4
[10,8,9,5,6,7,1,2,3,4]=>2
[10,8,9,4,5,6,1,2,3,7]=>4
[10,7,8,5,6,9,1,2,3,4]=>4
[10,7,8,4,5,9,1,2,3,6]=>4
[10,6,7,4,5,8,1,2,3,9]=>4
[10,7,8,3,4,9,1,2,5,6]=>4
[10,6,7,3,4,8,1,2,5,9]=>4
[9,8,10,5,6,7,1,2,3,4]=>4
[9,8,10,4,5,6,1,2,3,7]=>4
[9,7,10,5,6,8,1,2,3,4]=>4
[9,7,10,4,5,8,1,2,3,6]=>4
[9,6,10,4,5,7,1,2,3,8]=>4
[9,7,10,3,4,8,1,2,5,6]=>4
[9,6,10,3,4,7,1,2,5,8]=>4
[8,7,9,5,6,10,1,2,3,4]=>4
[8,7,9,4,5,10,1,2,3,6]=>4
[8,6,9,4,5,10,1,2,3,7]=>4
[7,6,8,4,5,9,1,2,3,10]=>4
[8,7,9,3,4,10,1,2,5,6]=>4
[8,6,9,3,4,10,1,2,5,7]=>4
[7,6,8,3,4,9,1,2,5,10]=>4
[9,6,10,5,7,8,1,2,3,4]=>4
[9,6,10,4,7,8,1,2,3,5]=>4
[9,5,10,4,6,7,1,2,3,8]=>4
[9,6,10,3,7,8,1,2,4,5]=>4
[9,5,10,3,6,7,1,2,4,8]=>4
[8,6,9,5,7,10,1,2,3,4]=>4
[8,6,9,4,7,10,1,2,3,5]=>4
[8,5,9,4,6,10,1,2,3,7]=>4
[7,5,8,4,6,9,1,2,3,10]=>4
[8,6,9,3,7,10,1,2,4,5]=>4
[8,5,9,3,6,10,1,2,4,7]=>4
[7,5,8,3,6,9,1,2,4,10]=>4
[8,4,9,3,5,10,1,2,6,7]=>4
[7,4,8,3,5,9,1,2,6,10]=>4
[9,6,10,2,7,8,1,3,4,5]=>4
[9,5,10,2,6,7,1,3,4,8]=>4
[8,6,9,2,7,10,1,3,4,5]=>4
[8,5,9,2,6,10,1,3,4,7]=>4
[7,5,8,2,6,9,1,3,4,10]=>4
[8,4,9,2,5,10,1,3,6,7]=>4
[7,4,8,2,5,9,1,3,6,10]=>2
[1,2,3,4,5,6,7,8,10,9]=>2
[2,1,3,4,5,6,7,8,9,10]=>2
[9,1,2,3,4,5,6,7,10,8]=>4
[2,10,1,3,4,5,6,7,8,9]=>4
[1,2,3,4,5,6,7,8,9,10]=>1
[9,8,7,6,5,4,3,2,1,10]=>2
[10,1,2,3,4,5,6,7,8,9]=>2
[10,9,1,2,3,4,5,6,7,8]=>2
[1,10,9,8,7,6,5,4,3,2]=>2
[9,8,7,5,6,4,3,2,1,10]=>4
[1,10,9,8,6,7,5,4,3,2]=>4
[10,2,1,3,4,5,6,7,8,9]=>4
[3,2,4,5,6,7,8,9,10,1]=>4
[2,4,6,8,10,1,3,5,7,9]=>2
[2,4,6,9,10,1,3,5,7,8]=>4
[2,4,7,8,10,1,3,5,6,9]=>4
[2,4,7,9,10,1,3,5,6,8]=>4
[2,4,8,9,10,1,3,5,6,7]=>4
[2,5,6,8,10,1,3,4,7,9]=>4
[2,5,6,9,10,1,3,4,7,8]=>4
[2,5,7,8,10,1,3,4,6,9]=>2
[2,5,7,9,10,1,3,4,6,8]=>4
[2,5,8,9,10,1,3,4,6,7]=>4
[2,6,7,8,10,1,3,4,5,9]=>2
[2,6,7,9,10,1,3,4,5,8]=>4
[2,6,8,9,10,1,3,4,5,7]=>4
[2,7,8,9,10,1,3,4,5,6]=>4
[3,4,6,8,10,1,2,5,7,9]=>4
[3,4,6,9,10,1,2,5,7,8]=>2
[3,4,7,8,10,1,2,5,6,9]=>4
[3,4,7,9,10,1,2,5,6,8]=>4
[3,4,8,9,10,1,2,5,6,7]=>4
[3,5,6,8,10,1,2,4,7,9]=>4
[3,5,6,9,10,1,2,4,7,8]=>4
[3,5,7,8,10,1,2,4,6,9]=>4
[3,5,7,9,10,1,2,4,6,8]=>2
[3,5,8,9,10,1,2,4,6,7]=>4
[3,6,7,8,10,1,2,4,5,9]=>4
[3,6,7,9,10,1,2,4,5,8]=>2
[3,6,8,9,10,1,2,4,5,7]=>4
[3,7,8,9,10,1,2,4,5,6]=>4
[4,5,6,8,10,1,2,3,7,9]=>4
[4,5,6,9,10,1,2,3,7,8]=>4
[4,5,7,8,10,1,2,3,6,9]=>4
[4,5,7,9,10,1,2,3,6,8]=>4
[4,5,8,9,10,1,2,3,6,7]=>2
[4,6,7,8,10,1,2,3,5,9]=>4
[4,6,7,9,10,1,2,3,5,8]=>4
[4,6,8,9,10,1,2,3,5,7]=>2
[4,7,8,9,10,1,2,3,5,6]=>4
[5,6,7,8,10,1,2,3,4,9]=>4
[5,6,7,9,10,1,2,3,4,8]=>4
[5,6,8,9,10,1,2,3,4,7]=>4
[5,7,8,9,10,1,2,3,4,6]=>2
[9,10,1,2,3,4,5,6,7,8]=>2
[8,9,10,1,2,3,4,5,6,7]=>2
[10,8,9,1,2,3,4,5,6,7]=>2
[10,9,8,1,2,3,4,5,6,7]=>2
[7,8,9,10,1,2,3,4,5,6]=>2
[10,7,8,9,1,2,3,4,5,6]=>2
[9,10,7,8,1,2,3,4,5,6]=>2
[10,9,7,8,1,2,3,4,5,6]=>2
[10,9,8,7,1,2,3,4,5,6]=>2
[10,6,7,8,9,1,2,3,4,5]=>2
[9,10,6,7,8,1,2,3,4,5]=>2
[10,9,6,7,8,1,2,3,4,5]=>2
[10,8,9,6,7,1,2,3,4,5]=>2
[10,9,8,6,7,1,2,3,4,5]=>2
[10,9,8,7,6,1,2,3,4,5]=>2
[9,10,5,6,7,8,1,2,3,4]=>2
[10,9,5,6,7,8,1,2,3,4]=>2
[8,9,10,5,6,7,1,2,3,4]=>2
[10,9,8,5,6,7,1,2,3,4]=>2
[9,10,7,8,5,6,1,2,3,4]=>2
[10,9,7,8,5,6,1,2,3,4]=>2
[10,9,8,7,5,6,1,2,3,4]=>2
[10,9,8,7,6,5,1,2,3,4]=>2
[10,7,8,9,4,5,6,1,2,3]=>2
[9,10,7,8,4,5,6,1,2,3]=>2
[10,9,7,8,4,5,6,1,2,3]=>2
[10,9,8,7,4,5,6,1,2,3]=>2
[10,8,9,6,7,4,5,1,2,3]=>2
[10,9,8,6,7,4,5,1,2,3]=>2
[10,9,8,7,6,4,5,1,2,3]=>2
[10,9,8,7,6,5,4,1,2,3]=>2
[9,10,7,8,5,6,3,4,1,2]=>1
[10,9,7,8,5,6,3,4,1,2]=>2
[10,9,8,7,5,6,3,4,1,2]=>2
[10,9,8,7,6,5,3,4,1,2]=>2
[10,9,8,7,6,5,4,3,1,2]=>2
[8,9,7,6,5,4,3,2,1,10]=>4
[1,9,10,8,7,6,5,4,3,2]=>4
[9,1,2,3,4,5,6,7,8,10]=>4
[1,10,2,3,4,5,6,7,8,9]=>4
[8,9,1,2,3,4,5,6,7,10]=>4
[1,9,10,2,3,4,5,6,7,8]=>4
[3,4,1,2,5,6,7,8,9,10]=>2
[3,2,1,4,5,6,7,8,9,10]=>2
[4,5,6,1,2,3,7,8,9,10]=>2
[4,2,5,1,3,6,7,8,9,10]=>2
[4,3,2,1,5,6,7,8,9,10]=>2
[5,6,7,8,1,2,3,4,9,10]=>2
[5,2,6,7,1,3,4,8,9,10]=>2
[5,6,3,4,1,2,7,8,9,10]=>2
[5,3,2,6,1,4,7,8,9,10]=>2
[5,4,3,2,1,6,7,8,9,10]=>2
[6,2,7,8,9,1,3,4,5,10]=>2
[6,7,3,4,8,1,2,5,9,10]=>2
[6,3,2,7,8,1,4,5,9,10]=>2
[6,4,7,2,5,1,3,8,9,10]=>2
[6,4,3,2,7,1,5,8,9,10]=>2
[6,5,4,3,2,1,7,8,9,10]=>2
[7,8,3,4,9,10,1,2,5,6]=>2
[7,8,9,4,5,6,1,2,3,10]=>2
[7,4,3,2,8,9,1,5,6,10]=>2
[7,8,5,6,3,4,1,2,9,10]=>2
[7,5,3,8,2,6,1,4,9,10]=>2
[7,5,4,3,2,8,1,6,9,10]=>2
[7,6,5,4,3,2,1,8,9,10]=>2
[8,5,9,10,2,6,7,1,3,4]=>2
[8,5,3,9,2,6,10,1,4,7]=>2
[8,6,9,4,7,2,5,1,3,10]=>2
[8,6,4,3,9,2,7,1,5,10]=>2
[8,6,5,4,3,2,9,1,7,10]=>2
[8,7,6,5,4,3,2,1,9,10]=>2
[9,7,5,4,3,10,2,8,1,6]=>2
[1,2,3,4,5,6,7,8,9,11,10]=>2
[2,1,3,4,5,6,7,8,9,10,11]=>2
[11,1,2,3,4,5,6,7,8,9,10]=>2
[10,9,8,7,6,5,4,3,2,1,11]=>2
[1,11,10,9,8,7,6,5,4,3,2]=>2
[2,3,4,5,6,7,8,9,10,11,1]=>2
[10,1,2,3,4,5,6,7,8,9,11]=>4
[1,11,2,3,4,5,6,7,8,9,10]=>4
[2,1,4,3,6,5,8,7,10,9,12,11]=>1
[2,1,4,3,6,5,8,7,12,11,10,9]=>2
[2,1,4,3,6,5,10,9,8,7,12,11]=>2
[2,1,4,3,6,5,12,9,8,11,10,7]=>2
[2,1,4,3,6,5,12,11,10,9,8,7]=>2
[2,1,4,3,8,7,6,5,10,9,12,11]=>1
[2,1,4,3,8,7,6,5,12,11,10,9]=>2
[2,1,4,3,10,7,6,9,8,5,12,11]=>2
[2,1,4,3,12,7,6,9,8,11,10,5]=>2
[2,1,4,3,12,7,6,11,10,9,8,5]=>2
[2,1,4,3,10,9,8,7,6,5,12,11]=>2
[2,1,4,3,12,9,8,7,6,11,10,5]=>2
[2,1,4,3,12,11,8,7,10,9,6,5]=>2
[2,1,4,3,12,11,10,9,8,7,6,5]=>2
[2,1,6,5,4,3,8,7,10,9,12,11]=>2
[2,1,6,5,4,3,8,7,12,11,10,9]=>2
[2,1,6,5,4,3,10,9,8,7,12,11]=>1
[2,1,6,5,4,3,12,9,8,11,10,7]=>2
[2,1,6,5,4,3,12,11,10,9,8,7]=>2
[2,1,8,5,4,7,6,3,10,9,12,11]=>2
[2,1,8,5,4,7,6,3,12,11,10,9]=>2
[2,1,10,5,4,7,6,9,8,3,12,11]=>1
[2,1,12,5,4,7,6,9,8,11,10,3]=>2
[2,1,12,5,4,7,6,11,10,9,8,3]=>2
[2,1,10,5,4,9,8,7,6,3,12,11]=>2
[2,1,12,5,4,9,8,7,6,11,10,3]=>2
[2,1,12,5,4,11,8,7,10,9,6,3]=>2
[2,1,12,5,4,11,10,9,8,7,6,3]=>2
[2,1,8,7,6,5,4,3,10,9,12,11]=>2
[2,1,8,7,6,5,4,3,12,11,10,9]=>2
[2,1,10,7,6,5,4,9,8,3,12,11]=>2
[2,1,12,7,6,5,4,9,8,11,10,3]=>2
[2,1,12,7,6,5,4,11,10,9,8,3]=>2
[2,1,10,9,6,5,8,7,4,3,12,11]=>1
[2,1,12,9,6,5,8,7,4,11,10,3]=>2
[2,1,12,11,6,5,8,7,10,9,4,3]=>2
[2,1,12,11,6,5,10,9,8,7,4,3]=>2
[2,1,10,9,8,7,6,5,4,3,12,11]=>1
[2,1,12,9,8,7,6,5,4,11,10,3]=>2
[2,1,12,11,8,7,6,5,10,9,4,3]=>2
[2,1,12,11,10,7,6,9,8,5,4,3]=>2
[2,1,12,11,10,9,8,7,6,5,4,3]=>2
[4,3,2,1,6,5,8,7,10,9,12,11]=>2
[4,3,2,1,6,5,8,7,12,11,10,9]=>1
[4,3,2,1,6,5,10,9,8,7,12,11]=>2
[4,3,2,1,6,5,12,9,8,11,10,7]=>2
[4,3,2,1,6,5,12,11,10,9,8,7]=>2
[4,3,2,1,8,7,6,5,10,9,12,11]=>2
[4,3,2,1,8,7,6,5,12,11,10,9]=>1
[4,3,2,1,10,7,6,9,8,5,12,11]=>2
[4,3,2,1,12,7,6,9,8,11,10,5]=>2
[4,3,2,1,12,7,6,11,10,9,8,5]=>2
[4,3,2,1,10,9,8,7,6,5,12,11]=>2
[4,3,2,1,12,9,8,7,6,11,10,5]=>2
[4,3,2,1,12,11,8,7,10,9,6,5]=>2
[4,3,2,1,12,11,10,9,8,7,6,5]=>2
[6,3,2,5,4,1,8,7,10,9,12,11]=>2
[6,3,2,5,4,1,8,7,12,11,10,9]=>2
[6,3,2,5,4,1,10,9,8,7,12,11]=>2
[6,3,2,5,4,1,12,9,8,11,10,7]=>1
[6,3,2,5,4,1,12,11,10,9,8,7]=>2
[8,3,2,5,4,7,6,1,10,9,12,11]=>2
[8,3,2,5,4,7,6,1,12,11,10,9]=>2
[10,3,2,5,4,7,6,9,8,1,12,11]=>2
[12,3,2,5,4,7,6,9,8,11,10,1]=>1
[12,3,2,5,4,7,6,11,10,9,8,1]=>2
[10,3,2,5,4,9,8,7,6,1,12,11]=>2
[12,3,2,5,4,9,8,7,6,11,10,1]=>2
[12,3,2,5,4,11,8,7,10,9,6,1]=>2
[12,3,2,5,4,11,10,9,8,7,6,1]=>2
[8,3,2,7,6,5,4,1,10,9,12,11]=>2
[8,3,2,7,6,5,4,1,12,11,10,9]=>2
[10,3,2,7,6,5,4,9,8,1,12,11]=>2
[12,3,2,7,6,5,4,9,8,11,10,1]=>2
[12,3,2,7,6,5,4,11,10,9,8,1]=>2
[10,3,2,9,6,5,8,7,4,1,12,11]=>2
[12,3,2,9,6,5,8,7,4,11,10,1]=>1
[12,3,2,11,6,5,8,7,10,9,4,1]=>2
[12,3,2,11,6,5,10,9,8,7,4,1]=>2
[10,3,2,9,8,7,6,5,4,1,12,11]=>2
[12,3,2,9,8,7,6,5,4,11,10,1]=>1
[12,3,2,11,8,7,6,5,10,9,4,1]=>2
[12,3,2,11,10,7,6,9,8,5,4,1]=>2
[12,3,2,11,10,9,8,7,6,5,4,1]=>2
[6,5,4,3,2,1,8,7,10,9,12,11]=>2
[6,5,4,3,2,1,8,7,12,11,10,9]=>2
[6,5,4,3,2,1,10,9,8,7,12,11]=>2
[6,5,4,3,2,1,12,9,8,11,10,7]=>2
[6,5,4,3,2,1,12,11,10,9,8,7]=>1
[8,5,4,3,2,7,6,1,10,9,12,11]=>2
[8,5,4,3,2,7,6,1,12,11,10,9]=>2
[10,5,4,3,2,7,6,9,8,1,12,11]=>2
[12,5,4,3,2,7,6,9,8,11,10,1]=>2
[12,5,4,3,2,7,6,11,10,9,8,1]=>1
[10,5,4,3,2,9,8,7,6,1,12,11]=>2
[12,5,4,3,2,9,8,7,6,11,10,1]=>2
[12,5,4,3,2,11,8,7,10,9,6,1]=>2
[12,5,4,3,2,11,10,9,8,7,6,1]=>2
[8,7,4,3,6,5,2,1,10,9,12,11]=>2
[8,7,4,3,6,5,2,1,12,11,10,9]=>2
[10,7,4,3,6,5,2,9,8,1,12,11]=>2
[12,7,4,3,6,5,2,9,8,11,10,1]=>2
[12,7,4,3,6,5,2,11,10,9,8,1]=>2
[10,9,4,3,6,5,8,7,2,1,12,11]=>2
[12,9,4,3,6,5,8,7,2,11,10,1]=>2
[12,11,4,3,6,5,8,7,10,9,2,1]=>1
[12,11,4,3,6,5,10,9,8,7,2,1]=>2
[10,9,4,3,8,7,6,5,2,1,12,11]=>2
[12,9,4,3,8,7,6,5,2,11,10,1]=>2
[12,11,4,3,8,7,6,5,10,9,2,1]=>1
[12,11,4,3,10,7,6,9,8,5,2,1]=>2
[12,11,4,3,10,9,8,7,6,5,2,1]=>2
[8,7,6,5,4,3,2,1,10,9,12,11]=>2
[8,7,6,5,4,3,2,1,12,11,10,9]=>2
[10,7,6,5,4,3,2,9,8,1,12,11]=>2
[12,7,6,5,4,3,2,9,8,11,10,1]=>2
[12,7,6,5,4,3,2,11,10,9,8,1]=>2
[10,9,6,5,4,3,8,7,2,1,12,11]=>2
[12,9,6,5,4,3,8,7,2,11,10,1]=>2
[12,11,6,5,4,3,8,7,10,9,2,1]=>2
[12,11,6,5,4,3,10,9,8,7,2,1]=>1
[10,9,8,5,4,7,6,3,2,1,12,11]=>2
[12,9,8,5,4,7,6,3,2,11,10,1]=>2
[12,11,8,5,4,7,6,3,10,9,2,1]=>2
[12,11,10,5,4,7,6,9,8,3,2,1]=>1
[12,11,10,5,4,9,8,7,6,3,2,1]=>2
[10,9,8,7,6,5,4,3,2,1,12,11]=>2
[12,9,8,7,6,5,4,3,2,11,10,1]=>2
[12,11,8,7,6,5,4,3,10,9,2,1]=>2
[12,11,10,7,6,5,4,9,8,3,2,1]=>2
[12,11,10,9,6,5,8,7,4,3,2,1]=>1
[12,11,10,9,8,7,6,5,4,3,2,1]=>1
[2,4,6,8,10,12,1,3,5,7,9,11]=>2
[2,4,6,8,11,12,1,3,5,7,9,10]=>4
[2,4,6,9,10,12,1,3,5,7,8,11]=>4
[2,4,6,9,11,12,1,3,5,7,8,10]=>4
[2,4,6,10,11,12,1,3,5,7,8,9]=>4
[2,4,7,8,10,12,1,3,5,6,9,11]=>2
[2,4,7,8,11,12,1,3,5,6,9,10]=>4
[2,4,7,9,10,12,1,3,5,6,8,11]=>4
[2,4,7,9,11,12,1,3,5,6,8,10]=>4
[2,4,7,10,11,12,1,3,5,6,8,9]=>4
[2,4,8,9,10,12,1,3,5,6,7,11]=>4
[2,4,8,9,11,12,1,3,5,6,7,10]=>4
[2,4,8,10,11,12,1,3,5,6,7,9]=>4
[2,4,9,10,11,12,1,3,5,6,7,8]=>4
[2,5,6,8,10,12,1,3,4,7,9,11]=>4
[2,5,6,8,11,12,1,3,4,7,9,10]=>4
[2,5,6,9,10,12,1,3,4,7,8,11]=>2
[2,5,6,9,11,12,1,3,4,7,8,10]=>4
[2,5,6,10,11,12,1,3,4,7,8,9]=>4
[2,5,7,8,10,12,1,3,4,6,9,11]=>4
[2,5,7,8,11,12,1,3,4,6,9,10]=>4
[2,5,7,9,10,12,1,3,4,6,8,11]=>2
[2,5,7,9,11,12,1,3,4,6,8,10]=>4
[2,5,7,10,11,12,1,3,4,6,8,9]=>4
[2,5,8,9,10,12,1,3,4,6,7,11]=>4
[2,5,8,9,11,12,1,3,4,6,7,10]=>4
[2,5,8,10,11,12,1,3,4,6,7,9]=>4
[2,5,9,10,11,12,1,3,4,6,7,8]=>4
[2,6,7,8,10,12,1,3,4,5,9,11]=>4
[2,6,7,8,11,12,1,3,4,5,9,10]=>4
[2,6,7,9,10,12,1,3,4,5,8,11]=>4
[2,6,7,9,11,12,1,3,4,5,8,10]=>4
[2,6,7,10,11,12,1,3,4,5,8,9]=>4
[2,6,8,9,10,12,1,3,4,5,7,11]=>2
[2,6,8,9,11,12,1,3,4,5,7,10]=>4
[2,6,8,10,11,12,1,3,4,5,7,9]=>4
[2,6,9,10,11,12,1,3,4,5,7,8]=>4
[2,7,8,9,10,12,1,3,4,5,6,11]=>2
[2,7,8,9,11,12,1,3,4,5,6,10]=>4
[2,7,8,10,11,12,1,3,4,5,6,9]=>4
[2,7,9,10,11,12,1,3,4,5,6,8]=>4
[2,8,9,10,11,12,1,3,4,5,6,7]=>4
[3,4,6,8,10,12,1,2,5,7,9,11]=>4
[3,4,6,8,11,12,1,2,5,7,9,10]=>2
[3,4,6,9,10,12,1,2,5,7,8,11]=>4
[3,4,6,9,11,12,1,2,5,7,8,10]=>4
[3,4,6,10,11,12,1,2,5,7,8,9]=>4
[3,4,7,8,10,12,1,2,5,6,9,11]=>4
[3,4,7,8,11,12,1,2,5,6,9,10]=>2
[3,4,7,9,10,12,1,2,5,6,8,11]=>4
[3,4,7,9,11,12,1,2,5,6,8,10]=>4
[3,4,7,10,11,12,1,2,5,6,8,9]=>4
[3,4,8,9,10,12,1,2,5,6,7,11]=>4
[3,4,8,9,11,12,1,2,5,6,7,10]=>4
[3,4,8,10,11,12,1,2,5,6,7,9]=>4
[3,4,9,10,11,12,1,2,5,6,7,8]=>4
[3,5,6,8,10,12,1,2,4,7,9,11]=>4
[3,5,6,8,11,12,1,2,4,7,9,10]=>4
[3,5,6,9,10,12,1,2,4,7,8,11]=>4
[3,5,6,9,11,12,1,2,4,7,8,10]=>2
[3,5,6,10,11,12,1,2,4,7,8,9]=>4
[3,5,7,8,10,12,1,2,4,6,9,11]=>4
[3,5,7,8,11,12,1,2,4,6,9,10]=>4
[3,5,7,9,10,12,1,2,4,6,8,11]=>4
[3,5,7,9,11,12,1,2,4,6,8,10]=>2
[3,5,7,10,11,12,1,2,4,6,8,9]=>4
[3,5,8,9,10,12,1,2,4,6,7,11]=>4
[3,5,8,9,11,12,1,2,4,6,7,10]=>4
[3,5,8,10,11,12,1,2,4,6,7,9]=>4
[3,5,9,10,11,12,1,2,4,6,7,8]=>4
[3,6,7,8,10,12,1,2,4,5,9,11]=>4
[3,6,7,8,11,12,1,2,4,5,9,10]=>4
[3,6,7,9,10,12,1,2,4,5,8,11]=>4
[3,6,7,9,11,12,1,2,4,5,8,10]=>4
[3,6,7,10,11,12,1,2,4,5,8,9]=>4
[3,6,8,9,10,12,1,2,4,5,7,11]=>4
[3,6,8,9,11,12,1,2,4,5,7,10]=>2
[3,6,8,10,11,12,1,2,4,5,7,9]=>4
[3,6,9,10,11,12,1,2,4,5,7,8]=>4
[3,7,8,9,10,12,1,2,4,5,6,11]=>4
[3,7,8,9,11,12,1,2,4,5,6,10]=>2
[3,7,8,10,11,12,1,2,4,5,6,9]=>4
[3,7,9,10,11,12,1,2,4,5,6,8]=>4
[3,8,9,10,11,12,1,2,4,5,6,7]=>4
[4,5,6,8,10,12,1,2,3,7,9,11]=>4
[4,5,6,8,11,12,1,2,3,7,9,10]=>4
[4,5,6,9,10,12,1,2,3,7,8,11]=>4
[4,5,6,9,11,12,1,2,3,7,8,10]=>4
[4,5,6,10,11,12,1,2,3,7,8,9]=>2
[4,5,7,8,10,12,1,2,3,6,9,11]=>4
[4,5,7,8,11,12,1,2,3,6,9,10]=>4
[4,5,7,9,10,12,1,2,3,6,8,11]=>4
[4,5,7,9,11,12,1,2,3,6,8,10]=>4
[4,5,7,10,11,12,1,2,3,6,8,9]=>2
[4,5,8,9,10,12,1,2,3,6,7,11]=>4
[4,5,8,9,11,12,1,2,3,6,7,10]=>4
[4,5,8,10,11,12,1,2,3,6,7,9]=>4
[4,5,9,10,11,12,1,2,3,6,7,8]=>4
[4,6,7,8,10,12,1,2,3,5,9,11]=>4
[4,6,7,8,11,12,1,2,3,5,9,10]=>4
[4,6,7,9,10,12,1,2,3,5,8,11]=>4
[4,6,7,9,11,12,1,2,3,5,8,10]=>4
[4,6,7,10,11,12,1,2,3,5,8,9]=>4
[4,6,8,9,10,12,1,2,3,5,7,11]=>4
[4,6,8,9,11,12,1,2,3,5,7,10]=>4
[4,6,8,10,11,12,1,2,3,5,7,9]=>2
[4,6,9,10,11,12,1,2,3,5,7,8]=>4
[4,7,8,9,10,12,1,2,3,5,6,11]=>4
[4,7,8,9,11,12,1,2,3,5,6,10]=>4
[4,7,8,10,11,12,1,2,3,5,6,9]=>2
[4,7,9,10,11,12,1,2,3,5,6,8]=>4
[4,8,9,10,11,12,1,2,3,5,6,7]=>4
[5,6,7,8,10,12,1,2,3,4,9,11]=>4
[5,6,7,8,11,12,1,2,3,4,9,10]=>4
[5,6,7,9,10,12,1,2,3,4,8,11]=>4
[5,6,7,9,11,12,1,2,3,4,8,10]=>4
[5,6,7,10,11,12,1,2,3,4,8,9]=>4
[5,6,8,9,10,12,1,2,3,4,7,11]=>4
[5,6,8,9,11,12,1,2,3,4,7,10]=>4
[5,6,8,10,11,12,1,2,3,4,7,9]=>4
[5,6,9,10,11,12,1,2,3,4,7,8]=>2
[5,7,8,9,10,12,1,2,3,4,6,11]=>4
[5,7,8,9,11,12,1,2,3,4,6,10]=>4
[5,7,8,10,11,12,1,2,3,4,6,9]=>4
[5,7,9,10,11,12,1,2,3,4,6,8]=>2
[5,8,9,10,11,12,1,2,3,4,6,7]=>4
[6,7,8,9,10,12,1,2,3,4,5,11]=>4
[6,7,8,9,11,12,1,2,3,4,5,10]=>4
[6,7,8,10,11,12,1,2,3,4,5,9]=>4
[6,7,9,10,11,12,1,2,3,4,5,8]=>4
[6,8,9,10,11,12,1,2,3,4,5,7]=>2
[7,8,9,10,11,12,1,2,3,4,5,6]=>1
                    

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Description

Half the size of the symmetry class of a permutation.
The symmetry class of a permutation $\pi$ is the set of all permutations that can be obtained from $\pi$ by the three elementary operations inverse (Mp00066inverse), reverse (Mp00064reverse), and complement (Mp00069complement).
This statistic is undefined for the unique permutation on one element, because its value would be $1/2$.

References

[1] Callan, D., Mansour, T. Five subsets of permutations enumerated as weak sorting permutations arXiv:1602.05182

Code

def eq_class(pi):
    cl = [pi]
    test = [pi]
    while test:
        tau = test.pop()
        tau1 = tau.reverse()
        tau2 = tau.complement()
        tau3 = tau.inverse()
        if tau1 not in cl:
            cl.append(tau1)
            test.append(tau1)
        if tau2 not in cl:
            cl.append(tau2)
            test.append(tau2)
        if tau3 not in cl:
            cl.append(tau3)
            test.append(tau3)
    return cl

def statistic(pi):
    return len(eq_class(pi))//2

Created

Feb 23, 2016 at 18:13 by Christian Stump

Updated

Feb 23, 2023 at 15:40 by Tilman Möller