- FindStat

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Identifier

Mp00204: Permutations —LLPS⟶ Integer partitions

Images

=>
            
              Cc0002;cc-rep-1
            

            []=>[]
[1]=>[1]
[1,2]=>[1,1]
[2,1]=>[2]
[1,2,3]=>[1,1,1]
[1,3,2]=>[2,1]
[2,1,3]=>[2,1]
[2,3,1]=>[2,1]
[3,1,2]=>[2,1]
[3,2,1]=>[3]
[1,2,3,4]=>[1,1,1,1]
[1,2,4,3]=>[2,1,1]
[1,3,2,4]=>[2,1,1]
[1,3,4,2]=>[2,1,1]
[1,4,2,3]=>[2,1,1]
[1,4,3,2]=>[3,1]
[2,1,3,4]=>[2,1,1]
[2,1,4,3]=>[2,2]
[2,3,1,4]=>[2,1,1]
[2,3,4,1]=>[2,1,1]
[2,4,1,3]=>[2,1,1]
[2,4,3,1]=>[3,1]
[3,1,2,4]=>[2,1,1]
[3,1,4,2]=>[2,2]
[3,2,1,4]=>[3,1]
[3,2,4,1]=>[3,1]
[3,4,1,2]=>[2,1,1]
[3,4,2,1]=>[3,1]
[4,1,2,3]=>[2,1,1]
[4,1,3,2]=>[3,1]
[4,2,1,3]=>[3,1]
[4,2,3,1]=>[3,1]
[4,3,1,2]=>[3,1]
[4,3,2,1]=>[4]
[1,2,3,4,5]=>[1,1,1,1,1]
[1,2,3,5,4]=>[2,1,1,1]
[1,2,4,3,5]=>[2,1,1,1]
[1,2,4,5,3]=>[2,1,1,1]
[1,2,5,3,4]=>[2,1,1,1]
[1,2,5,4,3]=>[3,1,1]
[1,3,2,4,5]=>[2,1,1,1]
[1,3,2,5,4]=>[2,2,1]
[1,3,4,2,5]=>[2,1,1,1]
[1,3,4,5,2]=>[2,1,1,1]
[1,3,5,2,4]=>[2,1,1,1]
[1,3,5,4,2]=>[3,1,1]
[1,4,2,3,5]=>[2,1,1,1]
[1,4,2,5,3]=>[2,2,1]
[1,4,3,2,5]=>[3,1,1]
[1,4,3,5,2]=>[3,1,1]
[1,4,5,2,3]=>[2,1,1,1]
[1,4,5,3,2]=>[3,1,1]
[1,5,2,3,4]=>[2,1,1,1]
[1,5,2,4,3]=>[3,1,1]
[1,5,3,2,4]=>[3,1,1]
[1,5,3,4,2]=>[3,1,1]
[1,5,4,2,3]=>[3,1,1]
[1,5,4,3,2]=>[4,1]
[2,1,3,4,5]=>[2,1,1,1]
[2,1,3,5,4]=>[2,2,1]
[2,1,4,3,5]=>[2,2,1]
[2,1,4,5,3]=>[2,2,1]
[2,1,5,3,4]=>[2,2,1]
[2,1,5,4,3]=>[3,2]
[2,3,1,4,5]=>[2,1,1,1]
[2,3,1,5,4]=>[2,2,1]
[2,3,4,1,5]=>[2,1,1,1]
[2,3,4,5,1]=>[2,1,1,1]
[2,3,5,1,4]=>[2,1,1,1]
[2,3,5,4,1]=>[3,1,1]
[2,4,1,3,5]=>[2,1,1,1]
[2,4,1,5,3]=>[2,2,1]
[2,4,3,1,5]=>[3,1,1]
[2,4,3,5,1]=>[3,1,1]
[2,4,5,1,3]=>[2,1,1,1]
[2,4,5,3,1]=>[3,1,1]
[2,5,1,3,4]=>[2,1,1,1]
[2,5,1,4,3]=>[3,1,1]
[2,5,3,1,4]=>[3,1,1]
[2,5,3,4,1]=>[3,1,1]
[2,5,4,1,3]=>[3,1,1]
[2,5,4,3,1]=>[4,1]
[3,1,2,4,5]=>[2,1,1,1]
[3,1,2,5,4]=>[2,2,1]
[3,1,4,2,5]=>[2,2,1]
[3,1,4,5,2]=>[2,2,1]
[3,1,5,2,4]=>[2,2,1]
[3,1,5,4,2]=>[3,2]
[3,2,1,4,5]=>[3,1,1]
[3,2,1,5,4]=>[3,2]
[3,2,4,1,5]=>[3,1,1]
[3,2,4,5,1]=>[3,1,1]
[3,2,5,1,4]=>[3,1,1]
[3,2,5,4,1]=>[3,2]
[3,4,1,2,5]=>[2,1,1,1]
[3,4,1,5,2]=>[2,2,1]
[3,4,2,1,5]=>[3,1,1]
[3,4,2,5,1]=>[3,1,1]
[3,4,5,1,2]=>[2,1,1,1]
[3,4,5,2,1]=>[3,1,1]
[3,5,1,2,4]=>[2,1,1,1]
[3,5,1,4,2]=>[3,1,1]
[3,5,2,1,4]=>[3,1,1]
[3,5,2,4,1]=>[3,1,1]
[3,5,4,1,2]=>[3,1,1]
[3,5,4,2,1]=>[4,1]
[4,1,2,3,5]=>[2,1,1,1]
[4,1,2,5,3]=>[2,2,1]
[4,1,3,2,5]=>[3,1,1]
[4,1,3,5,2]=>[3,1,1]
[4,1,5,2,3]=>[2,2,1]
[4,1,5,3,2]=>[3,2]
[4,2,1,3,5]=>[3,1,1]
[4,2,1,5,3]=>[3,2]
[4,2,3,1,5]=>[3,1,1]
[4,2,3,5,1]=>[3,1,1]
[4,2,5,1,3]=>[3,1,1]
[4,2,5,3,1]=>[3,2]
[4,3,1,2,5]=>[3,1,1]
[4,3,1,5,2]=>[3,2]
[4,3,2,1,5]=>[4,1]
[4,3,2,5,1]=>[4,1]
[4,3,5,1,2]=>[3,1,1]
[4,3,5,2,1]=>[4,1]
[4,5,1,2,3]=>[2,1,1,1]
[4,5,1,3,2]=>[3,1,1]
[4,5,2,1,3]=>[3,1,1]
[4,5,2,3,1]=>[3,1,1]
[4,5,3,1,2]=>[3,1,1]
[4,5,3,2,1]=>[4,1]
[5,1,2,3,4]=>[2,1,1,1]
[5,1,2,4,3]=>[3,1,1]
[5,1,3,2,4]=>[3,1,1]
[5,1,3,4,2]=>[3,1,1]
[5,1,4,2,3]=>[3,1,1]
[5,1,4,3,2]=>[4,1]
[5,2,1,3,4]=>[3,1,1]
[5,2,1,4,3]=>[3,2]
[5,2,3,1,4]=>[3,1,1]
[5,2,3,4,1]=>[3,1,1]
[5,2,4,1,3]=>[3,1,1]
[5,2,4,3,1]=>[4,1]
[5,3,1,2,4]=>[3,1,1]
[5,3,1,4,2]=>[3,2]
[5,3,2,1,4]=>[4,1]
[5,3,2,4,1]=>[4,1]
[5,3,4,1,2]=>[3,1,1]
[5,3,4,2,1]=>[4,1]
[5,4,1,2,3]=>[3,1,1]
[5,4,1,3,2]=>[4,1]
[5,4,2,1,3]=>[4,1]
[5,4,2,3,1]=>[4,1]
[5,4,3,1,2]=>[4,1]
[5,4,3,2,1]=>[5]
[1,2,3,4,5,6]=>[1,1,1,1,1,1]
[1,2,3,4,6,5]=>[2,1,1,1,1]
[1,2,3,5,4,6]=>[2,1,1,1,1]
[1,2,3,5,6,4]=>[2,1,1,1,1]
[1,2,3,6,4,5]=>[2,1,1,1,1]
[1,2,3,6,5,4]=>[3,1,1,1]
[1,2,4,3,5,6]=>[2,1,1,1,1]
[1,2,4,3,6,5]=>[2,2,1,1]
[1,2,4,5,3,6]=>[2,1,1,1,1]
[1,2,4,5,6,3]=>[2,1,1,1,1]
[1,2,4,6,3,5]=>[2,1,1,1,1]
[1,2,4,6,5,3]=>[3,1,1,1]
[1,2,5,3,4,6]=>[2,1,1,1,1]
[1,2,5,3,6,4]=>[2,2,1,1]
[1,2,5,4,3,6]=>[3,1,1,1]
[1,2,5,4,6,3]=>[3,1,1,1]
[1,2,5,6,3,4]=>[2,1,1,1,1]
[1,2,5,6,4,3]=>[3,1,1,1]
[1,2,6,3,4,5]=>[2,1,1,1,1]
[1,2,6,3,5,4]=>[3,1,1,1]
[1,2,6,4,3,5]=>[3,1,1,1]
[1,2,6,4,5,3]=>[3,1,1,1]
[1,2,6,5,3,4]=>[3,1,1,1]
[1,2,6,5,4,3]=>[4,1,1]
[1,3,2,4,5,6]=>[2,1,1,1,1]
[1,3,2,4,6,5]=>[2,2,1,1]
[1,3,2,5,4,6]=>[2,2,1,1]
[1,3,2,5,6,4]=>[2,2,1,1]
[1,3,2,6,4,5]=>[2,2,1,1]
[1,3,2,6,5,4]=>[3,2,1]
[1,3,4,2,5,6]=>[2,1,1,1,1]
[1,3,4,2,6,5]=>[2,2,1,1]
[1,3,4,5,2,6]=>[2,1,1,1,1]
[1,3,4,5,6,2]=>[2,1,1,1,1]
[1,3,4,6,2,5]=>[2,1,1,1,1]
[1,3,4,6,5,2]=>[3,1,1,1]
[1,3,5,2,4,6]=>[2,1,1,1,1]
[1,3,5,2,6,4]=>[2,2,1,1]
[1,3,5,4,2,6]=>[3,1,1,1]
[1,3,5,4,6,2]=>[3,1,1,1]
[1,3,5,6,2,4]=>[2,1,1,1,1]
[1,3,5,6,4,2]=>[3,1,1,1]
[1,3,6,2,4,5]=>[2,1,1,1,1]
[1,3,6,2,5,4]=>[3,1,1,1]
[1,3,6,4,2,5]=>[3,1,1,1]
[1,3,6,4,5,2]=>[3,1,1,1]
[1,3,6,5,2,4]=>[3,1,1,1]
[1,3,6,5,4,2]=>[4,1,1]
[1,4,2,3,5,6]=>[2,1,1,1,1]
[1,4,2,3,6,5]=>[2,2,1,1]
[1,4,2,5,3,6]=>[2,2,1,1]
[1,4,2,5,6,3]=>[2,2,1,1]
[1,4,2,6,3,5]=>[2,2,1,1]
[1,4,2,6,5,3]=>[3,2,1]
[1,4,3,2,5,6]=>[3,1,1,1]
[1,4,3,2,6,5]=>[3,2,1]
[1,4,3,5,2,6]=>[3,1,1,1]
[1,4,3,5,6,2]=>[3,1,1,1]
[1,4,3,6,2,5]=>[3,1,1,1]
[1,4,3,6,5,2]=>[3,2,1]
[1,4,5,2,3,6]=>[2,1,1,1,1]
[1,4,5,2,6,3]=>[2,2,1,1]
[1,4,5,3,2,6]=>[3,1,1,1]
[1,4,5,3,6,2]=>[3,1,1,1]
[1,4,5,6,2,3]=>[2,1,1,1,1]
[1,4,5,6,3,2]=>[3,1,1,1]
[1,4,6,2,3,5]=>[2,1,1,1,1]
[1,4,6,2,5,3]=>[3,1,1,1]
[1,4,6,3,2,5]=>[3,1,1,1]
[1,4,6,3,5,2]=>[3,1,1,1]
[1,4,6,5,2,3]=>[3,1,1,1]
[1,4,6,5,3,2]=>[4,1,1]
[1,5,2,3,4,6]=>[2,1,1,1,1]
[1,5,2,3,6,4]=>[2,2,1,1]
[1,5,2,4,3,6]=>[3,1,1,1]
[1,5,2,4,6,3]=>[3,1,1,1]
[1,5,2,6,3,4]=>[2,2,1,1]
[1,5,2,6,4,3]=>[3,2,1]
[1,5,3,2,4,6]=>[3,1,1,1]
[1,5,3,2,6,4]=>[3,2,1]
[1,5,3,4,2,6]=>[3,1,1,1]
[1,5,3,4,6,2]=>[3,1,1,1]
[1,5,3,6,2,4]=>[3,1,1,1]
[1,5,3,6,4,2]=>[3,2,1]
[1,5,4,2,3,6]=>[3,1,1,1]
[1,5,4,2,6,3]=>[3,2,1]
[1,5,4,3,2,6]=>[4,1,1]
[1,5,4,3,6,2]=>[4,1,1]
[1,5,4,6,2,3]=>[3,1,1,1]
[1,5,4,6,3,2]=>[4,1,1]
[1,5,6,2,3,4]=>[2,1,1,1,1]
[1,5,6,2,4,3]=>[3,1,1,1]
[1,5,6,3,2,4]=>[3,1,1,1]
[1,5,6,3,4,2]=>[3,1,1,1]
[1,5,6,4,2,3]=>[3,1,1,1]
[1,5,6,4,3,2]=>[4,1,1]
[1,6,2,3,4,5]=>[2,1,1,1,1]
[1,6,2,3,5,4]=>[3,1,1,1]
[1,6,2,4,3,5]=>[3,1,1,1]
[1,6,2,4,5,3]=>[3,1,1,1]
[1,6,2,5,3,4]=>[3,1,1,1]
[1,6,2,5,4,3]=>[4,1,1]
[1,6,3,2,4,5]=>[3,1,1,1]
[1,6,3,2,5,4]=>[3,2,1]
[1,6,3,4,2,5]=>[3,1,1,1]
[1,6,3,4,5,2]=>[3,1,1,1]
[1,6,3,5,2,4]=>[3,1,1,1]
[1,6,3,5,4,2]=>[4,1,1]
[1,6,4,2,3,5]=>[3,1,1,1]
[1,6,4,2,5,3]=>[3,2,1]
[1,6,4,3,2,5]=>[4,1,1]
[1,6,4,3,5,2]=>[4,1,1]
[1,6,4,5,2,3]=>[3,1,1,1]
[1,6,4,5,3,2]=>[4,1,1]
[1,6,5,2,3,4]=>[3,1,1,1]
[1,6,5,2,4,3]=>[4,1,1]
[1,6,5,3,2,4]=>[4,1,1]
[1,6,5,3,4,2]=>[4,1,1]
[1,6,5,4,2,3]=>[4,1,1]
[1,6,5,4,3,2]=>[5,1]
[2,1,3,4,5,6]=>[2,1,1,1,1]
[2,1,3,4,6,5]=>[2,2,1,1]
[2,1,3,5,4,6]=>[2,2,1,1]
[2,1,3,5,6,4]=>[2,2,1,1]
[2,1,3,6,4,5]=>[2,2,1,1]
[2,1,3,6,5,4]=>[3,2,1]
[2,1,4,3,5,6]=>[2,2,1,1]
[2,1,4,3,6,5]=>[2,2,2]
[2,1,4,5,3,6]=>[2,2,1,1]
[2,1,4,5,6,3]=>[2,2,1,1]
[2,1,4,6,3,5]=>[2,2,1,1]
[2,1,4,6,5,3]=>[3,2,1]
[2,1,5,3,4,6]=>[2,2,1,1]
[2,1,5,3,6,4]=>[2,2,2]
[2,1,5,4,3,6]=>[3,2,1]
[2,1,5,4,6,3]=>[3,2,1]
[2,1,5,6,3,4]=>[2,2,1,1]
[2,1,5,6,4,3]=>[3,2,1]
[2,1,6,3,4,5]=>[2,2,1,1]
[2,1,6,3,5,4]=>[3,2,1]
[2,1,6,4,3,5]=>[3,2,1]
[2,1,6,4,5,3]=>[3,2,1]
[2,1,6,5,3,4]=>[3,2,1]
[2,1,6,5,4,3]=>[4,2]
[2,3,1,4,5,6]=>[2,1,1,1,1]
[2,3,1,4,6,5]=>[2,2,1,1]
[2,3,1,5,4,6]=>[2,2,1,1]
[2,3,1,5,6,4]=>[2,2,1,1]
[2,3,1,6,4,5]=>[2,2,1,1]
[2,3,1,6,5,4]=>[3,2,1]
[2,3,4,1,5,6]=>[2,1,1,1,1]
[2,3,4,1,6,5]=>[2,2,1,1]
[2,3,4,5,1,6]=>[2,1,1,1,1]
[2,3,4,5,6,1]=>[2,1,1,1,1]
[2,3,4,6,1,5]=>[2,1,1,1,1]
[2,3,4,6,5,1]=>[3,1,1,1]
[2,3,5,1,4,6]=>[2,1,1,1,1]
[2,3,5,1,6,4]=>[2,2,1,1]
[2,3,5,4,1,6]=>[3,1,1,1]
[2,3,5,4,6,1]=>[3,1,1,1]
[2,3,5,6,1,4]=>[2,1,1,1,1]
[2,3,5,6,4,1]=>[3,1,1,1]
[2,3,6,1,4,5]=>[2,1,1,1,1]
[2,3,6,1,5,4]=>[3,1,1,1]
[2,3,6,4,1,5]=>[3,1,1,1]
[2,3,6,4,5,1]=>[3,1,1,1]
[2,3,6,5,1,4]=>[3,1,1,1]
[2,3,6,5,4,1]=>[4,1,1]
[2,4,1,3,5,6]=>[2,1,1,1,1]
[2,4,1,3,6,5]=>[2,2,1,1]
[2,4,1,5,3,6]=>[2,2,1,1]
[2,4,1,5,6,3]=>[2,2,1,1]
[2,4,1,6,3,5]=>[2,2,1,1]
[2,4,1,6,5,3]=>[3,2,1]
[2,4,3,1,5,6]=>[3,1,1,1]
[2,4,3,1,6,5]=>[3,2,1]
[2,4,3,5,1,6]=>[3,1,1,1]
[2,4,3,5,6,1]=>[3,1,1,1]
[2,4,3,6,1,5]=>[3,1,1,1]
[2,4,3,6,5,1]=>[3,2,1]
[2,4,5,1,3,6]=>[2,1,1,1,1]
[2,4,5,1,6,3]=>[2,2,1,1]
[2,4,5,3,1,6]=>[3,1,1,1]
[2,4,5,3,6,1]=>[3,1,1,1]
[2,4,5,6,1,3]=>[2,1,1,1,1]
[2,4,5,6,3,1]=>[3,1,1,1]
[2,4,6,1,3,5]=>[2,1,1,1,1]
[2,4,6,1,5,3]=>[3,1,1,1]
[2,4,6,3,1,5]=>[3,1,1,1]
[2,4,6,3,5,1]=>[3,1,1,1]
[2,4,6,5,1,3]=>[3,1,1,1]
[2,4,6,5,3,1]=>[4,1,1]
[2,5,1,3,4,6]=>[2,1,1,1,1]
[2,5,1,3,6,4]=>[2,2,1,1]
[2,5,1,4,3,6]=>[3,1,1,1]
[2,5,1,4,6,3]=>[3,1,1,1]
[2,5,1,6,3,4]=>[2,2,1,1]
[2,5,1,6,4,3]=>[3,2,1]
[2,5,3,1,4,6]=>[3,1,1,1]
[2,5,3,1,6,4]=>[3,2,1]
[2,5,3,4,1,6]=>[3,1,1,1]
[2,5,3,4,6,1]=>[3,1,1,1]
[2,5,3,6,1,4]=>[3,1,1,1]
[2,5,3,6,4,1]=>[3,2,1]
[2,5,4,1,3,6]=>[3,1,1,1]
[2,5,4,1,6,3]=>[3,2,1]
[2,5,4,3,1,6]=>[4,1,1]
[2,5,4,3,6,1]=>[4,1,1]
[2,5,4,6,1,3]=>[3,1,1,1]
[2,5,4,6,3,1]=>[4,1,1]
[2,5,6,1,3,4]=>[2,1,1,1,1]
[2,5,6,1,4,3]=>[3,1,1,1]
[2,5,6,3,1,4]=>[3,1,1,1]
[2,5,6,3,4,1]=>[3,1,1,1]
[2,5,6,4,1,3]=>[3,1,1,1]
[2,5,6,4,3,1]=>[4,1,1]
[2,6,1,3,4,5]=>[2,1,1,1,1]
[2,6,1,3,5,4]=>[3,1,1,1]
[2,6,1,4,3,5]=>[3,1,1,1]
[2,6,1,4,5,3]=>[3,1,1,1]
[2,6,1,5,3,4]=>[3,1,1,1]
[2,6,1,5,4,3]=>[4,1,1]
[2,6,3,1,4,5]=>[3,1,1,1]
[2,6,3,1,5,4]=>[3,2,1]
[2,6,3,4,1,5]=>[3,1,1,1]
[2,6,3,4,5,1]=>[3,1,1,1]
[2,6,3,5,1,4]=>[3,1,1,1]
[2,6,3,5,4,1]=>[4,1,1]
[2,6,4,1,3,5]=>[3,1,1,1]
[2,6,4,1,5,3]=>[3,2,1]
[2,6,4,3,1,5]=>[4,1,1]
[2,6,4,3,5,1]=>[4,1,1]
[2,6,4,5,1,3]=>[3,1,1,1]
[2,6,4,5,3,1]=>[4,1,1]
[2,6,5,1,3,4]=>[3,1,1,1]
[2,6,5,1,4,3]=>[4,1,1]
[2,6,5,3,1,4]=>[4,1,1]
[2,6,5,3,4,1]=>[4,1,1]
[2,6,5,4,1,3]=>[4,1,1]
[2,6,5,4,3,1]=>[5,1]
[3,1,2,4,5,6]=>[2,1,1,1,1]
[3,1,2,4,6,5]=>[2,2,1,1]
[3,1,2,5,4,6]=>[2,2,1,1]
[3,1,2,5,6,4]=>[2,2,1,1]
[3,1,2,6,4,5]=>[2,2,1,1]
[3,1,2,6,5,4]=>[3,2,1]
[3,1,4,2,5,6]=>[2,2,1,1]
[3,1,4,2,6,5]=>[2,2,2]
[3,1,4,5,2,6]=>[2,2,1,1]
[3,1,4,5,6,2]=>[2,2,1,1]
[3,1,4,6,2,5]=>[2,2,1,1]
[3,1,4,6,5,2]=>[3,2,1]
[3,1,5,2,4,6]=>[2,2,1,1]
[3,1,5,2,6,4]=>[2,2,2]
[3,1,5,4,2,6]=>[3,2,1]
[3,1,5,4,6,2]=>[3,2,1]
[3,1,5,6,2,4]=>[2,2,1,1]
[3,1,5,6,4,2]=>[3,2,1]
[3,1,6,2,4,5]=>[2,2,1,1]
[3,1,6,2,5,4]=>[3,2,1]
[3,1,6,4,2,5]=>[3,2,1]
[3,1,6,4,5,2]=>[3,2,1]
[3,1,6,5,2,4]=>[3,2,1]
[3,1,6,5,4,2]=>[4,2]
[3,2,1,4,5,6]=>[3,1,1,1]
[3,2,1,4,6,5]=>[3,2,1]
[3,2,1,5,4,6]=>[3,2,1]
[3,2,1,5,6,4]=>[3,2,1]
[3,2,1,6,4,5]=>[3,2,1]
[3,2,1,6,5,4]=>[3,3]
[3,2,4,1,5,6]=>[3,1,1,1]
[3,2,4,1,6,5]=>[3,2,1]
[3,2,4,5,1,6]=>[3,1,1,1]
[3,2,4,5,6,1]=>[3,1,1,1]
[3,2,4,6,1,5]=>[3,1,1,1]
[3,2,4,6,5,1]=>[3,2,1]
[3,2,5,1,4,6]=>[3,1,1,1]
[3,2,5,1,6,4]=>[3,2,1]
[3,2,5,4,1,6]=>[3,2,1]
[3,2,5,4,6,1]=>[3,2,1]
[3,2,5,6,1,4]=>[3,1,1,1]
[3,2,5,6,4,1]=>[3,2,1]
[3,2,6,1,4,5]=>[3,1,1,1]
[3,2,6,1,5,4]=>[3,2,1]
[3,2,6,4,1,5]=>[3,2,1]
[3,2,6,4,5,1]=>[3,2,1]
[3,2,6,5,1,4]=>[3,2,1]
[3,2,6,5,4,1]=>[4,2]
[3,4,1,2,5,6]=>[2,1,1,1,1]
[3,4,1,2,6,5]=>[2,2,1,1]
[3,4,1,5,2,6]=>[2,2,1,1]
[3,4,1,5,6,2]=>[2,2,1,1]
[3,4,1,6,2,5]=>[2,2,1,1]
[3,4,1,6,5,2]=>[3,2,1]
[3,4,2,1,5,6]=>[3,1,1,1]
[3,4,2,1,6,5]=>[3,2,1]
[3,4,2,5,1,6]=>[3,1,1,1]
[3,4,2,5,6,1]=>[3,1,1,1]
[3,4,2,6,1,5]=>[3,1,1,1]
[3,4,2,6,5,1]=>[3,2,1]
[3,4,5,1,2,6]=>[2,1,1,1,1]
[3,4,5,1,6,2]=>[2,2,1,1]
[3,4,5,2,1,6]=>[3,1,1,1]
[3,4,5,2,6,1]=>[3,1,1,1]
[3,4,5,6,1,2]=>[2,1,1,1,1]
[3,4,5,6,2,1]=>[3,1,1,1]
[3,4,6,1,2,5]=>[2,1,1,1,1]
[3,4,6,1,5,2]=>[3,1,1,1]
[3,4,6,2,1,5]=>[3,1,1,1]
[3,4,6,2,5,1]=>[3,1,1,1]
[3,4,6,5,1,2]=>[3,1,1,1]
[3,4,6,5,2,1]=>[4,1,1]
[3,5,1,2,4,6]=>[2,1,1,1,1]
[3,5,1,2,6,4]=>[2,2,1,1]
[3,5,1,4,2,6]=>[3,1,1,1]
[3,5,1,4,6,2]=>[3,1,1,1]
[3,5,1,6,2,4]=>[2,2,1,1]
[3,5,1,6,4,2]=>[3,2,1]
[3,5,2,1,4,6]=>[3,1,1,1]
[3,5,2,1,6,4]=>[3,2,1]
[3,5,2,4,1,6]=>[3,1,1,1]
[3,5,2,4,6,1]=>[3,1,1,1]
[3,5,2,6,1,4]=>[3,1,1,1]
[3,5,2,6,4,1]=>[3,2,1]
[3,5,4,1,2,6]=>[3,1,1,1]
[3,5,4,1,6,2]=>[3,2,1]
[3,5,4,2,1,6]=>[4,1,1]
[3,5,4,2,6,1]=>[4,1,1]
[3,5,4,6,1,2]=>[3,1,1,1]
[3,5,4,6,2,1]=>[4,1,1]
[3,5,6,1,2,4]=>[2,1,1,1,1]
[3,5,6,1,4,2]=>[3,1,1,1]
[3,5,6,2,1,4]=>[3,1,1,1]
[3,5,6,2,4,1]=>[3,1,1,1]
[3,5,6,4,1,2]=>[3,1,1,1]
[3,5,6,4,2,1]=>[4,1,1]
[3,6,1,2,4,5]=>[2,1,1,1,1]
[3,6,1,2,5,4]=>[3,1,1,1]
[3,6,1,4,2,5]=>[3,1,1,1]
[3,6,1,4,5,2]=>[3,1,1,1]
[3,6,1,5,2,4]=>[3,1,1,1]
[3,6,1,5,4,2]=>[4,1,1]
[3,6,2,1,4,5]=>[3,1,1,1]
[3,6,2,1,5,4]=>[3,2,1]
[3,6,2,4,1,5]=>[3,1,1,1]
[3,6,2,4,5,1]=>[3,1,1,1]
[3,6,2,5,1,4]=>[3,1,1,1]
[3,6,2,5,4,1]=>[4,1,1]
[3,6,4,1,2,5]=>[3,1,1,1]
[3,6,4,1,5,2]=>[3,2,1]
[3,6,4,2,1,5]=>[4,1,1]
[3,6,4,2,5,1]=>[4,1,1]
[3,6,4,5,1,2]=>[3,1,1,1]
[3,6,4,5,2,1]=>[4,1,1]
[3,6,5,1,2,4]=>[3,1,1,1]
[3,6,5,1,4,2]=>[4,1,1]
[3,6,5,2,1,4]=>[4,1,1]
[3,6,5,2,4,1]=>[4,1,1]
[3,6,5,4,1,2]=>[4,1,1]
[3,6,5,4,2,1]=>[5,1]
[4,1,2,3,5,6]=>[2,1,1,1,1]
[4,1,2,3,6,5]=>[2,2,1,1]
[4,1,2,5,3,6]=>[2,2,1,1]
[4,1,2,5,6,3]=>[2,2,1,1]
[4,1,2,6,3,5]=>[2,2,1,1]
[4,1,2,6,5,3]=>[3,2,1]
[4,1,3,2,5,6]=>[3,1,1,1]
[4,1,3,2,6,5]=>[3,2,1]
[4,1,3,5,2,6]=>[3,1,1,1]
[4,1,3,5,6,2]=>[3,1,1,1]
[4,1,3,6,2,5]=>[3,1,1,1]
[4,1,3,6,5,2]=>[3,2,1]
[4,1,5,2,3,6]=>[2,2,1,1]
[4,1,5,2,6,3]=>[2,2,2]
[4,1,5,3,2,6]=>[3,2,1]
[4,1,5,3,6,2]=>[3,2,1]
[4,1,5,6,2,3]=>[2,2,1,1]
[4,1,5,6,3,2]=>[3,2,1]
[4,1,6,2,3,5]=>[2,2,1,1]
[4,1,6,2,5,3]=>[3,2,1]
[4,1,6,3,2,5]=>[3,2,1]
[4,1,6,3,5,2]=>[3,2,1]
[4,1,6,5,2,3]=>[3,2,1]
[4,1,6,5,3,2]=>[4,2]
[4,2,1,3,5,6]=>[3,1,1,1]
[4,2,1,3,6,5]=>[3,2,1]
[4,2,1,5,3,6]=>[3,2,1]
[4,2,1,5,6,3]=>[3,2,1]
[4,2,1,6,3,5]=>[3,2,1]
[4,2,1,6,5,3]=>[3,3]
[4,2,3,1,5,6]=>[3,1,1,1]
[4,2,3,1,6,5]=>[3,2,1]
[4,2,3,5,1,6]=>[3,1,1,1]
[4,2,3,5,6,1]=>[3,1,1,1]
[4,2,3,6,1,5]=>[3,1,1,1]
[4,2,3,6,5,1]=>[3,2,1]
[4,2,5,1,3,6]=>[3,1,1,1]
[4,2,5,1,6,3]=>[3,2,1]
[4,2,5,3,1,6]=>[3,2,1]
[4,2,5,3,6,1]=>[3,2,1]
[4,2,5,6,1,3]=>[3,1,1,1]
[4,2,5,6,3,1]=>[3,2,1]
[4,2,6,1,3,5]=>[3,1,1,1]
[4,2,6,1,5,3]=>[3,2,1]
[4,2,6,3,1,5]=>[3,2,1]
[4,2,6,3,5,1]=>[3,2,1]
[4,2,6,5,1,3]=>[3,2,1]
[4,2,6,5,3,1]=>[4,2]
[4,3,1,2,5,6]=>[3,1,1,1]
[4,3,1,2,6,5]=>[3,2,1]
[4,3,1,5,2,6]=>[3,2,1]
[4,3,1,5,6,2]=>[3,2,1]
[4,3,1,6,2,5]=>[3,2,1]
[4,3,1,6,5,2]=>[3,3]
[4,3,2,1,5,6]=>[4,1,1]
[4,3,2,1,6,5]=>[4,2]
[4,3,2,5,1,6]=>[4,1,1]
[4,3,2,5,6,1]=>[4,1,1]
[4,3,2,6,1,5]=>[4,1,1]
[4,3,2,6,5,1]=>[4,2]
[4,3,5,1,2,6]=>[3,1,1,1]
[4,3,5,1,6,2]=>[3,2,1]
[4,3,5,2,1,6]=>[4,1,1]
[4,3,5,2,6,1]=>[4,1,1]
[4,3,5,6,1,2]=>[3,1,1,1]
[4,3,5,6,2,1]=>[4,1,1]
[4,3,6,1,2,5]=>[3,1,1,1]
[4,3,6,1,5,2]=>[3,2,1]
[4,3,6,2,1,5]=>[4,1,1]
[4,3,6,2,5,1]=>[4,1,1]
[4,3,6,5,1,2]=>[3,2,1]
[4,3,6,5,2,1]=>[4,2]
[4,5,1,2,3,6]=>[2,1,1,1,1]
[4,5,1,2,6,3]=>[2,2,1,1]
[4,5,1,3,2,6]=>[3,1,1,1]
[4,5,1,3,6,2]=>[3,1,1,1]
[4,5,1,6,2,3]=>[2,2,1,1]
[4,5,1,6,3,2]=>[3,2,1]
[4,5,2,1,3,6]=>[3,1,1,1]
[4,5,2,1,6,3]=>[3,2,1]
[4,5,2,3,1,6]=>[3,1,1,1]
[4,5,2,3,6,1]=>[3,1,1,1]
[4,5,2,6,1,3]=>[3,1,1,1]
[4,5,2,6,3,1]=>[3,2,1]
[4,5,3,1,2,6]=>[3,1,1,1]
[4,5,3,1,6,2]=>[3,2,1]
[4,5,3,2,1,6]=>[4,1,1]
[4,5,3,2,6,1]=>[4,1,1]
[4,5,3,6,1,2]=>[3,1,1,1]
[4,5,3,6,2,1]=>[4,1,1]
[4,5,6,1,2,3]=>[2,1,1,1,1]
[4,5,6,1,3,2]=>[3,1,1,1]
[4,5,6,2,1,3]=>[3,1,1,1]
[4,5,6,2,3,1]=>[3,1,1,1]
[4,5,6,3,1,2]=>[3,1,1,1]
[4,5,6,3,2,1]=>[4,1,1]
[4,6,1,2,3,5]=>[2,1,1,1,1]
[4,6,1,2,5,3]=>[3,1,1,1]
[4,6,1,3,2,5]=>[3,1,1,1]
[4,6,1,3,5,2]=>[3,1,1,1]
[4,6,1,5,2,3]=>[3,1,1,1]
[4,6,1,5,3,2]=>[4,1,1]
[4,6,2,1,3,5]=>[3,1,1,1]
[4,6,2,1,5,3]=>[3,2,1]
[4,6,2,3,1,5]=>[3,1,1,1]
[4,6,2,3,5,1]=>[3,1,1,1]
[4,6,2,5,1,3]=>[3,1,1,1]
[4,6,2,5,3,1]=>[4,1,1]
[4,6,3,1,2,5]=>[3,1,1,1]
[4,6,3,1,5,2]=>[3,2,1]
[4,6,3,2,1,5]=>[4,1,1]
[4,6,3,2,5,1]=>[4,1,1]
[4,6,3,5,1,2]=>[3,1,1,1]
[4,6,3,5,2,1]=>[4,1,1]
[4,6,5,1,2,3]=>[3,1,1,1]
[4,6,5,1,3,2]=>[4,1,1]
[4,6,5,2,1,3]=>[4,1,1]
[4,6,5,2,3,1]=>[4,1,1]
[4,6,5,3,1,2]=>[4,1,1]
[4,6,5,3,2,1]=>[5,1]
[5,1,2,3,4,6]=>[2,1,1,1,1]
[5,1,2,3,6,4]=>[2,2,1,1]
[5,1,2,4,3,6]=>[3,1,1,1]
[5,1,2,4,6,3]=>[3,1,1,1]
[5,1,2,6,3,4]=>[2,2,1,1]
[5,1,2,6,4,3]=>[3,2,1]
[5,1,3,2,4,6]=>[3,1,1,1]
[5,1,3,2,6,4]=>[3,2,1]
[5,1,3,4,2,6]=>[3,1,1,1]
[5,1,3,4,6,2]=>[3,1,1,1]
[5,1,3,6,2,4]=>[3,1,1,1]
[5,1,3,6,4,2]=>[3,2,1]
[5,1,4,2,3,6]=>[3,1,1,1]
[5,1,4,2,6,3]=>[3,2,1]
[5,1,4,3,2,6]=>[4,1,1]
[5,1,4,3,6,2]=>[4,1,1]
[5,1,4,6,2,3]=>[3,1,1,1]
[5,1,4,6,3,2]=>[4,1,1]
[5,1,6,2,3,4]=>[2,2,1,1]
[5,1,6,2,4,3]=>[3,2,1]
[5,1,6,3,2,4]=>[3,2,1]
[5,1,6,3,4,2]=>[3,2,1]
[5,1,6,4,2,3]=>[3,2,1]
[5,1,6,4,3,2]=>[4,2]
[5,2,1,3,4,6]=>[3,1,1,1]
[5,2,1,3,6,4]=>[3,2,1]
[5,2,1,4,3,6]=>[3,2,1]
[5,2,1,4,6,3]=>[3,2,1]
[5,2,1,6,3,4]=>[3,2,1]
[5,2,1,6,4,3]=>[3,3]
[5,2,3,1,4,6]=>[3,1,1,1]
[5,2,3,1,6,4]=>[3,2,1]
[5,2,3,4,1,6]=>[3,1,1,1]
[5,2,3,4,6,1]=>[3,1,1,1]
[5,2,3,6,1,4]=>[3,1,1,1]
[5,2,3,6,4,1]=>[3,2,1]
[5,2,4,1,3,6]=>[3,1,1,1]
[5,2,4,1,6,3]=>[3,2,1]
[5,2,4,3,1,6]=>[4,1,1]
[5,2,4,3,6,1]=>[4,1,1]
[5,2,4,6,1,3]=>[3,1,1,1]
[5,2,4,6,3,1]=>[4,1,1]
[5,2,6,1,3,4]=>[3,1,1,1]
[5,2,6,1,4,3]=>[3,2,1]
[5,2,6,3,1,4]=>[3,2,1]
[5,2,6,3,4,1]=>[3,2,1]
[5,2,6,4,1,3]=>[3,2,1]
[5,2,6,4,3,1]=>[4,2]
[5,3,1,2,4,6]=>[3,1,1,1]
[5,3,1,2,6,4]=>[3,2,1]
[5,3,1,4,2,6]=>[3,2,1]
[5,3,1,4,6,2]=>[3,2,1]
[5,3,1,6,2,4]=>[3,2,1]
[5,3,1,6,4,2]=>[3,3]
[5,3,2,1,4,6]=>[4,1,1]
[5,3,2,1,6,4]=>[4,2]
[5,3,2,4,1,6]=>[4,1,1]
[5,3,2,4,6,1]=>[4,1,1]
[5,3,2,6,1,4]=>[4,1,1]
[5,3,2,6,4,1]=>[4,2]
[5,3,4,1,2,6]=>[3,1,1,1]
[5,3,4,1,6,2]=>[3,2,1]
[5,3,4,2,1,6]=>[4,1,1]
[5,3,4,2,6,1]=>[4,1,1]
[5,3,4,6,1,2]=>[3,1,1,1]
[5,3,4,6,2,1]=>[4,1,1]
[5,3,6,1,2,4]=>[3,1,1,1]
[5,3,6,1,4,2]=>[3,2,1]
[5,3,6,2,1,4]=>[4,1,1]
[5,3,6,2,4,1]=>[4,1,1]
[5,3,6,4,1,2]=>[3,2,1]
[5,3,6,4,2,1]=>[4,2]
[5,4,1,2,3,6]=>[3,1,1,1]
[5,4,1,2,6,3]=>[3,2,1]
[5,4,1,3,2,6]=>[4,1,1]
[5,4,1,3,6,2]=>[4,1,1]
[5,4,1,6,2,3]=>[3,2,1]
[5,4,1,6,3,2]=>[4,2]
[5,4,2,1,3,6]=>[4,1,1]
[5,4,2,1,6,3]=>[4,2]
[5,4,2,3,1,6]=>[4,1,1]
[5,4,2,3,6,1]=>[4,1,1]
[5,4,2,6,1,3]=>[4,1,1]
[5,4,2,6,3,1]=>[4,2]
[5,4,3,1,2,6]=>[4,1,1]
[5,4,3,1,6,2]=>[4,2]
[5,4,3,2,1,6]=>[5,1]
[5,4,3,2,6,1]=>[5,1]
[5,4,3,6,1,2]=>[4,1,1]
[5,4,3,6,2,1]=>[5,1]
[5,4,6,1,2,3]=>[3,1,1,1]
[5,4,6,1,3,2]=>[4,1,1]
[5,4,6,2,1,3]=>[4,1,1]
[5,4,6,2,3,1]=>[4,1,1]
[5,4,6,3,1,2]=>[4,1,1]
[5,4,6,3,2,1]=>[5,1]
[5,6,1,2,3,4]=>[2,1,1,1,1]
[5,6,1,2,4,3]=>[3,1,1,1]
[5,6,1,3,2,4]=>[3,1,1,1]
[5,6,1,3,4,2]=>[3,1,1,1]
[5,6,1,4,2,3]=>[3,1,1,1]
[5,6,1,4,3,2]=>[4,1,1]
[5,6,2,1,3,4]=>[3,1,1,1]
[5,6,2,1,4,3]=>[3,2,1]
[5,6,2,3,1,4]=>[3,1,1,1]
[5,6,2,3,4,1]=>[3,1,1,1]
[5,6,2,4,1,3]=>[3,1,1,1]
[5,6,2,4,3,1]=>[4,1,1]
[5,6,3,1,2,4]=>[3,1,1,1]
[5,6,3,1,4,2]=>[3,2,1]
[5,6,3,2,1,4]=>[4,1,1]
[5,6,3,2,4,1]=>[4,1,1]
[5,6,3,4,1,2]=>[3,1,1,1]
[5,6,3,4,2,1]=>[4,1,1]
[5,6,4,1,2,3]=>[3,1,1,1]
[5,6,4,1,3,2]=>[4,1,1]
[5,6,4,2,1,3]=>[4,1,1]
[5,6,4,2,3,1]=>[4,1,1]
[5,6,4,3,1,2]=>[4,1,1]
[5,6,4,3,2,1]=>[5,1]
[6,1,2,3,4,5]=>[2,1,1,1,1]
[6,1,2,3,5,4]=>[3,1,1,1]
[6,1,2,4,3,5]=>[3,1,1,1]
[6,1,2,4,5,3]=>[3,1,1,1]
[6,1,2,5,3,4]=>[3,1,1,1]
[6,1,2,5,4,3]=>[4,1,1]
[6,1,3,2,4,5]=>[3,1,1,1]
[6,1,3,2,5,4]=>[3,2,1]
[6,1,3,4,2,5]=>[3,1,1,1]
[6,1,3,4,5,2]=>[3,1,1,1]
[6,1,3,5,2,4]=>[3,1,1,1]
[6,1,3,5,4,2]=>[4,1,1]
[6,1,4,2,3,5]=>[3,1,1,1]
[6,1,4,2,5,3]=>[3,2,1]
[6,1,4,3,2,5]=>[4,1,1]
[6,1,4,3,5,2]=>[4,1,1]
[6,1,4,5,2,3]=>[3,1,1,1]
[6,1,4,5,3,2]=>[4,1,1]
[6,1,5,2,3,4]=>[3,1,1,1]
[6,1,5,2,4,3]=>[4,1,1]
[6,1,5,3,2,4]=>[4,1,1]
[6,1,5,3,4,2]=>[4,1,1]
[6,1,5,4,2,3]=>[4,1,1]
[6,1,5,4,3,2]=>[5,1]
[6,2,1,3,4,5]=>[3,1,1,1]
[6,2,1,3,5,4]=>[3,2,1]
[6,2,1,4,3,5]=>[3,2,1]
[6,2,1,4,5,3]=>[3,2,1]
[6,2,1,5,3,4]=>[3,2,1]
[6,2,1,5,4,3]=>[4,2]
[6,2,3,1,4,5]=>[3,1,1,1]
[6,2,3,1,5,4]=>[3,2,1]
[6,2,3,4,1,5]=>[3,1,1,1]
[6,2,3,4,5,1]=>[3,1,1,1]
[6,2,3,5,1,4]=>[3,1,1,1]
[6,2,3,5,4,1]=>[4,1,1]
[6,2,4,1,3,5]=>[3,1,1,1]
[6,2,4,1,5,3]=>[3,2,1]
[6,2,4,3,1,5]=>[4,1,1]
[6,2,4,3,5,1]=>[4,1,1]
[6,2,4,5,1,3]=>[3,1,1,1]
[6,2,4,5,3,1]=>[4,1,1]
[6,2,5,1,3,4]=>[3,1,1,1]
[6,2,5,1,4,3]=>[4,1,1]
[6,2,5,3,1,4]=>[4,1,1]
[6,2,5,3,4,1]=>[4,1,1]
[6,2,5,4,1,3]=>[4,1,1]
[6,2,5,4,3,1]=>[5,1]
[6,3,1,2,4,5]=>[3,1,1,1]
[6,3,1,2,5,4]=>[3,2,1]
[6,3,1,4,2,5]=>[3,2,1]
[6,3,1,4,5,2]=>[3,2,1]
[6,3,1,5,2,4]=>[3,2,1]
[6,3,1,5,4,2]=>[4,2]
[6,3,2,1,4,5]=>[4,1,1]
[6,3,2,1,5,4]=>[4,2]
[6,3,2,4,1,5]=>[4,1,1]
[6,3,2,4,5,1]=>[4,1,1]
[6,3,2,5,1,4]=>[4,1,1]
[6,3,2,5,4,1]=>[4,2]
[6,3,4,1,2,5]=>[3,1,1,1]
[6,3,4,1,5,2]=>[3,2,1]
[6,3,4,2,1,5]=>[4,1,1]
[6,3,4,2,5,1]=>[4,1,1]
[6,3,4,5,1,2]=>[3,1,1,1]
[6,3,4,5,2,1]=>[4,1,1]
[6,3,5,1,2,4]=>[3,1,1,1]
[6,3,5,1,4,2]=>[4,1,1]
[6,3,5,2,1,4]=>[4,1,1]
[6,3,5,2,4,1]=>[4,1,1]
[6,3,5,4,1,2]=>[4,1,1]
[6,3,5,4,2,1]=>[5,1]
[6,4,1,2,3,5]=>[3,1,1,1]
[6,4,1,2,5,3]=>[3,2,1]
[6,4,1,3,2,5]=>[4,1,1]
[6,4,1,3,5,2]=>[4,1,1]
[6,4,1,5,2,3]=>[3,2,1]
[6,4,1,5,3,2]=>[4,2]
[6,4,2,1,3,5]=>[4,1,1]
[6,4,2,1,5,3]=>[4,2]
[6,4,2,3,1,5]=>[4,1,1]
[6,4,2,3,5,1]=>[4,1,1]
[6,4,2,5,1,3]=>[4,1,1]
[6,4,2,5,3,1]=>[4,2]
[6,4,3,1,2,5]=>[4,1,1]
[6,4,3,1,5,2]=>[4,2]
[6,4,3,2,1,5]=>[5,1]
[6,4,3,2,5,1]=>[5,1]
[6,4,3,5,1,2]=>[4,1,1]
[6,4,3,5,2,1]=>[5,1]
[6,4,5,1,2,3]=>[3,1,1,1]
[6,4,5,1,3,2]=>[4,1,1]
[6,4,5,2,1,3]=>[4,1,1]
[6,4,5,2,3,1]=>[4,1,1]
[6,4,5,3,1,2]=>[4,1,1]
[6,4,5,3,2,1]=>[5,1]
[6,5,1,2,3,4]=>[3,1,1,1]
[6,5,1,2,4,3]=>[4,1,1]
[6,5,1,3,2,4]=>[4,1,1]
[6,5,1,3,4,2]=>[4,1,1]
[6,5,1,4,2,3]=>[4,1,1]
[6,5,1,4,3,2]=>[5,1]
[6,5,2,1,3,4]=>[4,1,1]
[6,5,2,1,4,3]=>[4,2]
[6,5,2,3,1,4]=>[4,1,1]
[6,5,2,3,4,1]=>[4,1,1]
[6,5,2,4,1,3]=>[4,1,1]
[6,5,2,4,3,1]=>[5,1]
[6,5,3,1,2,4]=>[4,1,1]
[6,5,3,1,4,2]=>[4,2]
[6,5,3,2,1,4]=>[5,1]
[6,5,3,2,4,1]=>[5,1]
[6,5,3,4,1,2]=>[4,1,1]
[6,5,3,4,2,1]=>[5,1]
[6,5,4,1,2,3]=>[4,1,1]
[6,5,4,1,3,2]=>[5,1]
[6,5,4,2,1,3]=>[5,1]
[6,5,4,2,3,1]=>[5,1]
[6,5,4,3,1,2]=>[5,1]
[6,5,4,3,2,1]=>[6]
[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1]
[1,2,3,4,5,7,6]=>[2,1,1,1,1,1]
[1,2,3,4,6,5,7]=>[2,1,1,1,1,1]
[1,2,3,4,6,7,5]=>[2,1,1,1,1,1]
[1,2,3,4,7,5,6]=>[2,1,1,1,1,1]
[1,2,3,4,7,6,5]=>[3,1,1,1,1]
[1,2,3,5,4,6,7]=>[2,1,1,1,1,1]
[1,2,3,5,4,7,6]=>[2,2,1,1,1]
[1,2,3,5,6,4,7]=>[2,1,1,1,1,1]
[1,2,3,5,6,7,4]=>[2,1,1,1,1,1]
[1,2,3,5,7,4,6]=>[2,1,1,1,1,1]
[1,2,3,5,7,6,4]=>[3,1,1,1,1]
[1,2,3,6,4,5,7]=>[2,1,1,1,1,1]
[1,2,3,6,4,7,5]=>[2,2,1,1,1]
[1,2,3,6,5,4,7]=>[3,1,1,1,1]
[1,2,3,6,5,7,4]=>[3,1,1,1,1]
[1,2,3,6,7,4,5]=>[2,1,1,1,1,1]
[1,2,3,6,7,5,4]=>[3,1,1,1,1]
[1,2,3,7,4,5,6]=>[2,1,1,1,1,1]
[1,2,3,7,4,6,5]=>[3,1,1,1,1]
[1,2,3,7,5,4,6]=>[3,1,1,1,1]
[1,2,3,7,5,6,4]=>[3,1,1,1,1]
[1,2,3,7,6,4,5]=>[3,1,1,1,1]
[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,2,4,3,5,6,7]=>[2,1,1,1,1,1]
[1,2,4,3,5,7,6]=>[2,2,1,1,1]
[1,2,4,3,6,5,7]=>[2,2,1,1,1]
[1,2,4,3,6,7,5]=>[2,2,1,1,1]
[1,2,4,3,7,5,6]=>[2,2,1,1,1]
[1,2,4,3,7,6,5]=>[3,2,1,1]
[1,2,4,5,3,6,7]=>[2,1,1,1,1,1]
[1,2,4,5,3,7,6]=>[2,2,1,1,1]
[1,2,4,5,6,3,7]=>[2,1,1,1,1,1]
[1,2,4,5,6,7,3]=>[2,1,1,1,1,1]
[1,2,4,5,7,3,6]=>[2,1,1,1,1,1]
[1,2,4,5,7,6,3]=>[3,1,1,1,1]
[1,2,4,6,3,5,7]=>[2,1,1,1,1,1]
[1,2,4,6,3,7,5]=>[2,2,1,1,1]
[1,2,4,6,5,3,7]=>[3,1,1,1,1]
[1,2,4,6,5,7,3]=>[3,1,1,1,1]
[1,2,4,6,7,3,5]=>[2,1,1,1,1,1]
[1,2,4,6,7,5,3]=>[3,1,1,1,1]
[1,2,4,7,3,5,6]=>[2,1,1,1,1,1]
[1,2,4,7,3,6,5]=>[3,1,1,1,1]
[1,2,4,7,5,3,6]=>[3,1,1,1,1]
[1,2,4,7,5,6,3]=>[3,1,1,1,1]
[1,2,4,7,6,3,5]=>[3,1,1,1,1]
[1,2,4,7,6,5,3]=>[4,1,1,1]
[1,2,5,3,4,6,7]=>[2,1,1,1,1,1]
[1,2,5,3,4,7,6]=>[2,2,1,1,1]
[1,2,5,3,6,4,7]=>[2,2,1,1,1]
[1,2,5,3,6,7,4]=>[2,2,1,1,1]
[1,2,5,3,7,4,6]=>[2,2,1,1,1]
[1,2,5,3,7,6,4]=>[3,2,1,1]
[1,2,5,4,3,6,7]=>[3,1,1,1,1]
[1,2,5,4,3,7,6]=>[3,2,1,1]
[1,2,5,4,6,3,7]=>[3,1,1,1,1]
[1,2,5,4,6,7,3]=>[3,1,1,1,1]
[1,2,5,4,7,3,6]=>[3,1,1,1,1]
[1,2,5,4,7,6,3]=>[3,2,1,1]
[1,2,5,6,3,4,7]=>[2,1,1,1,1,1]
[1,2,5,6,3,7,4]=>[2,2,1,1,1]
[1,2,5,6,4,3,7]=>[3,1,1,1,1]
[1,2,5,6,4,7,3]=>[3,1,1,1,1]
[1,2,5,6,7,3,4]=>[2,1,1,1,1,1]
[1,2,5,6,7,4,3]=>[3,1,1,1,1]
[1,2,5,7,3,4,6]=>[2,1,1,1,1,1]
[1,2,5,7,3,6,4]=>[3,1,1,1,1]
[1,2,5,7,4,3,6]=>[3,1,1,1,1]
[1,2,5,7,4,6,3]=>[3,1,1,1,1]
[1,2,5,7,6,3,4]=>[3,1,1,1,1]
[1,2,5,7,6,4,3]=>[4,1,1,1]
[1,2,6,3,4,5,7]=>[2,1,1,1,1,1]
[1,2,6,3,4,7,5]=>[2,2,1,1,1]
[1,2,6,3,5,4,7]=>[3,1,1,1,1]
[1,2,6,3,5,7,4]=>[3,1,1,1,1]
[1,2,6,3,7,4,5]=>[2,2,1,1,1]
[1,2,6,3,7,5,4]=>[3,2,1,1]
[1,2,6,4,3,5,7]=>[3,1,1,1,1]
[1,2,6,4,3,7,5]=>[3,2,1,1]
[1,2,6,4,5,3,7]=>[3,1,1,1,1]
[1,2,6,4,5,7,3]=>[3,1,1,1,1]
[1,2,6,4,7,3,5]=>[3,1,1,1,1]
[1,2,6,4,7,5,3]=>[3,2,1,1]
[1,2,6,5,3,4,7]=>[3,1,1,1,1]
[1,2,6,5,3,7,4]=>[3,2,1,1]
[1,2,6,5,4,3,7]=>[4,1,1,1]
[1,2,6,5,4,7,3]=>[4,1,1,1]
[1,2,6,5,7,3,4]=>[3,1,1,1,1]
[1,2,6,5,7,4,3]=>[4,1,1,1]
[1,2,6,7,3,4,5]=>[2,1,1,1,1,1]
[1,2,6,7,3,5,4]=>[3,1,1,1,1]
[1,2,6,7,4,3,5]=>[3,1,1,1,1]
[1,2,6,7,4,5,3]=>[3,1,1,1,1]
[1,2,6,7,5,3,4]=>[3,1,1,1,1]
[1,2,6,7,5,4,3]=>[4,1,1,1]
[1,2,7,3,4,5,6]=>[2,1,1,1,1,1]
[1,2,7,3,4,6,5]=>[3,1,1,1,1]
[1,2,7,3,5,4,6]=>[3,1,1,1,1]
[1,2,7,3,5,6,4]=>[3,1,1,1,1]
[1,2,7,3,6,4,5]=>[3,1,1,1,1]
[1,2,7,3,6,5,4]=>[4,1,1,1]
[1,2,7,4,3,5,6]=>[3,1,1,1,1]
[1,2,7,4,3,6,5]=>[3,2,1,1]
[1,2,7,4,5,3,6]=>[3,1,1,1,1]
[1,2,7,4,5,6,3]=>[3,1,1,1,1]
[1,2,7,4,6,3,5]=>[3,1,1,1,1]
[1,2,7,4,6,5,3]=>[4,1,1,1]
[1,2,7,5,3,4,6]=>[3,1,1,1,1]
[1,2,7,5,3,6,4]=>[3,2,1,1]
[1,2,7,5,4,3,6]=>[4,1,1,1]
[1,2,7,5,4,6,3]=>[4,1,1,1]
[1,2,7,5,6,3,4]=>[3,1,1,1,1]
[1,2,7,5,6,4,3]=>[4,1,1,1]
[1,2,7,6,3,4,5]=>[3,1,1,1,1]
[1,2,7,6,3,5,4]=>[4,1,1,1]
[1,2,7,6,4,3,5]=>[4,1,1,1]
[1,2,7,6,4,5,3]=>[4,1,1,1]
[1,2,7,6,5,3,4]=>[4,1,1,1]
[1,2,7,6,5,4,3]=>[5,1,1]
[1,3,2,4,5,6,7]=>[2,1,1,1,1,1]
[1,3,2,4,5,7,6]=>[2,2,1,1,1]
[1,3,2,4,6,5,7]=>[2,2,1,1,1]
[1,3,2,4,6,7,5]=>[2,2,1,1,1]
[1,3,2,4,7,5,6]=>[2,2,1,1,1]
[1,3,2,4,7,6,5]=>[3,2,1,1]
[1,3,2,5,4,6,7]=>[2,2,1,1,1]
[1,3,2,5,4,7,6]=>[2,2,2,1]
[1,3,2,5,6,4,7]=>[2,2,1,1,1]
[1,3,2,5,6,7,4]=>[2,2,1,1,1]
[1,3,2,5,7,4,6]=>[2,2,1,1,1]
[1,3,2,5,7,6,4]=>[3,2,1,1]
[1,3,2,6,4,5,7]=>[2,2,1,1,1]
[1,3,2,6,4,7,5]=>[2,2,2,1]
[1,3,2,6,5,4,7]=>[3,2,1,1]
[1,3,2,6,5,7,4]=>[3,2,1,1]
[1,3,2,6,7,4,5]=>[2,2,1,1,1]
[1,3,2,6,7,5,4]=>[3,2,1,1]
[1,3,2,7,4,5,6]=>[2,2,1,1,1]
[1,3,2,7,4,6,5]=>[3,2,1,1]
[1,3,2,7,5,4,6]=>[3,2,1,1]
[1,3,2,7,5,6,4]=>[3,2,1,1]
[1,3,2,7,6,4,5]=>[3,2,1,1]
[1,3,2,7,6,5,4]=>[4,2,1]
[1,3,4,2,5,6,7]=>[2,1,1,1,1,1]
[1,3,4,2,5,7,6]=>[2,2,1,1,1]
[1,3,4,2,6,5,7]=>[2,2,1,1,1]
[1,3,4,2,6,7,5]=>[2,2,1,1,1]
[1,3,4,2,7,5,6]=>[2,2,1,1,1]
[1,3,4,2,7,6,5]=>[3,2,1,1]
[1,3,4,5,2,6,7]=>[2,1,1,1,1,1]
[1,3,4,5,2,7,6]=>[2,2,1,1,1]
[1,3,4,5,6,2,7]=>[2,1,1,1,1,1]
[1,3,4,5,6,7,2]=>[2,1,1,1,1,1]
[1,3,4,5,7,2,6]=>[2,1,1,1,1,1]
[1,3,4,5,7,6,2]=>[3,1,1,1,1]
[1,3,4,6,2,5,7]=>[2,1,1,1,1,1]
[1,3,4,6,2,7,5]=>[2,2,1,1,1]
[1,3,4,6,5,2,7]=>[3,1,1,1,1]
[1,3,4,6,5,7,2]=>[3,1,1,1,1]
[1,3,4,6,7,2,5]=>[2,1,1,1,1,1]
[1,3,4,6,7,5,2]=>[3,1,1,1,1]
[1,3,4,7,2,5,6]=>[2,1,1,1,1,1]
[1,3,4,7,2,6,5]=>[3,1,1,1,1]
[1,3,4,7,5,2,6]=>[3,1,1,1,1]
[1,3,4,7,5,6,2]=>[3,1,1,1,1]
[1,3,4,7,6,2,5]=>[3,1,1,1,1]
[1,3,4,7,6,5,2]=>[4,1,1,1]
[1,3,5,2,4,6,7]=>[2,1,1,1,1,1]
[1,3,5,2,4,7,6]=>[2,2,1,1,1]
[1,3,5,2,6,4,7]=>[2,2,1,1,1]
[1,3,5,2,6,7,4]=>[2,2,1,1,1]
[1,3,5,2,7,4,6]=>[2,2,1,1,1]
[1,3,5,2,7,6,4]=>[3,2,1,1]
[1,3,5,4,2,6,7]=>[3,1,1,1,1]
[1,3,5,4,2,7,6]=>[3,2,1,1]
[1,3,5,4,6,2,7]=>[3,1,1,1,1]
[1,3,5,4,6,7,2]=>[3,1,1,1,1]
[1,3,5,4,7,2,6]=>[3,1,1,1,1]
[1,3,5,4,7,6,2]=>[3,2,1,1]
[1,3,5,6,2,4,7]=>[2,1,1,1,1,1]
[1,3,5,6,2,7,4]=>[2,2,1,1,1]
[1,3,5,6,4,2,7]=>[3,1,1,1,1]
[1,3,5,6,4,7,2]=>[3,1,1,1,1]
[1,3,5,6,7,2,4]=>[2,1,1,1,1,1]
[1,3,5,6,7,4,2]=>[3,1,1,1,1]
[1,3,5,7,2,4,6]=>[2,1,1,1,1,1]
[1,3,5,7,2,6,4]=>[3,1,1,1,1]
[1,3,5,7,4,2,6]=>[3,1,1,1,1]
[1,3,5,7,4,6,2]=>[3,1,1,1,1]
[1,3,5,7,6,2,4]=>[3,1,1,1,1]
[1,3,5,7,6,4,2]=>[4,1,1,1]
[1,3,6,2,4,5,7]=>[2,1,1,1,1,1]
[1,3,6,2,4,7,5]=>[2,2,1,1,1]
[1,3,6,2,5,4,7]=>[3,1,1,1,1]
[1,3,6,2,5,7,4]=>[3,1,1,1,1]
[1,3,6,2,7,4,5]=>[2,2,1,1,1]
[1,3,6,2,7,5,4]=>[3,2,1,1]
[1,3,6,4,2,5,7]=>[3,1,1,1,1]
[1,3,6,4,2,7,5]=>[3,2,1,1]
[1,3,6,4,5,2,7]=>[3,1,1,1,1]
[1,3,6,4,5,7,2]=>[3,1,1,1,1]
[1,3,6,4,7,2,5]=>[3,1,1,1,1]
[1,3,6,4,7,5,2]=>[3,2,1,1]
[1,3,6,5,2,4,7]=>[3,1,1,1,1]
[1,3,6,5,2,7,4]=>[3,2,1,1]
[1,3,6,5,4,2,7]=>[4,1,1,1]
[1,3,6,5,4,7,2]=>[4,1,1,1]
[1,3,6,5,7,2,4]=>[3,1,1,1,1]
[1,3,6,5,7,4,2]=>[4,1,1,1]
[1,3,6,7,2,4,5]=>[2,1,1,1,1,1]
[1,3,6,7,2,5,4]=>[3,1,1,1,1]
[1,3,6,7,4,2,5]=>[3,1,1,1,1]
[1,3,6,7,4,5,2]=>[3,1,1,1,1]
[1,3,6,7,5,2,4]=>[3,1,1,1,1]
[1,3,6,7,5,4,2]=>[4,1,1,1]
[1,3,7,2,4,5,6]=>[2,1,1,1,1,1]
[1,3,7,2,4,6,5]=>[3,1,1,1,1]
[1,3,7,2,5,4,6]=>[3,1,1,1,1]
[1,3,7,2,5,6,4]=>[3,1,1,1,1]
[1,3,7,2,6,4,5]=>[3,1,1,1,1]
[1,3,7,2,6,5,4]=>[4,1,1,1]
[1,3,7,4,2,5,6]=>[3,1,1,1,1]
[1,3,7,4,2,6,5]=>[3,2,1,1]
[1,3,7,4,5,2,6]=>[3,1,1,1,1]
[1,3,7,4,5,6,2]=>[3,1,1,1,1]
[1,3,7,4,6,2,5]=>[3,1,1,1,1]
[1,3,7,4,6,5,2]=>[4,1,1,1]
[1,3,7,5,2,4,6]=>[3,1,1,1,1]
[1,3,7,5,2,6,4]=>[3,2,1,1]
[1,3,7,5,4,2,6]=>[4,1,1,1]
[1,3,7,5,4,6,2]=>[4,1,1,1]
[1,3,7,5,6,2,4]=>[3,1,1,1,1]
[1,3,7,5,6,4,2]=>[4,1,1,1]
[1,3,7,6,2,4,5]=>[3,1,1,1,1]
[1,3,7,6,2,5,4]=>[4,1,1,1]
[1,3,7,6,4,2,5]=>[4,1,1,1]
[1,3,7,6,4,5,2]=>[4,1,1,1]
[1,3,7,6,5,2,4]=>[4,1,1,1]
[1,3,7,6,5,4,2]=>[5,1,1]
[1,4,2,3,5,6,7]=>[2,1,1,1,1,1]
[1,4,2,3,5,7,6]=>[2,2,1,1,1]
[1,4,2,3,6,5,7]=>[2,2,1,1,1]
[1,4,2,3,6,7,5]=>[2,2,1,1,1]
[1,4,2,3,7,5,6]=>[2,2,1,1,1]
[1,4,2,3,7,6,5]=>[3,2,1,1]
[1,4,2,5,3,6,7]=>[2,2,1,1,1]
[1,4,2,5,3,7,6]=>[2,2,2,1]
[1,4,2,5,6,3,7]=>[2,2,1,1,1]
[1,4,2,5,6,7,3]=>[2,2,1,1,1]
[1,4,2,5,7,3,6]=>[2,2,1,1,1]
[1,4,2,5,7,6,3]=>[3,2,1,1]
[1,4,2,6,3,5,7]=>[2,2,1,1,1]
[1,4,2,6,3,7,5]=>[2,2,2,1]
[1,4,2,6,5,3,7]=>[3,2,1,1]
[1,4,2,6,5,7,3]=>[3,2,1,1]
[1,4,2,6,7,3,5]=>[2,2,1,1,1]
[1,4,2,6,7,5,3]=>[3,2,1,1]
[1,4,2,7,3,5,6]=>[2,2,1,1,1]
[1,4,2,7,3,6,5]=>[3,2,1,1]
[1,4,2,7,5,3,6]=>[3,2,1,1]
[1,4,2,7,5,6,3]=>[3,2,1,1]
[1,4,2,7,6,3,5]=>[3,2,1,1]
[1,4,2,7,6,5,3]=>[4,2,1]
[1,4,3,2,5,6,7]=>[3,1,1,1,1]
[1,4,3,2,5,7,6]=>[3,2,1,1]
[1,4,3,2,6,5,7]=>[3,2,1,1]
[1,4,3,2,6,7,5]=>[3,2,1,1]
[1,4,3,2,7,5,6]=>[3,2,1,1]
[1,4,3,2,7,6,5]=>[3,3,1]
[1,4,3,5,2,6,7]=>[3,1,1,1,1]
[1,4,3,5,2,7,6]=>[3,2,1,1]
[1,4,3,5,6,2,7]=>[3,1,1,1,1]
[1,4,3,5,6,7,2]=>[3,1,1,1,1]
[1,4,3,5,7,2,6]=>[3,1,1,1,1]
[1,4,3,5,7,6,2]=>[3,2,1,1]
[1,4,3,6,2,5,7]=>[3,1,1,1,1]
[1,4,3,6,2,7,5]=>[3,2,1,1]
[1,4,3,6,5,2,7]=>[3,2,1,1]
[1,4,3,6,5,7,2]=>[3,2,1,1]
[1,4,3,6,7,2,5]=>[3,1,1,1,1]
[1,4,3,6,7,5,2]=>[3,2,1,1]
[1,4,3,7,2,5,6]=>[3,1,1,1,1]
[1,4,3,7,2,6,5]=>[3,2,1,1]
[1,4,3,7,5,2,6]=>[3,2,1,1]
[1,4,3,7,5,6,2]=>[3,2,1,1]
[1,4,3,7,6,2,5]=>[3,2,1,1]
[1,4,3,7,6,5,2]=>[4,2,1]
[1,4,5,2,3,6,7]=>[2,1,1,1,1,1]
[1,4,5,2,3,7,6]=>[2,2,1,1,1]
[1,4,5,2,6,3,7]=>[2,2,1,1,1]
[1,4,5,2,6,7,3]=>[2,2,1,1,1]
[1,4,5,2,7,3,6]=>[2,2,1,1,1]
[1,4,5,2,7,6,3]=>[3,2,1,1]
[1,4,5,3,2,6,7]=>[3,1,1,1,1]
[1,4,5,3,2,7,6]=>[3,2,1,1]
[1,4,5,3,6,2,7]=>[3,1,1,1,1]
[1,4,5,3,6,7,2]=>[3,1,1,1,1]
[1,4,5,3,7,2,6]=>[3,1,1,1,1]
[1,4,5,3,7,6,2]=>[3,2,1,1]
[1,4,5,6,2,3,7]=>[2,1,1,1,1,1]
[1,4,5,6,2,7,3]=>[2,2,1,1,1]
[1,4,5,6,3,2,7]=>[3,1,1,1,1]
[1,4,5,6,3,7,2]=>[3,1,1,1,1]
[1,4,5,6,7,2,3]=>[2,1,1,1,1,1]
[1,4,5,6,7,3,2]=>[3,1,1,1,1]
[1,4,5,7,2,3,6]=>[2,1,1,1,1,1]
[1,4,5,7,2,6,3]=>[3,1,1,1,1]
[1,4,5,7,3,2,6]=>[3,1,1,1,1]
[1,4,5,7,3,6,2]=>[3,1,1,1,1]
[1,4,5,7,6,2,3]=>[3,1,1,1,1]
[1,4,5,7,6,3,2]=>[4,1,1,1]
[1,4,6,2,3,5,7]=>[2,1,1,1,1,1]
[1,4,6,2,3,7,5]=>[2,2,1,1,1]
[1,4,6,2,5,3,7]=>[3,1,1,1,1]
[1,4,6,2,5,7,3]=>[3,1,1,1,1]
[1,4,6,2,7,3,5]=>[2,2,1,1,1]
[1,4,6,2,7,5,3]=>[3,2,1,1]
[1,4,6,3,2,5,7]=>[3,1,1,1,1]
[1,4,6,3,2,7,5]=>[3,2,1,1]
[1,4,6,3,5,2,7]=>[3,1,1,1,1]
[1,4,6,3,5,7,2]=>[3,1,1,1,1]
[1,4,6,3,7,2,5]=>[3,1,1,1,1]
[1,4,6,3,7,5,2]=>[3,2,1,1]
[1,4,6,5,2,3,7]=>[3,1,1,1,1]
[1,4,6,5,2,7,3]=>[3,2,1,1]
[1,4,6,5,3,2,7]=>[4,1,1,1]
[1,4,6,5,3,7,2]=>[4,1,1,1]
[1,4,6,5,7,2,3]=>[3,1,1,1,1]
[1,4,6,5,7,3,2]=>[4,1,1,1]
[1,4,6,7,2,3,5]=>[2,1,1,1,1,1]
[1,4,6,7,2,5,3]=>[3,1,1,1,1]
[1,4,6,7,3,2,5]=>[3,1,1,1,1]
[1,4,6,7,3,5,2]=>[3,1,1,1,1]
[1,4,6,7,5,2,3]=>[3,1,1,1,1]
[1,4,6,7,5,3,2]=>[4,1,1,1]
[1,4,7,2,3,5,6]=>[2,1,1,1,1,1]
[1,4,7,2,3,6,5]=>[3,1,1,1,1]
[1,4,7,2,5,3,6]=>[3,1,1,1,1]
[1,4,7,2,5,6,3]=>[3,1,1,1,1]
[1,4,7,2,6,3,5]=>[3,1,1,1,1]
[1,4,7,2,6,5,3]=>[4,1,1,1]
[1,4,7,3,2,5,6]=>[3,1,1,1,1]
[1,4,7,3,2,6,5]=>[3,2,1,1]
[1,4,7,3,5,2,6]=>[3,1,1,1,1]
[1,4,7,3,5,6,2]=>[3,1,1,1,1]
[1,4,7,3,6,2,5]=>[3,1,1,1,1]
[1,4,7,3,6,5,2]=>[4,1,1,1]
[1,4,7,5,2,3,6]=>[3,1,1,1,1]
[1,4,7,5,2,6,3]=>[3,2,1,1]
[1,4,7,5,3,2,6]=>[4,1,1,1]
[1,4,7,5,3,6,2]=>[4,1,1,1]
[1,4,7,5,6,2,3]=>[3,1,1,1,1]
[1,4,7,5,6,3,2]=>[4,1,1,1]
[1,4,7,6,2,3,5]=>[3,1,1,1,1]
[1,4,7,6,2,5,3]=>[4,1,1,1]
[1,4,7,6,3,2,5]=>[4,1,1,1]
[1,4,7,6,3,5,2]=>[4,1,1,1]
[1,4,7,6,5,2,3]=>[4,1,1,1]
[1,4,7,6,5,3,2]=>[5,1,1]
[1,5,2,3,4,6,7]=>[2,1,1,1,1,1]
[1,5,2,3,4,7,6]=>[2,2,1,1,1]
[1,5,2,3,6,4,7]=>[2,2,1,1,1]
[1,5,2,3,6,7,4]=>[2,2,1,1,1]
[1,5,2,3,7,4,6]=>[2,2,1,1,1]
[1,5,2,3,7,6,4]=>[3,2,1,1]
[1,5,2,4,3,6,7]=>[3,1,1,1,1]
[1,5,2,4,3,7,6]=>[3,2,1,1]
[1,5,2,4,6,3,7]=>[3,1,1,1,1]
[1,5,2,4,6,7,3]=>[3,1,1,1,1]
[1,5,2,4,7,3,6]=>[3,1,1,1,1]
[1,5,2,4,7,6,3]=>[3,2,1,1]
[1,5,2,6,3,4,7]=>[2,2,1,1,1]
[1,5,2,6,3,7,4]=>[2,2,2,1]
[1,5,2,6,4,3,7]=>[3,2,1,1]
[1,5,2,6,4,7,3]=>[3,2,1,1]
[1,5,2,6,7,3,4]=>[2,2,1,1,1]
[1,5,2,6,7,4,3]=>[3,2,1,1]
[1,5,2,7,3,4,6]=>[2,2,1,1,1]
[1,5,2,7,3,6,4]=>[3,2,1,1]
[1,5,2,7,4,3,6]=>[3,2,1,1]
[1,5,2,7,4,6,3]=>[3,2,1,1]
[1,5,2,7,6,3,4]=>[3,2,1,1]
[1,5,2,7,6,4,3]=>[4,2,1]
[1,5,3,2,4,6,7]=>[3,1,1,1,1]
[1,5,3,2,4,7,6]=>[3,2,1,1]
[1,5,3,2,6,4,7]=>[3,2,1,1]
[1,5,3,2,6,7,4]=>[3,2,1,1]
[1,5,3,2,7,4,6]=>[3,2,1,1]
[1,5,3,2,7,6,4]=>[3,3,1]
[1,5,3,4,2,6,7]=>[3,1,1,1,1]
[1,5,3,4,2,7,6]=>[3,2,1,1]
[1,5,3,4,6,2,7]=>[3,1,1,1,1]
[1,5,3,4,6,7,2]=>[3,1,1,1,1]
[1,5,3,4,7,2,6]=>[3,1,1,1,1]
[1,5,3,4,7,6,2]=>[3,2,1,1]
[1,5,3,6,2,4,7]=>[3,1,1,1,1]
[1,5,3,6,2,7,4]=>[3,2,1,1]
[1,5,3,6,4,2,7]=>[3,2,1,1]
[1,5,3,6,4,7,2]=>[3,2,1,1]
[1,5,3,6,7,2,4]=>[3,1,1,1,1]
[1,5,3,6,7,4,2]=>[3,2,1,1]
[1,5,3,7,2,4,6]=>[3,1,1,1,1]
[1,5,3,7,2,6,4]=>[3,2,1,1]
[1,5,3,7,4,2,6]=>[3,2,1,1]
[1,5,3,7,4,6,2]=>[3,2,1,1]
[1,5,3,7,6,2,4]=>[3,2,1,1]
[1,5,3,7,6,4,2]=>[4,2,1]
[1,5,4,2,3,6,7]=>[3,1,1,1,1]
[1,5,4,2,3,7,6]=>[3,2,1,1]
[1,5,4,2,6,3,7]=>[3,2,1,1]
[1,5,4,2,6,7,3]=>[3,2,1,1]
[1,5,4,2,7,3,6]=>[3,2,1,1]
[1,5,4,2,7,6,3]=>[3,3,1]
[1,5,4,3,2,6,7]=>[4,1,1,1]
[1,5,4,3,2,7,6]=>[4,2,1]
[1,5,4,3,6,2,7]=>[4,1,1,1]
[1,5,4,3,6,7,2]=>[4,1,1,1]
[1,5,4,3,7,2,6]=>[4,1,1,1]
[1,5,4,3,7,6,2]=>[4,2,1]
[1,5,4,6,2,3,7]=>[3,1,1,1,1]
[1,5,4,6,2,7,3]=>[3,2,1,1]
[1,5,4,6,3,2,7]=>[4,1,1,1]
[1,5,4,6,3,7,2]=>[4,1,1,1]
[1,5,4,6,7,2,3]=>[3,1,1,1,1]
[1,5,4,6,7,3,2]=>[4,1,1,1]
[1,5,4,7,2,3,6]=>[3,1,1,1,1]
[1,5,4,7,2,6,3]=>[3,2,1,1]
[1,5,4,7,3,2,6]=>[4,1,1,1]
[1,5,4,7,3,6,2]=>[4,1,1,1]
[1,5,4,7,6,2,3]=>[3,2,1,1]
[1,5,4,7,6,3,2]=>[4,2,1]
[1,5,6,2,3,4,7]=>[2,1,1,1,1,1]
[1,5,6,2,3,7,4]=>[2,2,1,1,1]
[1,5,6,2,4,3,7]=>[3,1,1,1,1]
[1,5,6,2,4,7,3]=>[3,1,1,1,1]
[1,5,6,2,7,3,4]=>[2,2,1,1,1]
[1,5,6,2,7,4,3]=>[3,2,1,1]
[1,5,6,3,2,4,7]=>[3,1,1,1,1]
[1,5,6,3,2,7,4]=>[3,2,1,1]
[1,5,6,3,4,2,7]=>[3,1,1,1,1]
[1,5,6,3,4,7,2]=>[3,1,1,1,1]
[1,5,6,3,7,2,4]=>[3,1,1,1,1]
[1,5,6,3,7,4,2]=>[3,2,1,1]
[1,5,6,4,2,3,7]=>[3,1,1,1,1]
[1,5,6,4,2,7,3]=>[3,2,1,1]
[1,5,6,4,3,2,7]=>[4,1,1,1]
[1,5,6,4,3,7,2]=>[4,1,1,1]
[1,5,6,4,7,2,3]=>[3,1,1,1,1]
[1,5,6,4,7,3,2]=>[4,1,1,1]
[1,5,6,7,2,3,4]=>[2,1,1,1,1,1]
[1,5,6,7,2,4,3]=>[3,1,1,1,1]
[1,5,6,7,3,2,4]=>[3,1,1,1,1]
[1,5,6,7,3,4,2]=>[3,1,1,1,1]
[1,5,6,7,4,2,3]=>[3,1,1,1,1]
[1,5,6,7,4,3,2]=>[4,1,1,1]
[1,5,7,2,3,4,6]=>[2,1,1,1,1,1]
[1,5,7,2,3,6,4]=>[3,1,1,1,1]
[1,5,7,2,4,3,6]=>[3,1,1,1,1]
[1,5,7,2,4,6,3]=>[3,1,1,1,1]
[1,5,7,2,6,3,4]=>[3,1,1,1,1]
[1,5,7,2,6,4,3]=>[4,1,1,1]
[1,5,7,3,2,4,6]=>[3,1,1,1,1]
[1,5,7,3,2,6,4]=>[3,2,1,1]
[1,5,7,3,4,2,6]=>[3,1,1,1,1]
[1,5,7,3,4,6,2]=>[3,1,1,1,1]
[1,5,7,3,6,2,4]=>[3,1,1,1,1]
[1,5,7,3,6,4,2]=>[4,1,1,1]
[1,5,7,4,2,3,6]=>[3,1,1,1,1]
[1,5,7,4,2,6,3]=>[3,2,1,1]
[1,5,7,4,3,2,6]=>[4,1,1,1]
[1,5,7,4,3,6,2]=>[4,1,1,1]
[1,5,7,4,6,2,3]=>[3,1,1,1,1]
[1,5,7,4,6,3,2]=>[4,1,1,1]
[1,5,7,6,2,3,4]=>[3,1,1,1,1]
[1,5,7,6,2,4,3]=>[4,1,1,1]
[1,5,7,6,3,2,4]=>[4,1,1,1]
[1,5,7,6,3,4,2]=>[4,1,1,1]
[1,5,7,6,4,2,3]=>[4,1,1,1]
[1,5,7,6,4,3,2]=>[5,1,1]
[1,6,2,3,4,5,7]=>[2,1,1,1,1,1]
[1,6,2,3,4,7,5]=>[2,2,1,1,1]
[1,6,2,3,5,4,7]=>[3,1,1,1,1]
[1,6,2,3,5,7,4]=>[3,1,1,1,1]
[1,6,2,3,7,4,5]=>[2,2,1,1,1]
[1,6,2,3,7,5,4]=>[3,2,1,1]
[1,6,2,4,3,5,7]=>[3,1,1,1,1]
[1,6,2,4,3,7,5]=>[3,2,1,1]
[1,6,2,4,5,3,7]=>[3,1,1,1,1]
[1,6,2,4,5,7,3]=>[3,1,1,1,1]
[1,6,2,4,7,3,5]=>[3,1,1,1,1]
[1,6,2,4,7,5,3]=>[3,2,1,1]
[1,6,2,5,3,4,7]=>[3,1,1,1,1]
[1,6,2,5,3,7,4]=>[3,2,1,1]
[1,6,2,5,4,3,7]=>[4,1,1,1]
[1,6,2,5,4,7,3]=>[4,1,1,1]
[1,6,2,5,7,3,4]=>[3,1,1,1,1]
[1,6,2,5,7,4,3]=>[4,1,1,1]
[1,6,2,7,3,4,5]=>[2,2,1,1,1]
[1,6,2,7,3,5,4]=>[3,2,1,1]
[1,6,2,7,4,3,5]=>[3,2,1,1]
[1,6,2,7,4,5,3]=>[3,2,1,1]
[1,6,2,7,5,3,4]=>[3,2,1,1]
[1,6,2,7,5,4,3]=>[4,2,1]
[1,6,3,2,4,5,7]=>[3,1,1,1,1]
[1,6,3,2,4,7,5]=>[3,2,1,1]
[1,6,3,2,5,4,7]=>[3,2,1,1]
[1,6,3,2,5,7,4]=>[3,2,1,1]
[1,6,3,2,7,4,5]=>[3,2,1,1]
[1,6,3,2,7,5,4]=>[3,3,1]
[1,6,3,4,2,5,7]=>[3,1,1,1,1]
[1,6,3,4,2,7,5]=>[3,2,1,1]
[1,6,3,4,5,2,7]=>[3,1,1,1,1]
[1,6,3,4,5,7,2]=>[3,1,1,1,1]
[1,6,3,4,7,2,5]=>[3,1,1,1,1]
[1,6,3,4,7,5,2]=>[3,2,1,1]
[1,6,3,5,2,4,7]=>[3,1,1,1,1]
[1,6,3,5,2,7,4]=>[3,2,1,1]
[1,6,3,5,4,2,7]=>[4,1,1,1]
[1,6,3,5,4,7,2]=>[4,1,1,1]
[1,6,3,5,7,2,4]=>[3,1,1,1,1]
[1,6,3,5,7,4,2]=>[4,1,1,1]
[1,6,3,7,2,4,5]=>[3,1,1,1,1]
[1,6,3,7,2,5,4]=>[3,2,1,1]
[1,6,3,7,4,2,5]=>[3,2,1,1]
[1,6,3,7,4,5,2]=>[3,2,1,1]
[1,6,3,7,5,2,4]=>[3,2,1,1]
[1,6,3,7,5,4,2]=>[4,2,1]
[1,6,4,2,3,5,7]=>[3,1,1,1,1]
[1,6,4,2,3,7,5]=>[3,2,1,1]
[1,6,4,2,5,3,7]=>[3,2,1,1]
[1,6,4,2,5,7,3]=>[3,2,1,1]
[1,6,4,2,7,3,5]=>[3,2,1,1]
[1,6,4,2,7,5,3]=>[3,3,1]
[1,6,4,3,2,5,7]=>[4,1,1,1]
[1,6,4,3,2,7,5]=>[4,2,1]
[1,6,4,3,5,2,7]=>[4,1,1,1]
[1,6,4,3,5,7,2]=>[4,1,1,1]
[1,6,4,3,7,2,5]=>[4,1,1,1]
[1,6,4,3,7,5,2]=>[4,2,1]
[1,6,4,5,2,3,7]=>[3,1,1,1,1]
[1,6,4,5,2,7,3]=>[3,2,1,1]
[1,6,4,5,3,2,7]=>[4,1,1,1]
[1,6,4,5,3,7,2]=>[4,1,1,1]
[1,6,4,5,7,2,3]=>[3,1,1,1,1]
[1,6,4,5,7,3,2]=>[4,1,1,1]
[1,6,4,7,2,3,5]=>[3,1,1,1,1]
[1,6,4,7,2,5,3]=>[3,2,1,1]
[1,6,4,7,3,2,5]=>[4,1,1,1]
[1,6,4,7,3,5,2]=>[4,1,1,1]
[1,6,4,7,5,2,3]=>[3,2,1,1]
[1,6,4,7,5,3,2]=>[4,2,1]
[1,6,5,2,3,4,7]=>[3,1,1,1,1]
[1,6,5,2,3,7,4]=>[3,2,1,1]
[1,6,5,2,4,3,7]=>[4,1,1,1]
[1,6,5,2,4,7,3]=>[4,1,1,1]
[1,6,5,2,7,3,4]=>[3,2,1,1]
[1,6,5,2,7,4,3]=>[4,2,1]
[1,6,5,3,2,4,7]=>[4,1,1,1]
[1,6,5,3,2,7,4]=>[4,2,1]
[1,6,5,3,4,2,7]=>[4,1,1,1]
[1,6,5,3,4,7,2]=>[4,1,1,1]
[1,6,5,3,7,2,4]=>[4,1,1,1]
[1,6,5,3,7,4,2]=>[4,2,1]
[1,6,5,4,2,3,7]=>[4,1,1,1]
[1,6,5,4,2,7,3]=>[4,2,1]
[1,6,5,4,3,2,7]=>[5,1,1]
[1,6,5,4,3,7,2]=>[5,1,1]
[1,6,5,4,7,2,3]=>[4,1,1,1]
[1,6,5,4,7,3,2]=>[5,1,1]
[1,6,5,7,2,3,4]=>[3,1,1,1,1]
[1,6,5,7,2,4,3]=>[4,1,1,1]
[1,6,5,7,3,2,4]=>[4,1,1,1]
[1,6,5,7,3,4,2]=>[4,1,1,1]
[1,6,5,7,4,2,3]=>[4,1,1,1]
[1,6,5,7,4,3,2]=>[5,1,1]
[1,6,7,2,3,4,5]=>[2,1,1,1,1,1]
[1,6,7,2,3,5,4]=>[3,1,1,1,1]
[1,6,7,2,4,3,5]=>[3,1,1,1,1]
[1,6,7,2,4,5,3]=>[3,1,1,1,1]
[1,6,7,2,5,3,4]=>[3,1,1,1,1]
[1,6,7,2,5,4,3]=>[4,1,1,1]
[1,6,7,3,2,4,5]=>[3,1,1,1,1]
[1,6,7,3,2,5,4]=>[3,2,1,1]
[1,6,7,3,4,2,5]=>[3,1,1,1,1]
[1,6,7,3,4,5,2]=>[3,1,1,1,1]
[1,6,7,3,5,2,4]=>[3,1,1,1,1]
[1,6,7,3,5,4,2]=>[4,1,1,1]
[1,6,7,4,2,3,5]=>[3,1,1,1,1]
[1,6,7,4,2,5,3]=>[3,2,1,1]
[1,6,7,4,3,2,5]=>[4,1,1,1]
[1,6,7,4,3,5,2]=>[4,1,1,1]
[1,6,7,4,5,2,3]=>[3,1,1,1,1]
[1,6,7,4,5,3,2]=>[4,1,1,1]
[1,6,7,5,2,3,4]=>[3,1,1,1,1]
[1,6,7,5,2,4,3]=>[4,1,1,1]
[1,6,7,5,3,2,4]=>[4,1,1,1]
[1,6,7,5,3,4,2]=>[4,1,1,1]
[1,6,7,5,4,2,3]=>[4,1,1,1]
[1,6,7,5,4,3,2]=>[5,1,1]
[1,7,2,3,4,5,6]=>[2,1,1,1,1,1]
[1,7,2,3,4,6,5]=>[3,1,1,1,1]
[1,7,2,3,5,4,6]=>[3,1,1,1,1]
[1,7,2,3,5,6,4]=>[3,1,1,1,1]
[1,7,2,3,6,4,5]=>[3,1,1,1,1]
[1,7,2,3,6,5,4]=>[4,1,1,1]
[1,7,2,4,3,5,6]=>[3,1,1,1,1]
[1,7,2,4,3,6,5]=>[3,2,1,1]
[1,7,2,4,5,3,6]=>[3,1,1,1,1]
[1,7,2,4,5,6,3]=>[3,1,1,1,1]
[1,7,2,4,6,3,5]=>[3,1,1,1,1]
[1,7,2,4,6,5,3]=>[4,1,1,1]
[1,7,2,5,3,4,6]=>[3,1,1,1,1]
[1,7,2,5,3,6,4]=>[3,2,1,1]
[1,7,2,5,4,3,6]=>[4,1,1,1]
[1,7,2,5,4,6,3]=>[4,1,1,1]
[1,7,2,5,6,3,4]=>[3,1,1,1,1]
[1,7,2,5,6,4,3]=>[4,1,1,1]
[1,7,2,6,3,4,5]=>[3,1,1,1,1]
[1,7,2,6,3,5,4]=>[4,1,1,1]
[1,7,2,6,4,3,5]=>[4,1,1,1]
[1,7,2,6,4,5,3]=>[4,1,1,1]
[1,7,2,6,5,3,4]=>[4,1,1,1]
[1,7,2,6,5,4,3]=>[5,1,1]
[1,7,3,2,4,5,6]=>[3,1,1,1,1]
[1,7,3,2,4,6,5]=>[3,2,1,1]
[1,7,3,2,5,4,6]=>[3,2,1,1]
[1,7,3,2,5,6,4]=>[3,2,1,1]
[1,7,3,2,6,4,5]=>[3,2,1,1]
[1,7,3,2,6,5,4]=>[4,2,1]
[1,7,3,4,2,5,6]=>[3,1,1,1,1]
[1,7,3,4,2,6,5]=>[3,2,1,1]
[1,7,3,4,5,2,6]=>[3,1,1,1,1]
[1,7,3,4,5,6,2]=>[3,1,1,1,1]
[1,7,3,4,6,2,5]=>[3,1,1,1,1]
[1,7,3,4,6,5,2]=>[4,1,1,1]
[1,7,3,5,2,4,6]=>[3,1,1,1,1]
[1,7,3,5,2,6,4]=>[3,2,1,1]
[1,7,3,5,4,2,6]=>[4,1,1,1]
[1,7,3,5,4,6,2]=>[4,1,1,1]
[1,7,3,5,6,2,4]=>[3,1,1,1,1]
[1,7,3,5,6,4,2]=>[4,1,1,1]
[1,7,3,6,2,4,5]=>[3,1,1,1,1]
[1,7,3,6,2,5,4]=>[4,1,1,1]
[1,7,3,6,4,2,5]=>[4,1,1,1]
[1,7,3,6,4,5,2]=>[4,1,1,1]
[1,7,3,6,5,2,4]=>[4,1,1,1]
[1,7,3,6,5,4,2]=>[5,1,1]
[1,7,4,2,3,5,6]=>[3,1,1,1,1]
[1,7,4,2,3,6,5]=>[3,2,1,1]
[1,7,4,2,5,3,6]=>[3,2,1,1]
[1,7,4,2,5,6,3]=>[3,2,1,1]
[1,7,4,2,6,3,5]=>[3,2,1,1]
[1,7,4,2,6,5,3]=>[4,2,1]
[1,7,4,3,2,5,6]=>[4,1,1,1]
[1,7,4,3,2,6,5]=>[4,2,1]
[1,7,4,3,5,2,6]=>[4,1,1,1]
[1,7,4,3,5,6,2]=>[4,1,1,1]
[1,7,4,3,6,2,5]=>[4,1,1,1]
[1,7,4,3,6,5,2]=>[4,2,1]
[1,7,4,5,2,3,6]=>[3,1,1,1,1]
[1,7,4,5,2,6,3]=>[3,2,1,1]
[1,7,4,5,3,2,6]=>[4,1,1,1]
[1,7,4,5,3,6,2]=>[4,1,1,1]
[1,7,4,5,6,2,3]=>[3,1,1,1,1]
[1,7,4,5,6,3,2]=>[4,1,1,1]
[1,7,4,6,2,3,5]=>[3,1,1,1,1]
[1,7,4,6,2,5,3]=>[4,1,1,1]
[1,7,4,6,3,2,5]=>[4,1,1,1]
[1,7,4,6,3,5,2]=>[4,1,1,1]
[1,7,4,6,5,2,3]=>[4,1,1,1]
[1,7,4,6,5,3,2]=>[5,1,1]
[1,7,5,2,3,4,6]=>[3,1,1,1,1]
[1,7,5,2,3,6,4]=>[3,2,1,1]
[1,7,5,2,4,3,6]=>[4,1,1,1]
[1,7,5,2,4,6,3]=>[4,1,1,1]
[1,7,5,2,6,3,4]=>[3,2,1,1]
[1,7,5,2,6,4,3]=>[4,2,1]
[1,7,5,3,2,4,6]=>[4,1,1,1]
[1,7,5,3,2,6,4]=>[4,2,1]
[1,7,5,3,4,2,6]=>[4,1,1,1]
[1,7,5,3,4,6,2]=>[4,1,1,1]
[1,7,5,3,6,2,4]=>[4,1,1,1]
[1,7,5,3,6,4,2]=>[4,2,1]
[1,7,5,4,2,3,6]=>[4,1,1,1]
[1,7,5,4,2,6,3]=>[4,2,1]
[1,7,5,4,3,2,6]=>[5,1,1]
[1,7,5,4,3,6,2]=>[5,1,1]
[1,7,5,4,6,2,3]=>[4,1,1,1]
[1,7,5,4,6,3,2]=>[5,1,1]
[1,7,5,6,2,3,4]=>[3,1,1,1,1]
[1,7,5,6,2,4,3]=>[4,1,1,1]
[1,7,5,6,3,2,4]=>[4,1,1,1]
[1,7,5,6,3,4,2]=>[4,1,1,1]
[1,7,5,6,4,2,3]=>[4,1,1,1]
[1,7,5,6,4,3,2]=>[5,1,1]
[1,7,6,2,3,4,5]=>[3,1,1,1,1]
[1,7,6,2,3,5,4]=>[4,1,1,1]
[1,7,6,2,4,3,5]=>[4,1,1,1]
[1,7,6,2,4,5,3]=>[4,1,1,1]
[1,7,6,2,5,3,4]=>[4,1,1,1]
[1,7,6,2,5,4,3]=>[5,1,1]
[1,7,6,3,2,4,5]=>[4,1,1,1]
[1,7,6,3,2,5,4]=>[4,2,1]
[1,7,6,3,4,2,5]=>[4,1,1,1]
[1,7,6,3,4,5,2]=>[4,1,1,1]
[1,7,6,3,5,2,4]=>[4,1,1,1]
[1,7,6,3,5,4,2]=>[5,1,1]
[1,7,6,4,2,3,5]=>[4,1,1,1]
[1,7,6,4,2,5,3]=>[4,2,1]
[1,7,6,4,3,2,5]=>[5,1,1]
[1,7,6,4,3,5,2]=>[5,1,1]
[1,7,6,4,5,2,3]=>[4,1,1,1]
[1,7,6,4,5,3,2]=>[5,1,1]
[1,7,6,5,2,3,4]=>[4,1,1,1]
[1,7,6,5,2,4,3]=>[5,1,1]
[1,7,6,5,3,2,4]=>[5,1,1]
[1,7,6,5,3,4,2]=>[5,1,1]
[1,7,6,5,4,2,3]=>[5,1,1]
[1,7,6,5,4,3,2]=>[6,1]
[2,1,3,4,5,6,7]=>[2,1,1,1,1,1]
[2,1,3,4,5,7,6]=>[2,2,1,1,1]
[2,1,3,4,6,5,7]=>[2,2,1,1,1]
[2,1,3,4,6,7,5]=>[2,2,1,1,1]
[2,1,3,4,7,5,6]=>[2,2,1,1,1]
[2,1,3,4,7,6,5]=>[3,2,1,1]
[2,1,3,5,4,6,7]=>[2,2,1,1,1]
[2,1,3,5,4,7,6]=>[2,2,2,1]
[2,1,3,5,6,4,7]=>[2,2,1,1,1]
[2,1,3,5,6,7,4]=>[2,2,1,1,1]
[2,1,3,5,7,4,6]=>[2,2,1,1,1]
[2,1,3,5,7,6,4]=>[3,2,1,1]
[2,1,3,6,4,5,7]=>[2,2,1,1,1]
[2,1,3,6,4,7,5]=>[2,2,2,1]
[2,1,3,6,5,4,7]=>[3,2,1,1]
[2,1,3,6,5,7,4]=>[3,2,1,1]
[2,1,3,6,7,4,5]=>[2,2,1,1,1]
[2,1,3,6,7,5,4]=>[3,2,1,1]
[2,1,3,7,4,5,6]=>[2,2,1,1,1]
[2,1,3,7,4,6,5]=>[3,2,1,1]
[2,1,3,7,5,4,6]=>[3,2,1,1]
[2,1,3,7,5,6,4]=>[3,2,1,1]
[2,1,3,7,6,4,5]=>[3,2,1,1]
[2,1,3,7,6,5,4]=>[4,2,1]
[2,1,4,3,5,6,7]=>[2,2,1,1,1]
[2,1,4,3,5,7,6]=>[2,2,2,1]
[2,1,4,3,6,5,7]=>[2,2,2,1]
[2,1,4,3,6,7,5]=>[2,2,2,1]
[2,1,4,3,7,5,6]=>[2,2,2,1]
[2,1,4,3,7,6,5]=>[3,2,2]
[2,1,4,5,3,6,7]=>[2,2,1,1,1]
[2,1,4,5,3,7,6]=>[2,2,2,1]
[2,1,4,5,6,3,7]=>[2,2,1,1,1]
[2,1,4,5,6,7,3]=>[2,2,1,1,1]
[2,1,4,5,7,3,6]=>[2,2,1,1,1]
[2,1,4,5,7,6,3]=>[3,2,1,1]
[2,1,4,6,3,5,7]=>[2,2,1,1,1]
[2,1,4,6,3,7,5]=>[2,2,2,1]
[2,1,4,6,5,3,7]=>[3,2,1,1]
[2,1,4,6,5,7,3]=>[3,2,1,1]
[2,1,4,6,7,3,5]=>[2,2,1,1,1]
[2,1,4,6,7,5,3]=>[3,2,1,1]
[2,1,4,7,3,5,6]=>[2,2,1,1,1]
[2,1,4,7,3,6,5]=>[3,2,1,1]
[2,1,4,7,5,3,6]=>[3,2,1,1]
[2,1,4,7,5,6,3]=>[3,2,1,1]
[2,1,4,7,6,3,5]=>[3,2,1,1]
[2,1,4,7,6,5,3]=>[4,2,1]
[2,1,5,3,4,6,7]=>[2,2,1,1,1]
[2,1,5,3,4,7,6]=>[2,2,2,1]
[2,1,5,3,6,4,7]=>[2,2,2,1]
[2,1,5,3,6,7,4]=>[2,2,2,1]
[2,1,5,3,7,4,6]=>[2,2,2,1]
[2,1,5,3,7,6,4]=>[3,2,2]
[2,1,5,4,3,6,7]=>[3,2,1,1]
[2,1,5,4,3,7,6]=>[3,2,2]
[2,1,5,4,6,3,7]=>[3,2,1,1]
[2,1,5,4,6,7,3]=>[3,2,1,1]
[2,1,5,4,7,3,6]=>[3,2,1,1]
[2,1,5,4,7,6,3]=>[3,2,2]
[2,1,5,6,3,4,7]=>[2,2,1,1,1]
[2,1,5,6,3,7,4]=>[2,2,2,1]
[2,1,5,6,4,3,7]=>[3,2,1,1]
[2,1,5,6,4,7,3]=>[3,2,1,1]
[2,1,5,6,7,3,4]=>[2,2,1,1,1]
[2,1,5,6,7,4,3]=>[3,2,1,1]
[2,1,5,7,3,4,6]=>[2,2,1,1,1]
[2,1,5,7,3,6,4]=>[3,2,1,1]
[2,1,5,7,4,3,6]=>[3,2,1,1]
[2,1,5,7,4,6,3]=>[3,2,1,1]
[2,1,5,7,6,3,4]=>[3,2,1,1]
[2,1,5,7,6,4,3]=>[4,2,1]
[2,1,6,3,4,5,7]=>[2,2,1,1,1]
[2,1,6,3,4,7,5]=>[2,2,2,1]
[2,1,6,3,5,4,7]=>[3,2,1,1]
[2,1,6,3,5,7,4]=>[3,2,1,1]
[2,1,6,3,7,4,5]=>[2,2,2,1]
[2,1,6,3,7,5,4]=>[3,2,2]
[2,1,6,4,3,5,7]=>[3,2,1,1]
[2,1,6,4,3,7,5]=>[3,2,2]
[2,1,6,4,5,3,7]=>[3,2,1,1]
[2,1,6,4,5,7,3]=>[3,2,1,1]
[2,1,6,4,7,3,5]=>[3,2,1,1]
[2,1,6,4,7,5,3]=>[3,2,2]
[2,1,6,5,3,4,7]=>[3,2,1,1]
[2,1,6,5,3,7,4]=>[3,2,2]
[2,1,6,5,4,3,7]=>[4,2,1]
[2,1,6,5,4,7,3]=>[4,2,1]
[2,1,6,5,7,3,4]=>[3,2,1,1]
[2,1,6,5,7,4,3]=>[4,2,1]
[2,1,6,7,3,4,5]=>[2,2,1,1,1]
[2,1,6,7,3,5,4]=>[3,2,1,1]
[2,1,6,7,4,3,5]=>[3,2,1,1]
[2,1,6,7,4,5,3]=>[3,2,1,1]
[2,1,6,7,5,3,4]=>[3,2,1,1]
[2,1,6,7,5,4,3]=>[4,2,1]
[2,1,7,3,4,5,6]=>[2,2,1,1,1]
[2,1,7,3,4,6,5]=>[3,2,1,1]
[2,1,7,3,5,4,6]=>[3,2,1,1]
[2,1,7,3,5,6,4]=>[3,2,1,1]
[2,1,7,3,6,4,5]=>[3,2,1,1]
[2,1,7,3,6,5,4]=>[4,2,1]
[2,1,7,4,3,5,6]=>[3,2,1,1]
[2,1,7,4,3,6,5]=>[3,2,2]
[2,1,7,4,5,3,6]=>[3,2,1,1]
[2,1,7,4,5,6,3]=>[3,2,1,1]
[2,1,7,4,6,3,5]=>[3,2,1,1]
[2,1,7,4,6,5,3]=>[4,2,1]
[2,1,7,5,3,4,6]=>[3,2,1,1]
[2,1,7,5,3,6,4]=>[3,2,2]
[2,1,7,5,4,3,6]=>[4,2,1]
[2,1,7,5,4,6,3]=>[4,2,1]
[2,1,7,5,6,3,4]=>[3,2,1,1]
[2,1,7,5,6,4,3]=>[4,2,1]
[2,1,7,6,3,4,5]=>[3,2,1,1]
[2,1,7,6,3,5,4]=>[4,2,1]
[2,1,7,6,4,3,5]=>[4,2,1]
[2,1,7,6,4,5,3]=>[4,2,1]
[2,1,7,6,5,3,4]=>[4,2,1]
[2,1,7,6,5,4,3]=>[5,2]
[2,3,1,4,5,6,7]=>[2,1,1,1,1,1]
[2,3,1,4,5,7,6]=>[2,2,1,1,1]
[2,3,1,4,6,5,7]=>[2,2,1,1,1]
[2,3,1,4,6,7,5]=>[2,2,1,1,1]
[2,3,1,4,7,5,6]=>[2,2,1,1,1]
[2,3,1,4,7,6,5]=>[3,2,1,1]
[2,3,1,5,4,6,7]=>[2,2,1,1,1]
[2,3,1,5,4,7,6]=>[2,2,2,1]
[2,3,1,5,6,4,7]=>[2,2,1,1,1]
[2,3,1,5,6,7,4]=>[2,2,1,1,1]
[2,3,1,5,7,4,6]=>[2,2,1,1,1]
[2,3,1,5,7,6,4]=>[3,2,1,1]
[2,3,1,6,4,5,7]=>[2,2,1,1,1]
[2,3,1,6,4,7,5]=>[2,2,2,1]
[2,3,1,6,5,4,7]=>[3,2,1,1]
[2,3,1,6,5,7,4]=>[3,2,1,1]
[2,3,1,6,7,4,5]=>[2,2,1,1,1]
[2,3,1,6,7,5,4]=>[3,2,1,1]
[2,3,1,7,4,5,6]=>[2,2,1,1,1]
[2,3,1,7,4,6,5]=>[3,2,1,1]
[2,3,1,7,5,4,6]=>[3,2,1,1]
[2,3,1,7,5,6,4]=>[3,2,1,1]
[2,3,1,7,6,4,5]=>[3,2,1,1]
[2,3,1,7,6,5,4]=>[4,2,1]
[2,3,4,1,5,6,7]=>[2,1,1,1,1,1]
[2,3,4,1,5,7,6]=>[2,2,1,1,1]
[2,3,4,1,6,5,7]=>[2,2,1,1,1]
[2,3,4,1,6,7,5]=>[2,2,1,1,1]
[2,3,4,1,7,5,6]=>[2,2,1,1,1]
[2,3,4,1,7,6,5]=>[3,2,1,1]
[2,3,4,5,1,6,7]=>[2,1,1,1,1,1]
[2,3,4,5,1,7,6]=>[2,2,1,1,1]
[2,3,4,5,6,1,7]=>[2,1,1,1,1,1]
[2,3,4,5,6,7,1]=>[2,1,1,1,1,1]
[2,3,4,5,7,1,6]=>[2,1,1,1,1,1]
[2,3,4,5,7,6,1]=>[3,1,1,1,1]
[2,3,4,6,1,5,7]=>[2,1,1,1,1,1]
[2,3,4,6,1,7,5]=>[2,2,1,1,1]
[2,3,4,6,5,1,7]=>[3,1,1,1,1]
[2,3,4,6,5,7,1]=>[3,1,1,1,1]
[2,3,4,6,7,1,5]=>[2,1,1,1,1,1]
[2,3,4,6,7,5,1]=>[3,1,1,1,1]
[2,3,4,7,1,5,6]=>[2,1,1,1,1,1]
[2,3,4,7,1,6,5]=>[3,1,1,1,1]
[2,3,4,7,5,1,6]=>[3,1,1,1,1]
[2,3,4,7,5,6,1]=>[3,1,1,1,1]
[2,3,4,7,6,1,5]=>[3,1,1,1,1]
[2,3,4,7,6,5,1]=>[4,1,1,1]
[2,3,5,1,4,6,7]=>[2,1,1,1,1,1]
[2,3,5,1,4,7,6]=>[2,2,1,1,1]
[2,3,5,1,6,4,7]=>[2,2,1,1,1]
[2,3,5,1,6,7,4]=>[2,2,1,1,1]
[2,3,5,1,7,4,6]=>[2,2,1,1,1]
[2,3,5,1,7,6,4]=>[3,2,1,1]
[2,3,5,4,1,6,7]=>[3,1,1,1,1]
[2,3,5,4,1,7,6]=>[3,2,1,1]
[2,3,5,4,6,1,7]=>[3,1,1,1,1]
[2,3,5,4,6,7,1]=>[3,1,1,1,1]
[2,3,5,4,7,1,6]=>[3,1,1,1,1]
[2,3,5,4,7,6,1]=>[3,2,1,1]
[2,3,5,6,1,4,7]=>[2,1,1,1,1,1]
[2,3,5,6,1,7,4]=>[2,2,1,1,1]
[2,3,5,6,4,1,7]=>[3,1,1,1,1]
[2,3,5,6,4,7,1]=>[3,1,1,1,1]
[2,3,5,6,7,1,4]=>[2,1,1,1,1,1]
[2,3,5,6,7,4,1]=>[3,1,1,1,1]
[2,3,5,7,1,4,6]=>[2,1,1,1,1,1]
[2,3,5,7,1,6,4]=>[3,1,1,1,1]
[2,3,5,7,4,1,6]=>[3,1,1,1,1]
[2,3,5,7,4,6,1]=>[3,1,1,1,1]
[2,3,5,7,6,1,4]=>[3,1,1,1,1]
[2,3,5,7,6,4,1]=>[4,1,1,1]
[2,3,6,1,4,5,7]=>[2,1,1,1,1,1]
[2,3,6,1,4,7,5]=>[2,2,1,1,1]
[2,3,6,1,5,4,7]=>[3,1,1,1,1]
[2,3,6,1,5,7,4]=>[3,1,1,1,1]
[2,3,6,1,7,4,5]=>[2,2,1,1,1]
[2,3,6,1,7,5,4]=>[3,2,1,1]
[2,3,6,4,1,5,7]=>[3,1,1,1,1]
[2,3,6,4,1,7,5]=>[3,2,1,1]
[2,3,6,4,5,1,7]=>[3,1,1,1,1]
[2,3,6,4,5,7,1]=>[3,1,1,1,1]
[2,3,6,4,7,1,5]=>[3,1,1,1,1]
[2,3,6,4,7,5,1]=>[3,2,1,1]
[2,3,6,5,1,4,7]=>[3,1,1,1,1]
[2,3,6,5,1,7,4]=>[3,2,1,1]
[2,3,6,5,4,1,7]=>[4,1,1,1]
[2,3,6,5,4,7,1]=>[4,1,1,1]
[2,3,6,5,7,1,4]=>[3,1,1,1,1]
[2,3,6,5,7,4,1]=>[4,1,1,1]
[2,3,6,7,1,4,5]=>[2,1,1,1,1,1]
[2,3,6,7,1,5,4]=>[3,1,1,1,1]
[2,3,6,7,4,1,5]=>[3,1,1,1,1]
[2,3,6,7,4,5,1]=>[3,1,1,1,1]
[2,3,6,7,5,1,4]=>[3,1,1,1,1]
[2,3,6,7,5,4,1]=>[4,1,1,1]
[2,3,7,1,4,5,6]=>[2,1,1,1,1,1]
[2,3,7,1,4,6,5]=>[3,1,1,1,1]
[2,3,7,1,5,4,6]=>[3,1,1,1,1]
[2,3,7,1,5,6,4]=>[3,1,1,1,1]
[2,3,7,1,6,4,5]=>[3,1,1,1,1]
[2,3,7,1,6,5,4]=>[4,1,1,1]
[2,3,7,4,1,5,6]=>[3,1,1,1,1]
[2,3,7,4,1,6,5]=>[3,2,1,1]
[2,3,7,4,5,1,6]=>[3,1,1,1,1]
[2,3,7,4,5,6,1]=>[3,1,1,1,1]
[2,3,7,4,6,1,5]=>[3,1,1,1,1]
[2,3,7,4,6,5,1]=>[4,1,1,1]
[2,3,7,5,1,4,6]=>[3,1,1,1,1]
[2,3,7,5,1,6,4]=>[3,2,1,1]
[2,3,7,5,4,1,6]=>[4,1,1,1]
[2,3,7,5,4,6,1]=>[4,1,1,1]
[2,3,7,5,6,1,4]=>[3,1,1,1,1]
[2,3,7,5,6,4,1]=>[4,1,1,1]
[2,3,7,6,1,4,5]=>[3,1,1,1,1]
[2,3,7,6,1,5,4]=>[4,1,1,1]
[2,3,7,6,4,1,5]=>[4,1,1,1]
[2,3,7,6,4,5,1]=>[4,1,1,1]
[2,3,7,6,5,1,4]=>[4,1,1,1]
[2,3,7,6,5,4,1]=>[5,1,1]
[2,4,1,3,5,6,7]=>[2,1,1,1,1,1]
[2,4,1,3,5,7,6]=>[2,2,1,1,1]
[2,4,1,3,6,5,7]=>[2,2,1,1,1]
[2,4,1,3,6,7,5]=>[2,2,1,1,1]
[2,4,1,3,7,5,6]=>[2,2,1,1,1]
[2,4,1,3,7,6,5]=>[3,2,1,1]
[2,4,1,5,3,6,7]=>[2,2,1,1,1]
[2,4,1,5,3,7,6]=>[2,2,2,1]
[2,4,1,5,6,3,7]=>[2,2,1,1,1]
[2,4,1,5,6,7,3]=>[2,2,1,1,1]
[2,4,1,5,7,3,6]=>[2,2,1,1,1]
[2,4,1,5,7,6,3]=>[3,2,1,1]
[2,4,1,6,3,5,7]=>[2,2,1,1,1]
[2,4,1,6,3,7,5]=>[2,2,2,1]
[2,4,1,6,5,3,7]=>[3,2,1,1]
[2,4,1,6,5,7,3]=>[3,2,1,1]
[2,4,1,6,7,3,5]=>[2,2,1,1,1]
[2,4,1,6,7,5,3]=>[3,2,1,1]
[2,4,1,7,3,5,6]=>[2,2,1,1,1]
[2,4,1,7,3,6,5]=>[3,2,1,1]
[2,4,1,7,5,3,6]=>[3,2,1,1]
[2,4,1,7,5,6,3]=>[3,2,1,1]
[2,4,1,7,6,3,5]=>[3,2,1,1]
[2,4,1,7,6,5,3]=>[4,2,1]
[2,4,3,1,5,6,7]=>[3,1,1,1,1]
[2,4,3,1,5,7,6]=>[3,2,1,1]
[2,4,3,1,6,5,7]=>[3,2,1,1]
[2,4,3,1,6,7,5]=>[3,2,1,1]
[2,4,3,1,7,5,6]=>[3,2,1,1]
[2,4,3,1,7,6,5]=>[3,3,1]
[2,4,3,5,1,6,7]=>[3,1,1,1,1]
[2,4,3,5,1,7,6]=>[3,2,1,1]
[2,4,3,5,6,1,7]=>[3,1,1,1,1]
[2,4,3,5,6,7,1]=>[3,1,1,1,1]
[2,4,3,5,7,1,6]=>[3,1,1,1,1]
[2,4,3,5,7,6,1]=>[3,2,1,1]
[2,4,3,6,1,5,7]=>[3,1,1,1,1]
[2,4,3,6,1,7,5]=>[3,2,1,1]
[2,4,3,6,5,1,7]=>[3,2,1,1]
[2,4,3,6,5,7,1]=>[3,2,1,1]
[2,4,3,6,7,1,5]=>[3,1,1,1,1]
[2,4,3,6,7,5,1]=>[3,2,1,1]
[2,4,3,7,1,5,6]=>[3,1,1,1,1]
[2,4,3,7,1,6,5]=>[3,2,1,1]
[2,4,3,7,5,1,6]=>[3,2,1,1]
[2,4,3,7,5,6,1]=>[3,2,1,1]
[2,4,3,7,6,1,5]=>[3,2,1,1]
[2,4,3,7,6,5,1]=>[4,2,1]
[2,4,5,1,3,6,7]=>[2,1,1,1,1,1]
[2,4,5,1,3,7,6]=>[2,2,1,1,1]
[2,4,5,1,6,3,7]=>[2,2,1,1,1]
[2,4,5,1,6,7,3]=>[2,2,1,1,1]
[2,4,5,1,7,3,6]=>[2,2,1,1,1]
[2,4,5,1,7,6,3]=>[3,2,1,1]
[2,4,5,3,1,6,7]=>[3,1,1,1,1]
[2,4,5,3,1,7,6]=>[3,2,1,1]
[2,4,5,3,6,1,7]=>[3,1,1,1,1]
[2,4,5,3,6,7,1]=>[3,1,1,1,1]
[2,4,5,3,7,1,6]=>[3,1,1,1,1]
[2,4,5,3,7,6,1]=>[3,2,1,1]
[2,4,5,6,1,3,7]=>[2,1,1,1,1,1]
[2,4,5,6,1,7,3]=>[2,2,1,1,1]
[2,4,5,6,3,1,7]=>[3,1,1,1,1]
[2,4,5,6,3,7,1]=>[3,1,1,1,1]
[2,4,5,6,7,1,3]=>[2,1,1,1,1,1]
[2,4,5,6,7,3,1]=>[3,1,1,1,1]
[2,4,5,7,1,3,6]=>[2,1,1,1,1,1]
[2,4,5,7,1,6,3]=>[3,1,1,1,1]
[2,4,5,7,3,1,6]=>[3,1,1,1,1]
[2,4,5,7,3,6,1]=>[3,1,1,1,1]
[2,4,5,7,6,1,3]=>[3,1,1,1,1]
[2,4,5,7,6,3,1]=>[4,1,1,1]
[2,4,6,1,3,5,7]=>[2,1,1,1,1,1]
[2,4,6,1,3,7,5]=>[2,2,1,1,1]
[2,4,6,1,5,3,7]=>[3,1,1,1,1]
[2,4,6,1,5,7,3]=>[3,1,1,1,1]
[2,4,6,1,7,3,5]=>[2,2,1,1,1]
[2,4,6,1,7,5,3]=>[3,2,1,1]
[2,4,6,3,1,5,7]=>[3,1,1,1,1]
[2,4,6,3,1,7,5]=>[3,2,1,1]
[2,4,6,3,5,1,7]=>[3,1,1,1,1]
[2,4,6,3,5,7,1]=>[3,1,1,1,1]
[2,4,6,3,7,1,5]=>[3,1,1,1,1]
[2,4,6,3,7,5,1]=>[3,2,1,1]
[2,4,6,5,1,3,7]=>[3,1,1,1,1]
[2,4,6,5,1,7,3]=>[3,2,1,1]
[2,4,6,5,3,1,7]=>[4,1,1,1]
[2,4,6,5,3,7,1]=>[4,1,1,1]
[2,4,6,5,7,1,3]=>[3,1,1,1,1]
[2,4,6,5,7,3,1]=>[4,1,1,1]
[2,4,6,7,1,3,5]=>[2,1,1,1,1,1]
[2,4,6,7,1,5,3]=>[3,1,1,1,1]
[2,4,6,7,3,1,5]=>[3,1,1,1,1]
[2,4,6,7,3,5,1]=>[3,1,1,1,1]
[2,4,6,7,5,1,3]=>[3,1,1,1,1]
[2,4,6,7,5,3,1]=>[4,1,1,1]
[2,4,7,1,3,5,6]=>[2,1,1,1,1,1]
[2,4,7,1,3,6,5]=>[3,1,1,1,1]
[2,4,7,1,5,3,6]=>[3,1,1,1,1]
[2,4,7,1,5,6,3]=>[3,1,1,1,1]
[2,4,7,1,6,3,5]=>[3,1,1,1,1]
[2,4,7,1,6,5,3]=>[4,1,1,1]
[2,4,7,3,1,5,6]=>[3,1,1,1,1]
[2,4,7,3,1,6,5]=>[3,2,1,1]
[2,4,7,3,5,1,6]=>[3,1,1,1,1]
[2,4,7,3,5,6,1]=>[3,1,1,1,1]
[2,4,7,3,6,1,5]=>[3,1,1,1,1]
[2,4,7,3,6,5,1]=>[4,1,1,1]
[2,4,7,5,1,3,6]=>[3,1,1,1,1]
[2,4,7,5,1,6,3]=>[3,2,1,1]
[2,4,7,5,3,1,6]=>[4,1,1,1]
[2,4,7,5,3,6,1]=>[4,1,1,1]
[2,4,7,5,6,1,3]=>[3,1,1,1,1]
[2,4,7,5,6,3,1]=>[4,1,1,1]
[2,4,7,6,1,3,5]=>[3,1,1,1,1]
[2,4,7,6,1,5,3]=>[4,1,1,1]
[2,4,7,6,3,1,5]=>[4,1,1,1]
[2,4,7,6,3,5,1]=>[4,1,1,1]
[2,4,7,6,5,1,3]=>[4,1,1,1]
[2,4,7,6,5,3,1]=>[5,1,1]
[2,5,1,3,4,6,7]=>[2,1,1,1,1,1]
[2,5,1,3,4,7,6]=>[2,2,1,1,1]
[2,5,1,3,6,4,7]=>[2,2,1,1,1]
[2,5,1,3,6,7,4]=>[2,2,1,1,1]
[2,5,1,3,7,4,6]=>[2,2,1,1,1]
[2,5,1,3,7,6,4]=>[3,2,1,1]
[2,5,1,4,3,6,7]=>[3,1,1,1,1]
[2,5,1,4,3,7,6]=>[3,2,1,1]
[2,5,1,4,6,3,7]=>[3,1,1,1,1]
[2,5,1,4,6,7,3]=>[3,1,1,1,1]
[2,5,1,4,7,3,6]=>[3,1,1,1,1]
[2,5,1,4,7,6,3]=>[3,2,1,1]
[2,5,1,6,3,4,7]=>[2,2,1,1,1]
[2,5,1,6,3,7,4]=>[2,2,2,1]
[2,5,1,6,4,3,7]=>[3,2,1,1]
[2,5,1,6,4,7,3]=>[3,2,1,1]
[2,5,1,6,7,3,4]=>[2,2,1,1,1]
[2,5,1,6,7,4,3]=>[3,2,1,1]
[2,5,1,7,3,4,6]=>[2,2,1,1,1]
[2,5,1,7,3,6,4]=>[3,2,1,1]
[2,5,1,7,4,3,6]=>[3,2,1,1]
[2,5,1,7,4,6,3]=>[3,2,1,1]
[2,5,1,7,6,3,4]=>[3,2,1,1]
[2,5,1,7,6,4,3]=>[4,2,1]
[2,5,3,1,4,6,7]=>[3,1,1,1,1]
[2,5,3,1,4,7,6]=>[3,2,1,1]
[2,5,3,1,6,4,7]=>[3,2,1,1]
[2,5,3,1,6,7,4]=>[3,2,1,1]
[2,5,3,1,7,4,6]=>[3,2,1,1]
[2,5,3,1,7,6,4]=>[3,3,1]
[2,5,3,4,1,6,7]=>[3,1,1,1,1]
[2,5,3,4,1,7,6]=>[3,2,1,1]
[2,5,3,4,6,1,7]=>[3,1,1,1,1]
[2,5,3,4,6,7,1]=>[3,1,1,1,1]
[2,5,3,4,7,1,6]=>[3,1,1,1,1]
[2,5,3,4,7,6,1]=>[3,2,1,1]
[2,5,3,6,1,4,7]=>[3,1,1,1,1]
[2,5,3,6,1,7,4]=>[3,2,1,1]
[2,5,3,6,4,1,7]=>[3,2,1,1]
[2,5,3,6,4,7,1]=>[3,2,1,1]
[2,5,3,6,7,1,4]=>[3,1,1,1,1]
[2,5,3,6,7,4,1]=>[3,2,1,1]
[2,5,3,7,1,4,6]=>[3,1,1,1,1]
[2,5,3,7,1,6,4]=>[3,2,1,1]
[2,5,3,7,4,1,6]=>[3,2,1,1]
[2,5,3,7,4,6,1]=>[3,2,1,1]
[2,5,3,7,6,1,4]=>[3,2,1,1]
[2,5,3,7,6,4,1]=>[4,2,1]
[2,5,4,1,3,6,7]=>[3,1,1,1,1]
[2,5,4,1,3,7,6]=>[3,2,1,1]
[2,5,4,1,6,3,7]=>[3,2,1,1]
[2,5,4,1,6,7,3]=>[3,2,1,1]
[2,5,4,1,7,3,6]=>[3,2,1,1]
[2,5,4,1,7,6,3]=>[3,3,1]
[2,5,4,3,1,6,7]=>[4,1,1,1]
[2,5,4,3,1,7,6]=>[4,2,1]
[2,5,4,3,6,1,7]=>[4,1,1,1]
[2,5,4,3,6,7,1]=>[4,1,1,1]
[2,5,4,3,7,1,6]=>[4,1,1,1]
[2,5,4,3,7,6,1]=>[4,2,1]
[2,5,4,6,1,3,7]=>[3,1,1,1,1]
[2,5,4,6,1,7,3]=>[3,2,1,1]
[2,5,4,6,3,1,7]=>[4,1,1,1]
[2,5,4,6,3,7,1]=>[4,1,1,1]
[2,5,4,6,7,1,3]=>[3,1,1,1,1]
[2,5,4,6,7,3,1]=>[4,1,1,1]
[2,5,4,7,1,3,6]=>[3,1,1,1,1]
[2,5,4,7,1,6,3]=>[3,2,1,1]
[2,5,4,7,3,1,6]=>[4,1,1,1]
[2,5,4,7,3,6,1]=>[4,1,1,1]
[2,5,4,7,6,1,3]=>[3,2,1,1]
[2,5,4,7,6,3,1]=>[4,2,1]
[2,5,6,1,3,4,7]=>[2,1,1,1,1,1]
[2,5,6,1,3,7,4]=>[2,2,1,1,1]
[2,5,6,1,4,3,7]=>[3,1,1,1,1]
[2,5,6,1,4,7,3]=>[3,1,1,1,1]
[2,5,6,1,7,3,4]=>[2,2,1,1,1]
[2,5,6,1,7,4,3]=>[3,2,1,1]
[2,5,6,3,1,4,7]=>[3,1,1,1,1]
[2,5,6,3,1,7,4]=>[3,2,1,1]
[2,5,6,3,4,1,7]=>[3,1,1,1,1]
[2,5,6,3,4,7,1]=>[3,1,1,1,1]
[2,5,6,3,7,1,4]=>[3,1,1,1,1]
[2,5,6,3,7,4,1]=>[3,2,1,1]
[2,5,6,4,1,3,7]=>[3,1,1,1,1]
[2,5,6,4,1,7,3]=>[3,2,1,1]
[2,5,6,4,3,1,7]=>[4,1,1,1]
[2,5,6,4,3,7,1]=>[4,1,1,1]
[2,5,6,4,7,1,3]=>[3,1,1,1,1]
[2,5,6,4,7,3,1]=>[4,1,1,1]
[2,5,6,7,1,3,4]=>[2,1,1,1,1,1]
[2,5,6,7,1,4,3]=>[3,1,1,1,1]
[2,5,6,7,3,1,4]=>[3,1,1,1,1]
[2,5,6,7,3,4,1]=>[3,1,1,1,1]
[2,5,6,7,4,1,3]=>[3,1,1,1,1]
[2,5,6,7,4,3,1]=>[4,1,1,1]
[2,5,7,1,3,4,6]=>[2,1,1,1,1,1]
[2,5,7,1,3,6,4]=>[3,1,1,1,1]
[2,5,7,1,4,3,6]=>[3,1,1,1,1]
[2,5,7,1,4,6,3]=>[3,1,1,1,1]
[2,5,7,1,6,3,4]=>[3,1,1,1,1]
[2,5,7,1,6,4,3]=>[4,1,1,1]
[2,5,7,3,1,4,6]=>[3,1,1,1,1]
[2,5,7,3,1,6,4]=>[3,2,1,1]
[2,5,7,3,4,1,6]=>[3,1,1,1,1]
[2,5,7,3,4,6,1]=>[3,1,1,1,1]
[2,5,7,3,6,1,4]=>[3,1,1,1,1]
[2,5,7,3,6,4,1]=>[4,1,1,1]
[2,5,7,4,1,3,6]=>[3,1,1,1,1]
[2,5,7,4,1,6,3]=>[3,2,1,1]
[2,5,7,4,3,1,6]=>[4,1,1,1]
[2,5,7,4,3,6,1]=>[4,1,1,1]
[2,5,7,4,6,1,3]=>[3,1,1,1,1]
[2,5,7,4,6,3,1]=>[4,1,1,1]
[2,5,7,6,1,3,4]=>[3,1,1,1,1]
[2,5,7,6,1,4,3]=>[4,1,1,1]
[2,5,7,6,3,1,4]=>[4,1,1,1]
[2,5,7,6,3,4,1]=>[4,1,1,1]
[2,5,7,6,4,1,3]=>[4,1,1,1]
[2,5,7,6,4,3,1]=>[5,1,1]
[2,6,1,3,4,5,7]=>[2,1,1,1,1,1]
[2,6,1,3,4,7,5]=>[2,2,1,1,1]
[2,6,1,3,5,4,7]=>[3,1,1,1,1]
[2,6,1,3,5,7,4]=>[3,1,1,1,1]
[2,6,1,3,7,4,5]=>[2,2,1,1,1]
[2,6,1,3,7,5,4]=>[3,2,1,1]
[2,6,1,4,3,5,7]=>[3,1,1,1,1]
[2,6,1,4,3,7,5]=>[3,2,1,1]
[2,6,1,4,5,3,7]=>[3,1,1,1,1]
[2,6,1,4,5,7,3]=>[3,1,1,1,1]
[2,6,1,4,7,3,5]=>[3,1,1,1,1]
[2,6,1,4,7,5,3]=>[3,2,1,1]
[2,6,1,5,3,4,7]=>[3,1,1,1,1]
[2,6,1,5,3,7,4]=>[3,2,1,1]
[2,6,1,5,4,3,7]=>[4,1,1,1]
[2,6,1,5,4,7,3]=>[4,1,1,1]
[2,6,1,5,7,3,4]=>[3,1,1,1,1]
[2,6,1,5,7,4,3]=>[4,1,1,1]
[2,6,1,7,3,4,5]=>[2,2,1,1,1]
[2,6,1,7,3,5,4]=>[3,2,1,1]
[2,6,1,7,4,3,5]=>[3,2,1,1]
[2,6,1,7,4,5,3]=>[3,2,1,1]
[2,6,1,7,5,3,4]=>[3,2,1,1]
[2,6,1,7,5,4,3]=>[4,2,1]
[2,6,3,1,4,5,7]=>[3,1,1,1,1]
[2,6,3,1,4,7,5]=>[3,2,1,1]
[2,6,3,1,5,4,7]=>[3,2,1,1]
[2,6,3,1,5,7,4]=>[3,2,1,1]
[2,6,3,1,7,4,5]=>[3,2,1,1]
[2,6,3,1,7,5,4]=>[3,3,1]
[2,6,3,4,1,5,7]=>[3,1,1,1,1]
[2,6,3,4,1,7,5]=>[3,2,1,1]
[2,6,3,4,5,1,7]=>[3,1,1,1,1]
[2,6,3,4,5,7,1]=>[3,1,1,1,1]
[2,6,3,4,7,1,5]=>[3,1,1,1,1]
[2,6,3,4,7,5,1]=>[3,2,1,1]
[2,6,3,5,1,4,7]=>[3,1,1,1,1]
[2,6,3,5,1,7,4]=>[3,2,1,1]
[2,6,3,5,4,1,7]=>[4,1,1,1]
[2,6,3,5,4,7,1]=>[4,1,1,1]
[2,6,3,5,7,1,4]=>[3,1,1,1,1]
[2,6,3,5,7,4,1]=>[4,1,1,1]
[2,6,3,7,1,4,5]=>[3,1,1,1,1]
[2,6,3,7,1,5,4]=>[3,2,1,1]
[2,6,3,7,4,1,5]=>[3,2,1,1]
[2,6,3,7,4,5,1]=>[3,2,1,1]
[2,6,3,7,5,1,4]=>[3,2,1,1]
[2,6,3,7,5,4,1]=>[4,2,1]
[2,6,4,1,3,5,7]=>[3,1,1,1,1]
[2,6,4,1,3,7,5]=>[3,2,1,1]
[2,6,4,1,5,3,7]=>[3,2,1,1]
[2,6,4,1,5,7,3]=>[3,2,1,1]
[2,6,4,1,7,3,5]=>[3,2,1,1]
[2,6,4,1,7,5,3]=>[3,3,1]
[2,6,4,3,1,5,7]=>[4,1,1,1]
[2,6,4,3,1,7,5]=>[4,2,1]
[2,6,4,3,5,1,7]=>[4,1,1,1]
[2,6,4,3,5,7,1]=>[4,1,1,1]
[2,6,4,3,7,1,5]=>[4,1,1,1]
[2,6,4,3,7,5,1]=>[4,2,1]
[2,6,4,5,1,3,7]=>[3,1,1,1,1]
[2,6,4,5,1,7,3]=>[3,2,1,1]
[2,6,4,5,3,1,7]=>[4,1,1,1]
[2,6,4,5,3,7,1]=>[4,1,1,1]
[2,6,4,5,7,1,3]=>[3,1,1,1,1]
[2,6,4,5,7,3,1]=>[4,1,1,1]
[2,6,4,7,1,3,5]=>[3,1,1,1,1]
[2,6,4,7,1,5,3]=>[3,2,1,1]
[2,6,4,7,3,1,5]=>[4,1,1,1]
[2,6,4,7,3,5,1]=>[4,1,1,1]
[2,6,4,7,5,1,3]=>[3,2,1,1]
[2,6,4,7,5,3,1]=>[4,2,1]
[2,6,5,1,3,4,7]=>[3,1,1,1,1]
[2,6,5,1,3,7,4]=>[3,2,1,1]
[2,6,5,1,4,3,7]=>[4,1,1,1]
[2,6,5,1,4,7,3]=>[4,1,1,1]
[2,6,5,1,7,3,4]=>[3,2,1,1]
[2,6,5,1,7,4,3]=>[4,2,1]
[2,6,5,3,1,4,7]=>[4,1,1,1]
[2,6,5,3,1,7,4]=>[4,2,1]
[2,6,5,3,4,1,7]=>[4,1,1,1]
[2,6,5,3,4,7,1]=>[4,1,1,1]
[2,6,5,3,7,1,4]=>[4,1,1,1]
[2,6,5,3,7,4,1]=>[4,2,1]
[2,6,5,4,1,3,7]=>[4,1,1,1]
[2,6,5,4,1,7,3]=>[4,2,1]
[2,6,5,4,3,1,7]=>[5,1,1]
[2,6,5,4,3,7,1]=>[5,1,1]
[2,6,5,4,7,1,3]=>[4,1,1,1]
[2,6,5,4,7,3,1]=>[5,1,1]
[2,6,5,7,1,3,4]=>[3,1,1,1,1]
[2,6,5,7,1,4,3]=>[4,1,1,1]
[2,6,5,7,3,1,4]=>[4,1,1,1]
[2,6,5,7,3,4,1]=>[4,1,1,1]
[2,6,5,7,4,1,3]=>[4,1,1,1]
[2,6,5,7,4,3,1]=>[5,1,1]
[2,6,7,1,3,4,5]=>[2,1,1,1,1,1]
[2,6,7,1,3,5,4]=>[3,1,1,1,1]
[2,6,7,1,4,3,5]=>[3,1,1,1,1]
[2,6,7,1,4,5,3]=>[3,1,1,1,1]
[2,6,7,1,5,3,4]=>[3,1,1,1,1]
[2,6,7,1,5,4,3]=>[4,1,1,1]
[2,6,7,3,1,4,5]=>[3,1,1,1,1]
[2,6,7,3,1,5,4]=>[3,2,1,1]
[2,6,7,3,4,1,5]=>[3,1,1,1,1]
[2,6,7,3,4,5,1]=>[3,1,1,1,1]
[2,6,7,3,5,1,4]=>[3,1,1,1,1]
[2,6,7,3,5,4,1]=>[4,1,1,1]
[2,6,7,4,1,3,5]=>[3,1,1,1,1]
[2,6,7,4,1,5,3]=>[3,2,1,1]
[2,6,7,4,3,1,5]=>[4,1,1,1]
[2,6,7,4,3,5,1]=>[4,1,1,1]
[2,6,7,4,5,1,3]=>[3,1,1,1,1]
[2,6,7,4,5,3,1]=>[4,1,1,1]
[2,6,7,5,1,3,4]=>[3,1,1,1,1]
[2,6,7,5,1,4,3]=>[4,1,1,1]
[2,6,7,5,3,1,4]=>[4,1,1,1]
[2,6,7,5,3,4,1]=>[4,1,1,1]
[2,6,7,5,4,1,3]=>[4,1,1,1]
[2,6,7,5,4,3,1]=>[5,1,1]
[2,7,1,3,4,5,6]=>[2,1,1,1,1,1]
[2,7,1,3,4,6,5]=>[3,1,1,1,1]
[2,7,1,3,5,4,6]=>[3,1,1,1,1]
[2,7,1,3,5,6,4]=>[3,1,1,1,1]
[2,7,1,3,6,4,5]=>[3,1,1,1,1]
[2,7,1,3,6,5,4]=>[4,1,1,1]
[2,7,1,4,3,5,6]=>[3,1,1,1,1]
[2,7,1,4,3,6,5]=>[3,2,1,1]
[2,7,1,4,5,3,6]=>[3,1,1,1,1]
[2,7,1,4,5,6,3]=>[3,1,1,1,1]
[2,7,1,4,6,3,5]=>[3,1,1,1,1]
[2,7,1,4,6,5,3]=>[4,1,1,1]
[2,7,1,5,3,4,6]=>[3,1,1,1,1]
[2,7,1,5,3,6,4]=>[3,2,1,1]
[2,7,1,5,4,3,6]=>[4,1,1,1]
[2,7,1,5,4,6,3]=>[4,1,1,1]
[2,7,1,5,6,3,4]=>[3,1,1,1,1]
[2,7,1,5,6,4,3]=>[4,1,1,1]
[2,7,1,6,3,4,5]=>[3,1,1,1,1]
[2,7,1,6,3,5,4]=>[4,1,1,1]
[2,7,1,6,4,3,5]=>[4,1,1,1]
[2,7,1,6,4,5,3]=>[4,1,1,1]
[2,7,1,6,5,3,4]=>[4,1,1,1]
[2,7,1,6,5,4,3]=>[5,1,1]
[2,7,3,1,4,5,6]=>[3,1,1,1,1]
[2,7,3,1,4,6,5]=>[3,2,1,1]
[2,7,3,1,5,4,6]=>[3,2,1,1]
[2,7,3,1,5,6,4]=>[3,2,1,1]
[2,7,3,1,6,4,5]=>[3,2,1,1]
[2,7,3,1,6,5,4]=>[4,2,1]
[2,7,3,4,1,5,6]=>[3,1,1,1,1]
[2,7,3,4,1,6,5]=>[3,2,1,1]
[2,7,3,4,5,1,6]=>[3,1,1,1,1]
[2,7,3,4,5,6,1]=>[3,1,1,1,1]
[2,7,3,4,6,1,5]=>[3,1,1,1,1]
[2,7,3,4,6,5,1]=>[4,1,1,1]
[2,7,3,5,1,4,6]=>[3,1,1,1,1]
[2,7,3,5,1,6,4]=>[3,2,1,1]
[2,7,3,5,4,1,6]=>[4,1,1,1]
[2,7,3,5,4,6,1]=>[4,1,1,1]
[2,7,3,5,6,1,4]=>[3,1,1,1,1]
[2,7,3,5,6,4,1]=>[4,1,1,1]
[2,7,3,6,1,4,5]=>[3,1,1,1,1]
[2,7,3,6,1,5,4]=>[4,1,1,1]
[2,7,3,6,4,1,5]=>[4,1,1,1]
[2,7,3,6,4,5,1]=>[4,1,1,1]
[2,7,3,6,5,1,4]=>[4,1,1,1]
[2,7,3,6,5,4,1]=>[5,1,1]
[2,7,4,1,3,5,6]=>[3,1,1,1,1]
[2,7,4,1,3,6,5]=>[3,2,1,1]
[2,7,4,1,5,3,6]=>[3,2,1,1]
[2,7,4,1,5,6,3]=>[3,2,1,1]
[2,7,4,1,6,3,5]=>[3,2,1,1]
[2,7,4,1,6,5,3]=>[4,2,1]
[2,7,4,3,1,5,6]=>[4,1,1,1]
[2,7,4,3,1,6,5]=>[4,2,1]
[2,7,4,3,5,1,6]=>[4,1,1,1]
[2,7,4,3,5,6,1]=>[4,1,1,1]
[2,7,4,3,6,1,5]=>[4,1,1,1]
[2,7,4,3,6,5,1]=>[4,2,1]
[2,7,4,5,1,3,6]=>[3,1,1,1,1]
[2,7,4,5,1,6,3]=>[3,2,1,1]
[2,7,4,5,3,1,6]=>[4,1,1,1]
[2,7,4,5,3,6,1]=>[4,1,1,1]
[2,7,4,5,6,1,3]=>[3,1,1,1,1]
[2,7,4,5,6,3,1]=>[4,1,1,1]
[2,7,4,6,1,3,5]=>[3,1,1,1,1]
[2,7,4,6,1,5,3]=>[4,1,1,1]
[2,7,4,6,3,1,5]=>[4,1,1,1]
[2,7,4,6,3,5,1]=>[4,1,1,1]
[2,7,4,6,5,1,3]=>[4,1,1,1]
[2,7,4,6,5,3,1]=>[5,1,1]
[2,7,5,1,3,4,6]=>[3,1,1,1,1]
[2,7,5,1,3,6,4]=>[3,2,1,1]
[2,7,5,1,4,3,6]=>[4,1,1,1]
[2,7,5,1,4,6,3]=>[4,1,1,1]
[2,7,5,1,6,3,4]=>[3,2,1,1]
[2,7,5,1,6,4,3]=>[4,2,1]
[2,7,5,3,1,4,6]=>[4,1,1,1]
[2,7,5,3,1,6,4]=>[4,2,1]
[2,7,5,3,4,1,6]=>[4,1,1,1]
[2,7,5,3,4,6,1]=>[4,1,1,1]
[2,7,5,3,6,1,4]=>[4,1,1,1]
[2,7,5,3,6,4,1]=>[4,2,1]
[2,7,5,4,1,3,6]=>[4,1,1,1]
[2,7,5,4,1,6,3]=>[4,2,1]
[2,7,5,4,3,1,6]=>[5,1,1]
[2,7,5,4,3,6,1]=>[5,1,1]
[2,7,5,4,6,1,3]=>[4,1,1,1]
[2,7,5,4,6,3,1]=>[5,1,1]
[2,7,5,6,1,3,4]=>[3,1,1,1,1]
[2,7,5,6,1,4,3]=>[4,1,1,1]
[2,7,5,6,3,1,4]=>[4,1,1,1]
[2,7,5,6,3,4,1]=>[4,1,1,1]
[2,7,5,6,4,1,3]=>[4,1,1,1]
[2,7,5,6,4,3,1]=>[5,1,1]
[2,7,6,1,3,4,5]=>[3,1,1,1,1]
[2,7,6,1,3,5,4]=>[4,1,1,1]
[2,7,6,1,4,3,5]=>[4,1,1,1]
[2,7,6,1,4,5,3]=>[4,1,1,1]
[2,7,6,1,5,3,4]=>[4,1,1,1]
[2,7,6,1,5,4,3]=>[5,1,1]
[2,7,6,3,1,4,5]=>[4,1,1,1]
[2,7,6,3,1,5,4]=>[4,2,1]
[2,7,6,3,4,1,5]=>[4,1,1,1]
[2,7,6,3,4,5,1]=>[4,1,1,1]
[2,7,6,3,5,1,4]=>[4,1,1,1]
[2,7,6,3,5,4,1]=>[5,1,1]
[2,7,6,4,1,3,5]=>[4,1,1,1]
[2,7,6,4,1,5,3]=>[4,2,1]
[2,7,6,4,3,1,5]=>[5,1,1]
[2,7,6,4,3,5,1]=>[5,1,1]
[2,7,6,4,5,1,3]=>[4,1,1,1]
[2,7,6,4,5,3,1]=>[5,1,1]
[2,7,6,5,1,3,4]=>[4,1,1,1]
[2,7,6,5,1,4,3]=>[5,1,1]
[2,7,6,5,3,1,4]=>[5,1,1]
[2,7,6,5,3,4,1]=>[5,1,1]
[2,7,6,5,4,1,3]=>[5,1,1]
[2,7,6,5,4,3,1]=>[6,1]
[3,1,2,4,5,6,7]=>[2,1,1,1,1,1]
[3,1,2,4,5,7,6]=>[2,2,1,1,1]
[3,1,2,4,6,5,7]=>[2,2,1,1,1]
[3,1,2,4,6,7,5]=>[2,2,1,1,1]
[3,1,2,4,7,5,6]=>[2,2,1,1,1]
[3,1,2,4,7,6,5]=>[3,2,1,1]
[3,1,2,5,4,6,7]=>[2,2,1,1,1]
[3,1,2,5,4,7,6]=>[2,2,2,1]
[3,1,2,5,6,4,7]=>[2,2,1,1,1]
[3,1,2,5,6,7,4]=>[2,2,1,1,1]
[3,1,2,5,7,4,6]=>[2,2,1,1,1]
[3,1,2,5,7,6,4]=>[3,2,1,1]
[3,1,2,6,4,5,7]=>[2,2,1,1,1]
[3,1,2,6,4,7,5]=>[2,2,2,1]
[3,1,2,6,5,4,7]=>[3,2,1,1]
[3,1,2,6,5,7,4]=>[3,2,1,1]
[3,1,2,6,7,4,5]=>[2,2,1,1,1]
[3,1,2,6,7,5,4]=>[3,2,1,1]
[3,1,2,7,4,5,6]=>[2,2,1,1,1]
[3,1,2,7,4,6,5]=>[3,2,1,1]
[3,1,2,7,5,4,6]=>[3,2,1,1]
[3,1,2,7,5,6,4]=>[3,2,1,1]
[3,1,2,7,6,4,5]=>[3,2,1,1]
[3,1,2,7,6,5,4]=>[4,2,1]
[3,1,4,2,5,6,7]=>[2,2,1,1,1]
[3,1,4,2,5,7,6]=>[2,2,2,1]
[3,1,4,2,6,5,7]=>[2,2,2,1]
[3,1,4,2,6,7,5]=>[2,2,2,1]
[3,1,4,2,7,5,6]=>[2,2,2,1]
[3,1,4,2,7,6,5]=>[3,2,2]
[3,1,4,5,2,6,7]=>[2,2,1,1,1]
[3,1,4,5,2,7,6]=>[2,2,2,1]
[3,1,4,5,6,2,7]=>[2,2,1,1,1]
[3,1,4,5,6,7,2]=>[2,2,1,1,1]
[3,1,4,5,7,2,6]=>[2,2,1,1,1]
[3,1,4,5,7,6,2]=>[3,2,1,1]
[3,1,4,6,2,5,7]=>[2,2,1,1,1]
[3,1,4,6,2,7,5]=>[2,2,2,1]
[3,1,4,6,5,2,7]=>[3,2,1,1]
[3,1,4,6,5,7,2]=>[3,2,1,1]
[3,1,4,6,7,2,5]=>[2,2,1,1,1]
[3,1,4,6,7,5,2]=>[3,2,1,1]
[3,1,4,7,2,5,6]=>[2,2,1,1,1]
[3,1,4,7,2,6,5]=>[3,2,1,1]
[3,1,4,7,5,2,6]=>[3,2,1,1]
[3,1,4,7,5,6,2]=>[3,2,1,1]
[3,1,4,7,6,2,5]=>[3,2,1,1]
[3,1,4,7,6,5,2]=>[4,2,1]
[3,1,5,2,4,6,7]=>[2,2,1,1,1]
[3,1,5,2,4,7,6]=>[2,2,2,1]
[3,1,5,2,6,4,7]=>[2,2,2,1]
[3,1,5,2,6,7,4]=>[2,2,2,1]
[3,1,5,2,7,4,6]=>[2,2,2,1]
[3,1,5,2,7,6,4]=>[3,2,2]
[3,1,5,4,2,6,7]=>[3,2,1,1]
[3,1,5,4,2,7,6]=>[3,2,2]
[3,1,5,4,6,2,7]=>[3,2,1,1]
[3,1,5,4,6,7,2]=>[3,2,1,1]
[3,1,5,4,7,2,6]=>[3,2,1,1]
[3,1,5,4,7,6,2]=>[3,2,2]
[3,1,5,6,2,4,7]=>[2,2,1,1,1]
[3,1,5,6,2,7,4]=>[2,2,2,1]
[3,1,5,6,4,2,7]=>[3,2,1,1]
[3,1,5,6,4,7,2]=>[3,2,1,1]
[3,1,5,6,7,2,4]=>[2,2,1,1,1]
[3,1,5,6,7,4,2]=>[3,2,1,1]
[3,1,5,7,2,4,6]=>[2,2,1,1,1]
[3,1,5,7,2,6,4]=>[3,2,1,1]
[3,1,5,7,4,2,6]=>[3,2,1,1]
[3,1,5,7,4,6,2]=>[3,2,1,1]
[3,1,5,7,6,2,4]=>[3,2,1,1]
[3,1,5,7,6,4,2]=>[4,2,1]
[3,1,6,2,4,5,7]=>[2,2,1,1,1]
[3,1,6,2,4,7,5]=>[2,2,2,1]
[3,1,6,2,5,4,7]=>[3,2,1,1]
[3,1,6,2,5,7,4]=>[3,2,1,1]
[3,1,6,2,7,4,5]=>[2,2,2,1]
[3,1,6,2,7,5,4]=>[3,2,2]
[3,1,6,4,2,5,7]=>[3,2,1,1]
[3,1,6,4,2,7,5]=>[3,2,2]
[3,1,6,4,5,2,7]=>[3,2,1,1]
[3,1,6,4,5,7,2]=>[3,2,1,1]
[3,1,6,4,7,2,5]=>[3,2,1,1]
[3,1,6,4,7,5,2]=>[3,2,2]
[3,1,6,5,2,4,7]=>[3,2,1,1]
[3,1,6,5,2,7,4]=>[3,2,2]
[3,1,6,5,4,2,7]=>[4,2,1]
[3,1,6,5,4,7,2]=>[4,2,1]
[3,1,6,5,7,2,4]=>[3,2,1,1]
[3,1,6,5,7,4,2]=>[4,2,1]
[3,1,6,7,2,4,5]=>[2,2,1,1,1]
[3,1,6,7,2,5,4]=>[3,2,1,1]
[3,1,6,7,4,2,5]=>[3,2,1,1]
[3,1,6,7,4,5,2]=>[3,2,1,1]
[3,1,6,7,5,2,4]=>[3,2,1,1]
[3,1,6,7,5,4,2]=>[4,2,1]
[3,1,7,2,4,5,6]=>[2,2,1,1,1]
[3,1,7,2,4,6,5]=>[3,2,1,1]
[3,1,7,2,5,4,6]=>[3,2,1,1]
[3,1,7,2,5,6,4]=>[3,2,1,1]
[3,1,7,2,6,4,5]=>[3,2,1,1]
[3,1,7,2,6,5,4]=>[4,2,1]
[3,1,7,4,2,5,6]=>[3,2,1,1]
[3,1,7,4,2,6,5]=>[3,2,2]
[3,1,7,4,5,2,6]=>[3,2,1,1]
[3,1,7,4,5,6,2]=>[3,2,1,1]
[3,1,7,4,6,2,5]=>[3,2,1,1]
[3,1,7,4,6,5,2]=>[4,2,1]
[3,1,7,5,2,4,6]=>[3,2,1,1]
[3,1,7,5,2,6,4]=>[3,2,2]
[3,1,7,5,4,2,6]=>[4,2,1]
[3,1,7,5,4,6,2]=>[4,2,1]
[3,1,7,5,6,2,4]=>[3,2,1,1]
[3,1,7,5,6,4,2]=>[4,2,1]
[3,1,7,6,2,4,5]=>[3,2,1,1]
[3,1,7,6,2,5,4]=>[4,2,1]
[3,1,7,6,4,2,5]=>[4,2,1]
[3,1,7,6,4,5,2]=>[4,2,1]
[3,1,7,6,5,2,4]=>[4,2,1]
[3,1,7,6,5,4,2]=>[5,2]
[3,2,1,4,5,6,7]=>[3,1,1,1,1]
[3,2,1,4,5,7,6]=>[3,2,1,1]
[3,2,1,4,6,5,7]=>[3,2,1,1]
[3,2,1,4,6,7,5]=>[3,2,1,1]
[3,2,1,4,7,5,6]=>[3,2,1,1]
[3,2,1,4,7,6,5]=>[3,3,1]
[3,2,1,5,4,6,7]=>[3,2,1,1]
[3,2,1,5,4,7,6]=>[3,2,2]
[3,2,1,5,6,4,7]=>[3,2,1,1]
[3,2,1,5,6,7,4]=>[3,2,1,1]
[3,2,1,5,7,4,6]=>[3,2,1,1]
[3,2,1,5,7,6,4]=>[3,3,1]
[3,2,1,6,4,5,7]=>[3,2,1,1]
[3,2,1,6,4,7,5]=>[3,2,2]
[3,2,1,6,5,4,7]=>[3,3,1]
[3,2,1,6,5,7,4]=>[3,3,1]
[3,2,1,6,7,4,5]=>[3,2,1,1]
[3,2,1,6,7,5,4]=>[3,3,1]
[3,2,1,7,4,5,6]=>[3,2,1,1]
[3,2,1,7,4,6,5]=>[3,3,1]
[3,2,1,7,5,4,6]=>[3,3,1]
[3,2,1,7,5,6,4]=>[3,3,1]
[3,2,1,7,6,4,5]=>[3,3,1]
[3,2,1,7,6,5,4]=>[4,3]
[3,2,4,1,5,6,7]=>[3,1,1,1,1]
[3,2,4,1,5,7,6]=>[3,2,1,1]
[3,2,4,1,6,5,7]=>[3,2,1,1]
[3,2,4,1,6,7,5]=>[3,2,1,1]
[3,2,4,1,7,5,6]=>[3,2,1,1]
[3,2,4,1,7,6,5]=>[3,3,1]
[3,2,4,5,1,6,7]=>[3,1,1,1,1]
[3,2,4,5,1,7,6]=>[3,2,1,1]
[3,2,4,5,6,1,7]=>[3,1,1,1,1]
[3,2,4,5,6,7,1]=>[3,1,1,1,1]
[3,2,4,5,7,1,6]=>[3,1,1,1,1]
[3,2,4,5,7,6,1]=>[3,2,1,1]
[3,2,4,6,1,5,7]=>[3,1,1,1,1]
[3,2,4,6,1,7,5]=>[3,2,1,1]
[3,2,4,6,5,1,7]=>[3,2,1,1]
[3,2,4,6,5,7,1]=>[3,2,1,1]
[3,2,4,6,7,1,5]=>[3,1,1,1,1]
[3,2,4,6,7,5,1]=>[3,2,1,1]
[3,2,4,7,1,5,6]=>[3,1,1,1,1]
[3,2,4,7,1,6,5]=>[3,2,1,1]
[3,2,4,7,5,1,6]=>[3,2,1,1]
[3,2,4,7,5,6,1]=>[3,2,1,1]
[3,2,4,7,6,1,5]=>[3,2,1,1]
[3,2,4,7,6,5,1]=>[4,2,1]
[3,2,5,1,4,6,7]=>[3,1,1,1,1]
[3,2,5,1,4,7,6]=>[3,2,1,1]
[3,2,5,1,6,4,7]=>[3,2,1,1]
[3,2,5,1,6,7,4]=>[3,2,1,1]
[3,2,5,1,7,4,6]=>[3,2,1,1]
[3,2,5,1,7,6,4]=>[3,3,1]
[3,2,5,4,1,6,7]=>[3,2,1,1]
[3,2,5,4,1,7,6]=>[3,2,2]
[3,2,5,4,6,1,7]=>[3,2,1,1]
[3,2,5,4,6,7,1]=>[3,2,1,1]
[3,2,5,4,7,1,6]=>[3,2,1,1]
[3,2,5,4,7,6,1]=>[3,2,2]
[3,2,5,6,1,4,7]=>[3,1,1,1,1]
[3,2,5,6,1,7,4]=>[3,2,1,1]
[3,2,5,6,4,1,7]=>[3,2,1,1]
[3,2,5,6,4,7,1]=>[3,2,1,1]
[3,2,5,6,7,1,4]=>[3,1,1,1,1]
[3,2,5,6,7,4,1]=>[3,2,1,1]
[3,2,5,7,1,4,6]=>[3,1,1,1,1]
[3,2,5,7,1,6,4]=>[3,2,1,1]
[3,2,5,7,4,1,6]=>[3,2,1,1]
[3,2,5,7,4,6,1]=>[3,2,1,1]
[3,2,5,7,6,1,4]=>[3,2,1,1]
[3,2,5,7,6,4,1]=>[4,2,1]
[3,2,6,1,4,5,7]=>[3,1,1,1,1]
[3,2,6,1,4,7,5]=>[3,2,1,1]
[3,2,6,1,5,4,7]=>[3,2,1,1]
[3,2,6,1,5,7,4]=>[3,2,1,1]
[3,2,6,1,7,4,5]=>[3,2,1,1]
[3,2,6,1,7,5,4]=>[3,3,1]
[3,2,6,4,1,5,7]=>[3,2,1,1]
[3,2,6,4,1,7,5]=>[3,2,2]
[3,2,6,4,5,1,7]=>[3,2,1,1]
[3,2,6,4,5,7,1]=>[3,2,1,1]
[3,2,6,4,7,1,5]=>[3,2,1,1]
[3,2,6,4,7,5,1]=>[3,2,2]
[3,2,6,5,1,4,7]=>[3,2,1,1]
[3,2,6,5,1,7,4]=>[3,2,2]
[3,2,6,5,4,1,7]=>[4,2,1]
[3,2,6,5,4,7,1]=>[4,2,1]
[3,2,6,5,7,1,4]=>[3,2,1,1]
[3,2,6,5,7,4,1]=>[4,2,1]
[3,2,6,7,1,4,5]=>[3,1,1,1,1]
[3,2,6,7,1,5,4]=>[3,2,1,1]
[3,2,6,7,4,1,5]=>[3,2,1,1]
[3,2,6,7,4,5,1]=>[3,2,1,1]
[3,2,6,7,5,1,4]=>[3,2,1,1]
[3,2,6,7,5,4,1]=>[4,2,1]
[3,2,7,1,4,5,6]=>[3,1,1,1,1]
[3,2,7,1,4,6,5]=>[3,2,1,1]
[3,2,7,1,5,4,6]=>[3,2,1,1]
[3,2,7,1,5,6,4]=>[3,2,1,1]
[3,2,7,1,6,4,5]=>[3,2,1,1]
[3,2,7,1,6,5,4]=>[4,2,1]
[3,2,7,4,1,5,6]=>[3,2,1,1]
[3,2,7,4,1,6,5]=>[3,2,2]
[3,2,7,4,5,1,6]=>[3,2,1,1]
[3,2,7,4,5,6,1]=>[3,2,1,1]
[3,2,7,4,6,1,5]=>[3,2,1,1]
[3,2,7,4,6,5,1]=>[4,2,1]
[3,2,7,5,1,4,6]=>[3,2,1,1]
[3,2,7,5,1,6,4]=>[3,2,2]
[3,2,7,5,4,1,6]=>[4,2,1]
[3,2,7,5,4,6,1]=>[4,2,1]
[3,2,7,5,6,1,4]=>[3,2,1,1]
[3,2,7,5,6,4,1]=>[4,2,1]
[3,2,7,6,1,4,5]=>[3,2,1,1]
[3,2,7,6,1,5,4]=>[4,2,1]
[3,2,7,6,4,1,5]=>[4,2,1]
[3,2,7,6,4,5,1]=>[4,2,1]
[3,2,7,6,5,1,4]=>[4,2,1]
[3,2,7,6,5,4,1]=>[5,2]
[3,4,1,2,5,6,7]=>[2,1,1,1,1,1]
[3,4,1,2,5,7,6]=>[2,2,1,1,1]
[3,4,1,2,6,5,7]=>[2,2,1,1,1]
[3,4,1,2,6,7,5]=>[2,2,1,1,1]
[3,4,1,2,7,5,6]=>[2,2,1,1,1]
[3,4,1,2,7,6,5]=>[3,2,1,1]
[3,4,1,5,2,6,7]=>[2,2,1,1,1]
[3,4,1,5,2,7,6]=>[2,2,2,1]
[3,4,1,5,6,2,7]=>[2,2,1,1,1]
[3,4,1,5,6,7,2]=>[2,2,1,1,1]
[3,4,1,5,7,2,6]=>[2,2,1,1,1]
[3,4,1,5,7,6,2]=>[3,2,1,1]
[3,4,1,6,2,5,7]=>[2,2,1,1,1]
[3,4,1,6,2,7,5]=>[2,2,2,1]
[3,4,1,6,5,2,7]=>[3,2,1,1]
[3,4,1,6,5,7,2]=>[3,2,1,1]
[3,4,1,6,7,2,5]=>[2,2,1,1,1]
[3,4,1,6,7,5,2]=>[3,2,1,1]
[3,4,1,7,2,5,6]=>[2,2,1,1,1]
[3,4,1,7,2,6,5]=>[3,2,1,1]
[3,4,1,7,5,2,6]=>[3,2,1,1]
[3,4,1,7,5,6,2]=>[3,2,1,1]
[3,4,1,7,6,2,5]=>[3,2,1,1]
[3,4,1,7,6,5,2]=>[4,2,1]
[3,4,2,1,5,6,7]=>[3,1,1,1,1]
[3,4,2,1,5,7,6]=>[3,2,1,1]
[3,4,2,1,6,5,7]=>[3,2,1,1]
[3,4,2,1,6,7,5]=>[3,2,1,1]
[3,4,2,1,7,5,6]=>[3,2,1,1]
[3,4,2,1,7,6,5]=>[3,3,1]
[3,4,2,5,1,6,7]=>[3,1,1,1,1]
[3,4,2,5,1,7,6]=>[3,2,1,1]
[3,4,2,5,6,1,7]=>[3,1,1,1,1]
[3,4,2,5,6,7,1]=>[3,1,1,1,1]
[3,4,2,5,7,1,6]=>[3,1,1,1,1]
[3,4,2,5,7,6,1]=>[3,2,1,1]
[3,4,2,6,1,5,7]=>[3,1,1,1,1]
[3,4,2,6,1,7,5]=>[3,2,1,1]
[3,4,2,6,5,1,7]=>[3,2,1,1]
[3,4,2,6,5,7,1]=>[3,2,1,1]
[3,4,2,6,7,1,5]=>[3,1,1,1,1]
[3,4,2,6,7,5,1]=>[3,2,1,1]
[3,4,2,7,1,5,6]=>[3,1,1,1,1]
[3,4,2,7,1,6,5]=>[3,2,1,1]
[3,4,2,7,5,1,6]=>[3,2,1,1]
[3,4,2,7,5,6,1]=>[3,2,1,1]
[3,4,2,7,6,1,5]=>[3,2,1,1]
[3,4,2,7,6,5,1]=>[4,2,1]
[3,4,5,1,2,6,7]=>[2,1,1,1,1,1]
[3,4,5,1,2,7,6]=>[2,2,1,1,1]
[3,4,5,1,6,2,7]=>[2,2,1,1,1]
[3,4,5,1,6,7,2]=>[2,2,1,1,1]
[3,4,5,1,7,2,6]=>[2,2,1,1,1]
[3,4,5,1,7,6,2]=>[3,2,1,1]
[3,4,5,2,1,6,7]=>[3,1,1,1,1]
[3,4,5,2,1,7,6]=>[3,2,1,1]
[3,4,5,2,6,1,7]=>[3,1,1,1,1]
[3,4,5,2,6,7,1]=>[3,1,1,1,1]
[3,4,5,2,7,1,6]=>[3,1,1,1,1]
[3,4,5,2,7,6,1]=>[3,2,1,1]
[3,4,5,6,1,2,7]=>[2,1,1,1,1,1]
[3,4,5,6,1,7,2]=>[2,2,1,1,1]
[3,4,5,6,2,1,7]=>[3,1,1,1,1]
[3,4,5,6,2,7,1]=>[3,1,1,1,1]
[3,4,5,6,7,1,2]=>[2,1,1,1,1,1]
[3,4,5,6,7,2,1]=>[3,1,1,1,1]
[3,4,5,7,1,2,6]=>[2,1,1,1,1,1]
[3,4,5,7,1,6,2]=>[3,1,1,1,1]
[3,4,5,7,2,1,6]=>[3,1,1,1,1]
[3,4,5,7,2,6,1]=>[3,1,1,1,1]
[3,4,5,7,6,1,2]=>[3,1,1,1,1]
[3,4,5,7,6,2,1]=>[4,1,1,1]
[3,4,6,1,2,5,7]=>[2,1,1,1,1,1]
[3,4,6,1,2,7,5]=>[2,2,1,1,1]
[3,4,6,1,5,2,7]=>[3,1,1,1,1]
[3,4,6,1,5,7,2]=>[3,1,1,1,1]
[3,4,6,1,7,2,5]=>[2,2,1,1,1]
[3,4,6,1,7,5,2]=>[3,2,1,1]
[3,4,6,2,1,5,7]=>[3,1,1,1,1]
[3,4,6,2,1,7,5]=>[3,2,1,1]
[3,4,6,2,5,1,7]=>[3,1,1,1,1]
[3,4,6,2,5,7,1]=>[3,1,1,1,1]
[3,4,6,2,7,1,5]=>[3,1,1,1,1]
[3,4,6,2,7,5,1]=>[3,2,1,1]
[3,4,6,5,1,2,7]=>[3,1,1,1,1]
[3,4,6,5,1,7,2]=>[3,2,1,1]
[3,4,6,5,2,1,7]=>[4,1,1,1]
[3,4,6,5,2,7,1]=>[4,1,1,1]
[3,4,6,5,7,1,2]=>[3,1,1,1,1]
[3,4,6,5,7,2,1]=>[4,1,1,1]
[3,4,6,7,1,2,5]=>[2,1,1,1,1,1]
[3,4,6,7,1,5,2]=>[3,1,1,1,1]
[3,4,6,7,2,1,5]=>[3,1,1,1,1]
[3,4,6,7,2,5,1]=>[3,1,1,1,1]
[3,4,6,7,5,1,2]=>[3,1,1,1,1]
[3,4,6,7,5,2,1]=>[4,1,1,1]
[3,4,7,1,2,5,6]=>[2,1,1,1,1,1]
[3,4,7,1,2,6,5]=>[3,1,1,1,1]
[3,4,7,1,5,2,6]=>[3,1,1,1,1]
[3,4,7,1,5,6,2]=>[3,1,1,1,1]
[3,4,7,1,6,2,5]=>[3,1,1,1,1]
[3,4,7,1,6,5,2]=>[4,1,1,1]
[3,4,7,2,1,5,6]=>[3,1,1,1,1]
[3,4,7,2,1,6,5]=>[3,2,1,1]
[3,4,7,2,5,1,6]=>[3,1,1,1,1]
[3,4,7,2,5,6,1]=>[3,1,1,1,1]
[3,4,7,2,6,1,5]=>[3,1,1,1,1]
[3,4,7,2,6,5,1]=>[4,1,1,1]
[3,4,7,5,1,2,6]=>[3,1,1,1,1]
[3,4,7,5,1,6,2]=>[3,2,1,1]
[3,4,7,5,2,1,6]=>[4,1,1,1]
[3,4,7,5,2,6,1]=>[4,1,1,1]
[3,4,7,5,6,1,2]=>[3,1,1,1,1]
[3,4,7,5,6,2,1]=>[4,1,1,1]
[3,4,7,6,1,2,5]=>[3,1,1,1,1]
[3,4,7,6,1,5,2]=>[4,1,1,1]
[3,4,7,6,2,1,5]=>[4,1,1,1]
[3,4,7,6,2,5,1]=>[4,1,1,1]
[3,4,7,6,5,1,2]=>[4,1,1,1]
[3,4,7,6,5,2,1]=>[5,1,1]
[3,5,1,2,4,6,7]=>[2,1,1,1,1,1]
[3,5,1,2,4,7,6]=>[2,2,1,1,1]
[3,5,1,2,6,4,7]=>[2,2,1,1,1]
[3,5,1,2,6,7,4]=>[2,2,1,1,1]
[3,5,1,2,7,4,6]=>[2,2,1,1,1]
[3,5,1,2,7,6,4]=>[3,2,1,1]
[3,5,1,4,2,6,7]=>[3,1,1,1,1]
[3,5,1,4,2,7,6]=>[3,2,1,1]
[3,5,1,4,6,2,7]=>[3,1,1,1,1]
[3,5,1,4,6,7,2]=>[3,1,1,1,1]
[3,5,1,4,7,2,6]=>[3,1,1,1,1]
[3,5,1,4,7,6,2]=>[3,2,1,1]
[3,5,1,6,2,4,7]=>[2,2,1,1,1]
[3,5,1,6,2,7,4]=>[2,2,2,1]
[3,5,1,6,4,2,7]=>[3,2,1,1]
[3,5,1,6,4,7,2]=>[3,2,1,1]
[3,5,1,6,7,2,4]=>[2,2,1,1,1]
[3,5,1,6,7,4,2]=>[3,2,1,1]
[3,5,1,7,2,4,6]=>[2,2,1,1,1]
[3,5,1,7,2,6,4]=>[3,2,1,1]
[3,5,1,7,4,2,6]=>[3,2,1,1]
[3,5,1,7,4,6,2]=>[3,2,1,1]
[3,5,1,7,6,2,4]=>[3,2,1,1]
[3,5,1,7,6,4,2]=>[4,2,1]
[3,5,2,1,4,6,7]=>[3,1,1,1,1]
[3,5,2,1,4,7,6]=>[3,2,1,1]
[3,5,2,1,6,4,7]=>[3,2,1,1]
[3,5,2,1,6,7,4]=>[3,2,1,1]
[3,5,2,1,7,4,6]=>[3,2,1,1]
[3,5,2,1,7,6,4]=>[3,3,1]
[3,5,2,4,1,6,7]=>[3,1,1,1,1]
[3,5,2,4,1,7,6]=>[3,2,1,1]
[3,5,2,4,6,1,7]=>[3,1,1,1,1]
[3,5,2,4,6,7,1]=>[3,1,1,1,1]
[3,5,2,4,7,1,6]=>[3,1,1,1,1]
[3,5,2,4,7,6,1]=>[3,2,1,1]
[3,5,2,6,1,4,7]=>[3,1,1,1,1]
[3,5,2,6,1,7,4]=>[3,2,1,1]
[3,5,2,6,4,1,7]=>[3,2,1,1]
[3,5,2,6,4,7,1]=>[3,2,1,1]
[3,5,2,6,7,1,4]=>[3,1,1,1,1]
[3,5,2,6,7,4,1]=>[3,2,1,1]
[3,5,2,7,1,4,6]=>[3,1,1,1,1]
[3,5,2,7,1,6,4]=>[3,2,1,1]
[3,5,2,7,4,1,6]=>[3,2,1,1]
[3,5,2,7,4,6,1]=>[3,2,1,1]
[3,5,2,7,6,1,4]=>[3,2,1,1]
[3,5,2,7,6,4,1]=>[4,2,1]
[3,5,4,1,2,6,7]=>[3,1,1,1,1]
[3,5,4,1,2,7,6]=>[3,2,1,1]
[3,5,4,1,6,2,7]=>[3,2,1,1]
[3,5,4,1,6,7,2]=>[3,2,1,1]
[3,5,4,1,7,2,6]=>[3,2,1,1]
[3,5,4,1,7,6,2]=>[3,3,1]
[3,5,4,2,1,6,7]=>[4,1,1,1]
[3,5,4,2,1,7,6]=>[4,2,1]
[3,5,4,2,6,1,7]=>[4,1,1,1]
[3,5,4,2,6,7,1]=>[4,1,1,1]
[3,5,4,2,7,1,6]=>[4,1,1,1]
[3,5,4,2,7,6,1]=>[4,2,1]
[3,5,4,6,1,2,7]=>[3,1,1,1,1]
[3,5,4,6,1,7,2]=>[3,2,1,1]
[3,5,4,6,2,1,7]=>[4,1,1,1]
[3,5,4,6,2,7,1]=>[4,1,1,1]
[3,5,4,6,7,1,2]=>[3,1,1,1,1]
[3,5,4,6,7,2,1]=>[4,1,1,1]
[3,5,4,7,1,2,6]=>[3,1,1,1,1]
[3,5,4,7,1,6,2]=>[3,2,1,1]
[3,5,4,7,2,1,6]=>[4,1,1,1]
[3,5,4,7,2,6,1]=>[4,1,1,1]
[3,5,4,7,6,1,2]=>[3,2,1,1]
[3,5,4,7,6,2,1]=>[4,2,1]
[3,5,6,1,2,4,7]=>[2,1,1,1,1,1]
[3,5,6,1,2,7,4]=>[2,2,1,1,1]
[3,5,6,1,4,2,7]=>[3,1,1,1,1]
[3,5,6,1,4,7,2]=>[3,1,1,1,1]
[3,5,6,1,7,2,4]=>[2,2,1,1,1]
[3,5,6,1,7,4,2]=>[3,2,1,1]
[3,5,6,2,1,4,7]=>[3,1,1,1,1]
[3,5,6,2,1,7,4]=>[3,2,1,1]
[3,5,6,2,4,1,7]=>[3,1,1,1,1]
[3,5,6,2,4,7,1]=>[3,1,1,1,1]
[3,5,6,2,7,1,4]=>[3,1,1,1,1]
[3,5,6,2,7,4,1]=>[3,2,1,1]
[3,5,6,4,1,2,7]=>[3,1,1,1,1]
[3,5,6,4,1,7,2]=>[3,2,1,1]
[3,5,6,4,2,1,7]=>[4,1,1,1]
[3,5,6,4,2,7,1]=>[4,1,1,1]
[3,5,6,4,7,1,2]=>[3,1,1,1,1]
[3,5,6,4,7,2,1]=>[4,1,1,1]
[3,5,6,7,1,2,4]=>[2,1,1,1,1,1]
[3,5,6,7,1,4,2]=>[3,1,1,1,1]
[3,5,6,7,2,1,4]=>[3,1,1,1,1]
[3,5,6,7,2,4,1]=>[3,1,1,1,1]
[3,5,6,7,4,1,2]=>[3,1,1,1,1]
[3,5,6,7,4,2,1]=>[4,1,1,1]
[3,5,7,1,2,4,6]=>[2,1,1,1,1,1]
[3,5,7,1,2,6,4]=>[3,1,1,1,1]
[3,5,7,1,4,2,6]=>[3,1,1,1,1]
[3,5,7,1,4,6,2]=>[3,1,1,1,1]
[3,5,7,1,6,2,4]=>[3,1,1,1,1]
[3,5,7,1,6,4,2]=>[4,1,1,1]
[3,5,7,2,1,4,6]=>[3,1,1,1,1]
[3,5,7,2,1,6,4]=>[3,2,1,1]
[3,5,7,2,4,1,6]=>[3,1,1,1,1]
[3,5,7,2,4,6,1]=>[3,1,1,1,1]
[3,5,7,2,6,1,4]=>[3,1,1,1,1]
[3,5,7,2,6,4,1]=>[4,1,1,1]
[3,5,7,4,1,2,6]=>[3,1,1,1,1]
[3,5,7,4,1,6,2]=>[3,2,1,1]
[3,5,7,4,2,1,6]=>[4,1,1,1]
[3,5,7,4,2,6,1]=>[4,1,1,1]
[3,5,7,4,6,1,2]=>[3,1,1,1,1]
[3,5,7,4,6,2,1]=>[4,1,1,1]
[3,5,7,6,1,2,4]=>[3,1,1,1,1]
[3,5,7,6,1,4,2]=>[4,1,1,1]
[3,5,7,6,2,1,4]=>[4,1,1,1]
[3,5,7,6,2,4,1]=>[4,1,1,1]
[3,5,7,6,4,1,2]=>[4,1,1,1]
[3,5,7,6,4,2,1]=>[5,1,1]
[3,6,1,2,4,5,7]=>[2,1,1,1,1,1]
[3,6,1,2,4,7,5]=>[2,2,1,1,1]
[3,6,1,2,5,4,7]=>[3,1,1,1,1]
[3,6,1,2,5,7,4]=>[3,1,1,1,1]
[3,6,1,2,7,4,5]=>[2,2,1,1,1]
[3,6,1,2,7,5,4]=>[3,2,1,1]
[3,6,1,4,2,5,7]=>[3,1,1,1,1]
[3,6,1,4,2,7,5]=>[3,2,1,1]
[3,6,1,4,5,2,7]=>[3,1,1,1,1]
[3,6,1,4,5,7,2]=>[3,1,1,1,1]
[3,6,1,4,7,2,5]=>[3,1,1,1,1]
[3,6,1,4,7,5,2]=>[3,2,1,1]
[3,6,1,5,2,4,7]=>[3,1,1,1,1]
[3,6,1,5,2,7,4]=>[3,2,1,1]
[3,6,1,5,4,2,7]=>[4,1,1,1]
[3,6,1,5,4,7,2]=>[4,1,1,1]
[3,6,1,5,7,2,4]=>[3,1,1,1,1]
[3,6,1,5,7,4,2]=>[4,1,1,1]
[3,6,1,7,2,4,5]=>[2,2,1,1,1]
[3,6,1,7,2,5,4]=>[3,2,1,1]
[3,6,1,7,4,2,5]=>[3,2,1,1]
[3,6,1,7,4,5,2]=>[3,2,1,1]
[3,6,1,7,5,2,4]=>[3,2,1,1]
[3,6,1,7,5,4,2]=>[4,2,1]
[3,6,2,1,4,5,7]=>[3,1,1,1,1]
[3,6,2,1,4,7,5]=>[3,2,1,1]
[3,6,2,1,5,4,7]=>[3,2,1,1]
[3,6,2,1,5,7,4]=>[3,2,1,1]
[3,6,2,1,7,4,5]=>[3,2,1,1]
[3,6,2,1,7,5,4]=>[3,3,1]
[3,6,2,4,1,5,7]=>[3,1,1,1,1]
[3,6,2,4,1,7,5]=>[3,2,1,1]
[3,6,2,4,5,1,7]=>[3,1,1,1,1]
[3,6,2,4,5,7,1]=>[3,1,1,1,1]
[3,6,2,4,7,1,5]=>[3,1,1,1,1]
[3,6,2,4,7,5,1]=>[3,2,1,1]
[3,6,2,5,1,4,7]=>[3,1,1,1,1]
[3,6,2,5,1,7,4]=>[3,2,1,1]
[3,6,2,5,4,1,7]=>[4,1,1,1]
[3,6,2,5,4,7,1]=>[4,1,1,1]
[3,6,2,5,7,1,4]=>[3,1,1,1,1]
[3,6,2,5,7,4,1]=>[4,1,1,1]
[3,6,2,7,1,4,5]=>[3,1,1,1,1]
[3,6,2,7,1,5,4]=>[3,2,1,1]
[3,6,2,7,4,1,5]=>[3,2,1,1]
[3,6,2,7,4,5,1]=>[3,2,1,1]
[3,6,2,7,5,1,4]=>[3,2,1,1]
[3,6,2,7,5,4,1]=>[4,2,1]
[3,6,4,1,2,5,7]=>[3,1,1,1,1]
[3,6,4,1,2,7,5]=>[3,2,1,1]
[3,6,4,1,5,2,7]=>[3,2,1,1]
[3,6,4,1,5,7,2]=>[3,2,1,1]
[3,6,4,1,7,2,5]=>[3,2,1,1]
[3,6,4,1,7,5,2]=>[3,3,1]
[3,6,4,2,1,5,7]=>[4,1,1,1]
[3,6,4,2,1,7,5]=>[4,2,1]
[3,6,4,2,5,1,7]=>[4,1,1,1]
[3,6,4,2,5,7,1]=>[4,1,1,1]
[3,6,4,2,7,1,5]=>[4,1,1,1]
[3,6,4,2,7,5,1]=>[4,2,1]
[3,6,4,5,1,2,7]=>[3,1,1,1,1]
[3,6,4,5,1,7,2]=>[3,2,1,1]
[3,6,4,5,2,1,7]=>[4,1,1,1]
[3,6,4,5,2,7,1]=>[4,1,1,1]
[3,6,4,5,7,1,2]=>[3,1,1,1,1]
[3,6,4,5,7,2,1]=>[4,1,1,1]
[3,6,4,7,1,2,5]=>[3,1,1,1,1]
[3,6,4,7,1,5,2]=>[3,2,1,1]
[3,6,4,7,2,1,5]=>[4,1,1,1]
[3,6,4,7,2,5,1]=>[4,1,1,1]
[3,6,4,7,5,1,2]=>[3,2,1,1]
[3,6,4,7,5,2,1]=>[4,2,1]
[3,6,5,1,2,4,7]=>[3,1,1,1,1]
[3,6,5,1,2,7,4]=>[3,2,1,1]
[3,6,5,1,4,2,7]=>[4,1,1,1]
[3,6,5,1,4,7,2]=>[4,1,1,1]
[3,6,5,1,7,2,4]=>[3,2,1,1]
[3,6,5,1,7,4,2]=>[4,2,1]
[3,6,5,2,1,4,7]=>[4,1,1,1]
[3,6,5,2,1,7,4]=>[4,2,1]
[3,6,5,2,4,1,7]=>[4,1,1,1]
[3,6,5,2,4,7,1]=>[4,1,1,1]
[3,6,5,2,7,1,4]=>[4,1,1,1]
[3,6,5,2,7,4,1]=>[4,2,1]
[3,6,5,4,1,2,7]=>[4,1,1,1]
[3,6,5,4,1,7,2]=>[4,2,1]
[3,6,5,4,2,1,7]=>[5,1,1]
[3,6,5,4,2,7,1]=>[5,1,1]
[3,6,5,4,7,1,2]=>[4,1,1,1]
[3,6,5,4,7,2,1]=>[5,1,1]
[3,6,5,7,1,2,4]=>[3,1,1,1,1]
[3,6,5,7,1,4,2]=>[4,1,1,1]
[3,6,5,7,2,1,4]=>[4,1,1,1]
[3,6,5,7,2,4,1]=>[4,1,1,1]
[3,6,5,7,4,1,2]=>[4,1,1,1]
[3,6,5,7,4,2,1]=>[5,1,1]
[3,6,7,1,2,4,5]=>[2,1,1,1,1,1]
[3,6,7,1,2,5,4]=>[3,1,1,1,1]
[3,6,7,1,4,2,5]=>[3,1,1,1,1]
[3,6,7,1,4,5,2]=>[3,1,1,1,1]
[3,6,7,1,5,2,4]=>[3,1,1,1,1]
[3,6,7,1,5,4,2]=>[4,1,1,1]
[3,6,7,2,1,4,5]=>[3,1,1,1,1]
[3,6,7,2,1,5,4]=>[3,2,1,1]
[3,6,7,2,4,1,5]=>[3,1,1,1,1]
[3,6,7,2,4,5,1]=>[3,1,1,1,1]
[3,6,7,2,5,1,4]=>[3,1,1,1,1]
[3,6,7,2,5,4,1]=>[4,1,1,1]
[3,6,7,4,1,2,5]=>[3,1,1,1,1]
[3,6,7,4,1,5,2]=>[3,2,1,1]
[3,6,7,4,2,1,5]=>[4,1,1,1]
[3,6,7,4,2,5,1]=>[4,1,1,1]
[3,6,7,4,5,1,2]=>[3,1,1,1,1]
[3,6,7,4,5,2,1]=>[4,1,1,1]
[3,6,7,5,1,2,4]=>[3,1,1,1,1]
[3,6,7,5,1,4,2]=>[4,1,1,1]
[3,6,7,5,2,1,4]=>[4,1,1,1]
[3,6,7,5,2,4,1]=>[4,1,1,1]
[3,6,7,5,4,1,2]=>[4,1,1,1]
[3,6,7,5,4,2,1]=>[5,1,1]
[3,7,1,2,4,5,6]=>[2,1,1,1,1,1]
[3,7,1,2,4,6,5]=>[3,1,1,1,1]
[3,7,1,2,5,4,6]=>[3,1,1,1,1]
[3,7,1,2,5,6,4]=>[3,1,1,1,1]
[3,7,1,2,6,4,5]=>[3,1,1,1,1]
[3,7,1,2,6,5,4]=>[4,1,1,1]
[3,7,1,4,2,5,6]=>[3,1,1,1,1]
[3,7,1,4,2,6,5]=>[3,2,1,1]
[3,7,1,4,5,2,6]=>[3,1,1,1,1]
[3,7,1,4,5,6,2]=>[3,1,1,1,1]
[3,7,1,4,6,2,5]=>[3,1,1,1,1]
[3,7,1,4,6,5,2]=>[4,1,1,1]
[3,7,1,5,2,4,6]=>[3,1,1,1,1]
[3,7,1,5,2,6,4]=>[3,2,1,1]
[3,7,1,5,4,2,6]=>[4,1,1,1]
[3,7,1,5,4,6,2]=>[4,1,1,1]
[3,7,1,5,6,2,4]=>[3,1,1,1,1]
[3,7,1,5,6,4,2]=>[4,1,1,1]
[3,7,1,6,2,4,5]=>[3,1,1,1,1]
[3,7,1,6,2,5,4]=>[4,1,1,1]
[3,7,1,6,4,2,5]=>[4,1,1,1]
[3,7,1,6,4,5,2]=>[4,1,1,1]
[3,7,1,6,5,2,4]=>[4,1,1,1]
[3,7,1,6,5,4,2]=>[5,1,1]
[3,7,2,1,4,5,6]=>[3,1,1,1,1]
[3,7,2,1,4,6,5]=>[3,2,1,1]
[3,7,2,1,5,4,6]=>[3,2,1,1]
[3,7,2,1,5,6,4]=>[3,2,1,1]
[3,7,2,1,6,4,5]=>[3,2,1,1]
[3,7,2,1,6,5,4]=>[4,2,1]
[3,7,2,4,1,5,6]=>[3,1,1,1,1]
[3,7,2,4,1,6,5]=>[3,2,1,1]
[3,7,2,4,5,1,6]=>[3,1,1,1,1]
[3,7,2,4,5,6,1]=>[3,1,1,1,1]
[3,7,2,4,6,1,5]=>[3,1,1,1,1]
[3,7,2,4,6,5,1]=>[4,1,1,1]
[3,7,2,5,1,4,6]=>[3,1,1,1,1]
[3,7,2,5,1,6,4]=>[3,2,1,1]
[3,7,2,5,4,1,6]=>[4,1,1,1]
[3,7,2,5,4,6,1]=>[4,1,1,1]
[3,7,2,5,6,1,4]=>[3,1,1,1,1]
[3,7,2,5,6,4,1]=>[4,1,1,1]
[3,7,2,6,1,4,5]=>[3,1,1,1,1]
[3,7,2,6,1,5,4]=>[4,1,1,1]
[3,7,2,6,4,1,5]=>[4,1,1,1]
[3,7,2,6,4,5,1]=>[4,1,1,1]
[3,7,2,6,5,1,4]=>[4,1,1,1]
[3,7,2,6,5,4,1]=>[5,1,1]
[3,7,4,1,2,5,6]=>[3,1,1,1,1]
[3,7,4,1,2,6,5]=>[3,2,1,1]
[3,7,4,1,5,2,6]=>[3,2,1,1]
[3,7,4,1,5,6,2]=>[3,2,1,1]
[3,7,4,1,6,2,5]=>[3,2,1,1]
[3,7,4,1,6,5,2]=>[4,2,1]
[3,7,4,2,1,5,6]=>[4,1,1,1]
[3,7,4,2,1,6,5]=>[4,2,1]
[3,7,4,2,5,1,6]=>[4,1,1,1]
[3,7,4,2,5,6,1]=>[4,1,1,1]
[3,7,4,2,6,1,5]=>[4,1,1,1]
[3,7,4,2,6,5,1]=>[4,2,1]
[3,7,4,5,1,2,6]=>[3,1,1,1,1]
[3,7,4,5,1,6,2]=>[3,2,1,1]
[3,7,4,5,2,1,6]=>[4,1,1,1]
[3,7,4,5,2,6,1]=>[4,1,1,1]
[3,7,4,5,6,1,2]=>[3,1,1,1,1]
[3,7,4,5,6,2,1]=>[4,1,1,1]
[3,7,4,6,1,2,5]=>[3,1,1,1,1]
[3,7,4,6,1,5,2]=>[4,1,1,1]
[3,7,4,6,2,1,5]=>[4,1,1,1]
[3,7,4,6,2,5,1]=>[4,1,1,1]
[3,7,4,6,5,1,2]=>[4,1,1,1]
[3,7,4,6,5,2,1]=>[5,1,1]
[3,7,5,1,2,4,6]=>[3,1,1,1,1]
[3,7,5,1,2,6,4]=>[3,2,1,1]
[3,7,5,1,4,2,6]=>[4,1,1,1]
[3,7,5,1,4,6,2]=>[4,1,1,1]
[3,7,5,1,6,2,4]=>[3,2,1,1]
[3,7,5,1,6,4,2]=>[4,2,1]
[3,7,5,2,1,4,6]=>[4,1,1,1]
[3,7,5,2,1,6,4]=>[4,2,1]
[3,7,5,2,4,1,6]=>[4,1,1,1]
[3,7,5,2,4,6,1]=>[4,1,1,1]
[3,7,5,2,6,1,4]=>[4,1,1,1]
[3,7,5,2,6,4,1]=>[4,2,1]
[3,7,5,4,1,2,6]=>[4,1,1,1]
[3,7,5,4,1,6,2]=>[4,2,1]
[3,7,5,4,2,1,6]=>[5,1,1]
[3,7,5,4,2,6,1]=>[5,1,1]
[3,7,5,4,6,1,2]=>[4,1,1,1]
[3,7,5,4,6,2,1]=>[5,1,1]
[3,7,5,6,1,2,4]=>[3,1,1,1,1]
[3,7,5,6,1,4,2]=>[4,1,1,1]
[3,7,5,6,2,1,4]=>[4,1,1,1]
[3,7,5,6,2,4,1]=>[4,1,1,1]
[3,7,5,6,4,1,2]=>[4,1,1,1]
[3,7,5,6,4,2,1]=>[5,1,1]
[3,7,6,1,2,4,5]=>[3,1,1,1,1]
[3,7,6,1,2,5,4]=>[4,1,1,1]
[3,7,6,1,4,2,5]=>[4,1,1,1]
[3,7,6,1,4,5,2]=>[4,1,1,1]
[3,7,6,1,5,2,4]=>[4,1,1,1]
[3,7,6,1,5,4,2]=>[5,1,1]
[3,7,6,2,1,4,5]=>[4,1,1,1]
[3,7,6,2,1,5,4]=>[4,2,1]
[3,7,6,2,4,1,5]=>[4,1,1,1]
[3,7,6,2,4,5,1]=>[4,1,1,1]
[3,7,6,2,5,1,4]=>[4,1,1,1]
[3,7,6,2,5,4,1]=>[5,1,1]
[3,7,6,4,1,2,5]=>[4,1,1,1]
[3,7,6,4,1,5,2]=>[4,2,1]
[3,7,6,4,2,1,5]=>[5,1,1]
[3,7,6,4,2,5,1]=>[5,1,1]
[3,7,6,4,5,1,2]=>[4,1,1,1]
[3,7,6,4,5,2,1]=>[5,1,1]
[3,7,6,5,1,2,4]=>[4,1,1,1]
[3,7,6,5,1,4,2]=>[5,1,1]
[3,7,6,5,2,1,4]=>[5,1,1]
[3,7,6,5,2,4,1]=>[5,1,1]
[3,7,6,5,4,1,2]=>[5,1,1]
[3,7,6,5,4,2,1]=>[6,1]
[4,1,2,3,5,6,7]=>[2,1,1,1,1,1]
[4,1,2,3,5,7,6]=>[2,2,1,1,1]
[4,1,2,3,6,5,7]=>[2,2,1,1,1]
[4,1,2,3,6,7,5]=>[2,2,1,1,1]
[4,1,2,3,7,5,6]=>[2,2,1,1,1]
[4,1,2,3,7,6,5]=>[3,2,1,1]
[4,1,2,5,3,6,7]=>[2,2,1,1,1]
[4,1,2,5,3,7,6]=>[2,2,2,1]
[4,1,2,5,6,3,7]=>[2,2,1,1,1]
[4,1,2,5,6,7,3]=>[2,2,1,1,1]
[4,1,2,5,7,3,6]=>[2,2,1,1,1]
[4,1,2,5,7,6,3]=>[3,2,1,1]
[4,1,2,6,3,5,7]=>[2,2,1,1,1]
[4,1,2,6,3,7,5]=>[2,2,2,1]
[4,1,2,6,5,3,7]=>[3,2,1,1]
[4,1,2,6,5,7,3]=>[3,2,1,1]
[4,1,2,6,7,3,5]=>[2,2,1,1,1]
[4,1,2,6,7,5,3]=>[3,2,1,1]
[4,1,2,7,3,5,6]=>[2,2,1,1,1]
[4,1,2,7,3,6,5]=>[3,2,1,1]
[4,1,2,7,5,3,6]=>[3,2,1,1]
[4,1,2,7,5,6,3]=>[3,2,1,1]
[4,1,2,7,6,3,5]=>[3,2,1,1]
[4,1,2,7,6,5,3]=>[4,2,1]
[4,1,3,2,5,6,7]=>[3,1,1,1,1]
[4,1,3,2,5,7,6]=>[3,2,1,1]
[4,1,3,2,6,5,7]=>[3,2,1,1]
[4,1,3,2,6,7,5]=>[3,2,1,1]
[4,1,3,2,7,5,6]=>[3,2,1,1]
[4,1,3,2,7,6,5]=>[3,3,1]
[4,1,3,5,2,6,7]=>[3,1,1,1,1]
[4,1,3,5,2,7,6]=>[3,2,1,1]
[4,1,3,5,6,2,7]=>[3,1,1,1,1]
[4,1,3,5,6,7,2]=>[3,1,1,1,1]
[4,1,3,5,7,2,6]=>[3,1,1,1,1]
[4,1,3,5,7,6,2]=>[3,2,1,1]
[4,1,3,6,2,5,7]=>[3,1,1,1,1]
[4,1,3,6,2,7,5]=>[3,2,1,1]
[4,1,3,6,5,2,7]=>[3,2,1,1]
[4,1,3,6,5,7,2]=>[3,2,1,1]
[4,1,3,6,7,2,5]=>[3,1,1,1,1]
[4,1,3,6,7,5,2]=>[3,2,1,1]
[4,1,3,7,2,5,6]=>[3,1,1,1,1]
[4,1,3,7,2,6,5]=>[3,2,1,1]
[4,1,3,7,5,2,6]=>[3,2,1,1]
[4,1,3,7,5,6,2]=>[3,2,1,1]
[4,1,3,7,6,2,5]=>[3,2,1,1]
[4,1,3,7,6,5,2]=>[4,2,1]
[4,1,5,2,3,6,7]=>[2,2,1,1,1]
[4,1,5,2,3,7,6]=>[2,2,2,1]
[4,1,5,2,6,3,7]=>[2,2,2,1]
[4,1,5,2,6,7,3]=>[2,2,2,1]
[4,1,5,2,7,3,6]=>[2,2,2,1]
[4,1,5,2,7,6,3]=>[3,2,2]
[4,1,5,3,2,6,7]=>[3,2,1,1]
[4,1,5,3,2,7,6]=>[3,2,2]
[4,1,5,3,6,2,7]=>[3,2,1,1]
[4,1,5,3,6,7,2]=>[3,2,1,1]
[4,1,5,3,7,2,6]=>[3,2,1,1]
[4,1,5,3,7,6,2]=>[3,2,2]
[4,1,5,6,2,3,7]=>[2,2,1,1,1]
[4,1,5,6,2,7,3]=>[2,2,2,1]
[4,1,5,6,3,2,7]=>[3,2,1,1]
[4,1,5,6,3,7,2]=>[3,2,1,1]
[4,1,5,6,7,2,3]=>[2,2,1,1,1]
[4,1,5,6,7,3,2]=>[3,2,1,1]
[4,1,5,7,2,3,6]=>[2,2,1,1,1]
[4,1,5,7,2,6,3]=>[3,2,1,1]
[4,1,5,7,3,2,6]=>[3,2,1,1]
[4,1,5,7,3,6,2]=>[3,2,1,1]
[4,1,5,7,6,2,3]=>[3,2,1,1]
[4,1,5,7,6,3,2]=>[4,2,1]
[4,1,6,2,3,5,7]=>[2,2,1,1,1]
[4,1,6,2,3,7,5]=>[2,2,2,1]
[4,1,6,2,5,3,7]=>[3,2,1,1]
[4,1,6,2,5,7,3]=>[3,2,1,1]
[4,1,6,2,7,3,5]=>[2,2,2,1]
[4,1,6,2,7,5,3]=>[3,2,2]
[4,1,6,3,2,5,7]=>[3,2,1,1]
[4,1,6,3,2,7,5]=>[3,2,2]
[4,1,6,3,5,2,7]=>[3,2,1,1]
[4,1,6,3,5,7,2]=>[3,2,1,1]
[4,1,6,3,7,2,5]=>[3,2,1,1]
[4,1,6,3,7,5,2]=>[3,2,2]
[4,1,6,5,2,3,7]=>[3,2,1,1]
[4,1,6,5,2,7,3]=>[3,2,2]
[4,1,6,5,3,2,7]=>[4,2,1]
[4,1,6,5,3,7,2]=>[4,2,1]
[4,1,6,5,7,2,3]=>[3,2,1,1]
[4,1,6,5,7,3,2]=>[4,2,1]
[4,1,6,7,2,3,5]=>[2,2,1,1,1]
[4,1,6,7,2,5,3]=>[3,2,1,1]
[4,1,6,7,3,2,5]=>[3,2,1,1]
[4,1,6,7,3,5,2]=>[3,2,1,1]
[4,1,6,7,5,2,3]=>[3,2,1,1]
[4,1,6,7,5,3,2]=>[4,2,1]
[4,1,7,2,3,5,6]=>[2,2,1,1,1]
[4,1,7,2,3,6,5]=>[3,2,1,1]
[4,1,7,2,5,3,6]=>[3,2,1,1]
[4,1,7,2,5,6,3]=>[3,2,1,1]
[4,1,7,2,6,3,5]=>[3,2,1,1]
[4,1,7,2,6,5,3]=>[4,2,1]
[4,1,7,3,2,5,6]=>[3,2,1,1]
[4,1,7,3,2,6,5]=>[3,2,2]
[4,1,7,3,5,2,6]=>[3,2,1,1]
[4,1,7,3,5,6,2]=>[3,2,1,1]
[4,1,7,3,6,2,5]=>[3,2,1,1]
[4,1,7,3,6,5,2]=>[4,2,1]
[4,1,7,5,2,3,6]=>[3,2,1,1]
[4,1,7,5,2,6,3]=>[3,2,2]
[4,1,7,5,3,2,6]=>[4,2,1]
[4,1,7,5,3,6,2]=>[4,2,1]
[4,1,7,5,6,2,3]=>[3,2,1,1]
[4,1,7,5,6,3,2]=>[4,2,1]
[4,1,7,6,2,3,5]=>[3,2,1,1]
[4,1,7,6,2,5,3]=>[4,2,1]
[4,1,7,6,3,2,5]=>[4,2,1]
[4,1,7,6,3,5,2]=>[4,2,1]
[4,1,7,6,5,2,3]=>[4,2,1]
[4,1,7,6,5,3,2]=>[5,2]
[4,2,1,3,5,6,7]=>[3,1,1,1,1]
[4,2,1,3,5,7,6]=>[3,2,1,1]
[4,2,1,3,6,5,7]=>[3,2,1,1]
[4,2,1,3,6,7,5]=>[3,2,1,1]
[4,2,1,3,7,5,6]=>[3,2,1,1]
[4,2,1,3,7,6,5]=>[3,3,1]
[4,2,1,5,3,6,7]=>[3,2,1,1]
[4,2,1,5,3,7,6]=>[3,2,2]
[4,2,1,5,6,3,7]=>[3,2,1,1]
[4,2,1,5,6,7,3]=>[3,2,1,1]
[4,2,1,5,7,3,6]=>[3,2,1,1]
[4,2,1,5,7,6,3]=>[3,3,1]
[4,2,1,6,3,5,7]=>[3,2,1,1]
[4,2,1,6,3,7,5]=>[3,2,2]
[4,2,1,6,5,3,7]=>[3,3,1]
[4,2,1,6,5,7,3]=>[3,3,1]
[4,2,1,6,7,3,5]=>[3,2,1,1]
[4,2,1,6,7,5,3]=>[3,3,1]
[4,2,1,7,3,5,6]=>[3,2,1,1]
[4,2,1,7,3,6,5]=>[3,3,1]
[4,2,1,7,5,3,6]=>[3,3,1]
[4,2,1,7,5,6,3]=>[3,3,1]
[4,2,1,7,6,3,5]=>[3,3,1]
[4,2,1,7,6,5,3]=>[4,3]
[4,2,3,1,5,6,7]=>[3,1,1,1,1]
[4,2,3,1,5,7,6]=>[3,2,1,1]
[4,2,3,1,6,5,7]=>[3,2,1,1]
[4,2,3,1,6,7,5]=>[3,2,1,1]
[4,2,3,1,7,5,6]=>[3,2,1,1]
[4,2,3,1,7,6,5]=>[3,3,1]
[4,2,3,5,1,6,7]=>[3,1,1,1,1]
[4,2,3,5,1,7,6]=>[3,2,1,1]
[4,2,3,5,6,1,7]=>[3,1,1,1,1]
[4,2,3,5,6,7,1]=>[3,1,1,1,1]
[4,2,3,5,7,1,6]=>[3,1,1,1,1]
[4,2,3,5,7,6,1]=>[3,2,1,1]
[4,2,3,6,1,5,7]=>[3,1,1,1,1]
[4,2,3,6,1,7,5]=>[3,2,1,1]
[4,2,3,6,5,1,7]=>[3,2,1,1]
[4,2,3,6,5,7,1]=>[3,2,1,1]
[4,2,3,6,7,1,5]=>[3,1,1,1,1]
[4,2,3,6,7,5,1]=>[3,2,1,1]
[4,2,3,7,1,5,6]=>[3,1,1,1,1]
[4,2,3,7,1,6,5]=>[3,2,1,1]
[4,2,3,7,5,1,6]=>[3,2,1,1]
[4,2,3,7,5,6,1]=>[3,2,1,1]
[4,2,3,7,6,1,5]=>[3,2,1,1]
[4,2,3,7,6,5,1]=>[4,2,1]
[4,2,5,1,3,6,7]=>[3,1,1,1,1]
[4,2,5,1,3,7,6]=>[3,2,1,1]
[4,2,5,1,6,3,7]=>[3,2,1,1]
[4,2,5,1,6,7,3]=>[3,2,1,1]
[4,2,5,1,7,3,6]=>[3,2,1,1]
[4,2,5,1,7,6,3]=>[3,3,1]
[4,2,5,3,1,6,7]=>[3,2,1,1]
[4,2,5,3,1,7,6]=>[3,2,2]
[4,2,5,3,6,1,7]=>[3,2,1,1]
[4,2,5,3,6,7,1]=>[3,2,1,1]
[4,2,5,3,7,1,6]=>[3,2,1,1]
[4,2,5,3,7,6,1]=>[3,2,2]
[4,2,5,6,1,3,7]=>[3,1,1,1,1]
[4,2,5,6,1,7,3]=>[3,2,1,1]
[4,2,5,6,3,1,7]=>[3,2,1,1]
[4,2,5,6,3,7,1]=>[3,2,1,1]
[4,2,5,6,7,1,3]=>[3,1,1,1,1]
[4,2,5,6,7,3,1]=>[3,2,1,1]
[4,2,5,7,1,3,6]=>[3,1,1,1,1]
[4,2,5,7,1,6,3]=>[3,2,1,1]
[4,2,5,7,3,1,6]=>[3,2,1,1]
[4,2,5,7,3,6,1]=>[3,2,1,1]
[4,2,5,7,6,1,3]=>[3,2,1,1]
[4,2,5,7,6,3,1]=>[4,2,1]
[4,2,6,1,3,5,7]=>[3,1,1,1,1]
[4,2,6,1,3,7,5]=>[3,2,1,1]
[4,2,6,1,5,3,7]=>[3,2,1,1]
[4,2,6,1,5,7,3]=>[3,2,1,1]
[4,2,6,1,7,3,5]=>[3,2,1,1]
[4,2,6,1,7,5,3]=>[3,3,1]
[4,2,6,3,1,5,7]=>[3,2,1,1]
[4,2,6,3,1,7,5]=>[3,2,2]
[4,2,6,3,5,1,7]=>[3,2,1,1]
[4,2,6,3,5,7,1]=>[3,2,1,1]
[4,2,6,3,7,1,5]=>[3,2,1,1]
[4,2,6,3,7,5,1]=>[3,2,2]
[4,2,6,5,1,3,7]=>[3,2,1,1]
[4,2,6,5,1,7,3]=>[3,2,2]
[4,2,6,5,3,1,7]=>[4,2,1]
[4,2,6,5,3,7,1]=>[4,2,1]
[4,2,6,5,7,1,3]=>[3,2,1,1]
[4,2,6,5,7,3,1]=>[4,2,1]
[4,2,6,7,1,3,5]=>[3,1,1,1,1]
[4,2,6,7,1,5,3]=>[3,2,1,1]
[4,2,6,7,3,1,5]=>[3,2,1,1]
[4,2,6,7,3,5,1]=>[3,2,1,1]
[4,2,6,7,5,1,3]=>[3,2,1,1]
[4,2,6,7,5,3,1]=>[4,2,1]
[4,2,7,1,3,5,6]=>[3,1,1,1,1]
[4,2,7,1,3,6,5]=>[3,2,1,1]
[4,2,7,1,5,3,6]=>[3,2,1,1]
[4,2,7,1,5,6,3]=>[3,2,1,1]
[4,2,7,1,6,3,5]=>[3,2,1,1]
[4,2,7,1,6,5,3]=>[4,2,1]
[4,2,7,3,1,5,6]=>[3,2,1,1]
[4,2,7,3,1,6,5]=>[3,2,2]
[4,2,7,3,5,1,6]=>[3,2,1,1]
[4,2,7,3,5,6,1]=>[3,2,1,1]
[4,2,7,3,6,1,5]=>[3,2,1,1]
[4,2,7,3,6,5,1]=>[4,2,1]
[4,2,7,5,1,3,6]=>[3,2,1,1]
[4,2,7,5,1,6,3]=>[3,2,2]
[4,2,7,5,3,1,6]=>[4,2,1]
[4,2,7,5,3,6,1]=>[4,2,1]
[4,2,7,5,6,1,3]=>[3,2,1,1]
[4,2,7,5,6,3,1]=>[4,2,1]
[4,2,7,6,1,3,5]=>[3,2,1,1]
[4,2,7,6,1,5,3]=>[4,2,1]
[4,2,7,6,3,1,5]=>[4,2,1]
[4,2,7,6,3,5,1]=>[4,2,1]
[4,2,7,6,5,1,3]=>[4,2,1]
[4,2,7,6,5,3,1]=>[5,2]
[4,3,1,2,5,6,7]=>[3,1,1,1,1]
[4,3,1,2,5,7,6]=>[3,2,1,1]
[4,3,1,2,6,5,7]=>[3,2,1,1]
[4,3,1,2,6,7,5]=>[3,2,1,1]
[4,3,1,2,7,5,6]=>[3,2,1,1]
[4,3,1,2,7,6,5]=>[3,3,1]
[4,3,1,5,2,6,7]=>[3,2,1,1]
[4,3,1,5,2,7,6]=>[3,2,2]
[4,3,1,5,6,2,7]=>[3,2,1,1]
[4,3,1,5,6,7,2]=>[3,2,1,1]
[4,3,1,5,7,2,6]=>[3,2,1,1]
[4,3,1,5,7,6,2]=>[3,3,1]
[4,3,1,6,2,5,7]=>[3,2,1,1]
[4,3,1,6,2,7,5]=>[3,2,2]
[4,3,1,6,5,2,7]=>[3,3,1]
[4,3,1,6,5,7,2]=>[3,3,1]
[4,3,1,6,7,2,5]=>[3,2,1,1]
[4,3,1,6,7,5,2]=>[3,3,1]
[4,3,1,7,2,5,6]=>[3,2,1,1]
[4,3,1,7,2,6,5]=>[3,3,1]
[4,3,1,7,5,2,6]=>[3,3,1]
[4,3,1,7,5,6,2]=>[3,3,1]
[4,3,1,7,6,2,5]=>[3,3,1]
[4,3,1,7,6,5,2]=>[4,3]
[4,3,2,1,5,6,7]=>[4,1,1,1]
[4,3,2,1,5,7,6]=>[4,2,1]
[4,3,2,1,6,5,7]=>[4,2,1]
[4,3,2,1,6,7,5]=>[4,2,1]
[4,3,2,1,7,5,6]=>[4,2,1]
[4,3,2,1,7,6,5]=>[4,3]
[4,3,2,5,1,6,7]=>[4,1,1,1]
[4,3,2,5,1,7,6]=>[4,2,1]
[4,3,2,5,6,1,7]=>[4,1,1,1]
[4,3,2,5,6,7,1]=>[4,1,1,1]
[4,3,2,5,7,1,6]=>[4,1,1,1]
[4,3,2,5,7,6,1]=>[4,2,1]
[4,3,2,6,1,5,7]=>[4,1,1,1]
[4,3,2,6,1,7,5]=>[4,2,1]
[4,3,2,6,5,1,7]=>[4,2,1]
[4,3,2,6,5,7,1]=>[4,2,1]
[4,3,2,6,7,1,5]=>[4,1,1,1]
[4,3,2,6,7,5,1]=>[4,2,1]
[4,3,2,7,1,5,6]=>[4,1,1,1]
[4,3,2,7,1,6,5]=>[4,2,1]
[4,3,2,7,5,1,6]=>[4,2,1]
[4,3,2,7,5,6,1]=>[4,2,1]
[4,3,2,7,6,1,5]=>[4,2,1]
[4,3,2,7,6,5,1]=>[4,3]
[4,3,5,1,2,6,7]=>[3,1,1,1,1]
[4,3,5,1,2,7,6]=>[3,2,1,1]
[4,3,5,1,6,2,7]=>[3,2,1,1]
[4,3,5,1,6,7,2]=>[3,2,1,1]
[4,3,5,1,7,2,6]=>[3,2,1,1]
[4,3,5,1,7,6,2]=>[3,3,1]
[4,3,5,2,1,6,7]=>[4,1,1,1]
[4,3,5,2,1,7,6]=>[4,2,1]
[4,3,5,2,6,1,7]=>[4,1,1,1]
[4,3,5,2,6,7,1]=>[4,1,1,1]
[4,3,5,2,7,1,6]=>[4,1,1,1]
[4,3,5,2,7,6,1]=>[4,2,1]
[4,3,5,6,1,2,7]=>[3,1,1,1,1]
[4,3,5,6,1,7,2]=>[3,2,1,1]
[4,3,5,6,2,1,7]=>[4,1,1,1]
[4,3,5,6,2,7,1]=>[4,1,1,1]
[4,3,5,6,7,1,2]=>[3,1,1,1,1]
[4,3,5,6,7,2,1]=>[4,1,1,1]
[4,3,5,7,1,2,6]=>[3,1,1,1,1]
[4,3,5,7,1,6,2]=>[3,2,1,1]
[4,3,5,7,2,1,6]=>[4,1,1,1]
[4,3,5,7,2,6,1]=>[4,1,1,1]
[4,3,5,7,6,1,2]=>[3,2,1,1]
[4,3,5,7,6,2,1]=>[4,2,1]
[4,3,6,1,2,5,7]=>[3,1,1,1,1]
[4,3,6,1,2,7,5]=>[3,2,1,1]
[4,3,6,1,5,2,7]=>[3,2,1,1]
[4,3,6,1,5,7,2]=>[3,2,1,1]
[4,3,6,1,7,2,5]=>[3,2,1,1]
[4,3,6,1,7,5,2]=>[3,3,1]
[4,3,6,2,1,5,7]=>[4,1,1,1]
[4,3,6,2,1,7,5]=>[4,2,1]
[4,3,6,2,5,1,7]=>[4,1,1,1]
[4,3,6,2,5,7,1]=>[4,1,1,1]
[4,3,6,2,7,1,5]=>[4,1,1,1]
[4,3,6,2,7,5,1]=>[4,2,1]
[4,3,6,5,1,2,7]=>[3,2,1,1]
[4,3,6,5,1,7,2]=>[3,2,2]
[4,3,6,5,2,1,7]=>[4,2,1]
[4,3,6,5,2,7,1]=>[4,2,1]
[4,3,6,5,7,1,2]=>[3,2,1,1]
[4,3,6,5,7,2,1]=>[4,2,1]
[4,3,6,7,1,2,5]=>[3,1,1,1,1]
[4,3,6,7,1,5,2]=>[3,2,1,1]
[4,3,6,7,2,1,5]=>[4,1,1,1]
[4,3,6,7,2,5,1]=>[4,1,1,1]
[4,3,6,7,5,1,2]=>[3,2,1,1]
[4,3,6,7,5,2,1]=>[4,2,1]
[4,3,7,1,2,5,6]=>[3,1,1,1,1]
[4,3,7,1,2,6,5]=>[3,2,1,1]
[4,3,7,1,5,2,6]=>[3,2,1,1]
[4,3,7,1,5,6,2]=>[3,2,1,1]
[4,3,7,1,6,2,5]=>[3,2,1,1]
[4,3,7,1,6,5,2]=>[4,2,1]
[4,3,7,2,1,5,6]=>[4,1,1,1]
[4,3,7,2,1,6,5]=>[4,2,1]
[4,3,7,2,5,1,6]=>[4,1,1,1]
[4,3,7,2,5,6,1]=>[4,1,1,1]
[4,3,7,2,6,1,5]=>[4,1,1,1]
[4,3,7,2,6,5,1]=>[4,2,1]
[4,3,7,5,1,2,6]=>[3,2,1,1]
[4,3,7,5,1,6,2]=>[3,2,2]
[4,3,7,5,2,1,6]=>[4,2,1]
[4,3,7,5,2,6,1]=>[4,2,1]
[4,3,7,5,6,1,2]=>[3,2,1,1]
[4,3,7,5,6,2,1]=>[4,2,1]
[4,3,7,6,1,2,5]=>[3,2,1,1]
[4,3,7,6,1,5,2]=>[4,2,1]
[4,3,7,6,2,1,5]=>[4,2,1]
[4,3,7,6,2,5,1]=>[4,2,1]
[4,3,7,6,5,1,2]=>[4,2,1]
[4,3,7,6,5,2,1]=>[5,2]
[4,5,1,2,3,6,7]=>[2,1,1,1,1,1]
[4,5,1,2,3,7,6]=>[2,2,1,1,1]
[4,5,1,2,6,3,7]=>[2,2,1,1,1]
[4,5,1,2,6,7,3]=>[2,2,1,1,1]
[4,5,1,2,7,3,6]=>[2,2,1,1,1]
[4,5,1,2,7,6,3]=>[3,2,1,1]
[4,5,1,3,2,6,7]=>[3,1,1,1,1]
[4,5,1,3,2,7,6]=>[3,2,1,1]
[4,5,1,3,6,2,7]=>[3,1,1,1,1]
[4,5,1,3,6,7,2]=>[3,1,1,1,1]
[4,5,1,3,7,2,6]=>[3,1,1,1,1]
[4,5,1,3,7,6,2]=>[3,2,1,1]
[4,5,1,6,2,3,7]=>[2,2,1,1,1]
[4,5,1,6,2,7,3]=>[2,2,2,1]
[4,5,1,6,3,2,7]=>[3,2,1,1]
[4,5,1,6,3,7,2]=>[3,2,1,1]
[4,5,1,6,7,2,3]=>[2,2,1,1,1]
[4,5,1,6,7,3,2]=>[3,2,1,1]
[4,5,1,7,2,3,6]=>[2,2,1,1,1]
[4,5,1,7,2,6,3]=>[3,2,1,1]
[4,5,1,7,3,2,6]=>[3,2,1,1]
[4,5,1,7,3,6,2]=>[3,2,1,1]
[4,5,1,7,6,2,3]=>[3,2,1,1]
[4,5,1,7,6,3,2]=>[4,2,1]
[4,5,2,1,3,6,7]=>[3,1,1,1,1]
[4,5,2,1,3,7,6]=>[3,2,1,1]
[4,5,2,1,6,3,7]=>[3,2,1,1]
[4,5,2,1,6,7,3]=>[3,2,1,1]
[4,5,2,1,7,3,6]=>[3,2,1,1]
[4,5,2,1,7,6,3]=>[3,3,1]
[4,5,2,3,1,6,7]=>[3,1,1,1,1]
[4,5,2,3,1,7,6]=>[3,2,1,1]
[4,5,2,3,6,1,7]=>[3,1,1,1,1]
[4,5,2,3,6,7,1]=>[3,1,1,1,1]
[4,5,2,3,7,1,6]=>[3,1,1,1,1]
[4,5,2,3,7,6,1]=>[3,2,1,1]
[4,5,2,6,1,3,7]=>[3,1,1,1,1]
[4,5,2,6,1,7,3]=>[3,2,1,1]
[4,5,2,6,3,1,7]=>[3,2,1,1]
[4,5,2,6,3,7,1]=>[3,2,1,1]
[4,5,2,6,7,1,3]=>[3,1,1,1,1]
[4,5,2,6,7,3,1]=>[3,2,1,1]
[4,5,2,7,1,3,6]=>[3,1,1,1,1]
[4,5,2,7,1,6,3]=>[3,2,1,1]
[4,5,2,7,3,1,6]=>[3,2,1,1]
[4,5,2,7,3,6,1]=>[3,2,1,1]
[4,5,2,7,6,1,3]=>[3,2,1,1]
[4,5,2,7,6,3,1]=>[4,2,1]
[4,5,3,1,2,6,7]=>[3,1,1,1,1]
[4,5,3,1,2,7,6]=>[3,2,1,1]
[4,5,3,1,6,2,7]=>[3,2,1,1]
[4,5,3,1,6,7,2]=>[3,2,1,1]
[4,5,3,1,7,2,6]=>[3,2,1,1]
[4,5,3,1,7,6,2]=>[3,3,1]
[4,5,3,2,1,6,7]=>[4,1,1,1]
[4,5,3,2,1,7,6]=>[4,2,1]
[4,5,3,2,6,1,7]=>[4,1,1,1]
[4,5,3,2,6,7,1]=>[4,1,1,1]
[4,5,3,2,7,1,6]=>[4,1,1,1]
[4,5,3,2,7,6,1]=>[4,2,1]
[4,5,3,6,1,2,7]=>[3,1,1,1,1]
[4,5,3,6,1,7,2]=>[3,2,1,1]
[4,5,3,6,2,1,7]=>[4,1,1,1]
[4,5,3,6,2,7,1]=>[4,1,1,1]
[4,5,3,6,7,1,2]=>[3,1,1,1,1]
[4,5,3,6,7,2,1]=>[4,1,1,1]
[4,5,3,7,1,2,6]=>[3,1,1,1,1]
[4,5,3,7,1,6,2]=>[3,2,1,1]
[4,5,3,7,2,1,6]=>[4,1,1,1]
[4,5,3,7,2,6,1]=>[4,1,1,1]
[4,5,3,7,6,1,2]=>[3,2,1,1]
[4,5,3,7,6,2,1]=>[4,2,1]
[4,5,6,1,2,3,7]=>[2,1,1,1,1,1]
[4,5,6,1,2,7,3]=>[2,2,1,1,1]
[4,5,6,1,3,2,7]=>[3,1,1,1,1]
[4,5,6,1,3,7,2]=>[3,1,1,1,1]
[4,5,6,1,7,2,3]=>[2,2,1,1,1]
[4,5,6,1,7,3,2]=>[3,2,1,1]
[4,5,6,2,1,3,7]=>[3,1,1,1,1]
[4,5,6,2,1,7,3]=>[3,2,1,1]
[4,5,6,2,3,1,7]=>[3,1,1,1,1]
[4,5,6,2,3,7,1]=>[3,1,1,1,1]
[4,5,6,2,7,1,3]=>[3,1,1,1,1]
[4,5,6,2,7,3,1]=>[3,2,1,1]
[4,5,6,3,1,2,7]=>[3,1,1,1,1]
[4,5,6,3,1,7,2]=>[3,2,1,1]
[4,5,6,3,2,1,7]=>[4,1,1,1]
[4,5,6,3,2,7,1]=>[4,1,1,1]
[4,5,6,3,7,1,2]=>[3,1,1,1,1]
[4,5,6,3,7,2,1]=>[4,1,1,1]
[4,5,6,7,1,2,3]=>[2,1,1,1,1,1]
[4,5,6,7,1,3,2]=>[3,1,1,1,1]
[4,5,6,7,2,1,3]=>[3,1,1,1,1]
[4,5,6,7,2,3,1]=>[3,1,1,1,1]
[4,5,6,7,3,1,2]=>[3,1,1,1,1]
[4,5,6,7,3,2,1]=>[4,1,1,1]
[4,5,7,1,2,3,6]=>[2,1,1,1,1,1]
[4,5,7,1,2,6,3]=>[3,1,1,1,1]
[4,5,7,1,3,2,6]=>[3,1,1,1,1]
[4,5,7,1,3,6,2]=>[3,1,1,1,1]
[4,5,7,1,6,2,3]=>[3,1,1,1,1]
[4,5,7,1,6,3,2]=>[4,1,1,1]
[4,5,7,2,1,3,6]=>[3,1,1,1,1]
[4,5,7,2,1,6,3]=>[3,2,1,1]
[4,5,7,2,3,1,6]=>[3,1,1,1,1]
[4,5,7,2,3,6,1]=>[3,1,1,1,1]
[4,5,7,2,6,1,3]=>[3,1,1,1,1]
[4,5,7,2,6,3,1]=>[4,1,1,1]
[4,5,7,3,1,2,6]=>[3,1,1,1,1]
[4,5,7,3,1,6,2]=>[3,2,1,1]
[4,5,7,3,2,1,6]=>[4,1,1,1]
[4,5,7,3,2,6,1]=>[4,1,1,1]
[4,5,7,3,6,1,2]=>[3,1,1,1,1]
[4,5,7,3,6,2,1]=>[4,1,1,1]
[4,5,7,6,1,2,3]=>[3,1,1,1,1]
[4,5,7,6,1,3,2]=>[4,1,1,1]
[4,5,7,6,2,1,3]=>[4,1,1,1]
[4,5,7,6,2,3,1]=>[4,1,1,1]
[4,5,7,6,3,1,2]=>[4,1,1,1]
[4,5,7,6,3,2,1]=>[5,1,1]
[4,6,1,2,3,5,7]=>[2,1,1,1,1,1]
[4,6,1,2,3,7,5]=>[2,2,1,1,1]
[4,6,1,2,5,3,7]=>[3,1,1,1,1]
[4,6,1,2,5,7,3]=>[3,1,1,1,1]
[4,6,1,2,7,3,5]=>[2,2,1,1,1]
[4,6,1,2,7,5,3]=>[3,2,1,1]
[4,6,1,3,2,5,7]=>[3,1,1,1,1]
[4,6,1,3,2,7,5]=>[3,2,1,1]
[4,6,1,3,5,2,7]=>[3,1,1,1,1]
[4,6,1,3,5,7,2]=>[3,1,1,1,1]
[4,6,1,3,7,2,5]=>[3,1,1,1,1]
[4,6,1,3,7,5,2]=>[3,2,1,1]
[4,6,1,5,2,3,7]=>[3,1,1,1,1]
[4,6,1,5,2,7,3]=>[3,2,1,1]
[4,6,1,5,3,2,7]=>[4,1,1,1]
[4,6,1,5,3,7,2]=>[4,1,1,1]
[4,6,1,5,7,2,3]=>[3,1,1,1,1]
[4,6,1,5,7,3,2]=>[4,1,1,1]
[4,6,1,7,2,3,5]=>[2,2,1,1,1]
[4,6,1,7,2,5,3]=>[3,2,1,1]
[4,6,1,7,3,2,5]=>[3,2,1,1]
[4,6,1,7,3,5,2]=>[3,2,1,1]
[4,6,1,7,5,2,3]=>[3,2,1,1]
[4,6,1,7,5,3,2]=>[4,2,1]
[4,6,2,1,3,5,7]=>[3,1,1,1,1]
[4,6,2,1,3,7,5]=>[3,2,1,1]
[4,6,2,1,5,3,7]=>[3,2,1,1]
[4,6,2,1,5,7,3]=>[3,2,1,1]
[4,6,2,1,7,3,5]=>[3,2,1,1]
[4,6,2,1,7,5,3]=>[3,3,1]
[4,6,2,3,1,5,7]=>[3,1,1,1,1]
[4,6,2,3,1,7,5]=>[3,2,1,1]
[4,6,2,3,5,1,7]=>[3,1,1,1,1]
[4,6,2,3,5,7,1]=>[3,1,1,1,1]
[4,6,2,3,7,1,5]=>[3,1,1,1,1]
[4,6,2,3,7,5,1]=>[3,2,1,1]
[4,6,2,5,1,3,7]=>[3,1,1,1,1]
[4,6,2,5,1,7,3]=>[3,2,1,1]
[4,6,2,5,3,1,7]=>[4,1,1,1]
[4,6,2,5,3,7,1]=>[4,1,1,1]
[4,6,2,5,7,1,3]=>[3,1,1,1,1]
[4,6,2,5,7,3,1]=>[4,1,1,1]
[4,6,2,7,1,3,5]=>[3,1,1,1,1]
[4,6,2,7,1,5,3]=>[3,2,1,1]
[4,6,2,7,3,1,5]=>[3,2,1,1]
[4,6,2,7,3,5,1]=>[3,2,1,1]
[4,6,2,7,5,1,3]=>[3,2,1,1]
[4,6,2,7,5,3,1]=>[4,2,1]
[4,6,3,1,2,5,7]=>[3,1,1,1,1]
[4,6,3,1,2,7,5]=>[3,2,1,1]
[4,6,3,1,5,2,7]=>[3,2,1,1]
[4,6,3,1,5,7,2]=>[3,2,1,1]
[4,6,3,1,7,2,5]=>[3,2,1,1]
[4,6,3,1,7,5,2]=>[3,3,1]
[4,6,3,2,1,5,7]=>[4,1,1,1]
[4,6,3,2,1,7,5]=>[4,2,1]
[4,6,3,2,5,1,7]=>[4,1,1,1]
[4,6,3,2,5,7,1]=>[4,1,1,1]
[4,6,3,2,7,1,5]=>[4,1,1,1]
[4,6,3,2,7,5,1]=>[4,2,1]
[4,6,3,5,1,2,7]=>[3,1,1,1,1]
[4,6,3,5,1,7,2]=>[3,2,1,1]
[4,6,3,5,2,1,7]=>[4,1,1,1]
[4,6,3,5,2,7,1]=>[4,1,1,1]
[4,6,3,5,7,1,2]=>[3,1,1,1,1]
[4,6,3,5,7,2,1]=>[4,1,1,1]
[4,6,3,7,1,2,5]=>[3,1,1,1,1]
[4,6,3,7,1,5,2]=>[3,2,1,1]
[4,6,3,7,2,1,5]=>[4,1,1,1]
[4,6,3,7,2,5,1]=>[4,1,1,1]
[4,6,3,7,5,1,2]=>[3,2,1,1]
[4,6,3,7,5,2,1]=>[4,2,1]
[4,6,5,1,2,3,7]=>[3,1,1,1,1]
[4,6,5,1,2,7,3]=>[3,2,1,1]
[4,6,5,1,3,2,7]=>[4,1,1,1]
[4,6,5,1,3,7,2]=>[4,1,1,1]
[4,6,5,1,7,2,3]=>[3,2,1,1]
[4,6,5,1,7,3,2]=>[4,2,1]
[4,6,5,2,1,3,7]=>[4,1,1,1]
[4,6,5,2,1,7,3]=>[4,2,1]
[4,6,5,2,3,1,7]=>[4,1,1,1]
[4,6,5,2,3,7,1]=>[4,1,1,1]
[4,6,5,2,7,1,3]=>[4,1,1,1]
[4,6,5,2,7,3,1]=>[4,2,1]
[4,6,5,3,1,2,7]=>[4,1,1,1]
[4,6,5,3,1,7,2]=>[4,2,1]
[4,6,5,3,2,1,7]=>[5,1,1]
[4,6,5,3,2,7,1]=>[5,1,1]
[4,6,5,3,7,1,2]=>[4,1,1,1]
[4,6,5,3,7,2,1]=>[5,1,1]
[4,6,5,7,1,2,3]=>[3,1,1,1,1]
[4,6,5,7,1,3,2]=>[4,1,1,1]
[4,6,5,7,2,1,3]=>[4,1,1,1]
[4,6,5,7,2,3,1]=>[4,1,1,1]
[4,6,5,7,3,1,2]=>[4,1,1,1]
[4,6,5,7,3,2,1]=>[5,1,1]
[4,6,7,1,2,3,5]=>[2,1,1,1,1,1]
[4,6,7,1,2,5,3]=>[3,1,1,1,1]
[4,6,7,1,3,2,5]=>[3,1,1,1,1]
[4,6,7,1,3,5,2]=>[3,1,1,1,1]
[4,6,7,1,5,2,3]=>[3,1,1,1,1]
[4,6,7,1,5,3,2]=>[4,1,1,1]
[4,6,7,2,1,3,5]=>[3,1,1,1,1]
[4,6,7,2,1,5,3]=>[3,2,1,1]
[4,6,7,2,3,1,5]=>[3,1,1,1,1]
[4,6,7,2,3,5,1]=>[3,1,1,1,1]
[4,6,7,2,5,1,3]=>[3,1,1,1,1]
[4,6,7,2,5,3,1]=>[4,1,1,1]
[4,6,7,3,1,2,5]=>[3,1,1,1,1]
[4,6,7,3,1,5,2]=>[3,2,1,1]
[4,6,7,3,2,1,5]=>[4,1,1,1]
[4,6,7,3,2,5,1]=>[4,1,1,1]
[4,6,7,3,5,1,2]=>[3,1,1,1,1]
[4,6,7,3,5,2,1]=>[4,1,1,1]
[4,6,7,5,1,2,3]=>[3,1,1,1,1]
[4,6,7,5,1,3,2]=>[4,1,1,1]
[4,6,7,5,2,1,3]=>[4,1,1,1]
[4,6,7,5,2,3,1]=>[4,1,1,1]
[4,6,7,5,3,1,2]=>[4,1,1,1]
[4,6,7,5,3,2,1]=>[5,1,1]
[4,7,1,2,3,5,6]=>[2,1,1,1,1,1]
[4,7,1,2,3,6,5]=>[3,1,1,1,1]
[4,7,1,2,5,3,6]=>[3,1,1,1,1]
[4,7,1,2,5,6,3]=>[3,1,1,1,1]
[4,7,1,2,6,3,5]=>[3,1,1,1,1]
[4,7,1,2,6,5,3]=>[4,1,1,1]
[4,7,1,3,2,5,6]=>[3,1,1,1,1]
[4,7,1,3,2,6,5]=>[3,2,1,1]
[4,7,1,3,5,2,6]=>[3,1,1,1,1]
[4,7,1,3,5,6,2]=>[3,1,1,1,1]
[4,7,1,3,6,2,5]=>[3,1,1,1,1]
[4,7,1,3,6,5,2]=>[4,1,1,1]
[4,7,1,5,2,3,6]=>[3,1,1,1,1]
[4,7,1,5,2,6,3]=>[3,2,1,1]
[4,7,1,5,3,2,6]=>[4,1,1,1]
[4,7,1,5,3,6,2]=>[4,1,1,1]
[4,7,1,5,6,2,3]=>[3,1,1,1,1]
[4,7,1,5,6,3,2]=>[4,1,1,1]
[4,7,1,6,2,3,5]=>[3,1,1,1,1]
[4,7,1,6,2,5,3]=>[4,1,1,1]
[4,7,1,6,3,2,5]=>[4,1,1,1]
[4,7,1,6,3,5,2]=>[4,1,1,1]
[4,7,1,6,5,2,3]=>[4,1,1,1]
[4,7,1,6,5,3,2]=>[5,1,1]
[4,7,2,1,3,5,6]=>[3,1,1,1,1]
[4,7,2,1,3,6,5]=>[3,2,1,1]
[4,7,2,1,5,3,6]=>[3,2,1,1]
[4,7,2,1,5,6,3]=>[3,2,1,1]
[4,7,2,1,6,3,5]=>[3,2,1,1]
[4,7,2,1,6,5,3]=>[4,2,1]
[4,7,2,3,1,5,6]=>[3,1,1,1,1]
[4,7,2,3,1,6,5]=>[3,2,1,1]
[4,7,2,3,5,1,6]=>[3,1,1,1,1]
[4,7,2,3,5,6,1]=>[3,1,1,1,1]
[4,7,2,3,6,1,5]=>[3,1,1,1,1]
[4,7,2,3,6,5,1]=>[4,1,1,1]
[4,7,2,5,1,3,6]=>[3,1,1,1,1]
[4,7,2,5,1,6,3]=>[3,2,1,1]
[4,7,2,5,3,1,6]=>[4,1,1,1]
[4,7,2,5,3,6,1]=>[4,1,1,1]
[4,7,2,5,6,1,3]=>[3,1,1,1,1]
[4,7,2,5,6,3,1]=>[4,1,1,1]
[4,7,2,6,1,3,5]=>[3,1,1,1,1]
[4,7,2,6,1,5,3]=>[4,1,1,1]
[4,7,2,6,3,1,5]=>[4,1,1,1]
[4,7,2,6,3,5,1]=>[4,1,1,1]
[4,7,2,6,5,1,3]=>[4,1,1,1]
[4,7,2,6,5,3,1]=>[5,1,1]
[4,7,3,1,2,5,6]=>[3,1,1,1,1]
[4,7,3,1,2,6,5]=>[3,2,1,1]
[4,7,3,1,5,2,6]=>[3,2,1,1]
[4,7,3,1,5,6,2]=>[3,2,1,1]
[4,7,3,1,6,2,5]=>[3,2,1,1]
[4,7,3,1,6,5,2]=>[4,2,1]
[4,7,3,2,1,5,6]=>[4,1,1,1]
[4,7,3,2,1,6,5]=>[4,2,1]
[4,7,3,2,5,1,6]=>[4,1,1,1]
[4,7,3,2,5,6,1]=>[4,1,1,1]
[4,7,3,2,6,1,5]=>[4,1,1,1]
[4,7,3,2,6,5,1]=>[4,2,1]
[4,7,3,5,1,2,6]=>[3,1,1,1,1]
[4,7,3,5,1,6,2]=>[3,2,1,1]
[4,7,3,5,2,1,6]=>[4,1,1,1]
[4,7,3,5,2,6,1]=>[4,1,1,1]
[4,7,3,5,6,1,2]=>[3,1,1,1,1]
[4,7,3,5,6,2,1]=>[4,1,1,1]
[4,7,3,6,1,2,5]=>[3,1,1,1,1]
[4,7,3,6,1,5,2]=>[4,1,1,1]
[4,7,3,6,2,1,5]=>[4,1,1,1]
[4,7,3,6,2,5,1]=>[4,1,1,1]
[4,7,3,6,5,1,2]=>[4,1,1,1]
[4,7,3,6,5,2,1]=>[5,1,1]
[4,7,5,1,2,3,6]=>[3,1,1,1,1]
[4,7,5,1,2,6,3]=>[3,2,1,1]
[4,7,5,1,3,2,6]=>[4,1,1,1]
[4,7,5,1,3,6,2]=>[4,1,1,1]
[4,7,5,1,6,2,3]=>[3,2,1,1]
[4,7,5,1,6,3,2]=>[4,2,1]
[4,7,5,2,1,3,6]=>[4,1,1,1]
[4,7,5,2,1,6,3]=>[4,2,1]
[4,7,5,2,3,1,6]=>[4,1,1,1]
[4,7,5,2,3,6,1]=>[4,1,1,1]
[4,7,5,2,6,1,3]=>[4,1,1,1]
[4,7,5,2,6,3,1]=>[4,2,1]
[4,7,5,3,1,2,6]=>[4,1,1,1]
[4,7,5,3,1,6,2]=>[4,2,1]
[4,7,5,3,2,1,6]=>[5,1,1]
[4,7,5,3,2,6,1]=>[5,1,1]
[4,7,5,3,6,1,2]=>[4,1,1,1]
[4,7,5,3,6,2,1]=>[5,1,1]
[4,7,5,6,1,2,3]=>[3,1,1,1,1]
[4,7,5,6,1,3,2]=>[4,1,1,1]
[4,7,5,6,2,1,3]=>[4,1,1,1]
[4,7,5,6,2,3,1]=>[4,1,1,1]
[4,7,5,6,3,1,2]=>[4,1,1,1]
[4,7,5,6,3,2,1]=>[5,1,1]
[4,7,6,1,2,3,5]=>[3,1,1,1,1]
[4,7,6,1,2,5,3]=>[4,1,1,1]
[4,7,6,1,3,2,5]=>[4,1,1,1]
[4,7,6,1,3,5,2]=>[4,1,1,1]
[4,7,6,1,5,2,3]=>[4,1,1,1]
[4,7,6,1,5,3,2]=>[5,1,1]
[4,7,6,2,1,3,5]=>[4,1,1,1]
[4,7,6,2,1,5,3]=>[4,2,1]
[4,7,6,2,3,1,5]=>[4,1,1,1]
[4,7,6,2,3,5,1]=>[4,1,1,1]
[4,7,6,2,5,1,3]=>[4,1,1,1]
[4,7,6,2,5,3,1]=>[5,1,1]
[4,7,6,3,1,2,5]=>[4,1,1,1]
[4,7,6,3,1,5,2]=>[4,2,1]
[4,7,6,3,2,1,5]=>[5,1,1]
[4,7,6,3,2,5,1]=>[5,1,1]
[4,7,6,3,5,1,2]=>[4,1,1,1]
[4,7,6,3,5,2,1]=>[5,1,1]
[4,7,6,5,1,2,3]=>[4,1,1,1]
[4,7,6,5,1,3,2]=>[5,1,1]
[4,7,6,5,2,1,3]=>[5,1,1]
[4,7,6,5,2,3,1]=>[5,1,1]
[4,7,6,5,3,1,2]=>[5,1,1]
[4,7,6,5,3,2,1]=>[6,1]
[5,1,2,3,4,6,7]=>[2,1,1,1,1,1]
[5,1,2,3,4,7,6]=>[2,2,1,1,1]
[5,1,2,3,6,4,7]=>[2,2,1,1,1]
[5,1,2,3,6,7,4]=>[2,2,1,1,1]
[5,1,2,3,7,4,6]=>[2,2,1,1,1]
[5,1,2,3,7,6,4]=>[3,2,1,1]
[5,1,2,4,3,6,7]=>[3,1,1,1,1]
[5,1,2,4,3,7,6]=>[3,2,1,1]
[5,1,2,4,6,3,7]=>[3,1,1,1,1]
[5,1,2,4,6,7,3]=>[3,1,1,1,1]
[5,1,2,4,7,3,6]=>[3,1,1,1,1]
[5,1,2,4,7,6,3]=>[3,2,1,1]
[5,1,2,6,3,4,7]=>[2,2,1,1,1]
[5,1,2,6,3,7,4]=>[2,2,2,1]
[5,1,2,6,4,3,7]=>[3,2,1,1]
[5,1,2,6,4,7,3]=>[3,2,1,1]
[5,1,2,6,7,3,4]=>[2,2,1,1,1]
[5,1,2,6,7,4,3]=>[3,2,1,1]
[5,1,2,7,3,4,6]=>[2,2,1,1,1]
[5,1,2,7,3,6,4]=>[3,2,1,1]
[5,1,2,7,4,3,6]=>[3,2,1,1]
[5,1,2,7,4,6,3]=>[3,2,1,1]
[5,1,2,7,6,3,4]=>[3,2,1,1]
[5,1,2,7,6,4,3]=>[4,2,1]
[5,1,3,2,4,6,7]=>[3,1,1,1,1]
[5,1,3,2,4,7,6]=>[3,2,1,1]
[5,1,3,2,6,4,7]=>[3,2,1,1]
[5,1,3,2,6,7,4]=>[3,2,1,1]
[5,1,3,2,7,4,6]=>[3,2,1,1]
[5,1,3,2,7,6,4]=>[3,3,1]
[5,1,3,4,2,6,7]=>[3,1,1,1,1]
[5,1,3,4,2,7,6]=>[3,2,1,1]
[5,1,3,4,6,2,7]=>[3,1,1,1,1]
[5,1,3,4,6,7,2]=>[3,1,1,1,1]
[5,1,3,4,7,2,6]=>[3,1,1,1,1]
[5,1,3,4,7,6,2]=>[3,2,1,1]
[5,1,3,6,2,4,7]=>[3,1,1,1,1]
[5,1,3,6,2,7,4]=>[3,2,1,1]
[5,1,3,6,4,2,7]=>[3,2,1,1]
[5,1,3,6,4,7,2]=>[3,2,1,1]
[5,1,3,6,7,2,4]=>[3,1,1,1,1]
[5,1,3,6,7,4,2]=>[3,2,1,1]
[5,1,3,7,2,4,6]=>[3,1,1,1,1]
[5,1,3,7,2,6,4]=>[3,2,1,1]
[5,1,3,7,4,2,6]=>[3,2,1,1]
[5,1,3,7,4,6,2]=>[3,2,1,1]
[5,1,3,7,6,2,4]=>[3,2,1,1]
[5,1,3,7,6,4,2]=>[4,2,1]
[5,1,4,2,3,6,7]=>[3,1,1,1,1]
[5,1,4,2,3,7,6]=>[3,2,1,1]
[5,1,4,2,6,3,7]=>[3,2,1,1]
[5,1,4,2,6,7,3]=>[3,2,1,1]
[5,1,4,2,7,3,6]=>[3,2,1,1]
[5,1,4,2,7,6,3]=>[3,3,1]
[5,1,4,3,2,6,7]=>[4,1,1,1]
[5,1,4,3,2,7,6]=>[4,2,1]
[5,1,4,3,6,2,7]=>[4,1,1,1]
[5,1,4,3,6,7,2]=>[4,1,1,1]
[5,1,4,3,7,2,6]=>[4,1,1,1]
[5,1,4,3,7,6,2]=>[4,2,1]
[5,1,4,6,2,3,7]=>[3,1,1,1,1]
[5,1,4,6,2,7,3]=>[3,2,1,1]
[5,1,4,6,3,2,7]=>[4,1,1,1]
[5,1,4,6,3,7,2]=>[4,1,1,1]
[5,1,4,6,7,2,3]=>[3,1,1,1,1]
[5,1,4,6,7,3,2]=>[4,1,1,1]
[5,1,4,7,2,3,6]=>[3,1,1,1,1]
[5,1,4,7,2,6,3]=>[3,2,1,1]
[5,1,4,7,3,2,6]=>[4,1,1,1]
[5,1,4,7,3,6,2]=>[4,1,1,1]
[5,1,4,7,6,2,3]=>[3,2,1,1]
[5,1,4,7,6,3,2]=>[4,2,1]
[5,1,6,2,3,4,7]=>[2,2,1,1,1]
[5,1,6,2,3,7,4]=>[2,2,2,1]
[5,1,6,2,4,3,7]=>[3,2,1,1]
[5,1,6,2,4,7,3]=>[3,2,1,1]
[5,1,6,2,7,3,4]=>[2,2,2,1]
[5,1,6,2,7,4,3]=>[3,2,2]
[5,1,6,3,2,4,7]=>[3,2,1,1]
[5,1,6,3,2,7,4]=>[3,2,2]
[5,1,6,3,4,2,7]=>[3,2,1,1]
[5,1,6,3,4,7,2]=>[3,2,1,1]
[5,1,6,3,7,2,4]=>[3,2,1,1]
[5,1,6,3,7,4,2]=>[3,2,2]
[5,1,6,4,2,3,7]=>[3,2,1,1]
[5,1,6,4,2,7,3]=>[3,2,2]
[5,1,6,4,3,2,7]=>[4,2,1]
[5,1,6,4,3,7,2]=>[4,2,1]
[5,1,6,4,7,2,3]=>[3,2,1,1]
[5,1,6,4,7,3,2]=>[4,2,1]
[5,1,6,7,2,3,4]=>[2,2,1,1,1]
[5,1,6,7,2,4,3]=>[3,2,1,1]
[5,1,6,7,3,2,4]=>[3,2,1,1]
[5,1,6,7,3,4,2]=>[3,2,1,1]
[5,1,6,7,4,2,3]=>[3,2,1,1]
[5,1,6,7,4,3,2]=>[4,2,1]
[5,1,7,2,3,4,6]=>[2,2,1,1,1]
[5,1,7,2,3,6,4]=>[3,2,1,1]
[5,1,7,2,4,3,6]=>[3,2,1,1]
[5,1,7,2,4,6,3]=>[3,2,1,1]
[5,1,7,2,6,3,4]=>[3,2,1,1]
[5,1,7,2,6,4,3]=>[4,2,1]
[5,1,7,3,2,4,6]=>[3,2,1,1]
[5,1,7,3,2,6,4]=>[3,2,2]
[5,1,7,3,4,2,6]=>[3,2,1,1]
[5,1,7,3,4,6,2]=>[3,2,1,1]
[5,1,7,3,6,2,4]=>[3,2,1,1]
[5,1,7,3,6,4,2]=>[4,2,1]
[5,1,7,4,2,3,6]=>[3,2,1,1]
[5,1,7,4,2,6,3]=>[3,2,2]
[5,1,7,4,3,2,6]=>[4,2,1]
[5,1,7,4,3,6,2]=>[4,2,1]
[5,1,7,4,6,2,3]=>[3,2,1,1]
[5,1,7,4,6,3,2]=>[4,2,1]
[5,1,7,6,2,3,4]=>[3,2,1,1]
[5,1,7,6,2,4,3]=>[4,2,1]
[5,1,7,6,3,2,4]=>[4,2,1]
[5,1,7,6,3,4,2]=>[4,2,1]
[5,1,7,6,4,2,3]=>[4,2,1]
[5,1,7,6,4,3,2]=>[5,2]
[5,2,1,3,4,6,7]=>[3,1,1,1,1]
[5,2,1,3,4,7,6]=>[3,2,1,1]
[5,2,1,3,6,4,7]=>[3,2,1,1]
[5,2,1,3,6,7,4]=>[3,2,1,1]
[5,2,1,3,7,4,6]=>[3,2,1,1]
[5,2,1,3,7,6,4]=>[3,3,1]
[5,2,1,4,3,6,7]=>[3,2,1,1]
[5,2,1,4,3,7,6]=>[3,2,2]
[5,2,1,4,6,3,7]=>[3,2,1,1]
[5,2,1,4,6,7,3]=>[3,2,1,1]
[5,2,1,4,7,3,6]=>[3,2,1,1]
[5,2,1,4,7,6,3]=>[3,3,1]
[5,2,1,6,3,4,7]=>[3,2,1,1]
[5,2,1,6,3,7,4]=>[3,2,2]
[5,2,1,6,4,3,7]=>[3,3,1]
[5,2,1,6,4,7,3]=>[3,3,1]
[5,2,1,6,7,3,4]=>[3,2,1,1]
[5,2,1,6,7,4,3]=>[3,3,1]
[5,2,1,7,3,4,6]=>[3,2,1,1]
[5,2,1,7,3,6,4]=>[3,3,1]
[5,2,1,7,4,3,6]=>[3,3,1]
[5,2,1,7,4,6,3]=>[3,3,1]
[5,2,1,7,6,3,4]=>[3,3,1]
[5,2,1,7,6,4,3]=>[4,3]
[5,2,3,1,4,6,7]=>[3,1,1,1,1]
[5,2,3,1,4,7,6]=>[3,2,1,1]
[5,2,3,1,6,4,7]=>[3,2,1,1]
[5,2,3,1,6,7,4]=>[3,2,1,1]
[5,2,3,1,7,4,6]=>[3,2,1,1]
[5,2,3,1,7,6,4]=>[3,3,1]
[5,2,3,4,1,6,7]=>[3,1,1,1,1]
[5,2,3,4,1,7,6]=>[3,2,1,1]
[5,2,3,4,6,1,7]=>[3,1,1,1,1]
[5,2,3,4,6,7,1]=>[3,1,1,1,1]
[5,2,3,4,7,1,6]=>[3,1,1,1,1]
[5,2,3,4,7,6,1]=>[3,2,1,1]
[5,2,3,6,1,4,7]=>[3,1,1,1,1]
[5,2,3,6,1,7,4]=>[3,2,1,1]
[5,2,3,6,4,1,7]=>[3,2,1,1]
[5,2,3,6,4,7,1]=>[3,2,1,1]
[5,2,3,6,7,1,4]=>[3,1,1,1,1]
[5,2,3,6,7,4,1]=>[3,2,1,1]
[5,2,3,7,1,4,6]=>[3,1,1,1,1]
[5,2,3,7,1,6,4]=>[3,2,1,1]
[5,2,3,7,4,1,6]=>[3,2,1,1]
[5,2,3,7,4,6,1]=>[3,2,1,1]
[5,2,3,7,6,1,4]=>[3,2,1,1]
[5,2,3,7,6,4,1]=>[4,2,1]
[5,2,4,1,3,6,7]=>[3,1,1,1,1]
[5,2,4,1,3,7,6]=>[3,2,1,1]
[5,2,4,1,6,3,7]=>[3,2,1,1]
[5,2,4,1,6,7,3]=>[3,2,1,1]
[5,2,4,1,7,3,6]=>[3,2,1,1]
[5,2,4,1,7,6,3]=>[3,3,1]
[5,2,4,3,1,6,7]=>[4,1,1,1]
[5,2,4,3,1,7,6]=>[4,2,1]
[5,2,4,3,6,1,7]=>[4,1,1,1]
[5,2,4,3,6,7,1]=>[4,1,1,1]
[5,2,4,3,7,1,6]=>[4,1,1,1]
[5,2,4,3,7,6,1]=>[4,2,1]
[5,2,4,6,1,3,7]=>[3,1,1,1,1]
[5,2,4,6,1,7,3]=>[3,2,1,1]
[5,2,4,6,3,1,7]=>[4,1,1,1]
[5,2,4,6,3,7,1]=>[4,1,1,1]
[5,2,4,6,7,1,3]=>[3,1,1,1,1]
[5,2,4,6,7,3,1]=>[4,1,1,1]
[5,2,4,7,1,3,6]=>[3,1,1,1,1]
[5,2,4,7,1,6,3]=>[3,2,1,1]
[5,2,4,7,3,1,6]=>[4,1,1,1]
[5,2,4,7,3,6,1]=>[4,1,1,1]
[5,2,4,7,6,1,3]=>[3,2,1,1]
[5,2,4,7,6,3,1]=>[4,2,1]
[5,2,6,1,3,4,7]=>[3,1,1,1,1]
[5,2,6,1,3,7,4]=>[3,2,1,1]
[5,2,6,1,4,3,7]=>[3,2,1,1]
[5,2,6,1,4,7,3]=>[3,2,1,1]
[5,2,6,1,7,3,4]=>[3,2,1,1]
[5,2,6,1,7,4,3]=>[3,3,1]
[5,2,6,3,1,4,7]=>[3,2,1,1]
[5,2,6,3,1,7,4]=>[3,2,2]
[5,2,6,3,4,1,7]=>[3,2,1,1]
[5,2,6,3,4,7,1]=>[3,2,1,1]
[5,2,6,3,7,1,4]=>[3,2,1,1]
[5,2,6,3,7,4,1]=>[3,2,2]
[5,2,6,4,1,3,7]=>[3,2,1,1]
[5,2,6,4,1,7,3]=>[3,2,2]
[5,2,6,4,3,1,7]=>[4,2,1]
[5,2,6,4,3,7,1]=>[4,2,1]
[5,2,6,4,7,1,3]=>[3,2,1,1]
[5,2,6,4,7,3,1]=>[4,2,1]
[5,2,6,7,1,3,4]=>[3,1,1,1,1]
[5,2,6,7,1,4,3]=>[3,2,1,1]
[5,2,6,7,3,1,4]=>[3,2,1,1]
[5,2,6,7,3,4,1]=>[3,2,1,1]
[5,2,6,7,4,1,3]=>[3,2,1,1]
[5,2,6,7,4,3,1]=>[4,2,1]
[5,2,7,1,3,4,6]=>[3,1,1,1,1]
[5,2,7,1,3,6,4]=>[3,2,1,1]
[5,2,7,1,4,3,6]=>[3,2,1,1]
[5,2,7,1,4,6,3]=>[3,2,1,1]
[5,2,7,1,6,3,4]=>[3,2,1,1]
[5,2,7,1,6,4,3]=>[4,2,1]
[5,2,7,3,1,4,6]=>[3,2,1,1]
[5,2,7,3,1,6,4]=>[3,2,2]
[5,2,7,3,4,1,6]=>[3,2,1,1]
[5,2,7,3,4,6,1]=>[3,2,1,1]
[5,2,7,3,6,1,4]=>[3,2,1,1]
[5,2,7,3,6,4,1]=>[4,2,1]
[5,2,7,4,1,3,6]=>[3,2,1,1]
[5,2,7,4,1,6,3]=>[3,2,2]
[5,2,7,4,3,1,6]=>[4,2,1]
[5,2,7,4,3,6,1]=>[4,2,1]
[5,2,7,4,6,1,3]=>[3,2,1,1]
[5,2,7,4,6,3,1]=>[4,2,1]
[5,2,7,6,1,3,4]=>[3,2,1,1]
[5,2,7,6,1,4,3]=>[4,2,1]
[5,2,7,6,3,1,4]=>[4,2,1]
[5,2,7,6,3,4,1]=>[4,2,1]
[5,2,7,6,4,1,3]=>[4,2,1]
[5,2,7,6,4,3,1]=>[5,2]
[5,3,1,2,4,6,7]=>[3,1,1,1,1]
[5,3,1,2,4,7,6]=>[3,2,1,1]
[5,3,1,2,6,4,7]=>[3,2,1,1]
[5,3,1,2,6,7,4]=>[3,2,1,1]
[5,3,1,2,7,4,6]=>[3,2,1,1]
[5,3,1,2,7,6,4]=>[3,3,1]
[5,3,1,4,2,6,7]=>[3,2,1,1]
[5,3,1,4,2,7,6]=>[3,2,2]
[5,3,1,4,6,2,7]=>[3,2,1,1]
[5,3,1,4,6,7,2]=>[3,2,1,1]
[5,3,1,4,7,2,6]=>[3,2,1,1]
[5,3,1,4,7,6,2]=>[3,3,1]
[5,3,1,6,2,4,7]=>[3,2,1,1]
[5,3,1,6,2,7,4]=>[3,2,2]
[5,3,1,6,4,2,7]=>[3,3,1]
[5,3,1,6,4,7,2]=>[3,3,1]
[5,3,1,6,7,2,4]=>[3,2,1,1]
[5,3,1,6,7,4,2]=>[3,3,1]
[5,3,1,7,2,4,6]=>[3,2,1,1]
[5,3,1,7,2,6,4]=>[3,3,1]
[5,3,1,7,4,2,6]=>[3,3,1]
[5,3,1,7,4,6,2]=>[3,3,1]
[5,3,1,7,6,2,4]=>[3,3,1]
[5,3,1,7,6,4,2]=>[4,3]
[5,3,2,1,4,6,7]=>[4,1,1,1]
[5,3,2,1,4,7,6]=>[4,2,1]
[5,3,2,1,6,4,7]=>[4,2,1]
[5,3,2,1,6,7,4]=>[4,2,1]
[5,3,2,1,7,4,6]=>[4,2,1]
[5,3,2,1,7,6,4]=>[4,3]
[5,3,2,4,1,6,7]=>[4,1,1,1]
[5,3,2,4,1,7,6]=>[4,2,1]
[5,3,2,4,6,1,7]=>[4,1,1,1]
[5,3,2,4,6,7,1]=>[4,1,1,1]
[5,3,2,4,7,1,6]=>[4,1,1,1]
[5,3,2,4,7,6,1]=>[4,2,1]
[5,3,2,6,1,4,7]=>[4,1,1,1]
[5,3,2,6,1,7,4]=>[4,2,1]
[5,3,2,6,4,1,7]=>[4,2,1]
[5,3,2,6,4,7,1]=>[4,2,1]
[5,3,2,6,7,1,4]=>[4,1,1,1]
[5,3,2,6,7,4,1]=>[4,2,1]
[5,3,2,7,1,4,6]=>[4,1,1,1]
[5,3,2,7,1,6,4]=>[4,2,1]
[5,3,2,7,4,1,6]=>[4,2,1]
[5,3,2,7,4,6,1]=>[4,2,1]
[5,3,2,7,6,1,4]=>[4,2,1]
[5,3,2,7,6,4,1]=>[4,3]
[5,3,4,1,2,6,7]=>[3,1,1,1,1]
[5,3,4,1,2,7,6]=>[3,2,1,1]
[5,3,4,1,6,2,7]=>[3,2,1,1]
[5,3,4,1,6,7,2]=>[3,2,1,1]
[5,3,4,1,7,2,6]=>[3,2,1,1]
[5,3,4,1,7,6,2]=>[3,3,1]
[5,3,4,2,1,6,7]=>[4,1,1,1]
[5,3,4,2,1,7,6]=>[4,2,1]
[5,3,4,2,6,1,7]=>[4,1,1,1]
[5,3,4,2,6,7,1]=>[4,1,1,1]
[5,3,4,2,7,1,6]=>[4,1,1,1]
[5,3,4,2,7,6,1]=>[4,2,1]
[5,3,4,6,1,2,7]=>[3,1,1,1,1]
[5,3,4,6,1,7,2]=>[3,2,1,1]
[5,3,4,6,2,1,7]=>[4,1,1,1]
[5,3,4,6,2,7,1]=>[4,1,1,1]
[5,3,4,6,7,1,2]=>[3,1,1,1,1]
[5,3,4,6,7,2,1]=>[4,1,1,1]
[5,3,4,7,1,2,6]=>[3,1,1,1,1]
[5,3,4,7,1,6,2]=>[3,2,1,1]
[5,3,4,7,2,1,6]=>[4,1,1,1]
[5,3,4,7,2,6,1]=>[4,1,1,1]
[5,3,4,7,6,1,2]=>[3,2,1,1]
[5,3,4,7,6,2,1]=>[4,2,1]
[5,3,6,1,2,4,7]=>[3,1,1,1,1]
[5,3,6,1,2,7,4]=>[3,2,1,1]
[5,3,6,1,4,2,7]=>[3,2,1,1]
[5,3,6,1,4,7,2]=>[3,2,1,1]
[5,3,6,1,7,2,4]=>[3,2,1,1]
[5,3,6,1,7,4,2]=>[3,3,1]
[5,3,6,2,1,4,7]=>[4,1,1,1]
[5,3,6,2,1,7,4]=>[4,2,1]
[5,3,6,2,4,1,7]=>[4,1,1,1]
[5,3,6,2,4,7,1]=>[4,1,1,1]
[5,3,6,2,7,1,4]=>[4,1,1,1]
[5,3,6,2,7,4,1]=>[4,2,1]
[5,3,6,4,1,2,7]=>[3,2,1,1]
[5,3,6,4,1,7,2]=>[3,2,2]
[5,3,6,4,2,1,7]=>[4,2,1]
[5,3,6,4,2,7,1]=>[4,2,1]
[5,3,6,4,7,1,2]=>[3,2,1,1]
[5,3,6,4,7,2,1]=>[4,2,1]
[5,3,6,7,1,2,4]=>[3,1,1,1,1]
[5,3,6,7,1,4,2]=>[3,2,1,1]
[5,3,6,7,2,1,4]=>[4,1,1,1]
[5,3,6,7,2,4,1]=>[4,1,1,1]
[5,3,6,7,4,1,2]=>[3,2,1,1]
[5,3,6,7,4,2,1]=>[4,2,1]
[5,3,7,1,2,4,6]=>[3,1,1,1,1]
[5,3,7,1,2,6,4]=>[3,2,1,1]
[5,3,7,1,4,2,6]=>[3,2,1,1]
[5,3,7,1,4,6,2]=>[3,2,1,1]
[5,3,7,1,6,2,4]=>[3,2,1,1]
[5,3,7,1,6,4,2]=>[4,2,1]
[5,3,7,2,1,4,6]=>[4,1,1,1]
[5,3,7,2,1,6,4]=>[4,2,1]
[5,3,7,2,4,1,6]=>[4,1,1,1]
[5,3,7,2,4,6,1]=>[4,1,1,1]
[5,3,7,2,6,1,4]=>[4,1,1,1]
[5,3,7,2,6,4,1]=>[4,2,1]
[5,3,7,4,1,2,6]=>[3,2,1,1]
[5,3,7,4,1,6,2]=>[3,2,2]
[5,3,7,4,2,1,6]=>[4,2,1]
[5,3,7,4,2,6,1]=>[4,2,1]
[5,3,7,4,6,1,2]=>[3,2,1,1]
[5,3,7,4,6,2,1]=>[4,2,1]
[5,3,7,6,1,2,4]=>[3,2,1,1]
[5,3,7,6,1,4,2]=>[4,2,1]
[5,3,7,6,2,1,4]=>[4,2,1]
[5,3,7,6,2,4,1]=>[4,2,1]
[5,3,7,6,4,1,2]=>[4,2,1]
[5,3,7,6,4,2,1]=>[5,2]
[5,4,1,2,3,6,7]=>[3,1,1,1,1]
[5,4,1,2,3,7,6]=>[3,2,1,1]
[5,4,1,2,6,3,7]=>[3,2,1,1]
[5,4,1,2,6,7,3]=>[3,2,1,1]
[5,4,1,2,7,3,6]=>[3,2,1,1]
[5,4,1,2,7,6,3]=>[3,3,1]
[5,4,1,3,2,6,7]=>[4,1,1,1]
[5,4,1,3,2,7,6]=>[4,2,1]
[5,4,1,3,6,2,7]=>[4,1,1,1]
[5,4,1,3,6,7,2]=>[4,1,1,1]
[5,4,1,3,7,2,6]=>[4,1,1,1]
[5,4,1,3,7,6,2]=>[4,2,1]
[5,4,1,6,2,3,7]=>[3,2,1,1]
[5,4,1,6,2,7,3]=>[3,2,2]
[5,4,1,6,3,2,7]=>[4,2,1]
[5,4,1,6,3,7,2]=>[4,2,1]
[5,4,1,6,7,2,3]=>[3,2,1,1]
[5,4,1,6,7,3,2]=>[4,2,1]
[5,4,1,7,2,3,6]=>[3,2,1,1]
[5,4,1,7,2,6,3]=>[3,3,1]
[5,4,1,7,3,2,6]=>[4,2,1]
[5,4,1,7,3,6,2]=>[4,2,1]
[5,4,1,7,6,2,3]=>[3,3,1]
[5,4,1,7,6,3,2]=>[4,3]
[5,4,2,1,3,6,7]=>[4,1,1,1]
[5,4,2,1,3,7,6]=>[4,2,1]
[5,4,2,1,6,3,7]=>[4,2,1]
[5,4,2,1,6,7,3]=>[4,2,1]
[5,4,2,1,7,3,6]=>[4,2,1]
[5,4,2,1,7,6,3]=>[4,3]
[5,4,2,3,1,6,7]=>[4,1,1,1]
[5,4,2,3,1,7,6]=>[4,2,1]
[5,4,2,3,6,1,7]=>[4,1,1,1]
[5,4,2,3,6,7,1]=>[4,1,1,1]
[5,4,2,3,7,1,6]=>[4,1,1,1]
[5,4,2,3,7,6,1]=>[4,2,1]
[5,4,2,6,1,3,7]=>[4,1,1,1]
[5,4,2,6,1,7,3]=>[4,2,1]
[5,4,2,6,3,1,7]=>[4,2,1]
[5,4,2,6,3,7,1]=>[4,2,1]
[5,4,2,6,7,1,3]=>[4,1,1,1]
[5,4,2,6,7,3,1]=>[4,2,1]
[5,4,2,7,1,3,6]=>[4,1,1,1]
[5,4,2,7,1,6,3]=>[4,2,1]
[5,4,2,7,3,1,6]=>[4,2,1]
[5,4,2,7,3,6,1]=>[4,2,1]
[5,4,2,7,6,1,3]=>[4,2,1]
[5,4,2,7,6,3,1]=>[4,3]
[5,4,3,1,2,6,7]=>[4,1,1,1]
[5,4,3,1,2,7,6]=>[4,2,1]
[5,4,3,1,6,2,7]=>[4,2,1]
[5,4,3,1,6,7,2]=>[4,2,1]
[5,4,3,1,7,2,6]=>[4,2,1]
[5,4,3,1,7,6,2]=>[4,3]
[5,4,3,2,1,6,7]=>[5,1,1]
[5,4,3,2,1,7,6]=>[5,2]
[5,4,3,2,6,1,7]=>[5,1,1]
[5,4,3,2,6,7,1]=>[5,1,1]
[5,4,3,2,7,1,6]=>[5,1,1]
[5,4,3,2,7,6,1]=>[5,2]
[5,4,3,6,1,2,7]=>[4,1,1,1]
[5,4,3,6,1,7,2]=>[4,2,1]
[5,4,3,6,2,1,7]=>[5,1,1]
[5,4,3,6,2,7,1]=>[5,1,1]
[5,4,3,6,7,1,2]=>[4,1,1,1]
[5,4,3,6,7,2,1]=>[5,1,1]
[5,4,3,7,1,2,6]=>[4,1,1,1]
[5,4,3,7,1,6,2]=>[4,2,1]
[5,4,3,7,2,1,6]=>[5,1,1]
[5,4,3,7,2,6,1]=>[5,1,1]
[5,4,3,7,6,1,2]=>[4,2,1]
[5,4,3,7,6,2,1]=>[5,2]
[5,4,6,1,2,3,7]=>[3,1,1,1,1]
[5,4,6,1,2,7,3]=>[3,2,1,1]
[5,4,6,1,3,2,7]=>[4,1,1,1]
[5,4,6,1,3,7,2]=>[4,1,1,1]
[5,4,6,1,7,2,3]=>[3,2,1,1]
[5,4,6,1,7,3,2]=>[4,2,1]
[5,4,6,2,1,3,7]=>[4,1,1,1]
[5,4,6,2,1,7,3]=>[4,2,1]
[5,4,6,2,3,1,7]=>[4,1,1,1]
[5,4,6,2,3,7,1]=>[4,1,1,1]
[5,4,6,2,7,1,3]=>[4,1,1,1]
[5,4,6,2,7,3,1]=>[4,2,1]
[5,4,6,3,1,2,7]=>[4,1,1,1]
[5,4,6,3,1,7,2]=>[4,2,1]
[5,4,6,3,2,1,7]=>[5,1,1]
[5,4,6,3,2,7,1]=>[5,1,1]
[5,4,6,3,7,1,2]=>[4,1,1,1]
[5,4,6,3,7,2,1]=>[5,1,1]
[5,4,6,7,1,2,3]=>[3,1,1,1,1]
[5,4,6,7,1,3,2]=>[4,1,1,1]
[5,4,6,7,2,1,3]=>[4,1,1,1]
[5,4,6,7,2,3,1]=>[4,1,1,1]
[5,4,6,7,3,1,2]=>[4,1,1,1]
[5,4,6,7,3,2,1]=>[5,1,1]
[5,4,7,1,2,3,6]=>[3,1,1,1,1]
[5,4,7,1,2,6,3]=>[3,2,1,1]
[5,4,7,1,3,2,6]=>[4,1,1,1]
[5,4,7,1,3,6,2]=>[4,1,1,1]
[5,4,7,1,6,2,3]=>[3,2,1,1]
[5,4,7,1,6,3,2]=>[4,2,1]
[5,4,7,2,1,3,6]=>[4,1,1,1]
[5,4,7,2,1,6,3]=>[4,2,1]
[5,4,7,2,3,1,6]=>[4,1,1,1]
[5,4,7,2,3,6,1]=>[4,1,1,1]
[5,4,7,2,6,1,3]=>[4,1,1,1]
[5,4,7,2,6,3,1]=>[4,2,1]
[5,4,7,3,1,2,6]=>[4,1,1,1]
[5,4,7,3,1,6,2]=>[4,2,1]
[5,4,7,3,2,1,6]=>[5,1,1]
[5,4,7,3,2,6,1]=>[5,1,1]
[5,4,7,3,6,1,2]=>[4,1,1,1]
[5,4,7,3,6,2,1]=>[5,1,1]
[5,4,7,6,1,2,3]=>[3,2,1,1]
[5,4,7,6,1,3,2]=>[4,2,1]
[5,4,7,6,2,1,3]=>[4,2,1]
[5,4,7,6,2,3,1]=>[4,2,1]
[5,4,7,6,3,1,2]=>[4,2,1]
[5,4,7,6,3,2,1]=>[5,2]
[5,6,1,2,3,4,7]=>[2,1,1,1,1,1]
[5,6,1,2,3,7,4]=>[2,2,1,1,1]
[5,6,1,2,4,3,7]=>[3,1,1,1,1]
[5,6,1,2,4,7,3]=>[3,1,1,1,1]
[5,6,1,2,7,3,4]=>[2,2,1,1,1]
[5,6,1,2,7,4,3]=>[3,2,1,1]
[5,6,1,3,2,4,7]=>[3,1,1,1,1]
[5,6,1,3,2,7,4]=>[3,2,1,1]
[5,6,1,3,4,2,7]=>[3,1,1,1,1]
[5,6,1,3,4,7,2]=>[3,1,1,1,1]
[5,6,1,3,7,2,4]=>[3,1,1,1,1]
[5,6,1,3,7,4,2]=>[3,2,1,1]
[5,6,1,4,2,3,7]=>[3,1,1,1,1]
[5,6,1,4,2,7,3]=>[3,2,1,1]
[5,6,1,4,3,2,7]=>[4,1,1,1]
[5,6,1,4,3,7,2]=>[4,1,1,1]
[5,6,1,4,7,2,3]=>[3,1,1,1,1]
[5,6,1,4,7,3,2]=>[4,1,1,1]
[5,6,1,7,2,3,4]=>[2,2,1,1,1]
[5,6,1,7,2,4,3]=>[3,2,1,1]
[5,6,1,7,3,2,4]=>[3,2,1,1]
[5,6,1,7,3,4,2]=>[3,2,1,1]
[5,6,1,7,4,2,3]=>[3,2,1,1]
[5,6,1,7,4,3,2]=>[4,2,1]
[5,6,2,1,3,4,7]=>[3,1,1,1,1]
[5,6,2,1,3,7,4]=>[3,2,1,1]
[5,6,2,1,4,3,7]=>[3,2,1,1]
[5,6,2,1,4,7,3]=>[3,2,1,1]
[5,6,2,1,7,3,4]=>[3,2,1,1]
[5,6,2,1,7,4,3]=>[3,3,1]
[5,6,2,3,1,4,7]=>[3,1,1,1,1]
[5,6,2,3,1,7,4]=>[3,2,1,1]
[5,6,2,3,4,1,7]=>[3,1,1,1,1]
[5,6,2,3,4,7,1]=>[3,1,1,1,1]
[5,6,2,3,7,1,4]=>[3,1,1,1,1]
[5,6,2,3,7,4,1]=>[3,2,1,1]
[5,6,2,4,1,3,7]=>[3,1,1,1,1]
[5,6,2,4,1,7,3]=>[3,2,1,1]
[5,6,2,4,3,1,7]=>[4,1,1,1]
[5,6,2,4,3,7,1]=>[4,1,1,1]
[5,6,2,4,7,1,3]=>[3,1,1,1,1]
[5,6,2,4,7,3,1]=>[4,1,1,1]
[5,6,2,7,1,3,4]=>[3,1,1,1,1]
[5,6,2,7,1,4,3]=>[3,2,1,1]
[5,6,2,7,3,1,4]=>[3,2,1,1]
[5,6,2,7,3,4,1]=>[3,2,1,1]
[5,6,2,7,4,1,3]=>[3,2,1,1]
[5,6,2,7,4,3,1]=>[4,2,1]
[5,6,3,1,2,4,7]=>[3,1,1,1,1]
[5,6,3,1,2,7,4]=>[3,2,1,1]
[5,6,3,1,4,2,7]=>[3,2,1,1]
[5,6,3,1,4,7,2]=>[3,2,1,1]
[5,6,3,1,7,2,4]=>[3,2,1,1]
[5,6,3,1,7,4,2]=>[3,3,1]
[5,6,3,2,1,4,7]=>[4,1,1,1]
[5,6,3,2,1,7,4]=>[4,2,1]
[5,6,3,2,4,1,7]=>[4,1,1,1]
[5,6,3,2,4,7,1]=>[4,1,1,1]
[5,6,3,2,7,1,4]=>[4,1,1,1]
[5,6,3,2,7,4,1]=>[4,2,1]
[5,6,3,4,1,2,7]=>[3,1,1,1,1]
[5,6,3,4,1,7,2]=>[3,2,1,1]
[5,6,3,4,2,1,7]=>[4,1,1,1]
[5,6,3,4,2,7,1]=>[4,1,1,1]
[5,6,3,4,7,1,2]=>[3,1,1,1,1]
[5,6,3,4,7,2,1]=>[4,1,1,1]
[5,6,3,7,1,2,4]=>[3,1,1,1,1]
[5,6,3,7,1,4,2]=>[3,2,1,1]
[5,6,3,7,2,1,4]=>[4,1,1,1]
[5,6,3,7,2,4,1]=>[4,1,1,1]
[5,6,3,7,4,1,2]=>[3,2,1,1]
[5,6,3,7,4,2,1]=>[4,2,1]
[5,6,4,1,2,3,7]=>[3,1,1,1,1]
[5,6,4,1,2,7,3]=>[3,2,1,1]
[5,6,4,1,3,2,7]=>[4,1,1,1]
[5,6,4,1,3,7,2]=>[4,1,1,1]
[5,6,4,1,7,2,3]=>[3,2,1,1]
[5,6,4,1,7,3,2]=>[4,2,1]
[5,6,4,2,1,3,7]=>[4,1,1,1]
[5,6,4,2,1,7,3]=>[4,2,1]
[5,6,4,2,3,1,7]=>[4,1,1,1]
[5,6,4,2,3,7,1]=>[4,1,1,1]
[5,6,4,2,7,1,3]=>[4,1,1,1]
[5,6,4,2,7,3,1]=>[4,2,1]
[5,6,4,3,1,2,7]=>[4,1,1,1]
[5,6,4,3,1,7,2]=>[4,2,1]
[5,6,4,3,2,1,7]=>[5,1,1]
[5,6,4,3,2,7,1]=>[5,1,1]
[5,6,4,3,7,1,2]=>[4,1,1,1]
[5,6,4,3,7,2,1]=>[5,1,1]
[5,6,4,7,1,2,3]=>[3,1,1,1,1]
[5,6,4,7,1,3,2]=>[4,1,1,1]
[5,6,4,7,2,1,3]=>[4,1,1,1]
[5,6,4,7,2,3,1]=>[4,1,1,1]
[5,6,4,7,3,1,2]=>[4,1,1,1]
[5,6,4,7,3,2,1]=>[5,1,1]
[5,6,7,1,2,3,4]=>[2,1,1,1,1,1]
[5,6,7,1,2,4,3]=>[3,1,1,1,1]
[5,6,7,1,3,2,4]=>[3,1,1,1,1]
[5,6,7,1,3,4,2]=>[3,1,1,1,1]
[5,6,7,1,4,2,3]=>[3,1,1,1,1]
[5,6,7,1,4,3,2]=>[4,1,1,1]
[5,6,7,2,1,3,4]=>[3,1,1,1,1]
[5,6,7,2,1,4,3]=>[3,2,1,1]
[5,6,7,2,3,1,4]=>[3,1,1,1,1]
[5,6,7,2,3,4,1]=>[3,1,1,1,1]
[5,6,7,2,4,1,3]=>[3,1,1,1,1]
[5,6,7,2,4,3,1]=>[4,1,1,1]
[5,6,7,3,1,2,4]=>[3,1,1,1,1]
[5,6,7,3,1,4,2]=>[3,2,1,1]
[5,6,7,3,2,1,4]=>[4,1,1,1]
[5,6,7,3,2,4,1]=>[4,1,1,1]
[5,6,7,3,4,1,2]=>[3,1,1,1,1]
[5,6,7,3,4,2,1]=>[4,1,1,1]
[5,6,7,4,1,2,3]=>[3,1,1,1,1]
[5,6,7,4,1,3,2]=>[4,1,1,1]
[5,6,7,4,2,1,3]=>[4,1,1,1]
[5,6,7,4,2,3,1]=>[4,1,1,1]
[5,6,7,4,3,1,2]=>[4,1,1,1]
[5,6,7,4,3,2,1]=>[5,1,1]
[5,7,1,2,3,4,6]=>[2,1,1,1,1,1]
[5,7,1,2,3,6,4]=>[3,1,1,1,1]
[5,7,1,2,4,3,6]=>[3,1,1,1,1]
[5,7,1,2,4,6,3]=>[3,1,1,1,1]
[5,7,1,2,6,3,4]=>[3,1,1,1,1]
[5,7,1,2,6,4,3]=>[4,1,1,1]
[5,7,1,3,2,4,6]=>[3,1,1,1,1]
[5,7,1,3,2,6,4]=>[3,2,1,1]
[5,7,1,3,4,2,6]=>[3,1,1,1,1]
[5,7,1,3,4,6,2]=>[3,1,1,1,1]
[5,7,1,3,6,2,4]=>[3,1,1,1,1]
[5,7,1,3,6,4,2]=>[4,1,1,1]
[5,7,1,4,2,3,6]=>[3,1,1,1,1]
[5,7,1,4,2,6,3]=>[3,2,1,1]
[5,7,1,4,3,2,6]=>[4,1,1,1]
[5,7,1,4,3,6,2]=>[4,1,1,1]
[5,7,1,4,6,2,3]=>[3,1,1,1,1]
[5,7,1,4,6,3,2]=>[4,1,1,1]
[5,7,1,6,2,3,4]=>[3,1,1,1,1]
[5,7,1,6,2,4,3]=>[4,1,1,1]
[5,7,1,6,3,2,4]=>[4,1,1,1]
[5,7,1,6,3,4,2]=>[4,1,1,1]
[5,7,1,6,4,2,3]=>[4,1,1,1]
[5,7,1,6,4,3,2]=>[5,1,1]
[5,7,2,1,3,4,6]=>[3,1,1,1,1]
[5,7,2,1,3,6,4]=>[3,2,1,1]
[5,7,2,1,4,3,6]=>[3,2,1,1]
[5,7,2,1,4,6,3]=>[3,2,1,1]
[5,7,2,1,6,3,4]=>[3,2,1,1]
[5,7,2,1,6,4,3]=>[4,2,1]
[5,7,2,3,1,4,6]=>[3,1,1,1,1]
[5,7,2,3,1,6,4]=>[3,2,1,1]
[5,7,2,3,4,1,6]=>[3,1,1,1,1]
[5,7,2,3,4,6,1]=>[3,1,1,1,1]
[5,7,2,3,6,1,4]=>[3,1,1,1,1]
[5,7,2,3,6,4,1]=>[4,1,1,1]
[5,7,2,4,1,3,6]=>[3,1,1,1,1]
[5,7,2,4,1,6,3]=>[3,2,1,1]
[5,7,2,4,3,1,6]=>[4,1,1,1]
[5,7,2,4,3,6,1]=>[4,1,1,1]
[5,7,2,4,6,1,3]=>[3,1,1,1,1]
[5,7,2,4,6,3,1]=>[4,1,1,1]
[5,7,2,6,1,3,4]=>[3,1,1,1,1]
[5,7,2,6,1,4,3]=>[4,1,1,1]
[5,7,2,6,3,1,4]=>[4,1,1,1]
[5,7,2,6,3,4,1]=>[4,1,1,1]
[5,7,2,6,4,1,3]=>[4,1,1,1]
[5,7,2,6,4,3,1]=>[5,1,1]
[5,7,3,1,2,4,6]=>[3,1,1,1,1]
[5,7,3,1,2,6,4]=>[3,2,1,1]
[5,7,3,1,4,2,6]=>[3,2,1,1]
[5,7,3,1,4,6,2]=>[3,2,1,1]
[5,7,3,1,6,2,4]=>[3,2,1,1]
[5,7,3,1,6,4,2]=>[4,2,1]
[5,7,3,2,1,4,6]=>[4,1,1,1]
[5,7,3,2,1,6,4]=>[4,2,1]
[5,7,3,2,4,1,6]=>[4,1,1,1]
[5,7,3,2,4,6,1]=>[4,1,1,1]
[5,7,3,2,6,1,4]=>[4,1,1,1]
[5,7,3,2,6,4,1]=>[4,2,1]
[5,7,3,4,1,2,6]=>[3,1,1,1,1]
[5,7,3,4,1,6,2]=>[3,2,1,1]
[5,7,3,4,2,1,6]=>[4,1,1,1]
[5,7,3,4,2,6,1]=>[4,1,1,1]
[5,7,3,4,6,1,2]=>[3,1,1,1,1]
[5,7,3,4,6,2,1]=>[4,1,1,1]
[5,7,3,6,1,2,4]=>[3,1,1,1,1]
[5,7,3,6,1,4,2]=>[4,1,1,1]
[5,7,3,6,2,1,4]=>[4,1,1,1]
[5,7,3,6,2,4,1]=>[4,1,1,1]
[5,7,3,6,4,1,2]=>[4,1,1,1]
[5,7,3,6,4,2,1]=>[5,1,1]
[5,7,4,1,2,3,6]=>[3,1,1,1,1]
[5,7,4,1,2,6,3]=>[3,2,1,1]
[5,7,4,1,3,2,6]=>[4,1,1,1]
[5,7,4,1,3,6,2]=>[4,1,1,1]
[5,7,4,1,6,2,3]=>[3,2,1,1]
[5,7,4,1,6,3,2]=>[4,2,1]
[5,7,4,2,1,3,6]=>[4,1,1,1]
[5,7,4,2,1,6,3]=>[4,2,1]
[5,7,4,2,3,1,6]=>[4,1,1,1]
[5,7,4,2,3,6,1]=>[4,1,1,1]
[5,7,4,2,6,1,3]=>[4,1,1,1]
[5,7,4,2,6,3,1]=>[4,2,1]
[5,7,4,3,1,2,6]=>[4,1,1,1]
[5,7,4,3,1,6,2]=>[4,2,1]
[5,7,4,3,2,1,6]=>[5,1,1]
[5,7,4,3,2,6,1]=>[5,1,1]
[5,7,4,3,6,1,2]=>[4,1,1,1]
[5,7,4,3,6,2,1]=>[5,1,1]
[5,7,4,6,1,2,3]=>[3,1,1,1,1]
[5,7,4,6,1,3,2]=>[4,1,1,1]
[5,7,4,6,2,1,3]=>[4,1,1,1]
[5,7,4,6,2,3,1]=>[4,1,1,1]
[5,7,4,6,3,1,2]=>[4,1,1,1]
[5,7,4,6,3,2,1]=>[5,1,1]
[5,7,6,1,2,3,4]=>[3,1,1,1,1]
[5,7,6,1,2,4,3]=>[4,1,1,1]
[5,7,6,1,3,2,4]=>[4,1,1,1]
[5,7,6,1,3,4,2]=>[4,1,1,1]
[5,7,6,1,4,2,3]=>[4,1,1,1]
[5,7,6,1,4,3,2]=>[5,1,1]
[5,7,6,2,1,3,4]=>[4,1,1,1]
[5,7,6,2,1,4,3]=>[4,2,1]
[5,7,6,2,3,1,4]=>[4,1,1,1]
[5,7,6,2,3,4,1]=>[4,1,1,1]
[5,7,6,2,4,1,3]=>[4,1,1,1]
[5,7,6,2,4,3,1]=>[5,1,1]
[5,7,6,3,1,2,4]=>[4,1,1,1]
[5,7,6,3,1,4,2]=>[4,2,1]
[5,7,6,3,2,1,4]=>[5,1,1]
[5,7,6,3,2,4,1]=>[5,1,1]
[5,7,6,3,4,1,2]=>[4,1,1,1]
[5,7,6,3,4,2,1]=>[5,1,1]
[5,7,6,4,1,2,3]=>[4,1,1,1]
[5,7,6,4,1,3,2]=>[5,1,1]
[5,7,6,4,2,1,3]=>[5,1,1]
[5,7,6,4,2,3,1]=>[5,1,1]
[5,7,6,4,3,1,2]=>[5,1,1]
[5,7,6,4,3,2,1]=>[6,1]
[6,1,2,3,4,5,7]=>[2,1,1,1,1,1]
[6,1,2,3,4,7,5]=>[2,2,1,1,1]
[6,1,2,3,5,4,7]=>[3,1,1,1,1]
[6,1,2,3,5,7,4]=>[3,1,1,1,1]
[6,1,2,3,7,4,5]=>[2,2,1,1,1]
[6,1,2,3,7,5,4]=>[3,2,1,1]
[6,1,2,4,3,5,7]=>[3,1,1,1,1]
[6,1,2,4,3,7,5]=>[3,2,1,1]
[6,1,2,4,5,3,7]=>[3,1,1,1,1]
[6,1,2,4,5,7,3]=>[3,1,1,1,1]
[6,1,2,4,7,3,5]=>[3,1,1,1,1]
[6,1,2,4,7,5,3]=>[3,2,1,1]
[6,1,2,5,3,4,7]=>[3,1,1,1,1]
[6,1,2,5,3,7,4]=>[3,2,1,1]
[6,1,2,5,4,3,7]=>[4,1,1,1]
[6,1,2,5,4,7,3]=>[4,1,1,1]
[6,1,2,5,7,3,4]=>[3,1,1,1,1]
[6,1,2,5,7,4,3]=>[4,1,1,1]
[6,1,2,7,3,4,5]=>[2,2,1,1,1]
[6,1,2,7,3,5,4]=>[3,2,1,1]
[6,1,2,7,4,3,5]=>[3,2,1,1]
[6,1,2,7,4,5,3]=>[3,2,1,1]
[6,1,2,7,5,3,4]=>[3,2,1,1]
[6,1,2,7,5,4,3]=>[4,2,1]
[6,1,3,2,4,5,7]=>[3,1,1,1,1]
[6,1,3,2,4,7,5]=>[3,2,1,1]
[6,1,3,2,5,4,7]=>[3,2,1,1]
[6,1,3,2,5,7,4]=>[3,2,1,1]
[6,1,3,2,7,4,5]=>[3,2,1,1]
[6,1,3,2,7,5,4]=>[3,3,1]
[6,1,3,4,2,5,7]=>[3,1,1,1,1]
[6,1,3,4,2,7,5]=>[3,2,1,1]
[6,1,3,4,5,2,7]=>[3,1,1,1,1]
[6,1,3,4,5,7,2]=>[3,1,1,1,1]
[6,1,3,4,7,2,5]=>[3,1,1,1,1]
[6,1,3,4,7,5,2]=>[3,2,1,1]
[6,1,3,5,2,4,7]=>[3,1,1,1,1]
[6,1,3,5,2,7,4]=>[3,2,1,1]
[6,1,3,5,4,2,7]=>[4,1,1,1]
[6,1,3,5,4,7,2]=>[4,1,1,1]
[6,1,3,5,7,2,4]=>[3,1,1,1,1]
[6,1,3,5,7,4,2]=>[4,1,1,1]
[6,1,3,7,2,4,5]=>[3,1,1,1,1]
[6,1,3,7,2,5,4]=>[3,2,1,1]
[6,1,3,7,4,2,5]=>[3,2,1,1]
[6,1,3,7,4,5,2]=>[3,2,1,1]
[6,1,3,7,5,2,4]=>[3,2,1,1]
[6,1,3,7,5,4,2]=>[4,2,1]
[6,1,4,2,3,5,7]=>[3,1,1,1,1]
[6,1,4,2,3,7,5]=>[3,2,1,1]
[6,1,4,2,5,3,7]=>[3,2,1,1]
[6,1,4,2,5,7,3]=>[3,2,1,1]
[6,1,4,2,7,3,5]=>[3,2,1,1]
[6,1,4,2,7,5,3]=>[3,3,1]
[6,1,4,3,2,5,7]=>[4,1,1,1]
[6,1,4,3,2,7,5]=>[4,2,1]
[6,1,4,3,5,2,7]=>[4,1,1,1]
[6,1,4,3,5,7,2]=>[4,1,1,1]
[6,1,4,3,7,2,5]=>[4,1,1,1]
[6,1,4,3,7,5,2]=>[4,2,1]
[6,1,4,5,2,3,7]=>[3,1,1,1,1]
[6,1,4,5,2,7,3]=>[3,2,1,1]
[6,1,4,5,3,2,7]=>[4,1,1,1]
[6,1,4,5,3,7,2]=>[4,1,1,1]
[6,1,4,5,7,2,3]=>[3,1,1,1,1]
[6,1,4,5,7,3,2]=>[4,1,1,1]
[6,1,4,7,2,3,5]=>[3,1,1,1,1]
[6,1,4,7,2,5,3]=>[3,2,1,1]
[6,1,4,7,3,2,5]=>[4,1,1,1]
[6,1,4,7,3,5,2]=>[4,1,1,1]
[6,1,4,7,5,2,3]=>[3,2,1,1]
[6,1,4,7,5,3,2]=>[4,2,1]
[6,1,5,2,3,4,7]=>[3,1,1,1,1]
[6,1,5,2,3,7,4]=>[3,2,1,1]
[6,1,5,2,4,3,7]=>[4,1,1,1]
[6,1,5,2,4,7,3]=>[4,1,1,1]
[6,1,5,2,7,3,4]=>[3,2,1,1]
[6,1,5,2,7,4,3]=>[4,2,1]
[6,1,5,3,2,4,7]=>[4,1,1,1]
[6,1,5,3,2,7,4]=>[4,2,1]
[6,1,5,3,4,2,7]=>[4,1,1,1]
[6,1,5,3,4,7,2]=>[4,1,1,1]
[6,1,5,3,7,2,4]=>[4,1,1,1]
[6,1,5,3,7,4,2]=>[4,2,1]
[6,1,5,4,2,3,7]=>[4,1,1,1]
[6,1,5,4,2,7,3]=>[4,2,1]
[6,1,5,4,3,2,7]=>[5,1,1]
[6,1,5,4,3,7,2]=>[5,1,1]
[6,1,5,4,7,2,3]=>[4,1,1,1]
[6,1,5,4,7,3,2]=>[5,1,1]
[6,1,5,7,2,3,4]=>[3,1,1,1,1]
[6,1,5,7,2,4,3]=>[4,1,1,1]
[6,1,5,7,3,2,4]=>[4,1,1,1]
[6,1,5,7,3,4,2]=>[4,1,1,1]
[6,1,5,7,4,2,3]=>[4,1,1,1]
[6,1,5,7,4,3,2]=>[5,1,1]
[6,1,7,2,3,4,5]=>[2,2,1,1,1]
[6,1,7,2,3,5,4]=>[3,2,1,1]
[6,1,7,2,4,3,5]=>[3,2,1,1]
[6,1,7,2,4,5,3]=>[3,2,1,1]
[6,1,7,2,5,3,4]=>[3,2,1,1]
[6,1,7,2,5,4,3]=>[4,2,1]
[6,1,7,3,2,4,5]=>[3,2,1,1]
[6,1,7,3,2,5,4]=>[3,2,2]
[6,1,7,3,4,2,5]=>[3,2,1,1]
[6,1,7,3,4,5,2]=>[3,2,1,1]
[6,1,7,3,5,2,4]=>[3,2,1,1]
[6,1,7,3,5,4,2]=>[4,2,1]
[6,1,7,4,2,3,5]=>[3,2,1,1]
[6,1,7,4,2,5,3]=>[3,2,2]
[6,1,7,4,3,2,5]=>[4,2,1]
[6,1,7,4,3,5,2]=>[4,2,1]
[6,1,7,4,5,2,3]=>[3,2,1,1]
[6,1,7,4,5,3,2]=>[4,2,1]
[6,1,7,5,2,3,4]=>[3,2,1,1]
[6,1,7,5,2,4,3]=>[4,2,1]
[6,1,7,5,3,2,4]=>[4,2,1]
[6,1,7,5,3,4,2]=>[4,2,1]
[6,1,7,5,4,2,3]=>[4,2,1]
[6,1,7,5,4,3,2]=>[5,2]
[6,2,1,3,4,5,7]=>[3,1,1,1,1]
[6,2,1,3,4,7,5]=>[3,2,1,1]
[6,2,1,3,5,4,7]=>[3,2,1,1]
[6,2,1,3,5,7,4]=>[3,2,1,1]
[6,2,1,3,7,4,5]=>[3,2,1,1]
[6,2,1,3,7,5,4]=>[3,3,1]
[6,2,1,4,3,5,7]=>[3,2,1,1]
[6,2,1,4,3,7,5]=>[3,2,2]
[6,2,1,4,5,3,7]=>[3,2,1,1]
[6,2,1,4,5,7,3]=>[3,2,1,1]
[6,2,1,4,7,3,5]=>[3,2,1,1]
[6,2,1,4,7,5,3]=>[3,3,1]
[6,2,1,5,3,4,7]=>[3,2,1,1]
[6,2,1,5,3,7,4]=>[3,2,2]
[6,2,1,5,4,3,7]=>[4,2,1]
[6,2,1,5,4,7,3]=>[4,2,1]
[6,2,1,5,7,3,4]=>[3,2,1,1]
[6,2,1,5,7,4,3]=>[4,2,1]
[6,2,1,7,3,4,5]=>[3,2,1,1]
[6,2,1,7,3,5,4]=>[3,3,1]
[6,2,1,7,4,3,5]=>[3,3,1]
[6,2,1,7,4,5,3]=>[3,3,1]
[6,2,1,7,5,3,4]=>[3,3,1]
[6,2,1,7,5,4,3]=>[4,3]
[6,2,3,1,4,5,7]=>[3,1,1,1,1]
[6,2,3,1,4,7,5]=>[3,2,1,1]
[6,2,3,1,5,4,7]=>[3,2,1,1]
[6,2,3,1,5,7,4]=>[3,2,1,1]
[6,2,3,1,7,4,5]=>[3,2,1,1]
[6,2,3,1,7,5,4]=>[3,3,1]
[6,2,3,4,1,5,7]=>[3,1,1,1,1]
[6,2,3,4,1,7,5]=>[3,2,1,1]
[6,2,3,4,5,1,7]=>[3,1,1,1,1]
[6,2,3,4,5,7,1]=>[3,1,1,1,1]
[6,2,3,4,7,1,5]=>[3,1,1,1,1]
[6,2,3,4,7,5,1]=>[3,2,1,1]
[6,2,3,5,1,4,7]=>[3,1,1,1,1]
[6,2,3,5,1,7,4]=>[3,2,1,1]
[6,2,3,5,4,1,7]=>[4,1,1,1]
[6,2,3,5,4,7,1]=>[4,1,1,1]
[6,2,3,5,7,1,4]=>[3,1,1,1,1]
[6,2,3,5,7,4,1]=>[4,1,1,1]
[6,2,3,7,1,4,5]=>[3,1,1,1,1]
[6,2,3,7,1,5,4]=>[3,2,1,1]
[6,2,3,7,4,1,5]=>[3,2,1,1]
[6,2,3,7,4,5,1]=>[3,2,1,1]
[6,2,3,7,5,1,4]=>[3,2,1,1]
[6,2,3,7,5,4,1]=>[4,2,1]
[6,2,4,1,3,5,7]=>[3,1,1,1,1]
[6,2,4,1,3,7,5]=>[3,2,1,1]
[6,2,4,1,5,3,7]=>[3,2,1,1]
[6,2,4,1,5,7,3]=>[3,2,1,1]
[6,2,4,1,7,3,5]=>[3,2,1,1]
[6,2,4,1,7,5,3]=>[3,3,1]
[6,2,4,3,1,5,7]=>[4,1,1,1]
[6,2,4,3,1,7,5]=>[4,2,1]
[6,2,4,3,5,1,7]=>[4,1,1,1]
[6,2,4,3,5,7,1]=>[4,1,1,1]
[6,2,4,3,7,1,5]=>[4,1,1,1]
[6,2,4,3,7,5,1]=>[4,2,1]
[6,2,4,5,1,3,7]=>[3,1,1,1,1]
[6,2,4,5,1,7,3]=>[3,2,1,1]
[6,2,4,5,3,1,7]=>[4,1,1,1]
[6,2,4,5,3,7,1]=>[4,1,1,1]
[6,2,4,5,7,1,3]=>[3,1,1,1,1]
[6,2,4,5,7,3,1]=>[4,1,1,1]
[6,2,4,7,1,3,5]=>[3,1,1,1,1]
[6,2,4,7,1,5,3]=>[3,2,1,1]
[6,2,4,7,3,1,5]=>[4,1,1,1]
[6,2,4,7,3,5,1]=>[4,1,1,1]
[6,2,4,7,5,1,3]=>[3,2,1,1]
[6,2,4,7,5,3,1]=>[4,2,1]
[6,2,5,1,3,4,7]=>[3,1,1,1,1]
[6,2,5,1,3,7,4]=>[3,2,1,1]
[6,2,5,1,4,3,7]=>[4,1,1,1]
[6,2,5,1,4,7,3]=>[4,1,1,1]
[6,2,5,1,7,3,4]=>[3,2,1,1]
[6,2,5,1,7,4,3]=>[4,2,1]
[6,2,5,3,1,4,7]=>[4,1,1,1]
[6,2,5,3,1,7,4]=>[4,2,1]
[6,2,5,3,4,1,7]=>[4,1,1,1]
[6,2,5,3,4,7,1]=>[4,1,1,1]
[6,2,5,3,7,1,4]=>[4,1,1,1]
[6,2,5,3,7,4,1]=>[4,2,1]
[6,2,5,4,1,3,7]=>[4,1,1,1]
[6,2,5,4,1,7,3]=>[4,2,1]
[6,2,5,4,3,1,7]=>[5,1,1]
[6,2,5,4,3,7,1]=>[5,1,1]
[6,2,5,4,7,1,3]=>[4,1,1,1]
[6,2,5,4,7,3,1]=>[5,1,1]
[6,2,5,7,1,3,4]=>[3,1,1,1,1]
[6,2,5,7,1,4,3]=>[4,1,1,1]
[6,2,5,7,3,1,4]=>[4,1,1,1]
[6,2,5,7,3,4,1]=>[4,1,1,1]
[6,2,5,7,4,1,3]=>[4,1,1,1]
[6,2,5,7,4,3,1]=>[5,1,1]
[6,2,7,1,3,4,5]=>[3,1,1,1,1]
[6,2,7,1,3,5,4]=>[3,2,1,1]
[6,2,7,1,4,3,5]=>[3,2,1,1]
[6,2,7,1,4,5,3]=>[3,2,1,1]
[6,2,7,1,5,3,4]=>[3,2,1,1]
[6,2,7,1,5,4,3]=>[4,2,1]
[6,2,7,3,1,4,5]=>[3,2,1,1]
[6,2,7,3,1,5,4]=>[3,2,2]
[6,2,7,3,4,1,5]=>[3,2,1,1]
[6,2,7,3,4,5,1]=>[3,2,1,1]
[6,2,7,3,5,1,4]=>[3,2,1,1]
[6,2,7,3,5,4,1]=>[4,2,1]
[6,2,7,4,1,3,5]=>[3,2,1,1]
[6,2,7,4,1,5,3]=>[3,2,2]
[6,2,7,4,3,1,5]=>[4,2,1]
[6,2,7,4,3,5,1]=>[4,2,1]
[6,2,7,4,5,1,3]=>[3,2,1,1]
[6,2,7,4,5,3,1]=>[4,2,1]
[6,2,7,5,1,3,4]=>[3,2,1,1]
[6,2,7,5,1,4,3]=>[4,2,1]
[6,2,7,5,3,1,4]=>[4,2,1]
[6,2,7,5,3,4,1]=>[4,2,1]
[6,2,7,5,4,1,3]=>[4,2,1]
[6,2,7,5,4,3,1]=>[5,2]
[6,3,1,2,4,5,7]=>[3,1,1,1,1]
[6,3,1,2,4,7,5]=>[3,2,1,1]
[6,3,1,2,5,4,7]=>[3,2,1,1]
[6,3,1,2,5,7,4]=>[3,2,1,1]
[6,3,1,2,7,4,5]=>[3,2,1,1]
[6,3,1,2,7,5,4]=>[3,3,1]
[6,3,1,4,2,5,7]=>[3,2,1,1]
[6,3,1,4,2,7,5]=>[3,2,2]
[6,3,1,4,5,2,7]=>[3,2,1,1]
[6,3,1,4,5,7,2]=>[3,2,1,1]
[6,3,1,4,7,2,5]=>[3,2,1,1]
[6,3,1,4,7,5,2]=>[3,3,1]
[6,3,1,5,2,4,7]=>[3,2,1,1]
[6,3,1,5,2,7,4]=>[3,2,2]
[6,3,1,5,4,2,7]=>[4,2,1]
[6,3,1,5,4,7,2]=>[4,2,1]
[6,3,1,5,7,2,4]=>[3,2,1,1]
[6,3,1,5,7,4,2]=>[4,2,1]
[6,3,1,7,2,4,5]=>[3,2,1,1]
[6,3,1,7,2,5,4]=>[3,3,1]
[6,3,1,7,4,2,5]=>[3,3,1]
[6,3,1,7,4,5,2]=>[3,3,1]
[6,3,1,7,5,2,4]=>[3,3,1]
[6,3,1,7,5,4,2]=>[4,3]
[6,3,2,1,4,5,7]=>[4,1,1,1]
[6,3,2,1,4,7,5]=>[4,2,1]
[6,3,2,1,5,4,7]=>[4,2,1]
[6,3,2,1,5,7,4]=>[4,2,1]
[6,3,2,1,7,4,5]=>[4,2,1]
[6,3,2,1,7,5,4]=>[4,3]
[6,3,2,4,1,5,7]=>[4,1,1,1]
[6,3,2,4,1,7,5]=>[4,2,1]
[6,3,2,4,5,1,7]=>[4,1,1,1]
[6,3,2,4,5,7,1]=>[4,1,1,1]
[6,3,2,4,7,1,5]=>[4,1,1,1]
[6,3,2,4,7,5,1]=>[4,2,1]
[6,3,2,5,1,4,7]=>[4,1,1,1]
[6,3,2,5,1,7,4]=>[4,2,1]
[6,3,2,5,4,1,7]=>[4,2,1]
[6,3,2,5,4,7,1]=>[4,2,1]
[6,3,2,5,7,1,4]=>[4,1,1,1]
[6,3,2,5,7,4,1]=>[4,2,1]
[6,3,2,7,1,4,5]=>[4,1,1,1]
[6,3,2,7,1,5,4]=>[4,2,1]
[6,3,2,7,4,1,5]=>[4,2,1]
[6,3,2,7,4,5,1]=>[4,2,1]
[6,3,2,7,5,1,4]=>[4,2,1]
[6,3,2,7,5,4,1]=>[4,3]
[6,3,4,1,2,5,7]=>[3,1,1,1,1]
[6,3,4,1,2,7,5]=>[3,2,1,1]
[6,3,4,1,5,2,7]=>[3,2,1,1]
[6,3,4,1,5,7,2]=>[3,2,1,1]
[6,3,4,1,7,2,5]=>[3,2,1,1]
[6,3,4,1,7,5,2]=>[3,3,1]
[6,3,4,2,1,5,7]=>[4,1,1,1]
[6,3,4,2,1,7,5]=>[4,2,1]
[6,3,4,2,5,1,7]=>[4,1,1,1]
[6,3,4,2,5,7,1]=>[4,1,1,1]
[6,3,4,2,7,1,5]=>[4,1,1,1]
[6,3,4,2,7,5,1]=>[4,2,1]
[6,3,4,5,1,2,7]=>[3,1,1,1,1]
[6,3,4,5,1,7,2]=>[3,2,1,1]
[6,3,4,5,2,1,7]=>[4,1,1,1]
[6,3,4,5,2,7,1]=>[4,1,1,1]
[6,3,4,5,7,1,2]=>[3,1,1,1,1]
[6,3,4,5,7,2,1]=>[4,1,1,1]
[6,3,4,7,1,2,5]=>[3,1,1,1,1]
[6,3,4,7,1,5,2]=>[3,2,1,1]
[6,3,4,7,2,1,5]=>[4,1,1,1]
[6,3,4,7,2,5,1]=>[4,1,1,1]
[6,3,4,7,5,1,2]=>[3,2,1,1]
[6,3,4,7,5,2,1]=>[4,2,1]
[6,3,5,1,2,4,7]=>[3,1,1,1,1]
[6,3,5,1,2,7,4]=>[3,2,1,1]
[6,3,5,1,4,2,7]=>[4,1,1,1]
[6,3,5,1,4,7,2]=>[4,1,1,1]
[6,3,5,1,7,2,4]=>[3,2,1,1]
[6,3,5,1,7,4,2]=>[4,2,1]
[6,3,5,2,1,4,7]=>[4,1,1,1]
[6,3,5,2,1,7,4]=>[4,2,1]
[6,3,5,2,4,1,7]=>[4,1,1,1]
[6,3,5,2,4,7,1]=>[4,1,1,1]
[6,3,5,2,7,1,4]=>[4,1,1,1]
[6,3,5,2,7,4,1]=>[4,2,1]
[6,3,5,4,1,2,7]=>[4,1,1,1]
[6,3,5,4,1,7,2]=>[4,2,1]
[6,3,5,4,2,1,7]=>[5,1,1]
[6,3,5,4,2,7,1]=>[5,1,1]
[6,3,5,4,7,1,2]=>[4,1,1,1]
[6,3,5,4,7,2,1]=>[5,1,1]
[6,3,5,7,1,2,4]=>[3,1,1,1,1]
[6,3,5,7,1,4,2]=>[4,1,1,1]
[6,3,5,7,2,1,4]=>[4,1,1,1]
[6,3,5,7,2,4,1]=>[4,1,1,1]
[6,3,5,7,4,1,2]=>[4,1,1,1]
[6,3,5,7,4,2,1]=>[5,1,1]
[6,3,7,1,2,4,5]=>[3,1,1,1,1]
[6,3,7,1,2,5,4]=>[3,2,1,1]
[6,3,7,1,4,2,5]=>[3,2,1,1]
[6,3,7,1,4,5,2]=>[3,2,1,1]
[6,3,7,1,5,2,4]=>[3,2,1,1]
[6,3,7,1,5,4,2]=>[4,2,1]
[6,3,7,2,1,4,5]=>[4,1,1,1]
[6,3,7,2,1,5,4]=>[4,2,1]
[6,3,7,2,4,1,5]=>[4,1,1,1]
[6,3,7,2,4,5,1]=>[4,1,1,1]
[6,3,7,2,5,1,4]=>[4,1,1,1]
[6,3,7,2,5,4,1]=>[4,2,1]
[6,3,7,4,1,2,5]=>[3,2,1,1]
[6,3,7,4,1,5,2]=>[3,2,2]
[6,3,7,4,2,1,5]=>[4,2,1]
[6,3,7,4,2,5,1]=>[4,2,1]
[6,3,7,4,5,1,2]=>[3,2,1,1]
[6,3,7,4,5,2,1]=>[4,2,1]
[6,3,7,5,1,2,4]=>[3,2,1,1]
[6,3,7,5,1,4,2]=>[4,2,1]
[6,3,7,5,2,1,4]=>[4,2,1]
[6,3,7,5,2,4,1]=>[4,2,1]
[6,3,7,5,4,1,2]=>[4,2,1]
[6,3,7,5,4,2,1]=>[5,2]
[6,4,1,2,3,5,7]=>[3,1,1,1,1]
[6,4,1,2,3,7,5]=>[3,2,1,1]
[6,4,1,2,5,3,7]=>[3,2,1,1]
[6,4,1,2,5,7,3]=>[3,2,1,1]
[6,4,1,2,7,3,5]=>[3,2,1,1]
[6,4,1,2,7,5,3]=>[3,3,1]
[6,4,1,3,2,5,7]=>[4,1,1,1]
[6,4,1,3,2,7,5]=>[4,2,1]
[6,4,1,3,5,2,7]=>[4,1,1,1]
[6,4,1,3,5,7,2]=>[4,1,1,1]
[6,4,1,3,7,2,5]=>[4,1,1,1]
[6,4,1,3,7,5,2]=>[4,2,1]
[6,4,1,5,2,3,7]=>[3,2,1,1]
[6,4,1,5,2,7,3]=>[3,2,2]
[6,4,1,5,3,2,7]=>[4,2,1]
[6,4,1,5,3,7,2]=>[4,2,1]
[6,4,1,5,7,2,3]=>[3,2,1,1]
[6,4,1,5,7,3,2]=>[4,2,1]
[6,4,1,7,2,3,5]=>[3,2,1,1]
[6,4,1,7,2,5,3]=>[3,3,1]
[6,4,1,7,3,2,5]=>[4,2,1]
[6,4,1,7,3,5,2]=>[4,2,1]
[6,4,1,7,5,2,3]=>[3,3,1]
[6,4,1,7,5,3,2]=>[4,3]
[6,4,2,1,3,5,7]=>[4,1,1,1]
[6,4,2,1,3,7,5]=>[4,2,1]
[6,4,2,1,5,3,7]=>[4,2,1]
[6,4,2,1,5,7,3]=>[4,2,1]
[6,4,2,1,7,3,5]=>[4,2,1]
[6,4,2,1,7,5,3]=>[4,3]
[6,4,2,3,1,5,7]=>[4,1,1,1]
[6,4,2,3,1,7,5]=>[4,2,1]
[6,4,2,3,5,1,7]=>[4,1,1,1]
[6,4,2,3,5,7,1]=>[4,1,1,1]
[6,4,2,3,7,1,5]=>[4,1,1,1]
[6,4,2,3,7,5,1]=>[4,2,1]
[6,4,2,5,1,3,7]=>[4,1,1,1]
[6,4,2,5,1,7,3]=>[4,2,1]
[6,4,2,5,3,1,7]=>[4,2,1]
[6,4,2,5,3,7,1]=>[4,2,1]
[6,4,2,5,7,1,3]=>[4,1,1,1]
[6,4,2,5,7,3,1]=>[4,2,1]
[6,4,2,7,1,3,5]=>[4,1,1,1]
[6,4,2,7,1,5,3]=>[4,2,1]
[6,4,2,7,3,1,5]=>[4,2,1]
[6,4,2,7,3,5,1]=>[4,2,1]
[6,4,2,7,5,1,3]=>[4,2,1]
[6,4,2,7,5,3,1]=>[4,3]
[6,4,3,1,2,5,7]=>[4,1,1,1]
[6,4,3,1,2,7,5]=>[4,2,1]
[6,4,3,1,5,2,7]=>[4,2,1]
[6,4,3,1,5,7,2]=>[4,2,1]
[6,4,3,1,7,2,5]=>[4,2,1]
[6,4,3,1,7,5,2]=>[4,3]
[6,4,3,2,1,5,7]=>[5,1,1]
[6,4,3,2,1,7,5]=>[5,2]
[6,4,3,2,5,1,7]=>[5,1,1]
[6,4,3,2,5,7,1]=>[5,1,1]
[6,4,3,2,7,1,5]=>[5,1,1]
[6,4,3,2,7,5,1]=>[5,2]
[6,4,3,5,1,2,7]=>[4,1,1,1]
[6,4,3,5,1,7,2]=>[4,2,1]
[6,4,3,5,2,1,7]=>[5,1,1]
[6,4,3,5,2,7,1]=>[5,1,1]
[6,4,3,5,7,1,2]=>[4,1,1,1]
[6,4,3,5,7,2,1]=>[5,1,1]
[6,4,3,7,1,2,5]=>[4,1,1,1]
[6,4,3,7,1,5,2]=>[4,2,1]
[6,4,3,7,2,1,5]=>[5,1,1]
[6,4,3,7,2,5,1]=>[5,1,1]
[6,4,3,7,5,1,2]=>[4,2,1]
[6,4,3,7,5,2,1]=>[5,2]
[6,4,5,1,2,3,7]=>[3,1,1,1,1]
[6,4,5,1,2,7,3]=>[3,2,1,1]
[6,4,5,1,3,2,7]=>[4,1,1,1]
[6,4,5,1,3,7,2]=>[4,1,1,1]
[6,4,5,1,7,2,3]=>[3,2,1,1]
[6,4,5,1,7,3,2]=>[4,2,1]
[6,4,5,2,1,3,7]=>[4,1,1,1]
[6,4,5,2,1,7,3]=>[4,2,1]
[6,4,5,2,3,1,7]=>[4,1,1,1]
[6,4,5,2,3,7,1]=>[4,1,1,1]
[6,4,5,2,7,1,3]=>[4,1,1,1]
[6,4,5,2,7,3,1]=>[4,2,1]
[6,4,5,3,1,2,7]=>[4,1,1,1]
[6,4,5,3,1,7,2]=>[4,2,1]
[6,4,5,3,2,1,7]=>[5,1,1]
[6,4,5,3,2,7,1]=>[5,1,1]
[6,4,5,3,7,1,2]=>[4,1,1,1]
[6,4,5,3,7,2,1]=>[5,1,1]
[6,4,5,7,1,2,3]=>[3,1,1,1,1]
[6,4,5,7,1,3,2]=>[4,1,1,1]
[6,4,5,7,2,1,3]=>[4,1,1,1]
[6,4,5,7,2,3,1]=>[4,1,1,1]
[6,4,5,7,3,1,2]=>[4,1,1,1]
[6,4,5,7,3,2,1]=>[5,1,1]
[6,4,7,1,2,3,5]=>[3,1,1,1,1]
[6,4,7,1,2,5,3]=>[3,2,1,1]
[6,4,7,1,3,2,5]=>[4,1,1,1]
[6,4,7,1,3,5,2]=>[4,1,1,1]
[6,4,7,1,5,2,3]=>[3,2,1,1]
[6,4,7,1,5,3,2]=>[4,2,1]
[6,4,7,2,1,3,5]=>[4,1,1,1]
[6,4,7,2,1,5,3]=>[4,2,1]
[6,4,7,2,3,1,5]=>[4,1,1,1]
[6,4,7,2,3,5,1]=>[4,1,1,1]
[6,4,7,2,5,1,3]=>[4,1,1,1]
[6,4,7,2,5,3,1]=>[4,2,1]
[6,4,7,3,1,2,5]=>[4,1,1,1]
[6,4,7,3,1,5,2]=>[4,2,1]
[6,4,7,3,2,1,5]=>[5,1,1]
[6,4,7,3,2,5,1]=>[5,1,1]
[6,4,7,3,5,1,2]=>[4,1,1,1]
[6,4,7,3,5,2,1]=>[5,1,1]
[6,4,7,5,1,2,3]=>[3,2,1,1]
[6,4,7,5,1,3,2]=>[4,2,1]
[6,4,7,5,2,1,3]=>[4,2,1]
[6,4,7,5,2,3,1]=>[4,2,1]
[6,4,7,5,3,1,2]=>[4,2,1]
[6,4,7,5,3,2,1]=>[5,2]
[6,5,1,2,3,4,7]=>[3,1,1,1,1]
[6,5,1,2,3,7,4]=>[3,2,1,1]
[6,5,1,2,4,3,7]=>[4,1,1,1]
[6,5,1,2,4,7,3]=>[4,1,1,1]
[6,5,1,2,7,3,4]=>[3,2,1,1]
[6,5,1,2,7,4,3]=>[4,2,1]
[6,5,1,3,2,4,7]=>[4,1,1,1]
[6,5,1,3,2,7,4]=>[4,2,1]
[6,5,1,3,4,2,7]=>[4,1,1,1]
[6,5,1,3,4,7,2]=>[4,1,1,1]
[6,5,1,3,7,2,4]=>[4,1,1,1]
[6,5,1,3,7,4,2]=>[4,2,1]
[6,5,1,4,2,3,7]=>[4,1,1,1]
[6,5,1,4,2,7,3]=>[4,2,1]
[6,5,1,4,3,2,7]=>[5,1,1]
[6,5,1,4,3,7,2]=>[5,1,1]
[6,5,1,4,7,2,3]=>[4,1,1,1]
[6,5,1,4,7,3,2]=>[5,1,1]
[6,5,1,7,2,3,4]=>[3,2,1,1]
[6,5,1,7,2,4,3]=>[4,2,1]
[6,5,1,7,3,2,4]=>[4,2,1]
[6,5,1,7,3,4,2]=>[4,2,1]
[6,5,1,7,4,2,3]=>[4,2,1]
[6,5,1,7,4,3,2]=>[5,2]
[6,5,2,1,3,4,7]=>[4,1,1,1]
[6,5,2,1,3,7,4]=>[4,2,1]
[6,5,2,1,4,3,7]=>[4,2,1]
[6,5,2,1,4,7,3]=>[4,2,1]
[6,5,2,1,7,3,4]=>[4,2,1]
[6,5,2,1,7,4,3]=>[4,3]
[6,5,2,3,1,4,7]=>[4,1,1,1]
[6,5,2,3,1,7,4]=>[4,2,1]
[6,5,2,3,4,1,7]=>[4,1,1,1]
[6,5,2,3,4,7,1]=>[4,1,1,1]
[6,5,2,3,7,1,4]=>[4,1,1,1]
[6,5,2,3,7,4,1]=>[4,2,1]
[6,5,2,4,1,3,7]=>[4,1,1,1]
[6,5,2,4,1,7,3]=>[4,2,1]
[6,5,2,4,3,1,7]=>[5,1,1]
[6,5,2,4,3,7,1]=>[5,1,1]
[6,5,2,4,7,1,3]=>[4,1,1,1]
[6,5,2,4,7,3,1]=>[5,1,1]
[6,5,2,7,1,3,4]=>[4,1,1,1]
[6,5,2,7,1,4,3]=>[4,2,1]
[6,5,2,7,3,1,4]=>[4,2,1]
[6,5,2,7,3,4,1]=>[4,2,1]
[6,5,2,7,4,1,3]=>[4,2,1]
[6,5,2,7,4,3,1]=>[5,2]
[6,5,3,1,2,4,7]=>[4,1,1,1]
[6,5,3,1,2,7,4]=>[4,2,1]
[6,5,3,1,4,2,7]=>[4,2,1]
[6,5,3,1,4,7,2]=>[4,2,1]
[6,5,3,1,7,2,4]=>[4,2,1]
[6,5,3,1,7,4,2]=>[4,3]
[6,5,3,2,1,4,7]=>[5,1,1]
[6,5,3,2,1,7,4]=>[5,2]
[6,5,3,2,4,1,7]=>[5,1,1]
[6,5,3,2,4,7,1]=>[5,1,1]
[6,5,3,2,7,1,4]=>[5,1,1]
[6,5,3,2,7,4,1]=>[5,2]
[6,5,3,4,1,2,7]=>[4,1,1,1]
[6,5,3,4,1,7,2]=>[4,2,1]
[6,5,3,4,2,1,7]=>[5,1,1]
[6,5,3,4,2,7,1]=>[5,1,1]
[6,5,3,4,7,1,2]=>[4,1,1,1]
[6,5,3,4,7,2,1]=>[5,1,1]
[6,5,3,7,1,2,4]=>[4,1,1,1]
[6,5,3,7,1,4,2]=>[4,2,1]
[6,5,3,7,2,1,4]=>[5,1,1]
[6,5,3,7,2,4,1]=>[5,1,1]
[6,5,3,7,4,1,2]=>[4,2,1]
[6,5,3,7,4,2,1]=>[5,2]
[6,5,4,1,2,3,7]=>[4,1,1,1]
[6,5,4,1,2,7,3]=>[4,2,1]
[6,5,4,1,3,2,7]=>[5,1,1]
[6,5,4,1,3,7,2]=>[5,1,1]
[6,5,4,1,7,2,3]=>[4,2,1]
[6,5,4,1,7,3,2]=>[5,2]
[6,5,4,2,1,3,7]=>[5,1,1]
[6,5,4,2,1,7,3]=>[5,2]
[6,5,4,2,3,1,7]=>[5,1,1]
[6,5,4,2,3,7,1]=>[5,1,1]
[6,5,4,2,7,1,3]=>[5,1,1]
[6,5,4,2,7,3,1]=>[5,2]
[6,5,4,3,1,2,7]=>[5,1,1]
[6,5,4,3,1,7,2]=>[5,2]
[6,5,4,3,2,1,7]=>[6,1]
[6,5,4,3,2,7,1]=>[6,1]
[6,5,4,3,7,1,2]=>[5,1,1]
[6,5,4,3,7,2,1]=>[6,1]
[6,5,4,7,1,2,3]=>[4,1,1,1]
[6,5,4,7,1,3,2]=>[5,1,1]
[6,5,4,7,2,1,3]=>[5,1,1]
[6,5,4,7,2,3,1]=>[5,1,1]
[6,5,4,7,3,1,2]=>[5,1,1]
[6,5,4,7,3,2,1]=>[6,1]
[6,5,7,1,2,3,4]=>[3,1,1,1,1]
[6,5,7,1,2,4,3]=>[4,1,1,1]
[6,5,7,1,3,2,4]=>[4,1,1,1]
[6,5,7,1,3,4,2]=>[4,1,1,1]
[6,5,7,1,4,2,3]=>[4,1,1,1]
[6,5,7,1,4,3,2]=>[5,1,1]
[6,5,7,2,1,3,4]=>[4,1,1,1]
[6,5,7,2,1,4,3]=>[4,2,1]
[6,5,7,2,3,1,4]=>[4,1,1,1]
[6,5,7,2,3,4,1]=>[4,1,1,1]
[6,5,7,2,4,1,3]=>[4,1,1,1]
[6,5,7,2,4,3,1]=>[5,1,1]
[6,5,7,3,1,2,4]=>[4,1,1,1]
[6,5,7,3,1,4,2]=>[4,2,1]
[6,5,7,3,2,1,4]=>[5,1,1]
[6,5,7,3,2,4,1]=>[5,1,1]
[6,5,7,3,4,1,2]=>[4,1,1,1]
[6,5,7,3,4,2,1]=>[5,1,1]
[6,5,7,4,1,2,3]=>[4,1,1,1]
[6,5,7,4,1,3,2]=>[5,1,1]
[6,5,7,4,2,1,3]=>[5,1,1]
[6,5,7,4,2,3,1]=>[5,1,1]
[6,5,7,4,3,1,2]=>[5,1,1]
[6,5,7,4,3,2,1]=>[6,1]
[6,7,1,2,3,4,5]=>[2,1,1,1,1,1]
[6,7,1,2,3,5,4]=>[3,1,1,1,1]
[6,7,1,2,4,3,5]=>[3,1,1,1,1]
[6,7,1,2,4,5,3]=>[3,1,1,1,1]
[6,7,1,2,5,3,4]=>[3,1,1,1,1]
[6,7,1,2,5,4,3]=>[4,1,1,1]
[6,7,1,3,2,4,5]=>[3,1,1,1,1]
[6,7,1,3,2,5,4]=>[3,2,1,1]
[6,7,1,3,4,2,5]=>[3,1,1,1,1]
[6,7,1,3,4,5,2]=>[3,1,1,1,1]
[6,7,1,3,5,2,4]=>[3,1,1,1,1]
[6,7,1,3,5,4,2]=>[4,1,1,1]
[6,7,1,4,2,3,5]=>[3,1,1,1,1]
[6,7,1,4,2,5,3]=>[3,2,1,1]
[6,7,1,4,3,2,5]=>[4,1,1,1]
[6,7,1,4,3,5,2]=>[4,1,1,1]
[6,7,1,4,5,2,3]=>[3,1,1,1,1]
[6,7,1,4,5,3,2]=>[4,1,1,1]
[6,7,1,5,2,3,4]=>[3,1,1,1,1]
[6,7,1,5,2,4,3]=>[4,1,1,1]
[6,7,1,5,3,2,4]=>[4,1,1,1]
[6,7,1,5,3,4,2]=>[4,1,1,1]
[6,7,1,5,4,2,3]=>[4,1,1,1]
[6,7,1,5,4,3,2]=>[5,1,1]
[6,7,2,1,3,4,5]=>[3,1,1,1,1]
[6,7,2,1,3,5,4]=>[3,2,1,1]
[6,7,2,1,4,3,5]=>[3,2,1,1]
[6,7,2,1,4,5,3]=>[3,2,1,1]
[6,7,2,1,5,3,4]=>[3,2,1,1]
[6,7,2,1,5,4,3]=>[4,2,1]
[6,7,2,3,1,4,5]=>[3,1,1,1,1]
[6,7,2,3,1,5,4]=>[3,2,1,1]
[6,7,2,3,4,1,5]=>[3,1,1,1,1]
[6,7,2,3,4,5,1]=>[3,1,1,1,1]
[6,7,2,3,5,1,4]=>[3,1,1,1,1]
[6,7,2,3,5,4,1]=>[4,1,1,1]
[6,7,2,4,1,3,5]=>[3,1,1,1,1]
[6,7,2,4,1,5,3]=>[3,2,1,1]
[6,7,2,4,3,1,5]=>[4,1,1,1]
[6,7,2,4,3,5,1]=>[4,1,1,1]
[6,7,2,4,5,1,3]=>[3,1,1,1,1]
[6,7,2,4,5,3,1]=>[4,1,1,1]
[6,7,2,5,1,3,4]=>[3,1,1,1,1]
[6,7,2,5,1,4,3]=>[4,1,1,1]
[6,7,2,5,3,1,4]=>[4,1,1,1]
[6,7,2,5,3,4,1]=>[4,1,1,1]
[6,7,2,5,4,1,3]=>[4,1,1,1]
[6,7,2,5,4,3,1]=>[5,1,1]
[6,7,3,1,2,4,5]=>[3,1,1,1,1]
[6,7,3,1,2,5,4]=>[3,2,1,1]
[6,7,3,1,4,2,5]=>[3,2,1,1]
[6,7,3,1,4,5,2]=>[3,2,1,1]
[6,7,3,1,5,2,4]=>[3,2,1,1]
[6,7,3,1,5,4,2]=>[4,2,1]
[6,7,3,2,1,4,5]=>[4,1,1,1]
[6,7,3,2,1,5,4]=>[4,2,1]
[6,7,3,2,4,1,5]=>[4,1,1,1]
[6,7,3,2,4,5,1]=>[4,1,1,1]
[6,7,3,2,5,1,4]=>[4,1,1,1]
[6,7,3,2,5,4,1]=>[4,2,1]
[6,7,3,4,1,2,5]=>[3,1,1,1,1]
[6,7,3,4,1,5,2]=>[3,2,1,1]
[6,7,3,4,2,1,5]=>[4,1,1,1]
[6,7,3,4,2,5,1]=>[4,1,1,1]
[6,7,3,4,5,1,2]=>[3,1,1,1,1]
[6,7,3,4,5,2,1]=>[4,1,1,1]
[6,7,3,5,1,2,4]=>[3,1,1,1,1]
[6,7,3,5,1,4,2]=>[4,1,1,1]
[6,7,3,5,2,1,4]=>[4,1,1,1]
[6,7,3,5,2,4,1]=>[4,1,1,1]
[6,7,3,5,4,1,2]=>[4,1,1,1]
[6,7,3,5,4,2,1]=>[5,1,1]
[6,7,4,1,2,3,5]=>[3,1,1,1,1]
[6,7,4,1,2,5,3]=>[3,2,1,1]
[6,7,4,1,3,2,5]=>[4,1,1,1]
[6,7,4,1,3,5,2]=>[4,1,1,1]
[6,7,4,1,5,2,3]=>[3,2,1,1]
[6,7,4,1,5,3,2]=>[4,2,1]
[6,7,4,2,1,3,5]=>[4,1,1,1]
[6,7,4,2,1,5,3]=>[4,2,1]
[6,7,4,2,3,1,5]=>[4,1,1,1]
[6,7,4,2,3,5,1]=>[4,1,1,1]
[6,7,4,2,5,1,3]=>[4,1,1,1]
[6,7,4,2,5,3,1]=>[4,2,1]
[6,7,4,3,1,2,5]=>[4,1,1,1]
[6,7,4,3,1,5,2]=>[4,2,1]
[6,7,4,3,2,1,5]=>[5,1,1]
[6,7,4,3,2,5,1]=>[5,1,1]
[6,7,4,3,5,1,2]=>[4,1,1,1]
[6,7,4,3,5,2,1]=>[5,1,1]
[6,7,4,5,1,2,3]=>[3,1,1,1,1]
[6,7,4,5,1,3,2]=>[4,1,1,1]
[6,7,4,5,2,1,3]=>[4,1,1,1]
[6,7,4,5,2,3,1]=>[4,1,1,1]
[6,7,4,5,3,1,2]=>[4,1,1,1]
[6,7,4,5,3,2,1]=>[5,1,1]
[6,7,5,1,2,3,4]=>[3,1,1,1,1]
[6,7,5,1,2,4,3]=>[4,1,1,1]
[6,7,5,1,3,2,4]=>[4,1,1,1]
[6,7,5,1,3,4,2]=>[4,1,1,1]
[6,7,5,1,4,2,3]=>[4,1,1,1]
[6,7,5,1,4,3,2]=>[5,1,1]
[6,7,5,2,1,3,4]=>[4,1,1,1]
[6,7,5,2,1,4,3]=>[4,2,1]
[6,7,5,2,3,1,4]=>[4,1,1,1]
[6,7,5,2,3,4,1]=>[4,1,1,1]
[6,7,5,2,4,1,3]=>[4,1,1,1]
[6,7,5,2,4,3,1]=>[5,1,1]
[6,7,5,3,1,2,4]=>[4,1,1,1]
[6,7,5,3,1,4,2]=>[4,2,1]
[6,7,5,3,2,1,4]=>[5,1,1]
[6,7,5,3,2,4,1]=>[5,1,1]
[6,7,5,3,4,1,2]=>[4,1,1,1]
[6,7,5,3,4,2,1]=>[5,1,1]
[6,7,5,4,1,2,3]=>[4,1,1,1]
[6,7,5,4,1,3,2]=>[5,1,1]
[6,7,5,4,2,1,3]=>[5,1,1]
[6,7,5,4,2,3,1]=>[5,1,1]
[6,7,5,4,3,1,2]=>[5,1,1]
[6,7,5,4,3,2,1]=>[6,1]
[7,1,2,3,4,5,6]=>[2,1,1,1,1,1]
[7,1,2,3,4,6,5]=>[3,1,1,1,1]
[7,1,2,3,5,4,6]=>[3,1,1,1,1]
[7,1,2,3,5,6,4]=>[3,1,1,1,1]
[7,1,2,3,6,4,5]=>[3,1,1,1,1]
[7,1,2,3,6,5,4]=>[4,1,1,1]
[7,1,2,4,3,5,6]=>[3,1,1,1,1]
[7,1,2,4,3,6,5]=>[3,2,1,1]
[7,1,2,4,5,3,6]=>[3,1,1,1,1]
[7,1,2,4,5,6,3]=>[3,1,1,1,1]
[7,1,2,4,6,3,5]=>[3,1,1,1,1]
[7,1,2,4,6,5,3]=>[4,1,1,1]
[7,1,2,5,3,4,6]=>[3,1,1,1,1]
[7,1,2,5,3,6,4]=>[3,2,1,1]
[7,1,2,5,4,3,6]=>[4,1,1,1]
[7,1,2,5,4,6,3]=>[4,1,1,1]
[7,1,2,5,6,3,4]=>[3,1,1,1,1]
[7,1,2,5,6,4,3]=>[4,1,1,1]
[7,1,2,6,3,4,5]=>[3,1,1,1,1]
[7,1,2,6,3,5,4]=>[4,1,1,1]
[7,1,2,6,4,3,5]=>[4,1,1,1]
[7,1,2,6,4,5,3]=>[4,1,1,1]
[7,1,2,6,5,3,4]=>[4,1,1,1]
[7,1,2,6,5,4,3]=>[5,1,1]
[7,1,3,2,4,5,6]=>[3,1,1,1,1]
[7,1,3,2,4,6,5]=>[3,2,1,1]
[7,1,3,2,5,4,6]=>[3,2,1,1]
[7,1,3,2,5,6,4]=>[3,2,1,1]
[7,1,3,2,6,4,5]=>[3,2,1,1]
[7,1,3,2,6,5,4]=>[4,2,1]
[7,1,3,4,2,5,6]=>[3,1,1,1,1]
[7,1,3,4,2,6,5]=>[3,2,1,1]
[7,1,3,4,5,2,6]=>[3,1,1,1,1]
[7,1,3,4,5,6,2]=>[3,1,1,1,1]
[7,1,3,4,6,2,5]=>[3,1,1,1,1]
[7,1,3,4,6,5,2]=>[4,1,1,1]
[7,1,3,5,2,4,6]=>[3,1,1,1,1]
[7,1,3,5,2,6,4]=>[3,2,1,1]
[7,1,3,5,4,2,6]=>[4,1,1,1]
[7,1,3,5,4,6,2]=>[4,1,1,1]
[7,1,3,5,6,2,4]=>[3,1,1,1,1]
[7,1,3,5,6,4,2]=>[4,1,1,1]
[7,1,3,6,2,4,5]=>[3,1,1,1,1]
[7,1,3,6,2,5,4]=>[4,1,1,1]
[7,1,3,6,4,2,5]=>[4,1,1,1]
[7,1,3,6,4,5,2]=>[4,1,1,1]
[7,1,3,6,5,2,4]=>[4,1,1,1]
[7,1,3,6,5,4,2]=>[5,1,1]
[7,1,4,2,3,5,6]=>[3,1,1,1,1]
[7,1,4,2,3,6,5]=>[3,2,1,1]
[7,1,4,2,5,3,6]=>[3,2,1,1]
[7,1,4,2,5,6,3]=>[3,2,1,1]
[7,1,4,2,6,3,5]=>[3,2,1,1]
[7,1,4,2,6,5,3]=>[4,2,1]
[7,1,4,3,2,5,6]=>[4,1,1,1]
[7,1,4,3,2,6,5]=>[4,2,1]
[7,1,4,3,5,2,6]=>[4,1,1,1]
[7,1,4,3,5,6,2]=>[4,1,1,1]
[7,1,4,3,6,2,5]=>[4,1,1,1]
[7,1,4,3,6,5,2]=>[4,2,1]
[7,1,4,5,2,3,6]=>[3,1,1,1,1]
[7,1,4,5,2,6,3]=>[3,2,1,1]
[7,1,4,5,3,2,6]=>[4,1,1,1]
[7,1,4,5,3,6,2]=>[4,1,1,1]
[7,1,4,5,6,2,3]=>[3,1,1,1,1]
[7,1,4,5,6,3,2]=>[4,1,1,1]
[7,1,4,6,2,3,5]=>[3,1,1,1,1]
[7,1,4,6,2,5,3]=>[4,1,1,1]
[7,1,4,6,3,2,5]=>[4,1,1,1]
[7,1,4,6,3,5,2]=>[4,1,1,1]
[7,1,4,6,5,2,3]=>[4,1,1,1]
[7,1,4,6,5,3,2]=>[5,1,1]
[7,1,5,2,3,4,6]=>[3,1,1,1,1]
[7,1,5,2,3,6,4]=>[3,2,1,1]
[7,1,5,2,4,3,6]=>[4,1,1,1]
[7,1,5,2,4,6,3]=>[4,1,1,1]
[7,1,5,2,6,3,4]=>[3,2,1,1]
[7,1,5,2,6,4,3]=>[4,2,1]
[7,1,5,3,2,4,6]=>[4,1,1,1]
[7,1,5,3,2,6,4]=>[4,2,1]
[7,1,5,3,4,2,6]=>[4,1,1,1]
[7,1,5,3,4,6,2]=>[4,1,1,1]
[7,1,5,3,6,2,4]=>[4,1,1,1]
[7,1,5,3,6,4,2]=>[4,2,1]
[7,1,5,4,2,3,6]=>[4,1,1,1]
[7,1,5,4,2,6,3]=>[4,2,1]
[7,1,5,4,3,2,6]=>[5,1,1]
[7,1,5,4,3,6,2]=>[5,1,1]
[7,1,5,4,6,2,3]=>[4,1,1,1]
[7,1,5,4,6,3,2]=>[5,1,1]
[7,1,5,6,2,3,4]=>[3,1,1,1,1]
[7,1,5,6,2,4,3]=>[4,1,1,1]
[7,1,5,6,3,2,4]=>[4,1,1,1]
[7,1,5,6,3,4,2]=>[4,1,1,1]
[7,1,5,6,4,2,3]=>[4,1,1,1]
[7,1,5,6,4,3,2]=>[5,1,1]
[7,1,6,2,3,4,5]=>[3,1,1,1,1]
[7,1,6,2,3,5,4]=>[4,1,1,1]
[7,1,6,2,4,3,5]=>[4,1,1,1]
[7,1,6,2,4,5,3]=>[4,1,1,1]
[7,1,6,2,5,3,4]=>[4,1,1,1]
[7,1,6,2,5,4,3]=>[5,1,1]
[7,1,6,3,2,4,5]=>[4,1,1,1]
[7,1,6,3,2,5,4]=>[4,2,1]
[7,1,6,3,4,2,5]=>[4,1,1,1]
[7,1,6,3,4,5,2]=>[4,1,1,1]
[7,1,6,3,5,2,4]=>[4,1,1,1]
[7,1,6,3,5,4,2]=>[5,1,1]
[7,1,6,4,2,3,5]=>[4,1,1,1]
[7,1,6,4,2,5,3]=>[4,2,1]
[7,1,6,4,3,2,5]=>[5,1,1]
[7,1,6,4,3,5,2]=>[5,1,1]
[7,1,6,4,5,2,3]=>[4,1,1,1]
[7,1,6,4,5,3,2]=>[5,1,1]
[7,1,6,5,2,3,4]=>[4,1,1,1]
[7,1,6,5,2,4,3]=>[5,1,1]
[7,1,6,5,3,2,4]=>[5,1,1]
[7,1,6,5,3,4,2]=>[5,1,1]
[7,1,6,5,4,2,3]=>[5,1,1]
[7,1,6,5,4,3,2]=>[6,1]
[7,2,1,3,4,5,6]=>[3,1,1,1,1]
[7,2,1,3,4,6,5]=>[3,2,1,1]
[7,2,1,3,5,4,6]=>[3,2,1,1]
[7,2,1,3,5,6,4]=>[3,2,1,1]
[7,2,1,3,6,4,5]=>[3,2,1,1]
[7,2,1,3,6,5,4]=>[4,2,1]
[7,2,1,4,3,5,6]=>[3,2,1,1]
[7,2,1,4,3,6,5]=>[3,2,2]
[7,2,1,4,5,3,6]=>[3,2,1,1]
[7,2,1,4,5,6,3]=>[3,2,1,1]
[7,2,1,4,6,3,5]=>[3,2,1,1]
[7,2,1,4,6,5,3]=>[4,2,1]
[7,2,1,5,3,4,6]=>[3,2,1,1]
[7,2,1,5,3,6,4]=>[3,2,2]
[7,2,1,5,4,3,6]=>[4,2,1]
[7,2,1,5,4,6,3]=>[4,2,1]
[7,2,1,5,6,3,4]=>[3,2,1,1]
[7,2,1,5,6,4,3]=>[4,2,1]
[7,2,1,6,3,4,5]=>[3,2,1,1]
[7,2,1,6,3,5,4]=>[4,2,1]
[7,2,1,6,4,3,5]=>[4,2,1]
[7,2,1,6,4,5,3]=>[4,2,1]
[7,2,1,6,5,3,4]=>[4,2,1]
[7,2,1,6,5,4,3]=>[5,2]
[7,2,3,1,4,5,6]=>[3,1,1,1,1]
[7,2,3,1,4,6,5]=>[3,2,1,1]
[7,2,3,1,5,4,6]=>[3,2,1,1]
[7,2,3,1,5,6,4]=>[3,2,1,1]
[7,2,3,1,6,4,5]=>[3,2,1,1]
[7,2,3,1,6,5,4]=>[4,2,1]
[7,2,3,4,1,5,6]=>[3,1,1,1,1]
[7,2,3,4,1,6,5]=>[3,2,1,1]
[7,2,3,4,5,1,6]=>[3,1,1,1,1]
[7,2,3,4,5,6,1]=>[3,1,1,1,1]
[7,2,3,4,6,1,5]=>[3,1,1,1,1]
[7,2,3,4,6,5,1]=>[4,1,1,1]
[7,2,3,5,1,4,6]=>[3,1,1,1,1]
[7,2,3,5,1,6,4]=>[3,2,1,1]
[7,2,3,5,4,1,6]=>[4,1,1,1]
[7,2,3,5,4,6,1]=>[4,1,1,1]
[7,2,3,5,6,1,4]=>[3,1,1,1,1]
[7,2,3,5,6,4,1]=>[4,1,1,1]
[7,2,3,6,1,4,5]=>[3,1,1,1,1]
[7,2,3,6,1,5,4]=>[4,1,1,1]
[7,2,3,6,4,1,5]=>[4,1,1,1]
[7,2,3,6,4,5,1]=>[4,1,1,1]
[7,2,3,6,5,1,4]=>[4,1,1,1]
[7,2,3,6,5,4,1]=>[5,1,1]
[7,2,4,1,3,5,6]=>[3,1,1,1,1]
[7,2,4,1,3,6,5]=>[3,2,1,1]
[7,2,4,1,5,3,6]=>[3,2,1,1]
[7,2,4,1,5,6,3]=>[3,2,1,1]
[7,2,4,1,6,3,5]=>[3,2,1,1]
[7,2,4,1,6,5,3]=>[4,2,1]
[7,2,4,3,1,5,6]=>[4,1,1,1]
[7,2,4,3,1,6,5]=>[4,2,1]
[7,2,4,3,5,1,6]=>[4,1,1,1]
[7,2,4,3,5,6,1]=>[4,1,1,1]
[7,2,4,3,6,1,5]=>[4,1,1,1]
[7,2,4,3,6,5,1]=>[4,2,1]
[7,2,4,5,1,3,6]=>[3,1,1,1,1]
[7,2,4,5,1,6,3]=>[3,2,1,1]
[7,2,4,5,3,1,6]=>[4,1,1,1]
[7,2,4,5,3,6,1]=>[4,1,1,1]
[7,2,4,5,6,1,3]=>[3,1,1,1,1]
[7,2,4,5,6,3,1]=>[4,1,1,1]
[7,2,4,6,1,3,5]=>[3,1,1,1,1]
[7,2,4,6,1,5,3]=>[4,1,1,1]
[7,2,4,6,3,1,5]=>[4,1,1,1]
[7,2,4,6,3,5,1]=>[4,1,1,1]
[7,2,4,6,5,1,3]=>[4,1,1,1]
[7,2,4,6,5,3,1]=>[5,1,1]
[7,2,5,1,3,4,6]=>[3,1,1,1,1]
[7,2,5,1,3,6,4]=>[3,2,1,1]
[7,2,5,1,4,3,6]=>[4,1,1,1]
[7,2,5,1,4,6,3]=>[4,1,1,1]
[7,2,5,1,6,3,4]=>[3,2,1,1]
[7,2,5,1,6,4,3]=>[4,2,1]
[7,2,5,3,1,4,6]=>[4,1,1,1]
[7,2,5,3,1,6,4]=>[4,2,1]
[7,2,5,3,4,1,6]=>[4,1,1,1]
[7,2,5,3,4,6,1]=>[4,1,1,1]
[7,2,5,3,6,1,4]=>[4,1,1,1]
[7,2,5,3,6,4,1]=>[4,2,1]
[7,2,5,4,1,3,6]=>[4,1,1,1]
[7,2,5,4,1,6,3]=>[4,2,1]
[7,2,5,4,3,1,6]=>[5,1,1]
[7,2,5,4,3,6,1]=>[5,1,1]
[7,2,5,4,6,1,3]=>[4,1,1,1]
[7,2,5,4,6,3,1]=>[5,1,1]
[7,2,5,6,1,3,4]=>[3,1,1,1,1]
[7,2,5,6,1,4,3]=>[4,1,1,1]
[7,2,5,6,3,1,4]=>[4,1,1,1]
[7,2,5,6,3,4,1]=>[4,1,1,1]
[7,2,5,6,4,1,3]=>[4,1,1,1]
[7,2,5,6,4,3,1]=>[5,1,1]
[7,2,6,1,3,4,5]=>[3,1,1,1,1]
[7,2,6,1,3,5,4]=>[4,1,1,1]
[7,2,6,1,4,3,5]=>[4,1,1,1]
[7,2,6,1,4,5,3]=>[4,1,1,1]
[7,2,6,1,5,3,4]=>[4,1,1,1]
[7,2,6,1,5,4,3]=>[5,1,1]
[7,2,6,3,1,4,5]=>[4,1,1,1]
[7,2,6,3,1,5,4]=>[4,2,1]
[7,2,6,3,4,1,5]=>[4,1,1,1]
[7,2,6,3,4,5,1]=>[4,1,1,1]
[7,2,6,3,5,1,4]=>[4,1,1,1]
[7,2,6,3,5,4,1]=>[5,1,1]
[7,2,6,4,1,3,5]=>[4,1,1,1]
[7,2,6,4,1,5,3]=>[4,2,1]
[7,2,6,4,3,1,5]=>[5,1,1]
[7,2,6,4,3,5,1]=>[5,1,1]
[7,2,6,4,5,1,3]=>[4,1,1,1]
[7,2,6,4,5,3,1]=>[5,1,1]
[7,2,6,5,1,3,4]=>[4,1,1,1]
[7,2,6,5,1,4,3]=>[5,1,1]
[7,2,6,5,3,1,4]=>[5,1,1]
[7,2,6,5,3,4,1]=>[5,1,1]
[7,2,6,5,4,1,3]=>[5,1,1]
[7,2,6,5,4,3,1]=>[6,1]
[7,3,1,2,4,5,6]=>[3,1,1,1,1]
[7,3,1,2,4,6,5]=>[3,2,1,1]
[7,3,1,2,5,4,6]=>[3,2,1,1]
[7,3,1,2,5,6,4]=>[3,2,1,1]
[7,3,1,2,6,4,5]=>[3,2,1,1]
[7,3,1,2,6,5,4]=>[4,2,1]
[7,3,1,4,2,5,6]=>[3,2,1,1]
[7,3,1,4,2,6,5]=>[3,2,2]
[7,3,1,4,5,2,6]=>[3,2,1,1]
[7,3,1,4,5,6,2]=>[3,2,1,1]
[7,3,1,4,6,2,5]=>[3,2,1,1]
[7,3,1,4,6,5,2]=>[4,2,1]
[7,3,1,5,2,4,6]=>[3,2,1,1]
[7,3,1,5,2,6,4]=>[3,2,2]
[7,3,1,5,4,2,6]=>[4,2,1]
[7,3,1,5,4,6,2]=>[4,2,1]
[7,3,1,5,6,2,4]=>[3,2,1,1]
[7,3,1,5,6,4,2]=>[4,2,1]
[7,3,1,6,2,4,5]=>[3,2,1,1]
[7,3,1,6,2,5,4]=>[4,2,1]
[7,3,1,6,4,2,5]=>[4,2,1]
[7,3,1,6,4,5,2]=>[4,2,1]
[7,3,1,6,5,2,4]=>[4,2,1]
[7,3,1,6,5,4,2]=>[5,2]
[7,3,2,1,4,5,6]=>[4,1,1,1]
[7,3,2,1,4,6,5]=>[4,2,1]
[7,3,2,1,5,4,6]=>[4,2,1]
[7,3,2,1,5,6,4]=>[4,2,1]
[7,3,2,1,6,4,5]=>[4,2,1]
[7,3,2,1,6,5,4]=>[4,3]
[7,3,2,4,1,5,6]=>[4,1,1,1]
[7,3,2,4,1,6,5]=>[4,2,1]
[7,3,2,4,5,1,6]=>[4,1,1,1]
[7,3,2,4,5,6,1]=>[4,1,1,1]
[7,3,2,4,6,1,5]=>[4,1,1,1]
[7,3,2,4,6,5,1]=>[4,2,1]
[7,3,2,5,1,4,6]=>[4,1,1,1]
[7,3,2,5,1,6,4]=>[4,2,1]
[7,3,2,5,4,1,6]=>[4,2,1]
[7,3,2,5,4,6,1]=>[4,2,1]
[7,3,2,5,6,1,4]=>[4,1,1,1]
[7,3,2,5,6,4,1]=>[4,2,1]
[7,3,2,6,1,4,5]=>[4,1,1,1]
[7,3,2,6,1,5,4]=>[4,2,1]
[7,3,2,6,4,1,5]=>[4,2,1]
[7,3,2,6,4,5,1]=>[4,2,1]
[7,3,2,6,5,1,4]=>[4,2,1]
[7,3,2,6,5,4,1]=>[5,2]
[7,3,4,1,2,5,6]=>[3,1,1,1,1]
[7,3,4,1,2,6,5]=>[3,2,1,1]
[7,3,4,1,5,2,6]=>[3,2,1,1]
[7,3,4,1,5,6,2]=>[3,2,1,1]
[7,3,4,1,6,2,5]=>[3,2,1,1]
[7,3,4,1,6,5,2]=>[4,2,1]
[7,3,4,2,1,5,6]=>[4,1,1,1]
[7,3,4,2,1,6,5]=>[4,2,1]
[7,3,4,2,5,1,6]=>[4,1,1,1]
[7,3,4,2,5,6,1]=>[4,1,1,1]
[7,3,4,2,6,1,5]=>[4,1,1,1]
[7,3,4,2,6,5,1]=>[4,2,1]
[7,3,4,5,1,2,6]=>[3,1,1,1,1]
[7,3,4,5,1,6,2]=>[3,2,1,1]
[7,3,4,5,2,1,6]=>[4,1,1,1]
[7,3,4,5,2,6,1]=>[4,1,1,1]
[7,3,4,5,6,1,2]=>[3,1,1,1,1]
[7,3,4,5,6,2,1]=>[4,1,1,1]
[7,3,4,6,1,2,5]=>[3,1,1,1,1]
[7,3,4,6,1,5,2]=>[4,1,1,1]
[7,3,4,6,2,1,5]=>[4,1,1,1]
[7,3,4,6,2,5,1]=>[4,1,1,1]
[7,3,4,6,5,1,2]=>[4,1,1,1]
[7,3,4,6,5,2,1]=>[5,1,1]
[7,3,5,1,2,4,6]=>[3,1,1,1,1]
[7,3,5,1,2,6,4]=>[3,2,1,1]
[7,3,5,1,4,2,6]=>[4,1,1,1]
[7,3,5,1,4,6,2]=>[4,1,1,1]
[7,3,5,1,6,2,4]=>[3,2,1,1]
[7,3,5,1,6,4,2]=>[4,2,1]
[7,3,5,2,1,4,6]=>[4,1,1,1]
[7,3,5,2,1,6,4]=>[4,2,1]
[7,3,5,2,4,1,6]=>[4,1,1,1]
[7,3,5,2,4,6,1]=>[4,1,1,1]
[7,3,5,2,6,1,4]=>[4,1,1,1]
[7,3,5,2,6,4,1]=>[4,2,1]
[7,3,5,4,1,2,6]=>[4,1,1,1]
[7,3,5,4,1,6,2]=>[4,2,1]
[7,3,5,4,2,1,6]=>[5,1,1]
[7,3,5,4,2,6,1]=>[5,1,1]
[7,3,5,4,6,1,2]=>[4,1,1,1]
[7,3,5,4,6,2,1]=>[5,1,1]
[7,3,5,6,1,2,4]=>[3,1,1,1,1]
[7,3,5,6,1,4,2]=>[4,1,1,1]
[7,3,5,6,2,1,4]=>[4,1,1,1]
[7,3,5,6,2,4,1]=>[4,1,1,1]
[7,3,5,6,4,1,2]=>[4,1,1,1]
[7,3,5,6,4,2,1]=>[5,1,1]
[7,3,6,1,2,4,5]=>[3,1,1,1,1]
[7,3,6,1,2,5,4]=>[4,1,1,1]
[7,3,6,1,4,2,5]=>[4,1,1,1]
[7,3,6,1,4,5,2]=>[4,1,1,1]
[7,3,6,1,5,2,4]=>[4,1,1,1]
[7,3,6,1,5,4,2]=>[5,1,1]
[7,3,6,2,1,4,5]=>[4,1,1,1]
[7,3,6,2,1,5,4]=>[4,2,1]
[7,3,6,2,4,1,5]=>[4,1,1,1]
[7,3,6,2,4,5,1]=>[4,1,1,1]
[7,3,6,2,5,1,4]=>[4,1,1,1]
[7,3,6,2,5,4,1]=>[5,1,1]
[7,3,6,4,1,2,5]=>[4,1,1,1]
[7,3,6,4,1,5,2]=>[4,2,1]
[7,3,6,4,2,1,5]=>[5,1,1]
[7,3,6,4,2,5,1]=>[5,1,1]
[7,3,6,4,5,1,2]=>[4,1,1,1]
[7,3,6,4,5,2,1]=>[5,1,1]
[7,3,6,5,1,2,4]=>[4,1,1,1]
[7,3,6,5,1,4,2]=>[5,1,1]
[7,3,6,5,2,1,4]=>[5,1,1]
[7,3,6,5,2,4,1]=>[5,1,1]
[7,3,6,5,4,1,2]=>[5,1,1]
[7,3,6,5,4,2,1]=>[6,1]
[7,4,1,2,3,5,6]=>[3,1,1,1,1]
[7,4,1,2,3,6,5]=>[3,2,1,1]
[7,4,1,2,5,3,6]=>[3,2,1,1]
[7,4,1,2,5,6,3]=>[3,2,1,1]
[7,4,1,2,6,3,5]=>[3,2,1,1]
[7,4,1,2,6,5,3]=>[4,2,1]
[7,4,1,3,2,5,6]=>[4,1,1,1]
[7,4,1,3,2,6,5]=>[4,2,1]
[7,4,1,3,5,2,6]=>[4,1,1,1]
[7,4,1,3,5,6,2]=>[4,1,1,1]
[7,4,1,3,6,2,5]=>[4,1,1,1]
[7,4,1,3,6,5,2]=>[4,2,1]
[7,4,1,5,2,3,6]=>[3,2,1,1]
[7,4,1,5,2,6,3]=>[3,2,2]
[7,4,1,5,3,2,6]=>[4,2,1]
[7,4,1,5,3,6,2]=>[4,2,1]
[7,4,1,5,6,2,3]=>[3,2,1,1]
[7,4,1,5,6,3,2]=>[4,2,1]
[7,4,1,6,2,3,5]=>[3,2,1,1]
[7,4,1,6,2,5,3]=>[4,2,1]
[7,4,1,6,3,2,5]=>[4,2,1]
[7,4,1,6,3,5,2]=>[4,2,1]
[7,4,1,6,5,2,3]=>[4,2,1]
[7,4,1,6,5,3,2]=>[5,2]
[7,4,2,1,3,5,6]=>[4,1,1,1]
[7,4,2,1,3,6,5]=>[4,2,1]
[7,4,2,1,5,3,6]=>[4,2,1]
[7,4,2,1,5,6,3]=>[4,2,1]
[7,4,2,1,6,3,5]=>[4,2,1]
[7,4,2,1,6,5,3]=>[4,3]
[7,4,2,3,1,5,6]=>[4,1,1,1]
[7,4,2,3,1,6,5]=>[4,2,1]
[7,4,2,3,5,1,6]=>[4,1,1,1]
[7,4,2,3,5,6,1]=>[4,1,1,1]
[7,4,2,3,6,1,5]=>[4,1,1,1]
[7,4,2,3,6,5,1]=>[4,2,1]
[7,4,2,5,1,3,6]=>[4,1,1,1]
[7,4,2,5,1,6,3]=>[4,2,1]
[7,4,2,5,3,1,6]=>[4,2,1]
[7,4,2,5,3,6,1]=>[4,2,1]
[7,4,2,5,6,1,3]=>[4,1,1,1]
[7,4,2,5,6,3,1]=>[4,2,1]
[7,4,2,6,1,3,5]=>[4,1,1,1]
[7,4,2,6,1,5,3]=>[4,2,1]
[7,4,2,6,3,1,5]=>[4,2,1]
[7,4,2,6,3,5,1]=>[4,2,1]
[7,4,2,6,5,1,3]=>[4,2,1]
[7,4,2,6,5,3,1]=>[5,2]
[7,4,3,1,2,5,6]=>[4,1,1,1]
[7,4,3,1,2,6,5]=>[4,2,1]
[7,4,3,1,5,2,6]=>[4,2,1]
[7,4,3,1,5,6,2]=>[4,2,1]
[7,4,3,1,6,2,5]=>[4,2,1]
[7,4,3,1,6,5,2]=>[4,3]
[7,4,3,2,1,5,6]=>[5,1,1]
[7,4,3,2,1,6,5]=>[5,2]
[7,4,3,2,5,1,6]=>[5,1,1]
[7,4,3,2,5,6,1]=>[5,1,1]
[7,4,3,2,6,1,5]=>[5,1,1]
[7,4,3,2,6,5,1]=>[5,2]
[7,4,3,5,1,2,6]=>[4,1,1,1]
[7,4,3,5,1,6,2]=>[4,2,1]
[7,4,3,5,2,1,6]=>[5,1,1]
[7,4,3,5,2,6,1]=>[5,1,1]
[7,4,3,5,6,1,2]=>[4,1,1,1]
[7,4,3,5,6,2,1]=>[5,1,1]
[7,4,3,6,1,2,5]=>[4,1,1,1]
[7,4,3,6,1,5,2]=>[4,2,1]
[7,4,3,6,2,1,5]=>[5,1,1]
[7,4,3,6,2,5,1]=>[5,1,1]
[7,4,3,6,5,1,2]=>[4,2,1]
[7,4,3,6,5,2,1]=>[5,2]
[7,4,5,1,2,3,6]=>[3,1,1,1,1]
[7,4,5,1,2,6,3]=>[3,2,1,1]
[7,4,5,1,3,2,6]=>[4,1,1,1]
[7,4,5,1,3,6,2]=>[4,1,1,1]
[7,4,5,1,6,2,3]=>[3,2,1,1]
[7,4,5,1,6,3,2]=>[4,2,1]
[7,4,5,2,1,3,6]=>[4,1,1,1]
[7,4,5,2,1,6,3]=>[4,2,1]
[7,4,5,2,3,1,6]=>[4,1,1,1]
[7,4,5,2,3,6,1]=>[4,1,1,1]
[7,4,5,2,6,1,3]=>[4,1,1,1]
[7,4,5,2,6,3,1]=>[4,2,1]
[7,4,5,3,1,2,6]=>[4,1,1,1]
[7,4,5,3,1,6,2]=>[4,2,1]
[7,4,5,3,2,1,6]=>[5,1,1]
[7,4,5,3,2,6,1]=>[5,1,1]
[7,4,5,3,6,1,2]=>[4,1,1,1]
[7,4,5,3,6,2,1]=>[5,1,1]
[7,4,5,6,1,2,3]=>[3,1,1,1,1]
[7,4,5,6,1,3,2]=>[4,1,1,1]
[7,4,5,6,2,1,3]=>[4,1,1,1]
[7,4,5,6,2,3,1]=>[4,1,1,1]
[7,4,5,6,3,1,2]=>[4,1,1,1]
[7,4,5,6,3,2,1]=>[5,1,1]
[7,4,6,1,2,3,5]=>[3,1,1,1,1]
[7,4,6,1,2,5,3]=>[4,1,1,1]
[7,4,6,1,3,2,5]=>[4,1,1,1]
[7,4,6,1,3,5,2]=>[4,1,1,1]
[7,4,6,1,5,2,3]=>[4,1,1,1]
[7,4,6,1,5,3,2]=>[5,1,1]
[7,4,6,2,1,3,5]=>[4,1,1,1]
[7,4,6,2,1,5,3]=>[4,2,1]
[7,4,6,2,3,1,5]=>[4,1,1,1]
[7,4,6,2,3,5,1]=>[4,1,1,1]
[7,4,6,2,5,1,3]=>[4,1,1,1]
[7,4,6,2,5,3,1]=>[5,1,1]
[7,4,6,3,1,2,5]=>[4,1,1,1]
[7,4,6,3,1,5,2]=>[4,2,1]
[7,4,6,3,2,1,5]=>[5,1,1]
[7,4,6,3,2,5,1]=>[5,1,1]
[7,4,6,3,5,1,2]=>[4,1,1,1]
[7,4,6,3,5,2,1]=>[5,1,1]
[7,4,6,5,1,2,3]=>[4,1,1,1]
[7,4,6,5,1,3,2]=>[5,1,1]
[7,4,6,5,2,1,3]=>[5,1,1]
[7,4,6,5,2,3,1]=>[5,1,1]
[7,4,6,5,3,1,2]=>[5,1,1]
[7,4,6,5,3,2,1]=>[6,1]
[7,5,1,2,3,4,6]=>[3,1,1,1,1]
[7,5,1,2,3,6,4]=>[3,2,1,1]
[7,5,1,2,4,3,6]=>[4,1,1,1]
[7,5,1,2,4,6,3]=>[4,1,1,1]
[7,5,1,2,6,3,4]=>[3,2,1,1]
[7,5,1,2,6,4,3]=>[4,2,1]
[7,5,1,3,2,4,6]=>[4,1,1,1]
[7,5,1,3,2,6,4]=>[4,2,1]
[7,5,1,3,4,2,6]=>[4,1,1,1]
[7,5,1,3,4,6,2]=>[4,1,1,1]
[7,5,1,3,6,2,4]=>[4,1,1,1]
[7,5,1,3,6,4,2]=>[4,2,1]
[7,5,1,4,2,3,6]=>[4,1,1,1]
[7,5,1,4,2,6,3]=>[4,2,1]
[7,5,1,4,3,2,6]=>[5,1,1]
[7,5,1,4,3,6,2]=>[5,1,1]
[7,5,1,4,6,2,3]=>[4,1,1,1]
[7,5,1,4,6,3,2]=>[5,1,1]
[7,5,1,6,2,3,4]=>[3,2,1,1]
[7,5,1,6,2,4,3]=>[4,2,1]
[7,5,1,6,3,2,4]=>[4,2,1]
[7,5,1,6,3,4,2]=>[4,2,1]
[7,5,1,6,4,2,3]=>[4,2,1]
[7,5,1,6,4,3,2]=>[5,2]
[7,5,2,1,3,4,6]=>[4,1,1,1]
[7,5,2,1,3,6,4]=>[4,2,1]
[7,5,2,1,4,3,6]=>[4,2,1]
[7,5,2,1,4,6,3]=>[4,2,1]
[7,5,2,1,6,3,4]=>[4,2,1]
[7,5,2,1,6,4,3]=>[4,3]
[7,5,2,3,1,4,6]=>[4,1,1,1]
[7,5,2,3,1,6,4]=>[4,2,1]
[7,5,2,3,4,1,6]=>[4,1,1,1]
[7,5,2,3,4,6,1]=>[4,1,1,1]
[7,5,2,3,6,1,4]=>[4,1,1,1]
[7,5,2,3,6,4,1]=>[4,2,1]
[7,5,2,4,1,3,6]=>[4,1,1,1]
[7,5,2,4,1,6,3]=>[4,2,1]
[7,5,2,4,3,1,6]=>[5,1,1]
[7,5,2,4,3,6,1]=>[5,1,1]
[7,5,2,4,6,1,3]=>[4,1,1,1]
[7,5,2,4,6,3,1]=>[5,1,1]
[7,5,2,6,1,3,4]=>[4,1,1,1]
[7,5,2,6,1,4,3]=>[4,2,1]
[7,5,2,6,3,1,4]=>[4,2,1]
[7,5,2,6,3,4,1]=>[4,2,1]
[7,5,2,6,4,1,3]=>[4,2,1]
[7,5,2,6,4,3,1]=>[5,2]
[7,5,3,1,2,4,6]=>[4,1,1,1]
[7,5,3,1,2,6,4]=>[4,2,1]
[7,5,3,1,4,2,6]=>[4,2,1]
[7,5,3,1,4,6,2]=>[4,2,1]
[7,5,3,1,6,2,4]=>[4,2,1]
[7,5,3,1,6,4,2]=>[4,3]
[7,5,3,2,1,4,6]=>[5,1,1]
[7,5,3,2,1,6,4]=>[5,2]
[7,5,3,2,4,1,6]=>[5,1,1]
[7,5,3,2,4,6,1]=>[5,1,1]
[7,5,3,2,6,1,4]=>[5,1,1]
[7,5,3,2,6,4,1]=>[5,2]
[7,5,3,4,1,2,6]=>[4,1,1,1]
[7,5,3,4,1,6,2]=>[4,2,1]
[7,5,3,4,2,1,6]=>[5,1,1]
[7,5,3,4,2,6,1]=>[5,1,1]
[7,5,3,4,6,1,2]=>[4,1,1,1]
[7,5,3,4,6,2,1]=>[5,1,1]
[7,5,3,6,1,2,4]=>[4,1,1,1]
[7,5,3,6,1,4,2]=>[4,2,1]
[7,5,3,6,2,1,4]=>[5,1,1]
[7,5,3,6,2,4,1]=>[5,1,1]
[7,5,3,6,4,1,2]=>[4,2,1]
[7,5,3,6,4,2,1]=>[5,2]
[7,5,4,1,2,3,6]=>[4,1,1,1]
[7,5,4,1,2,6,3]=>[4,2,1]
[7,5,4,1,3,2,6]=>[5,1,1]
[7,5,4,1,3,6,2]=>[5,1,1]
[7,5,4,1,6,2,3]=>[4,2,1]
[7,5,4,1,6,3,2]=>[5,2]
[7,5,4,2,1,3,6]=>[5,1,1]
[7,5,4,2,1,6,3]=>[5,2]
[7,5,4,2,3,1,6]=>[5,1,1]
[7,5,4,2,3,6,1]=>[5,1,1]
[7,5,4,2,6,1,3]=>[5,1,1]
[7,5,4,2,6,3,1]=>[5,2]
[7,5,4,3,1,2,6]=>[5,1,1]
[7,5,4,3,1,6,2]=>[5,2]
[7,5,4,3,2,1,6]=>[6,1]
[7,5,4,3,2,6,1]=>[6,1]
[7,5,4,3,6,1,2]=>[5,1,1]
[7,5,4,3,6,2,1]=>[6,1]
[7,5,4,6,1,2,3]=>[4,1,1,1]
[7,5,4,6,1,3,2]=>[5,1,1]
[7,5,4,6,2,1,3]=>[5,1,1]
[7,5,4,6,2,3,1]=>[5,1,1]
[7,5,4,6,3,1,2]=>[5,1,1]
[7,5,4,6,3,2,1]=>[6,1]
[7,5,6,1,2,3,4]=>[3,1,1,1,1]
[7,5,6,1,2,4,3]=>[4,1,1,1]
[7,5,6,1,3,2,4]=>[4,1,1,1]
[7,5,6,1,3,4,2]=>[4,1,1,1]
[7,5,6,1,4,2,3]=>[4,1,1,1]
[7,5,6,1,4,3,2]=>[5,1,1]
[7,5,6,2,1,3,4]=>[4,1,1,1]
[7,5,6,2,1,4,3]=>[4,2,1]
[7,5,6,2,3,1,4]=>[4,1,1,1]
[7,5,6,2,3,4,1]=>[4,1,1,1]
[7,5,6,2,4,1,3]=>[4,1,1,1]
[7,5,6,2,4,3,1]=>[5,1,1]
[7,5,6,3,1,2,4]=>[4,1,1,1]
[7,5,6,3,1,4,2]=>[4,2,1]
[7,5,6,3,2,1,4]=>[5,1,1]
[7,5,6,3,2,4,1]=>[5,1,1]
[7,5,6,3,4,1,2]=>[4,1,1,1]
[7,5,6,3,4,2,1]=>[5,1,1]
[7,5,6,4,1,2,3]=>[4,1,1,1]
[7,5,6,4,1,3,2]=>[5,1,1]
[7,5,6,4,2,1,3]=>[5,1,1]
[7,5,6,4,2,3,1]=>[5,1,1]
[7,5,6,4,3,1,2]=>[5,1,1]
[7,5,6,4,3,2,1]=>[6,1]
[7,6,1,2,3,4,5]=>[3,1,1,1,1]
[7,6,1,2,3,5,4]=>[4,1,1,1]
[7,6,1,2,4,3,5]=>[4,1,1,1]
[7,6,1,2,4,5,3]=>[4,1,1,1]
[7,6,1,2,5,3,4]=>[4,1,1,1]
[7,6,1,2,5,4,3]=>[5,1,1]
[7,6,1,3,2,4,5]=>[4,1,1,1]
[7,6,1,3,2,5,4]=>[4,2,1]
[7,6,1,3,4,2,5]=>[4,1,1,1]
[7,6,1,3,4,5,2]=>[4,1,1,1]
[7,6,1,3,5,2,4]=>[4,1,1,1]
[7,6,1,3,5,4,2]=>[5,1,1]
[7,6,1,4,2,3,5]=>[4,1,1,1]
[7,6,1,4,2,5,3]=>[4,2,1]
[7,6,1,4,3,2,5]=>[5,1,1]
[7,6,1,4,3,5,2]=>[5,1,1]
[7,6,1,4,5,2,3]=>[4,1,1,1]
[7,6,1,4,5,3,2]=>[5,1,1]
[7,6,1,5,2,3,4]=>[4,1,1,1]
[7,6,1,5,2,4,3]=>[5,1,1]
[7,6,1,5,3,2,4]=>[5,1,1]
[7,6,1,5,3,4,2]=>[5,1,1]
[7,6,1,5,4,2,3]=>[5,1,1]
[7,6,1,5,4,3,2]=>[6,1]
[7,6,2,1,3,4,5]=>[4,1,1,1]
[7,6,2,1,3,5,4]=>[4,2,1]
[7,6,2,1,4,3,5]=>[4,2,1]
[7,6,2,1,4,5,3]=>[4,2,1]
[7,6,2,1,5,3,4]=>[4,2,1]
[7,6,2,1,5,4,3]=>[5,2]
[7,6,2,3,1,4,5]=>[4,1,1,1]
[7,6,2,3,1,5,4]=>[4,2,1]
[7,6,2,3,4,1,5]=>[4,1,1,1]
[7,6,2,3,4,5,1]=>[4,1,1,1]
[7,6,2,3,5,1,4]=>[4,1,1,1]
[7,6,2,3,5,4,1]=>[5,1,1]
[7,6,2,4,1,3,5]=>[4,1,1,1]
[7,6,2,4,1,5,3]=>[4,2,1]
[7,6,2,4,3,1,5]=>[5,1,1]
[7,6,2,4,3,5,1]=>[5,1,1]
[7,6,2,4,5,1,3]=>[4,1,1,1]
[7,6,2,4,5,3,1]=>[5,1,1]
[7,6,2,5,1,3,4]=>[4,1,1,1]
[7,6,2,5,1,4,3]=>[5,1,1]
[7,6,2,5,3,1,4]=>[5,1,1]
[7,6,2,5,3,4,1]=>[5,1,1]
[7,6,2,5,4,1,3]=>[5,1,1]
[7,6,2,5,4,3,1]=>[6,1]
[7,6,3,1,2,4,5]=>[4,1,1,1]
[7,6,3,1,2,5,4]=>[4,2,1]
[7,6,3,1,4,2,5]=>[4,2,1]
[7,6,3,1,4,5,2]=>[4,2,1]
[7,6,3,1,5,2,4]=>[4,2,1]
[7,6,3,1,5,4,2]=>[5,2]
[7,6,3,2,1,4,5]=>[5,1,1]
[7,6,3,2,1,5,4]=>[5,2]
[7,6,3,2,4,1,5]=>[5,1,1]
[7,6,3,2,4,5,1]=>[5,1,1]
[7,6,3,2,5,1,4]=>[5,1,1]
[7,6,3,2,5,4,1]=>[5,2]
[7,6,3,4,1,2,5]=>[4,1,1,1]
[7,6,3,4,1,5,2]=>[4,2,1]
[7,6,3,4,2,1,5]=>[5,1,1]
[7,6,3,4,2,5,1]=>[5,1,1]
[7,6,3,4,5,1,2]=>[4,1,1,1]
[7,6,3,4,5,2,1]=>[5,1,1]
[7,6,3,5,1,2,4]=>[4,1,1,1]
[7,6,3,5,1,4,2]=>[5,1,1]
[7,6,3,5,2,1,4]=>[5,1,1]
[7,6,3,5,2,4,1]=>[5,1,1]
[7,6,3,5,4,1,2]=>[5,1,1]
[7,6,3,5,4,2,1]=>[6,1]
[7,6,4,1,2,3,5]=>[4,1,1,1]
[7,6,4,1,2,5,3]=>[4,2,1]
[7,6,4,1,3,2,5]=>[5,1,1]
[7,6,4,1,3,5,2]=>[5,1,1]
[7,6,4,1,5,2,3]=>[4,2,1]
[7,6,4,1,5,3,2]=>[5,2]
[7,6,4,2,1,3,5]=>[5,1,1]
[7,6,4,2,1,5,3]=>[5,2]
[7,6,4,2,3,1,5]=>[5,1,1]
[7,6,4,2,3,5,1]=>[5,1,1]
[7,6,4,2,5,1,3]=>[5,1,1]
[7,6,4,2,5,3,1]=>[5,2]
[7,6,4,3,1,2,5]=>[5,1,1]
[7,6,4,3,1,5,2]=>[5,2]
[7,6,4,3,2,1,5]=>[6,1]
[7,6,4,3,2,5,1]=>[6,1]
[7,6,4,3,5,1,2]=>[5,1,1]
[7,6,4,3,5,2,1]=>[6,1]
[7,6,4,5,1,2,3]=>[4,1,1,1]
[7,6,4,5,1,3,2]=>[5,1,1]
[7,6,4,5,2,1,3]=>[5,1,1]
[7,6,4,5,2,3,1]=>[5,1,1]
[7,6,4,5,3,1,2]=>[5,1,1]
[7,6,4,5,3,2,1]=>[6,1]
[7,6,5,1,2,3,4]=>[4,1,1,1]
[7,6,5,1,2,4,3]=>[5,1,1]
[7,6,5,1,3,2,4]=>[5,1,1]
[7,6,5,1,3,4,2]=>[5,1,1]
[7,6,5,1,4,2,3]=>[5,1,1]
[7,6,5,1,4,3,2]=>[6,1]
[7,6,5,2,1,3,4]=>[5,1,1]
[7,6,5,2,1,4,3]=>[5,2]
[7,6,5,2,3,1,4]=>[5,1,1]
[7,6,5,2,3,4,1]=>[5,1,1]
[7,6,5,2,4,1,3]=>[5,1,1]
[7,6,5,2,4,3,1]=>[6,1]
[7,6,5,3,1,2,4]=>[5,1,1]
[7,6,5,3,1,4,2]=>[5,2]
[7,6,5,3,2,1,4]=>[6,1]
[7,6,5,3,2,4,1]=>[6,1]
[7,6,5,3,4,1,2]=>[5,1,1]
[7,6,5,3,4,2,1]=>[6,1]
[7,6,5,4,1,2,3]=>[5,1,1]
[7,6,5,4,1,3,2]=>[6,1]
[7,6,5,4,2,1,3]=>[6,1]
[7,6,5,4,2,3,1]=>[6,1]
[7,6,5,4,3,1,2]=>[6,1]
[7,6,5,4,3,2,1]=>[7]
[8,7,6,5,4,3,2,1]=>[8]
[7,8,6,5,4,3,2,1]=>[7,1]
[8,6,7,5,4,3,2,1]=>[7,1]
[7,6,8,5,4,3,2,1]=>[7,1]
[6,7,8,5,4,3,2,1]=>[6,1,1]
[8,7,5,6,4,3,2,1]=>[7,1]
[7,8,5,6,4,3,2,1]=>[6,1,1]
[8,6,5,7,4,3,2,1]=>[7,1]
[8,5,6,7,4,3,2,1]=>[6,1,1]
[7,6,5,8,4,3,2,1]=>[7,1]
[6,7,5,8,4,3,2,1]=>[6,1,1]
[7,5,6,8,4,3,2,1]=>[6,1,1]
[6,5,7,8,4,3,2,1]=>[6,1,1]
[5,6,7,8,4,3,2,1]=>[5,1,1,1]
[8,7,6,4,5,3,2,1]=>[7,1]
[7,8,6,4,5,3,2,1]=>[6,1,1]
[8,6,7,4,5,3,2,1]=>[6,1,1]
[7,6,8,4,5,3,2,1]=>[6,1,1]
[6,7,8,4,5,3,2,1]=>[5,1,1,1]
[8,7,5,4,6,3,2,1]=>[7,1]
[8,7,4,5,6,3,2,1]=>[6,1,1]
[8,6,5,4,7,3,2,1]=>[7,1]
[8,5,6,4,7,3,2,1]=>[6,1,1]
[8,6,4,5,7,3,2,1]=>[6,1,1]
[8,5,4,6,7,3,2,1]=>[6,1,1]
[8,4,5,6,7,3,2,1]=>[5,1,1,1]
[7,6,5,4,8,3,2,1]=>[7,1]
[6,7,5,4,8,3,2,1]=>[6,1,1]
[7,5,6,4,8,3,2,1]=>[6,1,1]
[6,5,7,4,8,3,2,1]=>[6,1,1]
[5,6,7,4,8,3,2,1]=>[5,1,1,1]
[7,6,4,5,8,3,2,1]=>[6,1,1]
[6,7,4,5,8,3,2,1]=>[5,1,1,1]
[7,5,4,6,8,3,2,1]=>[6,1,1]
[7,4,5,6,8,3,2,1]=>[5,1,1,1]
[6,5,4,7,8,3,2,1]=>[6,1,1]
[5,6,4,7,8,3,2,1]=>[5,1,1,1]
[6,4,5,7,8,3,2,1]=>[5,1,1,1]
[5,4,6,7,8,3,2,1]=>[5,1,1,1]
[4,5,6,7,8,3,2,1]=>[4,1,1,1,1]
[8,7,6,5,3,4,2,1]=>[7,1]
[7,8,6,5,3,4,2,1]=>[6,1,1]
[8,6,7,5,3,4,2,1]=>[6,1,1]
[7,6,8,5,3,4,2,1]=>[6,1,1]
[8,7,5,6,3,4,2,1]=>[6,1,1]
[7,8,5,6,3,4,2,1]=>[5,1,1,1]
[8,5,6,7,3,4,2,1]=>[5,1,1,1]
[7,6,5,8,3,4,2,1]=>[6,1,1]
[6,5,7,8,3,4,2,1]=>[5,1,1,1]
[5,6,7,8,3,4,2,1]=>[4,1,1,1,1]
[8,7,6,4,3,5,2,1]=>[7,1]
[7,8,6,4,3,5,2,1]=>[6,1,1]
[8,6,7,4,3,5,2,1]=>[6,1,1]
[7,6,8,4,3,5,2,1]=>[6,1,1]
[6,7,8,4,3,5,2,1]=>[5,1,1,1]
[8,7,6,3,4,5,2,1]=>[6,1,1]
[7,8,6,3,4,5,2,1]=>[5,1,1,1]
[8,6,7,3,4,5,2,1]=>[5,1,1,1]
[7,6,8,3,4,5,2,1]=>[5,1,1,1]
[6,7,8,3,4,5,2,1]=>[4,1,1,1,1]
[8,7,5,4,3,6,2,1]=>[7,1]
[7,8,5,4,3,6,2,1]=>[6,1,1]
[8,7,4,5,3,6,2,1]=>[6,1,1]
[7,8,5,3,4,6,2,1]=>[5,1,1,1]
[8,7,4,3,5,6,2,1]=>[6,1,1]
[8,7,3,4,5,6,2,1]=>[5,1,1,1]
[7,8,3,4,5,6,2,1]=>[4,1,1,1,1]
[8,6,5,4,3,7,2,1]=>[7,1]
[8,6,4,5,3,7,2,1]=>[6,1,1]
[8,6,4,3,5,7,2,1]=>[6,1,1]
[8,5,4,3,6,7,2,1]=>[6,1,1]
[8,5,3,4,6,7,2,1]=>[5,1,1,1]
[8,4,3,5,6,7,2,1]=>[5,1,1,1]
[8,3,4,5,6,7,2,1]=>[4,1,1,1,1]
[7,6,5,4,3,8,2,1]=>[7,1]
[6,7,5,4,3,8,2,1]=>[6,1,1]
[7,5,6,4,3,8,2,1]=>[6,1,1]
[5,6,7,4,3,8,2,1]=>[5,1,1,1]
[6,7,4,5,3,8,2,1]=>[5,1,1,1]
[7,5,4,6,3,8,2,1]=>[6,1,1]
[7,4,5,6,3,8,2,1]=>[5,1,1,1]
[6,5,4,7,3,8,2,1]=>[6,1,1]
[6,4,5,7,3,8,2,1]=>[5,1,1,1]
[5,4,6,7,3,8,2,1]=>[5,1,1,1]
[4,5,6,7,3,8,2,1]=>[4,1,1,1,1]
[7,6,5,3,4,8,2,1]=>[6,1,1]
[7,6,4,3,5,8,2,1]=>[6,1,1]
[7,6,3,4,5,8,2,1]=>[5,1,1,1]
[7,5,4,3,6,8,2,1]=>[6,1,1]
[7,5,3,4,6,8,2,1]=>[5,1,1,1]
[7,3,4,5,6,8,2,1]=>[4,1,1,1,1]
[6,5,4,3,7,8,2,1]=>[6,1,1]
[6,5,3,4,7,8,2,1]=>[5,1,1,1]
[6,3,4,5,7,8,2,1]=>[4,1,1,1,1]
[5,4,3,6,7,8,2,1]=>[5,1,1,1]
[4,3,5,6,7,8,2,1]=>[4,1,1,1,1]
[3,4,5,6,7,8,2,1]=>[3,1,1,1,1,1]
[8,7,6,5,4,2,3,1]=>[7,1]
[7,8,6,5,4,2,3,1]=>[6,1,1]
[8,6,7,5,4,2,3,1]=>[6,1,1]
[7,6,8,5,4,2,3,1]=>[6,1,1]
[8,6,5,7,4,2,3,1]=>[6,1,1]
[8,5,6,7,4,2,3,1]=>[5,1,1,1]
[7,6,5,8,4,2,3,1]=>[6,1,1]
[7,5,6,8,4,2,3,1]=>[5,1,1,1]
[5,6,7,8,4,2,3,1]=>[4,1,1,1,1]
[8,7,6,4,5,2,3,1]=>[6,1,1]
[8,6,7,4,5,2,3,1]=>[5,1,1,1]
[7,6,8,4,5,2,3,1]=>[5,1,1,1]
[6,7,8,4,5,2,3,1]=>[4,1,1,1,1]
[8,7,5,4,6,2,3,1]=>[6,1,1]
[8,7,4,5,6,2,3,1]=>[5,1,1,1]
[7,8,4,5,6,2,3,1]=>[4,1,1,1,1]
[8,6,5,4,7,2,3,1]=>[6,1,1]
[8,5,6,4,7,2,3,1]=>[5,1,1,1]
[8,6,4,5,7,2,3,1]=>[5,1,1,1]
[8,4,5,6,7,2,3,1]=>[4,1,1,1,1]
[7,6,5,4,8,2,3,1]=>[6,1,1]
[7,5,6,4,8,2,3,1]=>[5,1,1,1]
[6,5,7,4,8,2,3,1]=>[5,1,1,1]
[4,5,6,7,8,2,3,1]=>[3,1,1,1,1,1]
[8,7,6,5,3,2,4,1]=>[7,1]
[7,8,6,5,3,2,4,1]=>[6,1,1]
[8,6,7,5,3,2,4,1]=>[6,1,1]
[7,6,8,5,3,2,4,1]=>[6,1,1]
[6,7,8,5,3,2,4,1]=>[5,1,1,1]
[8,7,5,6,3,2,4,1]=>[6,1,1]
[8,6,5,7,3,2,4,1]=>[6,1,1]
[8,5,6,7,3,2,4,1]=>[5,1,1,1]
[7,6,5,8,3,2,4,1]=>[6,1,1]
[5,6,7,8,3,2,4,1]=>[4,1,1,1,1]
[8,7,6,5,2,3,4,1]=>[6,1,1]
[8,6,7,5,2,3,4,1]=>[5,1,1,1]
[7,6,8,5,2,3,4,1]=>[5,1,1,1]
[6,7,8,5,2,3,4,1]=>[4,1,1,1,1]
[8,7,5,6,2,3,4,1]=>[5,1,1,1]
[7,8,5,6,2,3,4,1]=>[4,1,1,1,1]
[8,6,5,7,2,3,4,1]=>[5,1,1,1]
[8,5,6,7,2,3,4,1]=>[4,1,1,1,1]
[7,6,5,8,2,3,4,1]=>[5,1,1,1]
[6,7,5,8,2,3,4,1]=>[4,1,1,1,1]
[6,5,7,8,2,3,4,1]=>[4,1,1,1,1]
[5,6,7,8,2,3,4,1]=>[3,1,1,1,1,1]
[8,7,6,4,3,2,5,1]=>[7,1]
[7,8,6,4,3,2,5,1]=>[6,1,1]
[8,6,7,4,3,2,5,1]=>[6,1,1]
[7,6,8,4,3,2,5,1]=>[6,1,1]
[6,7,8,4,3,2,5,1]=>[5,1,1,1]
[8,7,6,3,4,2,5,1]=>[6,1,1]
[7,8,6,3,4,2,5,1]=>[5,1,1,1]
[8,6,7,3,4,2,5,1]=>[5,1,1,1]
[7,6,8,3,4,2,5,1]=>[5,1,1,1]
[6,7,8,3,4,2,5,1]=>[4,1,1,1,1]
[8,7,6,4,2,3,5,1]=>[6,1,1]
[8,6,7,4,2,3,5,1]=>[5,1,1,1]
[7,6,8,4,2,3,5,1]=>[5,1,1,1]
[6,7,8,4,2,3,5,1]=>[4,1,1,1,1]
[8,7,6,3,2,4,5,1]=>[6,1,1]
[7,8,6,3,2,4,5,1]=>[5,1,1,1]
[8,6,7,3,2,4,5,1]=>[5,1,1,1]
[6,7,8,3,2,4,5,1]=>[4,1,1,1,1]
[8,7,6,2,3,4,5,1]=>[5,1,1,1]
[7,8,6,2,3,4,5,1]=>[4,1,1,1,1]
[8,6,7,2,3,4,5,1]=>[4,1,1,1,1]
[7,6,8,2,3,4,5,1]=>[4,1,1,1,1]
[6,7,8,2,3,4,5,1]=>[3,1,1,1,1,1]
[8,7,5,4,3,2,6,1]=>[7,1]
[7,8,5,4,3,2,6,1]=>[6,1,1]
[8,7,5,3,4,2,6,1]=>[6,1,1]
[7,8,5,3,4,2,6,1]=>[5,1,1,1]
[8,7,4,3,5,2,6,1]=>[6,1,1]
[8,7,5,3,2,4,6,1]=>[6,1,1]
[8,7,4,3,2,5,6,1]=>[6,1,1]
[7,8,4,3,2,5,6,1]=>[5,1,1,1]
[7,8,3,4,2,5,6,1]=>[4,1,1,1,1]
[7,8,4,2,3,5,6,1]=>[4,1,1,1,1]
[7,8,3,2,4,5,6,1]=>[4,1,1,1,1]
[8,7,2,3,4,5,6,1]=>[4,1,1,1,1]
[7,8,2,3,4,5,6,1]=>[3,1,1,1,1,1]
[8,6,5,4,3,2,7,1]=>[7,1]
[8,5,6,4,3,2,7,1]=>[6,1,1]
[8,6,4,5,3,2,7,1]=>[6,1,1]
[8,5,4,6,3,2,7,1]=>[6,1,1]
[8,6,5,3,4,2,7,1]=>[6,1,1]
[8,5,6,3,4,2,7,1]=>[5,1,1,1]
[8,6,4,3,5,2,7,1]=>[6,1,1]
[8,6,3,4,5,2,7,1]=>[5,1,1,1]
[8,5,4,3,6,2,7,1]=>[6,1,1]
[8,4,5,3,6,2,7,1]=>[5,1,1,1]
[8,4,3,5,6,2,7,1]=>[5,1,1,1]
[8,3,4,5,6,2,7,1]=>[4,1,1,1,1]
[8,6,5,4,2,3,7,1]=>[6,1,1]
[8,6,4,5,2,3,7,1]=>[5,1,1,1]
[8,6,5,3,2,4,7,1]=>[6,1,1]
[8,6,4,3,2,5,7,1]=>[6,1,1]
[8,6,4,2,3,5,7,1]=>[5,1,1,1]
[8,6,2,3,4,5,7,1]=>[4,1,1,1,1]
[8,5,4,3,2,6,7,1]=>[6,1,1]
[8,5,3,4,2,6,7,1]=>[5,1,1,1]
[8,3,4,5,2,6,7,1]=>[4,1,1,1,1]
[8,5,4,2,3,6,7,1]=>[5,1,1,1]
[8,4,5,2,3,6,7,1]=>[4,1,1,1,1]
[8,5,2,3,4,6,7,1]=>[4,1,1,1,1]
[8,4,3,2,5,6,7,1]=>[5,1,1,1]
[8,3,4,2,5,6,7,1]=>[4,1,1,1,1]
[8,4,2,3,5,6,7,1]=>[4,1,1,1,1]
[8,3,2,4,5,6,7,1]=>[4,1,1,1,1]
[8,2,3,4,5,6,7,1]=>[3,1,1,1,1,1]
[7,6,5,4,3,2,8,1]=>[7,1]
[6,7,5,4,3,2,8,1]=>[6,1,1]
[7,5,6,4,3,2,8,1]=>[6,1,1]
[6,5,7,4,3,2,8,1]=>[6,1,1]
[7,6,4,5,3,2,8,1]=>[6,1,1]
[6,7,4,5,3,2,8,1]=>[5,1,1,1]
[7,4,5,6,3,2,8,1]=>[5,1,1,1]
[6,4,5,7,3,2,8,1]=>[5,1,1,1]
[4,5,6,7,3,2,8,1]=>[4,1,1,1,1]
[7,6,5,3,4,2,8,1]=>[6,1,1]
[7,5,6,3,4,2,8,1]=>[5,1,1,1]
[6,5,7,3,4,2,8,1]=>[5,1,1,1]
[7,6,4,3,5,2,8,1]=>[6,1,1]
[7,6,3,4,5,2,8,1]=>[5,1,1,1]
[7,5,4,3,6,2,8,1]=>[6,1,1]
[7,4,5,3,6,2,8,1]=>[5,1,1,1]
[7,5,3,4,6,2,8,1]=>[5,1,1,1]
[6,5,4,3,7,2,8,1]=>[6,1,1]
[6,4,5,3,7,2,8,1]=>[5,1,1,1]
[5,4,6,3,7,2,8,1]=>[5,1,1,1]
[4,5,6,3,7,2,8,1]=>[4,1,1,1,1]
[6,5,3,4,7,2,8,1]=>[5,1,1,1]
[5,6,3,4,7,2,8,1]=>[4,1,1,1,1]
[6,4,3,5,7,2,8,1]=>[5,1,1,1]
[6,3,4,5,7,2,8,1]=>[4,1,1,1,1]
[5,4,3,6,7,2,8,1]=>[5,1,1,1]
[4,5,3,6,7,2,8,1]=>[4,1,1,1,1]
[3,4,5,6,7,2,8,1]=>[3,1,1,1,1,1]
[7,6,5,4,2,3,8,1]=>[6,1,1]
[6,7,5,4,2,3,8,1]=>[5,1,1,1]
[7,5,6,4,2,3,8,1]=>[5,1,1,1]
[6,5,7,4,2,3,8,1]=>[5,1,1,1]
[5,6,7,4,2,3,8,1]=>[4,1,1,1,1]
[7,6,4,5,2,3,8,1]=>[5,1,1,1]
[6,7,4,5,2,3,8,1]=>[4,1,1,1,1]
[7,5,4,6,2,3,8,1]=>[5,1,1,1]
[7,4,5,6,2,3,8,1]=>[4,1,1,1,1]
[6,5,4,7,2,3,8,1]=>[5,1,1,1]
[5,6,4,7,2,3,8,1]=>[4,1,1,1,1]
[6,4,5,7,2,3,8,1]=>[4,1,1,1,1]
[5,4,6,7,2,3,8,1]=>[4,1,1,1,1]
[4,5,6,7,2,3,8,1]=>[3,1,1,1,1,1]
[7,6,5,3,2,4,8,1]=>[6,1,1]
[6,7,5,3,2,4,8,1]=>[5,1,1,1]
[6,5,7,3,2,4,8,1]=>[5,1,1,1]
[7,6,5,2,3,4,8,1]=>[5,1,1,1]
[7,5,6,2,3,4,8,1]=>[4,1,1,1,1]
[5,6,7,2,3,4,8,1]=>[3,1,1,1,1,1]
[6,7,4,3,2,5,8,1]=>[5,1,1,1]
[7,6,4,2,3,5,8,1]=>[5,1,1,1]
[7,6,3,2,4,5,8,1]=>[5,1,1,1]
[6,7,3,2,4,5,8,1]=>[4,1,1,1,1]
[7,6,2,3,4,5,8,1]=>[4,1,1,1,1]
[6,7,2,3,4,5,8,1]=>[3,1,1,1,1,1]
[7,5,4,3,2,6,8,1]=>[6,1,1]
[7,4,3,5,2,6,8,1]=>[5,1,1,1]
[7,5,4,2,3,6,8,1]=>[5,1,1,1]
[7,4,5,2,3,6,8,1]=>[4,1,1,1,1]
[7,5,3,2,4,6,8,1]=>[5,1,1,1]
[7,5,2,3,4,6,8,1]=>[4,1,1,1,1]
[7,4,2,3,5,6,8,1]=>[4,1,1,1,1]
[7,3,2,4,5,6,8,1]=>[4,1,1,1,1]
[7,2,3,4,5,6,8,1]=>[3,1,1,1,1,1]
[6,5,4,3,2,7,8,1]=>[6,1,1]
[5,4,6,3,2,7,8,1]=>[5,1,1,1]
[4,5,6,3,2,7,8,1]=>[4,1,1,1,1]
[6,5,3,4,2,7,8,1]=>[5,1,1,1]
[5,4,3,6,2,7,8,1]=>[5,1,1,1]
[4,3,5,6,2,7,8,1]=>[4,1,1,1,1]
[3,4,5,6,2,7,8,1]=>[3,1,1,1,1,1]
[6,5,4,2,3,7,8,1]=>[5,1,1,1]
[6,4,5,2,3,7,8,1]=>[4,1,1,1,1]
[4,5,6,2,3,7,8,1]=>[3,1,1,1,1,1]
[6,5,3,2,4,7,8,1]=>[5,1,1,1]
[6,5,2,3,4,7,8,1]=>[4,1,1,1,1]
[6,2,3,4,5,7,8,1]=>[3,1,1,1,1,1]
[5,4,3,2,6,7,8,1]=>[5,1,1,1]
[4,5,3,2,6,7,8,1]=>[4,1,1,1,1]
[4,3,5,2,6,7,8,1]=>[4,1,1,1,1]
[3,4,5,2,6,7,8,1]=>[3,1,1,1,1,1]
[5,4,2,3,6,7,8,1]=>[4,1,1,1,1]
[4,5,2,3,6,7,8,1]=>[3,1,1,1,1,1]
[5,3,2,4,6,7,8,1]=>[4,1,1,1,1]
[5,2,3,4,6,7,8,1]=>[3,1,1,1,1,1]
[4,3,2,5,6,7,8,1]=>[4,1,1,1,1]
[3,4,2,5,6,7,8,1]=>[3,1,1,1,1,1]
[4,2,3,5,6,7,8,1]=>[3,1,1,1,1,1]
[3,2,4,5,6,7,8,1]=>[3,1,1,1,1,1]
[2,3,4,5,6,7,8,1]=>[2,1,1,1,1,1,1]
[8,7,6,5,4,3,1,2]=>[7,1]
[7,8,6,5,4,3,1,2]=>[6,1,1]
[8,6,7,5,4,3,1,2]=>[6,1,1]
[7,6,8,5,4,3,1,2]=>[6,1,1]
[6,7,8,5,4,3,1,2]=>[5,1,1,1]
[8,7,5,6,4,3,1,2]=>[6,1,1]
[7,8,5,6,4,3,1,2]=>[5,1,1,1]
[8,6,5,7,4,3,1,2]=>[6,1,1]
[7,6,5,8,4,3,1,2]=>[6,1,1]
[6,7,5,8,4,3,1,2]=>[5,1,1,1]
[7,5,6,8,4,3,1,2]=>[5,1,1,1]
[6,5,7,8,4,3,1,2]=>[5,1,1,1]
[5,6,7,8,4,3,1,2]=>[4,1,1,1,1]
[8,7,6,4,5,3,1,2]=>[6,1,1]
[7,8,6,4,5,3,1,2]=>[5,1,1,1]
[8,6,7,4,5,3,1,2]=>[5,1,1,1]
[6,7,8,4,5,3,1,2]=>[4,1,1,1,1]
[8,7,5,4,6,3,1,2]=>[6,1,1]
[8,5,6,4,7,3,1,2]=>[5,1,1,1]
[8,6,4,5,7,3,1,2]=>[5,1,1,1]
[8,5,4,6,7,3,1,2]=>[5,1,1,1]
[7,6,5,4,8,3,1,2]=>[6,1,1]
[7,5,6,4,8,3,1,2]=>[5,1,1,1]
[6,5,7,4,8,3,1,2]=>[5,1,1,1]
[7,6,4,5,8,3,1,2]=>[5,1,1,1]
[6,7,4,5,8,3,1,2]=>[4,1,1,1,1]
[6,5,4,7,8,3,1,2]=>[5,1,1,1]
[5,6,4,7,8,3,1,2]=>[4,1,1,1,1]
[5,4,6,7,8,3,1,2]=>[4,1,1,1,1]
[4,5,6,7,8,3,1,2]=>[3,1,1,1,1,1]
[8,7,6,5,3,4,1,2]=>[6,1,1]
[7,8,6,5,3,4,1,2]=>[5,1,1,1]
[7,6,8,5,3,4,1,2]=>[5,1,1,1]
[6,7,8,5,3,4,1,2]=>[4,1,1,1,1]
[8,7,5,6,3,4,1,2]=>[5,1,1,1]
[7,8,5,6,3,4,1,2]=>[4,1,1,1,1]
[8,6,5,7,3,4,1,2]=>[5,1,1,1]
[8,5,6,7,3,4,1,2]=>[4,1,1,1,1]
[7,6,5,8,3,4,1,2]=>[5,1,1,1]
[6,7,5,8,3,4,1,2]=>[4,1,1,1,1]
[7,5,6,8,3,4,1,2]=>[4,1,1,1,1]
[6,5,7,8,3,4,1,2]=>[4,1,1,1,1]
[5,6,7,8,3,4,1,2]=>[3,1,1,1,1,1]
[6,7,8,4,3,5,1,2]=>[4,1,1,1,1]
[8,7,6,3,4,5,1,2]=>[5,1,1,1]
[8,6,7,3,4,5,1,2]=>[4,1,1,1,1]
[6,7,8,3,4,5,1,2]=>[3,1,1,1,1,1]
[7,8,5,4,3,6,1,2]=>[5,1,1,1]
[8,7,4,5,3,6,1,2]=>[5,1,1,1]
[7,8,4,5,3,6,1,2]=>[4,1,1,1,1]
[7,8,5,3,4,6,1,2]=>[4,1,1,1,1]
[8,7,4,3,5,6,1,2]=>[5,1,1,1]
[7,8,4,3,5,6,1,2]=>[4,1,1,1,1]
[8,7,3,4,5,6,1,2]=>[4,1,1,1,1]
[7,8,3,4,5,6,1,2]=>[3,1,1,1,1,1]
[8,6,5,4,3,7,1,2]=>[6,1,1]
[8,5,4,6,3,7,1,2]=>[5,1,1,1]
[8,5,4,3,6,7,1,2]=>[5,1,1,1]
[8,5,3,4,6,7,1,2]=>[4,1,1,1,1]
[8,4,3,5,6,7,1,2]=>[4,1,1,1,1]
[8,3,4,5,6,7,1,2]=>[3,1,1,1,1,1]
[7,6,5,4,3,8,1,2]=>[6,1,1]
[6,5,7,4,3,8,1,2]=>[5,1,1,1]
[5,6,7,4,3,8,1,2]=>[4,1,1,1,1]
[6,7,4,5,3,8,1,2]=>[4,1,1,1,1]
[7,5,4,6,3,8,1,2]=>[5,1,1,1]
[6,5,4,7,3,8,1,2]=>[5,1,1,1]
[5,6,4,7,3,8,1,2]=>[4,1,1,1,1]
[5,4,6,7,3,8,1,2]=>[4,1,1,1,1]
[4,5,6,7,3,8,1,2]=>[3,1,1,1,1,1]
[7,6,5,3,4,8,1,2]=>[5,1,1,1]
[7,5,6,3,4,8,1,2]=>[4,1,1,1,1]
[7,6,4,3,5,8,1,2]=>[5,1,1,1]
[7,6,3,4,5,8,1,2]=>[4,1,1,1,1]
[7,5,4,3,6,8,1,2]=>[5,1,1,1]
[7,4,5,3,6,8,1,2]=>[4,1,1,1,1]
[7,5,3,4,6,8,1,2]=>[4,1,1,1,1]
[7,3,4,5,6,8,1,2]=>[3,1,1,1,1,1]
[6,5,4,3,7,8,1,2]=>[5,1,1,1]
[5,4,6,3,7,8,1,2]=>[4,1,1,1,1]
[4,5,6,3,7,8,1,2]=>[3,1,1,1,1,1]
[5,6,3,4,7,8,1,2]=>[3,1,1,1,1,1]
[6,4,3,5,7,8,1,2]=>[4,1,1,1,1]
[6,3,4,5,7,8,1,2]=>[3,1,1,1,1,1]
[5,4,3,6,7,8,1,2]=>[4,1,1,1,1]
[4,5,3,6,7,8,1,2]=>[3,1,1,1,1,1]
[5,3,4,6,7,8,1,2]=>[3,1,1,1,1,1]
[4,3,5,6,7,8,1,2]=>[3,1,1,1,1,1]
[3,4,5,6,7,8,1,2]=>[2,1,1,1,1,1,1]
[8,7,6,5,4,2,1,3]=>[7,1]
[7,8,6,5,4,2,1,3]=>[6,1,1]
[8,6,7,5,4,2,1,3]=>[6,1,1]
[7,6,8,5,4,2,1,3]=>[6,1,1]
[6,7,8,5,4,2,1,3]=>[5,1,1,1]
[8,7,5,6,4,2,1,3]=>[6,1,1]
[7,8,5,6,4,2,1,3]=>[5,1,1,1]
[8,6,5,7,4,2,1,3]=>[6,1,1]
[7,6,5,8,4,2,1,3]=>[6,1,1]
[6,7,5,8,4,2,1,3]=>[5,1,1,1]
[7,5,6,8,4,2,1,3]=>[5,1,1,1]
[6,5,7,8,4,2,1,3]=>[5,1,1,1]
[5,6,7,8,4,2,1,3]=>[4,1,1,1,1]
[8,7,6,4,5,2,1,3]=>[6,1,1]
[8,6,7,4,5,2,1,3]=>[5,1,1,1]
[7,6,8,4,5,2,1,3]=>[5,1,1,1]
[8,7,4,5,6,2,1,3]=>[5,1,1,1]
[8,6,5,4,7,2,1,3]=>[6,1,1]
[8,6,4,5,7,2,1,3]=>[5,1,1,1]
[8,4,5,6,7,2,1,3]=>[4,1,1,1,1]
[7,6,5,4,8,2,1,3]=>[6,1,1]
[6,7,5,4,8,2,1,3]=>[5,1,1,1]
[7,5,6,4,8,2,1,3]=>[5,1,1,1]
[6,5,7,4,8,2,1,3]=>[5,1,1,1]
[5,6,7,4,8,2,1,3]=>[4,1,1,1,1]
[7,6,4,5,8,2,1,3]=>[5,1,1,1]
[7,4,5,6,8,2,1,3]=>[4,1,1,1,1]
[5,4,6,7,8,2,1,3]=>[4,1,1,1,1]
[4,5,6,7,8,2,1,3]=>[3,1,1,1,1,1]
[8,7,6,5,4,1,2,3]=>[6,1,1]
[7,8,6,5,4,1,2,3]=>[5,1,1,1]
[7,6,8,5,4,1,2,3]=>[5,1,1,1]
[6,7,8,5,4,1,2,3]=>[4,1,1,1,1]
[7,8,5,6,4,1,2,3]=>[4,1,1,1,1]
[8,6,5,7,4,1,2,3]=>[5,1,1,1]
[8,5,6,7,4,1,2,3]=>[4,1,1,1,1]
[7,6,5,8,4,1,2,3]=>[5,1,1,1]
[6,7,5,8,4,1,2,3]=>[4,1,1,1,1]
[7,5,6,8,4,1,2,3]=>[4,1,1,1,1]
[6,5,7,8,4,1,2,3]=>[4,1,1,1,1]
[5,6,7,8,4,1,2,3]=>[3,1,1,1,1,1]
[8,7,6,4,5,1,2,3]=>[5,1,1,1]
[8,6,7,4,5,1,2,3]=>[4,1,1,1,1]
[6,7,8,4,5,1,2,3]=>[3,1,1,1,1,1]
[8,7,5,4,6,1,2,3]=>[5,1,1,1]
[7,8,5,4,6,1,2,3]=>[4,1,1,1,1]
[8,7,4,5,6,1,2,3]=>[4,1,1,1,1]
[7,8,4,5,6,1,2,3]=>[3,1,1,1,1,1]
[8,6,5,4,7,1,2,3]=>[5,1,1,1]
[8,5,6,4,7,1,2,3]=>[4,1,1,1,1]
[8,6,4,5,7,1,2,3]=>[4,1,1,1,1]
[8,5,4,6,7,1,2,3]=>[4,1,1,1,1]
[8,4,5,6,7,1,2,3]=>[3,1,1,1,1,1]
[7,6,5,4,8,1,2,3]=>[5,1,1,1]
[6,7,5,4,8,1,2,3]=>[4,1,1,1,1]
[6,5,7,4,8,1,2,3]=>[4,1,1,1,1]
[5,6,7,4,8,1,2,3]=>[3,1,1,1,1,1]
[6,7,4,5,8,1,2,3]=>[3,1,1,1,1,1]
[7,5,4,6,8,1,2,3]=>[4,1,1,1,1]
[6,5,4,7,8,1,2,3]=>[4,1,1,1,1]
[5,6,4,7,8,1,2,3]=>[3,1,1,1,1,1]
[5,4,6,7,8,1,2,3]=>[3,1,1,1,1,1]
[4,5,6,7,8,1,2,3]=>[2,1,1,1,1,1,1]
[8,7,6,5,3,2,1,4]=>[7,1]
[7,8,6,5,3,2,1,4]=>[6,1,1]
[8,6,7,5,3,2,1,4]=>[6,1,1]
[7,6,8,5,3,2,1,4]=>[6,1,1]
[6,7,8,5,3,2,1,4]=>[5,1,1,1]
[8,7,5,6,3,2,1,4]=>[6,1,1]
[7,8,5,6,3,2,1,4]=>[5,1,1,1]
[8,6,5,7,3,2,1,4]=>[6,1,1]
[8,5,6,7,3,2,1,4]=>[5,1,1,1]
[7,6,5,8,3,2,1,4]=>[6,1,1]
[6,7,5,8,3,2,1,4]=>[5,1,1,1]
[7,5,6,8,3,2,1,4]=>[5,1,1,1]
[6,5,7,8,3,2,1,4]=>[5,1,1,1]
[5,6,7,8,3,2,1,4]=>[4,1,1,1,1]
[8,7,6,5,2,3,1,4]=>[6,1,1]
[7,8,6,5,2,3,1,4]=>[5,1,1,1]
[8,6,7,5,2,3,1,4]=>[5,1,1,1]
[7,6,8,5,2,3,1,4]=>[5,1,1,1]
[8,7,5,6,2,3,1,4]=>[5,1,1,1]
[7,8,5,6,2,3,1,4]=>[4,1,1,1,1]
[8,5,6,7,2,3,1,4]=>[4,1,1,1,1]
[7,6,5,8,2,3,1,4]=>[5,1,1,1]
[6,7,5,8,2,3,1,4]=>[4,1,1,1,1]
[7,5,6,8,2,3,1,4]=>[4,1,1,1,1]
[5,6,7,8,2,3,1,4]=>[3,1,1,1,1,1]
[8,7,6,5,3,1,2,4]=>[6,1,1]
[7,8,6,5,3,1,2,4]=>[5,1,1,1]
[8,6,7,5,3,1,2,4]=>[5,1,1,1]
[7,6,8,5,3,1,2,4]=>[5,1,1,1]
[8,7,5,6,3,1,2,4]=>[5,1,1,1]
[7,8,5,6,3,1,2,4]=>[4,1,1,1,1]
[7,6,5,8,3,1,2,4]=>[5,1,1,1]
[6,7,5,8,3,1,2,4]=>[4,1,1,1,1]
[7,5,6,8,3,1,2,4]=>[4,1,1,1,1]
[6,5,7,8,3,1,2,4]=>[4,1,1,1,1]
[5,6,7,8,3,1,2,4]=>[3,1,1,1,1,1]
[8,7,6,5,2,1,3,4]=>[6,1,1]
[7,8,6,5,2,1,3,4]=>[5,1,1,1]
[7,6,8,5,2,1,3,4]=>[5,1,1,1]
[6,7,8,5,2,1,3,4]=>[4,1,1,1,1]
[8,7,5,6,2,1,3,4]=>[5,1,1,1]
[7,8,5,6,2,1,3,4]=>[4,1,1,1,1]
[8,6,5,7,2,1,3,4]=>[5,1,1,1]
[8,5,6,7,2,1,3,4]=>[4,1,1,1,1]
[7,6,5,8,2,1,3,4]=>[5,1,1,1]
[6,7,5,8,2,1,3,4]=>[4,1,1,1,1]
[7,5,6,8,2,1,3,4]=>[4,1,1,1,1]
[6,5,7,8,2,1,3,4]=>[4,1,1,1,1]
[5,6,7,8,2,1,3,4]=>[3,1,1,1,1,1]
[8,7,6,5,1,2,3,4]=>[5,1,1,1]
[7,8,6,5,1,2,3,4]=>[4,1,1,1,1]
[8,6,7,5,1,2,3,4]=>[4,1,1,1,1]
[7,6,8,5,1,2,3,4]=>[4,1,1,1,1]
[6,7,8,5,1,2,3,4]=>[3,1,1,1,1,1]
[8,7,5,6,1,2,3,4]=>[4,1,1,1,1]
[7,8,5,6,1,2,3,4]=>[3,1,1,1,1,1]
[8,6,5,7,1,2,3,4]=>[4,1,1,1,1]
[8,5,6,7,1,2,3,4]=>[3,1,1,1,1,1]
[7,6,5,8,1,2,3,4]=>[4,1,1,1,1]
[6,7,5,8,1,2,3,4]=>[3,1,1,1,1,1]
[7,5,6,8,1,2,3,4]=>[3,1,1,1,1,1]
[6,5,7,8,1,2,3,4]=>[3,1,1,1,1,1]
[5,6,7,8,1,2,3,4]=>[2,1,1,1,1,1,1]
[8,7,6,4,3,2,1,5]=>[7,1]
[7,8,6,4,3,2,1,5]=>[6,1,1]
[8,6,7,4,3,2,1,5]=>[6,1,1]
[7,6,8,4,3,2,1,5]=>[6,1,1]
[6,7,8,4,3,2,1,5]=>[5,1,1,1]
[8,7,6,3,4,2,1,5]=>[6,1,1]
[7,8,6,3,4,2,1,5]=>[5,1,1,1]
[6,7,8,3,4,2,1,5]=>[4,1,1,1,1]
[8,7,6,4,2,3,1,5]=>[6,1,1]
[8,6,7,4,2,3,1,5]=>[5,1,1,1]
[7,6,8,4,2,3,1,5]=>[5,1,1,1]
[6,7,8,4,2,3,1,5]=>[4,1,1,1,1]
[8,7,6,3,2,4,1,5]=>[6,1,1]
[8,6,7,3,2,4,1,5]=>[5,1,1,1]
[6,7,8,3,2,4,1,5]=>[4,1,1,1,1]
[8,7,6,2,3,4,1,5]=>[5,1,1,1]
[8,6,7,2,3,4,1,5]=>[4,1,1,1,1]
[7,6,8,2,3,4,1,5]=>[4,1,1,1,1]
[6,7,8,2,3,4,1,5]=>[3,1,1,1,1,1]
[8,7,6,4,3,1,2,5]=>[6,1,1]
[6,7,8,4,3,1,2,5]=>[4,1,1,1,1]
[8,7,6,3,4,1,2,5]=>[5,1,1,1]
[7,8,6,3,4,1,2,5]=>[4,1,1,1,1]
[8,6,7,3,4,1,2,5]=>[4,1,1,1,1]
[6,7,8,3,4,1,2,5]=>[3,1,1,1,1,1]
[8,7,6,4,2,1,3,5]=>[6,1,1]
[7,8,6,4,2,1,3,5]=>[5,1,1,1]
[8,6,7,4,2,1,3,5]=>[5,1,1,1]
[6,7,8,4,2,1,3,5]=>[4,1,1,1,1]
[8,7,6,4,1,2,3,5]=>[5,1,1,1]
[7,8,6,4,1,2,3,5]=>[4,1,1,1,1]
[7,6,8,4,1,2,3,5]=>[4,1,1,1,1]
[6,7,8,4,1,2,3,5]=>[3,1,1,1,1,1]
[8,7,6,3,2,1,4,5]=>[6,1,1]
[7,8,6,3,2,1,4,5]=>[5,1,1,1]
[8,6,7,3,2,1,4,5]=>[5,1,1,1]
[7,6,8,3,2,1,4,5]=>[5,1,1,1]
[6,7,8,3,2,1,4,5]=>[4,1,1,1,1]
[8,7,6,2,3,1,4,5]=>[5,1,1,1]
[7,8,6,2,3,1,4,5]=>[4,1,1,1,1]
[8,6,7,2,3,1,4,5]=>[4,1,1,1,1]
[6,7,8,2,3,1,4,5]=>[3,1,1,1,1,1]
[8,7,6,3,1,2,4,5]=>[5,1,1,1]
[7,8,6,3,1,2,4,5]=>[4,1,1,1,1]
[8,6,7,3,1,2,4,5]=>[4,1,1,1,1]
[7,6,8,3,1,2,4,5]=>[4,1,1,1,1]
[6,7,8,3,1,2,4,5]=>[3,1,1,1,1,1]
[8,7,6,2,1,3,4,5]=>[5,1,1,1]
[8,6,7,2,1,3,4,5]=>[4,1,1,1,1]
[6,7,8,2,1,3,4,5]=>[3,1,1,1,1,1]
[8,7,6,1,2,3,4,5]=>[4,1,1,1,1]
[7,8,6,1,2,3,4,5]=>[3,1,1,1,1,1]
[8,6,7,1,2,3,4,5]=>[3,1,1,1,1,1]
[7,6,8,1,2,3,4,5]=>[3,1,1,1,1,1]
[6,7,8,1,2,3,4,5]=>[2,1,1,1,1,1,1]
[8,7,5,4,3,2,1,6]=>[7,1]
[7,8,5,4,3,2,1,6]=>[6,1,1]
[8,7,4,5,3,2,1,6]=>[6,1,1]
[7,8,4,5,3,2,1,6]=>[5,1,1,1]
[8,7,5,3,4,2,1,6]=>[6,1,1]
[8,7,3,4,5,2,1,6]=>[5,1,1,1]
[7,8,3,4,5,2,1,6]=>[4,1,1,1,1]
[8,7,4,5,2,3,1,6]=>[5,1,1,1]
[7,8,4,5,2,3,1,6]=>[4,1,1,1,1]
[8,7,5,3,2,4,1,6]=>[6,1,1]
[7,8,5,2,3,4,1,6]=>[4,1,1,1,1]
[8,7,4,3,2,5,1,6]=>[6,1,1]
[7,8,4,3,2,5,1,6]=>[5,1,1,1]
[8,7,3,4,2,5,1,6]=>[5,1,1,1]
[7,8,3,4,2,5,1,6]=>[4,1,1,1,1]
[8,7,2,3,4,5,1,6]=>[4,1,1,1,1]
[7,8,2,3,4,5,1,6]=>[3,1,1,1,1,1]
[8,7,5,4,3,1,2,6]=>[6,1,1]
[7,8,5,4,3,1,2,6]=>[5,1,1,1]
[8,7,5,3,4,1,2,6]=>[5,1,1,1]
[7,8,5,3,4,1,2,6]=>[4,1,1,1,1]
[8,7,3,4,5,1,2,6]=>[4,1,1,1,1]
[7,8,3,4,5,1,2,6]=>[3,1,1,1,1,1]
[7,8,5,4,2,1,3,6]=>[5,1,1,1]
[8,7,5,4,1,2,3,6]=>[5,1,1,1]
[7,8,5,4,1,2,3,6]=>[4,1,1,1,1]
[8,7,4,5,1,2,3,6]=>[4,1,1,1,1]
[7,8,4,5,1,2,3,6]=>[3,1,1,1,1,1]
[8,7,5,3,2,1,4,6]=>[6,1,1]
[7,8,5,3,2,1,4,6]=>[5,1,1,1]
[8,7,5,2,3,1,4,6]=>[5,1,1,1]
[8,7,5,3,1,2,4,6]=>[5,1,1,1]
[7,8,5,3,1,2,4,6]=>[4,1,1,1,1]
[8,7,5,2,1,3,4,6]=>[5,1,1,1]
[7,8,5,2,1,3,4,6]=>[4,1,1,1,1]
[8,7,5,1,2,3,4,6]=>[4,1,1,1,1]
[7,8,5,1,2,3,4,6]=>[3,1,1,1,1,1]
[8,7,4,3,2,1,5,6]=>[6,1,1]
[7,8,4,3,2,1,5,6]=>[5,1,1,1]
[8,7,3,4,2,1,5,6]=>[5,1,1,1]
[7,8,3,4,2,1,5,6]=>[4,1,1,1,1]
[7,8,4,2,3,1,5,6]=>[4,1,1,1,1]
[8,7,3,2,4,1,5,6]=>[5,1,1,1]
[7,8,3,2,4,1,5,6]=>[4,1,1,1,1]
[8,7,2,3,4,1,5,6]=>[4,1,1,1,1]
[7,8,2,3,4,1,5,6]=>[3,1,1,1,1,1]
[7,8,4,3,1,2,5,6]=>[4,1,1,1,1]
[8,7,3,4,1,2,5,6]=>[4,1,1,1,1]
[7,8,3,4,1,2,5,6]=>[3,1,1,1,1,1]
[8,7,4,2,1,3,5,6]=>[5,1,1,1]
[7,8,4,2,1,3,5,6]=>[4,1,1,1,1]
[8,7,4,1,2,3,5,6]=>[4,1,1,1,1]
[7,8,4,1,2,3,5,6]=>[3,1,1,1,1,1]
[8,7,3,2,1,4,5,6]=>[5,1,1,1]
[7,8,3,2,1,4,5,6]=>[4,1,1,1,1]
[8,7,2,3,1,4,5,6]=>[4,1,1,1,1]
[7,8,2,3,1,4,5,6]=>[3,1,1,1,1,1]
[7,8,3,1,2,4,5,6]=>[3,1,1,1,1,1]
[8,7,2,1,3,4,5,6]=>[4,1,1,1,1]
[7,8,2,1,3,4,5,6]=>[3,1,1,1,1,1]
[8,7,1,2,3,4,5,6]=>[3,1,1,1,1,1]
[7,8,1,2,3,4,5,6]=>[2,1,1,1,1,1,1]
[8,6,5,4,3,2,1,7]=>[7,1]
[8,5,6,4,3,2,1,7]=>[6,1,1]
[8,6,4,5,3,2,1,7]=>[6,1,1]
[8,4,5,6,3,2,1,7]=>[5,1,1,1]
[8,6,5,3,4,2,1,7]=>[6,1,1]
[8,5,6,3,4,2,1,7]=>[5,1,1,1]
[8,6,4,3,5,2,1,7]=>[6,1,1]
[8,4,5,3,6,2,1,7]=>[5,1,1,1]
[8,4,3,5,6,2,1,7]=>[5,1,1,1]
[8,3,4,5,6,2,1,7]=>[4,1,1,1,1]
[8,6,5,4,2,3,1,7]=>[6,1,1]
[8,5,6,4,2,3,1,7]=>[5,1,1,1]
[8,6,4,5,2,3,1,7]=>[5,1,1,1]
[8,4,5,6,2,3,1,7]=>[4,1,1,1,1]
[8,6,5,3,2,4,1,7]=>[6,1,1]
[8,6,5,2,3,4,1,7]=>[5,1,1,1]
[8,5,6,2,3,4,1,7]=>[4,1,1,1,1]
[8,6,4,3,2,5,1,7]=>[6,1,1]
[8,6,4,2,3,5,1,7]=>[5,1,1,1]
[8,6,3,2,4,5,1,7]=>[5,1,1,1]
[8,5,4,3,2,6,1,7]=>[6,1,1]
[8,4,3,5,2,6,1,7]=>[5,1,1,1]
[8,5,4,2,3,6,1,7]=>[5,1,1,1]
[8,4,5,2,3,6,1,7]=>[4,1,1,1,1]
[8,5,3,2,4,6,1,7]=>[5,1,1,1]
[8,5,2,3,4,6,1,7]=>[4,1,1,1,1]
[8,3,4,2,5,6,1,7]=>[4,1,1,1,1]
[8,3,2,4,5,6,1,7]=>[4,1,1,1,1]
[8,2,3,4,5,6,1,7]=>[3,1,1,1,1,1]
[8,6,5,4,3,1,2,7]=>[6,1,1]
[8,6,4,5,3,1,2,7]=>[5,1,1,1]
[8,6,5,3,4,1,2,7]=>[5,1,1,1]
[8,5,6,3,4,1,2,7]=>[4,1,1,1,1]
[8,6,3,4,5,1,2,7]=>[4,1,1,1,1]
[8,5,4,3,6,1,2,7]=>[5,1,1,1]
[8,4,5,3,6,1,2,7]=>[4,1,1,1,1]
[8,5,3,4,6,1,2,7]=>[4,1,1,1,1]
[8,4,3,5,6,1,2,7]=>[4,1,1,1,1]
[8,3,4,5,6,1,2,7]=>[3,1,1,1,1,1]
[8,6,5,4,2,1,3,7]=>[6,1,1]
[8,5,6,4,2,1,3,7]=>[5,1,1,1]
[8,6,4,5,2,1,3,7]=>[5,1,1,1]
[8,4,5,6,2,1,3,7]=>[4,1,1,1,1]
[8,6,5,4,1,2,3,7]=>[5,1,1,1]
[8,5,6,4,1,2,3,7]=>[4,1,1,1,1]
[8,6,4,5,1,2,3,7]=>[4,1,1,1,1]
[8,4,5,6,1,2,3,7]=>[3,1,1,1,1,1]
[8,6,5,3,2,1,4,7]=>[6,1,1]
[8,5,6,3,2,1,4,7]=>[5,1,1,1]
[8,6,5,2,3,1,4,7]=>[5,1,1,1]
[8,5,6,2,3,1,4,7]=>[4,1,1,1,1]
[8,5,6,3,1,2,4,7]=>[4,1,1,1,1]
[8,6,5,2,1,3,4,7]=>[5,1,1,1]
[8,5,6,2,1,3,4,7]=>[4,1,1,1,1]
[8,6,5,1,2,3,4,7]=>[4,1,1,1,1]
[8,5,6,1,2,3,4,7]=>[3,1,1,1,1,1]
[8,6,4,3,2,1,5,7]=>[6,1,1]
[8,6,3,4,2,1,5,7]=>[5,1,1,1]
[8,6,4,2,3,1,5,7]=>[5,1,1,1]
[8,6,3,2,4,1,5,7]=>[5,1,1,1]
[8,6,2,3,4,1,5,7]=>[4,1,1,1,1]
[8,6,4,3,1,2,5,7]=>[5,1,1,1]
[8,6,3,4,1,2,5,7]=>[4,1,1,1,1]
[8,6,4,2,1,3,5,7]=>[5,1,1,1]
[8,6,4,1,2,3,5,7]=>[4,1,1,1,1]
[8,6,3,2,1,4,5,7]=>[5,1,1,1]
[8,6,1,2,3,4,5,7]=>[3,1,1,1,1,1]
[8,5,4,3,2,1,6,7]=>[6,1,1]
[8,4,5,3,2,1,6,7]=>[5,1,1,1]
[8,4,3,5,2,1,6,7]=>[5,1,1,1]
[8,3,4,5,2,1,6,7]=>[4,1,1,1,1]
[8,4,5,2,3,1,6,7]=>[4,1,1,1,1]
[8,5,2,3,4,1,6,7]=>[4,1,1,1,1]
[8,4,2,3,5,1,6,7]=>[4,1,1,1,1]
[8,2,3,4,5,1,6,7]=>[3,1,1,1,1,1]
[8,5,3,4,1,2,6,7]=>[4,1,1,1,1]
[8,3,4,5,1,2,6,7]=>[3,1,1,1,1,1]
[8,5,4,2,1,3,6,7]=>[5,1,1,1]
[8,5,4,1,2,3,6,7]=>[4,1,1,1,1]
[8,4,5,1,2,3,6,7]=>[3,1,1,1,1,1]
[8,5,3,2,1,4,6,7]=>[5,1,1,1]
[8,5,3,1,2,4,6,7]=>[4,1,1,1,1]
[8,5,2,1,3,4,6,7]=>[4,1,1,1,1]
[8,5,1,2,3,4,6,7]=>[3,1,1,1,1,1]
[8,4,3,2,1,5,6,7]=>[5,1,1,1]
[8,3,4,2,1,5,6,7]=>[4,1,1,1,1]
[8,4,2,3,1,5,6,7]=>[4,1,1,1,1]
[8,2,3,4,1,5,6,7]=>[3,1,1,1,1,1]
[8,3,4,1,2,5,6,7]=>[3,1,1,1,1,1]
[8,4,2,1,3,5,6,7]=>[4,1,1,1,1]
[8,4,1,2,3,5,6,7]=>[3,1,1,1,1,1]
[8,3,2,1,4,5,6,7]=>[4,1,1,1,1]
[8,2,3,1,4,5,6,7]=>[3,1,1,1,1,1]
[8,3,1,2,4,5,6,7]=>[3,1,1,1,1,1]
[8,2,1,3,4,5,6,7]=>[3,1,1,1,1,1]
[8,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[7,6,5,4,3,2,1,8]=>[7,1]
[6,7,5,4,3,2,1,8]=>[6,1,1]
[7,5,6,4,3,2,1,8]=>[6,1,1]
[6,5,7,4,3,2,1,8]=>[6,1,1]
[5,6,7,4,3,2,1,8]=>[5,1,1,1]
[7,6,4,5,3,2,1,8]=>[6,1,1]
[6,7,4,5,3,2,1,8]=>[5,1,1,1]
[7,5,4,6,3,2,1,8]=>[6,1,1]
[7,4,5,6,3,2,1,8]=>[5,1,1,1]
[6,5,4,7,3,2,1,8]=>[6,1,1]
[5,6,4,7,3,2,1,8]=>[5,1,1,1]
[5,4,6,7,3,2,1,8]=>[5,1,1,1]
[4,5,6,7,3,2,1,8]=>[4,1,1,1,1]
[7,6,5,3,4,2,1,8]=>[6,1,1]
[6,7,5,3,4,2,1,8]=>[5,1,1,1]
[7,5,6,3,4,2,1,8]=>[5,1,1,1]
[6,5,7,3,4,2,1,8]=>[5,1,1,1]
[5,6,7,3,4,2,1,8]=>[4,1,1,1,1]
[7,6,4,3,5,2,1,8]=>[6,1,1]
[6,7,4,3,5,2,1,8]=>[5,1,1,1]
[7,6,3,4,5,2,1,8]=>[5,1,1,1]
[7,5,4,3,6,2,1,8]=>[6,1,1]
[7,4,5,3,6,2,1,8]=>[5,1,1,1]
[7,3,4,5,6,2,1,8]=>[4,1,1,1,1]
[6,5,4,3,7,2,1,8]=>[6,1,1]
[5,6,4,3,7,2,1,8]=>[5,1,1,1]
[5,4,6,3,7,2,1,8]=>[5,1,1,1]
[5,4,3,6,7,2,1,8]=>[5,1,1,1]
[3,4,5,6,7,2,1,8]=>[3,1,1,1,1,1]
[7,6,5,4,2,3,1,8]=>[6,1,1]
[6,7,5,4,2,3,1,8]=>[5,1,1,1]
[7,5,6,4,2,3,1,8]=>[5,1,1,1]
[5,6,7,4,2,3,1,8]=>[4,1,1,1,1]
[7,6,4,5,2,3,1,8]=>[5,1,1,1]
[6,7,4,5,2,3,1,8]=>[4,1,1,1,1]
[7,5,4,6,2,3,1,8]=>[5,1,1,1]
[7,4,5,6,2,3,1,8]=>[4,1,1,1,1]
[6,5,4,7,2,3,1,8]=>[5,1,1,1]
[5,6,4,7,2,3,1,8]=>[4,1,1,1,1]
[5,4,6,7,2,3,1,8]=>[4,1,1,1,1]
[4,5,6,7,2,3,1,8]=>[3,1,1,1,1,1]
[7,6,5,3,2,4,1,8]=>[6,1,1]
[6,5,7,3,2,4,1,8]=>[5,1,1,1]
[5,6,7,3,2,4,1,8]=>[4,1,1,1,1]
[7,6,5,2,3,4,1,8]=>[5,1,1,1]
[6,7,5,2,3,4,1,8]=>[4,1,1,1,1]
[7,5,6,2,3,4,1,8]=>[4,1,1,1,1]
[6,5,7,2,3,4,1,8]=>[4,1,1,1,1]
[5,6,7,2,3,4,1,8]=>[3,1,1,1,1,1]
[7,6,4,3,2,5,1,8]=>[6,1,1]
[6,7,4,3,2,5,1,8]=>[5,1,1,1]
[6,7,3,4,2,5,1,8]=>[4,1,1,1,1]
[7,6,4,2,3,5,1,8]=>[5,1,1,1]
[6,7,4,2,3,5,1,8]=>[4,1,1,1,1]
[7,6,3,2,4,5,1,8]=>[5,1,1,1]
[6,7,3,2,4,5,1,8]=>[4,1,1,1,1]
[7,6,2,3,4,5,1,8]=>[4,1,1,1,1]
[6,7,2,3,4,5,1,8]=>[3,1,1,1,1,1]
[7,5,4,3,2,6,1,8]=>[6,1,1]
[7,4,5,3,2,6,1,8]=>[5,1,1,1]
[7,5,3,4,2,6,1,8]=>[5,1,1,1]
[7,4,3,5,2,6,1,8]=>[5,1,1,1]
[7,4,5,2,3,6,1,8]=>[4,1,1,1,1]
[7,5,3,2,4,6,1,8]=>[5,1,1,1]
[7,4,2,3,5,6,1,8]=>[4,1,1,1,1]
[7,2,3,4,5,6,1,8]=>[3,1,1,1,1,1]
[6,5,4,3,2,7,1,8]=>[6,1,1]
[5,6,4,3,2,7,1,8]=>[5,1,1,1]
[5,4,6,3,2,7,1,8]=>[5,1,1,1]
[5,6,3,4,2,7,1,8]=>[4,1,1,1,1]
[6,3,4,5,2,7,1,8]=>[4,1,1,1,1]
[5,4,3,6,2,7,1,8]=>[5,1,1,1]
[4,5,3,6,2,7,1,8]=>[4,1,1,1,1]
[5,3,4,6,2,7,1,8]=>[4,1,1,1,1]
[4,3,5,6,2,7,1,8]=>[4,1,1,1,1]
[3,4,5,6,2,7,1,8]=>[3,1,1,1,1,1]
[5,4,6,2,3,7,1,8]=>[4,1,1,1,1]
[6,5,3,2,4,7,1,8]=>[5,1,1,1]
[6,4,2,3,5,7,1,8]=>[4,1,1,1,1]
[6,3,2,4,5,7,1,8]=>[4,1,1,1,1]
[6,2,3,4,5,7,1,8]=>[3,1,1,1,1,1]
[5,4,3,2,6,7,1,8]=>[5,1,1,1]
[5,4,2,3,6,7,1,8]=>[4,1,1,1,1]
[4,5,2,3,6,7,1,8]=>[3,1,1,1,1,1]
[5,2,3,4,6,7,1,8]=>[3,1,1,1,1,1]
[4,3,2,5,6,7,1,8]=>[4,1,1,1,1]
[3,4,2,5,6,7,1,8]=>[3,1,1,1,1,1]
[4,2,3,5,6,7,1,8]=>[3,1,1,1,1,1]
[3,2,4,5,6,7,1,8]=>[3,1,1,1,1,1]
[2,3,4,5,6,7,1,8]=>[2,1,1,1,1,1,1]
[7,6,5,4,3,1,2,8]=>[6,1,1]
[6,7,5,4,3,1,2,8]=>[5,1,1,1]
[7,5,6,4,3,1,2,8]=>[5,1,1,1]
[7,6,4,5,3,1,2,8]=>[5,1,1,1]
[7,4,5,6,3,1,2,8]=>[4,1,1,1,1]
[5,4,6,7,3,1,2,8]=>[4,1,1,1,1]
[4,5,6,7,3,1,2,8]=>[3,1,1,1,1,1]
[7,6,5,3,4,1,2,8]=>[5,1,1,1]
[7,5,6,3,4,1,2,8]=>[4,1,1,1,1]
[6,7,3,4,5,1,2,8]=>[3,1,1,1,1,1]
[7,5,3,4,6,1,2,8]=>[4,1,1,1,1]
[6,5,4,3,7,1,2,8]=>[5,1,1,1]
[6,4,5,3,7,1,2,8]=>[4,1,1,1,1]
[6,4,3,5,7,1,2,8]=>[4,1,1,1,1]
[6,3,4,5,7,1,2,8]=>[3,1,1,1,1,1]
[4,3,5,6,7,1,2,8]=>[3,1,1,1,1,1]
[3,4,5,6,7,1,2,8]=>[2,1,1,1,1,1,1]
[7,6,5,4,2,1,3,8]=>[6,1,1]
[6,5,7,4,2,1,3,8]=>[5,1,1,1]
[7,6,4,5,2,1,3,8]=>[5,1,1,1]
[7,5,4,6,2,1,3,8]=>[5,1,1,1]
[7,4,5,6,2,1,3,8]=>[4,1,1,1,1]
[5,4,6,7,2,1,3,8]=>[4,1,1,1,1]
[4,5,6,7,2,1,3,8]=>[3,1,1,1,1,1]
[7,6,5,4,1,2,3,8]=>[5,1,1,1]
[7,5,6,4,1,2,3,8]=>[4,1,1,1,1]
[5,6,7,4,1,2,3,8]=>[3,1,1,1,1,1]
[7,6,4,5,1,2,3,8]=>[4,1,1,1,1]
[7,5,4,6,1,2,3,8]=>[4,1,1,1,1]
[7,4,5,6,1,2,3,8]=>[3,1,1,1,1,1]
[5,4,6,7,1,2,3,8]=>[3,1,1,1,1,1]
[4,5,6,7,1,2,3,8]=>[2,1,1,1,1,1,1]
[7,6,5,3,2,1,4,8]=>[6,1,1]
[7,6,5,2,3,1,4,8]=>[5,1,1,1]
[6,7,5,2,3,1,4,8]=>[4,1,1,1,1]
[7,5,6,2,3,1,4,8]=>[4,1,1,1,1]
[6,5,7,2,3,1,4,8]=>[4,1,1,1,1]
[5,6,7,2,3,1,4,8]=>[3,1,1,1,1,1]
[7,5,6,3,1,2,4,8]=>[4,1,1,1,1]
[7,6,5,2,1,3,4,8]=>[5,1,1,1]
[6,7,5,2,1,3,4,8]=>[4,1,1,1,1]
[7,5,6,2,1,3,4,8]=>[4,1,1,1,1]
[5,6,7,2,1,3,4,8]=>[3,1,1,1,1,1]
[7,6,5,1,2,3,4,8]=>[4,1,1,1,1]
[6,7,5,1,2,3,4,8]=>[3,1,1,1,1,1]
[7,5,6,1,2,3,4,8]=>[3,1,1,1,1,1]
[6,5,7,1,2,3,4,8]=>[3,1,1,1,1,1]
[5,6,7,1,2,3,4,8]=>[2,1,1,1,1,1,1]
[7,6,4,3,2,1,5,8]=>[6,1,1]
[6,7,4,3,2,1,5,8]=>[5,1,1,1]
[7,6,3,4,2,1,5,8]=>[5,1,1,1]
[6,7,3,4,2,1,5,8]=>[4,1,1,1,1]
[7,6,4,2,3,1,5,8]=>[5,1,1,1]
[7,6,3,2,4,1,5,8]=>[5,1,1,1]
[6,7,3,2,4,1,5,8]=>[4,1,1,1,1]
[7,6,2,3,4,1,5,8]=>[4,1,1,1,1]
[6,7,2,3,4,1,5,8]=>[3,1,1,1,1,1]
[7,6,4,3,1,2,5,8]=>[5,1,1,1]
[6,7,3,4,1,2,5,8]=>[3,1,1,1,1,1]
[7,6,4,2,1,3,5,8]=>[5,1,1,1]
[7,6,3,2,1,4,5,8]=>[5,1,1,1]
[6,7,3,2,1,4,5,8]=>[4,1,1,1,1]
[7,6,2,3,1,4,5,8]=>[4,1,1,1,1]
[6,7,2,3,1,4,5,8]=>[3,1,1,1,1,1]
[6,7,3,1,2,4,5,8]=>[3,1,1,1,1,1]
[7,6,1,2,3,4,5,8]=>[3,1,1,1,1,1]
[6,7,1,2,3,4,5,8]=>[2,1,1,1,1,1,1]
[7,5,4,3,2,1,6,8]=>[6,1,1]
[7,4,5,3,2,1,6,8]=>[5,1,1,1]
[7,4,3,5,2,1,6,8]=>[5,1,1,1]
[7,3,4,5,2,1,6,8]=>[4,1,1,1,1]
[7,5,4,2,3,1,6,8]=>[5,1,1,1]
[7,5,3,2,4,1,6,8]=>[5,1,1,1]
[7,5,2,3,4,1,6,8]=>[4,1,1,1,1]
[7,4,2,3,5,1,6,8]=>[4,1,1,1,1]
[7,2,3,4,5,1,6,8]=>[3,1,1,1,1,1]
[7,5,4,3,1,2,6,8]=>[5,1,1,1]
[7,5,3,4,1,2,6,8]=>[4,1,1,1,1]
[7,4,5,2,1,3,6,8]=>[4,1,1,1,1]
[7,4,5,1,2,3,6,8]=>[3,1,1,1,1,1]
[7,5,3,2,1,4,6,8]=>[5,1,1,1]
[7,5,2,3,1,4,6,8]=>[4,1,1,1,1]
[7,5,3,1,2,4,6,8]=>[4,1,1,1,1]
[7,5,1,2,3,4,6,8]=>[3,1,1,1,1,1]
[7,4,3,2,1,5,6,8]=>[5,1,1,1]
[7,2,3,4,1,5,6,8]=>[3,1,1,1,1,1]
[7,4,3,1,2,5,6,8]=>[4,1,1,1,1]
[7,3,4,1,2,5,6,8]=>[3,1,1,1,1,1]
[7,4,1,2,3,5,6,8]=>[3,1,1,1,1,1]
[7,3,2,1,4,5,6,8]=>[4,1,1,1,1]
[7,2,3,1,4,5,6,8]=>[3,1,1,1,1,1]
[7,3,1,2,4,5,6,8]=>[3,1,1,1,1,1]
[7,2,1,3,4,5,6,8]=>[3,1,1,1,1,1]
[7,1,2,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[6,5,4,3,2,1,7,8]=>[6,1,1]
[5,6,4,3,2,1,7,8]=>[5,1,1,1]
[5,4,6,3,2,1,7,8]=>[5,1,1,1]
[4,5,6,3,2,1,7,8]=>[4,1,1,1,1]
[6,5,3,4,2,1,7,8]=>[5,1,1,1]
[5,6,3,4,2,1,7,8]=>[4,1,1,1,1]
[5,4,3,6,2,1,7,8]=>[5,1,1,1]
[5,4,6,2,3,1,7,8]=>[4,1,1,1,1]
[5,6,3,2,4,1,7,8]=>[4,1,1,1,1]
[6,5,2,3,4,1,7,8]=>[4,1,1,1,1]
[5,6,2,3,4,1,7,8]=>[3,1,1,1,1,1]
[6,4,3,2,5,1,7,8]=>[5,1,1,1]
[6,2,3,4,5,1,7,8]=>[3,1,1,1,1,1]
[5,4,3,2,6,1,7,8]=>[5,1,1,1]
[4,5,3,2,6,1,7,8]=>[4,1,1,1,1]
[4,3,5,2,6,1,7,8]=>[4,1,1,1,1]
[3,4,5,2,6,1,7,8]=>[3,1,1,1,1,1]
[5,3,2,4,6,1,7,8]=>[4,1,1,1,1]
[5,2,3,4,6,1,7,8]=>[3,1,1,1,1,1]
[4,3,2,5,6,1,7,8]=>[4,1,1,1,1]
[3,4,2,5,6,1,7,8]=>[3,1,1,1,1,1]
[4,2,3,5,6,1,7,8]=>[3,1,1,1,1,1]
[3,2,4,5,6,1,7,8]=>[3,1,1,1,1,1]
[2,3,4,5,6,1,7,8]=>[2,1,1,1,1,1,1]
[6,5,4,3,1,2,7,8]=>[5,1,1,1]
[6,4,5,3,1,2,7,8]=>[4,1,1,1,1]
[5,6,3,4,1,2,7,8]=>[3,1,1,1,1,1]
[5,4,3,6,1,2,7,8]=>[4,1,1,1,1]
[4,3,5,6,1,2,7,8]=>[3,1,1,1,1,1]
[3,4,5,6,1,2,7,8]=>[2,1,1,1,1,1,1]
[6,5,4,2,1,3,7,8]=>[5,1,1,1]
[5,6,4,2,1,3,7,8]=>[4,1,1,1,1]
[6,4,5,2,1,3,7,8]=>[4,1,1,1,1]
[6,5,4,1,2,3,7,8]=>[4,1,1,1,1]
[4,5,6,1,2,3,7,8]=>[2,1,1,1,1,1,1]
[6,5,3,2,1,4,7,8]=>[5,1,1,1]
[5,6,3,2,1,4,7,8]=>[4,1,1,1,1]
[5,6,2,1,3,4,7,8]=>[3,1,1,1,1,1]
[6,4,3,2,1,5,7,8]=>[5,1,1,1]
[6,3,4,2,1,5,7,8]=>[4,1,1,1,1]
[6,4,3,1,2,5,7,8]=>[4,1,1,1,1]
[6,4,2,1,3,5,7,8]=>[4,1,1,1,1]
[6,4,1,2,3,5,7,8]=>[3,1,1,1,1,1]
[6,3,2,1,4,5,7,8]=>[4,1,1,1,1]
[6,2,3,1,4,5,7,8]=>[3,1,1,1,1,1]
[6,3,1,2,4,5,7,8]=>[3,1,1,1,1,1]
[6,2,1,3,4,5,7,8]=>[3,1,1,1,1,1]
[6,1,2,3,4,5,7,8]=>[2,1,1,1,1,1,1]
[5,4,3,2,1,6,7,8]=>[5,1,1,1]
[4,5,3,2,1,6,7,8]=>[4,1,1,1,1]
[5,3,4,2,1,6,7,8]=>[4,1,1,1,1]
[4,3,5,2,1,6,7,8]=>[4,1,1,1,1]
[3,4,5,2,1,6,7,8]=>[3,1,1,1,1,1]
[5,4,2,3,1,6,7,8]=>[4,1,1,1,1]
[4,5,2,3,1,6,7,8]=>[3,1,1,1,1,1]
[5,3,2,4,1,6,7,8]=>[4,1,1,1,1]
[5,2,3,4,1,6,7,8]=>[3,1,1,1,1,1]
[4,3,2,5,1,6,7,8]=>[4,1,1,1,1]
[3,4,2,5,1,6,7,8]=>[3,1,1,1,1,1]
[4,2,3,5,1,6,7,8]=>[3,1,1,1,1,1]
[3,2,4,5,1,6,7,8]=>[3,1,1,1,1,1]
[2,3,4,5,1,6,7,8]=>[2,1,1,1,1,1,1]
[5,4,3,1,2,6,7,8]=>[4,1,1,1,1]
[5,3,4,1,2,6,7,8]=>[3,1,1,1,1,1]
[4,3,5,1,2,6,7,8]=>[3,1,1,1,1,1]
[3,4,5,1,2,6,7,8]=>[2,1,1,1,1,1,1]
[5,4,2,1,3,6,7,8]=>[4,1,1,1,1]
[4,5,2,1,3,6,7,8]=>[3,1,1,1,1,1]
[5,4,1,2,3,6,7,8]=>[3,1,1,1,1,1]
[4,5,1,2,3,6,7,8]=>[2,1,1,1,1,1,1]
[5,3,2,1,4,6,7,8]=>[4,1,1,1,1]
[5,2,3,1,4,6,7,8]=>[3,1,1,1,1,1]
[5,3,1,2,4,6,7,8]=>[3,1,1,1,1,1]
[5,2,1,3,4,6,7,8]=>[3,1,1,1,1,1]
[5,1,2,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[4,3,2,1,5,6,7,8]=>[4,1,1,1,1]
[3,4,2,1,5,6,7,8]=>[3,1,1,1,1,1]
[4,2,3,1,5,6,7,8]=>[3,1,1,1,1,1]
[3,2,4,1,5,6,7,8]=>[3,1,1,1,1,1]
[2,3,4,1,5,6,7,8]=>[2,1,1,1,1,1,1]
[4,3,1,2,5,6,7,8]=>[3,1,1,1,1,1]
[3,4,1,2,5,6,7,8]=>[2,1,1,1,1,1,1]
[4,2,1,3,5,6,7,8]=>[3,1,1,1,1,1]
[4,1,2,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[3,2,1,4,5,6,7,8]=>[3,1,1,1,1,1]
[2,3,1,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
[6,8,7,5,4,3,2,1]=>[7,1]
[5,8,7,6,4,3,2,1]=>[7,1]
[5,7,8,6,4,3,2,1]=>[6,1,1]
[6,5,8,7,4,3,2,1]=>[6,2]
[5,6,8,7,4,3,2,1]=>[6,1,1]
[5,7,6,8,4,3,2,1]=>[6,1,1]
[4,8,7,6,5,3,2,1]=>[7,1]
[4,7,8,6,5,3,2,1]=>[6,1,1]
[4,6,8,7,5,3,2,1]=>[6,1,1]
[4,7,6,8,5,3,2,1]=>[6,1,1]
[4,5,8,7,6,3,2,1]=>[6,1,1]
[6,5,4,8,7,3,2,1]=>[6,2]
[4,6,5,8,7,3,2,1]=>[5,2,1]
[4,5,6,8,7,3,2,1]=>[5,1,1,1]
[5,7,6,4,8,3,2,1]=>[6,1,1]
[4,7,6,5,8,3,2,1]=>[6,1,1]
[4,6,7,5,8,3,2,1]=>[5,1,1,1]
[5,4,7,6,8,3,2,1]=>[5,2,1]
[4,5,7,6,8,3,2,1]=>[5,1,1,1]
[4,6,5,7,8,3,2,1]=>[5,1,1,1]
[3,8,7,6,5,4,2,1]=>[7,1]
[3,7,8,6,5,4,2,1]=>[6,1,1]
[3,6,8,7,5,4,2,1]=>[6,1,1]
[3,7,6,8,5,4,2,1]=>[6,1,1]
[3,5,8,7,6,4,2,1]=>[6,1,1]
[3,5,7,8,6,4,2,1]=>[5,1,1,1]
[3,5,6,8,7,4,2,1]=>[5,1,1,1]
[3,7,6,5,8,4,2,1]=>[6,1,1]
[3,6,7,5,8,4,2,1]=>[5,1,1,1]
[3,5,7,6,8,4,2,1]=>[5,1,1,1]
[3,5,6,7,8,4,2,1]=>[4,1,1,1,1]
[4,3,8,7,6,5,2,1]=>[6,2]
[4,3,6,7,8,5,2,1]=>[4,2,1,1]
[3,4,8,7,6,5,2,1]=>[6,1,1]
[3,4,6,7,8,5,2,1]=>[4,1,1,1,1]
[5,4,3,8,7,6,2,1]=>[5,3]
[5,4,3,7,8,6,2,1]=>[5,2,1]
[3,5,4,7,8,6,2,1]=>[4,2,1,1]
[3,4,5,8,7,6,2,1]=>[5,1,1,1]
[3,4,5,7,8,6,2,1]=>[4,1,1,1,1]
[6,5,4,3,8,7,2,1]=>[6,2]
[5,6,4,3,8,7,2,1]=>[5,2,1]
[4,5,6,3,8,7,2,1]=>[4,2,1,1]
[4,3,6,5,8,7,2,1]=>[4,2,2]
[5,4,3,6,8,7,2,1]=>[5,2,1]
[4,5,3,6,8,7,2,1]=>[4,2,1,1]
[3,4,5,6,8,7,2,1]=>[4,1,1,1,1]
[5,7,6,4,3,8,2,1]=>[6,1,1]
[4,7,6,5,3,8,2,1]=>[6,1,1]
[5,4,7,6,3,8,2,1]=>[5,2,1]
[3,7,6,5,4,8,2,1]=>[6,1,1]
[3,5,7,6,4,8,2,1]=>[5,1,1,1]
[3,5,6,7,4,8,2,1]=>[4,1,1,1,1]
[4,3,7,6,5,8,2,1]=>[5,2,1]
[3,4,7,6,5,8,2,1]=>[5,1,1,1]
[3,4,6,7,5,8,2,1]=>[4,1,1,1,1]
[4,5,3,7,6,8,2,1]=>[4,2,1,1]
[3,5,4,7,6,8,2,1]=>[4,2,1,1]
[4,3,5,7,6,8,2,1]=>[4,2,1,1]
[3,4,5,7,6,8,2,1]=>[4,1,1,1,1]
[3,6,5,4,7,8,2,1]=>[5,1,1,1]
[3,5,6,4,7,8,2,1]=>[4,1,1,1,1]
[4,3,6,5,7,8,2,1]=>[4,2,1,1]
[3,4,6,5,7,8,2,1]=>[4,1,1,1,1]
[3,5,4,6,7,8,2,1]=>[4,1,1,1,1]
[2,8,7,6,5,4,3,1]=>[7,1]
[2,7,8,6,5,4,3,1]=>[6,1,1]
[2,6,8,7,5,4,3,1]=>[6,1,1]
[2,7,6,8,5,4,3,1]=>[6,1,1]
[2,6,7,8,5,4,3,1]=>[5,1,1,1]
[2,5,8,7,6,4,3,1]=>[6,1,1]
[2,6,7,5,8,4,3,1]=>[5,1,1,1]
[2,6,5,7,8,4,3,1]=>[5,1,1,1]
[2,5,6,7,8,4,3,1]=>[4,1,1,1,1]
[2,4,8,7,6,5,3,1]=>[6,1,1]
[2,4,7,8,6,5,3,1]=>[5,1,1,1]
[2,4,6,8,7,5,3,1]=>[5,1,1,1]
[2,4,6,7,8,5,3,1]=>[4,1,1,1,1]
[2,5,4,8,7,6,3,1]=>[5,2,1]
[2,5,4,7,8,6,3,1]=>[4,2,1,1]
[2,4,5,7,8,6,3,1]=>[4,1,1,1,1]
[2,6,5,4,8,7,3,1]=>[5,2,1]
[2,5,6,4,8,7,3,1]=>[4,2,1,1]
[2,4,6,5,8,7,3,1]=>[4,2,1,1]
[2,4,5,6,8,7,3,1]=>[4,1,1,1,1]
[2,7,6,5,4,8,3,1]=>[6,1,1]
[2,6,7,5,4,8,3,1]=>[5,1,1,1]
[2,5,6,7,4,8,3,1]=>[4,1,1,1,1]
[2,4,7,6,5,8,3,1]=>[5,1,1,1]
[2,4,6,7,5,8,3,1]=>[4,1,1,1,1]
[2,5,4,7,6,8,3,1]=>[4,2,1,1]
[2,6,5,4,7,8,3,1]=>[5,1,1,1]
[2,5,6,4,7,8,3,1]=>[4,1,1,1,1]
[2,4,6,5,7,8,3,1]=>[4,1,1,1,1]
[2,5,4,6,7,8,3,1]=>[4,1,1,1,1]
[2,4,5,6,7,8,3,1]=>[3,1,1,1,1,1]
[3,2,8,7,6,5,4,1]=>[6,2]
[3,2,6,8,7,5,4,1]=>[5,2,1]
[3,2,5,7,8,6,4,1]=>[4,2,1,1]
[3,2,5,7,6,8,4,1]=>[4,2,1,1]
[3,2,5,6,7,8,4,1]=>[3,2,1,1,1]
[2,3,8,7,6,5,4,1]=>[6,1,1]
[2,3,6,7,8,5,4,1]=>[4,1,1,1,1]
[2,3,5,7,8,6,4,1]=>[4,1,1,1,1]
[2,3,6,5,8,7,4,1]=>[4,2,1,1]
[2,3,5,6,8,7,4,1]=>[4,1,1,1,1]
[2,3,7,6,5,8,4,1]=>[5,1,1,1]
[2,3,5,7,6,8,4,1]=>[4,1,1,1,1]
[2,3,5,6,7,8,4,1]=>[3,1,1,1,1,1]
[4,3,2,8,7,6,5,1]=>[5,3]
[4,3,2,7,8,6,5,1]=>[4,3,1]
[3,4,2,8,7,6,5,1]=>[5,2,1]
[3,4,2,7,8,6,5,1]=>[4,2,1,1]
[2,4,3,8,7,6,5,1]=>[5,2,1]
[2,4,3,6,8,7,5,1]=>[4,2,1,1]
[2,4,3,6,7,8,5,1]=>[3,2,1,1,1]
[3,2,4,8,7,6,5,1]=>[5,2,1]
[3,2,4,7,8,6,5,1]=>[4,2,1,1]
[2,3,4,8,7,6,5,1]=>[5,1,1,1]
[2,3,4,6,8,7,5,1]=>[4,1,1,1,1]
[2,3,4,7,6,8,5,1]=>[4,1,1,1,1]
[2,3,4,6,7,8,5,1]=>[3,1,1,1,1,1]
[5,4,3,2,8,7,6,1]=>[5,3]
[5,4,3,2,7,8,6,1]=>[5,2,1]
[3,5,4,2,7,8,6,1]=>[4,2,1,1]
[3,4,5,2,7,8,6,1]=>[3,2,1,1,1]
[2,5,4,3,8,7,6,1]=>[4,3,1]
[2,5,4,3,7,8,6,1]=>[4,2,1,1]
[2,4,5,3,8,7,6,1]=>[4,2,1,1]
[2,4,5,3,7,8,6,1]=>[3,2,1,1,1]
[3,2,5,4,7,8,6,1]=>[3,2,2,1]
[2,3,5,4,8,7,6,1]=>[4,2,1,1]
[2,3,5,4,7,8,6,1]=>[3,2,1,1,1]
[4,3,2,5,8,7,6,1]=>[4,3,1]
[4,3,2,5,7,8,6,1]=>[4,2,1,1]
[3,4,2,5,8,7,6,1]=>[4,2,1,1]
[3,4,2,5,7,8,6,1]=>[3,2,1,1,1]
[2,4,3,5,8,7,6,1]=>[4,2,1,1]
[3,2,4,5,7,8,6,1]=>[3,2,1,1,1]
[2,3,4,5,8,7,6,1]=>[4,1,1,1,1]
[2,3,4,5,7,8,6,1]=>[3,1,1,1,1,1]
[6,5,4,3,2,8,7,1]=>[6,2]
[4,6,5,3,2,8,7,1]=>[5,2,1]
[5,4,6,3,2,8,7,1]=>[5,2,1]
[4,5,6,3,2,8,7,1]=>[4,2,1,1]
[3,6,5,4,2,8,7,1]=>[5,2,1]
[3,5,6,4,2,8,7,1]=>[4,2,1,1]
[4,3,6,5,2,8,7,1]=>[4,2,2]
[5,4,3,6,2,8,7,1]=>[5,2,1]
[4,5,3,6,2,8,7,1]=>[4,2,1,1]
[2,6,5,4,3,8,7,1]=>[5,2,1]
[2,4,6,5,3,8,7,1]=>[4,2,1,1]
[2,4,5,6,3,8,7,1]=>[3,2,1,1,1]
[3,2,6,5,4,8,7,1]=>[4,2,2]
[2,3,5,6,4,8,7,1]=>[3,2,1,1,1]
[4,3,2,6,5,8,7,1]=>[4,2,2]
[2,4,3,6,5,8,7,1]=>[3,2,2,1]
[3,2,4,6,5,8,7,1]=>[3,2,2,1]
[2,3,4,6,5,8,7,1]=>[3,2,1,1,1]
[5,4,3,2,6,8,7,1]=>[5,2,1]
[4,5,3,2,6,8,7,1]=>[4,2,1,1]
[2,4,5,3,6,8,7,1]=>[3,2,1,1,1]
[3,2,5,4,6,8,7,1]=>[3,2,2,1]
[4,3,2,5,6,8,7,1]=>[4,2,1,1]
[3,4,2,5,6,8,7,1]=>[3,2,1,1,1]
[2,4,3,5,6,8,7,1]=>[3,2,1,1,1]
[3,2,4,5,6,8,7,1]=>[3,2,1,1,1]
[2,3,4,5,6,8,7,1]=>[3,1,1,1,1,1]
[5,7,6,4,3,2,8,1]=>[6,1,1]
[4,7,6,5,3,2,8,1]=>[6,1,1]
[4,6,7,5,3,2,8,1]=>[5,1,1,1]
[4,6,5,7,3,2,8,1]=>[5,1,1,1]
[3,5,7,6,4,2,8,1]=>[5,1,1,1]
[3,5,6,7,4,2,8,1]=>[4,1,1,1,1]
[4,3,7,6,5,2,8,1]=>[5,2,1]
[4,3,6,7,5,2,8,1]=>[4,2,1,1]
[3,4,7,6,5,2,8,1]=>[5,1,1,1]
[3,4,6,7,5,2,8,1]=>[4,1,1,1,1]
[5,4,3,7,6,2,8,1]=>[5,2,1]
[4,5,3,7,6,2,8,1]=>[4,2,1,1]
[3,5,4,7,6,2,8,1]=>[4,2,1,1]
[3,4,5,7,6,2,8,1]=>[4,1,1,1,1]
[4,6,5,3,7,2,8,1]=>[5,1,1,1]
[3,6,5,4,7,2,8,1]=>[5,1,1,1]
[3,5,6,4,7,2,8,1]=>[4,1,1,1,1]
[4,3,6,5,7,2,8,1]=>[4,2,1,1]
[3,4,6,5,7,2,8,1]=>[4,1,1,1,1]
[3,5,4,6,7,2,8,1]=>[4,1,1,1,1]
[2,7,6,5,4,3,8,1]=>[6,1,1]
[2,6,5,7,4,3,8,1]=>[5,1,1,1]
[2,5,6,7,4,3,8,1]=>[4,1,1,1,1]
[2,4,6,7,5,3,8,1]=>[4,1,1,1,1]
[2,5,4,7,6,3,8,1]=>[4,2,1,1]
[2,4,6,5,7,3,8,1]=>[4,1,1,1,1]
[2,5,4,6,7,3,8,1]=>[4,1,1,1,1]
[2,4,5,6,7,3,8,1]=>[3,1,1,1,1,1]
[3,2,7,6,5,4,8,1]=>[5,2,1]
[3,2,6,7,5,4,8,1]=>[4,2,1,1]
[3,2,5,7,6,4,8,1]=>[4,2,1,1]
[3,2,6,5,7,4,8,1]=>[4,2,1,1]
[3,2,5,6,7,4,8,1]=>[3,2,1,1,1]
[2,3,7,6,5,4,8,1]=>[5,1,1,1]
[2,3,5,7,6,4,8,1]=>[4,1,1,1,1]
[2,3,5,6,7,4,8,1]=>[3,1,1,1,1,1]
[4,3,2,7,6,5,8,1]=>[4,3,1]
[3,4,2,6,7,5,8,1]=>[3,2,1,1,1]
[2,4,3,6,7,5,8,1]=>[3,2,1,1,1]
[2,3,4,7,6,5,8,1]=>[4,1,1,1,1]
[2,3,4,6,7,5,8,1]=>[3,1,1,1,1,1]
[5,4,3,2,7,6,8,1]=>[5,2,1]
[3,5,4,2,7,6,8,1]=>[4,2,1,1]
[4,3,5,2,7,6,8,1]=>[4,2,1,1]
[3,4,5,2,7,6,8,1]=>[3,2,1,1,1]
[3,2,5,4,7,6,8,1]=>[3,2,2,1]
[2,3,5,4,7,6,8,1]=>[3,2,1,1,1]
[4,3,2,5,7,6,8,1]=>[4,2,1,1]
[3,4,2,5,7,6,8,1]=>[3,2,1,1,1]
[2,4,3,5,7,6,8,1]=>[3,2,1,1,1]
[3,2,4,5,7,6,8,1]=>[3,2,1,1,1]
[2,3,4,5,7,6,8,1]=>[3,1,1,1,1,1]
[3,6,5,4,2,7,8,1]=>[5,1,1,1]
[3,5,6,4,2,7,8,1]=>[4,1,1,1,1]
[3,4,6,5,2,7,8,1]=>[4,1,1,1,1]
[3,5,4,6,2,7,8,1]=>[4,1,1,1,1]
[2,6,5,4,3,7,8,1]=>[5,1,1,1]
[2,5,6,4,3,7,8,1]=>[4,1,1,1,1]
[2,4,6,5,3,7,8,1]=>[4,1,1,1,1]
[2,5,4,6,3,7,8,1]=>[4,1,1,1,1]
[2,4,5,6,3,7,8,1]=>[3,1,1,1,1,1]
[3,2,5,6,4,7,8,1]=>[3,2,1,1,1]
[2,3,6,5,4,7,8,1]=>[4,1,1,1,1]
[2,3,5,6,4,7,8,1]=>[3,1,1,1,1,1]
[3,4,2,6,5,7,8,1]=>[3,2,1,1,1]
[2,4,3,6,5,7,8,1]=>[3,2,1,1,1]
[2,3,4,6,5,7,8,1]=>[3,1,1,1,1,1]
[3,5,4,2,6,7,8,1]=>[4,1,1,1,1]
[2,4,5,3,6,7,8,1]=>[3,1,1,1,1,1]
[3,2,5,4,6,7,8,1]=>[3,2,1,1,1]
[2,3,5,4,6,7,8,1]=>[3,1,1,1,1,1]
[2,4,3,5,6,7,8,1]=>[3,1,1,1,1,1]
[1,8,7,6,5,4,3,2]=>[7,1]
[1,7,8,6,5,4,3,2]=>[6,1,1]
[1,6,8,7,5,4,3,2]=>[6,1,1]
[1,7,6,8,5,4,3,2]=>[6,1,1]
[1,6,7,8,5,4,3,2]=>[5,1,1,1]
[1,5,8,7,6,4,3,2]=>[6,1,1]
[1,6,5,8,7,4,3,2]=>[5,2,1]
[1,7,6,5,8,4,3,2]=>[6,1,1]
[1,6,7,5,8,4,3,2]=>[5,1,1,1]
[1,5,7,6,8,4,3,2]=>[5,1,1,1]
[1,6,5,7,8,4,3,2]=>[5,1,1,1]
[1,5,6,7,8,4,3,2]=>[4,1,1,1,1]
[1,4,8,7,6,5,3,2]=>[6,1,1]
[1,4,7,8,6,5,3,2]=>[5,1,1,1]
[1,4,6,8,7,5,3,2]=>[5,1,1,1]
[1,4,6,7,8,5,3,2]=>[4,1,1,1,1]
[1,5,4,7,8,6,3,2]=>[4,2,1,1]
[1,4,5,8,7,6,3,2]=>[5,1,1,1]
[1,4,5,7,8,6,3,2]=>[4,1,1,1,1]
[1,4,6,5,8,7,3,2]=>[4,2,1,1]
[1,5,4,6,8,7,3,2]=>[4,2,1,1]
[1,7,6,5,4,8,3,2]=>[6,1,1]
[1,4,7,6,5,8,3,2]=>[5,1,1,1]
[1,4,6,7,5,8,3,2]=>[4,1,1,1,1]
[1,6,5,4,7,8,3,2]=>[5,1,1,1]
[1,4,5,6,7,8,3,2]=>[3,1,1,1,1,1]
[1,3,8,7,6,5,4,2]=>[6,1,1]
[1,3,7,8,6,5,4,2]=>[5,1,1,1]
[1,3,6,8,7,5,4,2]=>[5,1,1,1]
[1,3,6,7,8,5,4,2]=>[4,1,1,1,1]
[1,3,5,8,7,6,4,2]=>[5,1,1,1]
[1,3,5,7,8,6,4,2]=>[4,1,1,1,1]
[1,3,5,6,8,7,4,2]=>[4,1,1,1,1]
[1,3,6,7,5,8,4,2]=>[4,1,1,1,1]
[1,3,5,7,6,8,4,2]=>[4,1,1,1,1]
[1,3,6,5,7,8,4,2]=>[4,1,1,1,1]
[1,3,5,6,7,8,4,2]=>[3,1,1,1,1,1]
[1,4,3,8,7,6,5,2]=>[5,2,1]
[1,4,3,7,8,6,5,2]=>[4,2,1,1]
[1,4,3,6,8,7,5,2]=>[4,2,1,1]
[1,4,3,6,7,8,5,2]=>[3,2,1,1,1]
[1,3,4,8,7,6,5,2]=>[5,1,1,1]
[1,3,4,7,6,8,5,2]=>[4,1,1,1,1]
[1,3,4,6,7,8,5,2]=>[3,1,1,1,1,1]
[1,5,4,3,8,7,6,2]=>[4,3,1]
[1,4,5,3,8,7,6,2]=>[4,2,1,1]
[1,4,5,3,7,8,6,2]=>[3,2,1,1,1]
[1,3,5,4,7,8,6,2]=>[3,2,1,1,1]
[1,4,3,5,8,7,6,2]=>[4,2,1,1]
[1,4,3,5,7,8,6,2]=>[3,2,1,1,1]
[1,3,4,5,8,7,6,2]=>[4,1,1,1,1]
[1,3,4,5,7,8,6,2]=>[3,1,1,1,1,1]
[1,6,5,4,3,8,7,2]=>[5,2,1]
[1,5,6,4,3,8,7,2]=>[4,2,1,1]
[1,4,6,5,3,8,7,2]=>[4,2,1,1]
[1,4,5,6,3,8,7,2]=>[3,2,1,1,1]
[1,3,6,5,4,8,7,2]=>[4,2,1,1]
[1,4,3,6,5,8,7,2]=>[3,2,2,1]
[1,5,4,3,6,8,7,2]=>[4,2,1,1]
[1,4,5,3,6,8,7,2]=>[3,2,1,1,1]
[1,3,4,5,6,8,7,2]=>[3,1,1,1,1,1]
[1,7,6,5,4,3,8,2]=>[6,1,1]
[1,6,7,5,4,3,8,2]=>[5,1,1,1]
[1,6,5,7,4,3,8,2]=>[5,1,1,1]
[1,4,6,7,5,3,8,2]=>[4,1,1,1,1]
[1,5,6,4,7,3,8,2]=>[4,1,1,1,1]
[1,4,6,5,7,3,8,2]=>[4,1,1,1,1]
[1,5,4,6,7,3,8,2]=>[4,1,1,1,1]
[1,4,5,6,7,3,8,2]=>[3,1,1,1,1,1]
[1,3,5,7,6,4,8,2]=>[4,1,1,1,1]
[1,3,6,5,7,4,8,2]=>[4,1,1,1,1]
[1,3,5,6,7,4,8,2]=>[3,1,1,1,1,1]
[1,4,3,6,7,5,8,2]=>[3,2,1,1,1]
[1,3,4,7,6,5,8,2]=>[4,1,1,1,1]
[1,3,4,6,7,5,8,2]=>[3,1,1,1,1,1]
[1,3,5,4,7,6,8,2]=>[3,2,1,1,1]
[1,3,4,5,7,6,8,2]=>[3,1,1,1,1,1]
[1,6,5,4,3,7,8,2]=>[5,1,1,1]
[1,5,4,6,3,7,8,2]=>[4,1,1,1,1]
[1,3,5,6,4,7,8,2]=>[3,1,1,1,1,1]
[1,4,3,6,5,7,8,2]=>[3,2,1,1,1]
[1,3,4,6,5,7,8,2]=>[3,1,1,1,1,1]
[1,5,4,3,6,7,8,2]=>[4,1,1,1,1]
[1,4,5,3,6,7,8,2]=>[3,1,1,1,1,1]
[1,3,5,4,6,7,8,2]=>[3,1,1,1,1,1]
[1,4,3,5,6,7,8,2]=>[3,1,1,1,1,1]
[1,3,4,5,6,7,8,2]=>[2,1,1,1,1,1,1]
[2,1,8,7,6,5,4,3]=>[6,2]
[2,1,7,8,6,5,4,3]=>[5,2,1]
[2,1,6,8,7,5,4,3]=>[5,2,1]
[2,1,7,6,8,5,4,3]=>[5,2,1]
[2,1,6,7,8,5,4,3]=>[4,2,1,1]
[2,1,5,8,7,6,4,3]=>[5,2,1]
[2,1,5,7,8,6,4,3]=>[4,2,1,1]
[2,1,6,5,8,7,4,3]=>[4,2,2]
[2,1,5,6,8,7,4,3]=>[4,2,1,1]
[2,1,7,6,5,8,4,3]=>[5,2,1]
[2,1,6,7,5,8,4,3]=>[4,2,1,1]
[2,1,5,7,6,8,4,3]=>[4,2,1,1]
[2,1,6,5,7,8,4,3]=>[4,2,1,1]
[2,1,5,6,7,8,4,3]=>[3,2,1,1,1]
[2,1,4,8,7,6,5,3]=>[5,2,1]
[2,1,4,7,8,6,5,3]=>[4,2,1,1]
[2,1,4,6,8,7,5,3]=>[4,2,1,1]
[2,1,4,6,7,8,5,3]=>[3,2,1,1,1]
[2,1,5,4,8,7,6,3]=>[4,2,2]
[2,1,5,4,7,8,6,3]=>[3,2,2,1]
[2,1,4,5,8,7,6,3]=>[4,2,1,1]
[2,1,4,5,7,8,6,3]=>[3,2,1,1,1]
[2,1,6,5,4,8,7,3]=>[4,2,2]
[2,1,5,6,4,8,7,3]=>[3,2,2,1]
[2,1,4,6,5,8,7,3]=>[3,2,2,1]
[2,1,5,4,6,8,7,3]=>[3,2,2,1]
[2,1,4,5,6,8,7,3]=>[3,2,1,1,1]
[2,1,7,6,5,4,8,3]=>[5,2,1]
[2,1,6,7,5,4,8,3]=>[4,2,1,1]
[2,1,5,7,6,4,8,3]=>[4,2,1,1]
[2,1,6,5,7,4,8,3]=>[4,2,1,1]
[2,1,5,6,7,4,8,3]=>[3,2,1,1,1]
[2,1,4,7,6,5,8,3]=>[4,2,1,1]
[2,1,4,6,7,5,8,3]=>[3,2,1,1,1]
[2,1,5,4,7,6,8,3]=>[3,2,2,1]
[2,1,5,6,4,7,8,3]=>[3,2,1,1,1]
[2,1,5,4,6,7,8,3]=>[3,2,1,1,1]
[2,1,4,5,6,7,8,3]=>[2,2,1,1,1,1]
[1,2,8,7,6,5,4,3]=>[6,1,1]
[1,2,7,8,6,5,4,3]=>[5,1,1,1]
[1,2,6,7,8,5,4,3]=>[4,1,1,1,1]
[1,2,6,5,8,7,4,3]=>[4,2,1,1]
[1,2,5,6,8,7,4,3]=>[4,1,1,1,1]
[1,2,7,6,5,8,4,3]=>[5,1,1,1]
[1,2,5,7,6,8,4,3]=>[4,1,1,1,1]
[1,2,6,5,7,8,4,3]=>[4,1,1,1,1]
[1,2,5,6,7,8,4,3]=>[3,1,1,1,1,1]
[1,2,4,8,7,6,5,3]=>[5,1,1,1]
[1,2,4,6,8,7,5,3]=>[4,1,1,1,1]
[1,2,4,6,7,8,5,3]=>[3,1,1,1,1,1]
[1,2,5,4,8,7,6,3]=>[4,2,1,1]
[1,2,4,5,8,7,6,3]=>[4,1,1,1,1]
[1,2,4,5,7,8,6,3]=>[3,1,1,1,1,1]
[1,2,6,5,4,8,7,3]=>[4,2,1,1]
[1,2,5,4,6,8,7,3]=>[3,2,1,1,1]
[1,2,4,5,6,8,7,3]=>[3,1,1,1,1,1]
[1,2,7,6,5,4,8,3]=>[5,1,1,1]
[1,2,5,7,6,4,8,3]=>[4,1,1,1,1]
[1,2,5,6,7,4,8,3]=>[3,1,1,1,1,1]
[1,2,4,7,6,5,8,3]=>[4,1,1,1,1]
[1,2,5,4,7,6,8,3]=>[3,2,1,1,1]
[1,2,6,5,4,7,8,3]=>[4,1,1,1,1]
[1,2,5,4,6,7,8,3]=>[3,1,1,1,1,1]
[1,2,4,5,6,7,8,3]=>[2,1,1,1,1,1,1]
[3,2,1,8,7,6,5,4]=>[5,3]
[3,2,1,7,8,6,5,4]=>[4,3,1]
[3,2,1,6,8,7,5,4]=>[4,3,1]
[3,2,1,7,6,8,5,4]=>[4,3,1]
[3,2,1,6,7,8,5,4]=>[3,3,1,1]
[3,2,1,5,8,7,6,4]=>[4,3,1]
[3,2,1,5,7,8,6,4]=>[3,3,1,1]
[3,2,1,6,5,8,7,4]=>[3,3,2]
[3,2,1,5,6,8,7,4]=>[3,3,1,1]
[3,2,1,7,6,5,8,4]=>[4,3,1]
[3,2,1,6,7,5,8,4]=>[3,3,1,1]
[3,2,1,5,7,6,8,4]=>[3,3,1,1]
[3,2,1,6,5,7,8,4]=>[3,3,1,1]
[3,2,1,5,6,7,8,4]=>[3,2,1,1,1]
[2,3,1,8,7,6,5,4]=>[5,2,1]
[2,3,1,6,8,7,5,4]=>[4,2,1,1]
[2,3,1,7,6,8,5,4]=>[4,2,1,1]
[2,3,1,6,7,8,5,4]=>[3,2,1,1,1]
[2,3,1,5,7,8,6,4]=>[3,2,1,1,1]
[2,3,1,6,5,8,7,4]=>[3,2,2,1]
[2,3,1,7,6,5,8,4]=>[4,2,1,1]
[2,3,1,6,7,5,8,4]=>[3,2,1,1,1]
[2,3,1,5,7,6,8,4]=>[3,2,1,1,1]
[2,3,1,5,6,7,8,4]=>[2,2,1,1,1,1]
[1,3,2,8,7,6,5,4]=>[5,2,1]
[1,3,2,6,8,7,5,4]=>[4,2,1,1]
[1,3,2,7,6,8,5,4]=>[4,2,1,1]
[1,3,2,6,7,8,5,4]=>[3,2,1,1,1]
[1,3,2,5,8,7,6,4]=>[4,2,1,1]
[1,3,2,5,7,8,6,4]=>[3,2,1,1,1]
[1,3,2,6,5,8,7,4]=>[3,2,2,1]
[1,3,2,5,6,8,7,4]=>[3,2,1,1,1]
[1,3,2,7,6,5,8,4]=>[4,2,1,1]
[1,3,2,6,7,5,8,4]=>[3,2,1,1,1]
[1,3,2,5,7,6,8,4]=>[3,2,1,1,1]
[1,3,2,6,5,7,8,4]=>[3,2,1,1,1]
[1,3,2,5,6,7,8,4]=>[2,2,1,1,1,1]
[2,1,3,8,7,6,5,4]=>[5,2,1]
[2,1,3,7,8,6,5,4]=>[4,2,1,1]
[2,1,3,6,8,7,5,4]=>[4,2,1,1]
[2,1,3,6,5,8,7,4]=>[3,2,2,1]
[2,1,3,5,6,7,8,4]=>[2,2,1,1,1,1]
[1,2,3,8,7,6,5,4]=>[5,1,1,1]
[1,2,3,7,8,6,5,4]=>[4,1,1,1,1]
[1,2,3,6,8,7,5,4]=>[4,1,1,1,1]
[1,2,3,7,6,8,5,4]=>[4,1,1,1,1]
[1,2,3,6,7,8,5,4]=>[3,1,1,1,1,1]
[1,2,3,5,8,7,6,4]=>[4,1,1,1,1]
[1,2,3,5,7,8,6,4]=>[3,1,1,1,1,1]
[1,2,3,6,5,8,7,4]=>[3,2,1,1,1]
[1,2,3,5,6,8,7,4]=>[3,1,1,1,1,1]
[1,2,3,7,6,5,8,4]=>[4,1,1,1,1]
[1,2,3,6,7,5,8,4]=>[3,1,1,1,1,1]
[1,2,3,5,7,6,8,4]=>[3,1,1,1,1,1]
[1,2,3,6,5,7,8,4]=>[3,1,1,1,1,1]
[1,2,3,5,6,7,8,4]=>[2,1,1,1,1,1,1]
[4,3,2,1,8,7,6,5]=>[4,4]
[4,3,2,1,7,8,6,5]=>[4,3,1]
[4,3,2,1,6,8,7,5]=>[4,3,1]
[4,3,2,1,7,6,8,5]=>[4,3,1]
[4,3,2,1,6,7,8,5]=>[4,2,1,1]
[3,4,2,1,8,7,6,5]=>[4,3,1]
[3,4,2,1,7,8,6,5]=>[3,3,1,1]
[3,4,2,1,6,8,7,5]=>[3,3,1,1]
[3,4,2,1,7,6,8,5]=>[3,3,1,1]
[3,4,2,1,6,7,8,5]=>[3,2,1,1,1]
[2,4,3,1,8,7,6,5]=>[4,3,1]
[2,4,3,1,7,8,6,5]=>[3,3,1,1]
[2,4,3,1,6,8,7,5]=>[3,3,1,1]
[2,4,3,1,7,6,8,5]=>[3,3,1,1]
[2,4,3,1,6,7,8,5]=>[3,2,1,1,1]
[3,2,4,1,8,7,6,5]=>[4,3,1]
[3,2,4,1,7,8,6,5]=>[3,3,1,1]
[3,2,4,1,6,8,7,5]=>[3,3,1,1]
[3,2,4,1,7,6,8,5]=>[3,3,1,1]
[3,2,4,1,6,7,8,5]=>[3,2,1,1,1]
[2,3,4,1,8,7,6,5]=>[4,2,1,1]
[2,3,4,1,7,8,6,5]=>[3,2,1,1,1]
[2,3,4,1,6,8,7,5]=>[3,2,1,1,1]
[2,3,4,1,7,6,8,5]=>[3,2,1,1,1]
[2,3,4,1,6,7,8,5]=>[2,2,1,1,1,1]
[1,4,3,2,8,7,6,5]=>[4,3,1]
[1,4,3,2,6,8,7,5]=>[3,3,1,1]
[1,4,3,2,7,6,8,5]=>[3,3,1,1]
[1,4,3,2,6,7,8,5]=>[3,2,1,1,1]
[1,3,4,2,8,7,6,5]=>[4,2,1,1]
[1,3,4,2,7,8,6,5]=>[3,2,1,1,1]
[1,3,4,2,6,8,7,5]=>[3,2,1,1,1]
[1,3,4,2,7,6,8,5]=>[3,2,1,1,1]
[1,3,4,2,6,7,8,5]=>[2,2,1,1,1,1]
[2,1,4,3,8,7,6,5]=>[4,2,2]
[2,1,4,3,7,8,6,5]=>[3,2,2,1]
[2,1,4,3,6,8,7,5]=>[3,2,2,1]
[2,1,4,3,7,6,8,5]=>[3,2,2,1]
[2,1,4,3,6,7,8,5]=>[2,2,2,1,1]
[1,2,4,3,8,7,6,5]=>[4,2,1,1]
[1,2,4,3,7,8,6,5]=>[3,2,1,1,1]
[1,2,4,3,6,8,7,5]=>[3,2,1,1,1]
[1,2,4,3,7,6,8,5]=>[3,2,1,1,1]
[1,2,4,3,6,7,8,5]=>[2,2,1,1,1,1]
[3,2,1,4,8,7,6,5]=>[4,3,1]
[3,2,1,4,7,8,6,5]=>[3,3,1,1]
[3,2,1,4,6,8,7,5]=>[3,3,1,1]
[3,2,1,4,7,6,8,5]=>[3,3,1,1]
[3,2,1,4,6,7,8,5]=>[3,2,1,1,1]
[2,3,1,4,8,7,6,5]=>[4,2,1,1]
[2,3,1,4,7,8,6,5]=>[3,2,1,1,1]
[2,3,1,4,7,6,8,5]=>[3,2,1,1,1]
[2,3,1,4,6,7,8,5]=>[2,2,1,1,1,1]
[1,3,2,4,8,7,6,5]=>[4,2,1,1]
[1,3,2,4,6,8,7,5]=>[3,2,1,1,1]
[1,3,2,4,7,6,8,5]=>[3,2,1,1,1]
[1,3,2,4,6,7,8,5]=>[2,2,1,1,1,1]
[2,1,3,4,8,7,6,5]=>[4,2,1,1]
[2,1,3,4,7,8,6,5]=>[3,2,1,1,1]
[2,1,3,4,7,6,8,5]=>[3,2,1,1,1]
[2,1,3,4,6,7,8,5]=>[2,2,1,1,1,1]
[1,2,3,4,8,7,6,5]=>[4,1,1,1,1]
[1,2,3,4,7,8,6,5]=>[3,1,1,1,1,1]
[1,2,3,4,6,8,7,5]=>[3,1,1,1,1,1]
[1,2,3,4,7,6,8,5]=>[3,1,1,1,1,1]
[1,2,3,4,6,7,8,5]=>[2,1,1,1,1,1,1]
[5,4,3,2,1,8,7,6]=>[5,3]
[5,4,3,2,1,7,8,6]=>[5,2,1]
[4,5,3,2,1,8,7,6]=>[4,3,1]
[3,5,4,2,1,8,7,6]=>[4,3,1]
[3,5,4,2,1,7,8,6]=>[4,2,1,1]
[4,3,5,2,1,8,7,6]=>[4,3,1]
[3,4,5,2,1,8,7,6]=>[3,3,1,1]
[3,4,5,2,1,7,8,6]=>[3,2,1,1,1]
[2,5,4,3,1,8,7,6]=>[4,3,1]
[2,5,4,3,1,7,8,6]=>[4,2,1,1]
[2,4,5,3,1,8,7,6]=>[3,3,1,1]
[2,4,5,3,1,7,8,6]=>[3,2,1,1,1]
[3,2,5,4,1,8,7,6]=>[3,3,2]
[3,2,5,4,1,7,8,6]=>[3,2,2,1]
[2,3,5,4,1,8,7,6]=>[3,3,1,1]
[4,3,2,5,1,8,7,6]=>[4,3,1]
[4,3,2,5,1,7,8,6]=>[4,2,1,1]
[3,4,2,5,1,8,7,6]=>[3,3,1,1]
[3,4,2,5,1,7,8,6]=>[3,2,1,1,1]
[2,4,3,5,1,8,7,6]=>[3,3,1,1]
[2,4,3,5,1,7,8,6]=>[3,2,1,1,1]
[3,2,4,5,1,8,7,6]=>[3,3,1,1]
[2,3,4,5,1,8,7,6]=>[3,2,1,1,1]
[2,3,4,5,1,7,8,6]=>[2,2,1,1,1,1]
[1,5,4,3,2,8,7,6]=>[4,3,1]
[1,5,4,3,2,7,8,6]=>[4,2,1,1]
[1,4,5,3,2,8,7,6]=>[3,3,1,1]
[1,4,5,3,2,7,8,6]=>[3,2,1,1,1]
[1,3,5,4,2,7,8,6]=>[3,2,1,1,1]
[1,4,3,5,2,8,7,6]=>[3,3,1,1]
[1,4,3,5,2,7,8,6]=>[3,2,1,1,1]
[1,3,4,5,2,8,7,6]=>[3,2,1,1,1]
[1,3,4,5,2,7,8,6]=>[2,2,1,1,1,1]
[2,1,4,5,3,8,7,6]=>[3,2,2,1]
[1,2,5,4,3,7,8,6]=>[3,2,1,1,1]
[1,2,4,5,3,8,7,6]=>[3,2,1,1,1]
[1,2,4,5,3,7,8,6]=>[2,2,1,1,1,1]
[1,3,2,5,4,8,7,6]=>[3,2,2,1]
[1,3,2,5,4,7,8,6]=>[2,2,2,1,1]
[2,1,3,5,4,8,7,6]=>[3,2,2,1]
[2,1,3,5,4,7,8,6]=>[2,2,2,1,1]
[1,2,3,5,4,8,7,6]=>[3,2,1,1,1]
[1,2,3,5,4,7,8,6]=>[2,2,1,1,1,1]
[4,3,2,1,5,7,8,6]=>[4,2,1,1]
[2,4,3,1,5,8,7,6]=>[3,3,1,1]
[3,2,4,1,5,8,7,6]=>[3,3,1,1]
[3,2,4,1,5,7,8,6]=>[3,2,1,1,1]
[2,3,4,1,5,8,7,6]=>[3,2,1,1,1]
[2,3,4,1,5,7,8,6]=>[2,2,1,1,1,1]
[1,4,3,2,5,8,7,6]=>[3,3,1,1]
[1,4,3,2,5,7,8,6]=>[3,2,1,1,1]
[1,3,4,2,5,8,7,6]=>[3,2,1,1,1]
[1,3,4,2,5,7,8,6]=>[2,2,1,1,1,1]
[2,1,4,3,5,8,7,6]=>[3,2,2,1]
[2,1,4,3,5,7,8,6]=>[2,2,2,1,1]
[1,2,4,3,5,8,7,6]=>[3,2,1,1,1]
[1,2,4,3,5,7,8,6]=>[2,2,1,1,1,1]
[3,2,1,4,5,8,7,6]=>[3,3,1,1]
[3,2,1,4,5,7,8,6]=>[3,2,1,1,1]
[2,3,1,4,5,7,8,6]=>[2,2,1,1,1,1]
[1,3,2,4,5,8,7,6]=>[3,2,1,1,1]
[1,3,2,4,5,7,8,6]=>[2,2,1,1,1,1]
[2,1,3,4,5,8,7,6]=>[3,2,1,1,1]
[2,1,3,4,5,7,8,6]=>[2,2,1,1,1,1]
[1,2,3,4,5,8,7,6]=>[3,1,1,1,1,1]
[1,2,3,4,5,7,8,6]=>[2,1,1,1,1,1,1]
[6,5,4,3,2,1,8,7]=>[6,2]
[5,6,4,3,2,1,8,7]=>[5,2,1]
[4,6,5,3,2,1,8,7]=>[5,2,1]
[5,4,6,3,2,1,8,7]=>[5,2,1]
[4,5,6,3,2,1,8,7]=>[4,2,1,1]
[3,6,5,4,2,1,8,7]=>[5,2,1]
[3,5,6,4,2,1,8,7]=>[4,2,1,1]
[4,3,6,5,2,1,8,7]=>[4,2,2]
[3,4,6,5,2,1,8,7]=>[4,2,1,1]
[5,4,3,6,2,1,8,7]=>[5,2,1]
[4,5,3,6,2,1,8,7]=>[4,2,1,1]
[4,3,5,6,2,1,8,7]=>[4,2,1,1]
[2,6,5,4,3,1,8,7]=>[5,2,1]
[2,5,6,4,3,1,8,7]=>[4,2,1,1]
[2,4,6,5,3,1,8,7]=>[4,2,1,1]
[3,2,6,5,4,1,8,7]=>[4,2,2]
[3,2,5,6,4,1,8,7]=>[3,2,2,1]
[2,3,6,5,4,1,8,7]=>[4,2,1,1]
[2,3,5,6,4,1,8,7]=>[3,2,1,1,1]
[4,3,2,6,5,1,8,7]=>[4,2,2]
[3,4,2,6,5,1,8,7]=>[3,2,2,1]
[2,4,3,6,5,1,8,7]=>[3,2,2,1]
[5,4,3,2,6,1,8,7]=>[5,2,1]
[3,5,4,2,6,1,8,7]=>[4,2,1,1]
[4,3,5,2,6,1,8,7]=>[4,2,1,1]
[3,4,5,2,6,1,8,7]=>[3,2,1,1,1]
[2,5,4,3,6,1,8,7]=>[4,2,1,1]
[2,4,5,3,6,1,8,7]=>[3,2,1,1,1]
[3,2,5,4,6,1,8,7]=>[3,2,2,1]
[4,3,2,5,6,1,8,7]=>[4,2,1,1]
[3,4,2,5,6,1,8,7]=>[3,2,1,1,1]
[2,4,3,5,6,1,8,7]=>[3,2,1,1,1]
[2,3,4,5,6,1,8,7]=>[2,2,1,1,1,1]
[1,6,5,4,3,2,8,7]=>[5,2,1]
[1,5,6,4,3,2,8,7]=>[4,2,1,1]
[1,5,4,6,3,2,8,7]=>[4,2,1,1]
[1,3,6,5,4,2,8,7]=>[4,2,1,1]
[1,3,4,5,6,2,8,7]=>[2,2,1,1,1,1]
[2,1,6,5,4,3,8,7]=>[4,2,2]
[2,1,5,6,4,3,8,7]=>[3,2,2,1]
[2,1,4,6,5,3,8,7]=>[3,2,2,1]
[2,1,5,4,6,3,8,7]=>[3,2,2,1]
[2,1,4,5,6,3,8,7]=>[2,2,2,1,1]
[1,2,4,5,6,3,8,7]=>[2,2,1,1,1,1]
[2,3,1,6,5,4,8,7]=>[3,2,2,1]
[1,3,2,6,5,4,8,7]=>[3,2,2,1]
[1,3,2,5,6,4,8,7]=>[2,2,2,1,1]
[2,1,3,5,6,4,8,7]=>[2,2,2,1,1]
[1,2,3,6,5,4,8,7]=>[3,2,1,1,1]
[1,2,3,5,6,4,8,7]=>[2,2,1,1,1,1]
[4,3,2,1,6,5,8,7]=>[4,2,2]
[3,4,2,1,6,5,8,7]=>[3,2,2,1]
[2,4,3,1,6,5,8,7]=>[3,2,2,1]
[3,2,4,1,6,5,8,7]=>[3,2,2,1]
[2,3,4,1,6,5,8,7]=>[2,2,2,1,1]
[1,3,4,2,6,5,8,7]=>[2,2,2,1,1]
[2,1,4,3,6,5,8,7]=>[2,2,2,2]
[1,2,4,3,6,5,8,7]=>[2,2,2,1,1]
[2,3,1,4,6,5,8,7]=>[2,2,2,1,1]
[1,3,2,4,6,5,8,7]=>[2,2,2,1,1]
[2,1,3,4,6,5,8,7]=>[2,2,2,1,1]
[1,2,3,4,6,5,8,7]=>[2,2,1,1,1,1]
[5,4,3,2,1,6,8,7]=>[5,2,1]
[4,5,3,2,1,6,8,7]=>[4,2,1,1]
[3,5,4,2,1,6,8,7]=>[4,2,1,1]
[4,3,5,2,1,6,8,7]=>[4,2,1,1]
[3,4,5,2,1,6,8,7]=>[3,2,1,1,1]
[2,5,4,3,1,6,8,7]=>[4,2,1,1]
[2,4,5,3,1,6,8,7]=>[3,2,1,1,1]
[3,2,5,4,1,6,8,7]=>[3,2,2,1]
[2,3,5,4,1,6,8,7]=>[3,2,1,1,1]
[2,4,3,5,1,6,8,7]=>[3,2,1,1,1]
[2,3,4,5,1,6,8,7]=>[2,2,1,1,1,1]
[1,4,5,3,2,6,8,7]=>[3,2,1,1,1]
[1,3,5,4,2,6,8,7]=>[3,2,1,1,1]
[1,3,4,5,2,6,8,7]=>[2,2,1,1,1,1]
[2,1,4,5,3,6,8,7]=>[2,2,2,1,1]
[1,2,5,4,3,6,8,7]=>[3,2,1,1,1]
[2,1,3,5,4,6,8,7]=>[2,2,2,1,1]
[1,2,3,5,4,6,8,7]=>[2,2,1,1,1,1]
[4,3,2,1,5,6,8,7]=>[4,2,1,1]
[3,2,4,1,5,6,8,7]=>[3,2,1,1,1]
[2,3,4,1,5,6,8,7]=>[2,2,1,1,1,1]
[1,4,3,2,5,6,8,7]=>[3,2,1,1,1]
[1,3,4,2,5,6,8,7]=>[2,2,1,1,1,1]
[2,1,4,3,5,6,8,7]=>[2,2,2,1,1]
[1,2,4,3,5,6,8,7]=>[2,2,1,1,1,1]
[3,2,1,4,5,6,8,7]=>[3,2,1,1,1]
[2,3,1,4,5,6,8,7]=>[2,2,1,1,1,1]
[1,3,2,4,5,6,8,7]=>[2,2,1,1,1,1]
[2,1,3,4,5,6,8,7]=>[2,2,1,1,1,1]
[1,2,3,4,5,6,8,7]=>[2,1,1,1,1,1,1]
[5,7,6,4,3,2,1,8]=>[6,1,1]
[4,7,6,5,3,2,1,8]=>[6,1,1]
[4,6,7,5,3,2,1,8]=>[5,1,1,1]
[5,4,7,6,3,2,1,8]=>[5,2,1]
[4,5,7,6,3,2,1,8]=>[5,1,1,1]
[4,6,5,7,3,2,1,8]=>[5,1,1,1]
[3,5,7,6,4,2,1,8]=>[5,1,1,1]
[3,5,6,7,4,2,1,8]=>[4,1,1,1,1]
[4,3,7,6,5,2,1,8]=>[5,2,1]
[3,4,7,6,5,2,1,8]=>[5,1,1,1]
[5,4,3,7,6,2,1,8]=>[5,2,1]
[3,5,4,7,6,2,1,8]=>[4,2,1,1]
[3,6,5,4,7,2,1,8]=>[5,1,1,1]
[3,5,6,4,7,2,1,8]=>[4,1,1,1,1]
[4,3,6,5,7,2,1,8]=>[4,2,1,1]
[2,7,6,5,4,3,1,8]=>[6,1,1]
[2,6,7,5,4,3,1,8]=>[5,1,1,1]
[2,5,7,6,4,3,1,8]=>[5,1,1,1]
[2,5,6,7,4,3,1,8]=>[4,1,1,1,1]
[2,4,6,7,5,3,1,8]=>[4,1,1,1,1]
[2,5,4,7,6,3,1,8]=>[4,2,1,1]
[2,5,6,4,7,3,1,8]=>[4,1,1,1,1]
[2,5,4,6,7,3,1,8]=>[4,1,1,1,1]
[2,4,5,6,7,3,1,8]=>[3,1,1,1,1,1]
[3,2,7,6,5,4,1,8]=>[5,2,1]
[3,2,6,7,5,4,1,8]=>[4,2,1,1]
[3,2,5,7,6,4,1,8]=>[4,2,1,1]
[3,2,6,5,7,4,1,8]=>[4,2,1,1]
[3,2,5,6,7,4,1,8]=>[3,2,1,1,1]
[2,3,7,6,5,4,1,8]=>[5,1,1,1]
[2,3,6,7,5,4,1,8]=>[4,1,1,1,1]
[2,3,5,7,6,4,1,8]=>[4,1,1,1,1]
[2,3,6,5,7,4,1,8]=>[4,1,1,1,1]
[2,3,5,6,7,4,1,8]=>[3,1,1,1,1,1]
[4,3,2,6,7,5,1,8]=>[4,2,1,1]
[3,4,2,7,6,5,1,8]=>[4,2,1,1]
[3,4,2,6,7,5,1,8]=>[3,2,1,1,1]
[3,2,4,6,7,5,1,8]=>[3,2,1,1,1]
[2,3,4,7,6,5,1,8]=>[4,1,1,1,1]
[2,3,4,6,7,5,1,8]=>[3,1,1,1,1,1]
[5,4,3,2,7,6,1,8]=>[5,2,1]
[4,5,3,2,7,6,1,8]=>[4,2,1,1]
[3,5,4,2,7,6,1,8]=>[4,2,1,1]
[4,3,5,2,7,6,1,8]=>[4,2,1,1]
[3,4,5,2,7,6,1,8]=>[3,2,1,1,1]
[3,2,5,4,7,6,1,8]=>[3,2,2,1]
[4,3,2,5,7,6,1,8]=>[4,2,1,1]
[3,4,2,5,7,6,1,8]=>[3,2,1,1,1]
[2,3,4,5,7,6,1,8]=>[3,1,1,1,1,1]
[3,6,5,4,2,7,1,8]=>[5,1,1,1]
[3,5,6,4,2,7,1,8]=>[4,1,1,1,1]
[3,4,6,5,2,7,1,8]=>[4,1,1,1,1]
[3,5,4,6,2,7,1,8]=>[4,1,1,1,1]
[2,5,4,6,3,7,1,8]=>[4,1,1,1,1]
[3,2,6,5,4,7,1,8]=>[4,2,1,1]
[2,3,5,6,4,7,1,8]=>[3,1,1,1,1,1]
[4,3,2,6,5,7,1,8]=>[4,2,1,1]
[3,4,2,6,5,7,1,8]=>[3,2,1,1,1]
[2,4,3,6,5,7,1,8]=>[3,2,1,1,1]
[2,3,4,6,5,7,1,8]=>[3,1,1,1,1,1]
[2,5,4,3,6,7,1,8]=>[4,1,1,1,1]
[2,3,5,4,6,7,1,8]=>[3,1,1,1,1,1]
[1,7,6,5,4,3,2,8]=>[6,1,1]
[1,6,7,5,4,3,2,8]=>[5,1,1,1]
[1,6,5,7,4,3,2,8]=>[5,1,1,1]
[1,5,6,7,4,3,2,8]=>[4,1,1,1,1]
[1,4,7,6,5,3,2,8]=>[5,1,1,1]
[1,4,6,7,5,3,2,8]=>[4,1,1,1,1]
[1,5,4,7,6,3,2,8]=>[4,2,1,1]
[1,5,6,4,7,3,2,8]=>[4,1,1,1,1]
[1,4,6,5,7,3,2,8]=>[4,1,1,1,1]
[1,5,4,6,7,3,2,8]=>[4,1,1,1,1]
[1,3,7,6,5,4,2,8]=>[5,1,1,1]
[1,3,6,7,5,4,2,8]=>[4,1,1,1,1]
[1,3,5,7,6,4,2,8]=>[4,1,1,1,1]
[1,3,6,5,7,4,2,8]=>[4,1,1,1,1]
[1,3,5,6,7,4,2,8]=>[3,1,1,1,1,1]
[1,3,4,6,7,5,2,8]=>[3,1,1,1,1,1]
[1,3,5,4,7,6,2,8]=>[3,2,1,1,1]
[1,4,3,5,7,6,2,8]=>[3,2,1,1,1]
[1,3,4,5,7,6,2,8]=>[3,1,1,1,1,1]
[1,5,4,6,3,7,2,8]=>[4,1,1,1,1]
[1,4,5,6,3,7,2,8]=>[3,1,1,1,1,1]
[1,3,6,5,4,7,2,8]=>[4,1,1,1,1]
[1,3,5,6,4,7,2,8]=>[3,1,1,1,1,1]
[1,4,3,6,5,7,2,8]=>[3,2,1,1,1]
[1,3,4,6,5,7,2,8]=>[3,1,1,1,1,1]
[1,5,4,3,6,7,2,8]=>[4,1,1,1,1]
[1,4,5,3,6,7,2,8]=>[3,1,1,1,1,1]
[1,3,5,4,6,7,2,8]=>[3,1,1,1,1,1]
[1,3,4,5,6,7,2,8]=>[2,1,1,1,1,1,1]
[2,1,7,6,5,4,3,8]=>[5,2,1]
[2,1,6,7,5,4,3,8]=>[4,2,1,1]
[2,1,5,6,7,4,3,8]=>[3,2,1,1,1]
[2,1,4,6,7,5,3,8]=>[3,2,1,1,1]
[2,1,4,5,6,7,3,8]=>[2,2,1,1,1,1]
[1,2,7,6,5,4,3,8]=>[5,1,1,1]
[1,2,6,7,5,4,3,8]=>[4,1,1,1,1]
[1,2,5,7,6,4,3,8]=>[4,1,1,1,1]
[1,2,5,6,7,4,3,8]=>[3,1,1,1,1,1]
[1,2,4,6,7,5,3,8]=>[3,1,1,1,1,1]
[1,2,5,6,4,7,3,8]=>[3,1,1,1,1,1]
[1,2,5,4,6,7,3,8]=>[3,1,1,1,1,1]
[1,2,4,5,6,7,3,8]=>[2,1,1,1,1,1,1]
[3,2,1,7,6,5,4,8]=>[4,3,1]
[3,2,1,6,7,5,4,8]=>[3,3,1,1]
[3,2,1,5,7,6,4,8]=>[3,3,1,1]
[3,2,1,5,6,7,4,8]=>[3,2,1,1,1]
[2,3,1,6,7,5,4,8]=>[3,2,1,1,1]
[2,3,1,6,5,7,4,8]=>[3,2,1,1,1]
[2,3,1,5,6,7,4,8]=>[2,2,1,1,1,1]
[1,3,2,7,6,5,4,8]=>[4,2,1,1]
[1,3,2,6,7,5,4,8]=>[3,2,1,1,1]
[1,3,2,5,7,6,4,8]=>[3,2,1,1,1]
[1,3,2,6,5,7,4,8]=>[3,2,1,1,1]
[1,3,2,5,6,7,4,8]=>[2,2,1,1,1,1]
[2,1,3,6,7,5,4,8]=>[3,2,1,1,1]
[1,2,3,7,6,5,4,8]=>[4,1,1,1,1]
[1,2,3,6,7,5,4,8]=>[3,1,1,1,1,1]
[1,2,3,5,7,6,4,8]=>[3,1,1,1,1,1]
[1,2,3,6,5,7,4,8]=>[3,1,1,1,1,1]
[1,2,3,5,6,7,4,8]=>[2,1,1,1,1,1,1]
[3,2,4,1,7,6,5,8]=>[3,3,1,1]
[3,2,4,1,6,7,5,8]=>[3,2,1,1,1]
[2,3,4,1,7,6,5,8]=>[3,2,1,1,1]
[2,3,4,1,6,7,5,8]=>[2,2,1,1,1,1]
[1,4,3,2,7,6,5,8]=>[3,3,1,1]
[1,4,3,2,6,7,5,8]=>[3,2,1,1,1]
[1,3,4,2,6,7,5,8]=>[2,2,1,1,1,1]
[1,2,4,3,6,7,5,8]=>[2,2,1,1,1,1]
[3,2,1,4,7,6,5,8]=>[3,3,1,1]
[2,3,1,4,6,7,5,8]=>[2,2,1,1,1,1]
[1,3,2,4,7,6,5,8]=>[3,2,1,1,1]
[2,1,3,4,6,7,5,8]=>[2,2,1,1,1,1]
[1,2,3,4,7,6,5,8]=>[3,1,1,1,1,1]
[1,2,3,4,6,7,5,8]=>[2,1,1,1,1,1,1]
[5,4,3,2,1,7,6,8]=>[5,2,1]
[4,5,3,2,1,7,6,8]=>[4,2,1,1]
[3,5,4,2,1,7,6,8]=>[4,2,1,1]
[3,4,5,2,1,7,6,8]=>[3,2,1,1,1]
[2,5,4,3,1,7,6,8]=>[4,2,1,1]
[2,4,5,3,1,7,6,8]=>[3,2,1,1,1]
[3,2,5,4,1,7,6,8]=>[3,2,2,1]
[2,3,5,4,1,7,6,8]=>[3,2,1,1,1]
[3,4,2,5,1,7,6,8]=>[3,2,1,1,1]
[2,4,3,5,1,7,6,8]=>[3,2,1,1,1]
[2,3,4,5,1,7,6,8]=>[2,2,1,1,1,1]
[1,5,4,3,2,7,6,8]=>[4,2,1,1]
[1,4,5,3,2,7,6,8]=>[3,2,1,1,1]
[1,3,5,4,2,7,6,8]=>[3,2,1,1,1]
[1,4,3,5,2,7,6,8]=>[3,2,1,1,1]
[1,3,4,5,2,7,6,8]=>[2,2,1,1,1,1]
[2,1,5,4,3,7,6,8]=>[3,2,2,1]
[1,2,4,5,3,7,6,8]=>[2,2,1,1,1,1]
[3,2,1,5,4,7,6,8]=>[3,2,2,1]
[2,3,1,5,4,7,6,8]=>[2,2,2,1,1]
[1,3,2,5,4,7,6,8]=>[2,2,2,1,1]
[1,2,3,5,4,7,6,8]=>[2,2,1,1,1,1]
[3,2,4,1,5,7,6,8]=>[3,2,1,1,1]
[2,3,4,1,5,7,6,8]=>[2,2,1,1,1,1]
[1,4,3,2,5,7,6,8]=>[3,2,1,1,1]
[1,3,4,2,5,7,6,8]=>[2,2,1,1,1,1]
[1,2,4,3,5,7,6,8]=>[2,2,1,1,1,1]
[2,3,1,4,5,7,6,8]=>[2,2,1,1,1,1]
[1,3,2,4,5,7,6,8]=>[2,2,1,1,1,1]
[2,1,3,4,5,7,6,8]=>[2,2,1,1,1,1]
[1,2,3,4,5,7,6,8]=>[2,1,1,1,1,1,1]
[3,6,5,4,2,1,7,8]=>[5,1,1,1]
[4,3,6,5,2,1,7,8]=>[4,2,1,1]
[2,4,6,5,3,1,7,8]=>[4,1,1,1,1]
[2,4,5,6,3,1,7,8]=>[3,1,1,1,1,1]
[2,3,5,6,4,1,7,8]=>[3,1,1,1,1,1]
[4,3,2,6,5,1,7,8]=>[4,2,1,1]
[2,4,3,6,5,1,7,8]=>[3,2,1,1,1]
[2,3,4,6,5,1,7,8]=>[3,1,1,1,1,1]
[3,5,4,2,6,1,7,8]=>[4,1,1,1,1]
[2,3,5,4,6,1,7,8]=>[3,1,1,1,1,1]
[1,6,5,4,3,2,7,8]=>[5,1,1,1]
[1,5,6,4,3,2,7,8]=>[4,1,1,1,1]
[1,4,6,5,3,2,7,8]=>[4,1,1,1,1]
[1,5,4,6,3,2,7,8]=>[4,1,1,1,1]
[1,4,5,6,3,2,7,8]=>[3,1,1,1,1,1]
[1,3,5,6,4,2,7,8]=>[3,1,1,1,1,1]
[1,4,3,6,5,2,7,8]=>[3,2,1,1,1]
[1,5,4,3,6,2,7,8]=>[4,1,1,1,1]
[1,4,5,3,6,2,7,8]=>[3,1,1,1,1,1]
[1,3,5,4,6,2,7,8]=>[3,1,1,1,1,1]
[1,4,3,5,6,2,7,8]=>[3,1,1,1,1,1]
[1,3,4,5,6,2,7,8]=>[2,1,1,1,1,1,1]
[2,1,5,6,4,3,7,8]=>[3,2,1,1,1]
[2,1,4,6,5,3,7,8]=>[3,2,1,1,1]
[1,2,6,5,4,3,7,8]=>[4,1,1,1,1]
[1,2,5,6,4,3,7,8]=>[3,1,1,1,1,1]
[1,2,4,6,5,3,7,8]=>[3,1,1,1,1,1]
[1,2,4,5,6,3,7,8]=>[2,1,1,1,1,1,1]
[3,2,1,6,5,4,7,8]=>[3,3,1,1]
[3,2,1,5,6,4,7,8]=>[3,2,1,1,1]
[2,3,1,6,5,4,7,8]=>[3,2,1,1,1]
[2,3,1,5,6,4,7,8]=>[2,2,1,1,1,1]
[1,3,2,6,5,4,7,8]=>[3,2,1,1,1]
[1,3,2,5,6,4,7,8]=>[2,2,1,1,1,1]
[1,2,3,6,5,4,7,8]=>[3,1,1,1,1,1]
[1,2,3,5,6,4,7,8]=>[2,1,1,1,1,1,1]
[4,3,2,1,6,5,7,8]=>[4,2,1,1]
[2,4,3,1,6,5,7,8]=>[3,2,1,1,1]
[3,2,4,1,6,5,7,8]=>[3,2,1,1,1]
[2,3,4,1,6,5,7,8]=>[2,2,1,1,1,1]
[2,1,4,3,6,5,7,8]=>[2,2,2,1,1]
[1,2,4,3,6,5,7,8]=>[2,2,1,1,1,1]
[1,3,2,4,6,5,7,8]=>[2,2,1,1,1,1]
[2,1,3,4,6,5,7,8]=>[2,2,1,1,1,1]
[1,2,3,4,6,5,7,8]=>[2,1,1,1,1,1,1]
[3,5,4,2,1,6,7,8]=>[4,1,1,1,1]
[2,5,4,3,1,6,7,8]=>[4,1,1,1,1]
[2,4,5,3,1,6,7,8]=>[3,1,1,1,1,1]
[3,2,5,4,1,6,7,8]=>[3,2,1,1,1]
[2,3,5,4,1,6,7,8]=>[3,1,1,1,1,1]
[2,4,3,5,1,6,7,8]=>[3,1,1,1,1,1]
[1,5,4,3,2,6,7,8]=>[4,1,1,1,1]
[1,4,5,3,2,6,7,8]=>[3,1,1,1,1,1]
[1,3,5,4,2,6,7,8]=>[3,1,1,1,1,1]
[1,3,4,5,2,6,7,8]=>[2,1,1,1,1,1,1]
[2,1,5,4,3,6,7,8]=>[3,2,1,1,1]
[2,1,4,5,3,6,7,8]=>[2,2,1,1,1,1]
[1,2,5,4,3,6,7,8]=>[3,1,1,1,1,1]
[2,3,1,5,4,6,7,8]=>[2,2,1,1,1,1]
[1,3,2,5,4,6,7,8]=>[2,2,1,1,1,1]
[1,2,3,5,4,6,7,8]=>[2,1,1,1,1,1,1]
[2,4,3,1,5,6,7,8]=>[3,1,1,1,1,1]
[1,4,3,2,5,6,7,8]=>[3,1,1,1,1,1]
[1,3,4,2,5,6,7,8]=>[2,1,1,1,1,1,1]
[2,1,4,3,5,6,7,8]=>[2,2,1,1,1,1]
[1,2,4,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,3,2,4,5,6,7,8]=>[2,1,1,1,1,1,1]
[1,2,3,4,8,6,7,5]=>[3,1,1,1,1,1]
[1,2,3,5,8,6,7,4]=>[3,1,1,1,1,1]
[1,2,3,7,5,6,4,8]=>[3,1,1,1,1,1]
[1,2,3,7,5,6,8,4]=>[3,1,1,1,1,1]
[1,2,3,8,5,6,7,4]=>[3,1,1,1,1,1]
[1,2,3,8,5,7,6,4]=>[4,1,1,1,1]
[1,2,3,8,6,5,7,4]=>[4,1,1,1,1]
[1,2,3,8,6,7,5,4]=>[4,1,1,1,1]
[1,2,4,5,8,6,7,3]=>[3,1,1,1,1,1]
[1,2,4,7,5,6,8,3]=>[3,1,1,1,1,1]
[1,2,4,8,5,6,7,3]=>[3,1,1,1,1,1]
[1,2,4,8,6,5,7,3]=>[4,1,1,1,1]
[1,2,5,4,8,6,7,3]=>[3,2,1,1,1]
[1,2,6,4,5,3,7,8]=>[3,1,1,1,1,1]
[1,2,6,4,5,7,8,3]=>[3,1,1,1,1,1]
[1,2,6,4,5,8,7,3]=>[3,2,1,1,1]
[1,2,7,4,5,6,8,3]=>[3,1,1,1,1,1]
[1,2,8,4,5,6,7,3]=>[3,1,1,1,1,1]
[1,2,8,4,6,7,5,3]=>[4,1,1,1,1]
[1,2,8,4,7,6,5,3]=>[5,1,1,1]
[1,2,8,5,4,6,7,3]=>[4,1,1,1,1]
[1,2,8,5,4,7,6,3]=>[4,2,1,1]
[1,2,8,5,6,4,7,3]=>[4,1,1,1,1]
[1,2,8,5,6,7,4,3]=>[4,1,1,1,1]
[1,2,8,6,5,4,7,3]=>[5,1,1,1]
[1,2,8,7,5,6,4,3]=>[5,1,1,1]
[1,3,2,4,8,6,7,5]=>[3,2,1,1,1]
[1,3,2,7,5,6,8,4]=>[3,2,1,1,1]
[1,3,2,8,5,7,6,4]=>[4,2,1,1]
[1,3,2,8,6,5,7,4]=>[4,2,1,1]
[1,3,2,8,6,7,5,4]=>[4,2,1,1]
[1,3,4,2,8,6,7,5]=>[3,2,1,1,1]
[1,3,4,5,8,6,7,2]=>[3,1,1,1,1,1]
[1,3,4,8,5,6,7,2]=>[3,1,1,1,1,1]
[1,3,4,8,6,5,7,2]=>[4,1,1,1,1]
[1,3,6,4,5,2,8,7]=>[3,2,1,1,1]
[1,3,6,4,5,7,2,8]=>[3,1,1,1,1,1]
[1,3,6,4,5,7,8,2]=>[3,1,1,1,1,1]
[1,3,6,4,5,8,7,2]=>[3,2,1,1,1]
[1,3,7,4,5,6,2,8]=>[3,1,1,1,1,1]
[1,3,7,4,5,6,8,2]=>[3,1,1,1,1,1]
[1,3,8,4,5,6,7,2]=>[3,1,1,1,1,1]
[1,3,8,4,6,5,7,2]=>[4,1,1,1,1]
[1,3,8,5,4,6,7,2]=>[4,1,1,1,1]
[1,3,8,5,4,7,6,2]=>[4,2,1,1]
[1,3,8,5,6,7,4,2]=>[4,1,1,1,1]
[1,3,8,5,7,6,4,2]=>[5,1,1,1]
[1,3,8,6,5,7,4,2]=>[5,1,1,1]
[1,3,8,7,5,6,4,2]=>[5,1,1,1]
[1,4,3,5,8,6,7,2]=>[3,2,1,1,1]
[1,4,3,8,5,6,7,2]=>[3,2,1,1,1]
[1,4,3,8,5,7,6,2]=>[4,2,1,1]
[1,4,3,8,6,5,7,2]=>[4,2,1,1]
[1,4,3,8,6,7,5,2]=>[4,2,1,1]
[1,5,3,4,2,6,7,8]=>[3,1,1,1,1,1]
[1,5,3,4,2,7,8,6]=>[3,2,1,1,1]
[1,5,3,4,2,8,7,6]=>[3,3,1,1]
[1,5,3,4,6,2,7,8]=>[3,1,1,1,1,1]
[1,5,3,4,6,2,8,7]=>[3,2,1,1,1]
[1,5,3,4,6,7,2,8]=>[3,1,1,1,1,1]
[1,5,3,4,6,7,8,2]=>[3,1,1,1,1,1]
[1,5,3,4,7,6,2,8]=>[3,2,1,1,1]
[1,5,3,4,8,6,7,2]=>[3,2,1,1,1]
[1,6,3,4,5,8,7,2]=>[3,2,1,1,1]
[1,7,3,4,5,6,8,2]=>[3,1,1,1,1,1]
[1,8,3,4,5,6,7,2]=>[3,1,1,1,1,1]
[1,8,3,4,6,7,5,2]=>[4,1,1,1,1]
[1,6,3,5,4,2,7,8]=>[4,1,1,1,1]
[1,6,3,5,4,8,7,2]=>[4,2,1,1]
[1,7,3,5,4,6,2,8]=>[4,1,1,1,1]
[1,8,3,5,4,6,7,2]=>[4,1,1,1,1]
[1,8,3,5,4,7,6,2]=>[4,2,1,1]
[1,8,3,5,6,4,7,2]=>[4,1,1,1,1]
[1,8,3,5,6,7,4,2]=>[4,1,1,1,1]
[1,8,3,5,7,6,4,2]=>[5,1,1,1]
[1,7,3,6,5,4,8,2]=>[5,1,1,1]
[1,8,3,6,5,4,7,2]=>[5,1,1,1]
[1,8,3,7,5,6,4,2]=>[5,1,1,1]
[1,8,3,7,6,5,4,2]=>[6,1,1]
[1,6,4,3,5,2,7,8]=>[4,1,1,1,1]
[1,6,4,3,5,8,7,2]=>[4,2,1,1]
[1,8,4,3,5,6,7,2]=>[4,1,1,1,1]
[1,8,4,3,5,7,6,2]=>[4,2,1,1]
[1,7,4,3,6,5,8,2]=>[4,2,1,1]
[1,8,4,3,6,5,7,2]=>[4,2,1,1]
[1,8,4,3,6,7,5,2]=>[4,2,1,1]
[1,6,4,5,3,2,7,8]=>[4,1,1,1,1]
[1,6,4,5,3,2,8,7]=>[4,2,1,1]
[1,6,4,5,3,8,7,2]=>[4,2,1,1]
[1,7,4,5,3,6,8,2]=>[4,1,1,1,1]
[1,8,4,5,3,6,7,2]=>[4,1,1,1,1]
[1,7,4,5,6,3,2,8]=>[4,1,1,1,1]
[1,7,4,5,6,3,8,2]=>[4,1,1,1,1]
[1,8,4,5,6,7,3,2]=>[4,1,1,1,1]
[1,7,4,6,5,3,2,8]=>[5,1,1,1]
[1,8,4,6,5,3,7,2]=>[5,1,1,1]
[1,8,4,6,5,7,3,2]=>[5,1,1,1]
[1,8,4,7,6,5,3,2]=>[6,1,1]
[1,7,5,4,3,6,2,8]=>[5,1,1,1]
[1,7,5,4,3,6,8,2]=>[5,1,1,1]
[1,8,5,4,3,6,7,2]=>[5,1,1,1]
[1,8,5,4,3,7,6,2]=>[5,2,1]
[1,8,5,4,6,3,7,2]=>[5,1,1,1]
[1,8,5,4,6,7,3,2]=>[5,1,1,1]
[1,8,5,4,7,6,3,2]=>[5,2,1]
[1,7,6,4,5,3,2,8]=>[5,1,1,1]
[1,8,6,4,5,3,7,2]=>[5,1,1,1]
[1,8,6,4,5,7,3,2]=>[5,1,1,1]
[1,8,7,4,5,6,3,2]=>[5,1,1,1]
[1,8,7,4,6,5,3,2]=>[6,1,1]
[1,8,6,5,4,3,7,2]=>[6,1,1]
[1,8,6,5,4,7,3,2]=>[6,1,1]
[1,8,7,5,4,6,3,2]=>[6,1,1]
[1,8,7,5,6,4,3,2]=>[6,1,1]
[2,1,3,4,8,6,7,5]=>[3,2,1,1,1]
[2,1,3,5,8,6,7,4]=>[3,2,1,1,1]
[2,1,3,8,5,6,7,4]=>[3,2,1,1,1]
[2,1,3,8,5,7,6,4]=>[4,2,1,1]
[2,1,3,8,6,5,7,4]=>[4,2,1,1]
[2,1,3,8,6,7,5,4]=>[4,2,1,1]
[2,1,4,3,8,6,7,5]=>[3,2,2,1]
[2,1,4,5,8,6,7,3]=>[3,2,1,1,1]
[2,1,4,8,5,6,7,3]=>[3,2,1,1,1]
[2,1,4,8,5,7,6,3]=>[4,2,1,1]
[2,1,4,8,6,5,7,3]=>[4,2,1,1]
[2,1,4,8,6,7,5,3]=>[4,2,1,1]
[2,1,5,4,8,6,7,3]=>[3,2,2,1]
[2,1,6,4,5,3,8,7]=>[3,2,2,1]
[2,1,6,4,5,7,8,3]=>[3,2,1,1,1]
[2,1,6,4,5,8,7,3]=>[3,2,2,1]
[2,1,8,4,5,6,7,3]=>[3,2,1,1,1]
[2,1,8,4,5,7,6,3]=>[4,2,1,1]
[2,1,7,4,6,5,8,3]=>[4,2,1,1]
[2,1,8,4,6,5,7,3]=>[4,2,1,1]
[2,1,8,4,6,7,5,3]=>[4,2,1,1]
[2,1,8,4,7,6,5,3]=>[5,2,1]
[2,1,8,5,4,7,6,3]=>[4,2,2]
[2,1,7,5,6,4,8,3]=>[4,2,1,1]
[2,1,8,5,6,4,7,3]=>[4,2,1,1]
[2,1,8,5,6,7,4,3]=>[4,2,1,1]
[2,1,8,5,7,6,4,3]=>[5,2,1]
[2,1,8,6,5,4,7,3]=>[5,2,1]
[2,1,8,6,5,7,4,3]=>[5,2,1]
[2,1,8,7,5,6,4,3]=>[5,2,1]
[2,3,1,5,8,6,7,4]=>[3,2,1,1,1]
[2,3,1,7,5,6,4,8]=>[3,2,1,1,1]
[2,3,1,8,5,6,7,4]=>[3,2,1,1,1]
[2,3,1,8,6,7,5,4]=>[4,2,1,1]
[2,3,4,1,8,6,7,5]=>[3,2,1,1,1]
[2,3,4,5,8,6,7,1]=>[3,1,1,1,1,1]
[2,3,4,7,5,6,1,8]=>[3,1,1,1,1,1]
[2,3,4,7,5,6,8,1]=>[3,1,1,1,1,1]
[2,3,4,8,5,6,7,1]=>[3,1,1,1,1,1]
[2,3,4,8,5,7,6,1]=>[4,1,1,1,1]
[2,3,4,8,6,5,7,1]=>[4,1,1,1,1]
[2,3,4,8,6,7,5,1]=>[4,1,1,1,1]
[2,3,5,4,8,6,7,1]=>[3,2,1,1,1]
[2,3,6,4,5,1,7,8]=>[3,1,1,1,1,1]
[2,3,6,4,5,1,8,7]=>[3,2,1,1,1]
[2,3,6,4,5,7,8,1]=>[3,1,1,1,1,1]
[2,3,6,4,5,8,7,1]=>[3,2,1,1,1]
[2,3,7,4,5,6,8,1]=>[3,1,1,1,1,1]
[2,3,8,4,5,6,7,1]=>[3,1,1,1,1,1]
[2,3,7,4,6,5,8,1]=>[4,1,1,1,1]
[2,3,8,4,6,7,5,1]=>[4,1,1,1,1]
[2,3,7,5,4,6,1,8]=>[4,1,1,1,1]
[2,3,7,5,4,6,8,1]=>[4,1,1,1,1]
[2,3,8,5,4,6,7,1]=>[4,1,1,1,1]
[2,3,7,5,6,4,1,8]=>[4,1,1,1,1]
[2,3,7,5,6,4,8,1]=>[4,1,1,1,1]
[2,3,8,5,6,4,7,1]=>[4,1,1,1,1]
[2,3,8,5,6,7,4,1]=>[4,1,1,1,1]
[2,3,8,5,7,6,4,1]=>[5,1,1,1]
[2,3,8,6,5,4,7,1]=>[5,1,1,1]
[2,4,3,1,8,6,7,5]=>[3,3,1,1]
[2,4,3,5,8,6,7,1]=>[3,2,1,1,1]
[2,4,3,7,5,6,8,1]=>[3,2,1,1,1]
[2,4,3,8,5,6,7,1]=>[3,2,1,1,1]
[2,4,3,8,5,7,6,1]=>[4,2,1,1]
[2,4,3,8,6,5,7,1]=>[4,2,1,1]
[2,4,3,8,6,7,5,1]=>[4,2,1,1]
[2,5,3,4,1,6,7,8]=>[3,1,1,1,1,1]
[2,5,3,4,1,8,7,6]=>[3,3,1,1]
[2,5,3,4,6,7,1,8]=>[3,1,1,1,1,1]
[2,5,3,4,6,7,8,1]=>[3,1,1,1,1,1]
[2,5,3,4,6,8,7,1]=>[3,2,1,1,1]
[2,5,3,4,7,6,8,1]=>[3,2,1,1,1]
[2,5,3,4,8,6,7,1]=>[3,2,1,1,1]
[2,5,3,4,8,7,6,1]=>[4,2,1,1]
[2,6,3,4,5,1,7,8]=>[3,1,1,1,1,1]
[2,6,3,4,5,7,8,1]=>[3,1,1,1,1,1]
[2,6,3,4,5,8,7,1]=>[3,2,1,1,1]
[2,7,3,4,5,6,1,8]=>[3,1,1,1,1,1]
[2,8,3,4,5,6,7,1]=>[3,1,1,1,1,1]
[2,8,3,4,5,7,6,1]=>[4,1,1,1,1]
[2,6,3,5,4,1,7,8]=>[4,1,1,1,1]
[2,6,3,5,4,1,8,7]=>[4,2,1,1]
[2,6,3,5,4,7,8,1]=>[4,1,1,1,1]
[2,6,3,5,4,8,7,1]=>[4,2,1,1]
[2,7,3,5,4,6,8,1]=>[4,1,1,1,1]
[2,8,3,5,4,7,6,1]=>[4,2,1,1]
[2,7,3,5,6,4,8,1]=>[4,1,1,1,1]
[2,8,3,5,6,7,4,1]=>[4,1,1,1,1]
[2,8,3,5,7,6,4,1]=>[5,1,1,1]
[2,7,3,6,5,4,1,8]=>[5,1,1,1]
[2,8,3,7,5,6,4,1]=>[5,1,1,1]
[2,8,3,7,6,5,4,1]=>[6,1,1]
[2,5,4,3,8,6,7,1]=>[4,2,1,1]
[2,6,4,3,5,1,8,7]=>[4,2,1,1]
[2,6,4,3,5,7,8,1]=>[4,1,1,1,1]
[2,6,4,3,5,8,7,1]=>[4,2,1,1]
[2,7,4,3,5,6,8,1]=>[4,1,1,1,1]
[2,8,4,3,5,6,7,1]=>[4,1,1,1,1]
[2,8,4,3,5,7,6,1]=>[4,2,1,1]
[2,7,4,3,6,5,8,1]=>[4,2,1,1]
[2,8,4,3,6,5,7,1]=>[4,2,1,1]
[2,8,4,3,6,7,5,1]=>[4,2,1,1]
[2,8,4,3,7,6,5,1]=>[5,2,1]
[2,6,4,5,3,1,8,7]=>[4,2,1,1]
[2,6,4,5,3,7,8,1]=>[4,1,1,1,1]
[2,6,4,5,3,8,7,1]=>[4,2,1,1]
[2,8,4,5,3,6,7,1]=>[4,1,1,1,1]
[2,7,4,5,6,3,1,8]=>[4,1,1,1,1]
[2,7,4,5,6,3,8,1]=>[4,1,1,1,1]
[2,8,4,5,6,3,7,1]=>[4,1,1,1,1]
[2,8,4,5,6,7,3,1]=>[4,1,1,1,1]
[2,7,4,6,5,3,1,8]=>[5,1,1,1]
[2,7,4,6,5,3,8,1]=>[5,1,1,1]
[2,8,4,6,5,3,7,1]=>[5,1,1,1]
[2,8,4,7,6,5,3,1]=>[6,1,1]
[2,7,5,4,3,6,8,1]=>[5,1,1,1]
[2,8,5,4,3,6,7,1]=>[5,1,1,1]
[2,8,5,4,3,7,6,1]=>[5,2,1]
[2,7,5,4,6,3,8,1]=>[5,1,1,1]
[2,8,5,4,6,7,3,1]=>[5,1,1,1]
[2,8,5,4,7,6,3,1]=>[5,2,1]
[2,7,6,4,5,3,8,1]=>[5,1,1,1]
[2,8,7,4,5,6,3,1]=>[5,1,1,1]
[2,8,7,4,6,5,3,1]=>[6,1,1]
[2,8,7,5,4,6,3,1]=>[6,1,1]
[2,8,7,5,6,4,3,1]=>[6,1,1]
[3,2,1,4,8,6,7,5]=>[3,3,1,1]
[3,2,1,5,8,6,7,4]=>[3,3,1,1]
[3,2,1,7,5,6,8,4]=>[3,3,1,1]
[3,2,1,8,5,6,7,4]=>[3,3,1,1]
[3,2,1,8,5,7,6,4]=>[4,3,1]
[3,2,1,8,6,5,7,4]=>[4,3,1]
[3,2,1,8,6,7,5,4]=>[4,3,1]
[3,2,4,1,8,6,7,5]=>[3,3,1,1]
[3,2,4,5,8,6,7,1]=>[3,2,1,1,1]
[3,2,4,7,5,6,8,1]=>[3,2,1,1,1]
[3,2,4,8,5,6,7,1]=>[3,2,1,1,1]
[3,2,4,8,6,7,5,1]=>[4,2,1,1]
[3,2,5,4,8,6,7,1]=>[3,2,2,1]
[3,2,6,4,5,1,8,7]=>[3,2,2,1]
[3,2,6,4,5,7,1,8]=>[3,2,1,1,1]
[3,2,7,4,5,6,1,8]=>[3,2,1,1,1]
[3,2,8,4,5,6,7,1]=>[3,2,1,1,1]
[3,2,7,4,6,5,1,8]=>[4,2,1,1]
[3,2,7,4,6,5,8,1]=>[4,2,1,1]
[3,2,8,4,6,5,7,1]=>[4,2,1,1]
[3,2,7,5,4,6,1,8]=>[4,2,1,1]
[3,2,8,5,4,6,7,1]=>[4,2,1,1]
[3,2,8,5,4,7,6,1]=>[4,2,2]
[3,2,7,5,6,4,1,8]=>[4,2,1,1]
[3,2,7,5,6,4,8,1]=>[4,2,1,1]
[3,2,8,5,6,4,7,1]=>[4,2,1,1]
[3,2,8,5,7,6,4,1]=>[5,2,1]
[3,2,8,6,5,7,4,1]=>[5,2,1]
[3,2,8,7,5,6,4,1]=>[5,2,1]
[4,2,3,1,5,7,8,6]=>[3,2,1,1,1]
[4,2,3,1,6,5,8,7]=>[3,2,2,1]
[4,2,3,1,6,7,8,5]=>[3,2,1,1,1]
[4,2,3,1,6,8,7,5]=>[3,3,1,1]
[4,2,3,1,7,6,8,5]=>[3,3,1,1]
[4,2,3,1,8,6,7,5]=>[3,3,1,1]
[4,2,3,1,8,7,6,5]=>[4,3,1]
[4,2,3,5,1,6,8,7]=>[3,2,1,1,1]
[4,2,3,5,1,7,8,6]=>[3,2,1,1,1]
[4,2,3,5,1,8,7,6]=>[3,3,1,1]
[4,2,3,5,6,1,8,7]=>[3,2,1,1,1]
[4,2,3,5,6,8,7,1]=>[3,2,1,1,1]
[4,2,3,5,8,7,6,1]=>[4,2,1,1]
[4,2,3,6,5,1,7,8]=>[3,2,1,1,1]
[4,2,3,6,5,1,8,7]=>[3,2,2,1]
[4,2,3,6,5,8,7,1]=>[3,2,2,1]
[4,2,3,7,5,6,1,8]=>[3,2,1,1,1]
[4,2,3,7,5,6,8,1]=>[3,2,1,1,1]
[4,2,3,8,5,6,7,1]=>[3,2,1,1,1]
[4,2,3,8,5,7,6,1]=>[4,2,1,1]
[4,2,3,7,6,5,8,1]=>[4,2,1,1]
[4,2,3,8,6,7,5,1]=>[4,2,1,1]
[4,2,3,8,7,6,5,1]=>[5,2,1]
[5,2,3,4,1,6,8,7]=>[3,2,1,1,1]
[5,2,3,4,1,7,8,6]=>[3,2,1,1,1]
[5,2,3,4,1,8,7,6]=>[3,3,1,1]
[5,2,3,4,6,1,8,7]=>[3,2,1,1,1]
[5,2,3,4,7,6,1,8]=>[3,2,1,1,1]
[5,2,3,4,8,6,7,1]=>[3,2,1,1,1]
[5,2,3,4,8,7,6,1]=>[4,2,1,1]
[6,2,3,4,5,1,8,7]=>[3,2,1,1,1]
[6,2,3,4,5,8,7,1]=>[3,2,1,1,1]
[8,2,3,4,5,7,6,1]=>[4,1,1,1,1]
[7,2,3,4,6,5,1,8]=>[4,1,1,1,1]
[8,2,3,4,7,6,5,1]=>[5,1,1,1]
[6,2,3,5,4,1,7,8]=>[4,1,1,1,1]
[6,2,3,5,4,1,8,7]=>[4,2,1,1]
[6,2,3,5,4,7,1,8]=>[4,1,1,1,1]
[6,2,3,5,4,7,8,1]=>[4,1,1,1,1]
[7,2,3,5,4,6,1,8]=>[4,1,1,1,1]
[8,2,3,5,4,6,7,1]=>[4,1,1,1,1]
[8,2,3,5,4,7,6,1]=>[4,2,1,1]
[7,2,3,5,6,4,1,8]=>[4,1,1,1,1]
[8,2,3,5,6,7,4,1]=>[4,1,1,1,1]
[8,2,3,5,7,6,4,1]=>[5,1,1,1]
[7,2,3,6,5,4,1,8]=>[5,1,1,1]
[8,2,3,7,5,6,4,1]=>[5,1,1,1]
[8,2,3,7,6,5,4,1]=>[6,1,1]
[5,2,4,3,1,6,7,8]=>[4,1,1,1,1]
[5,2,4,3,1,6,8,7]=>[4,2,1,1]
[5,2,4,3,1,7,6,8]=>[4,2,1,1]
[5,2,4,3,1,8,7,6]=>[4,3,1]
[5,2,4,3,6,1,7,8]=>[4,1,1,1,1]
[5,2,4,3,6,1,8,7]=>[4,2,1,1]
[5,2,4,3,7,6,1,8]=>[4,2,1,1]
[5,2,4,3,7,6,8,1]=>[4,2,1,1]
[5,2,4,3,8,7,6,1]=>[4,3,1]
[6,2,4,3,5,1,8,7]=>[4,2,1,1]
[7,2,4,3,6,5,1,8]=>[4,2,1,1]
[7,2,4,3,6,5,8,1]=>[4,2,1,1]
[8,2,4,3,6,5,7,1]=>[4,2,1,1]
[8,2,4,3,6,7,5,1]=>[4,2,1,1]
[8,2,4,3,7,6,5,1]=>[5,2,1]
[6,2,4,5,3,1,8,7]=>[4,2,1,1]
[6,2,4,5,3,8,7,1]=>[4,2,1,1]
[7,2,4,5,3,6,1,8]=>[4,1,1,1,1]
[7,2,4,5,3,6,8,1]=>[4,1,1,1,1]
[8,2,4,5,3,7,6,1]=>[4,2,1,1]
[8,2,4,5,6,3,7,1]=>[4,1,1,1,1]
[8,2,4,5,6,7,3,1]=>[4,1,1,1,1]
[8,2,4,5,7,6,3,1]=>[5,1,1,1]
[7,2,4,6,5,3,1,8]=>[5,1,1,1]
[7,2,4,6,5,3,8,1]=>[5,1,1,1]
[8,2,4,7,5,6,3,1]=>[5,1,1,1]
[8,2,4,7,6,5,3,1]=>[6,1,1]
[6,2,5,4,3,1,7,8]=>[5,1,1,1]
[6,2,5,4,3,1,8,7]=>[5,2,1]
[6,2,5,4,3,7,1,8]=>[5,1,1,1]
[6,2,5,4,3,7,8,1]=>[5,1,1,1]
[7,2,5,4,3,6,1,8]=>[5,1,1,1]
[8,2,5,4,3,6,7,1]=>[5,1,1,1]
[8,2,5,4,3,7,6,1]=>[5,2,1]
[7,2,5,4,6,3,8,1]=>[5,1,1,1]
[7,2,6,4,5,3,1,8]=>[5,1,1,1]
[7,2,6,4,5,3,8,1]=>[5,1,1,1]
[8,2,6,4,5,3,7,1]=>[5,1,1,1]
[8,2,6,4,5,7,3,1]=>[5,1,1,1]
[8,2,7,4,5,6,3,1]=>[5,1,1,1]
[8,2,7,4,6,5,3,1]=>[6,1,1]
[7,2,6,5,4,3,1,8]=>[6,1,1]
[7,2,6,5,4,3,8,1]=>[6,1,1]
[8,2,6,5,4,3,7,1]=>[6,1,1]
[8,2,6,5,4,7,3,1]=>[6,1,1]
[8,2,7,5,4,6,3,1]=>[6,1,1]
[8,2,7,5,6,4,3,1]=>[6,1,1]
[8,2,7,6,5,4,3,1]=>[7,1]
[4,3,2,1,8,6,7,5]=>[4,3,1]
[4,3,2,7,5,6,8,1]=>[4,2,1,1]
[4,3,2,8,5,6,7,1]=>[4,2,1,1]
[4,3,2,8,5,7,6,1]=>[4,3,1]
[4,3,2,8,6,7,5,1]=>[4,3,1]
[5,3,2,4,1,6,8,7]=>[4,2,1,1]
[5,3,2,4,1,7,6,8]=>[4,2,1,1]
[5,3,2,4,1,8,7,6]=>[4,3,1]
[5,3,2,4,6,1,8,7]=>[4,2,1,1]
[5,3,2,4,7,6,1,8]=>[4,2,1,1]
[8,3,2,4,6,5,7,1]=>[4,2,1,1]
[8,3,2,4,6,7,5,1]=>[4,2,1,1]
[8,3,2,4,7,6,5,1]=>[5,2,1]
[6,3,2,5,4,1,8,7]=>[4,2,2]
[6,3,2,5,4,7,1,8]=>[4,2,1,1]
[6,3,2,5,4,7,8,1]=>[4,2,1,1]
[6,3,2,5,4,8,7,1]=>[4,2,2]
[7,3,2,5,4,6,1,8]=>[4,2,1,1]
[8,3,2,5,4,7,6,1]=>[4,2,2]
[7,3,2,5,6,4,8,1]=>[4,2,1,1]
[8,3,2,5,6,7,4,1]=>[4,2,1,1]
[8,3,2,5,7,6,4,1]=>[5,2,1]
[8,3,2,6,5,7,4,1]=>[5,2,1]
[8,3,2,7,5,6,4,1]=>[5,2,1]
[8,3,2,7,6,5,4,1]=>[6,2]
[5,3,4,2,1,6,8,7]=>[4,2,1,1]
[5,3,4,2,1,7,8,6]=>[4,2,1,1]
[5,3,4,2,1,8,7,6]=>[4,3,1]
[5,3,4,2,6,1,8,7]=>[4,2,1,1]
[5,3,4,2,7,6,1,8]=>[4,2,1,1]
[5,3,4,2,7,6,8,1]=>[4,2,1,1]
[5,3,4,2,8,6,7,1]=>[4,2,1,1]
[6,3,4,2,5,1,8,7]=>[4,2,1,1]
[7,3,4,2,6,5,8,1]=>[4,2,1,1]
[6,3,4,5,2,1,8,7]=>[4,2,1,1]
[6,3,4,5,2,8,7,1]=>[4,2,1,1]
[8,3,4,5,2,7,6,1]=>[4,2,1,1]
[8,3,4,5,7,6,2,1]=>[5,1,1,1]
[8,3,4,7,6,5,2,1]=>[6,1,1]
[6,3,5,4,2,1,8,7]=>[5,2,1]
[6,3,5,4,2,7,1,8]=>[5,1,1,1]
[6,3,5,4,2,7,8,1]=>[5,1,1,1]
[6,3,5,4,2,8,7,1]=>[5,2,1]
[7,3,5,4,2,6,1,8]=>[5,1,1,1]
[8,3,5,4,2,6,7,1]=>[5,1,1,1]
[8,3,5,4,2,7,6,1]=>[5,2,1]
[7,3,5,4,6,2,1,8]=>[5,1,1,1]
[7,3,5,4,6,2,8,1]=>[5,1,1,1]
[8,3,5,4,6,7,2,1]=>[5,1,1,1]
[8,3,5,4,7,6,2,1]=>[5,2,1]
[7,3,6,4,5,2,1,8]=>[5,1,1,1]
[7,3,6,4,5,2,8,1]=>[5,1,1,1]
[8,3,6,4,5,2,7,1]=>[5,1,1,1]
[8,3,6,4,5,7,2,1]=>[5,1,1,1]
[8,3,7,4,5,6,2,1]=>[5,1,1,1]
[8,3,7,4,6,5,2,1]=>[6,1,1]
[7,3,6,5,4,2,1,8]=>[6,1,1]
[7,3,6,5,4,2,8,1]=>[6,1,1]
[8,3,6,5,4,2,7,1]=>[6,1,1]
[8,3,6,5,4,7,2,1]=>[6,1,1]
[8,3,7,5,4,6,2,1]=>[6,1,1]
[8,3,7,5,6,4,2,1]=>[6,1,1]
[8,3,7,6,5,4,2,1]=>[7,1]
[5,4,3,2,8,6,7,1]=>[5,2,1]
[6,4,3,2,5,1,8,7]=>[5,2,1]
[6,4,3,2,5,8,7,1]=>[5,2,1]
[8,4,3,2,5,7,6,1]=>[5,2,1]
[7,4,3,2,6,5,1,8]=>[5,2,1]
[7,4,3,2,6,5,8,1]=>[5,2,1]
[8,4,3,2,6,5,7,1]=>[5,2,1]
[8,4,3,2,6,7,5,1]=>[5,2,1]
[8,4,3,2,7,6,5,1]=>[5,3]
[6,4,3,5,2,1,8,7]=>[5,2,1]
[8,4,3,5,2,7,6,1]=>[5,2,1]
[8,4,3,5,7,6,2,1]=>[5,2,1]
[7,4,3,6,5,2,1,8]=>[5,2,1]
[7,4,3,6,5,2,8,1]=>[5,2,1]
[8,4,3,7,5,6,2,1]=>[5,2,1]
[8,4,3,7,6,5,2,1]=>[6,2]
[6,5,3,4,2,1,8,7]=>[5,2,1]
[8,5,3,4,2,7,6,1]=>[5,2,1]
[8,5,3,4,7,6,2,1]=>[5,2,1]
[8,7,3,4,6,5,2,1]=>[6,1,1]
[7,6,3,5,4,2,1,8]=>[6,1,1]
[7,6,3,5,4,2,8,1]=>[6,1,1]
[8,6,3,5,4,2,7,1]=>[6,1,1]
[8,6,3,5,4,7,2,1]=>[6,1,1]
[8,7,3,5,4,6,2,1]=>[6,1,1]
[8,7,3,5,6,4,2,1]=>[6,1,1]
[8,7,3,6,5,4,2,1]=>[7,1]
[8,5,4,3,2,7,6,1]=>[6,2]
[8,5,4,3,7,6,2,1]=>[6,2]
[8,7,4,3,6,5,2,1]=>[6,2]
[8,7,4,6,5,3,2,1]=>[7,1]
[2,4,1,3,6,5,8,7]=>[2,2,2,1,1]
[2,1,4,6,3,5,8,7]=>[2,2,2,1,1]
[2,4,1,6,3,5,8,7]=>[2,2,2,1,1]
[2,4,6,1,3,5,8,7]=>[2,2,1,1,1,1]
[2,1,4,3,6,8,5,7]=>[2,2,2,1,1]
[2,4,1,3,6,8,5,7]=>[2,2,1,1,1,1]
[2,1,4,6,3,8,5,7]=>[2,2,2,1,1]
[2,4,1,6,3,8,5,7]=>[2,2,2,1,1]
[2,4,6,1,3,8,5,7]=>[2,2,1,1,1,1]
[2,1,4,6,8,3,5,7]=>[2,2,1,1,1,1]
[2,4,1,6,8,3,5,7]=>[2,2,1,1,1,1]
[2,4,6,1,8,3,5,7]=>[2,2,1,1,1,1]
[2,4,6,8,1,3,5,7]=>[2,1,1,1,1,1,1]
[2,4,1,3,6,5,7,8]=>[2,2,1,1,1,1]
[2,1,4,6,3,5,7,8]=>[2,2,1,1,1,1]
[2,4,1,6,3,5,7,8]=>[2,2,1,1,1,1]
[2,4,6,1,3,5,7,8]=>[2,1,1,1,1,1,1]
[2,1,4,6,3,7,5,8]=>[2,2,2,1,1]
[2,4,1,6,3,7,5,8]=>[2,2,2,1,1]
[2,4,6,1,3,7,5,8]=>[2,2,1,1,1,1]
[2,1,4,6,7,3,5,8]=>[2,2,1,1,1,1]
[2,4,1,6,7,3,5,8]=>[2,2,1,1,1,1]
[2,4,6,7,1,3,5,8]=>[2,1,1,1,1,1,1]
[2,4,1,3,6,7,8,5]=>[2,2,1,1,1,1]
[2,1,4,6,3,7,8,5]=>[2,2,2,1,1]
[2,4,1,6,3,7,8,5]=>[2,2,2,1,1]
[2,4,6,1,3,7,8,5]=>[2,2,1,1,1,1]
[2,1,4,6,7,3,8,5]=>[2,2,2,1,1]
[2,4,1,6,7,3,8,5]=>[2,2,2,1,1]
[2,4,6,1,7,3,8,5]=>[2,2,2,1,1]
[2,4,6,7,1,3,8,5]=>[2,2,1,1,1,1]
[2,1,4,6,7,8,3,5]=>[2,2,1,1,1,1]
[2,4,1,6,7,8,3,5]=>[2,2,1,1,1,1]
[2,4,6,1,7,8,3,5]=>[2,2,1,1,1,1]
[2,4,6,7,1,8,3,5]=>[2,2,1,1,1,1]
[2,4,6,7,8,1,3,5]=>[2,1,1,1,1,1,1]
[2,1,4,3,7,5,8,6]=>[2,2,2,2]
[2,4,1,3,7,5,8,6]=>[2,2,2,1,1]
[2,1,4,7,3,5,8,6]=>[2,2,2,1,1]
[2,4,1,7,3,5,8,6]=>[2,2,2,1,1]
[2,4,7,1,3,5,8,6]=>[2,2,1,1,1,1]
[2,1,4,3,7,8,5,6]=>[2,2,2,1,1]
[2,4,1,3,7,8,5,6]=>[2,2,1,1,1,1]
[2,4,1,7,3,8,5,6]=>[2,2,2,1,1]
[2,4,7,1,3,8,5,6]=>[2,2,1,1,1,1]
[2,1,4,7,8,3,5,6]=>[2,2,1,1,1,1]
[2,4,1,7,8,3,5,6]=>[2,2,1,1,1,1]
[2,4,7,1,8,3,5,6]=>[2,2,1,1,1,1]
[2,4,7,8,1,3,5,6]=>[2,1,1,1,1,1,1]
[2,4,1,5,3,7,6,8]=>[2,2,2,1,1]
[2,4,5,1,3,7,6,8]=>[2,2,1,1,1,1]
[2,4,5,1,7,3,6,8]=>[2,2,1,1,1,1]
[2,4,1,5,3,7,8,6]=>[2,2,2,1,1]
[2,4,5,1,3,7,8,6]=>[2,2,1,1,1,1]
[2,1,4,5,7,3,8,6]=>[2,2,2,1,1]
[2,4,1,5,7,3,8,6]=>[2,2,2,1,1]
[2,4,5,1,7,3,8,6]=>[2,2,2,1,1]
[2,4,5,7,1,3,8,6]=>[2,2,1,1,1,1]
[2,1,4,5,7,8,3,6]=>[2,2,1,1,1,1]
[2,4,5,1,7,8,3,6]=>[2,2,1,1,1,1]
[2,4,5,7,1,8,3,6]=>[2,2,1,1,1,1]
[2,4,5,7,8,1,3,6]=>[2,1,1,1,1,1,1]
[2,1,4,3,8,5,6,7]=>[2,2,2,1,1]
[2,4,1,3,8,5,6,7]=>[2,2,1,1,1,1]
[2,1,4,8,3,5,6,7]=>[2,2,1,1,1,1]
[2,4,1,8,3,5,6,7]=>[2,2,1,1,1,1]
[2,4,8,1,3,5,6,7]=>[2,1,1,1,1,1,1]
[2,1,4,3,5,8,6,7]=>[2,2,2,1,1]
[2,4,1,5,3,8,6,7]=>[2,2,2,1,1]
[2,1,4,5,8,3,6,7]=>[2,2,1,1,1,1]
[2,4,1,5,8,3,6,7]=>[2,2,1,1,1,1]
[2,4,5,1,8,3,6,7]=>[2,2,1,1,1,1]
[2,4,1,5,3,6,8,7]=>[2,2,2,1,1]
[2,4,1,5,6,3,8,7]=>[2,2,2,1,1]
[2,4,5,1,6,3,8,7]=>[2,2,2,1,1]
[2,4,5,6,1,3,8,7]=>[2,2,1,1,1,1]
[2,1,4,5,6,8,3,7]=>[2,2,1,1,1,1]
[2,4,1,5,6,8,3,7]=>[2,2,1,1,1,1]
[2,4,5,1,6,8,3,7]=>[2,2,1,1,1,1]
[2,4,5,6,1,8,3,7]=>[2,2,1,1,1,1]
[2,4,5,6,8,1,3,7]=>[2,1,1,1,1,1,1]
[2,4,1,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[2,4,1,5,3,6,7,8]=>[2,2,1,1,1,1]
[2,4,5,1,3,6,7,8]=>[2,1,1,1,1,1,1]
[2,4,1,5,6,3,7,8]=>[2,2,1,1,1,1]
[2,4,5,1,6,3,7,8]=>[2,2,1,1,1,1]
[2,4,5,6,1,3,7,8]=>[2,1,1,1,1,1,1]
[2,4,1,5,6,7,3,8]=>[2,2,1,1,1,1]
[2,4,5,1,6,7,3,8]=>[2,2,1,1,1,1]
[2,4,5,6,1,7,3,8]=>[2,2,1,1,1,1]
[2,4,5,6,7,1,3,8]=>[2,1,1,1,1,1,1]
[2,4,1,5,6,7,8,3]=>[2,2,1,1,1,1]
[2,4,5,1,6,7,8,3]=>[2,2,1,1,1,1]
[2,4,5,6,1,7,8,3]=>[2,2,1,1,1,1]
[2,4,5,6,7,1,8,3]=>[2,2,1,1,1,1]
[2,4,5,6,7,8,1,3]=>[2,1,1,1,1,1,1]
[2,1,5,3,6,4,8,7]=>[2,2,2,2]
[2,5,1,3,6,4,8,7]=>[2,2,2,1,1]
[2,1,5,6,3,4,8,7]=>[2,2,2,1,1]
[2,5,1,6,3,4,8,7]=>[2,2,2,1,1]
[2,5,6,1,3,4,8,7]=>[2,2,1,1,1,1]
[2,1,5,3,6,8,4,7]=>[2,2,2,1,1]
[2,5,1,3,6,8,4,7]=>[2,2,1,1,1,1]
[2,5,1,6,3,8,4,7]=>[2,2,2,1,1]
[2,5,6,1,3,8,4,7]=>[2,2,1,1,1,1]
[2,1,5,6,8,3,4,7]=>[2,2,1,1,1,1]
[2,5,1,6,8,3,4,7]=>[2,2,1,1,1,1]
[2,5,6,8,1,3,4,7]=>[2,1,1,1,1,1,1]
[2,5,1,3,6,4,7,8]=>[2,2,1,1,1,1]
[2,1,5,6,3,4,7,8]=>[2,2,1,1,1,1]
[2,5,1,6,3,4,7,8]=>[2,2,1,1,1,1]
[2,1,5,3,6,7,4,8]=>[2,2,2,1,1]
[2,1,5,6,3,7,4,8]=>[2,2,2,1,1]
[2,5,1,6,3,7,4,8]=>[2,2,2,1,1]
[2,5,6,1,3,7,4,8]=>[2,2,1,1,1,1]
[2,1,5,6,7,3,4,8]=>[2,2,1,1,1,1]
[2,5,1,6,7,3,4,8]=>[2,2,1,1,1,1]
[2,5,6,1,7,3,4,8]=>[2,2,1,1,1,1]
[2,1,5,3,6,7,8,4]=>[2,2,2,1,1]
[2,5,1,3,6,7,8,4]=>[2,2,1,1,1,1]
[2,1,5,6,3,7,8,4]=>[2,2,2,1,1]
[2,5,1,6,3,7,8,4]=>[2,2,2,1,1]
[2,5,6,1,3,7,8,4]=>[2,2,1,1,1,1]
[2,1,5,6,7,3,8,4]=>[2,2,2,1,1]
[2,5,1,6,7,3,8,4]=>[2,2,2,1,1]
[2,5,6,7,1,3,8,4]=>[2,2,1,1,1,1]
[2,1,5,6,7,8,3,4]=>[2,2,1,1,1,1]
[2,5,1,6,7,8,3,4]=>[2,2,1,1,1,1]
[2,5,6,1,7,8,3,4]=>[2,2,1,1,1,1]
[2,5,6,7,1,8,3,4]=>[2,2,1,1,1,1]
[2,5,6,7,8,1,3,4]=>[2,1,1,1,1,1,1]
[2,1,5,3,7,4,8,6]=>[2,2,2,2]
[2,5,1,3,7,4,8,6]=>[2,2,2,1,1]
[2,1,5,7,3,4,8,6]=>[2,2,2,1,1]
[2,5,1,7,3,4,8,6]=>[2,2,2,1,1]
[2,5,7,1,3,4,8,6]=>[2,2,1,1,1,1]
[2,1,5,3,7,8,4,6]=>[2,2,2,1,1]
[2,5,1,3,7,8,4,6]=>[2,2,1,1,1,1]
[2,1,5,7,3,8,4,6]=>[2,2,2,1,1]
[2,5,1,7,3,8,4,6]=>[2,2,2,1,1]
[2,5,7,1,3,8,4,6]=>[2,2,1,1,1,1]
[2,1,5,7,8,3,4,6]=>[2,2,1,1,1,1]
[2,5,1,7,8,3,4,6]=>[2,2,1,1,1,1]
[2,5,7,1,8,3,4,6]=>[2,2,1,1,1,1]
[2,5,7,8,1,3,4,6]=>[2,1,1,1,1,1,1]
[2,1,5,7,3,4,6,8]=>[2,2,1,1,1,1]
[2,3,5,1,4,7,6,8]=>[2,2,1,1,1,1]
[2,3,5,7,1,4,6,8]=>[2,1,1,1,1,1,1]
[2,3,5,1,7,4,8,6]=>[2,2,2,1,1]
[2,3,5,7,1,4,8,6]=>[2,2,1,1,1,1]
[2,3,1,5,7,8,4,6]=>[2,2,1,1,1,1]
[2,3,5,7,1,8,4,6]=>[2,2,1,1,1,1]
[2,3,5,7,8,1,4,6]=>[2,1,1,1,1,1,1]
[2,1,5,3,8,4,6,7]=>[2,2,2,1,1]
[2,5,1,3,8,4,6,7]=>[2,2,1,1,1,1]
[2,1,5,8,3,4,6,7]=>[2,2,1,1,1,1]
[2,5,1,8,3,4,6,7]=>[2,2,1,1,1,1]
[2,5,8,1,3,4,6,7]=>[2,1,1,1,1,1,1]
[2,3,5,1,4,8,6,7]=>[2,2,1,1,1,1]
[2,1,3,5,8,4,6,7]=>[2,2,1,1,1,1]
[2,3,5,1,8,4,6,7]=>[2,2,1,1,1,1]
[2,3,5,8,1,4,6,7]=>[2,1,1,1,1,1,1]
[2,1,5,3,4,6,8,7]=>[2,2,2,1,1]
[2,3,5,1,6,4,8,7]=>[2,2,2,1,1]
[2,3,5,6,1,4,8,7]=>[2,2,1,1,1,1]
[2,3,1,5,6,8,4,7]=>[2,2,1,1,1,1]
[2,3,5,1,6,8,4,7]=>[2,2,1,1,1,1]
[2,3,5,6,1,8,4,7]=>[2,2,1,1,1,1]
[2,3,5,6,8,1,4,7]=>[2,1,1,1,1,1,1]
[2,1,5,3,4,6,7,8]=>[2,2,1,1,1,1]
[2,5,1,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[2,3,5,1,4,6,7,8]=>[2,1,1,1,1,1,1]
[2,3,5,6,1,4,7,8]=>[2,1,1,1,1,1,1]
[2,3,5,6,1,7,4,8]=>[2,2,1,1,1,1]
[2,3,5,6,7,1,4,8]=>[2,1,1,1,1,1,1]
[2,3,5,1,6,7,8,4]=>[2,2,1,1,1,1]
[2,3,5,6,1,7,8,4]=>[2,2,1,1,1,1]
[2,3,5,6,7,1,8,4]=>[2,2,1,1,1,1]
[2,3,5,6,7,8,1,4]=>[2,1,1,1,1,1,1]
[2,1,6,3,7,4,8,5]=>[2,2,2,2]
[2,6,1,3,7,4,8,5]=>[2,2,2,1,1]
[2,1,6,7,3,4,8,5]=>[2,2,2,1,1]
[2,6,1,7,3,4,8,5]=>[2,2,2,1,1]
[2,6,7,1,3,4,8,5]=>[2,2,1,1,1,1]
[2,1,6,3,7,8,4,5]=>[2,2,2,1,1]
[2,6,1,3,7,8,4,5]=>[2,2,1,1,1,1]
[2,1,6,7,3,8,4,5]=>[2,2,2,1,1]
[2,6,1,7,3,8,4,5]=>[2,2,2,1,1]
[2,1,6,7,8,3,4,5]=>[2,2,1,1,1,1]
[2,6,1,7,8,3,4,5]=>[2,2,1,1,1,1]
[2,6,7,1,8,3,4,5]=>[2,2,1,1,1,1]
[2,6,7,8,1,3,4,5]=>[2,1,1,1,1,1,1]
[2,1,6,3,7,4,5,8]=>[2,2,2,1,1]
[2,6,1,7,3,4,5,8]=>[2,2,1,1,1,1]
[2,6,7,1,3,4,5,8]=>[2,1,1,1,1,1,1]
[2,6,1,3,4,7,5,8]=>[2,2,1,1,1,1]
[2,3,1,6,4,7,5,8]=>[2,2,2,1,1]
[2,3,6,1,4,7,5,8]=>[2,2,1,1,1,1]
[2,3,6,7,1,4,5,8]=>[2,1,1,1,1,1,1]
[2,1,6,3,4,7,8,5]=>[2,2,2,1,1]
[2,6,1,3,4,7,8,5]=>[2,2,1,1,1,1]
[2,3,6,1,4,7,8,5]=>[2,2,1,1,1,1]
[2,1,3,6,7,4,8,5]=>[2,2,2,1,1]
[2,3,6,7,1,4,8,5]=>[2,2,1,1,1,1]
[2,1,3,6,7,8,4,5]=>[2,2,1,1,1,1]
[2,3,1,6,7,8,4,5]=>[2,2,1,1,1,1]
[2,3,6,1,7,8,4,5]=>[2,2,1,1,1,1]
[2,3,6,7,1,8,4,5]=>[2,2,1,1,1,1]
[2,3,6,7,8,1,4,5]=>[2,1,1,1,1,1,1]
[2,1,6,3,8,4,5,7]=>[2,2,2,1,1]
[2,6,1,3,8,4,5,7]=>[2,2,1,1,1,1]
[2,1,6,8,3,4,5,7]=>[2,2,1,1,1,1]
[2,6,1,8,3,4,5,7]=>[2,2,1,1,1,1]
[2,6,8,1,3,4,5,7]=>[2,1,1,1,1,1,1]
[2,1,6,3,4,8,5,7]=>[2,2,2,1,1]
[2,6,1,3,4,8,5,7]=>[2,2,1,1,1,1]
[2,3,1,6,4,8,5,7]=>[2,2,2,1,1]
[2,3,6,1,4,8,5,7]=>[2,2,1,1,1,1]
[2,3,1,6,8,4,5,7]=>[2,2,1,1,1,1]
[2,3,6,1,8,4,5,7]=>[2,2,1,1,1,1]
[2,3,6,8,1,4,5,7]=>[2,1,1,1,1,1,1]
[2,1,6,3,4,5,8,7]=>[2,2,2,1,1]
[2,6,1,3,4,5,8,7]=>[2,2,1,1,1,1]
[2,1,3,6,4,5,8,7]=>[2,2,2,1,1]
[2,3,6,1,4,5,8,7]=>[2,2,1,1,1,1]
[2,3,4,1,6,8,5,7]=>[2,2,1,1,1,1]
[2,3,4,6,1,8,5,7]=>[2,2,1,1,1,1]
[2,3,4,6,8,1,5,7]=>[2,1,1,1,1,1,1]
[2,6,1,3,4,5,7,8]=>[2,1,1,1,1,1,1]
[2,1,3,6,4,5,7,8]=>[2,2,1,1,1,1]
[2,3,1,6,4,5,7,8]=>[2,2,1,1,1,1]
[2,3,6,1,4,5,7,8]=>[2,1,1,1,1,1,1]
[2,3,4,6,1,5,7,8]=>[2,1,1,1,1,1,1]
[2,3,4,6,7,1,5,8]=>[2,1,1,1,1,1,1]
[2,3,4,6,1,7,8,5]=>[2,2,1,1,1,1]
[2,3,4,6,7,8,1,5]=>[2,1,1,1,1,1,1]
[2,1,7,3,8,4,5,6]=>[2,2,2,1,1]
[2,7,1,3,8,4,5,6]=>[2,2,1,1,1,1]
[2,1,7,8,3,4,5,6]=>[2,2,1,1,1,1]
[2,7,1,8,3,4,5,6]=>[2,2,1,1,1,1]
[2,7,8,1,3,4,5,6]=>[2,1,1,1,1,1,1]
[2,1,7,3,4,8,5,6]=>[2,2,2,1,1]
[2,1,3,7,4,8,5,6]=>[2,2,2,1,1]
[2,3,1,7,4,8,5,6]=>[2,2,2,1,1]
[2,3,7,1,4,8,5,6]=>[2,2,1,1,1,1]
[2,1,3,7,8,4,5,6]=>[2,2,1,1,1,1]
[2,3,1,7,8,4,5,6]=>[2,2,1,1,1,1]
[2,3,7,8,1,4,5,6]=>[2,1,1,1,1,1,1]
[2,1,7,3,4,5,8,6]=>[2,2,2,1,1]
[2,7,1,3,4,5,8,6]=>[2,2,1,1,1,1]
[2,3,1,7,4,5,8,6]=>[2,2,2,1,1]
[2,3,7,1,4,5,8,6]=>[2,2,1,1,1,1]
[2,1,3,4,7,5,8,6]=>[2,2,2,1,1]
[2,3,4,1,7,5,8,6]=>[2,2,2,1,1]
[2,3,4,7,1,5,8,6]=>[2,2,1,1,1,1]
[2,1,3,4,7,8,5,6]=>[2,2,1,1,1,1]
[2,3,1,4,7,8,5,6]=>[2,2,1,1,1,1]
[2,3,4,1,7,8,5,6]=>[2,2,1,1,1,1]
[2,3,4,7,1,8,5,6]=>[2,2,1,1,1,1]
[2,3,4,7,8,1,5,6]=>[2,1,1,1,1,1,1]
[2,1,7,3,4,5,6,8]=>[2,2,1,1,1,1]
[2,7,1,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[2,3,7,1,4,5,6,8]=>[2,1,1,1,1,1,1]
[2,1,3,4,7,5,6,8]=>[2,2,1,1,1,1]
[2,3,1,4,7,5,6,8]=>[2,2,1,1,1,1]
[2,3,4,1,7,5,6,8]=>[2,2,1,1,1,1]
[2,3,4,7,1,5,6,8]=>[2,1,1,1,1,1,1]
[2,3,4,5,7,1,6,8]=>[2,1,1,1,1,1,1]
[2,3,4,5,7,1,8,6]=>[2,2,1,1,1,1]
[2,3,4,5,7,8,1,6]=>[2,1,1,1,1,1,1]
[2,1,8,3,4,5,6,7]=>[2,2,1,1,1,1]
[2,8,1,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[2,1,3,8,4,5,6,7]=>[2,2,1,1,1,1]
[2,3,1,8,4,5,6,7]=>[2,2,1,1,1,1]
[2,3,8,1,4,5,6,7]=>[2,1,1,1,1,1,1]
[2,1,3,4,8,5,6,7]=>[2,2,1,1,1,1]
[2,3,1,4,8,5,6,7]=>[2,2,1,1,1,1]
[2,3,4,1,8,5,6,7]=>[2,2,1,1,1,1]
[2,3,4,8,1,5,6,7]=>[2,1,1,1,1,1,1]
[2,1,3,4,5,8,6,7]=>[2,2,1,1,1,1]
[2,3,1,4,5,8,6,7]=>[2,2,1,1,1,1]
[2,3,4,1,5,8,6,7]=>[2,2,1,1,1,1]
[2,3,4,5,1,8,6,7]=>[2,2,1,1,1,1]
[2,3,4,5,8,1,6,7]=>[2,1,1,1,1,1,1]
[2,3,4,5,6,8,1,7]=>[2,1,1,1,1,1,1]
[3,1,4,2,6,5,8,7]=>[2,2,2,2]
[3,4,1,2,6,5,8,7]=>[2,2,2,1,1]
[3,1,4,6,2,5,8,7]=>[2,2,2,1,1]
[3,4,1,6,2,5,8,7]=>[2,2,2,1,1]
[3,4,6,1,2,5,8,7]=>[2,2,1,1,1,1]
[3,1,4,2,6,8,5,7]=>[2,2,2,1,1]
[3,4,1,2,6,8,5,7]=>[2,2,1,1,1,1]
[3,1,4,6,2,8,5,7]=>[2,2,2,1,1]
[3,4,1,6,2,8,5,7]=>[2,2,2,1,1]
[3,1,4,6,8,2,5,7]=>[2,2,1,1,1,1]
[3,4,1,6,8,2,5,7]=>[2,2,1,1,1,1]
[3,4,6,8,1,2,5,7]=>[2,1,1,1,1,1,1]
[3,1,4,2,6,5,7,8]=>[2,2,2,1,1]
[3,4,1,2,6,5,7,8]=>[2,2,1,1,1,1]
[3,1,4,2,6,7,5,8]=>[2,2,2,1,1]
[3,4,1,2,6,7,5,8]=>[2,2,1,1,1,1]
[3,4,1,6,2,7,5,8]=>[2,2,2,1,1]
[3,4,6,1,2,7,5,8]=>[2,2,1,1,1,1]
[3,4,1,6,7,2,5,8]=>[2,2,1,1,1,1]
[3,4,6,7,1,2,5,8]=>[2,1,1,1,1,1,1]
[3,1,4,2,6,7,8,5]=>[2,2,2,1,1]
[3,4,1,2,6,7,8,5]=>[2,2,1,1,1,1]
[3,1,4,6,2,7,8,5]=>[2,2,2,1,1]
[3,4,1,6,2,7,8,5]=>[2,2,2,1,1]
[3,4,6,1,2,7,8,5]=>[2,2,1,1,1,1]
[3,1,4,6,7,2,8,5]=>[2,2,2,1,1]
[3,4,1,6,7,2,8,5]=>[2,2,2,1,1]
[3,4,6,1,7,2,8,5]=>[2,2,2,1,1]
[3,4,6,7,1,2,8,5]=>[2,2,1,1,1,1]
[3,1,4,6,7,8,2,5]=>[2,2,1,1,1,1]
[3,4,1,6,7,8,2,5]=>[2,2,1,1,1,1]
[3,4,6,1,7,8,2,5]=>[2,2,1,1,1,1]
[3,4,6,7,1,8,2,5]=>[2,2,1,1,1,1]
[3,4,6,7,8,1,2,5]=>[2,1,1,1,1,1,1]
[3,1,4,2,7,5,8,6]=>[2,2,2,2]
[3,4,1,2,7,5,8,6]=>[2,2,2,1,1]
[3,1,4,7,2,5,8,6]=>[2,2,2,1,1]
[3,4,1,7,2,5,8,6]=>[2,2,2,1,1]
[3,4,7,1,2,5,8,6]=>[2,2,1,1,1,1]
[3,1,4,2,7,8,5,6]=>[2,2,2,1,1]
[3,4,1,2,7,8,5,6]=>[2,2,1,1,1,1]
[3,1,4,7,2,8,5,6]=>[2,2,2,1,1]
[3,4,7,1,8,2,5,6]=>[2,2,1,1,1,1]
[3,4,7,8,1,2,5,6]=>[2,1,1,1,1,1,1]
[3,1,4,2,7,5,6,8]=>[2,2,2,1,1]
[3,4,1,2,7,5,6,8]=>[2,2,1,1,1,1]
[3,4,1,2,5,7,6,8]=>[2,2,1,1,1,1]
[3,1,4,5,2,7,6,8]=>[2,2,2,1,1]
[3,4,1,5,2,7,6,8]=>[2,2,2,1,1]
[3,4,1,5,7,2,6,8]=>[2,2,1,1,1,1]
[3,4,5,1,7,2,6,8]=>[2,2,1,1,1,1]
[3,4,5,7,1,2,6,8]=>[2,1,1,1,1,1,1]
[3,1,4,2,5,7,8,6]=>[2,2,2,1,1]
[3,4,1,2,5,7,8,6]=>[2,2,1,1,1,1]
[3,1,4,5,2,7,8,6]=>[2,2,2,1,1]
[3,4,5,1,2,7,8,6]=>[2,2,1,1,1,1]
[3,1,4,5,7,2,8,6]=>[2,2,2,1,1]
[3,4,1,5,7,2,8,6]=>[2,2,2,1,1]
[3,4,5,7,1,2,8,6]=>[2,2,1,1,1,1]
[3,1,4,5,7,8,2,6]=>[2,2,1,1,1,1]
[3,4,1,5,7,8,2,6]=>[2,2,1,1,1,1]
[3,4,5,1,7,8,2,6]=>[2,2,1,1,1,1]
[3,4,5,7,1,8,2,6]=>[2,2,1,1,1,1]
[3,4,5,7,8,1,2,6]=>[2,1,1,1,1,1,1]
[3,1,4,2,8,5,6,7]=>[2,2,2,1,1]
[3,4,1,2,8,5,6,7]=>[2,2,1,1,1,1]
[3,1,4,8,2,5,6,7]=>[2,2,1,1,1,1]
[3,4,1,8,2,5,6,7]=>[2,2,1,1,1,1]
[3,4,8,1,2,5,6,7]=>[2,1,1,1,1,1,1]
[3,1,4,2,5,8,6,7]=>[2,2,2,1,1]
[3,4,1,2,5,8,6,7]=>[2,2,1,1,1,1]
[3,4,1,5,2,8,6,7]=>[2,2,2,1,1]
[3,1,4,5,8,2,6,7]=>[2,2,1,1,1,1]
[3,4,1,5,8,2,6,7]=>[2,2,1,1,1,1]
[3,4,5,8,1,2,6,7]=>[2,1,1,1,1,1,1]
[3,4,1,2,5,6,8,7]=>[2,2,1,1,1,1]
[3,4,5,1,2,6,8,7]=>[2,2,1,1,1,1]
[3,1,4,5,6,2,8,7]=>[2,2,2,1,1]
[3,4,1,5,6,2,8,7]=>[2,2,2,1,1]
[3,4,5,1,6,2,8,7]=>[2,2,2,1,1]
[3,4,5,6,1,2,8,7]=>[2,2,1,1,1,1]
[3,1,4,5,6,8,2,7]=>[2,2,1,1,1,1]
[3,4,1,5,6,8,2,7]=>[2,2,1,1,1,1]
[3,4,5,6,1,8,2,7]=>[2,2,1,1,1,1]
[3,4,5,6,8,1,2,7]=>[2,1,1,1,1,1,1]
[3,1,4,2,5,6,7,8]=>[2,2,1,1,1,1]
[3,1,4,5,2,6,7,8]=>[2,2,1,1,1,1]
[3,4,1,5,2,6,7,8]=>[2,2,1,1,1,1]
[3,4,1,5,6,2,7,8]=>[2,2,1,1,1,1]
[3,4,5,1,6,2,7,8]=>[2,2,1,1,1,1]
[3,1,4,5,6,7,2,8]=>[2,2,1,1,1,1]
[3,4,1,5,6,7,2,8]=>[2,2,1,1,1,1]
[3,4,5,1,6,7,2,8]=>[2,2,1,1,1,1]
[3,4,5,6,1,7,2,8]=>[2,2,1,1,1,1]
[3,1,4,5,6,7,8,2]=>[2,2,1,1,1,1]
[3,4,1,5,6,7,8,2]=>[2,2,1,1,1,1]
[3,4,5,1,6,7,8,2]=>[2,2,1,1,1,1]
[3,4,5,6,1,7,8,2]=>[2,2,1,1,1,1]
[3,4,5,6,7,1,8,2]=>[2,2,1,1,1,1]
[3,1,5,2,6,4,8,7]=>[2,2,2,2]
[3,5,1,2,6,4,8,7]=>[2,2,2,1,1]
[3,1,5,6,2,4,8,7]=>[2,2,2,1,1]
[3,5,1,6,2,4,8,7]=>[2,2,2,1,1]
[3,5,6,1,2,4,8,7]=>[2,2,1,1,1,1]
[3,1,5,2,6,8,4,7]=>[2,2,2,1,1]
[3,5,1,2,6,8,4,7]=>[2,2,1,1,1,1]
[3,1,5,6,2,8,4,7]=>[2,2,2,1,1]
[3,5,6,1,2,8,4,7]=>[2,2,1,1,1,1]
[3,1,5,6,8,2,4,7]=>[2,2,1,1,1,1]
[3,5,1,6,8,2,4,7]=>[2,2,1,1,1,1]
[3,5,6,1,8,2,4,7]=>[2,2,1,1,1,1]
[3,5,6,8,1,2,4,7]=>[2,1,1,1,1,1,1]
[3,1,5,6,2,4,7,8]=>[2,2,1,1,1,1]
[3,5,1,6,2,4,7,8]=>[2,2,1,1,1,1]
[3,5,6,1,2,4,7,8]=>[2,1,1,1,1,1,1]
[3,5,1,2,6,7,4,8]=>[2,2,1,1,1,1]
[3,5,1,6,2,7,4,8]=>[2,2,2,1,1]
[3,5,6,1,2,7,4,8]=>[2,2,1,1,1,1]
[3,5,1,6,7,2,4,8]=>[2,2,1,1,1,1]
[3,5,6,1,7,2,4,8]=>[2,2,1,1,1,1]
[3,5,6,7,1,2,4,8]=>[2,1,1,1,1,1,1]
[3,1,5,2,6,7,8,4]=>[2,2,2,1,1]
[3,5,1,2,6,7,8,4]=>[2,2,1,1,1,1]
[3,1,5,6,2,7,8,4]=>[2,2,2,1,1]
[3,5,1,6,2,7,8,4]=>[2,2,2,1,1]
[3,5,6,1,2,7,8,4]=>[2,2,1,1,1,1]
[3,1,5,6,7,2,8,4]=>[2,2,2,1,1]
[3,5,1,6,7,2,8,4]=>[2,2,2,1,1]
[3,5,6,1,7,2,8,4]=>[2,2,2,1,1]
[3,5,6,7,1,2,8,4]=>[2,2,1,1,1,1]
[3,1,5,6,7,8,2,4]=>[2,2,1,1,1,1]
[3,5,1,6,7,8,2,4]=>[2,2,1,1,1,1]
[3,5,6,1,7,8,2,4]=>[2,2,1,1,1,1]
[3,5,6,7,1,8,2,4]=>[2,2,1,1,1,1]
[3,5,6,7,8,1,2,4]=>[2,1,1,1,1,1,1]
[3,1,5,2,7,4,8,6]=>[2,2,2,2]
[3,5,1,2,7,4,8,6]=>[2,2,2,1,1]
[3,1,5,7,2,4,8,6]=>[2,2,2,1,1]
[3,5,7,1,2,4,8,6]=>[2,2,1,1,1,1]
[3,1,5,2,7,8,4,6]=>[2,2,2,1,1]
[3,5,1,2,7,8,4,6]=>[2,2,1,1,1,1]
[3,1,5,7,2,8,4,6]=>[2,2,2,1,1]
[3,5,1,7,2,8,4,6]=>[2,2,2,1,1]
[3,5,7,1,2,8,4,6]=>[2,2,1,1,1,1]
[3,1,5,7,8,2,4,6]=>[2,2,1,1,1,1]
[3,5,1,7,8,2,4,6]=>[2,2,1,1,1,1]
[3,5,7,8,1,2,4,6]=>[2,1,1,1,1,1,1]
[3,1,5,2,7,4,6,8]=>[2,2,2,1,1]
[3,5,1,2,7,4,6,8]=>[2,2,1,1,1,1]
[3,1,5,7,2,4,6,8]=>[2,2,1,1,1,1]
[3,5,1,7,2,4,6,8]=>[2,2,1,1,1,1]
[3,5,7,1,2,4,6,8]=>[2,1,1,1,1,1,1]
[3,1,5,2,4,7,6,8]=>[2,2,2,1,1]
[3,5,1,2,4,7,6,8]=>[2,2,1,1,1,1]
[3,1,2,5,4,7,6,8]=>[2,2,2,1,1]
[1,3,5,2,4,7,6,8]=>[2,2,1,1,1,1]
[3,1,2,5,7,4,6,8]=>[2,2,1,1,1,1]
[1,3,2,5,7,4,6,8]=>[2,2,1,1,1,1]
[1,3,5,2,7,4,6,8]=>[2,2,1,1,1,1]
[1,3,5,7,2,4,6,8]=>[2,1,1,1,1,1,1]
[3,1,5,2,4,7,8,6]=>[2,2,2,1,1]
[3,5,1,2,4,7,8,6]=>[2,2,1,1,1,1]
[1,3,5,2,4,7,8,6]=>[2,2,1,1,1,1]
[3,1,2,5,7,4,8,6]=>[2,2,2,1,1]
[1,3,2,5,7,4,8,6]=>[2,2,2,1,1]
[1,3,5,2,7,4,8,6]=>[2,2,2,1,1]
[1,3,5,7,2,4,8,6]=>[2,2,1,1,1,1]
[3,1,2,5,7,8,4,6]=>[2,2,1,1,1,1]
[1,3,2,5,7,8,4,6]=>[2,2,1,1,1,1]
[1,3,5,2,7,8,4,6]=>[2,2,1,1,1,1]
[1,3,5,7,2,8,4,6]=>[2,2,1,1,1,1]
[1,3,5,7,8,2,4,6]=>[2,1,1,1,1,1,1]
[3,1,5,2,8,4,6,7]=>[2,2,2,1,1]
[3,5,1,2,8,4,6,7]=>[2,2,1,1,1,1]
[3,1,5,8,2,4,6,7]=>[2,2,1,1,1,1]
[3,5,1,8,2,4,6,7]=>[2,2,1,1,1,1]
[3,1,5,2,4,8,6,7]=>[2,2,2,1,1]
[3,5,1,2,4,8,6,7]=>[2,2,1,1,1,1]
[1,3,2,5,4,8,6,7]=>[2,2,2,1,1]
[1,3,5,2,4,8,6,7]=>[2,2,1,1,1,1]
[3,1,2,5,8,4,6,7]=>[2,2,1,1,1,1]
[1,3,2,5,8,4,6,7]=>[2,2,1,1,1,1]
[1,3,5,2,8,4,6,7]=>[2,2,1,1,1,1]
[1,3,5,8,2,4,6,7]=>[2,1,1,1,1,1,1]
[3,1,5,2,4,6,8,7]=>[2,2,2,1,1]
[3,5,1,2,4,6,8,7]=>[2,2,1,1,1,1]
[3,1,2,5,4,6,8,7]=>[2,2,2,1,1]
[1,3,5,2,4,6,8,7]=>[2,2,1,1,1,1]
[1,3,5,6,2,4,8,7]=>[2,2,1,1,1,1]
[3,1,2,5,6,8,4,7]=>[2,2,1,1,1,1]
[1,3,5,2,6,8,4,7]=>[2,2,1,1,1,1]
[1,3,5,6,2,8,4,7]=>[2,2,1,1,1,1]
[1,3,5,6,8,2,4,7]=>[2,1,1,1,1,1,1]
[3,1,5,2,4,6,7,8]=>[2,2,1,1,1,1]
[3,5,1,2,4,6,7,8]=>[2,1,1,1,1,1,1]
[1,3,5,2,4,6,7,8]=>[2,1,1,1,1,1,1]
[3,1,2,5,6,4,7,8]=>[2,2,1,1,1,1]
[1,3,5,2,6,4,7,8]=>[2,2,1,1,1,1]
[1,3,5,6,2,4,7,8]=>[2,1,1,1,1,1,1]
[3,1,2,5,6,7,4,8]=>[2,2,1,1,1,1]
[1,3,5,2,6,7,4,8]=>[2,2,1,1,1,1]
[1,3,5,6,2,7,4,8]=>[2,2,1,1,1,1]
[1,3,5,6,7,2,4,8]=>[2,1,1,1,1,1,1]
[3,1,2,5,6,7,8,4]=>[2,2,1,1,1,1]
[1,3,5,2,6,7,8,4]=>[2,2,1,1,1,1]
[1,3,5,6,2,7,8,4]=>[2,2,1,1,1,1]
[1,3,5,6,7,2,8,4]=>[2,2,1,1,1,1]
[1,3,5,6,7,8,2,4]=>[2,1,1,1,1,1,1]
[3,1,6,2,7,4,8,5]=>[2,2,2,2]
[3,6,1,2,7,4,8,5]=>[2,2,2,1,1]
[3,6,1,7,2,4,8,5]=>[2,2,2,1,1]
[3,6,7,1,2,4,8,5]=>[2,2,1,1,1,1]
[3,6,1,2,7,8,4,5]=>[2,2,1,1,1,1]
[3,1,6,7,2,8,4,5]=>[2,2,2,1,1]
[3,6,1,7,2,8,4,5]=>[2,2,2,1,1]
[3,6,7,1,2,8,4,5]=>[2,2,1,1,1,1]
[3,6,1,7,8,2,4,5]=>[2,2,1,1,1,1]
[3,6,7,8,1,2,4,5]=>[2,1,1,1,1,1,1]
[3,1,6,2,7,4,5,8]=>[2,2,2,1,1]
[3,1,6,7,2,4,5,8]=>[2,2,1,1,1,1]
[3,6,7,1,2,4,5,8]=>[2,1,1,1,1,1,1]
[3,6,1,2,4,7,5,8]=>[2,2,1,1,1,1]
[3,1,2,6,4,7,5,8]=>[2,2,2,1,1]
[1,3,2,6,4,7,5,8]=>[2,2,2,1,1]
[1,3,6,2,4,7,5,8]=>[2,2,1,1,1,1]
[1,3,2,6,7,4,5,8]=>[2,2,1,1,1,1]
[1,3,6,2,7,4,5,8]=>[2,2,1,1,1,1]
[3,1,6,2,4,7,8,5]=>[2,2,2,1,1]
[3,6,1,2,4,7,8,5]=>[2,2,1,1,1,1]
[3,1,2,6,4,7,8,5]=>[2,2,2,1,1]
[1,3,2,6,4,7,8,5]=>[2,2,2,1,1]
[1,3,6,2,4,7,8,5]=>[2,2,1,1,1,1]
[3,1,2,6,7,4,8,5]=>[2,2,2,1,1]
[1,3,2,6,7,4,8,5]=>[2,2,2,1,1]
[1,3,6,2,7,4,8,5]=>[2,2,2,1,1]
[3,1,2,6,7,8,4,5]=>[2,2,1,1,1,1]
[1,3,2,6,7,8,4,5]=>[2,2,1,1,1,1]
[1,3,6,2,7,8,4,5]=>[2,2,1,1,1,1]
[1,3,6,7,8,2,4,5]=>[2,1,1,1,1,1,1]
[3,1,6,2,8,4,5,7]=>[2,2,2,1,1]
[3,1,6,8,2,4,5,7]=>[2,2,1,1,1,1]
[3,6,1,8,2,4,5,7]=>[2,2,1,1,1,1]
[3,6,8,1,2,4,5,7]=>[2,1,1,1,1,1,1]
[3,1,6,2,4,8,5,7]=>[2,2,2,1,1]
[3,6,1,2,4,8,5,7]=>[2,2,1,1,1,1]
[1,3,2,6,4,8,5,7]=>[2,2,2,1,1]
[1,3,6,2,4,8,5,7]=>[2,2,1,1,1,1]
[3,1,2,6,8,4,5,7]=>[2,2,1,1,1,1]
[1,3,2,6,8,4,5,7]=>[2,2,1,1,1,1]
[3,1,6,2,4,5,8,7]=>[2,2,2,1,1]
[3,6,1,2,4,5,8,7]=>[2,2,1,1,1,1]
[3,1,2,6,4,5,8,7]=>[2,2,2,1,1]
[1,3,6,2,4,5,8,7]=>[2,2,1,1,1,1]
[3,1,2,4,6,5,8,7]=>[2,2,2,1,1]
[1,3,4,6,2,5,8,7]=>[2,2,1,1,1,1]
[3,1,2,4,6,8,5,7]=>[2,2,1,1,1,1]
[1,3,2,4,6,8,5,7]=>[2,2,1,1,1,1]
[1,3,4,6,8,2,5,7]=>[2,1,1,1,1,1,1]
[3,1,6,2,4,5,7,8]=>[2,2,1,1,1,1]
[3,6,1,2,4,5,7,8]=>[2,1,1,1,1,1,1]
[1,3,2,6,4,5,7,8]=>[2,2,1,1,1,1]
[1,3,6,2,4,5,7,8]=>[2,1,1,1,1,1,1]
[1,3,4,6,2,5,7,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,6,7,5,8]=>[2,2,1,1,1,1]
[1,3,4,6,2,7,5,8]=>[2,2,1,1,1,1]
[1,3,4,6,7,2,5,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,6,7,8,5]=>[2,2,1,1,1,1]
[1,3,4,6,7,2,8,5]=>[2,2,1,1,1,1]
[3,1,7,2,8,4,5,6]=>[2,2,2,1,1]
[3,7,1,2,8,4,5,6]=>[2,2,1,1,1,1]
[3,1,7,8,2,4,5,6]=>[2,2,1,1,1,1]
[3,7,1,8,2,4,5,6]=>[2,2,1,1,1,1]
[3,7,8,1,2,4,5,6]=>[2,1,1,1,1,1,1]
[3,7,1,2,4,8,5,6]=>[2,2,1,1,1,1]
[3,1,2,7,4,8,5,6]=>[2,2,2,1,1]
[1,3,2,7,4,8,5,6]=>[2,2,2,1,1]
[1,3,7,2,4,8,5,6]=>[2,2,1,1,1,1]
[3,1,2,7,8,4,5,6]=>[2,2,1,1,1,1]
[1,3,7,2,8,4,5,6]=>[2,2,1,1,1,1]
[1,3,7,8,2,4,5,6]=>[2,1,1,1,1,1,1]
[3,1,7,2,4,5,8,6]=>[2,2,2,1,1]
[3,7,1,2,4,5,8,6]=>[2,2,1,1,1,1]
[1,3,7,2,4,5,8,6]=>[2,2,1,1,1,1]
[3,1,2,4,7,5,8,6]=>[2,2,2,1,1]
[1,3,2,4,7,5,8,6]=>[2,2,2,1,1]
[1,3,4,2,7,5,8,6]=>[2,2,2,1,1]
[3,1,2,4,7,8,5,6]=>[2,2,1,1,1,1]
[1,3,2,4,7,8,5,6]=>[2,2,1,1,1,1]
[1,3,4,2,7,8,5,6]=>[2,2,1,1,1,1]
[1,3,4,7,8,2,5,6]=>[2,1,1,1,1,1,1]
[3,1,7,2,4,5,6,8]=>[2,2,1,1,1,1]
[3,7,1,2,4,5,6,8]=>[2,1,1,1,1,1,1]
[3,1,2,7,4,5,6,8]=>[2,2,1,1,1,1]
[1,3,2,7,4,5,6,8]=>[2,2,1,1,1,1]
[1,3,7,2,4,5,6,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,7,5,6,8]=>[2,2,1,1,1,1]
[1,3,4,7,2,5,6,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,5,7,6,8]=>[2,2,1,1,1,1]
[1,3,4,5,7,2,6,8]=>[2,1,1,1,1,1,1]
[3,1,2,4,5,7,8,6]=>[2,2,1,1,1,1]
[1,3,4,5,7,2,8,6]=>[2,2,1,1,1,1]
[1,3,4,5,7,8,2,6]=>[2,1,1,1,1,1,1]
[3,1,8,2,4,5,6,7]=>[2,2,1,1,1,1]
[3,8,1,2,4,5,6,7]=>[2,1,1,1,1,1,1]
[3,1,2,8,4,5,6,7]=>[2,2,1,1,1,1]
[1,3,2,8,4,5,6,7]=>[2,2,1,1,1,1]
[1,3,8,2,4,5,6,7]=>[2,1,1,1,1,1,1]
[3,1,2,4,8,5,6,7]=>[2,2,1,1,1,1]
[1,3,2,4,8,5,6,7]=>[2,2,1,1,1,1]
[1,3,4,2,8,5,6,7]=>[2,2,1,1,1,1]
[1,3,4,8,2,5,6,7]=>[2,1,1,1,1,1,1]
[3,1,2,4,5,8,6,7]=>[2,2,1,1,1,1]
[1,3,2,4,5,8,6,7]=>[2,2,1,1,1,1]
[1,3,4,2,5,8,6,7]=>[2,2,1,1,1,1]
[1,3,4,5,2,8,6,7]=>[2,2,1,1,1,1]
[1,3,4,5,8,2,6,7]=>[2,1,1,1,1,1,1]
[3,1,2,4,5,6,8,7]=>[2,2,1,1,1,1]
[1,3,4,5,6,8,2,7]=>[2,1,1,1,1,1,1]
[4,1,5,2,6,3,8,7]=>[2,2,2,2]
[4,5,1,2,6,3,8,7]=>[2,2,2,1,1]
[4,1,5,6,2,3,8,7]=>[2,2,2,1,1]
[4,5,1,6,2,3,8,7]=>[2,2,2,1,1]
[4,5,6,1,2,3,8,7]=>[2,2,1,1,1,1]
[4,1,5,2,6,8,3,7]=>[2,2,2,1,1]
[4,5,1,2,6,8,3,7]=>[2,2,1,1,1,1]
[4,1,5,6,2,8,3,7]=>[2,2,2,1,1]
[4,5,1,6,2,8,3,7]=>[2,2,2,1,1]
[4,5,6,1,2,8,3,7]=>[2,2,1,1,1,1]
[4,1,5,6,8,2,3,7]=>[2,2,1,1,1,1]
[4,5,1,6,8,2,3,7]=>[2,2,1,1,1,1]
[4,5,6,1,8,2,3,7]=>[2,2,1,1,1,1]
[4,5,6,8,1,2,3,7]=>[2,1,1,1,1,1,1]
[4,1,5,2,6,3,7,8]=>[2,2,2,1,1]
[4,1,5,6,2,3,7,8]=>[2,2,1,1,1,1]
[4,5,1,6,2,3,7,8]=>[2,2,1,1,1,1]
[4,5,1,2,6,7,3,8]=>[2,2,1,1,1,1]
[4,5,1,6,2,7,3,8]=>[2,2,2,1,1]
[4,5,6,1,2,7,3,8]=>[2,2,1,1,1,1]
[4,1,5,6,7,2,3,8]=>[2,2,1,1,1,1]
[4,5,1,6,7,2,3,8]=>[2,2,1,1,1,1]
[4,5,6,1,7,2,3,8]=>[2,2,1,1,1,1]
[4,1,5,2,6,7,8,3]=>[2,2,2,1,1]
[4,5,1,2,6,7,8,3]=>[2,2,1,1,1,1]
[4,5,1,6,2,7,8,3]=>[2,2,2,1,1]
[4,5,6,1,2,7,8,3]=>[2,2,1,1,1,1]
[4,1,5,6,7,2,8,3]=>[2,2,2,1,1]
[4,5,1,6,7,2,8,3]=>[2,2,2,1,1]
[4,5,6,1,7,2,8,3]=>[2,2,2,1,1]
[4,5,6,7,1,2,8,3]=>[2,2,1,1,1,1]
[4,1,5,6,7,8,2,3]=>[2,2,1,1,1,1]
[4,5,1,6,7,8,2,3]=>[2,2,1,1,1,1]
[4,5,6,1,7,8,2,3]=>[2,2,1,1,1,1]
[4,5,6,7,1,8,2,3]=>[2,2,1,1,1,1]
[4,1,5,2,7,3,8,6]=>[2,2,2,2]
[4,5,1,7,2,3,8,6]=>[2,2,2,1,1]
[4,5,7,1,2,3,8,6]=>[2,2,1,1,1,1]
[4,1,5,2,7,8,3,6]=>[2,2,2,1,1]
[4,5,1,2,7,8,3,6]=>[2,2,1,1,1,1]
[4,1,5,7,2,8,3,6]=>[2,2,2,1,1]
[4,5,1,7,2,8,3,6]=>[2,2,2,1,1]
[4,5,7,1,2,8,3,6]=>[2,2,1,1,1,1]
[4,5,1,7,8,2,3,6]=>[2,2,1,1,1,1]
[4,5,7,8,1,2,3,6]=>[2,1,1,1,1,1,1]
[4,1,5,2,7,3,6,8]=>[2,2,2,1,1]
[4,5,1,2,7,3,6,8]=>[2,2,1,1,1,1]
[4,1,5,7,2,3,6,8]=>[2,2,1,1,1,1]
[4,5,1,7,2,3,6,8]=>[2,2,1,1,1,1]
[4,1,5,2,3,7,6,8]=>[2,2,2,1,1]
[4,5,1,2,3,7,6,8]=>[2,2,1,1,1,1]
[4,1,2,5,3,7,6,8]=>[2,2,2,1,1]
[1,4,2,5,3,7,6,8]=>[2,2,2,1,1]
[1,4,5,2,3,7,6,8]=>[2,2,1,1,1,1]
[4,1,2,5,7,3,6,8]=>[2,2,1,1,1,1]
[1,4,2,5,7,3,6,8]=>[2,2,1,1,1,1]
[1,4,5,2,7,3,6,8]=>[2,2,1,1,1,1]
[1,4,5,7,2,3,6,8]=>[2,1,1,1,1,1,1]
[4,1,5,2,3,7,8,6]=>[2,2,2,1,1]
[4,1,2,5,3,7,8,6]=>[2,2,2,1,1]
[1,4,2,5,3,7,8,6]=>[2,2,2,1,1]
[1,4,5,2,3,7,8,6]=>[2,2,1,1,1,1]
[4,1,2,5,7,3,8,6]=>[2,2,2,1,1]
[1,4,2,5,7,3,8,6]=>[2,2,2,1,1]
[1,4,5,2,7,3,8,6]=>[2,2,2,1,1]
[1,4,5,7,2,3,8,6]=>[2,2,1,1,1,1]
[4,1,2,5,7,8,3,6]=>[2,2,1,1,1,1]
[1,4,2,5,7,8,3,6]=>[2,2,1,1,1,1]
[1,4,5,2,7,8,3,6]=>[2,2,1,1,1,1]
[1,4,5,7,8,2,3,6]=>[2,1,1,1,1,1,1]
[4,1,5,2,8,3,6,7]=>[2,2,2,1,1]
[4,5,1,2,8,3,6,7]=>[2,2,1,1,1,1]
[4,5,1,8,2,3,6,7]=>[2,2,1,1,1,1]
[4,5,8,1,2,3,6,7]=>[2,1,1,1,1,1,1]
[4,1,5,2,3,8,6,7]=>[2,2,2,1,1]
[4,5,1,2,3,8,6,7]=>[2,2,1,1,1,1]
[4,1,2,5,3,8,6,7]=>[2,2,2,1,1]
[1,4,2,5,3,8,6,7]=>[2,2,2,1,1]
[1,4,5,2,3,8,6,7]=>[2,2,1,1,1,1]
[4,1,2,5,8,3,6,7]=>[2,2,1,1,1,1]
[1,4,2,5,8,3,6,7]=>[2,2,1,1,1,1]
[1,4,5,2,8,3,6,7]=>[2,2,1,1,1,1]
[1,4,2,5,3,6,8,7]=>[2,2,2,1,1]
[4,1,2,5,6,3,8,7]=>[2,2,2,1,1]
[1,4,5,2,6,3,8,7]=>[2,2,2,1,1]
[1,4,5,6,2,3,8,7]=>[2,2,1,1,1,1]
[4,1,2,5,6,8,3,7]=>[2,2,1,1,1,1]
[1,4,2,5,6,8,3,7]=>[2,2,1,1,1,1]
[1,4,5,2,6,8,3,7]=>[2,2,1,1,1,1]
[1,4,5,6,2,8,3,7]=>[2,2,1,1,1,1]
[1,4,5,6,8,2,3,7]=>[2,1,1,1,1,1,1]
[4,1,5,2,3,6,7,8]=>[2,2,1,1,1,1]
[4,1,2,5,3,6,7,8]=>[2,2,1,1,1,1]
[1,4,2,5,3,6,7,8]=>[2,2,1,1,1,1]
[1,4,5,2,3,6,7,8]=>[2,1,1,1,1,1,1]
[4,1,2,5,6,3,7,8]=>[2,2,1,1,1,1]
[1,4,5,2,6,3,7,8]=>[2,2,1,1,1,1]
[1,4,5,6,2,3,7,8]=>[2,1,1,1,1,1,1]
[4,1,2,5,6,7,3,8]=>[2,2,1,1,1,1]
[1,4,2,5,6,7,3,8]=>[2,2,1,1,1,1]
[1,4,5,2,6,7,3,8]=>[2,2,1,1,1,1]
[1,4,5,6,2,7,3,8]=>[2,2,1,1,1,1]
[1,4,5,6,7,2,3,8]=>[2,1,1,1,1,1,1]
[4,1,2,5,6,7,8,3]=>[2,2,1,1,1,1]
[1,4,2,5,6,7,8,3]=>[2,2,1,1,1,1]
[1,4,5,2,6,7,8,3]=>[2,2,1,1,1,1]
[1,4,5,6,2,7,8,3]=>[2,2,1,1,1,1]
[1,4,5,6,7,2,8,3]=>[2,2,1,1,1,1]
[1,4,5,6,7,8,2,3]=>[2,1,1,1,1,1,1]
[4,1,6,2,7,3,8,5]=>[2,2,2,2]
[4,1,6,7,2,3,8,5]=>[2,2,2,1,1]
[4,6,1,7,2,3,8,5]=>[2,2,2,1,1]
[4,6,7,1,2,3,8,5]=>[2,2,1,1,1,1]
[4,6,1,2,7,8,3,5]=>[2,2,1,1,1,1]
[4,6,1,7,2,8,3,5]=>[2,2,2,1,1]
[4,6,7,1,2,8,3,5]=>[2,2,1,1,1,1]
[4,1,6,7,8,2,3,5]=>[2,2,1,1,1,1]
[4,6,1,7,8,2,3,5]=>[2,2,1,1,1,1]
[4,6,7,1,8,2,3,5]=>[2,2,1,1,1,1]
[4,6,7,8,1,2,3,5]=>[2,1,1,1,1,1,1]
[4,1,6,2,7,3,5,8]=>[2,2,2,1,1]
[4,6,1,2,7,3,5,8]=>[2,2,1,1,1,1]
[4,1,6,7,2,3,5,8]=>[2,2,1,1,1,1]
[4,6,1,7,2,3,5,8]=>[2,2,1,1,1,1]
[4,6,7,1,2,3,5,8]=>[2,1,1,1,1,1,1]
[4,1,6,2,3,7,5,8]=>[2,2,2,1,1]
[4,6,1,2,3,7,5,8]=>[2,2,1,1,1,1]
[4,1,2,6,3,7,5,8]=>[2,2,2,1,1]
[1,4,2,6,3,7,5,8]=>[2,2,2,1,1]
[4,1,2,6,7,3,5,8]=>[2,2,1,1,1,1]
[1,4,2,6,7,3,5,8]=>[2,2,1,1,1,1]
[1,4,6,2,7,3,5,8]=>[2,2,1,1,1,1]
[1,4,6,7,2,3,5,8]=>[2,1,1,1,1,1,1]
[4,1,6,2,3,7,8,5]=>[2,2,2,1,1]
[4,1,2,6,3,7,8,5]=>[2,2,2,1,1]
[1,4,6,2,3,7,8,5]=>[2,2,1,1,1,1]
[4,1,2,6,7,3,8,5]=>[2,2,2,1,1]
[1,4,6,2,7,3,8,5]=>[2,2,2,1,1]
[1,4,2,6,7,8,3,5]=>[2,2,1,1,1,1]
[1,4,6,2,7,8,3,5]=>[2,2,1,1,1,1]
[1,4,6,7,2,8,3,5]=>[2,2,1,1,1,1]
[1,4,6,7,8,2,3,5]=>[2,1,1,1,1,1,1]
[4,1,6,2,8,3,5,7]=>[2,2,2,1,1]
[4,6,1,2,8,3,5,7]=>[2,2,1,1,1,1]
[4,1,6,8,2,3,5,7]=>[2,2,1,1,1,1]
[4,6,1,8,2,3,5,7]=>[2,2,1,1,1,1]
[4,6,8,1,2,3,5,7]=>[2,1,1,1,1,1,1]
[4,1,6,2,3,8,5,7]=>[2,2,2,1,1]
[4,6,1,2,3,8,5,7]=>[2,2,1,1,1,1]
[4,1,2,6,3,8,5,7]=>[2,2,2,1,1]
[1,4,2,6,3,8,5,7]=>[2,2,2,1,1]
[1,4,6,2,3,8,5,7]=>[2,2,1,1,1,1]
[1,4,2,6,8,3,5,7]=>[2,2,1,1,1,1]
[1,4,6,2,8,3,5,7]=>[2,2,1,1,1,1]
[1,4,6,8,2,3,5,7]=>[2,1,1,1,1,1,1]
[4,1,6,2,3,5,8,7]=>[2,2,2,1,1]
[4,6,1,2,3,5,8,7]=>[2,2,1,1,1,1]
[4,1,2,6,3,5,8,7]=>[2,2,2,1,1]
[1,4,2,6,3,5,8,7]=>[2,2,2,1,1]
[1,4,6,2,3,5,8,7]=>[2,2,1,1,1,1]
[4,1,2,3,6,5,8,7]=>[2,2,2,1,1]
[1,4,2,3,6,5,8,7]=>[2,2,2,1,1]
[1,2,4,6,3,5,8,7]=>[2,2,1,1,1,1]
[4,1,2,3,6,8,5,7]=>[2,2,1,1,1,1]
[1,2,4,3,6,8,5,7]=>[2,2,1,1,1,1]
[1,2,4,6,8,3,5,7]=>[2,1,1,1,1,1,1]
[4,1,6,2,3,5,7,8]=>[2,2,1,1,1,1]
[4,6,1,2,3,5,7,8]=>[2,1,1,1,1,1,1]
[1,4,2,6,3,5,7,8]=>[2,2,1,1,1,1]
[1,4,6,2,3,5,7,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,6,5,7,8]=>[2,2,1,1,1,1]
[1,4,2,3,6,5,7,8]=>[2,2,1,1,1,1]
[1,2,4,6,3,5,7,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,6,7,5,8]=>[2,2,1,1,1,1]
[1,4,2,3,6,7,5,8]=>[2,2,1,1,1,1]
[1,2,4,6,7,3,5,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,6,7,8,5]=>[2,2,1,1,1,1]
[1,4,2,3,6,7,8,5]=>[2,2,1,1,1,1]
[1,2,4,6,3,7,8,5]=>[2,2,1,1,1,1]
[1,2,4,6,7,3,8,5]=>[2,2,1,1,1,1]
[1,2,4,6,7,8,3,5]=>[2,1,1,1,1,1,1]
[4,1,7,2,8,3,5,6]=>[2,2,2,1,1]
[4,7,1,2,8,3,5,6]=>[2,2,1,1,1,1]
[4,1,7,8,2,3,5,6]=>[2,2,1,1,1,1]
[4,7,1,8,2,3,5,6]=>[2,2,1,1,1,1]
[4,7,8,1,2,3,5,6]=>[2,1,1,1,1,1,1]
[4,1,7,2,3,8,5,6]=>[2,2,2,1,1]
[4,7,1,2,3,8,5,6]=>[2,2,1,1,1,1]
[1,4,2,7,3,8,5,6]=>[2,2,2,1,1]
[1,4,7,2,3,8,5,6]=>[2,2,1,1,1,1]
[4,1,2,7,8,3,5,6]=>[2,2,1,1,1,1]
[1,4,2,7,8,3,5,6]=>[2,2,1,1,1,1]
[1,4,7,2,8,3,5,6]=>[2,2,1,1,1,1]
[1,4,7,8,2,3,5,6]=>[2,1,1,1,1,1,1]
[4,1,7,2,3,5,8,6]=>[2,2,2,1,1]
[4,7,1,2,3,5,8,6]=>[2,2,1,1,1,1]
[4,1,2,7,3,5,8,6]=>[2,2,2,1,1]
[1,4,2,7,3,5,8,6]=>[2,2,2,1,1]
[1,4,7,2,3,5,8,6]=>[2,2,1,1,1,1]
[4,1,2,3,7,5,8,6]=>[2,2,2,1,1]
[1,4,2,3,7,5,8,6]=>[2,2,2,1,1]
[1,2,4,7,3,5,8,6]=>[2,2,1,1,1,1]
[4,1,2,3,7,8,5,6]=>[2,2,1,1,1,1]
[1,4,2,3,7,8,5,6]=>[2,2,1,1,1,1]
[1,2,4,3,7,8,5,6]=>[2,2,1,1,1,1]
[1,2,4,7,3,8,5,6]=>[2,2,1,1,1,1]
[1,2,4,7,8,3,5,6]=>[2,1,1,1,1,1,1]
[4,1,7,2,3,5,6,8]=>[2,2,1,1,1,1]
[4,7,1,2,3,5,6,8]=>[2,1,1,1,1,1,1]
[4,1,2,7,3,5,6,8]=>[2,2,1,1,1,1]
[1,4,2,7,3,5,6,8]=>[2,2,1,1,1,1]
[1,4,7,2,3,5,6,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,7,5,6,8]=>[2,2,1,1,1,1]
[1,4,2,3,7,5,6,8]=>[2,2,1,1,1,1]
[1,2,4,3,7,5,6,8]=>[2,2,1,1,1,1]
[1,2,4,7,3,5,6,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,5,7,6,8]=>[2,2,1,1,1,1]
[1,4,2,3,5,7,6,8]=>[2,2,1,1,1,1]
[1,2,4,5,7,3,6,8]=>[2,1,1,1,1,1,1]
[4,1,2,3,5,7,8,6]=>[2,2,1,1,1,1]
[1,4,2,3,5,7,8,6]=>[2,2,1,1,1,1]
[1,2,4,5,7,3,8,6]=>[2,2,1,1,1,1]
[1,2,4,5,7,8,3,6]=>[2,1,1,1,1,1,1]
[4,1,8,2,3,5,6,7]=>[2,2,1,1,1,1]
[4,8,1,2,3,5,6,7]=>[2,1,1,1,1,1,1]
[4,1,2,8,3,5,6,7]=>[2,2,1,1,1,1]
[1,4,2,8,3,5,6,7]=>[2,2,1,1,1,1]
[1,4,8,2,3,5,6,7]=>[2,1,1,1,1,1,1]
[4,1,2,3,8,5,6,7]=>[2,2,1,1,1,1]
[1,4,2,3,8,5,6,7]=>[2,2,1,1,1,1]
[1,2,4,3,8,5,6,7]=>[2,2,1,1,1,1]
[1,2,4,8,3,5,6,7]=>[2,1,1,1,1,1,1]
[4,1,2,3,5,8,6,7]=>[2,2,1,1,1,1]
[1,4,2,3,5,8,6,7]=>[2,2,1,1,1,1]
[1,2,4,3,5,8,6,7]=>[2,2,1,1,1,1]
[1,2,4,5,3,8,6,7]=>[2,2,1,1,1,1]
[1,2,4,5,8,3,6,7]=>[2,1,1,1,1,1,1]
[4,1,2,3,5,6,8,7]=>[2,2,1,1,1,1]
[1,4,2,3,5,6,8,7]=>[2,2,1,1,1,1]
[1,2,4,5,6,8,3,7]=>[2,1,1,1,1,1,1]
[1,4,2,3,5,6,7,8]=>[2,1,1,1,1,1,1]
[5,1,6,2,7,3,8,4]=>[2,2,2,2]
[5,6,1,2,7,3,8,4]=>[2,2,2,1,1]
[5,1,6,7,2,3,8,4]=>[2,2,2,1,1]
[5,6,1,7,2,3,8,4]=>[2,2,2,1,1]
[5,6,7,1,2,3,8,4]=>[2,2,1,1,1,1]
[5,1,6,2,7,8,3,4]=>[2,2,2,1,1]
[5,6,1,2,7,8,3,4]=>[2,2,1,1,1,1]
[5,1,6,7,2,8,3,4]=>[2,2,2,1,1]
[5,6,1,7,2,8,3,4]=>[2,2,2,1,1]
[5,6,7,1,2,8,3,4]=>[2,2,1,1,1,1]
[5,1,6,7,8,2,3,4]=>[2,2,1,1,1,1]
[5,6,1,7,8,2,3,4]=>[2,2,1,1,1,1]
[5,6,7,1,8,2,3,4]=>[2,2,1,1,1,1]
[5,1,6,2,7,3,4,8]=>[2,2,2,1,1]
[5,6,1,2,7,3,4,8]=>[2,2,1,1,1,1]
[5,6,1,7,2,3,4,8]=>[2,2,1,1,1,1]
[5,1,6,2,3,7,4,8]=>[2,2,2,1,1]
[5,1,2,6,3,7,4,8]=>[2,2,2,1,1]
[1,5,2,6,3,7,4,8]=>[2,2,2,1,1]
[5,1,2,6,7,3,4,8]=>[2,2,1,1,1,1]
[1,5,2,6,7,3,4,8]=>[2,2,1,1,1,1]
[1,5,6,2,7,3,4,8]=>[2,2,1,1,1,1]
[1,5,6,7,2,3,4,8]=>[2,1,1,1,1,1,1]
[5,1,6,2,3,7,8,4]=>[2,2,2,1,1]
[5,6,1,2,3,7,8,4]=>[2,2,1,1,1,1]
[5,1,2,6,3,7,8,4]=>[2,2,2,1,1]
[1,5,2,6,3,7,8,4]=>[2,2,2,1,1]
[1,5,6,2,3,7,8,4]=>[2,2,1,1,1,1]
[5,1,2,6,7,3,8,4]=>[2,2,2,1,1]
[1,5,6,7,2,3,8,4]=>[2,2,1,1,1,1]
[5,1,2,6,7,8,3,4]=>[2,2,1,1,1,1]
[1,5,2,6,7,8,3,4]=>[2,2,1,1,1,1]
[1,5,6,2,7,8,3,4]=>[2,2,1,1,1,1]
[1,5,6,7,2,8,3,4]=>[2,2,1,1,1,1]
[1,5,6,7,8,2,3,4]=>[2,1,1,1,1,1,1]
[5,1,6,2,8,3,4,7]=>[2,2,2,1,1]
[5,6,1,2,8,3,4,7]=>[2,2,1,1,1,1]
[5,6,1,8,2,3,4,7]=>[2,2,1,1,1,1]
[5,6,8,1,2,3,4,7]=>[2,1,1,1,1,1,1]
[5,1,6,2,3,8,4,7]=>[2,2,2,1,1]
[5,6,1,2,3,8,4,7]=>[2,2,1,1,1,1]
[5,1,2,6,3,8,4,7]=>[2,2,2,1,1]
[1,5,2,6,3,8,4,7]=>[2,2,2,1,1]
[1,5,6,2,3,8,4,7]=>[2,2,1,1,1,1]
[5,1,2,6,8,3,4,7]=>[2,2,1,1,1,1]
[1,5,2,6,8,3,4,7]=>[2,2,1,1,1,1]
[1,5,6,2,8,3,4,7]=>[2,2,1,1,1,1]
[1,5,6,8,2,3,4,7]=>[2,1,1,1,1,1,1]
[5,1,6,2,3,4,8,7]=>[2,2,2,1,1]
[5,6,1,2,3,4,8,7]=>[2,2,1,1,1,1]
[1,5,2,6,3,4,8,7]=>[2,2,2,1,1]
[1,5,6,2,3,4,8,7]=>[2,2,1,1,1,1]
[1,5,2,3,6,4,8,7]=>[2,2,2,1,1]
[1,2,5,3,6,4,8,7]=>[2,2,2,1,1]
[5,1,2,3,6,8,4,7]=>[2,2,1,1,1,1]
[1,5,2,3,6,8,4,7]=>[2,2,1,1,1,1]
[1,2,5,6,3,8,4,7]=>[2,2,1,1,1,1]
[5,1,6,2,3,4,7,8]=>[2,2,1,1,1,1]
[5,1,2,6,3,4,7,8]=>[2,2,1,1,1,1]
[1,5,2,6,3,4,7,8]=>[2,2,1,1,1,1]
[1,5,6,2,3,4,7,8]=>[2,1,1,1,1,1,1]
[5,1,2,3,6,4,7,8]=>[2,2,1,1,1,1]
[1,5,2,3,6,4,7,8]=>[2,2,1,1,1,1]
[1,2,5,3,6,4,7,8]=>[2,2,1,1,1,1]
[1,2,5,6,3,4,7,8]=>[2,1,1,1,1,1,1]
[5,1,2,3,6,7,4,8]=>[2,2,1,1,1,1]
[1,5,2,3,6,7,4,8]=>[2,2,1,1,1,1]
[1,2,5,3,6,7,4,8]=>[2,2,1,1,1,1]
[1,2,5,6,3,7,4,8]=>[2,2,1,1,1,1]
[5,1,2,3,6,7,8,4]=>[2,2,1,1,1,1]
[1,5,2,3,6,7,8,4]=>[2,2,1,1,1,1]
[1,2,5,3,6,7,8,4]=>[2,2,1,1,1,1]
[1,2,5,6,3,7,8,4]=>[2,2,1,1,1,1]
[1,2,5,6,7,3,8,4]=>[2,2,1,1,1,1]
[1,2,5,6,7,8,3,4]=>[2,1,1,1,1,1,1]
[5,1,7,2,8,3,4,6]=>[2,2,2,1,1]
[5,7,1,2,8,3,4,6]=>[2,2,1,1,1,1]
[5,1,7,8,2,3,4,6]=>[2,2,1,1,1,1]
[5,7,8,1,2,3,4,6]=>[2,1,1,1,1,1,1]
[5,1,2,7,3,8,4,6]=>[2,2,2,1,1]
[1,5,2,7,3,8,4,6]=>[2,2,2,1,1]
[1,5,7,2,3,8,4,6]=>[2,2,1,1,1,1]
[5,1,2,7,8,3,4,6]=>[2,2,1,1,1,1]
[1,5,2,7,8,3,4,6]=>[2,2,1,1,1,1]
[1,5,7,2,8,3,4,6]=>[2,2,1,1,1,1]
[1,5,7,8,2,3,4,6]=>[2,1,1,1,1,1,1]
[5,1,7,2,3,4,8,6]=>[2,2,2,1,1]
[5,7,1,2,3,4,8,6]=>[2,2,1,1,1,1]
[5,1,2,7,3,4,8,6]=>[2,2,2,1,1]
[1,5,2,7,3,4,8,6]=>[2,2,2,1,1]
[1,5,7,2,3,4,8,6]=>[2,2,1,1,1,1]
[5,1,2,3,7,4,8,6]=>[2,2,2,1,1]
[1,5,2,3,7,4,8,6]=>[2,2,2,1,1]
[1,2,5,3,7,4,8,6]=>[2,2,2,1,1]
[1,2,5,7,3,4,8,6]=>[2,2,1,1,1,1]
[5,1,2,3,7,8,4,6]=>[2,2,1,1,1,1]
[1,5,2,3,7,8,4,6]=>[2,2,1,1,1,1]
[1,2,5,7,3,8,4,6]=>[2,2,1,1,1,1]
[1,2,5,7,8,3,4,6]=>[2,1,1,1,1,1,1]
[5,7,1,2,3,4,6,8]=>[2,1,1,1,1,1,1]
[1,5,2,7,3,4,6,8]=>[2,2,1,1,1,1]
[1,5,7,2,3,4,6,8]=>[2,1,1,1,1,1,1]
[1,5,2,3,7,4,6,8]=>[2,2,1,1,1,1]
[1,2,5,3,7,4,6,8]=>[2,2,1,1,1,1]
[1,2,5,7,3,4,6,8]=>[2,1,1,1,1,1,1]
[1,5,2,3,4,7,6,8]=>[2,2,1,1,1,1]
[1,2,5,3,4,7,6,8]=>[2,2,1,1,1,1]
[1,2,3,5,7,4,6,8]=>[2,1,1,1,1,1,1]
[5,1,2,3,4,7,8,6]=>[2,2,1,1,1,1]
[1,5,2,3,4,7,8,6]=>[2,2,1,1,1,1]
[1,2,5,3,4,7,8,6]=>[2,2,1,1,1,1]
[1,2,3,5,7,4,8,6]=>[2,2,1,1,1,1]
[1,2,3,5,7,8,4,6]=>[2,1,1,1,1,1,1]
[5,1,8,2,3,4,6,7]=>[2,2,1,1,1,1]
[5,8,1,2,3,4,6,7]=>[2,1,1,1,1,1,1]
[5,1,2,8,3,4,6,7]=>[2,2,1,1,1,1]
[1,5,2,8,3,4,6,7]=>[2,2,1,1,1,1]
[1,5,8,2,3,4,6,7]=>[2,1,1,1,1,1,1]
[5,1,2,3,8,4,6,7]=>[2,2,1,1,1,1]
[1,5,2,3,8,4,6,7]=>[2,2,1,1,1,1]
[1,2,5,3,8,4,6,7]=>[2,2,1,1,1,1]
[1,2,5,8,3,4,6,7]=>[2,1,1,1,1,1,1]
[5,1,2,3,4,8,6,7]=>[2,2,1,1,1,1]
[1,5,2,3,4,8,6,7]=>[2,2,1,1,1,1]
[1,2,5,3,4,8,6,7]=>[2,2,1,1,1,1]
[1,2,3,5,4,8,6,7]=>[2,2,1,1,1,1]
[1,2,3,5,8,4,6,7]=>[2,1,1,1,1,1,1]
[5,1,2,3,4,6,8,7]=>[2,2,1,1,1,1]
[1,5,2,3,4,6,8,7]=>[2,2,1,1,1,1]
[1,2,5,3,4,6,8,7]=>[2,2,1,1,1,1]
[1,2,3,5,6,8,4,7]=>[2,1,1,1,1,1,1]
[1,5,2,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[1,2,5,3,4,6,7,8]=>[2,1,1,1,1,1,1]
[6,1,7,2,8,3,4,5]=>[2,2,2,1,1]
[6,7,1,2,8,3,4,5]=>[2,2,1,1,1,1]
[6,1,7,8,2,3,4,5]=>[2,2,1,1,1,1]
[6,7,1,8,2,3,4,5]=>[2,2,1,1,1,1]
[6,1,7,2,3,8,4,5]=>[2,2,2,1,1]
[6,7,1,2,3,8,4,5]=>[2,2,1,1,1,1]
[6,1,2,7,3,8,4,5]=>[2,2,2,1,1]
[1,6,2,7,3,8,4,5]=>[2,2,2,1,1]
[1,6,7,2,3,8,4,5]=>[2,2,1,1,1,1]
[6,1,2,7,8,3,4,5]=>[2,2,1,1,1,1]
[1,6,2,7,8,3,4,5]=>[2,2,1,1,1,1]
[1,6,7,2,8,3,4,5]=>[2,2,1,1,1,1]
[1,6,7,8,2,3,4,5]=>[2,1,1,1,1,1,1]
[6,1,7,2,3,4,8,5]=>[2,2,2,1,1]
[6,7,1,2,3,4,8,5]=>[2,2,1,1,1,1]
[6,1,2,7,3,4,8,5]=>[2,2,2,1,1]
[1,6,2,7,3,4,8,5]=>[2,2,2,1,1]
[6,1,2,3,7,4,8,5]=>[2,2,2,1,1]
[1,6,2,3,7,4,8,5]=>[2,2,2,1,1]
[1,2,6,3,7,4,8,5]=>[2,2,2,1,1]
[6,1,2,3,7,8,4,5]=>[2,2,1,1,1,1]
[1,6,2,3,7,8,4,5]=>[2,2,1,1,1,1]
[1,2,6,3,7,8,4,5]=>[2,2,1,1,1,1]
[1,2,6,7,3,8,4,5]=>[2,2,1,1,1,1]
[1,2,6,7,8,3,4,5]=>[2,1,1,1,1,1,1]
[6,1,7,2,3,4,5,8]=>[2,2,1,1,1,1]
[6,1,2,7,3,4,5,8]=>[2,2,1,1,1,1]
[1,6,2,7,3,4,5,8]=>[2,2,1,1,1,1]
[1,6,7,2,3,4,5,8]=>[2,1,1,1,1,1,1]
[6,1,2,3,7,4,5,8]=>[2,2,1,1,1,1]
[1,6,2,3,7,4,5,8]=>[2,2,1,1,1,1]
[1,2,6,3,7,4,5,8]=>[2,2,1,1,1,1]
[1,2,6,7,3,4,5,8]=>[2,1,1,1,1,1,1]
[6,1,2,3,4,7,5,8]=>[2,2,1,1,1,1]
[1,6,2,3,4,7,5,8]=>[2,2,1,1,1,1]
[1,2,6,3,4,7,5,8]=>[2,2,1,1,1,1]
[1,2,3,6,4,7,5,8]=>[2,2,1,1,1,1]
[1,2,3,6,7,4,5,8]=>[2,1,1,1,1,1,1]
[6,1,2,3,4,7,8,5]=>[2,2,1,1,1,1]
[1,6,2,3,4,7,8,5]=>[2,2,1,1,1,1]
[1,2,6,3,4,7,8,5]=>[2,2,1,1,1,1]
[1,2,3,6,4,7,8,5]=>[2,2,1,1,1,1]
[1,2,3,6,7,4,8,5]=>[2,2,1,1,1,1]
[1,2,3,6,7,8,4,5]=>[2,1,1,1,1,1,1]
[6,1,8,2,3,4,5,7]=>[2,2,1,1,1,1]
[6,8,1,2,3,4,5,7]=>[2,1,1,1,1,1,1]
[6,1,2,8,3,4,5,7]=>[2,2,1,1,1,1]
[1,6,2,8,3,4,5,7]=>[2,2,1,1,1,1]
[1,6,8,2,3,4,5,7]=>[2,1,1,1,1,1,1]
[6,1,2,3,8,4,5,7]=>[2,2,1,1,1,1]
[1,6,2,3,8,4,5,7]=>[2,2,1,1,1,1]
[1,2,6,3,8,4,5,7]=>[2,2,1,1,1,1]
[1,2,6,8,3,4,5,7]=>[2,1,1,1,1,1,1]
[6,1,2,3,4,8,5,7]=>[2,2,1,1,1,1]
[1,6,2,3,4,8,5,7]=>[2,2,1,1,1,1]
[1,2,6,3,4,8,5,7]=>[2,2,1,1,1,1]
[1,2,3,6,4,8,5,7]=>[2,2,1,1,1,1]
[1,2,3,6,8,4,5,7]=>[2,1,1,1,1,1,1]
[6,1,2,3,4,5,8,7]=>[2,2,1,1,1,1]
[1,6,2,3,4,5,8,7]=>[2,2,1,1,1,1]
[1,2,6,3,4,5,8,7]=>[2,2,1,1,1,1]
[1,2,3,6,4,5,8,7]=>[2,2,1,1,1,1]
[1,2,3,4,6,8,5,7]=>[2,1,1,1,1,1,1]
[1,6,2,3,4,5,7,8]=>[2,1,1,1,1,1,1]
[1,2,6,3,4,5,7,8]=>[2,1,1,1,1,1,1]
[1,2,3,6,4,5,7,8]=>[2,1,1,1,1,1,1]
[7,1,8,2,3,4,5,6]=>[2,2,1,1,1,1]
[7,1,2,8,3,4,5,6]=>[2,2,1,1,1,1]
[1,7,2,8,3,4,5,6]=>[2,2,1,1,1,1]
[1,7,8,2,3,4,5,6]=>[2,1,1,1,1,1,1]
[7,1,2,3,8,4,5,6]=>[2,2,1,1,1,1]
[1,7,2,3,8,4,5,6]=>[2,2,1,1,1,1]
[1,2,7,3,8,4,5,6]=>[2,2,1,1,1,1]
[1,2,7,8,3,4,5,6]=>[2,1,1,1,1,1,1]
[7,1,2,3,4,8,5,6]=>[2,2,1,1,1,1]
[1,7,2,3,4,8,5,6]=>[2,2,1,1,1,1]
[1,2,7,3,4,8,5,6]=>[2,2,1,1,1,1]
[1,2,3,7,4,8,5,6]=>[2,2,1,1,1,1]
[1,2,3,7,8,4,5,6]=>[2,1,1,1,1,1,1]
[7,1,2,3,4,5,8,6]=>[2,2,1,1,1,1]
[1,7,2,3,4,5,8,6]=>[2,2,1,1,1,1]
[1,2,7,3,4,5,8,6]=>[2,2,1,1,1,1]
[1,2,3,7,4,5,8,6]=>[2,2,1,1,1,1]
[1,2,3,4,7,5,8,6]=>[2,2,1,1,1,1]
[1,2,3,4,7,8,5,6]=>[2,1,1,1,1,1,1]
[1,7,2,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[1,2,7,3,4,5,6,8]=>[2,1,1,1,1,1,1]
[1,2,3,7,4,5,6,8]=>[2,1,1,1,1,1,1]
[1,2,3,4,7,5,6,8]=>[2,1,1,1,1,1,1]
[1,8,2,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[1,2,8,3,4,5,6,7]=>[2,1,1,1,1,1,1]
[1,2,3,8,4,5,6,7]=>[2,1,1,1,1,1,1]
[1,2,3,4,8,5,6,7]=>[2,1,1,1,1,1,1]
[1,2,3,4,5,8,6,7]=>[2,1,1,1,1,1,1]
[5,3,2,6,1,4,8,7]=>[4,2,1,1]
[7,3,2,5,4,8,1,6]=>[4,2,1,1]
[8,4,5,2,3,7,6,1]=>[4,2,1,1]
[7,4,5,2,3,8,1,6]=>[4,1,1,1,1]
[6,4,5,2,3,1,8,7]=>[4,2,1,1]
[5,4,6,2,1,3,8,7]=>[4,2,1,1]
[3,6,1,5,4,2,8,7]=>[4,2,1,1]
[4,6,5,1,3,2,8,7]=>[4,2,1,1]
[5,6,4,3,1,2,8,7]=>[4,2,1,1]
[7,5,4,3,2,8,1,6]=>[6,1,1]
[8,6,4,3,7,2,5,1]=>[6,1,1]
[7,6,4,3,8,2,1,5]=>[6,1,1]
[6,7,4,3,8,1,2,5]=>[4,1,1,1,1]
[5,7,4,3,1,8,2,6]=>[4,2,1,1]
[4,7,5,1,3,8,2,6]=>[4,1,1,1,1]
[3,7,1,5,4,8,2,6]=>[4,1,1,1,1]
[2,1,7,5,4,8,3,6]=>[4,2,1,1]
[3,8,1,5,4,7,6,2]=>[4,2,1,1]
[4,8,5,1,3,7,6,2]=>[4,2,1,1]
[5,8,4,3,1,7,6,2]=>[4,3,1]
[6,8,4,3,7,1,5,2]=>[4,2,1,1]
[7,8,4,3,6,5,1,2]=>[4,2,1,1]
[6,8,5,7,3,1,4,2]=>[4,2,1,1]
[5,8,6,7,1,3,4,2]=>[4,1,1,1,1]
[4,8,6,1,7,3,5,2]=>[4,2,1,1]
[3,8,1,6,7,4,5,2]=>[4,1,1,1,1]
[2,1,8,6,7,4,5,3]=>[4,2,1,1]
[2,1,7,6,8,4,3,5]=>[4,2,1,1]
[3,7,1,6,8,4,2,5]=>[4,1,1,1,1]
[4,7,6,1,8,3,2,5]=>[4,2,1,1]
[5,7,6,8,1,3,2,4]=>[4,1,1,1,1]
[5,4,7,2,1,8,3,6]=>[4,2,1,1]
[6,4,7,2,8,1,3,5]=>[4,1,1,1,1]
[7,4,6,2,8,3,1,5]=>[4,2,1,1]
[8,4,6,2,7,3,5,1]=>[4,2,1,1]
[8,3,2,6,7,4,5,1]=>[4,2,1,1]
[7,3,2,6,8,4,1,5]=>[4,2,1,1]
[6,3,2,7,8,1,4,5]=>[4,1,1,1,1]
[5,3,2,7,1,8,4,6]=>[4,2,1,1]
[4,3,2,1,7,8,5,6]=>[4,2,1,1]
[3,4,1,2,8,7,6,5]=>[4,2,1,1]
[5,3,2,8,1,7,6,4]=>[4,3,1]
[6,3,2,8,7,1,5,4]=>[4,3,1]
[7,3,2,8,6,5,1,4]=>[4,3,1]
[8,4,7,2,6,5,3,1]=>[6,1,1]
[7,4,8,2,6,5,1,3]=>[4,2,1,1]
[6,4,8,2,7,1,5,3]=>[4,2,1,1]
[5,4,8,2,1,7,6,3]=>[4,3,1]
[4,5,8,1,2,7,6,3]=>[4,1,1,1,1]
[3,5,1,8,2,7,6,4]=>[4,2,1,1]
[2,1,5,8,3,7,6,4]=>[4,2,1,1]
[2,1,6,8,7,3,5,4]=>[4,2,1,1]
[3,6,1,8,7,2,5,4]=>[4,2,1,1]
[4,6,8,1,7,2,5,3]=>[4,1,1,1,1]
[5,6,8,7,1,2,4,3]=>[4,1,1,1,1]
[6,5,8,7,2,1,4,3]=>[4,2,2]
[7,5,8,6,2,4,1,3]=>[4,2,1,1]
[8,5,7,6,2,4,3,1]=>[6,1,1]
[5,7,8,6,1,4,2,3]=>[4,1,1,1,1]
[4,7,8,1,6,5,2,3]=>[4,1,1,1,1]
[3,7,1,8,6,5,2,4]=>[4,2,1,1]
[2,1,7,8,6,5,3,4]=>[4,2,1,1]
[3,8,1,7,6,5,4,2]=>[6,1,1]
[4,8,7,1,6,5,3,2]=>[6,1,1]
[5,8,7,6,1,4,3,2]=>[6,1,1]
[6,8,7,5,4,1,3,2]=>[6,1,1]
[3,2,5,1,4,6,7,8]=>[3,1,1,1,1,1]
[4,2,5,1,3,6,7,8]=>[3,1,1,1,1,1]
[5,2,4,1,3,6,7,8]=>[3,1,1,1,1,1]
[3,2,6,1,4,5,7,8]=>[3,1,1,1,1,1]
[4,2,6,1,3,5,7,8]=>[3,1,1,1,1,1]
[5,3,6,1,2,4,7,8]=>[3,1,1,1,1,1]
[6,2,4,1,3,5,7,8]=>[3,1,1,1,1,1]
[6,3,5,1,2,4,7,8]=>[3,1,1,1,1,1]
[5,2,7,1,3,4,6,8]=>[3,1,1,1,1,1]
[5,3,7,1,2,4,6,8]=>[3,1,1,1,1,1]
[5,4,7,1,2,3,6,8]=>[3,1,1,1,1,1]
[6,2,7,1,3,4,5,8]=>[3,1,1,1,1,1]
[6,3,7,1,2,4,5,8]=>[3,1,1,1,1,1]
[6,4,7,1,2,3,5,8]=>[3,1,1,1,1,1]
[7,3,5,1,2,4,6,8]=>[3,1,1,1,1,1]
[7,3,6,1,2,4,5,8]=>[3,1,1,1,1,1]
[7,4,6,1,2,3,5,8]=>[3,1,1,1,1,1]
[3,2,8,1,4,5,6,7]=>[3,1,1,1,1,1]
[4,2,8,1,3,5,6,7]=>[3,1,1,1,1,1]
[5,2,8,1,3,4,6,7]=>[3,1,1,1,1,1]
[5,4,8,1,2,3,6,7]=>[3,1,1,1,1,1]
[6,2,8,1,3,4,5,7]=>[3,1,1,1,1,1]
[6,3,8,1,2,4,5,7]=>[3,1,1,1,1,1]
[6,4,8,1,2,3,5,7]=>[3,1,1,1,1,1]
[6,5,8,1,2,3,4,7]=>[3,1,1,1,1,1]
[7,2,8,1,3,4,5,6]=>[3,1,1,1,1,1]
[7,3,8,1,2,4,5,6]=>[3,1,1,1,1,1]
[7,4,8,1,2,3,5,6]=>[3,1,1,1,1,1]
[7,5,8,1,2,3,4,6]=>[3,1,1,1,1,1]
[8,2,4,1,3,5,6,7]=>[3,1,1,1,1,1]
[8,3,5,1,2,4,6,7]=>[3,1,1,1,1,1]
[8,3,6,1,2,4,5,7]=>[3,1,1,1,1,1]
[8,3,7,1,2,4,5,6]=>[3,1,1,1,1,1]
[8,4,7,1,2,3,5,6]=>[3,1,1,1,1,1]
[8,5,7,1,2,3,4,6]=>[3,1,1,1,1,1]
[3,2,5,7,1,4,6,8]=>[3,1,1,1,1,1]
[4,2,5,7,1,3,6,8]=>[3,1,1,1,1,1]
[4,3,5,7,1,2,6,8]=>[3,1,1,1,1,1]
[5,2,4,7,1,3,6,8]=>[3,1,1,1,1,1]
[5,3,4,7,1,2,6,8]=>[3,1,1,1,1,1]
[4,2,6,7,1,3,5,8]=>[3,1,1,1,1,1]
[5,2,6,7,1,3,4,8]=>[3,1,1,1,1,1]
[5,3,6,7,1,2,4,8]=>[3,1,1,1,1,1]
[6,2,5,7,1,3,4,8]=>[3,1,1,1,1,1]
[6,3,5,7,1,2,4,8]=>[3,1,1,1,1,1]
[7,2,4,6,1,3,5,8]=>[3,1,1,1,1,1]
[7,3,4,6,1,2,5,8]=>[3,1,1,1,1,1]
[7,3,5,6,1,2,4,8]=>[3,1,1,1,1,1]
[4,2,5,8,1,3,6,7]=>[3,1,1,1,1,1]
[5,2,4,8,1,3,6,7]=>[3,1,1,1,1,1]
[4,2,6,8,1,3,5,7]=>[3,1,1,1,1,1]
[4,3,6,8,1,2,5,7]=>[3,1,1,1,1,1]
[5,2,6,8,1,3,4,7]=>[3,1,1,1,1,1]
[6,2,4,8,1,3,5,7]=>[3,1,1,1,1,1]
[6,3,4,8,1,2,5,7]=>[3,1,1,1,1,1]
[6,3,5,8,1,2,4,7]=>[3,1,1,1,1,1]
[6,4,5,8,1,2,3,7]=>[3,1,1,1,1,1]
[3,2,7,8,1,4,5,6]=>[3,1,1,1,1,1]
[4,3,7,8,1,2,5,6]=>[3,1,1,1,1,1]
[5,3,7,8,1,2,4,6]=>[3,1,1,1,1,1]
[5,4,7,8,1,2,3,6]=>[3,1,1,1,1,1]
[6,2,7,8,1,3,4,5]=>[3,1,1,1,1,1]
[6,3,7,8,1,2,4,5]=>[3,1,1,1,1,1]
[6,4,7,8,1,2,3,5]=>[3,1,1,1,1,1]
[7,2,4,8,1,3,5,6]=>[3,1,1,1,1,1]
[7,3,4,8,1,2,5,6]=>[3,1,1,1,1,1]
[7,3,5,8,1,2,4,6]=>[3,1,1,1,1,1]
[7,4,5,8,1,2,3,6]=>[3,1,1,1,1,1]
[7,4,6,8,1,2,3,5]=>[3,1,1,1,1,1]
[8,2,4,6,1,3,5,7]=>[3,1,1,1,1,1]
[8,3,4,6,1,2,5,7]=>[3,1,1,1,1,1]
[8,2,5,6,1,3,4,7]=>[3,1,1,1,1,1]
[8,3,5,6,1,2,4,7]=>[3,1,1,1,1,1]
[8,3,5,7,1,2,4,6]=>[3,1,1,1,1,1]
[8,2,6,7,1,3,4,5]=>[3,1,1,1,1,1]
[8,4,6,7,1,2,3,5]=>[3,1,1,1,1,1]
[3,6,2,5,1,4,7,8]=>[3,1,1,1,1,1]
[4,6,2,5,1,3,7,8]=>[3,1,1,1,1,1]
[4,6,3,5,1,2,7,8]=>[3,1,1,1,1,1]
[3,7,2,5,1,4,6,8]=>[3,1,1,1,1,1]
[4,7,3,5,1,2,6,8]=>[3,1,1,1,1,1]
[5,7,2,4,1,3,6,8]=>[3,1,1,1,1,1]
[5,7,3,4,1,2,6,8]=>[3,1,1,1,1,1]
[3,7,2,6,1,4,5,8]=>[3,1,1,1,1,1]
[4,7,3,6,1,2,5,8]=>[3,1,1,1,1,1]
[5,7,2,6,1,3,4,8]=>[3,1,1,1,1,1]
[5,7,3,6,1,2,4,8]=>[3,1,1,1,1,1]
[6,7,2,5,1,3,4,8]=>[3,1,1,1,1,1]
[4,8,2,5,1,3,6,7]=>[3,1,1,1,1,1]
[5,8,2,4,1,3,6,7]=>[3,1,1,1,1,1]
[5,8,3,4,1,2,6,7]=>[3,1,1,1,1,1]
[3,8,2,6,1,4,5,7]=>[3,1,1,1,1,1]
[4,8,2,6,1,3,5,7]=>[3,1,1,1,1,1]
[5,8,3,6,1,2,4,7]=>[3,1,1,1,1,1]
[5,8,4,6,1,2,3,7]=>[3,1,1,1,1,1]
[6,8,2,4,1,3,5,7]=>[3,1,1,1,1,1]
[6,8,3,4,1,2,5,7]=>[3,1,1,1,1,1]
[6,8,3,5,1,2,4,7]=>[3,1,1,1,1,1]
[6,8,4,5,1,2,3,7]=>[3,1,1,1,1,1]
[3,8,2,7,1,4,5,6]=>[3,1,1,1,1,1]
[4,8,2,7,1,3,5,6]=>[3,1,1,1,1,1]
[4,8,3,7,1,2,5,6]=>[3,1,1,1,1,1]
[5,8,2,7,1,3,4,6]=>[3,1,1,1,1,1]
[5,8,3,7,1,2,4,6]=>[3,1,1,1,1,1]
[5,8,4,7,1,2,3,6]=>[3,1,1,1,1,1]
[6,8,2,7,1,3,4,5]=>[3,1,1,1,1,1]
[6,8,5,7,1,2,3,4]=>[3,1,1,1,1,1]
[7,8,2,4,1,3,5,6]=>[3,1,1,1,1,1]
[7,8,2,5,1,3,4,6]=>[3,1,1,1,1,1]
[7,8,3,5,1,2,4,6]=>[3,1,1,1,1,1]
[7,8,4,6,1,2,3,5]=>[3,1,1,1,1,1]
[4,3,2,6,1,5,7,8]=>[4,1,1,1,1]
[5,3,2,6,1,4,7,8]=>[4,1,1,1,1]
[6,3,2,5,1,4,7,8]=>[4,1,1,1,1]
[6,4,2,5,1,3,7,8]=>[4,1,1,1,1]
[6,5,2,4,1,3,7,8]=>[4,1,1,1,1]
[4,3,2,7,1,5,6,8]=>[4,1,1,1,1]
[5,3,2,7,1,4,6,8]=>[4,1,1,1,1]
[6,3,2,7,1,4,5,8]=>[4,1,1,1,1]
[6,4,2,7,1,3,5,8]=>[4,1,1,1,1]
[6,4,3,7,1,2,5,8]=>[4,1,1,1,1]
[6,5,2,7,1,3,4,8]=>[4,1,1,1,1]
[6,5,3,7,1,2,4,8]=>[4,1,1,1,1]
[7,3,2,5,1,4,6,8]=>[4,1,1,1,1]
[7,4,2,5,1,3,6,8]=>[4,1,1,1,1]
[7,3,2,6,1,4,5,8]=>[4,1,1,1,1]
[7,4,2,6,1,3,5,8]=>[4,1,1,1,1]
[7,4,3,6,1,2,5,8]=>[4,1,1,1,1]
[7,5,2,6,1,3,4,8]=>[4,1,1,1,1]
[7,5,3,6,1,2,4,8]=>[4,1,1,1,1]
[7,6,3,5,1,2,4,8]=>[4,1,1,1,1]
[4,3,2,8,1,5,6,7]=>[4,1,1,1,1]
[6,4,2,8,1,3,5,7]=>[4,1,1,1,1]
[6,4,3,8,1,2,5,7]=>[4,1,1,1,1]
[6,5,2,8,1,3,4,7]=>[4,1,1,1,1]
[6,5,3,8,1,2,4,7]=>[4,1,1,1,1]
[6,5,4,8,1,2,3,7]=>[4,1,1,1,1]
[7,3,2,8,1,4,5,6]=>[4,1,1,1,1]
[7,4,2,8,1,3,5,6]=>[4,1,1,1,1]
[7,4,3,8,1,2,5,6]=>[4,1,1,1,1]
[7,5,3,8,1,2,4,6]=>[4,1,1,1,1]
[7,5,4,8,1,2,3,6]=>[4,1,1,1,1]
[7,6,2,8,1,3,4,5]=>[4,1,1,1,1]
[8,3,2,5,1,4,6,7]=>[4,1,1,1,1]
[8,4,2,5,1,3,6,7]=>[4,1,1,1,1]
[8,3,2,6,1,4,5,7]=>[4,1,1,1,1]
[8,4,2,6,1,3,5,7]=>[4,1,1,1,1]
[8,5,3,6,1,2,4,7]=>[4,1,1,1,1]
[8,6,2,4,1,3,5,7]=>[4,1,1,1,1]
[8,6,2,5,1,3,4,7]=>[4,1,1,1,1]
[8,3,2,7,1,4,5,6]=>[4,1,1,1,1]
[8,4,2,7,1,3,5,6]=>[4,1,1,1,1]
[8,4,3,7,1,2,5,6]=>[4,1,1,1,1]
[8,5,2,7,1,3,4,6]=>[4,1,1,1,1]
[8,5,3,7,1,2,4,6]=>[4,1,1,1,1]
[8,5,4,7,1,2,3,6]=>[4,1,1,1,1]
[8,6,3,7,1,2,4,5]=>[4,1,1,1,1]
[8,7,2,4,1,3,5,6]=>[4,1,1,1,1]
[8,7,2,5,1,3,4,6]=>[4,1,1,1,1]
[8,7,3,5,1,2,4,6]=>[4,1,1,1,1]
[8,7,2,6,1,3,4,5]=>[4,1,1,1,1]
[8,7,3,6,1,2,4,5]=>[4,1,1,1,1]
[8,7,4,6,1,2,3,5]=>[4,1,1,1,1]
[3,6,2,5,8,1,4,7]=>[3,1,1,1,1,1]
[4,6,3,5,8,1,2,7]=>[3,1,1,1,1,1]
[5,6,2,4,8,1,3,7]=>[3,1,1,1,1,1]
[4,7,2,5,8,1,3,6]=>[3,1,1,1,1,1]
[4,7,3,5,8,1,2,6]=>[3,1,1,1,1,1]
[5,7,2,4,8,1,3,6]=>[3,1,1,1,1,1]
[5,7,3,4,8,1,2,6]=>[3,1,1,1,1,1]
[3,7,2,6,8,1,4,5]=>[3,1,1,1,1,1]
[4,7,3,6,8,1,2,5]=>[3,1,1,1,1,1]
[5,7,2,6,8,1,3,4]=>[3,1,1,1,1,1]
[5,7,4,6,8,1,2,3]=>[3,1,1,1,1,1]
[6,7,3,4,8,1,2,5]=>[3,1,1,1,1,1]
[6,7,3,5,8,1,2,4]=>[3,1,1,1,1,1]
[3,8,2,5,7,1,4,6]=>[3,1,1,1,1,1]
[4,8,2,5,7,1,3,6]=>[3,1,1,1,1,1]
[4,8,3,5,7,1,2,6]=>[3,1,1,1,1,1]
[5,8,2,4,7,1,3,6]=>[3,1,1,1,1,1]
[3,8,2,6,7,1,4,5]=>[3,1,1,1,1,1]
[4,8,3,6,7,1,2,5]=>[3,1,1,1,1,1]
[5,8,2,6,7,1,3,4]=>[3,1,1,1,1,1]
[5,8,3,6,7,1,2,4]=>[3,1,1,1,1,1]
[5,8,4,6,7,1,2,3]=>[3,1,1,1,1,1]
[6,8,2,5,7,1,3,4]=>[3,1,1,1,1,1]
[6,8,3,5,7,1,2,4]=>[3,1,1,1,1,1]
[6,8,4,5,7,1,2,3]=>[3,1,1,1,1,1]
[7,8,2,4,6,1,3,5]=>[3,1,1,1,1,1]
[7,8,2,5,6,1,3,4]=>[3,1,1,1,1,1]
[7,8,3,5,6,1,2,4]=>[3,1,1,1,1,1]
[4,3,2,6,8,1,5,7]=>[4,1,1,1,1]
[5,3,2,6,8,1,4,7]=>[4,1,1,1,1]
[5,4,2,6,8,1,3,7]=>[4,1,1,1,1]
[5,4,3,6,8,1,2,7]=>[4,1,1,1,1]
[6,3,2,5,8,1,4,7]=>[4,1,1,1,1]
[6,4,3,5,8,1,2,7]=>[4,1,1,1,1]
[6,5,2,4,8,1,3,7]=>[4,1,1,1,1]
[4,3,2,7,8,1,5,6]=>[4,1,1,1,1]
[5,3,2,7,8,1,4,6]=>[4,1,1,1,1]
[5,4,2,7,8,1,3,6]=>[4,1,1,1,1]
[5,4,3,7,8,1,2,6]=>[4,1,1,1,1]
[6,4,2,7,8,1,3,5]=>[4,1,1,1,1]
[6,4,3,7,8,1,2,5]=>[4,1,1,1,1]
[6,5,2,7,8,1,3,4]=>[4,1,1,1,1]
[7,4,2,5,8,1,3,6]=>[4,1,1,1,1]
[7,4,3,5,8,1,2,6]=>[4,1,1,1,1]
[7,3,2,6,8,1,4,5]=>[4,1,1,1,1]
[7,5,2,6,8,1,3,4]=>[4,1,1,1,1]
[7,5,3,6,8,1,2,4]=>[4,1,1,1,1]
[7,6,2,4,8,1,3,5]=>[4,1,1,1,1]
[7,6,3,5,8,1,2,4]=>[4,1,1,1,1]
[8,4,2,5,7,1,3,6]=>[4,1,1,1,1]
[8,5,2,4,7,1,3,6]=>[4,1,1,1,1]
[8,3,2,6,7,1,4,5]=>[4,1,1,1,1]
[8,4,2,6,7,1,3,5]=>[4,1,1,1,1]
[8,5,2,6,7,1,3,4]=>[4,1,1,1,1]
[8,5,3,6,7,1,2,4]=>[4,1,1,1,1]
[8,6,2,4,7,1,3,5]=>[4,1,1,1,1]
[8,6,3,5,7,1,2,4]=>[4,1,1,1,1]
[8,7,2,4,6,1,3,5]=>[4,1,1,1,1]
[8,7,3,4,6,1,2,5]=>[4,1,1,1,1]
[8,7,2,5,6,1,3,4]=>[4,1,1,1,1]
[8,7,3,5,6,1,2,4]=>[4,1,1,1,1]
[4,3,7,2,6,1,5,8]=>[4,1,1,1,1]
[5,3,7,2,6,1,4,8]=>[4,1,1,1,1]
[5,4,7,2,6,1,3,8]=>[4,1,1,1,1]
[6,3,7,2,5,1,4,8]=>[4,1,1,1,1]
[6,4,7,2,5,1,3,8]=>[4,1,1,1,1]
[7,3,6,2,5,1,4,8]=>[4,1,1,1,1]
[4,3,8,2,6,1,5,7]=>[4,1,1,1,1]
[5,3,8,2,6,1,4,7]=>[4,1,1,1,1]
[5,4,8,2,6,1,3,7]=>[4,1,1,1,1]
[5,4,8,3,6,1,2,7]=>[4,1,1,1,1]
[6,4,8,2,5,1,3,7]=>[4,1,1,1,1]
[6,4,8,3,5,1,2,7]=>[4,1,1,1,1]
[6,5,8,2,4,1,3,7]=>[4,1,1,1,1]
[6,5,8,3,4,1,2,7]=>[4,1,1,1,1]
[4,3,8,2,7,1,5,6]=>[4,1,1,1,1]
[5,3,8,2,7,1,4,6]=>[4,1,1,1,1]
[5,4,8,2,7,1,3,6]=>[4,1,1,1,1]
[5,4,8,3,7,1,2,6]=>[4,1,1,1,1]
[6,3,8,2,7,1,4,5]=>[4,1,1,1,1]
[6,4,8,2,7,1,3,5]=>[4,1,1,1,1]
[6,4,8,3,7,1,2,5]=>[4,1,1,1,1]
[6,5,8,2,7,1,3,4]=>[4,1,1,1,1]
[7,3,8,2,5,1,4,6]=>[4,1,1,1,1]
[7,4,8,3,5,1,2,6]=>[4,1,1,1,1]
[7,5,8,2,4,1,3,6]=>[4,1,1,1,1]
[7,5,8,3,4,1,2,6]=>[4,1,1,1,1]
[7,3,8,2,6,1,4,5]=>[4,1,1,1,1]
[7,4,8,2,6,1,3,5]=>[4,1,1,1,1]
[7,5,8,2,6,1,3,4]=>[4,1,1,1,1]
[7,5,8,3,6,1,2,4]=>[4,1,1,1,1]
[7,5,8,4,6,1,2,3]=>[4,1,1,1,1]
[7,6,8,2,5,1,3,4]=>[4,1,1,1,1]
[7,6,8,3,5,1,2,4]=>[4,1,1,1,1]
[8,3,6,2,5,1,4,7]=>[4,1,1,1,1]
[8,5,6,2,4,1,3,7]=>[4,1,1,1,1]
[8,3,7,2,5,1,4,6]=>[4,1,1,1,1]
[8,4,7,3,5,1,2,6]=>[4,1,1,1,1]
[8,5,7,2,4,1,3,6]=>[4,1,1,1,1]
[8,3,7,2,6,1,4,5]=>[4,1,1,1,1]
[8,4,7,2,6,1,3,5]=>[4,1,1,1,1]
[8,4,7,3,6,1,2,5]=>[4,1,1,1,1]
[8,5,7,2,6,1,3,4]=>[4,1,1,1,1]
[8,6,7,2,4,1,3,5]=>[4,1,1,1,1]
[8,6,7,2,5,1,3,4]=>[4,1,1,1,1]
[8,6,7,3,5,1,2,4]=>[4,1,1,1,1]
[5,4,3,2,7,1,6,8]=>[5,1,1,1]
[6,4,3,2,7,1,5,8]=>[5,1,1,1]
[6,5,3,2,7,1,4,8]=>[5,1,1,1]
[6,5,4,2,7,1,3,8]=>[5,1,1,1]
[7,5,3,2,6,1,4,8]=>[5,1,1,1]
[7,5,4,2,6,1,3,8]=>[5,1,1,1]
[7,6,3,2,5,1,4,8]=>[5,1,1,1]
[5,4,3,2,8,1,6,7]=>[5,1,1,1]
[6,5,3,2,8,1,4,7]=>[5,1,1,1]
[6,5,4,2,8,1,3,7]=>[5,1,1,1]
[6,5,4,3,8,1,2,7]=>[5,1,1,1]
[7,5,3,2,8,1,4,6]=>[5,1,1,1]
[7,5,4,2,8,1,3,6]=>[5,1,1,1]
[7,6,3,2,8,1,4,5]=>[5,1,1,1]
[7,6,4,3,8,1,2,5]=>[5,1,1,1]
[7,6,5,2,8,1,3,4]=>[5,1,1,1]
[7,6,5,3,8,1,2,4]=>[5,1,1,1]
[8,5,3,2,6,1,4,7]=>[5,1,1,1]
[8,5,4,2,6,1,3,7]=>[5,1,1,1]
[8,6,4,2,5,1,3,7]=>[5,1,1,1]
[8,6,5,2,4,1,3,7]=>[5,1,1,1]
[8,5,3,2,7,1,4,6]=>[5,1,1,1]
[8,6,3,2,7,1,4,5]=>[5,1,1,1]
[8,6,4,2,7,1,3,5]=>[5,1,1,1]
[8,6,4,3,7,1,2,5]=>[5,1,1,1]
[8,6,5,3,7,1,2,4]=>[5,1,1,1]
[8,7,3,2,6,1,4,5]=>[5,1,1,1]
[8,7,4,2,6,1,3,5]=>[5,1,1,1]
[8,7,4,3,6,1,2,5]=>[5,1,1,1]
[8,7,5,2,6,1,3,4]=>[5,1,1,1]
[8,7,5,3,6,1,2,4]=>[5,1,1,1]
[8,7,6,2,4,1,3,5]=>[5,1,1,1]
[8,7,6,2,5,1,3,4]=>[5,1,1,1]
[8,7,6,3,5,1,2,4]=>[5,1,1,1]
[4,8,3,7,2,6,1,5]=>[4,1,1,1,1]
[5,8,3,7,2,6,1,4]=>[4,1,1,1,1]
[5,8,4,7,2,6,1,3]=>[4,1,1,1,1]
[5,8,4,7,3,6,1,2]=>[4,1,1,1,1]
[6,8,3,7,2,5,1,4]=>[4,1,1,1,1]
[6,8,4,7,2,5,1,3]=>[4,1,1,1,1]
[6,8,4,7,3,5,1,2]=>[4,1,1,1,1]
[6,8,5,7,2,4,1,3]=>[4,1,1,1,1]
[6,8,5,7,3,4,1,2]=>[4,1,1,1,1]
[7,8,3,6,2,5,1,4]=>[4,1,1,1,1]
[7,8,4,6,2,5,1,3]=>[4,1,1,1,1]
[7,8,4,6,3,5,1,2]=>[4,1,1,1,1]
[7,8,5,6,2,4,1,3]=>[4,1,1,1,1]
[5,4,3,8,2,7,1,6]=>[5,1,1,1]
[6,4,3,8,2,7,1,5]=>[5,1,1,1]
[6,5,3,8,2,7,1,4]=>[5,1,1,1]
[6,5,4,8,2,7,1,3]=>[5,1,1,1]
[6,5,4,8,3,7,1,2]=>[5,1,1,1]
[7,4,3,8,2,6,1,5]=>[5,1,1,1]
[7,5,3,8,2,6,1,4]=>[5,1,1,1]
[7,5,4,8,2,6,1,3]=>[5,1,1,1]
[7,6,3,8,2,5,1,4]=>[5,1,1,1]
[7,6,4,8,2,5,1,3]=>[5,1,1,1]
[7,6,5,8,2,4,1,3]=>[5,1,1,1]
[8,4,3,7,2,6,1,5]=>[5,1,1,1]
[8,5,3,7,2,6,1,4]=>[5,1,1,1]
[8,5,4,7,2,6,1,3]=>[5,1,1,1]
[8,5,4,7,3,6,1,2]=>[5,1,1,1]
[8,6,3,7,2,5,1,4]=>[5,1,1,1]
[8,6,4,7,2,5,1,3]=>[5,1,1,1]
[8,6,4,7,3,5,1,2]=>[5,1,1,1]
[8,6,5,7,2,4,1,3]=>[5,1,1,1]
[8,7,3,6,2,5,1,4]=>[5,1,1,1]
[8,7,4,6,2,5,1,3]=>[5,1,1,1]
[8,7,4,6,3,5,1,2]=>[5,1,1,1]
[8,7,5,6,2,4,1,3]=>[5,1,1,1]
[6,5,4,3,2,8,1,7]=>[6,1,1]
[7,6,4,3,2,8,1,5]=>[6,1,1]
[7,6,5,4,2,8,1,3]=>[6,1,1]
[8,5,4,3,2,7,1,6]=>[6,1,1]
[8,6,4,3,2,7,1,5]=>[6,1,1]
[8,6,5,4,2,7,1,3]=>[6,1,1]
[8,7,4,3,2,6,1,5]=>[6,1,1]
[8,7,5,3,2,6,1,4]=>[6,1,1]
[8,7,5,4,2,6,1,3]=>[6,1,1]
[8,7,6,3,2,5,1,4]=>[6,1,1]
[8,7,6,4,2,5,1,3]=>[6,1,1]
[8,7,6,5,2,4,1,3]=>[6,1,1]
[8,1,2,3,4,7,5,6]=>[3,1,1,1,1,1]
[8,1,2,3,6,4,5,7]=>[3,1,1,1,1,1]
[8,1,2,3,7,4,5,6]=>[3,1,1,1,1,1]
[7,1,2,3,6,4,8,5]=>[3,2,1,1,1]
[5,1,2,3,8,7,4,6]=>[3,2,1,1,1]
[8,1,2,3,6,7,4,5]=>[3,1,1,1,1,1]
[4,1,2,8,3,7,5,6]=>[3,2,1,1,1]
[8,1,2,5,3,4,6,7]=>[3,1,1,1,1,1]
[7,1,2,5,3,4,8,6]=>[3,2,1,1,1]
[8,1,2,6,3,4,5,7]=>[3,1,1,1,1,1]
[7,1,2,6,3,4,8,5]=>[3,2,1,1,1]
[6,1,2,5,3,8,4,7]=>[3,2,1,1,1]
[8,1,2,5,3,7,4,6]=>[3,2,1,1,1]
[8,1,2,6,3,7,4,5]=>[3,2,1,1,1]
[6,1,2,5,3,7,8,4]=>[3,2,1,1,1]
[4,1,2,8,6,3,5,7]=>[3,2,1,1,1]
[4,1,2,8,7,3,5,6]=>[3,2,1,1,1]
[4,1,2,7,6,3,8,5]=>[3,2,2,1]
[8,1,2,5,6,3,4,7]=>[3,1,1,1,1,1]
[8,1,2,5,7,3,4,6]=>[3,1,1,1,1,1]
[8,1,2,7,6,3,4,5]=>[4,1,1,1,1]
[7,1,2,5,6,3,8,4]=>[3,2,1,1,1]
[4,1,2,5,8,7,3,6]=>[3,2,1,1,1]
[4,1,2,8,6,7,3,5]=>[3,2,1,1,1]
[8,1,2,5,6,7,3,4]=>[3,1,1,1,1,1]
[3,1,8,2,4,7,5,6]=>[3,2,1,1,1]
[3,1,8,2,6,4,5,7]=>[3,2,1,1,1]
[3,1,8,2,7,4,5,6]=>[3,2,1,1,1]
[3,1,7,2,6,4,8,5]=>[3,2,2,1]
[3,1,5,2,8,7,4,6]=>[3,2,2,1]
[3,1,8,2,6,7,4,5]=>[3,2,1,1,1]
[8,1,4,2,3,5,6,7]=>[3,1,1,1,1,1]
[7,1,4,2,3,5,8,6]=>[3,2,1,1,1]
[6,1,4,2,3,8,5,7]=>[3,2,1,1,1]
[8,1,4,2,3,7,5,6]=>[3,2,1,1,1]
[6,1,4,2,3,7,8,5]=>[3,2,1,1,1]
[8,1,5,2,3,4,6,7]=>[3,1,1,1,1,1]
[7,1,5,2,3,4,8,6]=>[3,2,1,1,1]
[8,1,7,2,3,4,5,6]=>[3,1,1,1,1,1]
[6,1,5,2,3,8,4,7]=>[3,2,1,1,1]
[8,1,5,2,3,7,4,6]=>[3,2,1,1,1]
[6,1,8,2,3,7,4,5]=>[3,2,1,1,1]
[6,1,5,2,3,7,8,4]=>[3,2,1,1,1]
[5,1,4,2,8,3,6,7]=>[3,2,1,1,1]
[5,1,4,2,7,3,8,6]=>[3,2,2,1]
[8,1,4,2,6,3,5,7]=>[3,2,1,1,1]
[8,1,4,2,7,3,5,6]=>[3,2,1,1,1]
[7,1,4,2,6,3,8,5]=>[3,2,2,1]
[8,1,5,2,6,3,4,7]=>[3,2,1,1,1]
[8,1,5,2,7,3,4,6]=>[3,2,1,1,1]
[7,1,8,2,6,3,4,5]=>[3,2,1,1,1]
[7,1,5,2,6,3,8,4]=>[3,2,2,1]
[5,1,4,2,6,8,3,7]=>[3,2,1,1,1]
[5,1,4,2,8,7,3,6]=>[3,3,1,1]
[8,1,4,2,6,7,3,5]=>[3,2,1,1,1]
[8,1,5,2,6,7,3,4]=>[3,2,1,1,1]
[5,1,4,2,6,7,8,3]=>[3,2,1,1,1]
[3,1,4,8,2,7,5,6]=>[3,2,1,1,1]
[3,1,8,5,2,4,6,7]=>[3,2,1,1,1]
[3,1,7,5,2,4,8,6]=>[3,2,2,1]
[3,1,8,6,2,4,5,7]=>[3,2,1,1,1]
[3,1,7,6,2,4,8,5]=>[3,2,2,1]
[3,1,6,5,2,8,4,7]=>[3,2,2,1]
[3,1,8,5,2,7,4,6]=>[3,2,2,1]
[3,1,8,6,2,7,4,5]=>[3,2,2,1]
[3,1,6,5,2,7,8,4]=>[3,2,2,1]
[8,1,4,5,2,3,6,7]=>[3,1,1,1,1,1]
[7,1,4,5,2,3,8,6]=>[3,2,1,1,1]
[8,1,4,6,2,3,5,7]=>[3,1,1,1,1,1]
[7,1,4,8,2,3,5,6]=>[3,1,1,1,1,1]
[7,1,4,6,2,3,8,5]=>[3,2,1,1,1]
[8,1,6,5,2,3,4,7]=>[4,1,1,1,1]
[7,1,8,5,2,3,4,6]=>[3,2,1,1,1]
[7,1,8,6,2,3,4,5]=>[3,2,1,1,1]
[7,1,6,5,2,3,8,4]=>[4,2,1,1]
[6,1,4,5,2,8,3,7]=>[3,2,1,1,1]
[8,1,4,5,2,7,3,6]=>[3,2,1,1,1]
[8,1,4,6,2,7,3,5]=>[3,2,1,1,1]
[8,1,6,5,2,7,3,4]=>[4,2,1,1]
[6,1,4,5,2,7,8,3]=>[3,2,1,1,1]
[3,1,4,8,6,2,5,7]=>[3,2,1,1,1]
[3,1,4,8,7,2,5,6]=>[3,2,1,1,1]
[3,1,4,7,6,2,8,5]=>[3,2,2,1]
[3,1,8,5,6,2,4,7]=>[3,2,1,1,1]
[3,1,8,5,7,2,4,6]=>[3,2,1,1,1]
[3,1,8,7,6,2,4,5]=>[4,2,1,1]
[3,1,7,5,6,2,8,4]=>[3,2,2,1]
[8,1,4,5,6,2,3,7]=>[3,1,1,1,1,1]
[8,1,4,5,7,2,3,6]=>[3,1,1,1,1,1]
[8,1,4,7,6,2,3,5]=>[4,1,1,1,1]
[8,1,7,5,6,2,3,4]=>[4,1,1,1,1]
[7,1,4,5,6,2,8,3]=>[3,2,1,1,1]
[3,1,4,5,8,7,2,6]=>[3,2,1,1,1]
[3,1,4,8,6,7,2,5]=>[3,2,1,1,1]
[3,1,8,5,6,7,2,4]=>[3,2,1,1,1]
[8,1,4,5,6,7,2,3]=>[3,1,1,1,1,1]
[2,8,1,3,4,7,5,6]=>[3,1,1,1,1,1]
[2,8,1,3,6,4,5,7]=>[3,1,1,1,1,1]
[2,8,1,3,7,4,5,6]=>[3,1,1,1,1,1]
[2,7,1,3,6,4,8,5]=>[3,2,1,1,1]
[2,5,1,3,8,7,4,6]=>[3,2,1,1,1]
[2,8,1,3,6,7,4,5]=>[3,1,1,1,1,1]
[2,4,1,8,3,7,5,6]=>[3,2,1,1,1]
[2,8,1,5,3,4,6,7]=>[3,1,1,1,1,1]
[2,7,1,5,3,4,8,6]=>[3,2,1,1,1]
[2,8,1,6,3,4,5,7]=>[3,1,1,1,1,1]
[2,7,1,6,3,4,8,5]=>[3,2,1,1,1]
[2,6,1,5,3,8,4,7]=>[3,2,1,1,1]
[2,8,1,5,3,7,4,6]=>[3,2,1,1,1]
[2,6,1,5,3,7,8,4]=>[3,2,1,1,1]
[2,4,1,8,6,3,5,7]=>[3,2,1,1,1]
[2,4,1,8,7,3,5,6]=>[3,2,1,1,1]
[2,4,1,7,6,3,8,5]=>[3,2,2,1]
[2,8,1,5,6,3,4,7]=>[3,1,1,1,1,1]
[2,8,1,5,7,3,4,6]=>[3,1,1,1,1,1]
[2,8,1,7,6,3,4,5]=>[4,1,1,1,1]
[2,7,1,5,6,3,8,4]=>[3,2,1,1,1]
[2,4,1,5,8,7,3,6]=>[3,2,1,1,1]
[2,4,1,8,6,7,3,5]=>[3,2,1,1,1]
[2,8,1,5,6,7,3,4]=>[3,1,1,1,1,1]
[7,3,1,2,4,5,8,6]=>[3,2,1,1,1]
[6,3,1,2,4,8,5,7]=>[3,2,1,1,1]
[8,3,1,2,4,7,5,6]=>[3,2,1,1,1]
[6,3,1,2,4,7,8,5]=>[3,2,1,1,1]
[5,3,1,2,8,4,6,7]=>[3,2,1,1,1]
[5,3,1,2,7,4,8,6]=>[3,2,2,1]
[8,3,1,2,6,4,5,7]=>[3,2,1,1,1]
[8,3,1,2,7,4,5,6]=>[3,2,1,1,1]
[7,3,1,2,6,4,8,5]=>[3,2,2,1]
[5,3,1,2,6,8,4,7]=>[3,2,1,1,1]
[5,3,1,2,8,7,4,6]=>[3,3,1,1]
[8,3,1,2,6,7,4,5]=>[3,2,1,1,1]
[5,3,1,2,6,7,8,4]=>[3,2,1,1,1]
[7,4,1,2,3,5,8,6]=>[3,2,1,1,1]
[6,4,1,2,3,8,5,7]=>[3,2,1,1,1]
[8,4,1,2,3,7,5,6]=>[3,2,1,1,1]
[6,4,1,2,3,7,8,5]=>[3,2,1,1,1]
[7,6,1,2,3,4,8,5]=>[3,2,1,1,1]
[5,8,1,2,3,7,4,6]=>[3,1,1,1,1,1]
[8,6,1,2,3,7,4,5]=>[3,2,1,1,1]
[5,4,1,2,8,3,6,7]=>[3,2,1,1,1]
[5,4,1,2,7,3,8,6]=>[3,2,2,1]
[8,4,1,2,6,3,5,7]=>[3,2,1,1,1]
[8,4,1,2,7,3,5,6]=>[3,2,1,1,1]
[7,4,1,2,6,3,8,5]=>[3,2,2,1]
[5,8,1,2,6,3,4,7]=>[3,1,1,1,1,1]
[5,8,1,2,7,3,4,6]=>[3,1,1,1,1,1]
[8,7,1,2,6,3,4,5]=>[4,1,1,1,1]
[5,7,1,2,6,3,8,4]=>[3,2,1,1,1]
[5,4,1,2,6,8,3,7]=>[3,2,1,1,1]
[5,4,1,2,8,7,3,6]=>[3,3,1,1]
[8,4,1,2,6,7,3,5]=>[3,2,1,1,1]
[5,8,1,2,6,7,3,4]=>[3,1,1,1,1,1]
[5,4,1,2,6,7,8,3]=>[3,2,1,1,1]
[4,3,1,8,2,5,6,7]=>[3,2,1,1,1]
[4,3,1,7,2,5,8,6]=>[3,2,2,1]
[4,3,1,6,2,8,5,7]=>[3,2,2,1]
[4,3,1,8,2,7,5,6]=>[3,3,1,1]
[4,3,1,6,2,7,8,5]=>[3,2,2,1]
[8,3,1,5,2,4,6,7]=>[3,2,1,1,1]
[7,3,1,5,2,4,8,6]=>[3,2,2,1]
[8,3,1,6,2,4,5,7]=>[3,2,1,1,1]
[7,3,1,8,2,4,5,6]=>[3,2,1,1,1]
[7,3,1,6,2,4,8,5]=>[3,2,2,1]
[6,3,1,5,2,8,4,7]=>[3,2,2,1]
[8,3,1,5,2,7,4,6]=>[3,2,2,1]
[8,3,1,6,2,7,4,5]=>[3,2,2,1]
[6,3,1,5,2,7,8,4]=>[3,2,2,1]
[8,4,1,5,2,3,6,7]=>[3,2,1,1,1]
[7,4,1,5,2,3,8,6]=>[3,2,2,1]
[8,4,1,6,2,3,5,7]=>[3,2,1,1,1]
[7,4,1,8,2,3,5,6]=>[3,2,1,1,1]
[7,4,1,6,2,3,8,5]=>[3,2,2,1]
[6,8,1,5,2,3,4,7]=>[3,1,1,1,1,1]
[8,7,1,5,2,3,4,6]=>[4,1,1,1,1]
[8,7,1,6,2,3,4,5]=>[4,1,1,1,1]
[6,7,1,5,2,3,8,4]=>[3,2,1,1,1]
[6,4,1,5,2,8,3,7]=>[3,2,2,1]
[8,4,1,5,2,7,3,6]=>[3,2,2,1]
[8,4,1,6,2,7,3,5]=>[3,2,2,1]
[6,8,1,5,2,7,3,4]=>[3,2,1,1,1]
[6,4,1,5,2,7,8,3]=>[3,2,2,1]
[4,3,1,5,8,2,6,7]=>[3,2,1,1,1]
[4,3,1,5,7,2,8,6]=>[3,2,2,1]
[4,3,1,8,6,2,5,7]=>[3,3,1,1]
[4,3,1,8,7,2,5,6]=>[3,3,1,1]
[4,3,1,7,6,2,8,5]=>[3,3,2]
[8,3,1,5,6,2,4,7]=>[3,2,1,1,1]
[8,3,1,5,7,2,4,6]=>[3,2,1,1,1]
[8,3,1,7,6,2,4,5]=>[4,2,1,1]
[7,3,1,5,6,2,8,4]=>[3,2,2,1]
[8,4,1,5,6,2,3,7]=>[3,2,1,1,1]
[8,4,1,5,7,2,3,6]=>[3,2,1,1,1]
[8,4,1,7,6,2,3,5]=>[4,2,1,1]
[7,8,1,5,6,2,3,4]=>[3,1,1,1,1,1]
[7,4,1,5,6,2,8,3]=>[3,2,2,1]
[4,3,1,5,6,8,2,7]=>[3,2,1,1,1]
[4,3,1,5,8,7,2,6]=>[3,3,1,1]
[4,3,1,8,6,7,2,5]=>[3,3,1,1]
[8,3,1,5,6,7,2,4]=>[3,2,1,1,1]
[8,4,1,5,6,7,2,3]=>[3,2,1,1,1]
[4,3,1,5,6,7,8,2]=>[3,2,1,1,1]
[2,3,8,1,4,7,5,6]=>[3,1,1,1,1,1]
[2,3,8,1,6,4,5,7]=>[3,1,1,1,1,1]
[2,3,8,1,7,4,5,6]=>[3,1,1,1,1,1]
[2,3,7,1,6,4,8,5]=>[3,2,1,1,1]
[2,3,5,1,8,7,4,6]=>[3,2,1,1,1]
[2,3,8,1,6,7,4,5]=>[3,1,1,1,1,1]
[2,8,4,1,3,5,6,7]=>[3,1,1,1,1,1]
[2,7,4,1,3,5,8,6]=>[3,2,1,1,1]
[2,6,4,1,3,8,5,7]=>[3,2,1,1,1]
[2,8,4,1,3,7,5,6]=>[3,2,1,1,1]
[2,6,4,1,3,7,8,5]=>[3,2,1,1,1]
[2,8,5,1,3,4,6,7]=>[3,1,1,1,1,1]
[2,7,5,1,3,4,8,6]=>[3,2,1,1,1]
[2,8,7,1,3,4,5,6]=>[3,1,1,1,1,1]
[2,6,5,1,3,8,4,7]=>[3,2,1,1,1]
[2,8,5,1,3,7,4,6]=>[3,2,1,1,1]
[2,6,8,1,3,7,4,5]=>[3,1,1,1,1,1]
[2,6,5,1,3,7,8,4]=>[3,2,1,1,1]
[2,5,4,1,8,3,6,7]=>[3,2,1,1,1]
[2,5,4,1,7,3,8,6]=>[3,2,2,1]
[2,8,4,1,6,3,5,7]=>[3,2,1,1,1]
[2,8,4,1,7,3,5,6]=>[3,2,1,1,1]
[2,7,4,1,6,3,8,5]=>[3,2,2,1]
[2,8,5,1,6,3,4,7]=>[3,2,1,1,1]
[2,8,5,1,7,3,4,6]=>[3,2,1,1,1]
[2,7,8,1,6,3,4,5]=>[3,1,1,1,1,1]
[2,7,5,1,6,3,8,4]=>[3,2,2,1]
[2,5,4,1,6,8,3,7]=>[3,2,1,1,1]
[2,5,4,1,8,7,3,6]=>[3,3,1,1]
[2,8,4,1,6,7,3,5]=>[3,2,1,1,1]
[2,8,5,1,6,7,3,4]=>[3,2,1,1,1]
[2,5,4,1,6,7,8,3]=>[3,2,1,1,1]
[7,3,4,1,2,5,8,6]=>[3,2,1,1,1]
[6,3,4,1,2,8,5,7]=>[3,2,1,1,1]
[8,3,4,1,2,7,5,6]=>[3,2,1,1,1]
[6,3,4,1,2,7,8,5]=>[3,2,1,1,1]
[7,3,5,1,2,4,8,6]=>[3,2,1,1,1]
[6,3,7,1,2,4,8,5]=>[3,2,1,1,1]
[6,3,5,1,2,8,4,7]=>[3,2,1,1,1]
[8,3,5,1,2,7,4,6]=>[3,2,1,1,1]
[6,3,8,1,2,7,4,5]=>[3,2,1,1,1]
[6,3,5,1,2,7,8,4]=>[3,2,1,1,1]
[7,5,4,1,2,3,8,6]=>[4,2,1,1]
[6,8,4,1,2,3,5,7]=>[3,1,1,1,1,1]
[6,7,4,1,2,3,8,5]=>[3,2,1,1,1]
[6,8,5,1,2,3,4,7]=>[3,1,1,1,1,1]
[6,7,5,1,2,3,8,4]=>[3,2,1,1,1]
[6,5,4,1,2,8,3,7]=>[4,2,1,1]
[8,5,4,1,2,7,3,6]=>[4,2,1,1]
[6,8,4,1,2,7,3,5]=>[3,2,1,1,1]
[6,8,5,1,2,7,3,4]=>[3,2,1,1,1]
[6,5,4,1,2,7,8,3]=>[4,2,1,1]
[5,3,4,1,8,2,6,7]=>[3,2,1,1,1]
[5,3,4,1,7,2,8,6]=>[3,2,2,1]
[8,3,4,1,6,2,5,7]=>[3,2,1,1,1]
[8,3,4,1,7,2,5,6]=>[3,2,1,1,1]
[7,3,4,1,6,2,8,5]=>[3,2,2,1]
[8,3,5,1,6,2,4,7]=>[3,2,1,1,1]
[8,3,5,1,7,2,4,6]=>[3,2,1,1,1]
[7,3,8,1,6,2,4,5]=>[3,2,1,1,1]
[7,3,5,1,6,2,8,4]=>[3,2,2,1]
[8,5,4,1,6,2,3,7]=>[4,2,1,1]
[8,5,4,1,7,2,3,6]=>[4,2,1,1]
[7,8,4,1,6,2,3,5]=>[3,2,1,1,1]
[7,8,5,1,6,2,3,4]=>[3,2,1,1,1]
[7,5,4,1,6,2,8,3]=>[4,2,2]
[5,3,4,1,6,8,2,7]=>[3,2,1,1,1]
[5,3,4,1,8,7,2,6]=>[3,3,1,1]
[8,3,4,1,6,7,2,5]=>[3,2,1,1,1]
[8,3,5,1,6,7,2,4]=>[3,2,1,1,1]
[8,5,4,1,6,7,2,3]=>[4,2,1,1]
[5,3,4,1,6,7,8,2]=>[3,2,1,1,1]
[2,3,4,8,1,7,5,6]=>[3,1,1,1,1,1]
[2,3,8,5,1,4,6,7]=>[3,1,1,1,1,1]
[2,3,7,5,1,4,8,6]=>[3,2,1,1,1]
[2,3,8,6,1,4,5,7]=>[3,1,1,1,1,1]
[2,3,7,6,1,4,8,5]=>[3,2,1,1,1]
[2,3,6,5,1,8,4,7]=>[3,2,1,1,1]
[2,3,8,5,1,7,4,6]=>[3,2,1,1,1]
[2,3,8,6,1,7,4,5]=>[3,2,1,1,1]
[2,3,6,5,1,7,8,4]=>[3,2,1,1,1]
[2,8,4,5,1,3,6,7]=>[3,1,1,1,1,1]
[2,7,4,5,1,3,8,6]=>[3,2,1,1,1]
[2,8,4,6,1,3,5,7]=>[3,1,1,1,1,1]
[2,7,4,8,1,3,5,6]=>[3,1,1,1,1,1]
[2,7,4,6,1,3,8,5]=>[3,2,1,1,1]
[2,8,6,5,1,3,4,7]=>[4,1,1,1,1]
[2,7,8,5,1,3,4,6]=>[3,1,1,1,1,1]
[2,7,8,6,1,3,4,5]=>[3,1,1,1,1,1]
[2,7,6,5,1,3,8,4]=>[4,2,1,1]
[2,6,4,5,1,8,3,7]=>[3,2,1,1,1]
[2,8,4,5,1,7,3,6]=>[3,2,1,1,1]
[2,8,4,6,1,7,3,5]=>[3,2,1,1,1]
[2,8,6,5,1,7,3,4]=>[4,2,1,1]
[2,6,4,5,1,7,8,3]=>[3,2,1,1,1]
[7,3,4,5,1,2,8,6]=>[3,2,1,1,1]
[7,3,4,6,1,2,8,5]=>[3,2,1,1,1]
[8,3,6,5,1,2,4,7]=>[4,1,1,1,1]
[7,3,8,5,1,2,4,6]=>[3,2,1,1,1]
[7,3,8,6,1,2,4,5]=>[3,2,1,1,1]
[7,3,6,5,1,2,8,4]=>[4,2,1,1]
[7,6,4,5,1,2,8,3]=>[4,2,1,1]
[6,3,4,5,1,8,2,7]=>[3,2,1,1,1]
[8,3,4,5,1,7,2,6]=>[3,2,1,1,1]
[8,3,4,6,1,7,2,5]=>[3,2,1,1,1]
[8,3,6,5,1,7,2,4]=>[4,2,1,1]
[8,6,4,5,1,7,2,3]=>[4,2,1,1]
[6,3,4,5,1,7,8,2]=>[3,2,1,1,1]
[2,3,4,8,6,1,5,7]=>[3,1,1,1,1,1]
[2,3,4,8,7,1,5,6]=>[3,1,1,1,1,1]
[2,3,4,7,6,1,8,5]=>[3,2,1,1,1]
[2,3,8,5,6,1,4,7]=>[3,1,1,1,1,1]
[2,3,8,5,7,1,4,6]=>[3,1,1,1,1,1]
[2,3,8,7,6,1,4,5]=>[4,1,1,1,1]
[2,3,7,5,6,1,8,4]=>[3,2,1,1,1]
[2,8,4,5,6,1,3,7]=>[3,1,1,1,1,1]
[2,8,4,5,7,1,3,6]=>[3,1,1,1,1,1]
[2,8,4,7,6,1,3,5]=>[4,1,1,1,1]
[2,8,7,5,6,1,3,4]=>[4,1,1,1,1]
[2,7,4,5,6,1,8,3]=>[3,2,1,1,1]
[8,3,4,5,7,1,2,6]=>[3,1,1,1,1,1]
[8,3,4,7,6,1,2,5]=>[4,1,1,1,1]
[8,3,7,5,6,1,2,4]=>[4,1,1,1,1]
[7,3,4,5,6,1,8,2]=>[3,2,1,1,1]
[2,3,4,5,8,7,1,6]=>[3,1,1,1,1,1]
[2,3,4,8,6,7,1,5]=>[3,1,1,1,1,1]
[2,3,8,5,6,7,1,4]=>[3,1,1,1,1,1]
[2,8,4,5,6,7,1,3]=>[3,1,1,1,1,1]
[3,5,2,6,1,4,8,7]=>[3,2,1,1,1]
[3,5,2,6,4,1,8,7]=>[3,2,2,1]
[3,5,2,7,4,8,1,6]=>[3,2,1,1,1]
[3,5,2,7,4,8,6,1]=>[3,2,2,1]
[4,5,7,2,3,8,6,1]=>[3,2,1,1,1]
[4,5,7,2,3,8,1,6]=>[3,1,1,1,1,1]
[4,5,6,2,3,1,8,7]=>[3,2,1,1,1]
[4,5,6,2,1,3,8,7]=>[3,2,1,1,1]
[3,5,1,6,4,2,8,7]=>[3,2,2,1]
[4,5,6,1,3,2,8,7]=>[3,2,1,1,1]
[4,5,6,3,1,2,8,7]=>[3,2,1,1,1]
[4,5,7,3,2,8,1,6]=>[4,1,1,1,1]
[4,5,7,3,2,8,6,1]=>[4,2,1,1]
[4,6,7,3,8,2,5,1]=>[4,1,1,1,1]
[4,6,7,3,8,2,1,5]=>[4,1,1,1,1]
[4,6,7,3,8,1,2,5]=>[3,1,1,1,1,1]
[4,5,7,3,1,8,2,6]=>[3,2,1,1,1]
[4,5,7,1,3,8,2,6]=>[3,1,1,1,1,1]
[3,5,1,7,4,8,2,6]=>[3,2,1,1,1]
[2,1,5,7,4,8,3,6]=>[3,2,1,1,1]
[2,1,5,7,4,8,6,3]=>[3,2,2,1]
[3,5,1,7,4,8,6,2]=>[3,2,2,1]
[4,5,7,1,3,8,6,2]=>[3,2,1,1,1]
[4,5,7,3,1,8,6,2]=>[3,3,1,1]
[4,6,7,3,8,1,5,2]=>[3,2,1,1,1]
[4,6,7,3,8,5,1,2]=>[3,2,1,1,1]
[4,6,7,3,8,5,2,1]=>[4,2,1,1]
[5,6,7,8,3,1,4,2]=>[3,2,1,1,1]
[5,6,7,8,1,3,4,2]=>[3,1,1,1,1,1]
[4,6,7,1,8,3,5,2]=>[3,2,1,1,1]
[3,6,1,7,8,4,5,2]=>[3,2,1,1,1]
[2,1,6,7,8,4,5,3]=>[3,2,1,1,1]
[2,1,6,7,8,4,3,5]=>[3,2,1,1,1]
[3,6,1,7,8,4,2,5]=>[3,2,1,1,1]
[4,6,7,1,8,3,2,5]=>[3,2,1,1,1]
[5,6,7,8,1,3,2,4]=>[3,1,1,1,1,1]
[4,5,7,2,1,8,3,6]=>[3,2,1,1,1]
[4,6,7,2,8,1,3,5]=>[3,1,1,1,1,1]
[4,6,7,2,8,3,1,5]=>[3,2,1,1,1]
[4,6,7,2,8,3,5,1]=>[3,2,1,1,1]
[3,6,2,7,8,4,5,1]=>[3,2,1,1,1]
[3,6,2,7,8,4,1,5]=>[3,2,1,1,1]
[3,6,2,7,8,1,4,5]=>[3,1,1,1,1,1]
[3,5,2,7,1,8,4,6]=>[3,2,1,1,1]
[3,4,2,1,7,8,5,6]=>[3,2,1,1,1]
[3,4,1,2,7,8,6,5]=>[3,2,1,1,1]
[3,5,2,7,1,8,6,4]=>[3,3,1,1]
[3,6,2,7,8,1,5,4]=>[3,2,1,1,1]
[3,6,2,7,8,5,1,4]=>[3,2,1,1,1]
[3,6,2,7,8,5,4,1]=>[4,2,1,1]
[4,6,7,2,8,5,3,1]=>[4,2,1,1]
[4,6,7,2,8,5,1,3]=>[3,2,1,1,1]
[4,6,7,2,8,1,5,3]=>[3,2,1,1,1]
[4,5,7,2,1,8,6,3]=>[3,3,1,1]
[4,5,7,1,2,8,6,3]=>[3,2,1,1,1]
[3,5,1,7,2,8,6,4]=>[3,2,2,1]
[2,1,5,7,3,8,6,4]=>[3,2,2,1]
[2,1,6,7,8,3,5,4]=>[3,2,1,1,1]
[3,6,1,7,8,2,5,4]=>[3,2,1,1,1]
[4,6,7,1,8,2,5,3]=>[3,2,1,1,1]
[5,6,7,8,1,2,4,3]=>[3,1,1,1,1,1]
[5,6,7,8,2,1,4,3]=>[3,2,1,1,1]
[5,6,7,8,2,4,1,3]=>[3,1,1,1,1,1]
[5,6,7,8,2,4,3,1]=>[4,1,1,1,1]
[5,6,7,8,1,4,2,3]=>[3,1,1,1,1,1]
[4,6,7,1,8,5,2,3]=>[3,2,1,1,1]
[3,6,1,7,8,5,2,4]=>[3,2,1,1,1]
[2,1,6,7,8,5,3,4]=>[3,2,1,1,1]
[3,6,1,7,8,5,4,2]=>[4,2,1,1]
[4,6,7,1,8,5,3,2]=>[4,2,1,1]
[5,6,7,8,1,4,3,2]=>[4,1,1,1,1]
[5,6,7,8,4,1,3,2]=>[4,1,1,1,1]
[6,5,8,7,3,4,1,2]=>[4,2,1,1]
[3,6,7,4,5,8,1,2]=>[3,1,1,1,1,1]
[2,6,7,4,5,1,8,3]=>[3,2,1,1,1]
[1,6,7,4,5,2,3,8]=>[3,1,1,1,1,1]
[1,5,4,7,6,2,3,8]=>[3,2,1,1,1]
[2,5,4,7,6,1,8,3]=>[3,2,2,1]
[3,5,4,7,6,8,1,2]=>[3,2,1,1,1]
[4,5,3,7,8,6,1,2]=>[3,2,1,1,1]
[5,4,3,8,7,6,1,2]=>[4,3,1]
[6,4,8,3,7,5,1,2]=>[4,2,1,1]
[6,3,8,4,5,7,1,2]=>[3,2,1,1,1]
[5,3,4,8,6,7,1,2]=>[3,2,1,1,1]
[4,3,5,6,8,7,1,2]=>[3,2,1,1,1]
[3,2,5,6,1,8,7,4]=>[3,3,1,1]
[4,2,5,6,8,1,7,3]=>[3,2,1,1,1]
[5,2,4,8,6,1,7,3]=>[3,2,2,1]
[6,2,8,4,5,1,7,3]=>[3,2,2,1]
[7,8,2,4,5,1,6,3]=>[3,2,1,1,1]
[7,8,1,4,5,2,3,6]=>[3,1,1,1,1,1]
[6,1,8,4,5,2,3,7]=>[3,2,1,1,1]
[5,1,4,8,6,2,3,7]=>[3,2,1,1,1]
[4,1,3,2,8,6,5,7]=>[3,3,1,1]
[5,1,3,8,2,6,4,7]=>[3,2,1,1,1]
[6,1,8,3,2,5,4,7]=>[3,2,2,1]
[7,8,1,3,2,5,4,6]=>[3,2,1,1,1]
[7,8,2,3,1,5,6,4]=>[3,2,1,1,1]
[6,2,8,3,1,5,7,4]=>[3,2,2,1]
[5,2,3,8,1,6,7,4]=>[3,2,1,1,1]
[6,3,8,2,1,7,5,4]=>[4,3,1]
[7,8,3,2,1,6,5,4]=>[4,3,1]
[7,8,4,2,6,1,5,3]=>[4,2,1,1]
[5,4,2,8,7,1,6,3]=>[4,3,1]
[4,5,2,7,8,1,6,3]=>[3,2,1,1,1]
[2,5,3,7,1,6,8,4]=>[3,2,1,1,1]
[1,5,3,7,2,6,4,8]=>[3,2,1,1,1]
[1,6,7,3,2,5,4,8]=>[3,2,1,1,1]
[2,6,7,3,1,5,8,4]=>[3,2,1,1,1]
[3,6,7,2,1,8,5,4]=>[3,3,1,1]
[7,8,5,6,2,1,4,3]=>[4,2,1,1]
[6,5,8,7,1,2,3,4]=>[3,2,1,1,1]
[5,4,1,8,7,2,3,6]=>[3,3,1,1]
[6,4,8,1,7,2,3,5]=>[3,2,1,1,1]
[7,8,3,1,2,6,4,5]=>[3,2,1,1,1]
[5,3,1,8,2,7,4,6]=>[3,3,1,1]
[4,3,1,2,8,7,5,6]=>[3,3,1,1]
[4,2,1,3,8,5,7,6]=>[3,3,1,1]
[5,2,1,8,3,4,7,6]=>[3,3,1,1]
[6,2,8,1,3,4,7,5]=>[3,2,1,1,1]
[7,8,2,1,3,4,6,5]=>[3,2,1,1,1]
[4,3,1,2,6,5,8,7]=>[3,2,2,1]
[5,3,1,6,2,4,8,7]=>[3,2,2,1]
[6,3,1,5,2,4,8,7]=>[3,2,2,1]
[7,3,1,5,2,8,4,6]=>[3,2,2,1]
[8,4,5,1,2,7,3,6]=>[3,2,1,1,1]
[7,4,5,1,2,8,3,6]=>[3,2,1,1,1]
[6,4,5,1,2,3,8,7]=>[3,2,1,1,1]
[5,4,6,1,2,3,8,7]=>[3,2,1,1,1]
[2,1,6,5,3,4,8,7]=>[3,2,2,1]
[3,6,1,5,2,4,8,7]=>[3,2,1,1,1]
[4,6,5,1,2,3,8,7]=>[3,2,1,1,1]
[5,6,4,1,2,3,8,7]=>[3,2,1,1,1]
[6,5,4,1,2,3,8,7]=>[4,2,1,1]
[7,5,4,1,2,8,3,6]=>[4,2,1,1]
[8,6,4,1,7,2,3,5]=>[4,2,1,1]
[7,6,4,1,8,2,3,5]=>[4,2,1,1]
[6,7,4,1,8,2,3,5]=>[3,2,1,1,1]
[5,7,4,1,2,8,3,6]=>[3,2,1,1,1]
[4,7,5,1,2,8,3,6]=>[3,2,1,1,1]
[3,7,1,5,2,8,4,6]=>[3,2,1,1,1]
[2,1,7,5,3,8,4,6]=>[3,2,2,1]
[2,1,8,5,3,7,4,6]=>[3,2,2,1]
[3,8,1,5,2,7,4,6]=>[3,2,1,1,1]
[4,8,5,1,2,7,3,6]=>[3,2,1,1,1]
[5,8,4,1,2,7,3,6]=>[3,2,1,1,1]
[6,8,4,1,7,2,3,5]=>[3,2,1,1,1]
[8,7,4,1,6,2,3,5]=>[4,2,1,1]
[5,8,6,7,1,2,3,4]=>[3,1,1,1,1,1]
[4,8,6,1,7,2,3,5]=>[3,2,1,1,1]
[3,8,1,6,7,2,4,5]=>[3,1,1,1,1,1]
[2,1,8,6,7,3,4,5]=>[3,2,1,1,1]
[2,1,7,6,8,3,4,5]=>[3,2,1,1,1]
[3,7,1,6,8,2,4,5]=>[3,1,1,1,1,1]
[4,7,6,1,8,2,3,5]=>[3,2,1,1,1]
[5,7,6,8,1,2,3,4]=>[3,1,1,1,1,1]
[5,4,7,1,2,8,3,6]=>[3,2,1,1,1]
[6,4,7,1,8,2,3,5]=>[3,2,1,1,1]
[7,4,6,1,8,2,3,5]=>[3,2,1,1,1]
[8,4,6,1,7,2,3,5]=>[3,2,1,1,1]
[8,3,1,6,7,2,4,5]=>[3,2,1,1,1]
[7,3,1,6,8,2,4,5]=>[3,2,1,1,1]
[6,3,1,7,8,2,4,5]=>[3,2,1,1,1]
[5,3,1,7,2,8,4,6]=>[3,2,2,1]
[4,3,1,2,7,8,5,6]=>[3,2,1,1,1]
[2,1,4,3,8,7,5,6]=>[3,2,2,1]
[3,4,1,2,8,7,5,6]=>[3,2,1,1,1]
[6,3,1,8,7,2,4,5]=>[3,3,1,1]
[7,3,1,8,6,2,4,5]=>[3,3,1,1]
[8,4,7,1,6,2,3,5]=>[4,1,1,1,1]
[7,4,8,1,6,2,3,5]=>[3,2,1,1,1]
[5,4,8,1,2,7,3,6]=>[3,2,1,1,1]
[4,5,8,1,2,7,3,6]=>[3,1,1,1,1,1]
[3,5,1,8,2,7,4,6]=>[3,2,1,1,1]
[2,1,5,8,3,7,4,6]=>[3,2,1,1,1]
[2,1,6,8,7,3,4,5]=>[3,2,1,1,1]
[3,6,1,8,7,2,4,5]=>[3,2,1,1,1]
[4,6,8,1,7,2,3,5]=>[3,1,1,1,1,1]
[5,6,8,7,1,2,3,4]=>[3,1,1,1,1,1]
[7,5,8,6,1,2,3,4]=>[3,2,1,1,1]
[8,5,7,6,1,2,3,4]=>[4,1,1,1,1]
[5,7,8,6,1,2,3,4]=>[3,1,1,1,1,1]
[4,7,8,1,6,2,3,5]=>[3,1,1,1,1,1]
[3,7,1,8,6,2,4,5]=>[3,2,1,1,1]
[2,1,7,8,6,3,4,5]=>[3,2,1,1,1]
[2,1,8,7,6,3,4,5]=>[4,2,1,1]
[3,8,1,7,6,2,4,5]=>[4,1,1,1,1]
[4,8,7,1,6,2,3,5]=>[4,1,1,1,1]
[5,8,7,6,1,2,3,4]=>[4,1,1,1,1]
[6,8,7,5,1,2,3,4]=>[4,1,1,1,1]
[6,4,7,3,8,5,1,2]=>[4,2,1,1]
[6,4,7,3,5,8,1,2]=>[4,1,1,1,1]
[6,4,7,2,5,1,8,3]=>[4,2,1,1]
[5,4,3,7,6,8,1,2]=>[4,2,1,1]
[6,4,8,3,5,7,1,2]=>[4,1,1,1,1]
[5,4,3,6,8,7,1,2]=>[4,2,1,1]
[5,4,2,6,7,1,8,3]=>[4,2,1,1]
[5,4,2,6,7,1,3,8]=>[4,1,1,1,1]
[5,4,2,6,8,1,7,3]=>[4,2,1,1]
[5,4,2,8,6,1,7,3]=>[4,2,2]
[6,4,8,2,5,1,7,3]=>[4,2,1,1]
[7,8,4,2,5,1,6,3]=>[4,2,1,1]
[7,8,4,2,5,1,3,6]=>[4,1,1,1,1]
[5,4,2,8,6,1,3,7]=>[4,2,1,1]
[4,3,2,1,6,8,5,7]=>[4,2,1,1]
[4,3,2,1,8,6,5,7]=>[4,3,1]
[5,3,2,8,1,6,4,7]=>[4,2,1,1]
[7,8,3,2,1,5,4,6]=>[4,2,1,1]
[7,8,3,2,1,5,6,4]=>[4,2,1,1]
[6,3,8,2,1,5,7,4]=>[4,2,1,1]
[5,3,2,7,1,8,6,4]=>[4,3,1]
[5,3,2,7,1,6,8,4]=>[4,2,1,1]
[6,3,7,2,1,8,5,4]=>[4,3,1]
[6,4,7,2,8,1,5,3]=>[4,2,1,1]
[6,5,7,8,2,1,4,3]=>[4,2,1,1]
[6,5,8,7,2,1,3,4]=>[4,2,1,1]
[6,3,7,2,1,8,4,5]=>[4,2,1,1]
[6,3,7,2,1,4,5,8]=>[4,1,1,1,1]
[5,3,2,7,1,4,8,6]=>[4,2,1,1]
[7,8,4,2,6,1,3,5]=>[4,1,1,1,1]
[7,8,3,2,1,6,4,5]=>[4,2,1,1]
[6,3,8,2,1,7,4,5]=>[4,2,1,1]
[5,3,2,8,1,7,4,6]=>[4,2,1,1]
[4,3,2,1,8,7,5,6]=>[4,3,1]
[4,3,2,1,8,5,7,6]=>[4,3,1]
[6,3,8,2,1,4,7,5]=>[4,2,1,1]
[7,8,3,2,1,4,6,5]=>[4,2,1,1]
[6,3,8,2,1,4,5,7]=>[4,1,1,1,1]
[4,3,2,1,8,5,6,7]=>[4,2,1,1]
[4,3,2,1,5,8,6,7]=>[4,2,1,1]
[7,8,5,6,1,2,4,3]=>[4,1,1,1,1]
[7,8,4,1,6,2,5,3]=>[4,2,1,1]
[7,8,1,4,6,2,5,3]=>[4,1,1,1,1]
[6,1,8,4,7,2,5,3]=>[4,2,1,1]
[1,6,8,4,7,2,5,3]=>[4,1,1,1,1]
[1,6,8,3,2,7,5,4]=>[4,2,1,1]
[6,1,8,3,2,7,5,4]=>[4,2,2]
[7,8,1,3,2,6,5,4]=>[4,2,1,1]
[7,8,3,1,2,6,5,4]=>[4,2,1,1]
[7,8,3,4,6,5,1,2]=>[4,1,1,1,1]
[7,8,2,4,6,1,5,3]=>[4,1,1,1,1]
[7,8,2,3,1,6,5,4]=>[4,2,1,1]
[7,8,2,1,3,6,5,4]=>[4,2,1,1]
[7,8,1,2,3,6,5,4]=>[4,1,1,1,1]
[6,1,8,2,3,7,5,4]=>[4,2,1,1]
[1,6,8,2,3,7,5,4]=>[4,1,1,1,1]
[1,5,2,8,3,7,6,4]=>[4,2,1,1]
[5,1,2,8,3,7,6,4]=>[4,2,1,1]
[5,2,1,8,3,7,6,4]=>[4,3,1]
[6,2,8,1,3,7,5,4]=>[4,2,1,1]
[6,2,8,3,1,7,5,4]=>[4,2,2]
[6,2,8,4,7,1,5,3]=>[4,2,1,1]
[6,3,8,4,7,5,1,2]=>[4,2,1,1]
[3,6,8,4,7,5,1,2]=>[4,1,1,1,1]
[2,6,8,4,7,1,5,3]=>[4,1,1,1,1]
[2,6,8,3,1,7,5,4]=>[4,2,1,1]
[2,6,8,1,3,7,5,4]=>[4,1,1,1,1]
[2,5,1,8,3,7,6,4]=>[4,2,1,1]
[1,2,5,8,3,7,6,4]=>[4,1,1,1,1]
[2,4,1,3,8,7,6,5]=>[4,2,1,1]
[2,5,3,8,1,7,6,4]=>[4,2,1,1]
[2,5,4,8,7,1,6,3]=>[4,2,1,1]
[3,5,4,8,7,6,1,2]=>[4,2,1,1]
[5,3,4,8,7,6,1,2]=>[4,2,1,1]
[5,2,4,8,7,1,6,3]=>[4,2,1,1]
[5,2,3,8,1,7,6,4]=>[4,2,1,1]
[4,2,1,3,8,7,6,5]=>[4,3,1]
[4,1,2,3,8,7,6,5]=>[4,2,1,1]
[1,4,2,3,8,7,6,5]=>[4,2,1,1]
[4,1,3,2,8,7,6,5]=>[4,3,1]
[4,3,1,2,8,7,6,5]=>[4,3,1]
[6,3,8,1,2,7,5,4]=>[4,2,1,1]
[5,3,1,8,2,7,6,4]=>[4,3,1]
[5,1,3,8,2,7,6,4]=>[4,2,1,1]
[1,5,3,8,2,7,6,4]=>[4,2,1,1]
[1,5,4,8,7,2,6,3]=>[4,2,1,1]
[5,1,4,8,7,2,6,3]=>[4,2,1,1]
[5,4,1,8,7,2,6,3]=>[4,3,1]
[6,4,8,1,7,2,5,3]=>[4,2,1,1]
[6,5,8,7,1,2,4,3]=>[4,2,1,1]
[5,6,8,7,3,4,1,2]=>[4,1,1,1,1]
[5,6,8,7,2,1,4,3]=>[4,2,1,1]
[4,5,1,8,7,2,6,3]=>[4,2,1,1]
[4,1,5,8,7,2,6,3]=>[4,2,1,1]
[1,4,5,8,7,2,6,3]=>[4,1,1,1,1]
[1,3,5,8,2,7,6,4]=>[4,1,1,1,1]
[3,1,5,8,2,7,6,4]=>[4,2,1,1]
[3,6,8,1,2,7,5,4]=>[4,1,1,1,1]
[3,6,8,2,1,7,5,4]=>[4,2,1,1]
[4,6,8,2,7,1,5,3]=>[4,1,1,1,1]
[4,6,8,3,7,5,1,2]=>[4,1,1,1,1]
[4,5,3,8,7,6,1,2]=>[4,2,1,1]
[4,5,2,8,7,1,6,3]=>[4,2,1,1]
[3,5,2,8,1,7,6,4]=>[4,2,1,1]
[3,1,4,2,8,7,6,5]=>[4,2,2]
[3,1,2,4,8,7,6,5]=>[4,2,1,1]
[3,2,5,8,1,7,6,4]=>[4,2,1,1]
[4,2,5,8,7,1,6,3]=>[4,2,1,1]
[4,3,5,8,7,6,1,2]=>[4,2,1,1]
[3,4,5,8,7,6,1,2]=>[4,1,1,1,1]
[2,4,5,8,7,1,6,3]=>[4,1,1,1,1]
[2,3,5,8,1,7,6,4]=>[4,1,1,1,1]
[4,1,3,2,6,5,8,7]=>[3,2,2,1]
[5,1,3,2,6,4,8,7]=>[3,2,2,1]
[6,1,3,2,5,4,8,7]=>[3,2,2,1]
[7,1,3,2,5,4,8,6]=>[3,2,2,1]
[8,1,3,2,5,4,7,6]=>[3,2,2,1]
[8,1,4,2,5,3,7,6]=>[3,2,2,1]
[7,1,4,2,5,3,8,6]=>[3,2,2,1]
[6,1,4,2,5,3,8,7]=>[3,2,2,1]
[5,1,4,2,6,3,8,7]=>[3,2,2,1]
[2,1,6,3,5,4,8,7]=>[3,2,2,1]
[3,1,6,2,5,4,8,7]=>[3,2,2,1]
[4,1,6,2,5,3,8,7]=>[3,2,2,1]
[6,2,5,1,4,3,8,7]=>[4,2,1,1]
[5,2,6,1,4,3,8,7]=>[3,2,2,1]
[5,2,7,1,4,3,8,6]=>[3,2,2,1]
[5,2,8,1,4,3,7,6]=>[3,2,2,1]
[6,2,8,1,4,3,7,5]=>[3,2,2,1]
[6,2,7,1,4,3,8,5]=>[3,2,2,1]
[7,2,6,1,4,3,8,5]=>[4,2,1,1]
[7,2,5,1,4,3,8,6]=>[4,2,1,1]
[4,1,7,2,5,3,8,6]=>[3,2,2,1]
[3,1,7,2,5,4,8,6]=>[3,2,2,1]
[2,1,7,3,5,4,8,6]=>[3,2,2,1]
[2,1,8,3,5,4,7,6]=>[3,2,2,1]
[3,1,8,2,5,4,7,6]=>[3,2,2,1]
[4,1,8,2,5,3,7,6]=>[3,2,2,1]
[8,2,5,1,4,3,7,6]=>[4,2,1,1]
[8,2,6,1,4,3,7,5]=>[4,2,1,1]
[7,1,4,3,8,2,6,5]=>[4,2,1,1]
[8,1,4,3,7,2,6,5]=>[4,2,1,1]
[8,1,5,3,7,2,6,4]=>[4,2,1,1]
[7,1,5,3,8,2,6,4]=>[4,2,1,1]
[8,2,6,1,5,3,7,4]=>[4,2,1,1]
[5,1,8,2,6,3,7,4]=>[3,2,2,1]
[4,1,8,2,6,3,7,5]=>[3,2,2,1]
[3,1,8,2,6,4,7,5]=>[3,2,2,1]
[2,1,8,3,6,4,7,5]=>[3,2,2,1]
[2,1,7,3,6,4,8,5]=>[3,2,2,1]
[4,1,7,2,6,3,8,5]=>[3,2,2,1]
[5,1,7,2,6,3,8,4]=>[3,2,2,1]
[7,2,6,1,5,3,8,4]=>[4,2,1,1]
[6,2,7,1,5,3,8,4]=>[3,2,2,1]
[6,2,8,1,5,3,7,4]=>[3,2,2,1]
[8,1,5,2,6,3,7,4]=>[3,2,2,1]
[6,1,5,2,7,3,8,4]=>[3,2,2,1]
[6,1,4,2,7,3,8,5]=>[3,2,2,1]
[8,1,4,2,6,3,7,5]=>[3,2,2,1]
[8,1,3,2,6,4,7,5]=>[3,2,2,1]
[7,1,3,2,6,4,8,5]=>[3,2,2,1]
[6,1,3,2,7,4,8,5]=>[3,2,2,1]
[5,1,3,2,7,4,8,6]=>[3,2,2,1]
[4,1,3,2,7,5,8,6]=>[3,2,2,1]
[2,1,4,3,8,5,7,6]=>[3,2,2,1]
[3,1,4,2,8,5,7,6]=>[3,2,2,1]
[4,1,3,2,8,5,7,6]=>[3,3,1,1]
[5,1,3,2,8,4,7,6]=>[3,3,1,1]
[6,1,3,2,8,4,7,5]=>[3,3,1,1]
[8,4,7,1,3,2,6,5]=>[4,2,1,1]
[7,4,8,1,3,2,6,5]=>[4,2,1,1]
[7,3,8,1,4,2,6,5]=>[3,2,2,1]
[8,3,7,1,4,2,6,5]=>[4,2,1,1]
[6,1,4,2,8,3,7,5]=>[3,3,1,1]
[5,1,4,2,8,3,7,6]=>[3,3,1,1]
[4,1,5,2,8,3,7,6]=>[3,2,2,1]
[3,1,5,2,8,4,7,6]=>[3,2,2,1]
[2,1,5,3,8,4,7,6]=>[3,2,2,1]
[2,1,6,3,8,4,7,5]=>[3,2,2,1]
[3,1,6,2,8,4,7,5]=>[3,2,2,1]
[4,1,6,2,8,3,7,5]=>[3,2,2,1]
[5,1,6,2,8,3,7,4]=>[3,2,2,1]
[6,1,5,2,8,3,7,4]=>[3,3,1,1]
[8,3,7,1,5,2,6,4]=>[4,2,1,1]
[7,3,8,1,5,2,6,4]=>[3,2,2,1]
[6,2,7,3,8,1,5,4]=>[3,2,2,1]
[6,2,8,3,7,1,5,4]=>[4,2,1,1]
[8,3,7,2,6,1,5,4]=>[5,1,1,1]
[5,1,8,3,7,2,6,4]=>[4,2,1,1]
[4,1,8,3,7,2,6,5]=>[4,2,1,1]
[3,1,8,4,7,2,6,5]=>[4,2,1,1]
[2,1,8,4,7,3,6,5]=>[4,2,1,1]
[2,1,7,4,8,3,6,5]=>[3,2,2,1]
[3,1,7,4,8,2,6,5]=>[3,2,2,1]
[4,1,7,3,8,2,6,5]=>[3,2,2,1]
[5,1,7,3,8,2,6,4]=>[3,2,2,1]
[7,3,8,2,6,1,5,4]=>[4,2,1,1]
[8,2,6,3,7,1,5,4]=>[4,2,1,1]
[7,2,6,3,8,1,5,4]=>[4,2,1,1]
[3,4,2,6,8,1,5,7]=>[3,1,1,1,1,1]
[5,3,6,2,8,1,4,7]=>[4,1,1,1,1]
[5,3,6,2,4,8,1,7]=>[4,1,1,1,1]
[5,7,3,8,2,4,1,6]=>[4,1,1,1,1]
[5,7,3,8,2,4,6,1]=>[4,1,1,1,1]
[7,4,2,5,8,3,6,1]=>[4,2,1,1]
[7,4,2,5,8,3,1,6]=>[4,2,1,1]
[4,5,2,6,3,8,1,7]=>[3,2,1,1,1]
[4,5,2,1,6,8,3,7]=>[3,2,1,1,1]
[5,3,1,6,8,2,4,7]=>[3,2,1,1,1]
[5,6,2,8,1,3,4,7]=>[3,1,1,1,1,1]
[3,5,6,1,4,8,2,7]=>[3,1,1,1,1,1]
[4,1,5,6,3,8,2,7]=>[3,2,1,1,1]
[4,5,1,6,3,8,2,7]=>[3,2,1,1,1]
[4,5,6,3,2,8,1,7]=>[4,1,1,1,1]
[7,4,5,3,8,2,1,6]=>[5,1,1,1]
[7,4,5,3,8,2,6,1]=>[5,1,1,1]
[6,7,4,8,3,2,5,1]=>[5,1,1,1]
[6,7,4,8,3,2,1,5]=>[5,1,1,1]
[6,7,4,1,8,3,2,5]=>[4,2,1,1]
[7,4,5,3,1,8,2,6]=>[4,2,1,1]
[4,7,1,5,8,3,2,6]=>[4,1,1,1,1]
[5,3,7,8,1,4,2,6]=>[3,2,1,1,1]
[7,5,8,2,4,6,1,3]=>[4,1,1,1,1]
[7,3,5,8,1,4,6,2]=>[4,1,1,1,1]
[4,5,1,7,8,3,6,2]=>[3,2,1,1,1]
[7,4,1,5,8,3,6,2]=>[4,2,1,1]
[6,7,4,3,8,1,5,2]=>[4,2,1,1]
[6,7,4,8,3,1,5,2]=>[4,2,1,1]
[6,7,4,8,3,5,2,1]=>[5,1,1,1]
[5,6,7,3,8,4,2,1]=>[4,2,1,1]
[5,6,7,3,1,8,4,2]=>[3,3,1,1]
[5,6,1,7,3,8,4,2]=>[3,2,2,1]
[5,1,6,7,3,8,4,2]=>[3,2,2,1]
[6,4,7,1,8,3,5,2]=>[4,2,1,1]
[6,7,8,3,1,4,5,2]=>[3,2,1,1,1]
[6,7,2,8,4,5,1,3]=>[3,2,1,1,1]
[6,7,2,8,4,1,3,5]=>[3,2,1,1,1]
[6,1,7,4,8,3,2,5]=>[4,2,1,1]
[5,1,6,7,3,2,8,4]=>[3,2,2,1]
[5,6,1,7,3,2,8,4]=>[3,2,2,1]
[5,6,7,3,2,1,8,4]=>[4,2,1,1]
[5,6,7,3,2,8,4,1]=>[4,2,1,1]
[5,6,2,7,3,8,4,1]=>[3,2,2,1]
[5,6,2,7,3,1,8,4]=>[3,2,2,1]
[5,6,2,1,7,3,8,4]=>[3,2,2,1]
[6,1,7,4,2,8,3,5]=>[3,2,2,1]
[6,7,2,1,8,3,4,5]=>[3,2,1,1,1]
[7,5,8,2,1,3,4,6]=>[4,1,1,1,1]
[5,7,3,1,8,2,4,6]=>[3,2,1,1,1]
[4,7,1,5,2,8,3,6]=>[3,2,1,1,1]
[7,4,2,5,1,8,3,6]=>[4,2,1,1]
[6,7,4,2,1,8,3,5]=>[4,2,1,1]
[6,7,4,2,8,3,1,5]=>[4,2,1,1]
[6,7,4,2,8,3,5,1]=>[4,2,1,1]
[3,6,7,2,8,4,5,1]=>[3,2,1,1,1]
[3,6,7,2,8,4,1,5]=>[3,2,1,1,1]
[3,6,7,2,1,8,4,5]=>[3,2,1,1,1]
[5,7,3,8,2,1,4,6]=>[4,1,1,1,1]
[3,4,7,8,2,1,5,6]=>[3,1,1,1,1,1]
[3,7,8,1,4,6,2,5]=>[3,1,1,1,1,1]
[3,4,7,8,2,6,1,5]=>[3,1,1,1,1,1]
[5,7,3,8,2,6,1,4]=>[4,1,1,1,1]
[3,6,7,2,8,5,1,4]=>[3,2,1,1,1]
[3,6,7,8,5,2,1,4]=>[4,1,1,1,1]
[3,6,7,8,5,2,4,1]=>[4,1,1,1,1]
[6,4,7,8,2,5,3,1]=>[4,2,1,1]
[6,4,7,8,2,1,5,3]=>[4,2,1,1]
[4,1,5,7,8,2,6,3]=>[3,2,1,1,1]
[5,3,7,8,1,6,2,4]=>[3,2,1,1,1]
[6,7,2,8,5,1,3,4]=>[3,2,1,1,1]
[6,4,1,7,8,2,5,3]=>[3,3,1,1]
[5,1,6,2,7,8,4,3]=>[3,2,2,1]
[5,6,2,1,7,8,4,3]=>[3,3,1,1]
[5,6,2,7,1,8,4,3]=>[3,3,1,1]
[5,6,2,7,8,4,3,1]=>[4,2,1,1]
[5,6,7,2,8,4,3,1]=>[4,2,1,1]
[5,6,7,2,1,8,4,3]=>[3,3,1,1]
[5,6,1,7,2,8,4,3]=>[3,2,2,1]
[5,1,6,7,2,8,4,3]=>[3,2,2,1]
[6,4,7,1,8,2,5,3]=>[3,3,1,1]
[3,6,7,1,8,5,2,4]=>[3,2,1,1,1]
[6,7,8,5,2,4,1,3]=>[4,1,1,1,1]
[6,7,8,3,5,1,4,2]=>[4,1,1,1,1]
[4,6,7,8,1,5,3,2]=>[4,1,1,1,1]
[5,1,6,7,8,4,3,2]=>[4,2,1,1]
[5,6,1,7,8,4,3,2]=>[4,2,1,1]
[5,6,7,1,8,4,3,2]=>[4,2,1,1]
[8,6,1,3,4,2,5,7]=>[4,1,1,1,1]
[8,3,2,5,1,6,4,7]=>[4,2,1,1]
[8,5,3,6,2,4,1,7]=>[5,1,1,1]
[5,3,2,7,4,1,8,6]=>[4,2,2]
[7,5,3,8,2,4,6,1]=>[5,1,1,1]
[7,2,4,5,8,3,6,1]=>[4,1,1,1,1]
[2,4,5,3,7,1,8,6]=>[3,2,1,1,1]
[8,2,4,5,6,3,1,7]=>[4,1,1,1,1]
[8,2,4,5,6,1,3,7]=>[3,1,1,1,1,1]
[8,1,2,4,5,6,3,7]=>[3,1,1,1,1,1]
[8,2,5,1,3,6,4,7]=>[3,2,1,1,1]
[8,5,6,2,1,4,3,7]=>[4,2,1,1]
[8,5,3,6,4,1,2,7]=>[4,2,1,1]
[8,4,1,5,6,3,2,7]=>[4,2,1,1]
[8,1,4,5,6,3,2,7]=>[4,1,1,1,1]
[4,5,3,7,2,1,8,6]=>[4,2,1,1]
[7,4,5,8,3,2,6,1]=>[5,1,1,1]
[4,3,6,7,2,8,5,1]=>[4,2,1,1]
[4,3,6,7,2,8,1,5]=>[4,1,1,1,1]
[1,4,3,6,7,2,8,5]=>[3,2,1,1,1]
[4,5,3,7,1,8,2,6]=>[3,2,1,1,1]
[4,1,5,3,7,2,8,6]=>[3,2,2,1]
[5,3,4,7,1,2,8,6]=>[3,2,1,1,1]
[7,5,8,2,1,4,6,3]=>[4,2,1,1]
[7,5,3,8,4,1,6,2]=>[4,2,2]
[7,4,5,8,3,6,1,2]=>[4,1,1,1,1]
[4,3,6,7,8,1,5,2]=>[3,2,1,1,1]
[1,6,4,7,8,3,5,2]=>[4,1,1,1,1]
[6,4,7,8,3,5,2,1]=>[5,1,1,1]
[3,5,6,7,8,4,1,2]=>[3,1,1,1,1,1]
[3,1,5,6,7,8,4,2]=>[3,2,1,1,1]
[4,6,1,7,8,3,5,2]=>[3,2,1,1,1]
[3,6,7,1,4,8,5,2]=>[3,2,1,1,1]
[6,2,4,1,7,8,5,3]=>[3,3,1,1]
[2,6,7,1,4,8,3,5]=>[3,1,1,1,1,1]
[4,3,6,7,8,1,2,5]=>[3,1,1,1,1,1]
[1,5,3,6,7,8,2,4]=>[3,1,1,1,1,1]
[3,5,6,7,8,2,1,4]=>[3,1,1,1,1,1]
[3,5,6,7,8,2,4,1]=>[3,1,1,1,1,1]
[5,2,7,1,3,8,4,6]=>[3,2,1,1,1]
[5,3,1,7,8,2,4,6]=>[3,2,1,1,1]
[4,5,2,7,8,1,3,6]=>[3,1,1,1,1,1]
[4,2,6,7,8,3,1,5]=>[3,2,1,1,1]
[4,2,6,7,8,3,5,1]=>[3,2,1,1,1]
[3,6,2,7,4,8,5,1]=>[3,2,2,1]
[3,6,2,7,4,8,1,5]=>[3,2,1,1,1]
[3,2,1,6,4,7,8,5]=>[3,2,2,1]
[3,7,4,2,1,5,8,6]=>[4,2,1,1]
[1,7,3,4,2,5,8,6]=>[3,2,1,1,1]
[4,7,2,1,3,5,8,6]=>[3,2,1,1,1]
[7,8,4,2,1,3,6,5]=>[4,2,1,1]
[7,8,1,3,4,2,6,5]=>[3,2,1,1,1]
[7,8,3,4,2,1,6,5]=>[4,2,1,1]
[6,3,2,7,1,8,5,4]=>[4,3,1]
[3,6,2,7,1,8,5,4]=>[3,3,1,1]
[6,7,3,8,2,5,4,1]=>[4,2,1,1]
[6,4,7,8,5,2,3,1]=>[4,2,1,1]
[2,6,4,7,8,1,5,3]=>[3,2,1,1,1]
[4,6,2,7,8,1,5,3]=>[3,2,1,1,1]
[7,4,5,8,6,2,1,3]=>[4,2,1,1]
[7,4,1,5,8,6,2,3]=>[3,3,1,1]
[7,5,3,8,6,1,2,4]=>[4,2,1,1]
[7,5,8,2,1,6,3,4]=>[4,2,1,1]
[6,2,7,1,3,8,5,4]=>[3,3,1,1]
[6,3,1,7,8,2,5,4]=>[3,3,1,1]
[4,6,1,7,8,5,2,3]=>[3,2,1,1,1]
[5,1,2,6,7,8,4,3]=>[3,2,1,1,1]
[5,2,6,7,8,4,1,3]=>[3,2,1,1,1]
[5,2,6,7,8,4,3,1]=>[4,2,1,1]
[2,5,6,7,8,4,1,3]=>[3,1,1,1,1,1]
[1,5,2,6,7,8,4,3]=>[3,2,1,1,1]
[1,6,4,7,8,5,2,3]=>[3,2,1,1,1]
[2,6,7,1,3,8,5,4]=>[3,2,1,1,1]
[6,7,8,2,1,5,4,3]=>[4,2,1,1]
[6,7,3,8,5,1,4,2]=>[4,2,1,1]
[6,4,7,8,5,3,1,2]=>[4,2,1,1]
[4,5,2,3,7,6,1,8]=>[3,2,1,1,1]
[6,4,3,7,2,5,1,8]=>[5,1,1,1]
[8,4,3,6,5,1,2,7]=>[4,2,1,1]
[1,5,6,3,4,8,7,2]=>[3,2,1,1,1]
[4,6,2,7,3,5,1,8]=>[3,2,1,1,1]
[3,2,6,7,4,5,1,8]=>[3,2,1,1,1]
[4,7,2,6,5,3,1,8]=>[5,1,1,1]
[5,7,6,2,4,3,1,8]=>[5,1,1,1]
[1,7,5,4,8,3,6,2]=>[5,1,1,1]
[8,7,5,4,1,3,2,6]=>[6,1,1]
[6,8,5,4,2,1,3,7]=>[5,1,1,1]
[5,8,6,2,4,1,3,7]=>[4,1,1,1,1]
[4,8,2,6,5,1,3,7]=>[4,1,1,1,1]
[3,2,8,6,5,1,4,7]=>[4,2,1,1]
[4,1,2,6,5,8,7,3]=>[3,2,2,1]
[5,1,6,2,4,8,7,3]=>[3,2,2,1]
[6,1,5,4,2,8,7,3]=>[4,3,1]
[7,1,5,4,8,2,6,3]=>[4,2,1,1]
[8,1,5,4,7,6,2,3]=>[4,2,1,1]
[1,8,6,7,4,5,3,2]=>[5,1,1,1]
[8,1,6,7,4,5,2,3]=>[4,1,1,1,1]
[7,1,6,8,4,2,5,3]=>[4,2,1,1]
[6,1,7,8,2,4,5,3]=>[3,2,1,1,1]
[5,1,7,2,8,4,6,3]=>[3,2,2,1]
[4,1,2,7,8,5,6,3]=>[3,2,1,1,1]
[3,2,1,7,8,5,6,4]=>[3,3,1,1]
[3,2,8,7,1,5,4,6]=>[4,2,1,1]
[4,8,2,7,1,5,3,6]=>[4,1,1,1,1]
[5,8,7,2,1,4,3,6]=>[4,2,1,1]
[6,8,7,1,2,4,3,5]=>[4,1,1,1,1]
[7,8,6,1,4,2,3,5]=>[4,1,1,1,1]
[8,7,6,1,4,3,2,5]=>[6,1,1]
[1,7,6,8,4,3,5,2]=>[5,1,1,1]
[1,6,7,8,3,4,5,2]=>[3,1,1,1,1,1]
[8,6,7,1,3,4,2,5]=>[4,1,1,1,1]
[7,6,8,1,3,2,4,5]=>[4,1,1,1,1]
[5,7,8,2,1,3,4,6]=>[3,1,1,1,1,1]
[4,7,2,8,1,3,5,6]=>[3,1,1,1,1,1]
[3,2,6,8,4,1,5,7]=>[3,2,1,1,1]
[4,6,2,8,3,1,5,7]=>[3,2,1,1,1]
[5,6,8,2,3,1,4,7]=>[3,1,1,1,1,1]
[6,5,8,3,2,1,4,7]=>[5,1,1,1]
[7,5,8,3,1,2,4,6]=>[4,1,1,1,1]
[8,5,7,3,1,4,2,6]=>[4,2,1,1]
[1,5,7,3,8,4,6,2]=>[3,2,1,1,1]
[1,4,3,7,8,5,6,2]=>[3,2,1,1,1]
[8,4,3,7,1,5,2,6]=>[4,2,1,1]
[6,4,3,8,2,1,5,7]=>[5,1,1,1]
[4,5,2,3,8,1,6,7]=>[3,1,1,1,1,1]
[3,2,5,4,8,1,6,7]=>[3,2,1,1,1]
[4,5,2,3,1,8,7,6]=>[3,3,1,1]
[6,4,3,1,2,8,7,5]=>[4,3,1]
[7,4,3,1,8,2,6,5]=>[4,3,1]
[8,4,3,1,7,6,2,5]=>[4,3,1]
[1,5,8,3,7,6,4,2]=>[5,1,1,1]
[8,5,1,3,7,6,2,4]=>[4,2,1,1]
[7,5,1,3,8,2,6,4]=>[4,2,1,1]
[6,5,1,3,2,8,7,4]=>[4,3,1]
[5,6,1,2,3,8,7,4]=>[3,2,1,1,1]
[4,6,2,1,3,8,7,5]=>[3,3,1,1]
[3,2,6,1,4,8,7,5]=>[3,3,1,1]
[3,2,7,1,8,4,6,5]=>[3,3,1,1]
[4,7,2,1,8,3,6,5]=>[3,3,1,1]
[5,7,1,2,8,3,6,4]=>[3,2,1,1,1]
[6,7,1,8,2,3,5,4]=>[3,2,1,1,1]
[7,6,1,8,3,2,5,4]=>[4,2,2]
[8,6,1,7,3,5,2,4]=>[4,2,1,1]
[1,6,8,7,3,5,4,2]=>[5,1,1,1]
[1,7,8,6,5,3,4,2]=>[5,1,1,1]
[8,7,1,6,5,3,2,4]=>[6,1,1]
[7,8,1,6,5,2,3,4]=>[4,1,1,1,1]
[6,8,1,7,2,5,3,4]=>[4,1,1,1,1]
[5,8,1,2,7,6,3,4]=>[4,1,1,1,1]
[4,8,2,1,7,6,3,5]=>[4,2,1,1]
[3,2,8,1,7,6,4,5]=>[4,2,1,1]
[4,1,2,8,7,6,5,3]=>[5,2,1]
[5,1,8,2,7,6,4,3]=>[5,2,1]
[6,1,8,7,2,5,4,3]=>[5,2,1]
[7,1,8,6,5,2,4,3]=>[5,2,1]
[8,1,7,6,5,4,2,3]=>[6,1,1]
[3,1,2,6,5,8,7,4]=>[3,2,2,1]
[3,1,6,2,4,8,7,5]=>[3,2,2,1]
[3,1,5,2,4,8,7,6]=>[3,2,2,1]
[4,5,1,2,3,8,7,6]=>[3,2,1,1,1]
[4,6,1,2,3,8,7,5]=>[3,2,1,1,1]
[1,6,5,3,4,8,7,2]=>[4,2,1,1]
[6,1,5,2,4,8,7,3]=>[4,2,1,1]
[6,5,1,2,3,8,7,4]=>[3,3,1,1]
[6,4,1,2,3,8,7,5]=>[3,3,1,1]
[5,4,1,2,3,8,7,6]=>[3,3,1,1]
[5,4,1,2,7,3,6,8]=>[3,2,1,1,1]
[6,4,1,7,2,3,5,8]=>[3,2,1,1,1]
[6,4,1,8,2,3,5,7]=>[3,2,1,1,1]
[7,4,1,2,8,3,6,5]=>[3,3,1,1]
[7,5,1,2,8,3,6,4]=>[3,3,1,1]
[7,1,5,2,8,4,6,3]=>[4,2,1,1]
[1,7,5,3,8,4,6,2]=>[4,2,1,1]
[1,8,5,3,7,4,6,2]=>[4,2,1,1]
[8,1,5,2,7,4,6,3]=>[4,2,1,1]
[8,5,1,2,7,3,6,4]=>[4,2,1,1]
[8,4,1,2,7,3,6,5]=>[4,2,1,1]
[8,4,1,7,2,3,5,6]=>[3,2,1,1,1]
[7,4,1,6,2,3,5,8]=>[3,2,1,1,1]
[8,6,1,7,2,3,5,4]=>[4,2,1,1]
[8,1,6,7,2,4,5,3]=>[4,1,1,1,1]
[1,8,6,7,3,4,5,2]=>[4,1,1,1,1]
[1,7,6,8,3,4,5,2]=>[4,1,1,1,1]
[7,1,6,8,2,4,5,3]=>[4,1,1,1,1]
[7,6,1,8,2,3,5,4]=>[4,2,1,1]
[4,7,1,2,8,3,6,5]=>[3,2,1,1,1]
[3,1,7,2,8,4,6,5]=>[3,2,2,1]
[3,1,2,7,8,5,6,4]=>[3,2,1,1,1]
[1,4,3,8,7,5,6,2]=>[4,2,1,1]
[4,1,2,8,7,5,6,3]=>[4,2,1,1]
[3,1,2,8,7,5,6,4]=>[4,2,1,1]
[3,1,8,2,7,4,6,5]=>[4,2,1,1]
[3,1,8,7,2,4,5,6]=>[3,2,1,1,1]
[3,1,7,6,2,4,5,8]=>[3,2,1,1,1]
[4,7,1,6,2,3,5,8]=>[3,1,1,1,1,1]
[4,8,1,6,2,3,5,7]=>[3,1,1,1,1,1]
[4,8,1,7,2,3,5,6]=>[3,1,1,1,1,1]
[4,8,1,2,7,3,6,5]=>[4,1,1,1,1]
[5,8,1,2,7,3,6,4]=>[4,1,1,1,1]
[5,1,8,2,7,4,6,3]=>[4,2,1,1]
[1,5,8,3,7,4,6,2]=>[4,1,1,1,1]
[1,6,8,7,3,4,5,2]=>[4,1,1,1,1]
[6,1,8,7,2,4,5,3]=>[4,2,1,1]
[6,8,1,7,2,3,5,4]=>[4,1,1,1,1]
[6,8,7,1,2,3,4,5]=>[3,1,1,1,1,1]
[5,8,7,1,2,3,4,6]=>[3,1,1,1,1,1]
[5,8,6,1,2,3,4,7]=>[3,1,1,1,1,1]
[5,7,6,1,2,3,4,8]=>[3,1,1,1,1,1]
[7,8,1,6,2,3,5,4]=>[4,1,1,1,1]
[7,1,8,6,2,4,5,3]=>[4,2,1,1]
[1,7,8,6,3,4,5,2]=>[4,1,1,1,1]
[1,8,7,6,3,4,5,2]=>[5,1,1,1]
[8,1,7,6,2,4,5,3]=>[5,1,1,1]
[8,7,1,6,2,3,5,4]=>[5,1,1,1]
[3,2,5,1,6,4,8,7]=>[3,2,2,1]
[3,2,5,4,7,1,8,6]=>[3,2,2,1]
[4,2,5,3,7,6,8,1]=>[3,2,2,1]
[4,2,5,3,7,1,8,6]=>[3,2,2,1]
[4,2,5,3,6,1,8,7]=>[3,2,2,1]
[4,2,5,1,6,3,8,7]=>[3,2,2,1]
[3,1,5,4,6,2,8,7]=>[3,2,2,1]
[4,1,5,3,6,2,8,7]=>[3,2,2,1]
[4,3,5,1,6,2,8,7]=>[3,2,2,1]
[4,3,5,2,7,1,8,6]=>[4,2,1,1]
[4,3,6,2,7,5,8,1]=>[4,2,1,1]
[4,3,6,2,7,1,8,5]=>[4,2,1,1]
[4,3,6,1,7,2,8,5]=>[3,2,2,1]
[4,3,5,1,7,2,8,6]=>[3,2,2,1]
[3,1,5,4,7,2,8,6]=>[3,2,2,1]
[2,1,5,4,7,3,8,6]=>[3,2,2,1]
[3,1,5,4,7,6,8,2]=>[3,2,2,1]
[4,1,5,3,7,6,8,2]=>[3,2,2,1]
[4,3,5,1,7,6,8,2]=>[3,3,1,1]
[4,3,6,1,7,5,8,2]=>[3,3,1,1]
[4,3,6,5,7,1,8,2]=>[3,2,2,1]
[5,3,6,4,7,2,8,1]=>[4,2,1,1]
[5,3,6,4,7,1,8,2]=>[3,2,2,1]
[5,3,6,1,7,4,8,2]=>[3,3,1,1]
[5,1,6,3,7,4,8,2]=>[3,2,2,1]
[4,1,6,3,7,5,8,2]=>[3,2,2,1]
[3,1,6,4,7,5,8,2]=>[3,2,2,1]
[2,1,6,4,7,5,8,3]=>[3,2,2,1]
[2,1,6,4,7,3,8,5]=>[3,2,2,1]
[3,1,6,4,7,2,8,5]=>[3,2,2,1]
[4,1,6,3,7,2,8,5]=>[3,2,2,1]
[5,1,6,3,7,2,8,4]=>[3,2,2,1]
[5,3,6,1,7,2,8,4]=>[3,2,2,1]
[5,3,6,2,7,1,8,4]=>[4,2,1,1]
[5,3,6,2,7,4,8,1]=>[4,2,1,1]
[5,2,6,3,7,4,8,1]=>[3,2,2,1]
[5,2,6,3,7,1,8,4]=>[3,2,2,1]
[5,2,6,1,7,3,8,4]=>[3,2,2,1]
[4,2,5,1,7,3,8,6]=>[3,2,2,1]
[4,2,6,1,7,3,8,5]=>[3,2,2,1]
[4,2,6,3,7,1,8,5]=>[3,2,2,1]
[4,2,6,3,7,5,8,1]=>[3,2,2,1]
[3,2,6,4,7,5,8,1]=>[3,2,2,1]
[3,2,6,4,7,1,8,5]=>[3,2,2,1]
[3,2,6,1,7,4,8,5]=>[3,2,2,1]
[3,2,5,1,7,4,8,6]=>[3,2,2,1]
[3,2,4,1,7,5,8,6]=>[3,2,2,1]
[3,1,4,2,7,6,8,5]=>[3,2,2,1]
[3,2,5,1,7,6,8,4]=>[3,3,1,1]
[3,2,6,1,7,5,8,4]=>[3,3,1,1]
[3,2,6,5,7,1,8,4]=>[3,2,2,1]
[4,2,6,5,7,3,8,1]=>[4,2,1,1]
[4,2,6,5,7,1,8,3]=>[3,2,2,1]
[4,2,6,1,7,5,8,3]=>[3,3,1,1]
[4,2,5,1,7,6,8,3]=>[3,3,1,1]
[4,1,5,2,7,6,8,3]=>[3,2,2,1]
[3,1,5,2,7,6,8,4]=>[3,2,2,1]
[2,1,5,3,7,6,8,4]=>[3,2,2,1]
[2,1,6,3,7,5,8,4]=>[3,2,2,1]
[3,1,6,2,7,5,8,4]=>[3,2,2,1]
[4,1,6,2,7,5,8,3]=>[3,2,2,1]
[5,1,6,2,7,4,8,3]=>[3,2,2,1]
[5,2,6,1,7,4,8,3]=>[3,3,1,1]
[5,2,6,4,7,1,8,3]=>[3,2,2,1]
[5,2,6,4,7,3,8,1]=>[4,2,1,1]
[5,4,6,2,7,3,8,1]=>[4,2,1,1]
[5,4,6,2,7,1,8,3]=>[4,2,1,1]
[5,4,6,1,7,2,8,3]=>[3,2,2,1]
[5,1,6,4,7,2,8,3]=>[3,2,2,1]
[4,1,6,5,7,2,8,3]=>[3,2,2,1]
[3,1,6,5,7,2,8,4]=>[3,2,2,1]
[2,1,6,5,7,3,8,4]=>[3,2,2,1]
[3,1,6,5,7,4,8,2]=>[4,2,1,1]
[4,1,6,5,7,3,8,2]=>[4,2,1,1]
[5,1,6,4,7,3,8,2]=>[4,2,1,1]
[5,4,6,1,7,3,8,2]=>[4,2,1,1]
[5,4,6,3,7,1,8,2]=>[4,2,1,1]
[8,3,5,2,1,6,4,7]=>[4,2,1,1]
[8,6,3,5,2,4,1,7]=>[5,1,1,1]
[3,7,5,2,4,1,8,6]=>[4,2,1,1]
[8,3,7,5,2,4,6,1]=>[5,1,1,1]
[8,2,4,5,7,3,6,1]=>[4,1,1,1,1]
[2,4,5,7,3,1,8,6]=>[3,2,1,1,1]
[8,2,4,6,5,3,1,7]=>[5,1,1,1]
[8,2,5,4,6,1,3,7]=>[4,1,1,1,1]
[8,6,3,5,1,4,2,7]=>[5,1,1,1]
[8,6,1,4,5,3,2,7]=>[5,1,1,1]
[8,1,5,6,4,3,2,7]=>[5,1,1,1]
[5,7,4,3,2,1,8,6]=>[5,2,1]
[8,5,7,4,3,2,6,1]=>[6,1,1]
[4,6,8,3,2,7,5,1]=>[4,2,1,1]
[4,7,6,3,2,8,1,5]=>[5,1,1,1]
[1,4,6,7,3,2,8,5]=>[3,2,1,1,1]
[5,4,7,3,1,8,2,6]=>[4,2,1,1]
[1,7,4,5,3,2,8,6]=>[4,2,1,1]
[3,7,5,1,4,2,8,6]=>[4,2,1,1]
[5,7,4,2,1,3,8,6]=>[4,2,1,1]
[8,5,7,4,2,1,6,3]=>[5,2,1]
[8,3,7,5,1,4,6,2]=>[5,1,1,1]
[8,4,1,7,5,3,6,2]=>[5,2,1]
[4,6,3,8,7,1,5,2]=>[4,2,1,1]
[1,7,4,8,6,3,5,2]=>[4,2,1,1]
[8,4,7,6,3,5,2,1]=>[6,1,1]
[3,6,5,8,7,4,1,2]=>[4,2,1,1]
[3,1,5,8,6,7,4,2]=>[4,2,1,1]
[4,8,1,6,7,3,5,2]=>[4,1,1,1,1]
[3,6,4,1,8,7,5,2]=>[4,3,1]
[8,2,6,1,4,7,5,3]=>[4,2,1,1]
[2,7,6,8,1,4,3,5]=>[4,1,1,1,1]
[3,7,1,6,4,8,2,5]=>[4,1,1,1,1]
[1,7,3,5,6,8,2,4]=>[3,1,1,1,1,1]
[1,3,6,7,5,8,2,4]=>[3,1,1,1,1,1]
[3,7,6,5,8,2,1,4]=>[5,1,1,1]
[3,6,8,5,7,2,4,1]=>[4,1,1,1,1]
[2,3,5,7,6,8,1,4]=>[3,1,1,1,1,1]
[2,1,6,5,7,8,3,4]=>[3,2,1,1,1]
[4,2,7,6,8,3,1,5]=>[4,2,1,1]
[4,2,6,8,7,3,5,1]=>[4,2,1,1]
[3,8,2,4,6,7,5,1]=>[4,1,1,1,1]
[3,7,2,6,4,8,1,5]=>[4,1,1,1,1]
[3,2,6,1,4,7,8,5]=>[3,2,1,1,1]
[5,3,7,2,1,8,4,6]=>[4,2,1,1]
[4,7,3,2,1,5,8,6]=>[4,2,1,1]
[8,7,6,1,3,4,2,5]=>[5,1,1,1]
[8,5,7,3,2,1,6,4]=>[5,2,1]
[8,3,6,7,2,1,5,4]=>[4,2,1,1]
[3,7,8,6,2,1,5,4]=>[4,2,1,1]
[8,7,6,3,5,2,4,1]=>[6,1,1]
[2,7,4,8,1,6,5,3]=>[4,2,1,1]
[4,6,8,2,1,7,5,3]=>[4,2,1,1]
[8,4,1,5,7,2,6,3]=>[4,2,1,1]
[8,5,3,7,1,6,2,4]=>[4,2,1,1]
[8,5,7,2,1,3,6,4]=>[4,2,1,1]
[8,2,6,7,1,3,5,4]=>[4,1,1,1,1]
[8,3,6,1,7,5,2,4]=>[4,2,1,1]
[4,6,1,8,7,2,5,3]=>[4,2,1,1]
[8,1,2,5,6,7,4,3]=>[4,1,1,1,1]
[8,2,6,5,7,4,1,3]=>[5,1,1,1]
[2,1,7,8,5,6,4,3]=>[4,2,1,1]
[8,2,5,7,6,4,3,1]=>[6,1,1]
[2,7,6,8,5,4,1,3]=>[5,1,1,1]
[1,7,2,5,8,6,4,3]=>[4,2,1,1]
[1,7,4,8,2,6,5,3]=>[4,2,1,1]
[3,7,8,1,6,5,2,4]=>[4,1,1,1,1]
[2,7,8,6,1,3,5,4]=>[4,1,1,1,1]
[8,7,6,3,5,1,4,2]=>[6,1,1]
[8,4,7,6,5,1,3,2]=>[6,1,1]
[8,7,1,5,6,4,3,2]=>[6,1,1]
[8,1,6,7,5,4,3,2]=>[6,1,1]
[6,5,3,1,2,4,8,7]=>[4,2,1,1]
[4,6,3,5,1,2,8,7]=>[3,2,1,1,1]
[8,5,3,7,2,1,4,6]=>[5,1,1,1]
[6,8,1,4,5,7,3,2]=>[4,1,1,1,1]
[8,7,2,4,5,1,3,6]=>[4,1,1,1,1]
[3,6,2,4,5,1,8,7]=>[3,2,1,1,1]
[2,6,1,4,5,3,8,7]=>[3,2,1,1,1]
[6,1,2,4,5,3,8,7]=>[3,2,1,1,1]
[5,6,3,2,1,4,8,7]=>[4,2,1,1]
[5,4,3,6,1,2,8,7]=>[4,2,1,1]
[6,3,1,4,5,2,8,7]=>[3,2,2,1]
[3,1,6,4,5,2,8,7]=>[3,2,2,1]
[8,3,7,4,5,1,2,6]=>[4,1,1,1,1]
[5,8,7,4,2,6,3,1]=>[5,2,1]
[2,8,7,4,1,6,3,5]=>[4,2,1,1]
[8,1,7,4,2,6,3,5]=>[4,2,1,1]
[3,7,8,4,5,1,2,6]=>[3,1,1,1,1,1]
[2,1,8,7,5,3,4,6]=>[4,2,1,1]
[2,1,6,8,5,7,3,4]=>[3,2,1,1,1]
[5,6,3,8,1,7,2,4]=>[3,2,1,1,1]
[7,6,1,4,5,8,3,2]=>[5,1,1,1]
[3,7,6,4,5,8,2,1]=>[5,1,1,1]
[8,5,7,4,1,6,3,2]=>[5,2,1]
[5,1,8,4,7,6,2,3]=>[4,2,1,1]
[2,5,8,4,7,6,1,3]=>[4,1,1,1,1]
[2,4,8,3,5,6,7,1]=>[3,1,1,1,1,1]
[4,1,8,3,5,6,7,2]=>[3,2,1,1,1]
[3,8,4,2,5,6,7,1]=>[4,1,1,1,1]
[8,4,1,3,5,6,7,2]=>[4,1,1,1,1]
[7,5,8,4,3,6,1,2]=>[5,1,1,1]
[6,5,3,8,4,1,7,2]=>[4,2,2]
[2,1,5,8,4,6,7,3]=>[3,2,1,1,1]
[2,1,4,8,3,6,7,5]=>[3,2,1,1,1]
[6,4,3,8,2,1,7,5]=>[5,2,1]
[7,3,8,4,2,6,1,5]=>[4,2,1,1]
[8,3,1,2,5,6,7,4]=>[3,2,1,1,1]
[3,1,8,2,5,6,7,4]=>[3,2,1,1,1]
[2,3,8,1,5,6,7,4]=>[3,1,1,1,1,1]
[4,3,8,2,5,6,7,1]=>[4,1,1,1,1]
[4,8,2,3,5,6,7,1]=>[3,1,1,1,1,1]
[3,8,2,1,5,6,7,4]=>[3,2,1,1,1]
[2,8,1,3,5,6,7,4]=>[3,1,1,1,1,1]
[8,1,2,3,5,6,7,4]=>[3,1,1,1,1,1]
[7,8,2,4,3,6,1,5]=>[4,1,1,1,1]
[6,8,3,2,4,1,7,5]=>[4,2,1,1]
[2,1,8,3,4,6,7,5]=>[3,2,1,1,1]
[2,1,7,8,5,4,3,6]=>[4,2,1,1]
[5,7,3,8,1,4,2,6]=>[3,2,1,1,1]
[7,1,8,4,5,3,2,6]=>[4,2,1,1]
[2,7,8,4,5,3,1,6]=>[4,1,1,1,1]
[8,7,1,4,3,6,2,5]=>[5,1,1,1]
[3,8,7,4,2,6,1,5]=>[5,1,1,1]
[5,7,8,4,3,6,2,1]=>[5,1,1,1]
[5,6,3,8,4,2,7,1]=>[4,2,1,1]
[4,8,3,6,2,1,7,5]=>[4,2,1,1]
[8,6,3,1,4,2,7,5]=>[4,2,2]
[7,5,3,8,2,4,1,6]=>[5,1,1,1]
[2,4,3,1,8,5,7,6]=>[3,3,1,1]
[4,1,3,2,6,8,7,5]=>[3,3,1,1]
[7,5,3,6,2,8,1,4]=>[5,1,1,1]
[8,6,3,5,1,2,7,4]=>[4,2,1,1]
[5,8,3,2,6,1,7,4]=>[4,2,1,1]
[4,5,3,8,6,2,7,1]=>[4,2,1,1]
[3,5,8,4,7,6,2,1]=>[5,1,1,1]
[5,8,2,4,7,6,1,3]=>[4,1,1,1,1]
[8,7,5,4,1,6,2,3]=>[5,2,1]
[2,7,6,4,5,8,1,3]=>[4,1,1,1,1]
[7,1,6,4,5,8,2,3]=>[4,1,1,1,1]
[5,7,3,6,1,8,2,4]=>[3,2,1,1,1]
[2,1,7,6,5,8,3,4]=>[4,2,1,1]
[2,1,8,5,3,6,7,4]=>[3,2,2,1]
[6,8,3,5,2,1,7,4]=>[4,2,1,1]
[7,8,5,4,2,6,1,3]=>[5,1,1,1]
[8,1,4,2,5,6,7,3]=>[3,2,1,1,1]
[2,8,4,1,5,6,7,3]=>[3,2,1,1,1]
[4,8,1,2,5,6,7,3]=>[3,1,1,1,1,1]
[3,4,8,1,5,6,7,2]=>[3,1,1,1,1,1]
[3,4,2,8,5,6,7,1]=>[3,2,1,1,1]
[2,4,1,8,5,6,7,3]=>[3,2,1,1,1]
[4,1,2,8,5,6,7,3]=>[3,2,1,1,1]
[8,4,2,1,5,6,7,3]=>[4,2,1,1]
[7,5,2,4,8,6,1,3]=>[4,2,1,1]
[6,5,3,2,8,1,7,4]=>[5,2,1]
[2,1,5,3,8,6,7,4]=>[3,2,2,1]
[6,4,3,5,8,1,7,2]=>[4,2,1,1]
[7,3,5,4,8,6,1,2]=>[4,2,1,1]
[8,3,4,1,5,6,7,2]=>[3,2,1,1,1]
[4,3,1,8,5,6,7,2]=>[3,3,1,1]
[3,1,4,8,5,6,7,2]=>[3,2,1,1,1]
[6,5,3,7,2,8,4,1]=>[5,2,1]
[6,3,7,4,5,8,2,1]=>[4,2,1,1]
[6,7,2,4,5,8,3,1]=>[4,1,1,1,1]
[5,1,7,4,8,6,3,2]=>[4,2,2]
[2,5,7,4,8,6,3,1]=>[4,2,1,1]
[5,6,3,7,1,8,4,2]=>[3,3,1,1]
[3,8,7,4,5,2,1,6]=>[5,1,1,1]
[3,7,5,4,8,6,2,1]=>[5,2,1]
[5,7,1,4,8,6,2,3]=>[3,2,1,1,1]
[5,6,3,1,8,2,7,4]=>[3,3,1,1]
[4,6,3,5,8,2,7,1]=>[4,1,1,1,1]
[4,6,3,8,1,2,7,5]=>[3,2,1,1,1]
[3,7,8,4,1,6,2,5]=>[3,2,1,1,1]
[3,2,5,1,6,8,4,7]=>[3,2,1,1,1]
[3,6,2,5,4,8,1,7]=>[4,1,1,1,1]
[3,5,2,4,7,1,8,6]=>[3,2,1,1,1]
[3,5,8,2,4,7,6,1]=>[4,1,1,1,1]
[4,2,5,8,3,7,6,1]=>[4,2,1,1]
[4,2,6,5,3,8,1,7]=>[4,2,1,1]
[5,4,2,1,6,8,3,7]=>[4,2,1,1]
[6,3,5,1,4,8,2,7]=>[4,1,1,1,1]
[4,6,1,5,3,8,2,7]=>[4,1,1,1,1]
[5,1,6,4,3,8,2,7]=>[4,2,1,1]
[5,4,3,2,7,1,8,6]=>[5,2,1]
[5,4,3,8,2,7,6,1]=>[5,2,1]
[4,3,6,2,8,7,5,1]=>[4,3,1]
[4,3,7,6,2,1,8,5]=>[4,2,2]
[6,4,3,1,7,2,8,5]=>[4,2,2]
[7,5,4,3,1,8,2,6]=>[5,2,1]
[1,4,7,5,8,3,2,6]=>[4,1,1,1,1]
[7,1,3,5,8,4,2,6]=>[4,1,1,1,1]
[7,2,5,8,4,1,3,6]=>[4,1,1,1,1]
[2,8,5,7,4,6,1,3]=>[4,1,1,1,1]
[3,5,8,7,1,4,6,2]=>[4,1,1,1,1]
[1,4,5,8,7,3,6,2]=>[4,1,1,1,1]
[1,5,4,8,7,3,6,2]=>[4,2,1,1]
[6,4,3,8,1,7,5,2]=>[4,3,1]
[4,3,7,1,8,6,5,2]=>[4,3,1]
[4,8,3,7,6,5,2,1]=>[6,1,1]
[5,3,8,7,6,4,2,1]=>[6,2]
[7,5,3,1,8,6,4,2]=>[4,4]
[1,8,6,5,3,7,4,2]=>[5,2,1]
[1,5,8,6,3,7,4,2]=>[4,2,1,1]
[4,6,1,8,7,3,5,2]=>[4,2,1,1]
[6,8,7,3,1,4,5,2]=>[4,2,1,1]
[6,2,8,7,4,5,1,3]=>[4,2,1,1]
[7,6,2,8,4,1,3,5]=>[4,2,1,1]
[7,3,1,6,8,4,2,5]=>[4,2,1,1]
[1,7,6,4,8,3,2,5]=>[5,1,1,1]
[5,7,1,6,3,2,8,4]=>[4,2,1,1]
[6,1,7,5,3,2,8,4]=>[4,2,2]
[7,6,5,3,2,1,8,4]=>[6,2]
[6,5,3,2,8,7,4,1]=>[5,3]
[5,2,6,3,8,7,4,1]=>[4,2,2]
[5,2,7,6,3,1,8,4]=>[4,2,2]
[6,5,2,1,7,3,8,4]=>[4,2,2]
[5,2,7,4,1,8,3,6]=>[3,2,2,1]
[4,7,2,6,3,1,8,5]=>[4,2,1,1]
[2,4,8,6,3,7,5,1]=>[4,2,1,1]
[3,8,6,2,4,7,5,1]=>[4,2,1,1]
[7,3,6,2,4,1,8,5]=>[4,2,1,1]
[3,6,7,2,1,4,8,5]=>[3,2,1,1,1]
[4,3,7,8,2,1,5,6]=>[4,1,1,1,1]
[8,3,7,1,4,6,2,5]=>[4,1,1,1,1]
[3,8,2,5,7,1,6,4]=>[4,1,1,1,1]
[8,3,6,2,7,1,5,4]=>[4,2,1,1]
[7,8,3,6,2,1,5,4]=>[4,2,1,1]
[8,7,3,6,2,5,4,1]=>[6,1,1]
[4,7,8,2,1,6,5,3]=>[4,2,1,1]
[4,2,6,8,1,7,5,3]=>[4,2,1,1]
[5,4,8,2,7,1,6,3]=>[4,2,1,1]
[4,8,1,5,7,2,6,3]=>[4,1,1,1,1]
[5,8,3,7,1,6,2,4]=>[4,1,1,1,1]
[5,8,7,2,6,1,3,4]=>[4,1,1,1,1]
[8,6,2,7,5,1,3,4]=>[4,2,1,1]
[3,6,8,1,7,5,2,4]=>[4,1,1,1,1]
[5,1,6,8,2,7,4,3]=>[4,2,1,1]
[6,5,2,8,1,7,4,3]=>[4,3,1]
[5,2,7,1,8,6,4,3]=>[4,3,1]
[5,8,2,7,6,4,3,1]=>[6,1,1]
[6,2,8,7,5,4,3,1]=>[6,2]
[7,6,2,1,8,5,4,3]=>[5,3]
[6,1,7,2,8,5,4,3]=>[4,2,2]
[7,5,1,8,2,6,4,3]=>[4,3,1]
[4,7,1,8,6,2,5,3]=>[4,2,1,1]
[7,8,3,1,6,5,2,4]=>[4,2,1,1]
[8,7,4,6,1,5,3,2]=>[6,1,1]
[8,5,7,1,6,4,3,2]=>[6,1,1]
[6,8,1,7,5,4,3,2]=>[6,1,1]
[7,1,8,6,5,4,3,2]=>[6,2]
[5,4,2,3,7,6,1,8]=>[4,2,1,1]
[6,4,2,7,3,5,1,8]=>[4,2,1,1]
[7,4,2,6,3,5,1,8]=>[4,2,1,1]
[8,4,2,6,3,1,5,7]=>[4,2,1,1]
[3,2,7,6,4,5,1,8]=>[4,2,1,1]
[4,7,2,6,3,5,1,8]=>[4,1,1,1,1]
[5,7,6,2,3,4,1,8]=>[4,1,1,1,1]
[1,6,5,2,3,8,4,7]=>[3,2,1,1,1]
[1,7,5,2,8,3,4,6]=>[3,2,1,1,1]
[6,8,5,2,3,1,4,7]=>[4,1,1,1,1]
[5,8,6,2,3,1,4,7]=>[4,1,1,1,1]
[4,8,2,6,3,1,5,7]=>[4,1,1,1,1]
[3,2,8,6,4,1,5,7]=>[4,2,1,1]
[3,2,1,6,4,8,5,7]=>[3,2,2,1]
[7,1,5,2,8,3,4,6]=>[3,2,1,1,1]
[1,8,5,2,7,3,4,6]=>[3,2,1,1,1]
[1,8,6,7,2,3,4,5]=>[3,1,1,1,1,1]
[8,1,6,7,2,3,4,5]=>[3,1,1,1,1,1]
[7,1,6,8,2,3,4,5]=>[3,1,1,1,1,1]
[3,2,1,7,8,4,5,6]=>[3,2,1,1,1]
[3,2,8,7,1,4,5,6]=>[3,2,1,1,1]
[5,8,7,2,1,3,4,6]=>[4,1,1,1,1]
[1,7,6,8,2,3,4,5]=>[3,1,1,1,1,1]
[6,5,8,2,3,1,4,7]=>[4,1,1,1,1]
[8,5,7,2,1,3,4,6]=>[4,1,1,1,1]
[6,4,2,8,3,1,5,7]=>[4,2,1,1]
[5,4,2,3,8,1,6,7]=>[4,1,1,1,1]
[3,2,5,4,1,8,6,7]=>[3,2,2,1]
[4,5,2,3,1,8,6,7]=>[3,2,1,1,1]
[5,4,2,3,1,8,6,7]=>[4,2,1,1]
[6,4,2,1,3,8,5,7]=>[4,2,1,1]
[7,4,2,1,8,3,5,6]=>[4,2,1,1]
[8,4,2,1,7,3,5,6]=>[4,2,1,1]
[1,4,2,8,7,3,5,6]=>[3,2,1,1,1]
[1,5,8,2,7,3,4,6]=>[3,1,1,1,1,1]
[8,5,1,2,7,3,4,6]=>[3,2,1,1,1]
[7,5,1,2,8,3,4,6]=>[3,2,1,1,1]
[6,5,1,2,3,8,4,7]=>[3,2,1,1,1]
[4,6,2,1,3,8,5,7]=>[3,2,1,1,1]
[3,2,6,1,4,8,5,7]=>[3,2,1,1,1]
[3,2,7,1,8,4,5,6]=>[3,2,1,1,1]
[4,7,2,1,8,3,5,6]=>[3,2,1,1,1]
[7,6,1,8,2,3,4,5]=>[3,2,1,1,1]
[8,6,1,7,2,3,4,5]=>[3,2,1,1,1]
[1,6,8,7,2,3,4,5]=>[3,1,1,1,1,1]
[1,7,8,6,2,3,4,5]=>[3,1,1,1,1,1]
[7,8,1,6,2,3,4,5]=>[3,1,1,1,1,1]
[6,8,1,7,2,3,4,5]=>[3,1,1,1,1,1]
[4,8,2,1,7,3,5,6]=>[3,2,1,1,1]
[3,2,8,1,7,4,5,6]=>[3,2,1,1,1]
[3,2,1,8,7,4,5,6]=>[3,3,1,1]
[5,1,8,2,7,3,4,6]=>[3,2,1,1,1]
[6,1,8,7,2,3,4,5]=>[3,2,1,1,1]
[8,1,7,6,2,3,4,5]=>[4,1,1,1,1]
[1,8,7,6,2,3,4,5]=>[4,1,1,1,1]
[6,3,5,1,2,4,8,7]=>[3,2,1,1,1]
[4,3,5,6,1,2,8,7]=>[3,2,1,1,1]
[8,3,7,5,2,1,4,6]=>[5,1,1,1]
[6,3,7,5,1,8,4,2]=>[4,2,2]
[6,5,2,7,1,8,3,4]=>[4,2,1,1]
[8,5,2,7,4,1,3,6]=>[4,2,1,1]
[2,6,1,5,4,3,8,7]=>[4,2,1,1]
[6,4,3,5,1,2,8,7]=>[4,2,1,1]
[5,3,1,4,6,2,8,7]=>[3,2,2,1]
[3,1,4,6,5,2,8,7]=>[3,2,2,1]
[5,7,4,6,2,8,3,1]=>[4,2,1,1]
[8,1,4,7,2,6,3,5]=>[4,1,1,1,1]
[3,4,7,8,5,2,1,6]=>[4,1,1,1,1]
[2,1,8,5,7,3,4,6]=>[3,2,1,1,1]
[8,6,3,5,1,7,4,2]=>[5,2,1]
[5,8,2,4,6,7,3,1]=>[4,1,1,1,1]
[3,4,8,6,5,7,1,2]=>[4,1,1,1,1]
[7,5,4,8,1,6,3,2]=>[5,2,1]
[5,1,4,6,8,2,7,3]=>[3,2,1,1,1]
[2,5,4,6,7,1,8,3]=>[3,2,1,1,1]
[2,4,6,3,7,5,8,1]=>[3,2,1,1,1]
[4,1,6,3,8,5,7,2]=>[3,2,2,1]
[3,7,4,2,8,6,5,1]=>[4,3,1]
[7,4,1,3,5,8,6,2]=>[4,2,1,1]
[6,5,8,4,1,7,3,2]=>[5,2,1]
[8,5,3,7,4,1,6,2]=>[4,2,2]
[2,1,4,8,3,7,6,5]=>[4,2,1,1]
[7,4,3,8,2,1,6,5]=>[5,2,1]
[6,3,7,4,1,8,2,5]=>[3,2,2,1]
[8,3,1,2,5,7,6,4]=>[4,2,1,1]
[3,1,8,2,7,6,5,4]=>[5,2,1]
[2,3,8,1,6,7,5,4]=>[4,1,1,1,1]
[4,3,7,2,6,8,5,1]=>[4,2,1,1]
[4,7,2,3,8,5,6,1]=>[3,2,1,1,1]
[3,8,2,1,7,5,6,4]=>[4,2,1,1]
[2,8,1,3,6,5,7,4]=>[4,1,1,1,1]
[2,7,8,5,4,3,1,6]=>[5,1,1,1]
[8,7,1,6,3,4,2,5]=>[5,1,1,1]
[3,8,6,7,2,4,1,5]=>[4,1,1,1,1]
[5,3,8,7,4,2,6,1]=>[5,2,1]
[4,3,8,7,2,1,6,5]=>[4,2,2]
[8,3,6,1,4,2,7,5]=>[4,2,1,1]
[7,3,5,8,2,4,1,6]=>[4,1,1,1,1]
[2,3,4,1,8,5,7,6]=>[3,2,1,1,1]
[4,1,3,2,6,7,8,5]=>[3,2,1,1,1]
[8,3,5,6,2,7,1,4]=>[4,1,1,1,1]
[5,3,6,1,8,7,2,4]=>[3,3,1,1]
[5,6,2,8,7,4,1,3]=>[4,2,1,1]
[7,8,5,6,1,4,2,3]=>[4,1,1,1,1]
[2,8,6,5,4,7,1,3]=>[5,1,1,1]
[8,1,6,4,5,7,2,3]=>[4,1,1,1,1]
[5,8,3,6,1,7,2,4]=>[3,2,1,1,1]
[2,1,8,6,5,7,3,4]=>[4,2,1,1]
[2,1,7,5,3,6,8,4]=>[3,2,2,1]
[6,7,3,5,2,1,8,4]=>[4,2,1,1]
[7,1,4,2,5,6,8,3]=>[3,2,1,1,1]
[2,7,4,1,6,5,8,3]=>[4,2,1,1]
[4,6,1,2,8,7,3,5]=>[3,2,1,1,1]
[2,4,1,5,8,7,6,3]=>[4,2,1,1]
[4,1,2,5,8,6,7,3]=>[3,2,1,1,1]
[6,4,2,1,5,8,7,3]=>[4,3,1]
[8,5,2,4,6,1,7,3]=>[4,2,1,1]
[7,5,3,2,6,8,1,4]=>[5,1,1,1]
[2,1,5,3,6,8,7,4]=>[3,2,2,1]
[7,3,5,4,6,1,8,2]=>[4,2,1,1]
[6,3,4,1,5,7,8,2]=>[3,2,1,1,1]
[4,3,1,5,7,6,8,2]=>[3,3,1,1]
[3,1,4,5,6,8,7,2]=>[3,2,1,1,1]
[4,5,2,6,3,1,8,7]=>[3,2,2,1]
[6,5,2,1,4,3,8,7]=>[4,2,2]
[6,5,2,7,4,8,3,1]=>[5,2,1]
[8,5,2,7,4,1,6,3]=>[4,2,2]
[8,3,7,5,2,1,6,4]=>[5,2,1]
[6,3,7,5,2,8,4,1]=>[4,2,2]
[3,1,6,5,4,2,8,7]=>[4,2,2]
[5,6,3,2,4,1,8,7]=>[4,2,1,1]
[3,6,2,4,1,5,8,7]=>[3,2,1,1,1]
[2,6,1,3,5,4,8,7]=>[3,2,1,1,1]
[6,7,2,3,4,8,5,1]=>[3,2,1,1,1]
[8,7,2,3,4,1,6,5]=>[4,2,1,1]
[5,1,7,3,8,4,6,2]=>[3,2,2,1]
[2,5,7,3,8,6,4,1]=>[4,2,1,1]
[7,6,1,3,5,8,4,2]=>[5,1,1,1]
[3,6,7,4,1,8,5,2]=>[3,3,1,1]
[5,6,3,7,4,8,1,2]=>[3,2,1,1,1]
[2,1,6,7,4,8,5,3]=>[3,2,2,1]
[2,1,8,7,4,3,6,5]=>[4,2,2]
[5,8,3,7,4,2,6,1]=>[5,1,1,1]
[3,8,7,4,1,2,6,5]=>[4,2,1,1]
[7,8,1,3,5,2,6,4]=>[3,2,1,1,1]
[5,8,7,3,2,6,1,4]=>[5,1,1,1]
[2,8,6,3,1,5,7,4]=>[4,2,1,1]
[8,1,6,3,2,5,4,7]=>[4,2,1,1]
[2,8,4,1,6,3,7,5]=>[3,2,2,1]
[4,8,1,2,7,6,3,5]=>[4,1,1,1,1]
[3,8,4,2,5,7,1,6]=>[4,1,1,1,1]
[6,8,3,5,2,7,4,1]=>[4,2,1,1]
[2,1,5,3,8,7,6,4]=>[4,2,2]
[6,5,3,2,8,7,1,4]=>[5,2,1]
[7,5,2,4,8,1,6,3]=>[4,2,1,1]
[3,4,2,8,5,7,6,1]=>[4,2,1,1]
[2,4,1,8,7,6,5,3]=>[5,2,1]
[8,4,2,1,7,5,3,6]=>[4,3,1]
[4,3,1,8,6,7,5,2]=>[4,3,1]
[3,1,4,8,6,5,7,2]=>[4,2,1,1]
[7,1,6,5,4,8,2,3]=>[5,1,1,1]
[3,7,5,6,8,4,2,1]=>[5,1,1,1]
[5,7,1,6,8,2,4,3]=>[4,1,1,1,1]
[8,6,2,5,1,7,4,3]=>[5,2,1]
[5,6,2,1,8,7,3,4]=>[3,3,1,1]
[4,6,2,5,8,3,7,1]=>[4,1,1,1,1]
[7,5,2,6,3,8,1,4]=>[4,2,1,1]
[4,1,2,3,6,8,7,5]=>[3,2,1,1,1]
[2,4,3,1,8,5,6,7]=>[3,2,1,1,1]
[7,5,2,8,3,4,6,1]=>[4,2,1,1]
[5,6,2,8,4,3,1,7]=>[4,2,1,1]
[4,7,2,8,1,5,3,6]=>[3,2,1,1,1]
[8,7,2,1,4,5,6,3]=>[4,2,1,1]
[3,6,8,7,1,5,4,2]=>[5,1,1,1]
[5,7,8,6,3,4,1,2]=>[4,1,1,1,1]
[7,1,8,5,4,3,6,2]=>[5,2,1]
[2,7,8,4,5,3,6,1]=>[4,1,1,1,1]
[5,7,3,8,1,4,6,2]=>[3,2,1,1,1]
[2,1,7,8,5,4,6,3]=>[4,2,1,1]
[2,1,5,8,4,6,3,7]=>[3,2,1,1,1]
[6,5,3,8,4,1,2,7]=>[4,2,1,1]
[7,5,8,4,3,6,2,1]=>[6,1,1]
[2,4,8,3,5,6,1,7]=>[3,1,1,1,1,1]
[4,1,8,3,6,5,2,7]=>[4,2,1,1]
[3,4,8,1,7,2,5,6]=>[3,1,1,1,1,1]
[8,4,1,3,7,2,6,5]=>[4,2,1,1]
[3,1,8,2,4,7,6,5]=>[4,2,1,1]
[2,3,8,1,4,6,7,5]=>[3,1,1,1,1,1]
[4,3,8,2,5,1,7,6]=>[4,2,1,1]
[6,3,8,4,2,5,7,1]=>[4,2,1,1]
[7,4,3,8,2,5,1,6]=>[5,1,1,1]
[2,1,4,8,3,5,7,6]=>[3,2,1,1,1]
[6,8,2,4,3,5,1,7]=>[4,1,1,1,1]
[4,8,2,3,5,1,6,7]=>[3,1,1,1,1,1]
[3,8,2,1,4,6,5,7]=>[3,2,1,1,1]
[2,8,1,3,4,5,7,6]=>[3,1,1,1,1,1]
[2,8,4,1,6,5,3,7]=>[4,2,1,1]
[2,8,4,1,6,5,7,3]=>[4,2,1,1]
[2,8,7,6,1,4,3,5]=>[5,1,1,1]
[2,8,5,6,7,4,3,1]=>[5,1,1,1]
[7,5,8,6,1,4,2,3]=>[4,2,1,1]
[3,5,7,6,1,4,2,8]=>[4,1,1,1,1]
[3,5,7,2,4,1,6,8]=>[3,1,1,1,1,1]
[7,5,8,2,4,1,6,3]=>[4,2,1,1]
[2,8,5,3,4,7,6,1]=>[4,2,1,1]
[2,8,5,3,4,1,7,6]=>[4,2,1,1]
[2,8,5,3,4,1,6,7]=>[4,1,1,1,1]
[2,8,7,6,1,4,5,3]=>[5,1,1,1]
[2,8,5,3,6,1,7,4]=>[4,2,1,1]
[2,8,5,6,7,4,1,3]=>[4,1,1,1,1]
[2,8,5,3,4,7,1,6]=>[4,1,1,1,1]
[2,8,5,3,4,6,1,7]=>[4,1,1,1,1]
[2,8,5,3,4,6,7,1]=>[4,1,1,1,1]
[3,5,7,2,4,6,1,8]=>[3,1,1,1,1,1]
[6,5,2,7,3,1,4,8]=>[4,2,1,1]
[6,5,2,8,3,1,7,4]=>[4,2,2]
[6,5,2,8,3,1,4,7]=>[4,2,1,1]
[7,5,8,2,4,6,3,1]=>[5,1,1,1]
[7,5,8,6,1,4,3,2]=>[5,2,1]
[6,5,8,2,1,3,7,4]=>[4,2,1,1]
[3,5,6,2,1,8,7,4]=>[3,3,1,1]
[3,5,7,6,1,4,8,2]=>[4,1,1,1,1]
[3,5,7,2,4,1,8,6]=>[3,2,1,1,1]
[3,5,7,2,4,6,8,1]=>[3,1,1,1,1,1]
[6,5,2,7,3,1,8,4]=>[4,2,2]
[4,5,2,6,3,1,7,8]=>[3,2,1,1,1]
[4,1,2,3,7,6,8,5]=>[3,2,1,1,1]
[6,5,2,7,3,4,8,1]=>[4,2,1,1]
[5,1,6,7,4,3,8,2]=>[4,2,1,1]
[5,1,2,6,4,8,7,3]=>[3,2,2,1]
[5,1,2,8,6,4,7,3]=>[4,2,1,1]
[5,1,6,8,7,3,4,2]=>[4,2,1,1]
[6,5,2,8,3,7,4,1]=>[4,3,1]
[4,1,2,3,8,7,5,6]=>[3,2,1,1,1]
[4,1,2,3,8,6,5,7]=>[3,2,1,1,1]
[4,1,2,3,8,6,7,5]=>[3,2,1,1,1]
[4,1,2,3,7,6,5,8]=>[3,2,1,1,1]
[4,1,2,3,8,5,7,6]=>[3,2,1,1,1]
[7,1,6,8,4,3,5,2]=>[5,1,1,1]
[6,1,2,8,4,5,7,3]=>[3,2,1,1,1]
[5,6,8,2,3,1,7,4]=>[3,2,1,1,1]
[6,5,8,2,4,3,1,7]=>[5,1,1,1]
[6,5,8,2,4,3,7,1]=>[5,1,1,1]
[7,5,2,8,3,4,1,6]=>[4,2,1,1]
[6,5,2,8,3,7,1,4]=>[4,2,1,1]
[6,5,2,7,3,4,1,8]=>[4,2,1,1]
[5,1,6,7,4,3,2,8]=>[4,2,1,1]
[5,1,6,8,7,3,2,4]=>[4,2,1,1]
[7,1,6,8,4,3,2,5]=>[5,1,1,1]
[5,7,8,6,3,4,2,1]=>[5,1,1,1]
[4,1,8,3,6,5,7,2]=>[4,2,1,1]
[4,1,8,3,6,2,7,5]=>[3,2,2,1]
[3,1,4,8,6,2,7,5]=>[3,2,2,1]
[3,1,4,8,6,5,2,7]=>[4,2,1,1]
[7,1,6,5,8,3,2,4]=>[5,1,1,1]
[4,1,6,7,8,3,2,5]=>[3,2,1,1,1]
[4,1,6,5,7,3,2,8]=>[4,2,1,1]
[4,5,2,6,3,7,1,8]=>[3,2,1,1,1]
[4,5,2,7,3,8,1,6]=>[3,2,1,1,1]
[3,5,6,2,4,8,7,1]=>[3,2,1,1,1]
[3,5,6,2,4,8,1,7]=>[3,1,1,1,1,1]
[3,7,5,6,8,4,1,2]=>[4,1,1,1,1]
[3,6,5,2,8,1,7,4]=>[4,2,1,1]
[6,1,2,5,8,4,7,3]=>[4,1,1,1,1]
[7,1,6,5,8,3,4,2]=>[5,1,1,1]
[7,5,2,6,3,8,4,1]=>[4,2,2]
[4,1,2,3,5,8,7,6]=>[3,2,1,1,1]
[4,1,2,3,7,8,6,5]=>[3,2,1,1,1]
[4,5,2,7,3,8,6,1]=>[3,2,2,1]
[4,1,6,7,8,3,5,2]=>[3,2,1,1,1]
[4,1,2,6,8,5,7,3]=>[3,2,1,1,1]
[4,1,2,5,6,8,7,3]=>[3,2,1,1,1]
[4,5,2,6,3,7,8,1]=>[3,2,1,1,1]
[7,8,5,6,1,4,3,2]=>[5,1,1,1]
[7,8,4,2,1,5,3,6]=>[4,2,1,1]
[7,8,2,1,6,5,3,4]=>[4,2,1,1]
[6,4,1,2,5,7,3,8]=>[3,2,1,1,1]
[2,4,8,1,5,7,3,6]=>[3,1,1,1,1,1]
[4,3,8,1,7,2,5,6]=>[3,2,1,1,1]
[6,3,1,4,7,2,5,8]=>[3,2,1,1,1]
[7,8,3,4,5,1,6,2]=>[3,2,1,1,1]
[7,8,3,5,4,2,1,6]=>[5,1,1,1]
[7,8,4,1,2,3,6,5]=>[3,2,1,1,1]
[7,8,3,6,5,4,1,2]=>[5,1,1,1]
[7,8,2,1,5,3,4,6]=>[3,2,1,1,1]
[7,8,2,6,4,1,3,5]=>[4,1,1,1,1]
[7,8,2,5,6,4,1,3]=>[4,1,1,1,1]
[7,8,1,6,5,4,3,2]=>[6,1,1]
[6,2,1,7,5,4,3,8]=>[4,3,1]
[2,1,8,7,5,4,3,6]=>[5,2,1]
[1,3,8,2,6,4,7,5]=>[3,2,1,1,1]
[5,3,7,1,6,4,8,2]=>[4,2,1,1]
[5,3,6,2,7,4,1,8]=>[4,2,1,1]
[6,1,2,5,8,7,4,3]=>[4,2,1,1]
[6,3,1,8,4,2,7,5]=>[3,3,2]
[6,4,2,1,5,3,8,7]=>[4,2,2]
[6,4,3,7,5,8,1,2]=>[4,2,1,1]
[4,3,8,7,5,6,1,2]=>[4,2,1,1]
[2,4,7,1,5,3,6,8]=>[3,1,1,1,1,1]
[1,3,7,6,4,2,8,5]=>[4,2,1,1]
[2,1,7,5,6,8,4,3]=>[4,2,1,1]
[3,7,2,8,6,4,1,5]=>[4,2,1,1]
[3,8,1,7,6,4,5,2]=>[5,1,1,1]
[1,8,5,7,3,6,4,2]=>[5,1,1,1]
[2,7,5,8,3,6,1,4]=>[4,1,1,1,1]
[1,5,6,8,2,4,7,3]=>[3,1,1,1,1,1]
[2,6,8,5,3,1,4,7]=>[4,1,1,1,1]
[2,6,1,4,7,3,5,8]=>[3,1,1,1,1,1]
[5,6,7,3,8,4,1,2]=>[3,2,1,1,1]
[5,2,8,1,4,7,3,6]=>[3,2,1,1,1]
[4,6,7,5,2,1,3,8]=>[4,1,1,1,1]
[4,5,6,7,2,8,1,3]=>[3,1,1,1,1,1]
[4,5,7,6,1,8,3,2]=>[4,2,1,1]
[1,5,8,6,2,7,3,4]=>[3,2,1,1,1]
[1,6,5,8,3,2,7,4]=>[4,2,1,1]
[4,6,5,7,1,2,8,3]=>[3,2,1,1,1]
[4,7,5,6,3,1,8,2]=>[4,2,1,1]
[5,1,6,3,4,2,8,7]=>[3,2,2,1]
[5,7,1,4,2,3,8,6]=>[3,2,1,1,1]
[5,7,6,4,3,8,1,2]=>[5,1,1,1]
[6,3,4,5,8,7,1,2]=>[3,2,1,1,1]
[6,2,4,1,8,3,7,5]=>[3,3,1,1]
[6,2,3,5,4,8,1,7]=>[4,1,1,1,1]
[6,1,3,4,5,8,7,2]=>[3,2,1,1,1]
[5,1,4,2,7,6,8,3]=>[3,3,1,1]
[1,6,2,4,7,8,3,5]=>[3,1,1,1,1,1]
[5,7,2,4,1,6,3,8]=>[3,2,1,1,1]
[6,1,4,2,8,5,3,7]=>[3,3,1,1]
[6,7,5,8,1,4,3,2]=>[5,1,1,1]
[5,8,7,6,3,4,1,2]=>[5,1,1,1]
[5,8,7,6,2,3,1,4]=>[5,1,1,1]
[4,1,7,2,6,5,3,8]=>[4,2,1,1]
[4,8,2,1,5,6,3,7]=>[3,2,1,1,1]
[4,2,7,8,1,6,3,5]=>[3,2,1,1,1]
[2,1,8,7,6,5,3,4]=>[5,2,1]
[3,1,4,7,8,2,6,5]=>[3,2,1,1,1]
[3,1,7,4,5,6,8,2]=>[3,2,1,1,1]
[4,2,7,1,6,3,8,5]=>[3,2,2,1]
[4,3,7,5,6,8,1,2]=>[3,2,1,1,1]
[4,8,6,3,5,7,1,2]=>[4,1,1,1,1]
[4,8,1,2,5,3,7,6]=>[3,2,1,1,1]
[3,8,6,5,2,4,1,7]=>[5,1,1,1]
[3,8,5,6,1,4,7,2]=>[4,1,1,1,1]
[5,3,7,8,2,1,6,4]=>[4,2,1,1]
[5,2,8,7,1,6,4,3]=>[5,2,1]
[1,6,8,7,5,2,4,3]=>[5,1,1,1]
[3,6,7,8,5,1,4,2]=>[4,1,1,1,1]
[3,7,6,8,5,2,1,4]=>[5,1,1,1]
[3,7,8,5,1,2,4,6]=>[3,1,1,1,1,1]
[3,7,1,6,4,2,5,8]=>[4,1,1,1,1]
[4,1,8,6,2,3,5,7]=>[3,2,1,1,1]
[4,7,8,6,3,5,1,2]=>[4,1,1,1,1]
[3,8,7,6,5,4,1,2]=>[6,1,1]
[2,1,7,6,5,3,4,8]=>[4,2,1,1]
[2,8,1,6,4,5,3,7]=>[4,1,1,1,1]
[2,8,7,5,1,4,3,6]=>[5,1,1,1]
[2,8,6,7,5,1,3,4]=>[4,1,1,1,1]
[2,7,8,6,5,4,1,3]=>[5,1,1,1]
[6,3,1,2,7,4,8,5]=>[3,2,2,1]
[6,4,2,7,1,3,8,5]=>[4,2,1,1]
[7,4,2,5,1,3,8,6]=>[4,2,1,1]
[7,5,3,6,1,8,2,4]=>[4,2,1,1]
[8,5,3,6,1,7,2,4]=>[4,2,1,1]
[8,3,6,2,4,7,1,5]=>[4,1,1,1,1]
[7,3,6,2,4,8,1,5]=>[4,1,1,1,1]
[4,3,7,1,2,5,8,6]=>[3,2,1,1,1]
[3,6,2,7,1,4,8,5]=>[3,2,1,1,1]
[5,3,6,7,1,2,8,4]=>[3,2,1,1,1]
[6,3,7,4,1,2,8,5]=>[3,2,2,1]
[4,7,1,5,2,3,8,6]=>[3,2,1,1,1]
[3,7,5,1,2,4,8,6]=>[3,2,1,1,1]
[7,6,4,2,3,8,1,5]=>[5,1,1,1]
[8,6,4,2,3,7,1,5]=>[5,1,1,1]
[4,7,6,3,8,1,2,5]=>[4,1,1,1,1]
[5,7,4,2,3,8,1,6]=>[4,1,1,1,1]
[3,7,6,1,4,8,2,5]=>[4,1,1,1,1]
[5,7,2,6,1,8,3,4]=>[3,2,1,1,1]
[6,4,7,5,2,8,1,3]=>[4,2,1,1]
[7,4,8,5,2,6,1,3]=>[4,2,1,1]
[5,8,2,6,3,7,1,4]=>[4,1,1,1,1]
[3,8,6,1,2,7,4,5]=>[3,2,1,1,1]
[3,8,6,2,4,7,1,5]=>[4,1,1,1,1]
[6,8,4,3,7,1,2,5]=>[4,1,1,1,1]
[6,8,5,3,7,1,2,4]=>[4,1,1,1,1]
[3,8,5,7,1,2,4,6]=>[3,1,1,1,1,1]
[2,8,5,7,1,3,4,6]=>[3,1,1,1,1,1]
[4,8,6,2,7,1,3,5]=>[4,1,1,1,1]
[7,3,8,5,6,1,2,4]=>[3,2,1,1,1]
[6,3,7,5,8,1,2,4]=>[3,2,1,1,1]
[2,7,6,4,8,1,3,5]=>[4,1,1,1,1]
[2,6,5,8,1,3,4,7]=>[3,1,1,1,1,1]
[3,6,5,8,1,2,4,7]=>[3,1,1,1,1,1]
[2,5,7,4,8,1,3,6]=>[3,1,1,1,1,1]
[5,4,6,7,2,8,1,3]=>[4,1,1,1,1]
[4,6,3,7,1,8,2,5]=>[3,2,1,1,1]
[3,5,7,1,4,8,2,6]=>[3,1,1,1,1,1]
[5,3,7,2,4,8,1,6]=>[4,1,1,1,1]
[5,4,7,3,8,1,2,6]=>[4,1,1,1,1]
[7,4,6,3,8,1,2,5]=>[4,1,1,1,1]
[8,4,6,3,7,1,2,5]=>[4,1,1,1,1]
[8,4,1,6,7,2,3,5]=>[3,2,1,1,1]
[7,4,1,6,8,2,3,5]=>[3,2,1,1,1]
[5,4,1,7,8,2,3,6]=>[3,2,1,1,1]
[6,5,3,7,1,8,2,4]=>[4,2,1,1]
[6,5,1,2,7,8,3,4]=>[3,2,1,1,1]
[5,3,6,4,7,8,1,2]=>[3,2,1,1,1]
[6,3,7,4,8,5,1,2]=>[3,2,2,1]
[4,7,1,5,8,6,2,3]=>[3,2,1,1,1]
[7,5,1,2,8,6,3,4]=>[3,3,1,1]
[7,5,3,8,1,6,2,4]=>[4,2,1,1]
[7,4,1,8,6,2,3,5]=>[3,3,1,1]
[7,6,1,8,5,2,3,4]=>[4,2,1,1]
[8,6,1,7,5,2,3,4]=>[4,2,1,1]
[5,7,2,8,1,6,3,4]=>[3,2,1,1,1]
[6,4,7,8,2,5,1,3]=>[4,1,1,1,1]
[6,3,7,8,5,1,2,4]=>[3,2,1,1,1]
[3,6,8,2,7,1,4,5]=>[3,1,1,1,1,1]
[2,4,8,7,1,3,5,6]=>[3,1,1,1,1,1]
[4,3,8,7,1,2,5,6]=>[3,2,1,1,1]
[5,3,8,7,1,2,4,6]=>[3,2,1,1,1]
[8,3,7,6,1,2,4,5]=>[4,1,1,1,1]
[8,4,7,6,1,2,3,5]=>[4,1,1,1,1]
[5,4,8,7,1,2,3,6]=>[3,2,1,1,1]
[3,5,8,7,1,2,4,6]=>[3,1,1,1,1,1]
[2,5,8,7,1,3,4,6]=>[3,1,1,1,1,1]
[4,6,8,2,7,1,3,5]=>[3,1,1,1,1,1]
[4,7,1,8,6,2,3,5]=>[3,2,1,1,1]
[7,5,8,6,4,1,2,3]=>[4,2,1,1]
[6,8,4,7,5,1,2,3]=>[4,1,1,1,1]
[5,8,7,1,6,2,3,4]=>[4,1,1,1,1]
[2,8,7,6,1,3,4,5]=>[4,1,1,1,1]
[3,8,7,6,1,2,4,5]=>[4,1,1,1,1]
[4,8,7,6,1,2,3,5]=>[4,1,1,1,1]
[5,6,3,1,4,2,8,7]=>[3,2,2,1]
[7,5,3,8,2,1,6,4]=>[5,2,1]
[3,8,7,4,5,1,6,2]=>[4,2,1,1]
[6,7,1,4,5,8,2,3]=>[3,1,1,1,1,1]
[2,1,7,8,5,3,6,4]=>[3,2,2,1]
[5,7,3,8,1,2,6,4]=>[3,2,1,1,1]
[8,7,1,4,5,3,2,6]=>[5,1,1,1]
[2,7,8,4,1,6,5,3]=>[4,2,1,1]
[7,1,8,4,2,6,5,3]=>[4,2,2]
[7,5,1,4,8,6,3,2]=>[5,2,1]
[6,5,3,1,8,4,7,2]=>[4,3,1]
[6,4,3,8,1,5,7,2]=>[4,2,1,1]
[8,6,3,1,2,5,7,4]=>[4,2,1,1]
[8,7,1,4,2,6,5,3]=>[5,2,1]
[7,3,8,4,1,6,5,2]=>[4,2,2]
[3,6,4,5,7,2,8,1]=>[4,1,1,1,1]
[5,3,2,7,4,6,8,1]=>[4,2,1,1]
[7,5,3,6,2,4,8,1]=>[5,1,1,1]
[6,3,2,5,1,8,4,7]=>[4,2,1,1]
[8,5,3,6,2,7,1,4]=>[5,1,1,1]
[8,2,6,3,4,7,1,5]=>[4,1,1,1,1]
[7,2,6,3,4,5,8,1]=>[4,1,1,1,1]
[6,2,7,3,4,5,8,1]=>[3,2,1,1,1]
[3,6,2,7,4,5,8,1]=>[3,2,1,1,1]
[4,2,5,7,3,6,8,1]=>[3,2,1,1,1]
[5,4,7,6,2,3,8,1]=>[4,2,1,1]
[6,7,3,5,2,4,8,1]=>[4,1,1,1,1]
[3,7,6,2,4,5,8,1]=>[4,1,1,1,1]
[2,7,6,3,4,5,8,1]=>[4,1,1,1,1]
[6,5,3,1,2,8,4,7]=>[4,2,1,1]
[8,6,5,2,3,7,1,4]=>[5,1,1,1]
[8,5,2,1,7,3,4,6]=>[4,2,1,1]
[7,5,2,1,8,3,4,6]=>[4,2,1,1]
[1,6,3,2,8,4,5,7]=>[3,2,1,1,1]
[5,7,3,1,2,8,4,6]=>[3,2,1,1,1]
[5,6,2,3,1,8,4,7]=>[3,2,1,1,1]
[4,2,6,5,1,8,3,7]=>[3,2,2,1]
[5,4,8,6,2,7,1,3]=>[4,2,1,1]
[6,8,3,5,2,7,1,4]=>[4,1,1,1,1]
[7,8,5,2,3,6,1,4]=>[4,1,1,1,1]
[6,8,2,1,7,3,4,5]=>[3,2,1,1,1]
[1,8,6,3,7,2,4,5]=>[4,1,1,1,1]
[1,8,2,7,3,4,5,6]=>[3,1,1,1,1,1]
[2,8,1,7,3,4,5,6]=>[3,1,1,1,1,1]
[3,8,6,1,7,2,4,5]=>[3,2,1,1,1]
[4,8,1,5,7,2,3,6]=>[3,1,1,1,1,1]
[4,2,8,3,7,1,5,6]=>[3,2,1,1,1]
[4,1,7,5,8,2,3,6]=>[3,2,1,1,1]
[1,7,3,8,2,4,5,6]=>[3,1,1,1,1,1]
[8,1,2,7,3,4,5,6]=>[3,1,1,1,1,1]
[4,2,5,7,1,8,3,6]=>[3,2,1,1,1]
[3,6,2,7,1,8,4,5]=>[3,2,1,1,1]
[6,3,7,1,2,8,4,5]=>[3,2,1,1,1]
[7,2,6,1,8,3,4,5]=>[3,2,1,1,1]
[8,2,6,1,7,3,4,5]=>[3,2,1,1,1]
[7,3,1,5,8,2,4,6]=>[3,2,1,1,1]
[3,2,1,5,8,4,6,7]=>[3,2,1,1,1]
[5,4,1,3,6,8,2,7]=>[4,1,1,1,1]
[1,5,3,4,6,8,2,7]=>[3,1,1,1,1,1]
[4,3,5,1,6,8,2,7]=>[3,2,1,1,1]
[5,4,6,3,8,7,1,2]=>[4,2,1,1]
[3,6,4,5,8,7,1,2]=>[3,2,1,1,1]
[6,5,3,4,8,7,1,2]=>[4,2,1,1]
[5,3,2,8,7,1,4,6]=>[4,2,1,1]
[5,3,1,8,7,2,4,6]=>[3,3,1,1]
[8,5,3,7,6,1,2,4]=>[4,2,1,1]
[6,1,8,3,7,2,4,5]=>[3,2,1,1,1]
[6,3,8,1,7,2,4,5]=>[3,2,1,1,1]
[7,6,8,2,3,5,1,4]=>[4,1,1,1,1]
[3,7,8,2,4,6,1,5]=>[3,1,1,1,1,1]
[6,7,3,8,2,5,1,4]=>[4,1,1,1,1]
[5,4,7,8,2,6,1,3]=>[4,1,1,1,1]
[4,2,5,8,7,1,3,6]=>[3,2,1,1,1]
[3,6,2,8,7,1,4,5]=>[3,2,1,1,1]
[3,7,8,1,6,2,4,5]=>[3,1,1,1,1,1]
[2,3,8,7,1,4,5,6]=>[3,1,1,1,1,1]
[7,2,8,6,1,3,4,5]=>[3,2,1,1,1]
[2,1,8,7,3,4,5,6]=>[3,2,1,1,1]
[8,2,7,6,1,3,4,5]=>[4,1,1,1,1]
[1,2,8,7,3,4,5,6]=>[3,1,1,1,1,1]
[1,3,8,7,2,4,5,6]=>[3,1,1,1,1,1]
[1,7,8,3,6,2,4,5]=>[3,1,1,1,1,1]
[4,1,5,8,7,2,3,6]=>[3,2,1,1,1]
[5,4,8,7,6,1,2,3]=>[4,2,1,1]
[6,8,3,7,5,1,2,4]=>[4,1,1,1,1]
[7,8,6,2,5,1,3,4]=>[4,1,1,1,1]
[8,1,6,7,3,2,5,4]=>[4,2,1,1]
[8,1,6,7,3,2,4,5]=>[4,1,1,1,1]
[8,1,5,3,7,2,4,6]=>[4,1,1,1,1]
[8,1,5,3,6,2,4,7]=>[4,1,1,1,1]
[7,5,1,3,6,2,4,8]=>[4,1,1,1,1]
[7,5,8,3,6,2,4,1]=>[5,1,1,1]
[7,4,8,3,2,6,5,1]=>[5,2,1]
[7,4,1,3,2,6,5,8]=>[4,2,1,1]
[8,1,4,3,2,6,5,7]=>[4,2,1,1]
[8,1,4,3,2,7,5,6]=>[4,2,1,1]
[8,1,4,3,2,7,6,5]=>[4,3,1]
[8,1,5,4,6,7,2,3]=>[4,1,1,1,1]
[8,1,5,3,6,2,7,4]=>[4,2,1,1]
[8,1,4,3,2,6,7,5]=>[4,2,1,1]
[8,1,4,3,2,5,7,6]=>[4,2,1,1]
[8,1,4,3,2,5,6,7]=>[4,1,1,1,1]
[7,4,1,3,2,5,6,8]=>[4,1,1,1,1]
[7,4,8,3,2,5,6,1]=>[5,1,1,1]
[6,4,3,8,2,5,7,1]=>[5,1,1,1]
[6,4,3,1,2,5,8,7]=>[4,2,1,1]
[7,4,1,3,2,5,8,6]=>[4,2,1,1]
[7,4,1,3,2,6,8,5]=>[4,2,1,1]
[7,5,1,3,6,2,8,4]=>[4,2,1,1]
[7,5,1,4,6,8,2,3]=>[4,1,1,1,1]
[7,5,8,3,6,2,1,4]=>[5,1,1,1]
[7,4,8,3,2,6,1,5]=>[5,1,1,1]
[7,4,8,3,2,5,1,6]=>[5,1,1,1]
[6,4,3,8,2,5,1,7]=>[5,1,1,1]
[6,4,3,7,2,5,8,1]=>[5,1,1,1]
[5,4,3,2,8,6,1,7]=>[5,2,1]
[5,4,3,2,8,7,1,6]=>[5,2,1]
[6,5,3,8,7,2,1,4]=>[5,2,1]
[6,5,4,8,7,1,2,3]=>[4,2,1,1]
[6,5,4,1,7,8,2,3]=>[4,2,1,1]
[6,5,3,1,7,2,8,4]=>[4,2,2]
[6,4,3,1,2,7,8,5]=>[4,2,1,1]
[5,4,3,2,1,8,6,7]=>[5,2,1]
[6,5,3,1,8,2,7,4]=>[4,3,1]
[6,5,4,1,8,7,2,3]=>[4,3,1]
[7,5,1,4,8,6,2,3]=>[4,2,1,1]
[7,4,1,3,2,8,6,5]=>[4,3,1]
[7,4,1,3,2,8,5,6]=>[4,2,1,1]
[6,4,3,1,2,8,5,7]=>[4,2,1,1]
[6,4,3,1,2,7,5,8]=>[4,2,1,1]
[6,4,3,8,2,7,5,1]=>[5,2,1]
[6,5,3,8,7,2,4,1]=>[5,2,1]
[6,5,3,1,7,2,4,8]=>[4,2,1,1]
[6,5,3,1,8,2,4,7]=>[4,2,1,1]
[7,5,1,3,8,2,4,6]=>[4,1,1,1,1]
[7,6,1,8,3,2,4,5]=>[4,2,1,1]
[7,6,1,8,4,5,2,3]=>[4,2,1,1]
[7,6,8,1,4,5,2,3]=>[4,1,1,1,1]
[7,6,8,1,3,2,5,4]=>[4,2,1,1]
[6,5,3,7,8,2,4,1]=>[5,1,1,1]
[6,4,3,7,2,8,5,1]=>[5,2,1]
[6,4,3,7,2,1,5,8]=>[5,1,1,1]
[7,4,8,3,2,1,5,6]=>[5,1,1,1]
[7,4,8,3,2,1,6,5]=>[5,2,1]
[7,5,8,3,1,2,6,4]=>[4,2,1,1]
[7,5,8,4,1,6,2,3]=>[4,2,1,1]
[6,5,4,8,1,7,2,3]=>[4,2,1,1]
[6,5,3,8,1,2,7,4]=>[4,2,1,1]
[5,4,3,2,8,1,7,6]=>[5,2,1]
[6,4,3,7,2,1,8,5]=>[5,2,1]
[6,5,3,7,1,2,8,4]=>[4,2,1,1]
[6,5,4,7,1,8,2,3]=>[4,2,1,1]
[6,5,3,7,8,2,1,4]=>[5,1,1,1]
[6,4,3,7,2,8,1,5]=>[5,1,1,1]
[5,4,3,2,7,8,1,6]=>[5,1,1,1]
[5,4,3,2,6,8,1,7]=>[5,1,1,1]
[5,6,2,1,3,4,8,7]=>[3,2,1,1,1]
[5,8,2,7,4,1,3,6]=>[4,1,1,1,1]
[5,3,7,8,2,1,4,6]=>[4,1,1,1,1]
[7,6,1,2,5,8,3,4]=>[4,1,1,1,1]
[2,1,7,8,4,3,5,6]=>[3,2,1,1,1]
[8,3,7,4,1,5,6,2]=>[4,2,1,1]
[7,8,1,2,5,4,6,3]=>[4,1,1,1,1]
[2,6,8,3,1,4,7,5]=>[3,2,1,1,1]
[6,1,8,3,2,4,5,7]=>[3,2,1,1,1]
[8,4,1,3,7,6,2,5]=>[4,2,1,1]
[5,8,7,4,2,1,6,3]=>[5,2,1]
[7,5,1,6,8,3,4,2]=>[4,2,1,1]
[6,5,2,1,8,7,4,3]=>[4,4]
[4,7,2,8,1,3,6,5]=>[3,2,1,1,1]
[7,3,8,6,1,2,5,4]=>[4,2,1,1]
[3,4,7,1,8,2,6,5]=>[3,2,1,1,1]
[1,8,2,4,3,5,6,7]=>[3,1,1,1,1,1]
[1,7,2,4,3,5,6,8]=>[3,1,1,1,1,1]
[1,6,2,4,3,5,7,8]=>[3,1,1,1,1,1]
[1,5,2,4,3,6,7,8]=>[3,1,1,1,1,1]
[1,6,2,5,3,4,7,8]=>[3,1,1,1,1,1]
[1,7,2,5,3,4,6,8]=>[3,1,1,1,1,1]
[1,8,2,5,3,4,6,7]=>[3,1,1,1,1,1]
[1,8,2,6,3,4,5,7]=>[3,1,1,1,1,1]
[1,7,2,6,3,4,5,8]=>[3,1,1,1,1,1]
[1,8,2,7,3,5,4,6]=>[4,1,1,1,1]
[1,7,2,8,3,5,4,6]=>[3,2,1,1,1]
[1,6,2,8,3,5,4,7]=>[3,2,1,1,1]
[1,5,2,8,3,6,4,7]=>[3,2,1,1,1]
[1,4,2,8,3,6,5,7]=>[3,2,1,1,1]
[1,3,2,8,4,6,5,7]=>[3,2,1,1,1]
[1,2,3,8,4,6,5,7]=>[3,1,1,1,1,1]
[1,2,3,7,4,6,5,8]=>[3,1,1,1,1,1]
[1,3,2,7,4,6,5,8]=>[3,2,1,1,1]
[1,4,2,7,3,6,5,8]=>[3,2,1,1,1]
[1,5,2,7,3,6,4,8]=>[3,2,1,1,1]
[1,6,2,7,3,5,4,8]=>[3,2,1,1,1]
[1,7,2,6,3,5,4,8]=>[4,1,1,1,1]
[1,8,2,6,3,5,4,7]=>[4,1,1,1,1]
[1,8,2,5,3,6,4,7]=>[3,2,1,1,1]
[1,7,2,5,3,6,4,8]=>[3,2,1,1,1]
[1,6,2,5,3,7,4,8]=>[3,2,1,1,1]
[1,5,2,4,3,7,6,8]=>[3,2,1,1,1]
[1,6,2,4,3,7,5,8]=>[3,2,1,1,1]
[1,7,2,4,3,6,5,8]=>[3,2,1,1,1]
[1,8,2,4,3,6,5,7]=>[3,2,1,1,1]
[1,8,2,3,4,6,5,7]=>[3,1,1,1,1,1]
[1,7,2,3,4,6,5,8]=>[3,1,1,1,1,1]
[1,8,2,3,4,7,5,6]=>[3,1,1,1,1,1]
[1,8,2,4,3,7,5,6]=>[3,2,1,1,1]
[1,7,2,4,3,8,5,6]=>[3,2,1,1,1]
[1,6,2,4,3,8,5,7]=>[3,2,1,1,1]
[1,5,2,4,3,8,6,7]=>[3,2,1,1,1]
[1,6,2,5,3,8,4,7]=>[3,2,1,1,1]
[1,7,2,5,3,8,4,6]=>[3,2,1,1,1]
[1,8,2,5,3,7,4,6]=>[3,2,1,1,1]
[1,8,2,6,3,7,4,5]=>[3,2,1,1,1]
[1,7,2,6,3,8,4,5]=>[3,2,1,1,1]
[1,2,3,8,4,7,5,6]=>[3,1,1,1,1,1]
[1,3,2,8,4,7,5,6]=>[3,2,1,1,1]
[1,4,2,8,3,7,5,6]=>[3,2,1,1,1]
[1,5,2,8,3,7,4,6]=>[3,2,1,1,1]
[1,6,2,8,3,7,4,5]=>[3,2,1,1,1]
[1,7,2,8,3,6,4,5]=>[3,2,1,1,1]
[1,8,2,7,3,6,4,5]=>[4,1,1,1,1]
[4,6,3,7,2,5,1,8]=>[4,1,1,1,1]
[4,6,3,7,5,2,1,8]=>[4,2,1,1]
[4,6,3,8,5,1,7,2]=>[3,2,2,1]
[4,6,3,8,5,1,2,7]=>[3,2,1,1,1]
[5,6,8,3,4,1,2,7]=>[3,1,1,1,1,1]
[5,6,8,3,4,1,7,2]=>[3,2,1,1,1]
[4,6,2,7,5,3,1,8]=>[4,2,1,1]
[5,6,7,2,4,3,1,8]=>[4,1,1,1,1]
[5,6,8,4,3,1,7,2]=>[4,2,1,1]
[5,6,8,4,3,1,2,7]=>[4,1,1,1,1]
[5,7,8,4,1,6,2,3]=>[3,2,1,1,1]
[5,7,8,4,1,6,3,2]=>[4,2,1,1]
[5,7,8,4,1,3,6,2]=>[4,1,1,1,1]
[5,6,8,4,2,1,7,3]=>[4,2,1,1]
[5,6,8,2,4,1,7,3]=>[3,2,1,1,1]
[4,6,2,8,5,1,7,3]=>[3,2,2,1]
[3,2,6,8,5,1,7,4]=>[3,2,2,1]
[3,2,6,8,5,1,4,7]=>[3,2,1,1,1]
[4,6,2,8,5,1,3,7]=>[3,2,1,1,1]
[5,6,8,2,4,1,3,7]=>[3,1,1,1,1,1]
[5,6,8,4,2,1,3,7]=>[4,1,1,1,1]
[5,7,8,4,1,3,2,6]=>[4,1,1,1,1]
[5,7,8,4,1,2,6,3]=>[3,2,1,1,1]
[5,7,8,4,1,2,3,6]=>[3,1,1,1,1,1]
[6,7,8,1,5,2,3,4]=>[3,1,1,1,1,1]
[6,7,8,1,5,2,4,3]=>[4,1,1,1,1]
[6,7,8,1,5,3,2,4]=>[4,1,1,1,1]
[6,7,8,1,3,5,2,4]=>[3,1,1,1,1,1]
[5,7,8,2,1,6,3,4]=>[3,2,1,1,1]
[4,7,2,8,1,6,3,5]=>[3,2,1,1,1]
[3,2,7,8,1,6,4,5]=>[3,2,1,1,1]
[3,2,7,8,1,6,5,4]=>[4,2,1,1]
[4,7,2,8,1,6,5,3]=>[4,2,1,1]
[5,7,8,2,1,6,4,3]=>[4,2,1,1]
[6,7,8,1,3,5,4,2]=>[4,1,1,1,1]
[6,7,8,1,5,3,4,2]=>[4,1,1,1,1]
[6,7,8,1,5,4,3,2]=>[5,1,1,1]
[6,7,8,1,5,4,2,3]=>[4,1,1,1,1]
[6,7,8,1,4,5,2,3]=>[3,1,1,1,1,1]
[6,7,8,1,4,5,3,2]=>[4,1,1,1,1]
[6,7,8,1,4,3,5,2]=>[4,1,1,1,1]
[6,7,8,1,3,4,5,2]=>[3,1,1,1,1,1]
[5,7,8,2,1,4,6,3]=>[3,2,1,1,1]
[4,7,2,8,1,5,6,3]=>[3,2,1,1,1]
[3,2,7,8,1,5,6,4]=>[3,2,1,1,1]
[3,2,6,8,4,1,7,5]=>[3,2,2,1]
[4,6,2,8,3,1,7,5]=>[3,2,2,1]
[5,6,8,3,2,1,7,4]=>[4,2,1,1]
[5,7,8,3,1,4,6,2]=>[3,2,1,1,1]
[5,7,8,3,1,6,4,2]=>[4,2,1,1]
[5,7,8,3,1,6,2,4]=>[3,2,1,1,1]
[4,7,3,8,1,6,2,5]=>[3,2,1,1,1]
[4,7,3,8,1,6,5,2]=>[4,2,1,1]
[4,7,3,8,1,5,6,2]=>[3,2,1,1,1]
[4,6,3,8,2,1,7,5]=>[4,2,1,1]
[4,5,3,2,8,1,7,6]=>[4,2,1,1]
[4,5,2,3,8,1,7,6]=>[3,2,1,1,1]
[3,2,5,4,8,1,7,6]=>[3,2,2,1]
[4,5,3,2,8,1,6,7]=>[4,1,1,1,1]
[4,6,3,8,2,1,5,7]=>[4,1,1,1,1]
[4,7,3,8,1,5,2,6]=>[3,2,1,1,1]
[4,7,3,8,1,2,6,5]=>[3,2,1,1,1]
[4,7,3,8,1,2,5,6]=>[3,1,1,1,1,1]
[5,7,8,3,1,2,4,6]=>[3,1,1,1,1,1]
[5,7,8,3,1,2,6,4]=>[3,2,1,1,1]
[5,7,8,3,1,4,2,6]=>[3,2,1,1,1]
[5,6,8,3,2,1,4,7]=>[4,1,1,1,1]
[3,2,7,8,1,5,4,6]=>[3,2,1,1,1]
[5,7,8,2,1,4,3,6]=>[3,2,1,1,1]
[6,7,8,1,3,4,2,5]=>[3,1,1,1,1,1]
[6,7,8,1,4,3,2,5]=>[4,1,1,1,1]
[6,7,8,1,4,2,5,3]=>[3,2,1,1,1]
[6,7,8,1,4,2,3,5]=>[3,1,1,1,1,1]
[6,7,8,1,2,5,3,4]=>[3,1,1,1,1,1]
[6,7,8,1,2,5,4,3]=>[4,1,1,1,1]
[6,7,8,1,2,4,5,3]=>[3,1,1,1,1,1]
[6,7,8,1,3,2,5,4]=>[3,2,1,1,1]
[5,7,8,2,1,3,6,4]=>[3,2,1,1,1]
[3,2,7,8,1,4,6,5]=>[3,2,1,1,1]
[6,7,8,1,3,2,4,5]=>[3,1,1,1,1,1]
[6,7,8,1,2,4,3,5]=>[3,1,1,1,1,1]
[6,7,8,1,2,3,5,4]=>[3,1,1,1,1,1]
[7,2,8,5,1,6,4,3]=>[4,2,2]
[1,3,7,5,2,6,4,8]=>[3,2,1,1,1]
[1,3,7,5,4,2,6,8]=>[4,1,1,1,1]
[7,2,8,5,4,1,6,3]=>[4,2,2]
[2,8,5,4,3,1,7,6]=>[5,2,1]
[2,8,4,5,6,1,7,3]=>[3,2,1,1,1]
[2,8,6,5,7,3,1,4]=>[5,1,1,1]
[2,8,4,5,3,7,1,6]=>[4,1,1,1,1]
[2,8,4,3,5,6,1,7]=>[4,1,1,1,1]
[7,2,8,4,5,6,1,3]=>[3,2,1,1,1]
[1,6,3,7,5,2,4,8]=>[3,2,1,1,1]
[6,2,3,8,5,1,7,4]=>[3,2,2,1]
[6,3,2,8,5,1,4,7]=>[4,2,1,1]
[7,4,8,2,5,6,3,1]=>[4,2,1,1]
[7,4,8,5,2,1,3,6]=>[4,2,1,1]
[6,4,8,5,1,3,7,2]=>[4,2,1,1]
[6,3,7,5,2,1,8,4]=>[4,2,2]
[4,3,7,5,1,2,8,6]=>[3,2,2,1]
[4,3,7,1,5,6,8,2]=>[3,2,1,1,1]
[3,6,1,7,5,2,8,4]=>[3,2,2,1]
[3,4,1,2,7,6,8,5]=>[3,2,1,1,1]
[3,4,2,1,7,5,8,6]=>[3,2,2,1]
[3,6,5,7,1,4,8,2]=>[4,1,1,1,1]
[6,5,2,7,4,1,8,3]=>[4,2,2]
[3,5,2,6,4,8,7,1]=>[3,2,2,1]
[5,3,1,8,6,4,7,2]=>[4,3,1]
[5,6,1,8,7,2,4,3]=>[4,2,1,1]
[6,3,5,8,2,7,4,1]=>[4,2,1,1]
[6,5,8,4,2,3,7,1]=>[5,1,1,1]
[6,2,5,8,3,7,1,4]=>[4,1,1,1,1]
[1,6,5,7,3,4,2,8]=>[4,1,1,1,1]
[1,5,2,7,4,6,3,8]=>[3,2,1,1,1]
[5,2,1,8,7,6,3,4]=>[4,3,1]
[7,1,3,8,4,6,2,5]=>[3,2,1,1,1]
[2,3,4,8,6,1,7,5]=>[3,2,1,1,1]
[2,3,4,8,6,5,1,7]=>[4,1,1,1,1]
[2,7,3,5,8,6,1,4]=>[3,2,1,1,1]
[3,2,4,7,8,6,1,5]=>[3,2,1,1,1]
[1,5,4,6,2,7,3,8]=>[3,2,1,1,1]
[5,2,4,7,1,8,3,6]=>[3,2,1,1,1]
[5,3,6,4,1,8,7,2]=>[3,3,2]
[5,3,6,1,4,8,2,7]=>[3,2,1,1,1]
[7,3,5,6,8,4,2,1]=>[5,1,1,1]
[6,3,5,1,8,2,7,4]=>[3,3,1,1]
[2,6,1,5,8,4,7,3]=>[4,1,1,1,1]
[2,7,6,5,8,3,4,1]=>[5,1,1,1]
[5,7,1,6,3,8,4,2]=>[4,2,1,1]
[3,2,4,1,7,8,5,6]=>[3,2,1,1,1]
[3,1,4,2,7,8,6,5]=>[3,2,2,1]
[5,1,4,7,2,8,6,3]=>[3,3,1,1]
[3,6,4,7,8,2,5,1]=>[4,1,1,1,1]
[3,1,4,6,8,5,7,2]=>[3,2,1,1,1]
[6,3,4,5,7,1,8,2]=>[3,2,1,1,1]
[2,5,4,6,1,7,8,3]=>[3,2,1,1,1]
[7,2,1,4,3,6,5,8]=>[3,2,2,1]
[7,3,4,1,2,6,5,8]=>[3,2,1,1,1]
[7,4,3,2,1,6,5,8]=>[5,2,1]
[7,6,3,2,5,4,1,8]=>[5,2,1]
[6,7,3,2,5,4,8,1]=>[4,2,1,1]
[1,8,3,2,5,4,7,6]=>[3,2,2,1]
[1,8,4,5,2,3,7,6]=>[3,2,1,1,1]
[7,3,5,1,6,2,4,8]=>[3,2,1,1,1]
[7,2,1,5,6,3,4,8]=>[3,2,1,1,1]
[7,2,1,6,5,4,3,8]=>[5,2,1]
[7,3,6,1,5,4,2,8]=>[5,1,1,1]
[7,4,6,5,1,3,2,8]=>[5,1,1,1]
[1,8,5,4,3,2,7,6]=>[5,2,1]
[1,8,6,4,3,7,2,5]=>[5,1,1,1]
[6,5,7,4,3,1,8,2]=>[5,2,1]
[6,4,7,5,1,3,8,2]=>[4,2,1,1]
[6,3,7,1,5,4,8,2]=>[4,2,1,1]
[6,2,1,7,5,4,8,3]=>[4,3,1]
[3,2,1,8,5,4,7,6]=>[3,3,2]
[2,3,8,1,5,4,7,6]=>[3,2,1,1,1]
[2,4,8,5,1,3,7,6]=>[3,2,1,1,1]
[2,5,8,4,3,1,7,6]=>[4,2,1,1]
[2,6,8,4,3,7,1,5]=>[4,1,1,1,1]
[2,7,8,4,3,6,5,1]=>[4,2,1,1]
[1,8,7,4,3,6,5,2]=>[5,2,1]
[1,8,7,5,6,3,4,2]=>[5,1,1,1]
[2,7,8,5,6,3,4,1]=>[4,1,1,1,1]
[2,6,8,5,7,3,1,4]=>[4,1,1,1,1]
[2,5,8,6,7,1,3,4]=>[3,1,1,1,1,1]
[2,4,8,6,1,7,3,5]=>[3,2,1,1,1]
[3,2,1,8,6,7,4,5]=>[3,3,1,1]
[5,2,1,7,6,8,4,3]=>[4,3,1]
[5,3,7,1,6,8,4,2]=>[4,2,1,1]
[5,4,7,6,1,8,3,2]=>[4,2,2]
[4,5,7,6,8,1,3,2]=>[4,1,1,1,1]
[4,6,7,5,8,3,1,2]=>[4,1,1,1,1]
[1,8,6,5,7,3,2,4]=>[5,1,1,1]
[1,8,5,6,7,2,3,4]=>[3,1,1,1,1,1]
[4,7,5,6,8,2,3,1]=>[4,1,1,1,1]
[4,6,5,7,8,2,1,3]=>[4,1,1,1,1]
[5,4,6,7,1,8,2,3]=>[3,2,1,1,1]
[5,3,6,1,7,8,2,4]=>[3,2,1,1,1]
[5,2,1,6,7,8,3,4]=>[3,2,1,1,1]
[6,2,1,5,7,3,8,4]=>[3,2,2,1]
[6,3,5,1,7,2,8,4]=>[3,2,2,1]
[6,4,5,7,1,2,8,3]=>[3,2,1,1,1]
[6,5,4,7,2,1,8,3]=>[5,2,1]
[5,6,4,7,2,8,1,3]=>[4,1,1,1,1]
[1,8,4,6,2,7,3,5]=>[3,2,1,1,1]
[1,8,3,2,6,7,4,5]=>[3,2,1,1,1]
[5,7,3,2,6,8,4,1]=>[4,2,1,1]
[5,6,3,2,7,8,1,4]=>[4,1,1,1,1]
[6,5,3,2,7,1,8,4]=>[5,2,1]
[6,4,3,2,1,7,8,5]=>[5,2,1]
[6,2,1,4,3,7,8,5]=>[3,2,2,1]
[5,2,1,4,3,8,7,6]=>[3,3,2]
[5,3,4,1,2,8,7,6]=>[3,3,1,1]
[4,6,3,2,8,7,1,5]=>[4,2,1,1]
[4,7,3,2,8,6,5,1]=>[4,3,1]
[1,8,3,2,7,6,5,4]=>[5,2,1]
[1,8,4,7,2,6,5,3]=>[5,1,1,1]
[3,7,4,8,2,6,5,1]=>[4,2,1,1]
[3,6,4,8,2,7,1,5]=>[4,1,1,1,1]
[3,5,4,8,2,1,7,6]=>[4,2,1,1]
[3,4,5,8,1,2,7,6]=>[3,1,1,1,1,1]
[4,3,5,1,8,2,7,6]=>[3,3,1,1]
[4,2,1,5,8,3,7,6]=>[3,3,1,1]
[4,2,1,6,8,7,3,5]=>[3,3,1,1]
[4,3,6,1,8,7,2,5]=>[3,3,1,1]
[3,4,6,8,1,7,2,5]=>[3,1,1,1,1,1]
[3,5,6,8,7,1,2,4]=>[3,1,1,1,1,1]
[3,6,5,8,7,2,1,4]=>[4,2,1,1]
[3,7,5,8,6,2,4,1]=>[4,2,1,1]
[1,8,5,7,6,2,4,3]=>[5,1,1,1]
[1,8,6,7,5,4,2,3]=>[5,1,1,1]
[3,6,7,8,5,4,1,2]=>[4,1,1,1,1]
[3,5,7,8,6,1,4,2]=>[4,1,1,1,1]
[3,4,7,8,1,6,5,2]=>[4,1,1,1,1]
[4,2,1,7,8,6,5,3]=>[4,3,1]
[2,3,8,1,7,6,5,4]=>[5,1,1,1]
[2,4,8,7,1,6,5,3]=>[5,1,1,1]
[2,5,8,7,6,1,4,3]=>[5,1,1,1]
[2,6,8,7,5,4,1,3]=>[5,1,1,1]
[7,4,6,1,8,3,5,2]=>[4,2,1,1]
[8,3,5,1,7,4,6,2]=>[4,2,1,1]
[8,3,4,1,7,5,6,2]=>[4,2,1,1]
[4,8,3,1,7,5,6,2]=>[4,2,1,1]
[4,6,2,1,7,5,8,3]=>[3,3,1,1]
[1,4,6,2,7,5,8,3]=>[3,2,1,1,1]
[1,7,5,2,6,8,4,3]=>[4,2,1,1]
[7,5,2,1,6,8,4,3]=>[4,3,1]
[6,8,4,3,1,7,5,2]=>[4,3,1]
[3,6,8,4,1,7,5,2]=>[4,2,1,1]
[3,6,7,5,1,8,4,2]=>[4,2,1,1]
[7,5,6,1,8,3,4,2]=>[4,2,1,1]
[3,4,6,5,7,1,8,2]=>[3,2,1,1,1]
[4,7,5,6,1,8,3,2]=>[4,2,1,1]
[6,7,5,1,8,4,3,2]=>[5,2,1]
[6,8,4,1,7,5,3,2]=>[5,2,1]
[6,7,5,3,1,8,4,2]=>[4,3,1]
[8,4,2,1,6,7,5,3]=>[4,3,1]
[1,8,4,2,6,7,5,3]=>[4,2,1,1]
[1,5,3,2,7,6,8,4]=>[3,3,1,1]
[5,3,2,1,7,6,8,4]=>[4,3,1]
[2,5,3,1,7,6,8,4]=>[3,3,1,1]
[2,8,4,1,6,7,5,3]=>[4,2,1,1]
[2,7,5,1,6,8,4,3]=>[4,2,1,1]
[2,4,6,1,7,5,8,3]=>[3,2,1,1,1]
[4,7,1,6,5,8,2,3]=>[4,1,1,1,1]
[4,8,2,6,5,7,1,3]=>[4,1,1,1,1]
[4,6,1,2,7,5,8,3]=>[3,2,1,1,1]
[7,5,1,2,6,8,4,3]=>[4,2,1,1]
[8,4,1,2,6,7,5,3]=>[4,2,1,1]
[5,3,1,2,7,6,8,4]=>[3,3,1,1]
[1,2,5,3,7,6,8,4]=>[3,2,1,1,1]
[4,3,1,2,7,6,8,5]=>[3,3,1,1]
[3,5,1,2,7,6,8,4]=>[3,2,1,1,1]
[6,7,1,5,8,2,3,4]=>[3,1,1,1,1,1]
[2,7,6,1,5,8,3,4]=>[4,1,1,1,1]
[2,3,5,1,7,6,8,4]=>[3,2,1,1,1]
[7,6,1,5,8,3,2,4]=>[5,1,1,1]
[3,6,7,1,5,8,2,4]=>[3,1,1,1,1,1]
[7,1,6,5,8,2,4,3]=>[5,1,1,1]
[7,5,1,6,8,4,2,3]=>[4,2,1,1]
[8,4,1,6,7,5,2,3]=>[4,2,1,1]
[5,2,3,1,7,6,8,4]=>[3,3,1,1]
[3,5,2,1,7,6,8,4]=>[3,3,1,1]
[1,3,5,2,7,6,8,4]=>[3,2,1,1,1]
[1,7,6,2,5,8,3,4]=>[4,1,1,1,1]
[7,6,2,1,5,8,3,4]=>[4,2,1,1]
[8,3,1,5,7,6,2,4]=>[4,2,1,1]
[6,2,4,1,7,5,8,3]=>[3,3,1,1]
[6,2,5,1,7,4,8,3]=>[4,2,1,1]
[7,1,6,4,8,2,5,3]=>[4,2,1,1]
[8,2,6,4,7,1,5,3]=>[4,2,1,1]
[6,1,5,2,7,4,8,3]=>[4,2,1,1]
[7,6,2,5,8,3,1,4]=>[5,1,1,1]
[8,3,5,7,6,2,1,4]=>[5,1,1,1]
[1,8,3,5,7,6,2,4]=>[4,1,1,1,1]
[1,5,2,3,7,6,8,4]=>[3,2,1,1,1]
[5,2,1,3,7,6,8,4]=>[3,3,1,1]
[7,5,2,6,8,4,1,3]=>[4,2,1,1]
[8,4,2,6,7,5,1,3]=>[4,2,1,1]
[6,1,4,2,7,5,8,3]=>[3,3,1,1]
[8,2,6,5,7,1,4,3]=>[5,1,1,1]
[3,6,8,2,5,7,1,4]=>[3,1,1,1,1,1]
[8,3,2,5,7,6,1,4]=>[4,2,1,1]
[5,1,3,2,7,6,8,4]=>[3,3,1,1]
[4,1,3,2,7,6,8,5]=>[3,3,1,1]
[4,2,1,3,7,6,8,5]=>[3,3,1,1]
[1,4,2,3,7,6,8,5]=>[3,2,1,1,1]
[2,4,1,3,7,6,8,5]=>[3,2,1,1,1]
[2,5,1,3,7,6,8,4]=>[3,2,1,1,1]
[2,8,3,5,7,6,1,4]=>[4,1,1,1,1]
[6,8,2,3,5,7,1,4]=>[3,1,1,1,1,1]
[6,7,1,3,5,8,2,4]=>[3,1,1,1,1,1]
[8,3,5,7,6,1,2,4]=>[4,1,1,1,1]
[5,1,2,3,7,6,8,4]=>[3,2,1,1,1]
[3,1,2,4,7,6,8,5]=>[3,2,1,1,1]
[8,1,2,4,3,6,5,7]=>[3,2,1,1,1]
[8,1,3,5,6,2,7,4]=>[3,2,1,1,1]
[8,1,3,4,2,6,7,5]=>[3,2,1,1,1]
[8,1,3,2,4,5,7,6]=>[3,2,1,1,1]
[2,7,8,3,4,5,6,1]=>[3,1,1,1,1,1]
[2,6,3,8,4,5,7,1]=>[3,2,1,1,1]
[6,3,2,1,4,5,8,7]=>[4,2,1,1]
[7,3,1,4,2,6,8,5]=>[3,2,2,1]
[7,4,1,5,6,8,2,3]=>[3,2,1,1,1]
[4,7,8,5,6,1,2,3]=>[3,1,1,1,1,1]
[3,7,8,5,6,2,1,4]=>[4,1,1,1,1]
[3,7,8,4,2,6,1,5]=>[4,1,1,1,1]
[3,7,8,2,4,5,1,6]=>[3,1,1,1,1,1]
[3,6,2,8,4,5,1,7]=>[3,2,1,1,1]
[2,3,6,7,4,5,8,1]=>[3,1,1,1,1,1]
[3,5,2,4,8,6,1,7]=>[3,2,1,1,1]
[3,5,4,2,8,7,1,6]=>[4,2,1,1]
[4,6,5,8,7,1,2,3]=>[3,2,1,1,1]
[6,4,5,1,7,8,2,3]=>[3,2,1,1,1]
[7,4,1,2,3,8,5,6]=>[3,2,1,1,1]
[6,2,4,1,3,7,5,8]=>[3,2,1,1,1]
[2,6,4,8,3,7,5,1]=>[4,2,1,1]
[2,6,5,8,7,3,4,1]=>[4,2,1,1]
[6,2,5,1,7,3,4,8]=>[3,2,1,1,1]
[6,5,2,1,8,3,4,7]=>[4,2,1,1]
[2,5,6,7,8,3,4,1]=>[3,1,1,1,1,1]
[2,4,6,7,3,8,5,1]=>[3,2,1,1,1]
[4,2,6,7,3,1,5,8]=>[3,2,1,1,1]
[4,7,8,2,3,1,5,6]=>[3,1,1,1,1,1]
[4,7,8,3,2,1,6,5]=>[4,2,1,1]
[5,6,4,8,1,7,2,3]=>[3,2,1,1,1]
[5,6,3,8,1,2,7,4]=>[3,2,1,1,1]
[4,2,5,3,7,1,6,8]=>[3,2,1,1,1]
[4,3,6,7,2,1,8,5]=>[4,2,1,1]
[3,4,6,7,2,8,1,5]=>[3,1,1,1,1,1]
[3,4,5,2,7,8,1,6]=>[3,1,1,1,1,1]
[3,4,2,5,6,8,1,7]=>[3,1,1,1,1,1]
[5,2,7,8,6,4,1,3]=>[4,2,1,1]
[5,1,2,7,8,6,4,3]=>[4,2,1,1]
[4,7,1,8,6,5,2,3]=>[4,2,1,1]
[4,7,1,2,8,6,5,3]=>[4,2,1,1]
[4,6,8,1,2,7,5,3]=>[4,1,1,1,1]
[6,8,7,1,5,3,2,4]=>[5,1,1,1]
[6,8,7,3,5,1,2,4]=>[4,1,1,1,1]
[7,8,1,6,3,5,2,4]=>[4,1,1,1,1]
[7,8,1,3,6,5,2,4]=>[4,1,1,1,1]
[7,8,3,6,5,2,1,4]=>[5,1,1,1]
[4,7,2,8,6,1,5,3]=>[4,2,1,1]
[1,7,3,4,8,6,5,2]=>[4,2,1,1]
[4,2,7,1,8,6,5,3]=>[4,3,1]
[7,8,2,3,6,5,1,4]=>[4,1,1,1,1]
[8,5,7,1,6,2,3,4]=>[4,1,1,1,1]
[8,5,7,1,2,6,3,4]=>[4,1,1,1,1]
[6,8,2,7,1,3,5,4]=>[4,1,1,1,1]
[6,8,7,2,5,3,1,4]=>[5,1,1,1]
[6,2,4,8,7,1,5,3]=>[4,2,1,1]
[1,6,8,3,7,4,5,2]=>[4,1,1,1,1]
[1,6,8,3,4,7,5,2]=>[4,1,1,1,1]
[6,2,4,8,1,7,5,3]=>[4,2,1,1]
[6,8,7,2,3,5,1,4]=>[4,1,1,1,1]
[6,8,2,1,7,3,5,4]=>[4,2,1,1]
[8,5,7,2,1,6,3,4]=>[4,2,1,1]
[8,5,7,1,2,3,6,4]=>[4,1,1,1,1]
[8,7,6,2,1,4,3,5]=>[5,2,1]
[8,5,7,2,3,1,6,4]=>[4,2,1,1]
[5,8,4,2,7,1,6,3]=>[4,2,1,1]
[1,8,7,5,3,4,6,2]=>[5,1,1,1]
[1,8,7,3,5,4,6,2]=>[5,1,1,1]
[8,2,5,4,7,1,6,3]=>[4,2,1,1]
[8,5,2,7,3,1,6,4]=>[4,2,2]
[8,7,6,2,4,3,1,5]=>[6,1,1]
[8,7,6,1,2,4,3,5]=>[5,1,1,1]
[8,7,6,1,4,2,3,5]=>[5,1,1,1]
[8,7,6,4,1,3,2,5]=>[6,1,1]
[5,8,4,7,2,1,6,3]=>[4,2,1,1]
[1,8,7,5,4,3,6,2]=>[6,1,1]
[1,6,8,4,3,7,5,2]=>[4,2,1,1]
[6,8,7,3,2,5,1,4]=>[5,1,1,1]
[6,8,1,7,3,2,5,4]=>[4,2,1,1]
[8,5,7,3,1,6,2,4]=>[4,2,1,1]
[8,5,7,1,3,2,6,4]=>[4,2,1,1]
[8,5,7,3,1,2,6,4]=>[4,2,1,1]
[5,8,4,7,1,2,6,3]=>[4,1,1,1,1]
[5,8,4,1,7,2,6,3]=>[4,2,1,1]
[5,8,4,7,1,6,2,3]=>[4,1,1,1,1]
[8,1,2,6,5,7,4,3]=>[5,1,1,1]
[8,2,5,6,7,4,1,3]=>[4,1,1,1,1]
[4,8,5,7,1,6,2,3]=>[4,1,1,1,1]
[4,8,5,7,1,2,6,3]=>[4,1,1,1,1]
[4,8,5,1,7,2,6,3]=>[4,2,1,1]
[8,5,3,1,7,2,6,4]=>[4,3,1]
[8,5,3,7,1,2,6,4]=>[4,2,1,1]
[6,8,1,3,7,2,5,4]=>[4,1,1,1,1]
[4,6,2,8,1,7,5,3]=>[4,2,1,1]
[1,6,4,8,3,7,5,2]=>[4,2,1,1]
[1,8,7,4,5,3,6,2]=>[5,1,1,1]
[4,8,5,7,2,1,6,3]=>[4,2,1,1]
[8,5,3,7,2,1,6,4]=>[5,2,1]
[8,7,6,3,1,4,2,5]=>[5,2,1]
[8,7,6,1,3,2,4,5]=>[5,1,1,1]
[8,5,3,2,7,1,6,4]=>[5,2,1]
[4,8,5,2,7,1,6,3]=>[4,2,1,1]
[1,8,7,4,3,5,6,2]=>[5,1,1,1]
[1,8,7,3,4,5,6,2]=>[4,1,1,1,1]
[8,2,4,5,7,1,6,3]=>[4,1,1,1,1]
[8,5,2,3,7,1,6,4]=>[4,2,1,1]
[6,3,1,5,4,2,8,7]=>[4,2,2]
[8,3,1,5,2,7,6,4]=>[4,2,2]
[8,5,4,2,1,7,3,6]=>[5,2,1]
[8,5,4,2,1,7,6,3]=>[5,3]
[6,5,4,2,1,3,8,7]=>[5,2,1]
[6,5,4,2,3,1,8,7]=>[5,2,1]
[6,3,2,5,1,4,8,7]=>[4,2,1,1]
[6,5,4,3,1,2,8,7]=>[5,2,1]
[6,5,4,1,3,2,8,7]=>[5,2,1]
[8,5,4,1,2,7,6,3]=>[4,3,1]
[8,7,4,1,6,3,2,5]=>[5,2,1]
[8,7,4,1,6,3,5,2]=>[5,2,1]
[8,7,4,1,6,5,3,2]=>[6,2]
[8,5,4,1,3,7,6,2]=>[5,2,1]
[8,5,4,3,1,7,6,2]=>[5,3]
[8,3,2,5,1,7,6,4]=>[4,3,1]
[2,1,8,5,3,7,6,4]=>[4,2,2]
[8,3,2,5,1,7,4,6]=>[4,2,1,1]
[8,5,4,3,1,7,2,6]=>[5,2,1]
[8,5,4,1,3,7,2,6]=>[5,1,1,1]
[8,7,4,1,6,5,2,3]=>[5,2,1]
[8,7,4,1,6,2,5,3]=>[5,2,1]
[8,7,6,5,2,1,4,3]=>[6,2]
[8,7,4,3,6,2,1,5]=>[6,1,1]
[8,3,2,7,6,4,1,5]=>[5,2,1]
[2,1,8,7,6,4,3,5]=>[5,2,1]
[2,1,8,7,6,4,5,3]=>[5,2,1]
[8,3,2,7,6,4,5,1]=>[5,2,1]
[8,7,4,3,6,2,5,1]=>[6,1,1]
[8,7,6,5,2,4,3,1]=>[7,1]
[8,5,4,2,3,7,6,1]=>[5,2,1]
[8,7,4,2,6,5,3,1]=>[6,2]
[8,7,4,2,6,3,5,1]=>[5,2,1]
[8,7,4,2,6,3,1,5]=>[5,2,1]
[8,3,1,7,6,4,2,5]=>[5,2,1]
[8,3,1,7,6,4,5,2]=>[5,2,1]
[8,3,1,7,6,5,4,2]=>[6,2]
[8,3,1,5,4,7,6,2]=>[4,2,2]
[8,3,1,5,4,7,2,6]=>[4,2,1,1]
[8,3,1,7,6,5,2,4]=>[5,2,1]
[8,3,1,7,6,2,5,4]=>[5,2,1]
[8,7,4,2,6,1,5,3]=>[5,2,1]
[8,7,4,2,6,5,1,3]=>[5,2,1]
[8,5,4,2,3,7,1,6]=>[5,1,1,1]
[8,3,2,5,4,7,1,6]=>[4,2,1,1]
[2,1,8,5,4,7,3,6]=>[4,2,1,1]
[8,3,2,7,6,5,1,4]=>[5,2,1]
[8,7,4,3,6,5,1,2]=>[5,2,1]
[8,7,6,5,3,1,4,2]=>[6,2]
[8,7,6,5,1,3,2,4]=>[6,1,1]
[8,7,6,5,1,3,4,2]=>[6,1,1]
[8,7,6,5,1,4,3,2]=>[7,1]
[8,7,6,5,4,1,3,2]=>[7,1]
[8,7,4,3,6,1,5,2]=>[5,2,1]
[8,3,2,7,6,1,5,4]=>[5,2,1]
[2,1,8,7,6,3,5,4]=>[5,2,1]
[8,3,2,7,6,1,4,5]=>[4,2,1,1]
[8,7,6,5,1,4,2,3]=>[6,1,1]
[8,7,6,5,1,2,4,3]=>[6,1,1]
[7,3,5,1,8,4,6,2]=>[4,2,1,1]
[7,3,4,1,8,5,6,2]=>[3,3,1,1]
[4,5,6,2,1,8,7,3]=>[3,3,1,1]
[1,6,5,2,7,4,3,8]=>[4,2,1,1]
[7,4,3,1,8,6,5,2]=>[4,4]
[7,6,5,1,8,4,3,2]=>[6,2]
[7,6,4,1,8,5,3,2]=>[5,3]
[6,4,2,1,8,7,5,3]=>[4,4]
[1,6,4,2,7,5,3,8]=>[3,3,1,1]
[1,5,3,2,7,6,4,8]=>[3,3,1,1]
[5,3,2,1,8,7,6,4]=>[4,4]
[2,5,3,1,7,8,6,4]=>[3,3,1,1]
[2,6,4,1,7,8,5,3]=>[3,3,1,1]
[2,6,5,1,7,8,4,3]=>[4,2,1,1]
[4,5,7,1,6,8,2,3]=>[3,1,1,1,1,1]
[6,5,1,2,8,4,3,7]=>[4,2,1,1]
[6,4,1,2,8,5,3,7]=>[3,3,1,1]
[5,3,1,2,8,6,4,7]=>[3,3,1,1]
[4,3,1,2,8,6,5,7]=>[3,3,1,1]
[6,1,2,5,8,3,4,7]=>[3,1,1,1,1,1]
[7,1,3,4,8,2,5,6]=>[3,1,1,1,1,1]
[7,1,5,6,8,2,3,4]=>[3,1,1,1,1,1]
[2,6,1,5,7,8,3,4]=>[3,1,1,1,1,1]
[7,4,1,6,8,5,2,3]=>[4,2,1,1]
[5,2,3,1,8,6,7,4]=>[3,3,1,1]
[3,5,2,1,6,8,7,4]=>[3,3,1,1]
[1,6,2,5,7,3,4,8]=>[3,1,1,1,1,1]
[6,2,1,5,8,7,3,4]=>[3,3,1,1]
[7,3,1,5,8,6,2,4]=>[3,3,1,1]
[6,2,4,1,8,5,7,3]=>[3,3,1,1]
[6,2,5,1,8,4,7,3]=>[4,2,1,1]
[7,3,1,4,8,6,2,5]=>[3,3,1,1]
[6,2,1,4,8,7,3,5]=>[3,3,1,1]
[1,6,2,4,7,3,5,8]=>[3,1,1,1,1,1]
[5,2,1,3,8,7,4,6]=>[3,3,1,1]
[7,4,1,3,8,5,2,6]=>[4,2,1,1]
[7,5,1,3,8,4,2,6]=>[4,2,1,1]
[3,6,7,1,4,8,2,5]=>[3,1,1,1,1,1]
[7,6,1,4,8,3,2,5]=>[5,1,1,1]
[4,2,1,3,8,7,5,6]=>[3,3,1,1]
[2,6,1,4,7,8,3,5]=>[3,1,1,1,1,1]
[7,1,4,6,8,2,3,5]=>[3,1,1,1,1,1]
[7,1,3,5,8,2,4,6]=>[3,1,1,1,1,1]
[6,1,2,4,8,3,5,7]=>[3,1,1,1,1,1]
[5,2,3,1,6,4,8,7]=>[3,2,2,1]
[7,4,5,2,3,1,8,6]=>[4,2,1,1]
[8,6,7,3,5,2,4,1]=>[5,1,1,1]
[7,3,5,2,4,1,8,6]=>[4,2,1,1]
[6,3,5,2,4,1,8,7]=>[4,2,1,1]
[5,2,4,1,6,3,8,7]=>[3,2,2,1]
[4,1,6,3,5,2,8,7]=>[3,2,2,1]
[6,3,4,1,5,2,8,7]=>[3,2,2,1]
[5,2,6,3,4,1,8,7]=>[3,2,2,1]
[5,2,7,3,4,1,8,6]=>[3,2,2,1]
[5,2,8,6,7,3,4,1]=>[4,2,1,1]
[6,2,8,5,7,3,4,1]=>[4,2,1,1]
[6,2,7,3,4,1,8,5]=>[3,2,2,1]
[7,3,4,1,5,2,8,6]=>[3,2,2,1]
[4,1,7,3,5,2,8,6]=>[3,2,2,1]
[3,1,7,4,5,2,8,6]=>[3,2,2,1]
[2,1,7,4,5,3,8,6]=>[3,2,2,1]
[3,1,8,6,7,4,5,2]=>[4,2,1,1]
[4,1,8,6,7,3,5,2]=>[4,2,1,1]
[8,6,7,3,4,1,5,2]=>[4,2,1,1]
[8,5,7,3,4,1,6,2]=>[4,2,1,1]
[8,5,6,2,7,3,4,1]=>[4,2,1,1]
[8,4,7,3,5,1,6,2]=>[4,2,1,1]
[5,1,8,4,7,3,6,2]=>[4,2,1,1]
[4,1,8,5,7,3,6,2]=>[4,2,1,1]
[3,1,8,5,7,4,6,2]=>[4,2,1,1]
[2,1,8,5,7,4,6,3]=>[4,2,1,1]
[2,1,7,4,6,3,8,5]=>[3,2,2,1]
[3,1,7,4,6,2,8,5]=>[3,2,2,1]
[4,1,7,3,6,2,8,5]=>[3,2,2,1]
[5,1,7,3,6,2,8,4]=>[3,2,2,1]
[6,2,7,3,5,1,8,4]=>[3,2,2,1]
[6,2,8,4,7,3,5,1]=>[4,2,1,1]
[8,4,7,3,6,2,5,1]=>[5,1,1,1]
[7,3,6,2,5,1,8,4]=>[4,2,1,1]
[6,2,5,1,7,3,8,4]=>[3,2,2,1]
[5,2,4,1,7,3,8,6]=>[3,2,2,1]
[6,2,4,1,7,3,8,5]=>[3,2,2,1]
[8,5,7,3,6,2,4,1]=>[5,1,1,1]
[8,5,7,4,6,2,3,1]=>[5,1,1,1]
[7,4,6,2,3,1,8,5]=>[4,2,1,1]
[6,2,3,1,7,4,8,5]=>[3,2,2,1]
[5,2,3,1,7,4,8,6]=>[3,2,2,1]
[4,2,3,1,7,5,8,6]=>[3,2,2,1]
[3,1,4,2,8,6,7,5]=>[3,2,2,1]
[6,2,3,1,8,5,7,4]=>[3,3,1,1]
[8,5,6,2,3,1,7,4]=>[4,2,1,1]
[7,4,8,5,6,2,3,1]=>[4,2,1,1]
[7,3,8,5,6,2,4,1]=>[4,2,1,1]
[8,5,6,2,4,1,7,3]=>[4,2,1,1]
[5,2,4,1,8,6,7,3]=>[3,3,1,1]
[4,1,5,2,8,6,7,3]=>[3,2,2,1]
[3,1,5,2,8,6,7,4]=>[3,2,2,1]
[2,1,6,3,8,5,7,4]=>[3,2,2,1]
[3,1,6,2,8,5,7,4]=>[3,2,2,1]
[4,1,6,2,8,5,7,3]=>[3,2,2,1]
[5,1,6,2,8,4,7,3]=>[3,2,2,1]
[8,4,6,2,5,1,7,3]=>[4,2,1,1]
[7,3,8,4,6,2,5,1]=>[4,2,1,1]
[6,2,7,3,8,4,5,1]=>[3,2,2,1]
[8,4,5,1,6,2,7,3]=>[3,2,2,1]
[5,1,8,4,6,2,7,3]=>[3,2,2,1]
[4,1,8,5,6,2,7,3]=>[3,2,2,1]
[3,1,8,5,6,2,7,4]=>[3,2,2,1]
[2,1,8,5,6,3,7,4]=>[3,2,2,1]
[2,1,7,4,8,5,6,3]=>[3,2,2,1]
[3,1,7,4,8,5,6,2]=>[3,2,2,1]
[4,1,7,3,8,5,6,2]=>[3,2,2,1]
[7,3,8,4,5,1,6,2]=>[3,2,2,1]
[8,4,5,1,7,3,6,2]=>[4,2,1,1]
[7,3,6,2,8,4,5,1]=>[4,2,1,1]
[7,8,5,6,1,3,4,2]=>[4,1,1,1,1]
[7,8,1,3,6,2,5,4]=>[4,1,1,1,1]
[1,3,8,4,7,2,5,6]=>[3,1,1,1,1,1]
[3,6,1,4,7,2,5,8]=>[3,1,1,1,1,1]
[4,6,1,2,5,7,3,8]=>[3,1,1,1,1,1]
[1,4,8,2,5,7,3,6]=>[3,1,1,1,1,1]
[7,8,2,4,5,6,1,3]=>[3,1,1,1,1,1]
[7,8,1,5,4,6,3,2]=>[5,1,1,1]
[7,8,2,1,6,3,4,5]=>[3,2,1,1,1]
[7,8,3,5,6,4,1,2]=>[4,1,1,1,1]
[7,8,1,4,2,3,6,5]=>[3,2,1,1,1]
[7,8,5,1,4,2,6,3]=>[4,2,1,1]
[7,8,4,5,3,1,6,2]=>[4,2,1,1]
[1,5,8,4,3,2,7,6]=>[4,2,1,1]
[5,6,1,4,3,2,7,8]=>[4,1,1,1,1]
[2,6,4,8,3,7,1,5]=>[4,1,1,1,1]
[1,4,6,8,3,7,5,2]=>[4,1,1,1,1]
[2,4,8,5,3,1,6,7]=>[4,1,1,1,1]
[2,5,8,1,4,7,6,3]=>[4,1,1,1,1]
[3,5,8,4,7,6,1,2]=>[4,1,1,1,1]
[1,6,2,4,7,3,8,5]=>[3,2,1,1,1]
[5,6,2,1,4,7,8,3]=>[3,2,1,1,1]
[4,6,2,5,3,1,8,7]=>[4,2,1,1]
[4,7,5,1,3,6,8,2]=>[4,1,1,1,1]
[7,5,3,6,2,4,1,8]=>[5,1,1,1]
[5,7,3,6,1,4,8,2]=>[4,1,1,1,1]
[5,3,6,7,2,1,8,4]=>[4,2,1,1]
[6,1,7,5,2,4,8,3]=>[4,2,1,1]
[6,3,1,2,4,5,8,7]=>[3,2,1,1,1]
[1,4,7,2,5,3,8,6]=>[3,2,1,1,1]
[4,6,7,8,3,5,1,2]=>[3,1,1,1,1,1]
[3,6,1,8,4,2,5,7]=>[3,2,1,1,1]
[1,6,7,5,8,2,4,3]=>[4,1,1,1,1]
[3,5,6,7,8,1,4,2]=>[3,1,1,1,1,1]
[3,6,5,7,8,2,1,4]=>[4,1,1,1,1]
[5,2,7,6,1,4,3,8]=>[4,2,1,1]
[2,5,7,6,8,1,3,4]=>[3,1,1,1,1,1]
[2,7,5,6,8,4,1,3]=>[4,1,1,1,1]
[2,1,6,8,4,5,3,7]=>[3,2,1,1,1]
[2,7,1,8,5,3,4,6]=>[3,2,1,1,1]
[3,7,6,8,5,4,1,2]=>[5,1,1,1]
[4,3,8,5,6,7,1,2]=>[3,2,1,1,1]
[4,2,8,1,6,3,7,5]=>[3,2,2,1]
[3,1,8,5,4,6,7,2]=>[4,2,1,1]
[3,2,8,4,5,6,1,7]=>[3,2,1,1,1]
[3,4,2,8,6,1,7,5]=>[3,2,2,1]
[3,4,7,1,5,2,6,8]=>[3,1,1,1,1,1]
[4,3,7,8,1,2,6,5]=>[3,2,1,1,1]
[1,7,3,8,5,2,6,4]=>[3,2,2,1]
[4,1,8,3,6,2,5,7]=>[3,2,1,1,1]
[5,7,8,6,3,2,1,4]=>[5,1,1,1]
[5,7,8,6,1,3,4,2]=>[4,1,1,1,1]
[7,6,5,8,1,3,4,2]=>[5,1,1,1]
[1,6,4,3,8,2,5,7]=>[4,1,1,1,1]
[7,1,3,4,8,2,6,5]=>[3,2,1,1,1]
[3,6,5,4,1,2,7,8]=>[4,1,1,1,1]
[2,4,5,1,7,8,6,3]=>[3,2,1,1,1]
[2,6,3,4,5,8,1,7]=>[3,1,1,1,1,1]
[2,6,4,1,8,3,7,5]=>[3,3,1,1]
[7,3,6,4,8,5,1,2]=>[4,2,1,1]
[7,2,1,4,8,3,5,6]=>[3,2,1,1,1]
[7,1,6,5,3,8,4,2]=>[5,2,1]
[7,2,5,6,3,8,1,4]=>[4,1,1,1,1]
[6,5,2,7,1,8,4,3]=>[4,3,1]
[5,6,2,7,3,1,4,8]=>[3,2,1,1,1]
[5,6,7,4,2,8,1,3]=>[4,1,1,1,1]
[5,7,6,4,1,8,3,2]=>[5,2,1]
[6,7,1,5,2,8,3,4]=>[3,2,1,1,1]
[1,7,5,2,4,8,3,6]=>[4,1,1,1,1]
[6,1,5,2,8,3,4,7]=>[3,2,1,1,1]
[6,7,5,3,8,4,1,2]=>[4,2,1,1]
[1,6,5,4,2,3,8,7]=>[4,2,1,1]
[7,1,5,3,4,2,8,6]=>[4,2,1,1]
[7,6,1,5,3,2,8,4]=>[5,2,1]
[7,5,6,4,1,2,8,3]=>[4,2,1,1]
[6,7,5,4,3,1,8,2]=>[5,2,1]
[7,5,2,4,3,1,6,8]=>[5,1,1,1]
[7,4,6,1,2,5,3,8]=>[4,1,1,1,1]
[7,1,4,2,5,3,6,8]=>[3,2,1,1,1]
[6,8,1,4,2,5,7,3]=>[3,2,1,1,1]
[1,6,4,2,5,7,3,8]=>[3,2,1,1,1]
[1,6,3,7,5,4,2,8]=>[4,2,1,1]
[6,8,1,3,7,5,4,2]=>[5,1,1,1]
[7,1,3,5,6,4,2,8]=>[4,1,1,1,1]
[7,3,1,6,4,5,2,8]=>[4,2,1,1]
[7,4,2,6,5,1,3,8]=>[4,2,1,1]
[7,4,6,3,1,5,2,8]=>[4,2,1,1]
[7,2,4,1,5,3,6,8]=>[3,2,1,1,1]
[7,2,3,5,4,1,6,8]=>[4,1,1,1,1]
[6,8,1,2,3,4,7,5]=>[3,1,1,1,1,1]
[1,5,7,2,3,8,6,4]=>[3,2,1,1,1]
[5,1,8,2,3,6,7,4]=>[3,2,1,1,1]
[5,8,2,3,7,6,4,1]=>[5,1,1,1]
[6,2,8,1,3,7,4,5]=>[3,2,1,1,1]
[6,8,2,3,5,4,7,1]=>[4,1,1,1,1]
[6,8,2,4,1,5,7,3]=>[3,2,1,1,1]
[6,8,3,1,2,4,7,5]=>[3,2,1,1,1]
[2,6,4,1,5,7,3,8]=>[3,2,1,1,1]
[2,6,3,5,7,1,4,8]=>[3,1,1,1,1,1]
[2,5,1,7,8,3,6,4]=>[3,2,1,1,1]
[2,5,3,6,8,4,7,1]=>[3,2,1,1,1]
[2,1,4,7,8,5,6,3]=>[3,2,1,1,1]
[2,4,7,6,8,5,1,3]=>[4,1,1,1,1]
[2,5,3,7,6,1,8,4]=>[3,2,2,1]
[2,5,7,8,1,4,6,3]=>[3,1,1,1,1,1]
[3,5,7,4,1,6,2,8]=>[3,2,1,1,1]
[5,3,4,1,8,6,7,2]=>[3,3,1,1]
[5,2,8,4,6,1,7,3]=>[3,2,2,1]
[5,2,1,8,6,3,7,4]=>[3,3,2]
[4,2,8,6,5,3,7,1]=>[5,2,1]
[4,2,8,5,7,6,3,1]=>[5,2,1]
[1,4,2,7,5,8,6,3]=>[3,2,2,1]
[4,1,8,6,7,5,3,2]=>[5,2,1]
[5,3,8,7,6,2,4,1]=>[5,2,1]
[5,8,4,7,6,2,1,3]=>[5,1,1,1]
[5,8,7,4,3,6,1,2]=>[5,1,1,1]
[6,4,8,3,1,7,2,5]=>[4,2,1,1]
[6,4,2,8,7,1,3,5]=>[4,2,1,1]
[6,3,8,7,2,5,1,4]=>[4,2,1,1]
[5,8,3,7,1,6,4,2]=>[5,1,1,1]
[5,1,3,8,6,7,2,4]=>[3,2,1,1,1]
[1,5,3,7,8,6,2,4]=>[3,2,1,1,1]
[1,5,7,6,4,2,8,3]=>[4,2,1,1]
[5,8,7,4,1,6,2,3]=>[4,2,1,1]
[6,4,8,1,2,7,3,5]=>[3,2,1,1,1]
[6,8,5,1,2,3,7,4]=>[3,2,1,1,1]
[6,8,5,2,4,3,7,1]=>[5,1,1,1]
[6,8,5,3,1,2,7,4]=>[4,2,1,1]
[4,5,1,2,7,6,3,8]=>[3,2,1,1,1]
[4,5,1,2,6,8,7,3]=>[3,2,1,1,1]
[3,5,6,1,8,4,7,2]=>[3,2,1,1,1]
[3,5,7,1,2,8,6,4]=>[3,2,1,1,1]
[3,6,2,7,5,1,4,8]=>[3,2,1,1,1]
[4,2,6,1,7,3,5,8]=>[3,2,1,1,1]
[4,6,3,1,2,7,5,8]=>[3,2,1,1,1]
[4,5,3,1,7,6,2,8]=>[3,3,1,1]
[4,2,5,7,1,6,3,8]=>[3,2,1,1,1]
[3,5,2,7,8,1,6,4]=>[3,2,1,1,1]
[3,1,4,7,5,6,2,8]=>[3,2,1,1,1]
[3,4,6,5,8,7,1,2]=>[3,2,1,1,1]
[3,1,4,5,8,6,7,2]=>[3,2,1,1,1]
[3,4,6,8,5,2,7,1]=>[4,1,1,1,1]
[3,5,6,2,8,4,7,1]=>[3,2,1,1,1]
[4,2,5,6,1,8,7,3]=>[3,3,1,1]
[4,5,3,1,6,8,7,2]=>[3,3,1,1]
[2,1,7,5,8,6,4,3]=>[4,2,2]
[1,2,7,5,3,8,6,4]=>[3,3,1,1]
[4,1,2,7,3,8,6,5]=>[3,2,2,1]
[6,4,1,7,5,2,3,8]=>[3,3,1,1]
[6,1,3,7,5,2,4,8]=>[3,2,1,1,1]
[3,1,2,6,8,5,4,7]=>[3,2,1,1,1]
[3,7,1,2,5,4,8,6]=>[3,2,1,1,1]
[1,3,7,2,4,8,6,5]=>[3,2,1,1,1]
[2,4,1,7,8,6,5,3]=>[4,2,1,1]
[3,4,7,5,1,8,6,2]=>[3,3,1,1]
[2,7,4,1,5,8,6,3]=>[3,3,1,1]
[2,3,7,1,5,8,6,4]=>[3,2,1,1,1]
[5,2,8,1,3,7,4,6]=>[3,2,1,1,1]
[2,1,6,8,3,4,7,5]=>[3,2,1,1,1]
[2,6,8,3,1,5,7,4]=>[3,2,1,1,1]
[2,8,6,4,1,5,7,3]=>[4,2,1,1]
[3,6,4,8,5,1,7,2]=>[3,2,2,1]
[6,3,7,4,5,1,8,2]=>[3,2,2,1]
[2,6,3,7,5,8,1,4]=>[3,2,1,1,1]
[5,2,1,7,8,3,4,6]=>[3,2,1,1,1]
[4,7,2,3,6,8,1,5]=>[3,1,1,1,1,1]
[5,2,7,3,6,8,1,4]=>[3,2,1,1,1]
[5,7,4,6,2,8,1,3]=>[4,1,1,1,1]
[5,7,3,4,6,1,8,2]=>[3,2,1,1,1]
[5,3,8,4,6,1,7,2]=>[3,2,2,1]
[8,5,2,4,1,6,7,3]=>[4,2,1,1]
[8,2,3,5,1,6,7,4]=>[3,2,1,1,1]
[4,2,8,3,6,7,1,5]=>[3,2,1,1,1]
[2,4,8,1,7,3,5,6]=>[3,1,1,1,1,1]
[8,4,1,3,6,2,5,7]=>[4,1,1,1,1]
[4,8,3,1,7,2,5,6]=>[3,2,1,1,1]
[5,2,8,4,7,1,6,3]=>[4,2,1,1]
[5,8,4,7,3,1,6,2]=>[4,2,1,1]
[4,6,8,3,1,7,5,2]=>[4,2,1,1]
[6,3,8,2,7,1,5,4]=>[4,2,1,1]
[6,3,1,8,2,4,7,5]=>[3,3,1,1]
[5,3,8,1,2,6,4,7]=>[3,2,1,1,1]
[5,7,4,1,6,2,3,8]=>[3,2,1,1,1]
[8,5,4,1,2,6,3,7]=>[4,2,1,1]
[5,1,8,4,2,7,3,6]=>[3,2,2,1]
[1,6,2,8,5,3,7,4]=>[3,2,2,1]
[6,8,5,3,1,7,4,2]=>[4,3,1]
[8,4,5,1,2,6,3,7]=>[3,2,1,1,1]
[5,6,3,7,1,2,4,8]=>[3,1,1,1,1,1]
[1,6,3,7,2,8,4,5]=>[3,2,1,1,1]
[6,3,2,7,8,5,1,4]=>[4,2,1,1]
[4,5,7,8,3,1,6,2]=>[3,2,1,1,1]
[4,7,2,5,8,1,6,3]=>[3,2,1,1,1]
[8,1,3,4,6,2,5,7]=>[3,1,1,1,1,1]
[3,8,2,4,6,7,1,5]=>[3,1,1,1,1,1]
[3,5,6,8,2,7,1,4]=>[3,1,1,1,1,1]
[2,4,5,6,8,1,7,3]=>[3,1,1,1,1,1]
[4,8,3,5,6,1,7,2]=>[3,2,1,1,1]
[5,6,2,3,7,8,1,4]=>[3,1,1,1,1,1]
[5,8,7,3,4,1,2,6]=>[4,1,1,1,1]
[6,8,7,3,4,1,2,5]=>[4,1,1,1,1]
[6,8,4,7,1,5,3,2]=>[5,1,1,1]
[6,8,4,7,2,5,3,1]=>[5,1,1,1]
[5,4,8,7,2,6,3,1]=>[5,2,1]
[5,4,8,7,1,6,3,2]=>[5,2,1]
[5,3,8,7,6,1,2,4]=>[4,2,1,1]
[4,3,8,7,6,1,2,5]=>[4,2,1,1]
[4,8,3,7,5,1,2,6]=>[4,1,1,1,1]
[8,3,4,6,5,1,2,7]=>[4,1,1,1,1]
[3,8,4,7,5,1,2,6]=>[4,1,1,1,1]
[3,4,8,7,6,1,2,5]=>[4,1,1,1,1]
[3,5,8,7,6,1,2,4]=>[4,1,1,1,1]
[4,5,8,7,6,1,2,3]=>[4,1,1,1,1]
[4,5,8,7,1,6,3,2]=>[5,1,1,1]
[4,5,8,7,2,6,3,1]=>[5,1,1,1]
[3,5,8,2,7,6,4,1]=>[5,1,1,1]
[3,5,8,1,7,6,4,2]=>[5,1,1,1]
[2,5,8,1,7,6,4,3]=>[5,1,1,1]
[2,5,8,7,1,6,3,4]=>[4,1,1,1,1]
[2,4,8,7,1,6,3,5]=>[4,1,1,1,1]
[2,8,4,7,1,5,3,6]=>[4,1,1,1,1]
[8,2,4,6,1,5,3,7]=>[4,1,1,1,1]
[8,1,4,6,2,5,3,7]=>[4,1,1,1,1]
[1,8,4,7,2,5,3,6]=>[4,1,1,1,1]
[1,4,8,7,2,6,3,5]=>[4,1,1,1,1]
[1,5,8,7,2,6,3,4]=>[4,1,1,1,1]
[1,5,8,2,7,6,4,3]=>[5,1,1,1]
[2,5,8,3,7,6,4,1]=>[5,1,1,1]
[1,4,2,8,7,6,5,3]=>[5,2,1]
[1,3,8,2,7,6,4,5]=>[4,1,1,1,1]
[1,8,3,2,7,5,4,6]=>[4,2,1,1]
[8,1,3,2,6,5,4,7]=>[4,2,1,1]
[8,2,3,1,6,5,4,7]=>[4,2,1,1]
[2,8,3,1,7,5,4,6]=>[4,2,1,1]
[2,3,8,1,7,6,4,5]=>[4,1,1,1,1]
[3,4,1,8,7,6,5,2]=>[5,2,1]
[4,3,1,8,7,6,5,2]=>[5,3]
[4,2,1,8,7,6,5,3]=>[5,3]
[3,8,2,1,7,5,4,6]=>[4,2,1,1]
[8,3,2,1,6,5,4,7]=>[4,3,1]
[8,4,2,6,1,5,3,7]=>[4,2,1,1]
[4,2,8,7,1,6,3,5]=>[4,2,1,1]
[5,2,8,7,1,6,3,4]=>[4,2,1,1]
[5,2,8,1,7,6,4,3]=>[5,2,1]
[5,3,8,1,7,6,4,2]=>[5,2,1]
[5,3,8,2,7,6,4,1]=>[5,2,1]
[6,8,3,2,7,5,4,1]=>[5,2,1]
[6,8,3,1,7,5,4,2]=>[5,2,1]
[6,8,2,1,7,5,4,3]=>[5,2,1]
[6,8,2,7,1,5,3,4]=>[4,1,1,1,1]
[6,8,7,2,1,4,3,5]=>[4,2,1,1]
[8,5,6,1,2,4,3,7]=>[4,1,1,1,1]
[5,8,7,1,2,4,3,6]=>[4,1,1,1,1]
[6,8,1,2,7,5,4,3]=>[5,1,1,1]
[6,8,2,3,7,5,4,1]=>[5,1,1,1]
[5,2,8,3,7,6,4,1]=>[5,2,1]
[5,1,8,3,7,6,4,2]=>[5,2,1]
[5,1,8,7,2,6,3,4]=>[4,2,1,1]
[4,1,8,7,2,6,3,5]=>[4,2,1,1]
[4,8,1,7,2,5,3,6]=>[4,1,1,1,1]
[8,4,1,6,2,5,3,7]=>[4,2,1,1]
[8,3,1,2,6,5,4,7]=>[4,2,1,1]
[3,8,1,2,7,5,4,6]=>[4,1,1,1,1]
[3,1,8,2,7,6,4,5]=>[4,2,1,1]
[3,1,2,8,7,6,5,4]=>[5,2,1]
[4,1,3,8,7,6,5,2]=>[5,2,1]
[3,1,4,8,7,6,5,2]=>[5,2,1]
[2,1,8,3,7,6,4,5]=>[4,2,1,1]
[2,8,1,3,7,5,4,6]=>[4,1,1,1,1]
[8,2,1,3,6,5,4,7]=>[4,2,1,1]
[8,1,2,3,6,5,4,7]=>[4,1,1,1,1]
[1,8,2,3,7,5,4,6]=>[4,1,1,1,1]
[1,2,8,3,7,6,4,5]=>[4,1,1,1,1]
[1,4,3,6,8,2,5,7]=>[3,1,1,1,1,1]
[3,1,6,2,5,8,4,7]=>[3,2,1,1,1]
[3,5,1,8,2,4,7,6]=>[3,2,1,1,1]
[1,4,5,2,8,3,7,6]=>[3,2,1,1,1]
[1,4,2,6,5,8,3,7]=>[3,2,1,1,1]
[1,5,4,2,6,8,3,7]=>[3,2,1,1,1]
[3,1,6,5,8,2,4,7]=>[3,2,1,1,1]
[1,6,4,2,5,8,3,7]=>[3,2,1,1,1]
[1,5,2,6,4,8,3,7]=>[3,2,1,1,1]
[1,2,6,5,4,8,3,7]=>[4,1,1,1,1]
[1,2,5,4,7,3,8,6]=>[3,2,1,1,1]
[4,1,2,6,3,8,7,5]=>[3,2,2,1]
[7,1,5,4,2,8,3,6]=>[4,2,1,1]
[1,4,7,5,2,8,3,6]=>[3,2,1,1,1]
[7,1,3,5,2,8,4,6]=>[3,2,1,1,1]
[7,2,5,1,8,3,4,6]=>[3,2,1,1,1]
[1,4,5,2,8,7,3,6]=>[3,2,1,1,1]
[1,6,4,2,8,3,7,5]=>[3,3,1,1]
[1,4,2,8,3,7,6,5]=>[4,2,1,1]
[1,2,5,3,8,7,6,4]=>[4,2,1,1]
[1,2,8,6,5,3,7,4]=>[4,2,1,1]
[1,5,2,8,6,3,7,4]=>[3,2,2,1]
[1,6,4,2,8,7,3,5]=>[3,3,1,1]
[6,2,1,8,7,3,4,5]=>[3,3,1,1]
[7,6,2,1,8,3,4,5]=>[4,2,1,1]
[7,3,1,6,2,8,4,5]=>[3,2,2,1]
[1,7,6,4,2,8,3,5]=>[4,2,1,1]
[1,7,5,2,6,3,8,4]=>[3,2,2,1]
[1,6,2,7,5,3,8,4]=>[3,2,2,1]
[1,2,7,6,5,3,8,4]=>[4,2,1,1]
[1,2,6,5,3,8,7,4]=>[3,3,1,1]
[1,5,2,6,3,8,7,4]=>[3,2,2,1]
[1,5,2,7,6,3,8,4]=>[3,2,2,1]
[1,6,5,2,7,3,8,4]=>[3,2,2,1]
[1,5,7,4,2,8,3,6]=>[3,2,1,1,1]
[4,1,2,8,6,3,7,5]=>[3,2,2,1]
[3,1,8,6,2,4,7,5]=>[3,2,2,1]
[4,3,7,1,8,2,5,6]=>[3,2,1,1,1]
[8,3,1,6,2,4,7,5]=>[3,2,2,1]
[7,1,8,3,2,4,6,5]=>[3,2,2,1]
[1,8,7,3,2,4,6,5]=>[4,2,1,1]
[1,4,2,8,7,3,6,5]=>[4,2,1,1]
[1,7,4,2,8,3,6,5]=>[3,3,1,1]
[8,1,5,4,2,7,3,6]=>[4,2,1,1]
[1,4,8,5,2,7,3,6]=>[3,2,1,1,1]
[8,5,3,1,7,2,4,6]=>[4,2,1,1]
[8,6,2,1,7,3,4,5]=>[4,2,1,1]
[1,8,6,4,2,7,3,5]=>[4,2,1,1]
[1,8,5,2,6,3,7,4]=>[3,2,2,1]
[1,5,2,7,3,8,6,4]=>[3,2,2,1]
[1,2,8,5,3,7,6,4]=>[4,2,1,1]
[1,2,6,3,8,7,5,4]=>[4,2,1,1]
[1,2,7,6,3,8,5,4]=>[4,2,1,1]
[1,6,2,7,3,8,5,4]=>[3,2,2,1]
[1,7,2,8,5,3,6,4]=>[3,2,2,1]
[1,7,4,2,8,6,3,5]=>[3,3,1,1]
[7,1,8,3,2,6,4,5]=>[3,2,2,1]
[7,2,1,8,6,3,4,5]=>[3,3,1,1]
[1,8,7,3,2,6,4,5]=>[4,2,1,1]
[1,4,2,8,7,6,3,5]=>[4,2,1,1]
[1,2,8,7,5,3,6,4]=>[4,2,1,1]
[1,2,8,6,3,7,5,4]=>[4,2,1,1]
[1,2,7,3,8,6,5,4]=>[4,2,1,1]
[4,1,7,3,6,5,8,2]=>[4,2,1,1]
[5,1,8,7,6,2,4,3]=>[5,2,1]
[8,1,7,6,3,4,5,2]=>[5,1,1,1]
[5,7,8,6,2,4,1,3]=>[4,1,1,1,1]
[5,7,1,6,2,4,3,8]=>[4,1,1,1,1]
[6,4,1,5,2,7,3,8]=>[3,2,2,1]
[8,1,4,5,3,7,6,2]=>[4,2,1,1]
[6,1,4,5,3,8,7,2]=>[4,2,1,1]
[6,1,4,5,3,7,8,2]=>[4,1,1,1,1]
[5,1,7,8,6,2,4,3]=>[4,2,1,1]
[6,1,4,8,3,5,7,2]=>[4,1,1,1,1]
[7,1,8,6,3,4,5,2]=>[4,2,1,1]
[7,1,4,5,3,8,6,2]=>[4,2,1,1]
[7,1,4,5,3,6,8,2]=>[4,1,1,1,1]
[8,1,4,5,3,6,7,2]=>[4,1,1,1,1]
[7,4,1,5,2,6,3,8]=>[3,2,2,1]
[6,3,5,7,2,1,4,8]=>[4,1,1,1,1]
[6,3,5,8,2,1,7,4]=>[4,2,1,1]
[6,3,5,7,2,1,8,4]=>[4,2,1,1]
[8,4,5,7,3,6,1,2]=>[4,1,1,1,1]
[6,4,5,8,3,7,2,1]=>[5,1,1,1]
[5,8,7,6,2,4,1,3]=>[5,1,1,1]
[5,4,8,6,3,1,7,2]=>[4,2,2]
[5,4,1,8,2,3,7,6]=>[3,3,1,1]
[5,8,1,6,2,4,3,7]=>[4,1,1,1,1]
[8,4,1,5,2,6,3,7]=>[3,2,2,1]
[6,3,5,8,2,1,4,7]=>[4,1,1,1,1]
[2,3,4,1,8,6,5,7]=>[3,2,1,1,1]
[8,3,5,6,2,1,4,7]=>[4,1,1,1,1]
[2,3,8,5,1,4,7,6]=>[3,2,1,1,1]
[2,3,8,6,1,5,7,4]=>[4,1,1,1,1]
[2,8,6,7,1,3,5,4]=>[4,1,1,1,1]
[8,3,5,7,2,1,6,4]=>[4,2,1,1]
[2,3,8,5,6,1,7,4]=>[3,2,1,1,1]
[7,4,5,6,3,1,8,2]=>[4,2,1,1]
[8,4,5,6,3,1,7,2]=>[4,2,1,1]
[7,3,5,6,2,8,1,4]=>[4,1,1,1,1]
[7,3,5,8,2,1,6,4]=>[4,2,1,1]
[7,3,5,6,2,1,4,8]=>[4,1,1,1,1]
[2,7,6,5,1,3,4,8]=>[4,1,1,1,1]
[2,7,6,8,1,3,5,4]=>[4,1,1,1,1]
[2,7,6,5,8,3,1,4]=>[5,1,1,1]
[8,7,5,6,1,4,2,3]=>[5,1,1,1]
[2,6,4,1,8,5,7,3]=>[3,3,1,1]
[2,6,1,3,8,5,7,4]=>[3,2,1,1,1]
[2,7,1,3,6,5,8,4]=>[4,1,1,1,1]
[2,7,6,8,4,3,1,5]=>[5,1,1,1]
[2,7,6,1,8,3,4,5]=>[3,2,1,1,1]
[2,7,6,1,4,3,5,8]=>[4,1,1,1,1]
[7,3,5,1,2,8,4,6]=>[3,2,1,1,1]
[8,4,1,5,2,3,7,6]=>[3,2,2,1]
[7,8,1,6,3,4,2,5]=>[4,1,1,1,1]
[6,4,1,8,3,2,7,5]=>[4,2,2]
[2,3,8,6,4,1,7,5]=>[4,2,1,1]
[2,8,6,7,4,3,1,5]=>[5,1,1,1]
[8,3,5,7,2,4,1,6]=>[4,1,1,1,1]
[2,3,4,1,8,7,5,6]=>[3,2,1,1,1]
[2,8,6,1,7,3,4,5]=>[3,2,1,1,1]
[2,3,8,1,6,4,7,5]=>[3,2,1,1,1]
[2,3,8,1,4,5,7,6]=>[3,1,1,1,1,1]
[2,8,6,1,4,3,5,7]=>[4,1,1,1,1]
[8,4,3,6,5,1,7,2]=>[4,2,2]
[8,5,6,3,4,1,7,2]=>[4,2,1,1]
[8,6,5,4,3,1,7,2]=>[6,2]
[1,7,6,5,4,2,3,8]=>[5,1,1,1]
[1,8,6,5,2,7,3,4]=>[4,2,1,1]
[8,7,5,4,1,6,3,2]=>[6,2]
[7,8,5,4,1,3,6,2]=>[5,1,1,1]
[6,8,5,4,2,1,7,3]=>[5,2,1]
[5,8,6,2,4,1,7,3]=>[4,2,1,1]
[4,8,2,6,5,1,7,3]=>[4,2,1,1]
[3,2,8,6,5,1,7,4]=>[4,2,2]
[3,2,1,7,6,4,5,8]=>[3,3,1,1]
[4,1,3,7,6,2,5,8]=>[3,2,1,1,1]
[5,1,7,3,6,2,4,8]=>[3,2,1,1,1]
[6,1,7,5,3,2,4,8]=>[4,2,1,1]
[7,1,6,5,2,4,3,8]=>[5,1,1,1]
[8,1,6,5,2,3,7,4]=>[4,2,1,1]
[1,2,7,6,3,4,5,8]=>[3,1,1,1,1,1]
[1,2,8,3,7,4,5,6]=>[3,1,1,1,1,1]
[8,1,7,2,6,3,5,4]=>[5,1,1,1]
[7,1,8,2,6,4,3,5]=>[4,2,1,1]
[6,1,8,2,4,7,3,5]=>[3,2,1,1,1]
[5,1,8,3,2,7,4,6]=>[3,2,2,1]
[4,1,3,8,2,7,5,6]=>[3,2,1,1,1]
[3,2,1,8,4,7,5,6]=>[3,3,1,1]
[3,2,8,7,1,6,5,4]=>[5,2,1]
[4,8,2,7,1,6,5,3]=>[5,1,1,1]
[5,8,7,2,1,6,4,3]=>[5,2,1]
[6,8,7,1,3,5,4,2]=>[5,1,1,1]
[7,8,6,1,5,3,4,2]=>[5,1,1,1]
[8,7,6,1,5,4,3,2]=>[7,1]
[1,8,7,2,6,5,3,4]=>[5,1,1,1]
[1,7,8,2,5,6,3,4]=>[3,1,1,1,1,1]
[8,6,7,1,4,5,3,2]=>[5,1,1,1]
[7,6,8,1,4,3,5,2]=>[5,1,1,1]
[6,5,8,3,2,1,7,4]=>[5,2,1]
[7,5,8,3,1,4,6,2]=>[4,2,1,1]
[8,5,7,3,1,6,4,2]=>[5,2,1]
[1,6,8,4,2,7,3,5]=>[3,2,1,1,1]
[1,5,4,8,2,7,3,6]=>[3,2,1,1,1]
[8,4,3,7,1,6,5,2]=>[5,2,1]
[7,4,3,8,1,5,6,2]=>[4,2,1,1]
[6,4,3,1,5,2,7,8]=>[4,2,1,1]
[7,4,3,1,2,6,5,8]=>[4,2,1,1]
[8,4,3,1,2,5,7,6]=>[4,2,1,1]
[1,5,4,2,3,6,7,8]=>[3,1,1,1,1,1]
[8,5,1,4,2,3,7,6]=>[4,2,1,1]
[7,5,1,4,2,6,3,8]=>[4,2,1,1]
[6,5,1,4,3,2,7,8]=>[5,1,1,1]
[5,6,1,3,4,2,7,8]=>[3,1,1,1,1,1]
[4,6,2,1,5,3,7,8]=>[3,2,1,1,1]
[3,2,6,1,5,4,7,8]=>[3,2,1,1,1]
[3,2,7,1,4,6,5,8]=>[3,2,1,1,1]
[4,7,2,1,3,6,5,8]=>[3,2,1,1,1]
[5,7,1,3,2,6,4,8]=>[3,2,1,1,1]
[6,7,1,2,4,5,3,8]=>[3,1,1,1,1,1]
[7,6,1,2,5,4,3,8]=>[5,1,1,1]
[8,6,1,2,5,3,7,4]=>[4,2,1,1]
[1,7,2,3,6,4,5,8]=>[3,1,1,1,1,1]
[8,7,1,2,3,6,5,4]=>[5,1,1,1]
[7,8,1,2,3,5,6,4]=>[3,1,1,1,1,1]
[6,8,1,2,4,3,7,5]=>[3,2,1,1,1]
[5,8,1,3,2,4,7,6]=>[3,2,1,1,1]
[4,8,2,1,3,5,7,6]=>[3,2,1,1,1]
[3,2,8,1,4,5,7,6]=>[3,2,1,1,1]
[4,1,3,2,5,6,7,8]=>[3,1,1,1,1,1]
[5,1,2,4,3,6,7,8]=>[3,1,1,1,1,1]
[6,1,2,3,5,4,7,8]=>[3,1,1,1,1,1]
[7,1,2,3,4,6,5,8]=>[3,1,1,1,1,1]
[8,1,2,3,4,5,7,6]=>[3,1,1,1,1,1]
[6,7,3,8,5,1,2,4]=>[3,2,1,1,1]
[6,7,4,5,1,8,3,2]=>[4,2,1,1]
[5,4,7,6,8,1,2,3]=>[3,2,1,1,1]
[5,3,7,8,6,1,2,4]=>[3,2,1,1,1]
[3,8,4,5,7,1,2,6]=>[3,1,1,1,1,1]
[3,4,8,6,7,1,2,5]=>[3,1,1,1,1,1]
[4,5,6,7,1,8,3,2]=>[3,2,1,1,1]
[3,5,6,2,7,4,8,1]=>[3,2,1,1,1]
[3,5,6,1,7,8,4,2]=>[3,2,1,1,1]
[2,5,6,1,8,7,4,3]=>[4,2,1,1]
[2,5,6,8,1,7,3,4]=>[3,1,1,1,1,1]
[8,2,4,5,1,6,3,7]=>[3,2,1,1,1]
[1,4,8,6,2,3,7,5]=>[3,2,1,1,1]
[1,5,6,8,2,3,7,4]=>[3,1,1,1,1,1]
[1,5,6,2,8,4,7,3]=>[3,2,1,1,1]
[2,5,6,3,4,7,8,1]=>[3,1,1,1,1,1]
[1,4,2,6,8,5,7,3]=>[3,2,1,1,1]
[8,1,3,2,5,4,6,7]=>[3,2,1,1,1]
[8,2,3,1,5,6,4,7]=>[3,2,1,1,1]
[2,8,3,1,5,7,4,6]=>[3,2,1,1,1]
[2,4,1,6,8,7,5,3]=>[4,2,1,1]
[3,4,1,6,7,8,5,2]=>[3,2,1,1,1]
[4,3,1,7,6,8,5,2]=>[4,3,1]
[5,2,7,8,1,6,3,4]=>[3,2,1,1,1]
[5,3,7,2,6,4,8,1]=>[4,2,1,1]
[6,7,3,1,5,8,4,2]=>[4,2,1,1]
[6,7,2,1,8,5,4,3]=>[4,3,1]
[6,7,2,8,1,5,3,4]=>[3,2,1,1,1]
[6,7,8,2,1,4,3,5]=>[3,2,1,1,1]
[6,7,1,2,8,4,5,3]=>[3,2,1,1,1]
[6,7,1,3,4,8,5,2]=>[3,2,1,1,1]
[5,2,7,3,4,6,8,1]=>[3,2,1,1,1]
[5,1,7,3,4,8,6,2]=>[3,2,2,1]
[5,1,7,8,2,3,6,4]=>[3,2,1,1,1]
[4,1,8,7,2,3,6,5]=>[4,2,1,1]
[3,8,1,2,7,4,5,6]=>[3,1,1,1,1,1]
[4,1,3,7,5,8,6,2]=>[3,2,2,1]
[3,1,4,5,7,8,6,2]=>[3,2,1,1,1]
[2,1,8,3,4,7,6,5]=>[4,2,1,1]
[8,2,1,3,4,6,5,7]=>[3,2,1,1,1]
[1,8,2,3,4,5,7,6]=>[3,1,1,1,1,1]
[1,2,8,3,4,6,7,5]=>[3,1,1,1,1,1]
[4,2,1,6,5,8,7,3]=>[3,3,2]
[5,2,6,1,4,8,7,3]=>[3,3,1,1]
[5,2,6,4,1,8,7,3]=>[3,3,2]
[5,2,7,4,8,1,6,3]=>[3,2,2,1]
[5,2,7,4,8,6,1,3]=>[3,2,2,1]
[5,7,2,3,8,6,1,4]=>[3,2,1,1,1]
[5,7,2,3,8,1,6,4]=>[3,2,1,1,1]
[5,6,2,3,1,8,7,4]=>[3,3,1,1]
[5,6,2,1,3,8,7,4]=>[3,3,1,1]
[5,1,6,4,2,8,7,3]=>[3,3,2]
[5,6,1,3,2,8,7,4]=>[3,3,1,1]
[5,6,3,1,2,8,7,4]=>[3,3,1,1]
[5,6,3,2,1,8,7,4]=>[4,3,1]
[5,7,3,2,8,1,6,4]=>[4,2,1,1]
[5,7,3,2,8,6,1,4]=>[4,2,1,1]
[6,7,3,8,2,1,5,4]=>[4,2,1,1]
[6,7,3,8,1,2,5,4]=>[3,2,1,1,1]
[5,7,3,1,8,2,6,4]=>[3,3,1,1]
[5,7,1,3,8,2,6,4]=>[3,2,1,1,1]
[5,1,7,4,8,2,6,3]=>[3,2,2,1]
[1,5,7,4,8,3,6,2]=>[4,1,1,1,1]
[1,5,7,4,8,6,3,2]=>[4,2,1,1]
[5,1,7,4,8,6,2,3]=>[3,2,2,1]
[5,7,1,3,8,6,2,4]=>[3,2,1,1,1]
[5,7,3,1,8,6,2,4]=>[3,3,1,1]
[6,7,3,8,1,5,2,4]=>[3,2,1,1,1]
[6,7,3,8,5,2,1,4]=>[4,2,1,1]
[6,7,8,3,1,4,2,5]=>[3,2,1,1,1]
[6,7,1,8,3,5,2,4]=>[3,2,1,1,1]
[6,1,7,8,4,5,2,3]=>[3,2,1,1,1]
[1,6,7,8,4,5,3,2]=>[4,1,1,1,1]
[1,6,7,8,4,3,5,2]=>[4,1,1,1,1]
[6,1,7,8,4,2,5,3]=>[3,2,2,1]
[6,7,1,8,3,2,5,4]=>[3,2,2,1]
[5,7,2,1,8,3,6,4]=>[3,3,1,1]
[6,7,2,8,1,3,5,4]=>[3,2,1,1,1]
[6,7,2,8,3,1,5,4]=>[3,2,2,1]
[6,7,2,8,3,5,1,4]=>[3,2,1,1,1]
[6,2,7,8,4,5,1,3]=>[3,2,1,1,1]
[6,2,7,8,4,1,5,3]=>[3,2,2,1]
[6,2,7,8,1,4,5,3]=>[3,2,1,1,1]
[5,2,7,1,8,4,6,3]=>[3,3,1,1]
[4,2,1,7,8,5,6,3]=>[3,3,1,1]
[4,1,2,7,8,6,5,3]=>[4,2,1,1]
[6,2,7,8,1,5,4,3]=>[4,2,1,1]
[6,2,7,8,5,1,4,3]=>[4,2,1,1]
[6,2,7,8,5,4,1,3]=>[4,2,1,1]
[6,7,2,8,5,3,1,4]=>[4,2,1,1]
[5,7,2,1,8,6,3,4]=>[3,3,1,1]
[5,7,1,2,8,6,3,4]=>[3,2,1,1,1]
[5,1,7,2,8,6,4,3]=>[4,2,2]
[1,5,7,3,8,6,4,2]=>[4,2,1,1]
[1,6,7,8,3,5,4,2]=>[4,1,1,1,1]
[6,1,7,8,2,5,4,3]=>[4,2,1,1]
[6,7,1,8,2,5,3,4]=>[3,2,1,1,1]
[6,7,8,2,4,1,3,5]=>[3,1,1,1,1,1]
[6,7,8,2,4,3,1,5]=>[4,1,1,1,1]
[6,7,1,8,5,2,3,4]=>[3,2,1,1,1]
[6,1,7,8,5,2,4,3]=>[4,2,1,1]
[1,6,7,8,5,3,4,2]=>[4,1,1,1,1]
[6,1,7,8,5,4,2,3]=>[4,2,1,1]
[6,7,1,8,5,3,2,4]=>[4,2,1,1]
[6,7,8,4,1,3,2,5]=>[4,1,1,1,1]
[6,3,8,5,2,7,4,1]=>[4,2,2]
[6,5,2,8,4,7,3,1]=>[5,2,1]
[6,3,4,5,8,7,2,1]=>[4,2,1,1]
[3,8,4,7,5,2,1,6]=>[5,1,1,1]
[5,8,1,4,7,2,3,6]=>[3,1,1,1,1,1]
[5,6,1,4,8,7,3,2]=>[4,2,1,1]
[3,6,4,8,5,7,1,2]=>[3,2,1,1,1]
[5,1,4,8,6,3,7,2]=>[4,2,1,1]
[3,4,7,1,8,6,5,2]=>[4,2,1,1]
[6,3,8,4,2,7,1,5]=>[4,2,1,1]
[3,6,8,7,1,4,2,5]=>[4,1,1,1,1]
[5,3,7,1,6,8,2,4]=>[3,2,1,1,1]
[4,3,8,5,6,7,2,1]=>[4,2,1,1]
[5,8,1,7,6,2,4,3]=>[5,1,1,1]
[4,6,1,2,7,8,5,3]=>[3,2,1,1,1]
[3,6,4,2,8,7,5,1]=>[4,3,1]
[6,3,7,5,2,8,1,4]=>[4,2,1,1]
[6,5,2,7,4,8,1,3]=>[4,2,1,1]
[5,7,1,4,8,3,2,6]=>[4,1,1,1,1]
[7,8,3,5,1,4,6,2]=>[4,1,1,1,1]
[5,8,1,4,6,7,2,3]=>[3,1,1,1,1,1]
[6,5,8,4,3,7,2,1]=>[6,1,1]
[6,3,7,4,2,8,5,1]=>[4,2,2]
[8,7,1,6,2,4,5,3]=>[5,1,1,1]
[3,8,6,7,1,4,5,2]=>[4,1,1,1,1]
[5,3,8,7,4,1,2,6]=>[4,2,1,1]
[4,3,8,7,1,5,6,2]=>[4,2,1,1]
[8,3,6,1,2,5,7,4]=>[4,1,1,1,1]
[5,6,1,8,7,3,2,4]=>[4,2,1,1]
[5,4,2,7,3,6,8,1]=>[4,2,1,1]
[7,5,3,6,4,2,8,1]=>[5,2,1]
[6,4,1,5,3,8,2,7]=>[4,2,1,1]
[8,5,2,6,4,7,3,1]=>[5,2,1]
[8,2,6,3,4,7,5,1]=>[4,2,1,1]
[7,2,6,3,5,4,8,1]=>[5,1,1,1]
[6,2,7,4,3,5,8,1]=>[4,2,1,1]
[5,7,3,6,4,2,8,1]=>[5,1,1,1]
[3,7,6,4,5,2,8,1]=>[5,1,1,1]
[2,7,6,5,3,4,8,1]=>[5,1,1,1]
[6,5,4,3,1,8,2,7]=>[5,2,1]
[8,6,5,4,2,7,3,1]=>[6,2]
[8,5,4,1,7,2,6,3]=>[4,3,1]
[7,5,4,1,8,3,2,6]=>[5,2,1]
[1,6,5,2,8,3,4,7]=>[3,2,1,1,1]
[5,7,4,2,1,8,3,6]=>[4,2,1,1]
[1,6,5,3,4,8,2,7]=>[4,1,1,1,1]
[5,4,6,3,1,8,2,7]=>[4,2,1,1]
[6,5,8,4,2,7,3,1]=>[5,2,1]
[5,8,2,6,4,7,3,1]=>[5,1,1,1]
[3,8,6,2,5,7,4,1]=>[5,1,1,1]
[7,8,5,3,2,6,4,1]=>[5,2,1]
[6,8,3,1,7,2,5,4]=>[4,2,1,1]
[1,8,6,3,7,5,2,4]=>[4,2,1,1]
[8,7,5,2,6,4,3,1]=>[6,2]
[8,7,1,6,2,5,4,3]=>[6,1,1]
[7,8,1,6,3,2,5,4]=>[4,2,1,1]
[2,8,1,7,3,5,6,4]=>[4,1,1,1,1]
[3,8,6,1,7,4,5,2]=>[4,2,1,1]
[4,8,1,3,7,2,6,5]=>[4,1,1,1,1]
[4,2,8,5,7,3,6,1]=>[4,2,1,1]
[5,1,7,6,8,3,2,4]=>[4,2,1,1]
[3,7,1,5,8,4,2,6]=>[4,1,1,1,1]
[6,7,3,1,8,4,2,5]=>[3,3,1,1]
[1,7,3,8,4,5,2,6]=>[3,2,1,1,1]
[1,7,2,8,5,3,4,6]=>[3,2,1,1,1]
[7,6,1,8,4,3,2,5]=>[5,2,1]
[8,6,1,7,4,2,5,3]=>[4,2,2]
[8,1,2,7,3,4,6,5]=>[4,1,1,1,1]
[7,1,2,8,3,5,4,6]=>[3,2,1,1,1]
[7,2,6,1,8,4,3,5]=>[4,2,1,1]
[8,2,6,1,7,3,5,4]=>[4,2,1,1]
[8,3,1,4,7,5,6,2]=>[4,2,1,1]
[7,3,1,5,8,4,2,6]=>[4,2,1,1]
[4,2,1,5,8,3,6,7]=>[3,2,1,1,1]
[5,4,2,7,1,8,3,6]=>[4,2,1,1]
[5,4,3,1,6,8,2,7]=>[4,2,1,1]
[4,7,5,6,8,3,2,1]=>[5,1,1,1]
[6,5,4,8,2,7,3,1]=>[5,2,1]
[6,5,2,8,7,3,4,1]=>[4,3,1]
[6,5,1,8,7,4,2,3]=>[4,3,1]
[8,6,4,7,5,3,2,1]=>[6,2]
[5,1,8,3,7,6,2,4]=>[4,2,1,1]
[5,4,8,1,7,2,6,3]=>[4,2,1,1]
[7,5,8,3,2,6,4,1]=>[5,2,1]
[3,6,8,2,4,7,5,1]=>[4,1,1,1,1]
[5,7,3,8,2,6,4,1]=>[4,2,1,1]
[5,4,6,8,2,7,3,1]=>[4,2,1,1]
[5,2,6,8,7,3,4,1]=>[4,2,1,1]
[4,7,2,8,6,3,5,1]=>[4,2,1,1]
[3,6,8,1,7,2,5,4]=>[4,1,1,1,1]
[2,3,8,7,4,5,6,1]=>[4,1,1,1,1]
[7,2,8,6,4,3,5,1]=>[5,2,1]
[2,1,8,7,5,6,3,4]=>[4,2,1,1]
[8,2,7,6,3,5,4,1]=>[6,1,1]
[8,1,7,6,5,2,4,3]=>[6,1,1]
[7,1,8,6,5,3,2,4]=>[5,2,1]
[1,2,8,7,6,3,4,5]=>[4,1,1,1,1]
[1,3,8,7,4,6,2,5]=>[4,1,1,1,1]
[1,5,8,3,7,6,2,4]=>[4,1,1,1,1]
[5,1,6,8,7,4,2,3]=>[4,2,1,1]
[6,8,4,7,5,3,2,1]=>[6,1,1]
[6,8,7,2,5,4,3,1]=>[6,1,1]
[3,8,7,6,4,5,2,1]=>[6,1,1]
[2,8,7,6,5,3,4,1]=>[6,1,1]
[1,8,7,6,5,4,2,3]=>[6,1,1]
[5,8,6,7,3,4,1,2]=>[4,1,1,1,1]
[4,8,6,7,3,5,1,2]=>[4,1,1,1,1]
[3,8,6,7,4,5,1,2]=>[4,1,1,1,1]
[2,8,6,7,4,5,1,3]=>[4,1,1,1,1]
[1,8,6,7,4,5,2,3]=>[4,1,1,1,1]
[1,8,5,7,4,6,2,3]=>[4,1,1,1,1]
[3,8,5,7,4,6,1,2]=>[4,1,1,1,1]
[4,8,5,7,3,6,1,2]=>[4,1,1,1,1]
[7,8,3,6,4,5,1,2]=>[4,1,1,1,1]
[6,8,3,7,4,5,1,2]=>[4,1,1,1,1]
[5,8,3,7,4,6,1,2]=>[4,1,1,1,1]
[4,7,3,8,5,6,1,2]=>[3,2,1,1,1]
[4,7,2,8,5,6,1,3]=>[3,2,1,1,1]
[4,7,1,8,5,6,2,3]=>[3,2,1,1,1]
[3,7,1,8,5,6,2,4]=>[3,2,1,1,1]
[3,7,2,8,5,6,1,4]=>[3,2,1,1,1]
[2,7,3,8,5,6,1,4]=>[3,2,1,1,1]
[2,7,4,8,5,6,1,3]=>[3,2,1,1,1]
[5,8,2,7,4,6,1,3]=>[4,1,1,1,1]
[6,8,2,7,4,5,1,3]=>[4,1,1,1,1]
[7,8,2,6,4,5,1,3]=>[4,1,1,1,1]
[7,8,1,6,4,5,2,3]=>[4,1,1,1,1]
[6,8,1,7,4,5,2,3]=>[4,1,1,1,1]
[5,8,1,7,4,6,2,3]=>[4,1,1,1,1]
[1,7,4,8,5,6,2,3]=>[3,2,1,1,1]
[1,7,3,8,5,6,2,4]=>[3,2,1,1,1]
[1,8,5,6,2,7,3,4]=>[3,2,1,1,1]
[1,7,3,8,4,6,2,5]=>[3,2,1,1,1]
[4,8,1,7,3,6,2,5]=>[4,1,1,1,1]
[5,8,1,7,3,6,2,4]=>[4,1,1,1,1]
[6,8,1,7,3,5,2,4]=>[4,1,1,1,1]
[7,8,2,6,3,5,1,4]=>[4,1,1,1,1]
[6,8,2,7,3,5,1,4]=>[4,1,1,1,1]
[5,8,2,7,3,6,1,4]=>[4,1,1,1,1]
[4,8,2,7,3,6,1,5]=>[4,1,1,1,1]
[2,7,3,8,4,6,1,5]=>[3,2,1,1,1]
[3,7,2,8,4,6,1,5]=>[3,2,1,1,1]
[1,8,4,7,3,6,2,5]=>[4,1,1,1,1]
[2,8,4,7,3,6,1,5]=>[4,1,1,1,1]
[3,8,4,7,2,6,1,5]=>[4,1,1,1,1]
[4,8,5,7,2,6,1,3]=>[4,1,1,1,1]
[3,8,5,7,2,6,1,4]=>[4,1,1,1,1]
[2,8,5,7,3,6,1,4]=>[4,1,1,1,1]
[1,8,5,7,3,6,2,4]=>[4,1,1,1,1]
[1,8,6,7,3,5,2,4]=>[4,1,1,1,1]
[2,8,6,7,3,5,1,4]=>[4,1,1,1,1]
[3,8,6,7,2,5,1,4]=>[4,1,1,1,1]
[4,8,6,7,2,5,1,3]=>[4,1,1,1,1]
[5,8,6,7,2,4,1,3]=>[4,1,1,1,1]
[6,8,5,7,1,4,2,3]=>[4,1,1,1,1]
[5,8,6,7,1,4,2,3]=>[4,1,1,1,1]
[4,8,6,7,1,5,2,3]=>[4,1,1,1,1]
[3,8,6,7,1,5,2,4]=>[4,1,1,1,1]
[1,5,2,8,6,7,3,4]=>[3,2,1,1,1]
[2,5,1,8,6,7,3,4]=>[3,2,1,1,1]
[2,6,1,8,5,7,3,4]=>[3,2,1,1,1]
[1,6,2,8,5,7,3,4]=>[3,2,1,1,1]
[3,8,5,7,1,6,2,4]=>[4,1,1,1,1]
[6,8,4,7,1,5,2,3]=>[4,1,1,1,1]
[7,8,4,6,1,5,2,3]=>[4,1,1,1,1]
[7,8,3,6,1,5,2,4]=>[4,1,1,1,1]
[6,8,3,7,1,5,2,4]=>[4,1,1,1,1]
[4,8,3,7,1,6,2,5]=>[4,1,1,1,1]
[3,8,4,7,1,6,2,5]=>[4,1,1,1,1]
[1,6,2,8,4,7,3,5]=>[3,2,1,1,1]
[2,6,1,8,4,7,3,5]=>[3,2,1,1,1]
[3,7,1,6,2,8,4,5]=>[3,2,1,1,1]
[4,8,1,6,2,7,3,5]=>[3,2,1,1,1]
[5,8,1,6,2,7,3,4]=>[3,2,1,1,1]
[7,8,1,5,2,6,3,4]=>[3,2,1,1,1]
[7,8,2,5,1,6,3,4]=>[3,2,1,1,1]
[6,8,2,5,1,7,3,4]=>[3,2,1,1,1]
[5,8,2,6,1,7,3,4]=>[3,2,1,1,1]
[4,8,2,6,1,7,3,5]=>[3,2,1,1,1]
[1,7,3,6,2,8,4,5]=>[3,2,1,1,1]
[6,7,4,8,3,5,1,2]=>[4,1,1,1,1]
[6,7,4,5,2,8,1,3]=>[4,1,1,1,1]
[5,7,4,6,2,3,1,8]=>[4,1,1,1,1]
[5,7,4,6,3,8,1,2]=>[4,1,1,1,1]
[5,7,4,8,3,6,1,2]=>[4,1,1,1,1]
[6,8,4,5,3,7,1,2]=>[4,1,1,1,1]
[5,8,4,6,3,7,1,2]=>[4,1,1,1,1]
[5,6,4,8,3,7,1,2]=>[4,1,1,1,1]
[5,6,3,7,2,4,1,8]=>[4,1,1,1,1]
[5,6,3,7,2,8,1,4]=>[4,1,1,1,1]
[5,6,3,8,2,7,1,4]=>[4,1,1,1,1]
[5,6,4,8,2,7,1,3]=>[4,1,1,1,1]
[5,8,4,6,2,7,1,3]=>[4,1,1,1,1]
[6,8,4,5,2,7,1,3]=>[4,1,1,1,1]
[7,8,4,5,2,6,1,3]=>[4,1,1,1,1]
[6,8,4,5,2,3,1,7]=>[4,1,1,1,1]
[5,8,4,6,2,3,1,7]=>[4,1,1,1,1]
[5,6,4,8,2,3,1,7]=>[4,1,1,1,1]
[5,6,3,8,2,4,1,7]=>[4,1,1,1,1]
[5,6,3,4,2,8,1,7]=>[4,1,1,1,1]
[4,6,3,5,2,7,1,8]=>[4,1,1,1,1]
[4,6,3,5,2,8,1,7]=>[4,1,1,1,1]
[4,6,3,8,2,5,1,7]=>[4,1,1,1,1]
[4,8,3,6,2,5,1,7]=>[4,1,1,1,1]
[5,8,3,6,2,4,1,7]=>[4,1,1,1,1]
[6,8,3,5,2,4,1,7]=>[4,1,1,1,1]
[7,8,3,5,2,4,1,6]=>[4,1,1,1,1]
[7,8,3,5,2,6,1,4]=>[4,1,1,1,1]
[5,8,3,6,2,7,1,4]=>[4,1,1,1,1]
[4,8,3,6,2,7,1,5]=>[4,1,1,1,1]
[4,6,3,8,2,7,1,5]=>[4,1,1,1,1]
[4,6,3,7,2,8,1,5]=>[4,1,1,1,1]
[4,7,3,6,2,5,1,8]=>[4,1,1,1,1]
[4,7,3,6,2,8,1,5]=>[4,1,1,1,1]
[4,7,3,8,2,6,1,5]=>[4,1,1,1,1]
[5,7,4,8,2,6,1,3]=>[4,1,1,1,1]
[5,7,3,6,2,8,1,4]=>[4,1,1,1,1]
[5,7,3,6,2,4,1,8]=>[4,1,1,1,1]
[6,7,3,5,2,4,1,8]=>[4,1,1,1,1]
[6,7,3,5,2,8,1,4]=>[4,1,1,1,1]
[6,7,4,8,2,5,1,3]=>[4,1,1,1,1]
[6,7,5,8,2,4,1,3]=>[4,1,1,1,1]
[6,8,5,7,2,3,1,4]=>[4,1,1,1,1]
[6,7,4,8,2,3,1,5]=>[4,1,1,1,1]
[6,7,3,8,2,4,1,5]=>[4,1,1,1,1]
[6,7,3,4,2,8,1,5]=>[4,1,1,1,1]
[5,7,3,4,2,6,1,8]=>[4,1,1,1,1]
[5,7,3,4,2,8,1,6]=>[4,1,1,1,1]
[5,7,4,8,2,3,1,6]=>[4,1,1,1,1]
[5,8,4,7,2,3,1,6]=>[4,1,1,1,1]
[6,8,4,7,2,3,1,5]=>[4,1,1,1,1]
[7,8,4,6,2,3,1,5]=>[4,1,1,1,1]
[7,8,3,6,2,4,1,5]=>[4,1,1,1,1]
[6,8,3,7,2,4,1,5]=>[4,1,1,1,1]
[5,8,3,7,2,4,1,6]=>[4,1,1,1,1]
[4,8,3,7,2,5,1,6]=>[4,1,1,1,1]
[4,7,3,8,2,5,1,6]=>[4,1,1,1,1]
[4,7,3,5,2,8,1,6]=>[4,1,1,1,1]
[4,7,3,5,2,6,1,8]=>[4,1,1,1,1]
[4,5,3,7,2,6,1,8]=>[4,1,1,1,1]
[4,5,3,7,2,8,1,6]=>[4,1,1,1,1]
[4,5,3,8,2,7,1,6]=>[4,1,1,1,1]
[4,8,3,5,2,7,1,6]=>[4,1,1,1,1]
[5,8,3,4,2,7,1,6]=>[4,1,1,1,1]
[6,8,3,4,2,7,1,5]=>[4,1,1,1,1]
[7,8,3,4,2,6,1,5]=>[4,1,1,1,1]
[6,8,3,4,2,5,1,7]=>[4,1,1,1,1]
[5,8,3,4,2,6,1,7]=>[4,1,1,1,1]
[4,8,3,5,2,6,1,7]=>[4,1,1,1,1]
[4,5,3,8,2,6,1,7]=>[4,1,1,1,1]
[4,5,3,6,2,8,1,7]=>[4,1,1,1,1]
[4,7,5,2,1,8,3,6]=>[4,2,1,1]
[4,8,5,2,1,7,6,3]=>[4,3,1]
[4,6,5,2,1,3,8,7]=>[4,2,1,1]
[5,6,4,2,3,1,8,7]=>[4,2,1,1]
[6,4,5,3,1,2,8,7]=>[4,2,1,1]
[5,4,6,1,3,2,8,7]=>[4,2,1,1]
[4,6,8,1,7,3,2,5]=>[4,1,1,1,1]
[4,7,8,1,6,3,5,2]=>[4,1,1,1,1]
[7,4,8,1,6,5,3,2]=>[5,2,1]
[5,4,8,1,3,7,6,2]=>[4,2,1,1]
[8,4,5,3,1,7,6,2]=>[4,3,1]
[5,4,7,1,3,8,2,6]=>[4,1,1,1,1]
[6,4,8,1,7,5,2,3]=>[4,2,1,1]
[5,6,8,7,2,1,3,4]=>[4,1,1,1,1]
[8,5,7,6,4,2,1,3]=>[6,1,1]
[8,4,6,3,7,2,1,5]=>[5,1,1,1]
[6,3,2,8,7,4,1,5]=>[4,3,1]
[2,1,6,8,7,4,3,5]=>[4,2,1,1]
[2,1,7,8,6,4,5,3]=>[4,2,1,1]
[7,3,2,8,6,4,5,1]=>[4,3,1]
[7,6,8,5,2,4,3,1]=>[6,1,1]
[5,7,8,6,2,3,1,4]=>[4,1,1,1,1]
[5,8,7,6,3,2,1,4]=>[6,1,1]
[6,8,7,5,3,2,4,1]=>[6,1,1]
[5,8,4,2,3,7,6,1]=>[4,2,1,1]
[7,8,4,2,6,5,3,1]=>[5,2,1]
[4,8,7,2,6,3,5,1]=>[5,1,1,1]
[4,8,6,2,7,3,1,5]=>[4,2,1,1]
[3,6,1,8,7,4,2,5]=>[4,2,1,1]
[3,7,1,8,6,4,5,2]=>[4,2,1,1]
[3,8,1,6,7,5,2,4]=>[4,1,1,1,1]
[3,7,1,6,8,2,5,4]=>[4,1,1,1,1]
[4,7,6,2,8,1,3,5]=>[4,1,1,1,1]
[6,7,4,2,8,1,5,3]=>[4,2,1,1]
[6,8,4,2,7,5,1,3]=>[4,2,1,1]
[2,1,8,6,7,5,3,4]=>[4,2,1,1]
[8,3,2,6,7,5,1,4]=>[4,2,1,1]
[8,6,4,3,7,5,1,2]=>[5,2,1]
[5,8,6,7,3,1,2,4]=>[4,1,1,1,1]
[6,7,5,8,1,3,4,2]=>[4,1,1,1,1]
[7,6,5,8,1,4,3,2]=>[6,1,1]
[8,6,5,7,4,1,3,2]=>[6,1,1]
[7,6,4,3,8,1,5,2]=>[5,2,1]
[7,3,2,6,8,1,5,4]=>[4,2,1,1]
[2,1,7,6,8,3,5,4]=>[4,2,1,1]
[7,5,6,8,1,4,2,3]=>[4,1,1,1,1]
[6,5,7,8,1,2,4,3]=>[4,1,1,1,1]
[8,1,3,7,4,6,5,2]=>[5,1,1,1]
[5,2,8,7,4,6,1,3]=>[4,2,1,1]
[1,6,2,5,4,7,3,8]=>[4,1,1,1,1]
[6,2,7,5,4,8,3,1]=>[5,2,1]
[8,1,3,5,4,7,6,2]=>[4,2,1,1]
[6,1,5,4,3,8,7,2]=>[5,2,1]
[6,1,8,3,4,5,7,2]=>[3,2,1,1,1]
[7,1,5,3,4,8,6,2]=>[4,2,1,1]
[7,1,4,3,5,6,8,2]=>[4,1,1,1,1]
[8,1,3,4,5,6,7,2]=>[3,1,1,1,1,1]
[1,7,2,4,5,6,3,8]=>[3,1,1,1,1,1]
[6,3,2,7,5,1,8,4]=>[4,2,2]
[8,4,7,2,5,6,1,3]=>[4,1,1,1,1]
[6,5,8,2,4,7,3,1]=>[5,1,1,1]
[8,5,2,1,4,3,7,6]=>[4,2,2]
[6,5,2,8,4,1,3,7]=>[4,2,1,1]
[5,6,2,1,4,8,3,7]=>[3,2,1,1,1]
[3,6,1,8,5,2,4,7]=>[3,2,1,1,1]
[1,2,6,3,5,4,7,8]=>[3,1,1,1,1,1]
[3,4,1,2,8,6,5,7]=>[3,2,1,1,1]
[4,3,1,2,6,8,5,7]=>[3,2,1,1,1]
[5,8,1,6,3,2,4,7]=>[4,1,1,1,1]
[6,3,8,5,2,1,4,7]=>[4,2,1,1]
[8,3,1,5,2,4,7,6]=>[3,2,2,1]
[3,8,2,6,1,5,7,4]=>[4,1,1,1,1]
[3,8,6,7,2,1,5,4]=>[4,2,1,1]
[8,5,6,4,2,1,7,3]=>[5,2,1]
[7,2,5,8,3,1,6,4]=>[4,2,1,1]
[1,7,5,6,3,2,4,8]=>[4,1,1,1,1]
[6,1,2,3,8,5,7,4]=>[3,2,1,1,1]
[7,1,2,3,6,5,8,4]=>[4,1,1,1,1]
[7,2,1,3,8,6,4,5]=>[3,3,1,1]
[1,5,7,3,2,4,6,8]=>[3,1,1,1,1,1]
[5,2,7,3,1,8,4,6]=>[3,2,2,1]
[5,8,2,4,1,3,7,6]=>[3,2,1,1,1]
[8,7,2,6,3,4,1,5]=>[5,1,1,1]
[4,8,1,6,3,2,7,5]=>[4,2,1,1]
[3,1,8,6,4,2,7,5]=>[4,2,2]
[8,1,6,7,4,3,2,5]=>[5,1,1,1]
[3,5,8,7,2,4,1,6]=>[4,1,1,1,1]
[4,2,1,3,7,8,5,6]=>[3,2,1,1,1]
[2,4,1,3,8,7,5,6]=>[3,2,1,1,1]
[2,5,8,3,1,7,4,6]=>[3,2,1,1,1]
[8,6,1,3,7,2,4,5]=>[4,1,1,1,1]
[2,8,1,3,6,4,7,5]=>[3,2,1,1,1]
[6,8,2,3,4,1,5,7]=>[3,1,1,1,1,1]
[5,1,8,3,2,4,6,7]=>[3,2,1,1,1]
[1,4,2,7,8,6,3,5]=>[3,2,1,1,1]
[1,6,2,4,8,5,3,7]=>[3,2,1,1,1]
[1,6,2,4,7,5,3,8]=>[3,2,1,1,1]
[1,7,3,8,5,2,4,6]=>[3,2,1,1,1]
[1,7,3,2,8,6,4,5]=>[3,3,1,1]
[4,2,5,7,8,6,1,3]=>[3,2,1,1,1]
[7,2,3,1,8,5,6,4]=>[3,3,1,1]
[8,2,5,1,7,3,4,6]=>[3,2,1,1,1]
[6,2,1,8,3,4,7,5]=>[3,3,1,1]
[6,2,8,3,5,1,7,4]=>[3,2,2,1]
[6,2,4,8,5,7,1,3]=>[3,2,1,1,1]
[1,3,6,4,8,5,7,2]=>[3,2,1,1,1]
[1,3,6,4,7,5,8,2]=>[3,2,1,1,1]
[6,2,4,7,5,8,1,3]=>[3,2,1,1,1]
[6,2,1,3,7,8,4,5]=>[3,2,1,1,1]
[7,8,2,1,4,3,5,6]=>[3,2,1,1,1]
[7,6,4,2,3,1,8,5]=>[5,2,1]
[5,7,2,3,1,6,8,4]=>[3,2,1,1,1]
[7,5,4,2,6,8,1,3]=>[5,1,1,1]
[1,7,5,3,4,6,8,2]=>[4,1,1,1,1]
[8,2,5,4,6,7,1,3]=>[4,1,1,1,1]
[5,2,6,3,1,8,7,4]=>[3,3,2]
[8,2,6,4,3,1,7,5]=>[5,2,1]
[8,2,7,4,1,3,5,6]=>[4,1,1,1,1]
[1,2,8,4,3,5,6,7]=>[3,1,1,1,1,1]
[1,7,4,2,3,5,6,8]=>[3,1,1,1,1,1]
[6,8,4,1,3,2,5,7]=>[4,1,1,1,1]
[1,8,7,4,3,2,5,6]=>[5,1,1,1]
[1,6,3,8,2,4,7,5]=>[3,2,1,1,1]
[5,3,8,1,2,7,4,6]=>[3,2,1,1,1]
[5,1,8,3,2,6,4,7]=>[3,2,2,1]
[5,7,3,1,2,6,4,8]=>[3,2,1,1,1]
[1,7,5,4,2,6,3,8]=>[4,2,1,1]
[1,5,8,2,4,6,3,7]=>[3,1,1,1,1,1]
[1,5,8,4,2,7,3,6]=>[3,2,1,1,1]
[1,4,6,2,8,3,7,5]=>[3,2,1,1,1]
[5,3,1,6,7,2,4,8]=>[3,2,1,1,1]
[5,3,6,1,2,8,4,7]=>[3,2,1,1,1]
[1,6,3,2,7,8,4,5]=>[3,2,1,1,1]
[1,7,4,5,3,8,6,2]=>[4,2,1,1]
[6,3,4,1,2,5,8,7]=>[3,2,1,1,1]
[6,3,1,4,2,7,5,8]=>[3,2,2,1]
[1,8,3,2,4,5,6,7]=>[3,1,1,1,1,1]
[8,6,3,2,4,1,7,5]=>[5,2,1]
[8,5,3,2,6,7,1,4]=>[5,1,1,1]
[4,5,2,6,8,1,7,3]=>[3,2,1,1,1]
[4,2,5,6,7,8,1,3]=>[3,1,1,1,1,1]
[5,2,3,6,7,1,8,4]=>[3,2,1,1,1]
[6,2,3,4,1,7,8,5]=>[3,2,1,1,1]
[7,2,3,1,4,5,8,6]=>[3,2,1,1,1]
[8,6,1,4,3,2,5,7]=>[5,1,1,1]
[8,3,1,6,5,2,4,7]=>[4,2,1,1]
[3,7,5,1,8,2,4,6]=>[3,2,1,1,1]
[4,1,5,2,8,7,3,6]=>[3,2,2,1]
[8,1,2,4,6,5,3,7]=>[4,1,1,1,1]
[8,1,2,5,4,6,3,7]=>[4,1,1,1,1]
[8,2,6,5,1,3,4,7]=>[4,1,1,1,1]
[8,3,1,6,2,5,4,7]=>[4,2,1,1]
[8,1,2,6,4,5,3,7]=>[4,1,1,1,1]
[8,1,2,5,6,4,3,7]=>[4,1,1,1,1]
[8,1,2,6,5,4,3,7]=>[5,1,1,1]
[1,7,5,4,2,8,3,6]=>[4,2,1,1]
[5,1,4,8,2,7,3,6]=>[3,2,1,1,1]
[1,4,6,8,2,7,3,5]=>[3,1,1,1,1,1]
[1,4,7,6,2,8,3,5]=>[3,2,1,1,1]
[5,1,4,7,2,8,3,6]=>[3,2,1,1,1]
[1,7,4,5,2,8,3,6]=>[3,2,1,1,1]
[3,7,5,1,2,8,4,6]=>[3,2,1,1,1]
[5,7,2,8,1,3,4,6]=>[3,1,1,1,1,1]
[5,2,8,7,1,3,4,6]=>[3,2,1,1,1]
[4,1,5,8,2,7,3,6]=>[3,2,1,1,1]
[1,4,6,2,8,7,3,5]=>[3,2,1,1,1]
[1,4,2,8,6,7,3,5]=>[3,2,1,1,1]
[3,1,2,6,4,8,7,5]=>[3,2,2,1]
[2,1,7,6,3,4,8,5]=>[3,2,2,1]
[3,1,2,7,4,6,8,5]=>[3,2,1,1,1]
[1,4,7,2,6,8,3,5]=>[3,1,1,1,1,1]
[1,2,3,6,8,5,7,4]=>[3,1,1,1,1,1]
[5,1,4,2,7,8,3,6]=>[3,2,1,1,1]
[1,4,2,7,6,8,3,5]=>[3,2,1,1,1]
[1,4,2,6,8,7,3,5]=>[3,2,1,1,1]
[3,1,2,8,4,6,7,5]=>[3,2,1,1,1]
[3,1,2,7,6,4,8,5]=>[3,2,2,1]
[5,3,7,1,8,2,4,6]=>[3,2,1,1,1]
[1,7,4,3,2,5,8,6]=>[4,2,1,1]
[4,8,7,2,1,3,5,6]=>[4,1,1,1,1]
[1,8,7,3,4,2,5,6]=>[4,1,1,1,1]
[3,1,7,8,2,6,4,5]=>[3,2,1,1,1]
[1,4,2,7,8,3,6,5]=>[3,2,1,1,1]
[5,2,8,1,3,4,7,6]=>[3,2,1,1,1]
[2,1,8,6,3,4,7,5]=>[3,2,2,1]
[1,4,2,6,8,3,7,5]=>[3,2,1,1,1]
[1,2,3,7,8,5,6,4]=>[3,1,1,1,1,1]
[1,2,3,7,5,8,6,4]=>[3,2,1,1,1]
[1,4,2,7,3,8,6,5]=>[3,2,2,1]
[3,1,7,2,8,6,4,5]=>[3,2,2,1]
[2,1,7,8,3,4,6,5]=>[3,2,1,1,1]
[1,2,3,8,7,5,6,4]=>[4,1,1,1,1]
[4,7,8,5,6,2,1,3]=>[4,1,1,1,1]
[5,7,8,4,2,6,1,3]=>[4,1,1,1,1]
[8,6,3,7,2,1,5,4]=>[5,2,1]
[7,6,3,8,2,1,5,4]=>[5,2,1]
[4,7,8,3,2,1,5,6]=>[4,1,1,1,1]
[5,7,8,3,2,1,4,6]=>[4,1,1,1,1]
[7,6,3,8,2,1,4,5]=>[5,1,1,1]
[8,6,3,7,2,1,4,5]=>[5,1,1,1]
[5,6,3,8,2,1,4,7]=>[4,1,1,1,1]
[2,6,4,7,3,5,8,1]=>[4,1,1,1,1]
[3,6,4,7,2,5,1,8]=>[4,1,1,1,1]
[5,6,3,7,2,1,4,8]=>[4,1,1,1,1]
[8,4,3,2,1,6,5,7]=>[5,2,1]
[6,4,3,2,1,7,5,8]=>[5,2,1]
[6,4,3,2,1,8,5,7]=>[5,2,1]
[7,4,3,2,1,8,5,6]=>[5,2,1]
[8,4,3,2,1,7,5,6]=>[5,2,1]
[8,4,3,2,1,7,6,5]=>[5,3]
[7,4,3,2,1,8,6,5]=>[5,3]
[6,4,3,2,1,8,7,5]=>[5,3]
[7,5,3,2,8,1,6,4]=>[5,2,1]
[8,5,4,2,7,6,1,3]=>[5,2,1]
[7,5,4,2,8,6,1,3]=>[5,2,1]
[6,5,4,2,8,7,1,3]=>[5,2,1]
[4,6,5,8,7,2,1,3]=>[4,2,1,1]
[2,6,5,7,8,3,4,1]=>[4,1,1,1,1]
[6,5,4,2,7,8,1,3]=>[5,1,1,1]
[8,5,4,2,6,7,1,3]=>[5,1,1,1]
[8,5,3,2,6,1,7,4]=>[5,2,1]
[7,5,3,2,6,1,8,4]=>[5,2,1]
[5,6,3,7,2,1,8,4]=>[4,2,1,1]
[4,6,3,7,2,1,8,5]=>[4,2,1,1]
[3,6,4,7,2,8,1,5]=>[4,1,1,1,1]
[2,6,4,7,3,8,5,1]=>[4,2,1,1]
[3,5,4,2,7,8,1,6]=>[4,1,1,1,1]
[4,5,3,2,7,1,8,6]=>[4,2,1,1]
[7,4,3,2,1,6,8,5]=>[5,2,1]
[8,4,3,2,1,6,7,5]=>[5,2,1]
[8,4,3,2,1,5,7,6]=>[5,2,1]
[7,4,3,2,1,5,8,6]=>[5,2,1]
[6,4,3,2,1,5,8,7]=>[5,2,1]
[5,6,3,4,1,2,8,7]=>[3,2,1,1,1]
[8,5,3,7,2,6,4,1]=>[5,2,1]
[8,5,7,4,2,6,3,1]=>[5,2,1]
[7,5,8,4,2,6,1,3]=>[5,1,1,1]
[2,1,7,8,5,6,3,4]=>[3,2,1,1,1]
[6,8,3,7,5,1,4,2]=>[5,1,1,1]
[5,7,3,8,1,6,2,4]=>[3,2,1,1,1]
[3,2,6,4,8,5,1,7]=>[3,2,2,1]
[3,5,2,4,1,7,6,8]=>[3,2,1,1,1]
[4,2,5,8,3,1,6,7]=>[3,2,1,1,1]
[3,1,5,4,2,8,6,7]=>[3,2,2,1]
[4,1,5,8,3,2,6,7]=>[3,2,1,1,1]
[4,3,8,5,2,1,6,7]=>[4,2,1,1]
[4,7,3,5,2,1,6,8]=>[4,1,1,1,1]
[4,3,2,7,5,1,6,8]=>[4,2,1,1]
[4,3,6,2,5,1,7,8]=>[4,1,1,1,1]
[4,6,3,2,5,1,7,8]=>[4,1,1,1,1]
[4,5,1,7,3,2,6,8]=>[3,2,1,1,1]
[5,2,1,4,3,7,8,6]=>[3,2,2,1]
[4,3,6,1,5,2,7,8]=>[3,2,1,1,1]
[4,6,3,1,5,2,7,8]=>[3,2,1,1,1]
[5,3,6,4,1,2,7,8]=>[3,2,1,1,1]
[4,3,6,1,7,2,5,8]=>[3,2,1,1,1]
[6,2,4,1,3,7,8,5]=>[3,2,1,1,1]
[3,6,4,1,2,7,5,8]=>[3,2,1,1,1]
[4,6,3,1,7,2,5,8]=>[3,2,1,1,1]
[5,6,2,7,1,3,4,8]=>[3,1,1,1,1,1]
[4,5,2,7,3,1,6,8]=>[3,2,1,1,1]
[4,6,2,1,7,3,5,8]=>[3,2,1,1,1]
[3,2,6,1,4,7,5,8]=>[3,2,1,1,1]
[3,5,2,7,4,6,1,8]=>[3,2,1,1,1]
[3,7,2,4,8,5,1,6]=>[3,2,1,1,1]
[7,3,1,4,6,8,2,5]=>[3,2,1,1,1]
[3,2,6,1,5,7,4,8]=>[3,2,1,1,1]
[6,3,2,1,5,7,4,8]=>[4,2,1,1]
[6,4,2,1,5,3,7,8]=>[4,2,1,1]
[4,2,6,1,5,3,7,8]=>[3,2,1,1,1]
[4,2,1,7,5,3,6,8]=>[3,3,1,1]
[7,4,1,5,6,2,3,8]=>[3,2,1,1,1]
[7,3,1,5,2,6,4,8]=>[3,2,2,1]
[6,3,5,1,2,7,4,8]=>[3,2,1,1,1]
[5,2,6,4,1,3,7,8]=>[3,2,1,1,1]
[3,6,5,1,2,7,4,8]=>[3,2,1,1,1]
[6,5,3,1,4,7,2,8]=>[4,2,1,1]
[2,3,1,8,5,4,7,6]=>[3,2,2,1]
[2,4,1,5,8,3,7,6]=>[3,2,1,1,1]
[2,4,1,5,3,8,7,6]=>[3,2,2,1]
[3,4,5,1,2,8,7,6]=>[3,2,1,1,1]
[3,4,5,1,8,2,7,6]=>[3,2,1,1,1]
[1,8,4,5,3,2,7,6]=>[4,2,1,1]
[2,4,8,5,3,1,7,6]=>[4,2,1,1]
[3,4,5,8,2,1,7,6]=>[3,2,1,1,1]
[3,4,5,2,8,1,7,6]=>[3,2,1,1,1]
[3,4,6,2,1,7,8,5]=>[3,2,1,1,1]
[3,4,6,2,1,7,5,8]=>[3,2,1,1,1]
[3,5,6,2,7,1,4,8]=>[3,1,1,1,1,1]
[3,5,6,2,7,1,8,4]=>[3,2,1,1,1]
[3,5,6,2,7,8,1,4]=>[3,1,1,1,1,1]
[3,4,6,2,8,7,1,5]=>[3,2,1,1,1]
[3,4,6,8,2,7,1,5]=>[3,1,1,1,1,1]
[2,4,8,6,3,7,1,5]=>[4,1,1,1,1]
[1,8,4,6,3,7,2,5]=>[4,1,1,1,1]
[1,8,4,6,3,7,5,2]=>[4,2,1,1]
[3,4,6,8,2,7,5,1]=>[4,1,1,1,1]
[3,4,6,2,8,7,5,1]=>[4,2,1,1]
[3,5,6,2,7,8,4,1]=>[3,2,1,1,1]
[3,5,6,2,7,4,1,8]=>[3,2,1,1,1]
[4,5,6,7,2,8,3,1]=>[3,2,1,1,1]
[3,5,6,8,7,2,4,1]=>[4,1,1,1,1]
[2,5,8,6,7,3,4,1]=>[4,1,1,1,1]
[1,8,5,6,7,3,4,2]=>[4,1,1,1,1]
[1,8,5,6,7,3,2,4]=>[4,1,1,1,1]
[2,5,8,6,7,3,1,4]=>[4,1,1,1,1]
[3,5,6,8,7,2,1,4]=>[4,1,1,1,1]
[4,5,6,7,2,1,8,3]=>[3,2,1,1,1]
[3,4,6,1,8,7,2,5]=>[3,2,1,1,1]
[2,4,1,6,8,7,3,5]=>[3,2,1,1,1]
[2,3,1,8,6,7,4,5]=>[3,2,1,1,1]
[1,8,3,2,6,7,5,4]=>[4,2,1,1]
[2,5,1,6,7,8,4,3]=>[3,2,1,1,1]
[2,5,1,6,7,4,8,3]=>[3,2,1,1,1]
[2,5,1,6,7,4,3,8]=>[3,2,1,1,1]
[3,5,6,1,7,4,2,8]=>[3,2,1,1,1]
[3,5,6,1,7,4,8,2]=>[3,2,1,1,1]
[3,4,6,1,8,7,5,2]=>[4,2,1,1]
[3,4,6,8,1,7,5,2]=>[4,1,1,1,1]
[2,4,8,6,1,7,5,3]=>[4,2,1,1]
[1,8,4,6,2,7,5,3]=>[4,2,1,1]
[1,8,5,6,7,2,4,3]=>[4,1,1,1,1]
[2,5,8,6,7,1,4,3]=>[4,1,1,1,1]
[3,5,6,8,7,1,4,2]=>[4,1,1,1,1]
[4,5,6,7,8,1,3,2]=>[3,1,1,1,1,1]
[4,5,6,7,1,3,8,2]=>[3,1,1,1,1,1]
[4,5,6,7,1,3,2,8]=>[3,1,1,1,1,1]
[4,5,6,7,3,1,8,2]=>[3,2,1,1,1]
[3,5,6,8,7,4,1,2]=>[4,1,1,1,1]
[2,5,8,6,7,4,1,3]=>[4,1,1,1,1]
[1,8,5,6,7,4,2,3]=>[4,1,1,1,1]
[1,8,5,6,7,4,3,2]=>[5,1,1,1]
[2,5,8,6,7,4,3,1]=>[5,1,1,1]
[8,2,5,3,7,1,6,4]=>[4,2,1,1]
[8,2,4,3,7,1,6,5]=>[4,2,1,1]
[5,8,2,4,3,7,1,6]=>[4,1,1,1,1]
[4,2,5,6,1,8,3,7]=>[3,2,1,1,1]
[4,2,5,6,1,7,3,8]=>[3,2,1,1,1]
[6,1,5,7,3,2,4,8]=>[4,1,1,1,1]
[6,1,5,8,3,2,4,7]=>[4,1,1,1,1]
[3,8,2,4,7,1,5,6]=>[3,1,1,1,1,1]
[3,6,8,2,4,7,1,5]=>[3,1,1,1,1,1]
[4,3,5,6,7,1,8,2]=>[3,2,1,1,1]
[3,7,1,5,6,8,2,4]=>[3,1,1,1,1,1]
[3,7,1,5,8,2,4,6]=>[3,1,1,1,1,1]
[8,3,2,4,6,1,5,7]=>[4,1,1,1,1]
[7,3,2,4,6,1,5,8]=>[4,1,1,1,1]
[3,2,5,1,7,4,6,8]=>[3,2,1,1,1]
[3,2,5,1,8,4,6,7]=>[3,2,1,1,1]
[3,2,5,1,7,8,4,6]=>[3,2,1,1,1]
[7,8,3,2,4,6,1,5]=>[4,1,1,1,1]
[6,1,5,7,8,3,2,4]=>[4,1,1,1,1]
[4,2,5,6,1,7,8,3]=>[3,2,1,1,1]
[5,7,6,1,8,3,4,2]=>[4,2,1,1]
[5,8,6,1,7,3,4,2]=>[4,2,1,1]
[6,1,5,8,7,3,2,4]=>[4,2,1,1]
[8,7,3,2,4,6,1,5]=>[5,1,1,1]
[3,2,5,1,8,7,4,6]=>[3,3,1,1]
[3,2,5,1,6,4,7,8]=>[3,2,1,1,1]
[3,2,4,1,8,7,5,6]=>[3,3,1,1]
[3,2,5,1,6,8,7,4]=>[3,3,1,1]
[3,8,6,5,1,7,4,2]=>[5,2,1]
[3,7,6,5,1,8,4,2]=>[5,2,1]
[6,5,1,7,8,4,2,3]=>[4,2,1,1]
[3,2,5,1,6,7,8,4]=>[3,2,1,1,1]
[3,2,4,1,8,5,6,7]=>[3,2,1,1,1]
[3,2,4,1,7,5,6,8]=>[3,2,1,1,1]
[3,2,4,1,6,8,5,7]=>[3,2,1,1,1]
[3,2,4,1,8,5,7,6]=>[3,3,1,1]
[8,3,2,4,7,6,1,5]=>[4,2,1,1]
[3,2,5,1,8,4,7,6]=>[3,3,1,1]
[3,2,5,1,6,7,4,8]=>[3,2,1,1,1]
[6,5,1,7,4,2,3,8]=>[4,2,1,1]
[6,5,1,8,4,2,3,7]=>[4,2,1,1]
[8,4,2,3,7,5,1,6]=>[4,2,1,1]
[4,2,6,1,8,3,7,5]=>[3,3,1,1]
[5,2,6,1,8,3,7,4]=>[3,3,1,1]
[8,4,6,1,7,3,5,2]=>[4,2,1,1]
[5,2,6,1,8,4,7,3]=>[3,3,1,1]
[7,4,2,3,8,5,1,6]=>[4,2,1,1]
[8,5,1,6,4,2,3,7]=>[4,2,1,1]
[7,5,1,6,4,2,3,8]=>[4,2,1,1]
[3,2,5,1,7,6,4,8]=>[3,3,1,1]
[3,2,5,1,8,6,4,7]=>[3,3,1,1]
[7,3,2,4,8,6,1,5]=>[4,2,1,1]
[8,6,1,5,7,3,2,4]=>[5,1,1,1]
[4,2,6,1,8,5,7,3]=>[3,3,1,1]
[8,5,6,1,7,3,4,2]=>[4,2,1,1]
[3,6,8,5,1,7,4,2]=>[4,2,1,1]
[8,5,1,6,7,4,2,3]=>[4,2,1,1]
[3,2,5,1,8,6,7,4]=>[3,3,1,1]
[3,2,4,1,8,6,5,7]=>[3,3,1,1]
[3,2,4,1,5,8,6,7]=>[3,2,1,1,1]
[3,2,5,1,7,8,6,4]=>[3,3,1,1]
[7,8,5,1,6,4,2,3]=>[4,2,1,1]
[3,8,5,1,7,6,4,2]=>[5,2,1]
[3,7,5,1,8,6,4,2]=>[4,3,1]
[8,7,5,1,6,4,2,3]=>[5,2,1]
[3,2,5,1,8,7,6,4]=>[4,3,1]
[6,5,7,3,1,8,4,2]=>[4,3,1]
[4,6,3,7,1,8,5,2]=>[3,3,1,1]
[4,6,3,7,5,1,8,2]=>[3,2,2,1]
[4,2,6,1,7,5,3,8]=>[3,3,1,1]
[2,5,7,4,1,6,3,8]=>[3,2,1,1,1]
[2,5,7,4,1,6,8,3]=>[3,2,1,1,1]
[5,4,7,3,6,1,8,2]=>[4,2,1,1]
[5,4,7,8,3,1,6,2]=>[4,2,1,1]
[4,3,7,5,1,8,6,2]=>[3,3,2]
[6,4,3,8,5,1,7,2]=>[4,2,2]
[5,8,4,3,6,1,7,2]=>[4,2,1,1]
[5,4,8,3,6,1,7,2]=>[4,2,1,1]
[5,4,3,6,7,1,8,2]=>[4,2,1,1]
[2,5,4,6,1,7,3,8]=>[3,2,1,1,1]
[3,2,5,8,1,6,7,4]=>[3,2,1,1,1]
[2,5,4,6,8,1,7,3]=>[3,2,1,1,1]
[5,2,8,4,1,6,7,3]=>[3,2,2,1]
[4,6,2,1,8,5,7,3]=>[3,3,1,1]
[2,4,1,7,5,8,6,3]=>[3,2,2,1]
[2,4,1,7,5,3,8,6]=>[3,2,2,1]
[2,6,4,1,8,5,3,7]=>[3,3,1,1]
[5,4,8,2,1,6,3,7]=>[4,2,1,1]
[2,5,8,4,1,6,3,7]=>[3,2,1,1,1]
[3,2,5,6,1,8,4,7]=>[3,2,1,1,1]
[4,8,3,2,6,1,5,7]=>[4,1,1,1,1]
[3,5,2,8,1,6,4,7]=>[3,2,1,1,1]
[3,2,1,6,8,5,4,7]=>[3,3,1,1]
[3,2,7,1,5,4,8,6]=>[3,2,2,1]
[3,2,7,1,5,8,6,4]=>[3,3,1,1]
[3,8,2,5,1,6,7,4]=>[3,2,1,1,1]
[4,8,3,2,6,7,1,5]=>[4,1,1,1,1]
[4,3,8,2,6,7,1,5]=>[4,1,1,1,1]
[4,3,2,6,7,8,1,5]=>[4,1,1,1,1]
[4,3,2,6,7,1,5,8]=>[4,1,1,1,1]
[4,3,7,2,6,8,1,5]=>[4,1,1,1,1]
[4,3,7,8,2,6,1,5]=>[4,1,1,1,1]
[2,5,7,4,8,1,6,3]=>[3,2,1,1,1]
[3,2,5,7,8,1,6,4]=>[3,2,1,1,1]
[3,2,5,7,1,6,8,4]=>[3,2,1,1,1]
[3,2,5,7,1,6,4,8]=>[3,2,1,1,1]
[6,3,2,7,1,5,4,8]=>[4,2,1,1]
[6,3,2,7,1,5,8,4]=>[4,2,1,1]
[6,3,2,7,8,1,5,4]=>[4,2,1,1]
[4,2,6,1,7,8,5,3]=>[3,3,1,1]
[6,5,2,1,7,8,4,3]=>[4,3,1]
[2,1,7,5,3,8,6,4]=>[3,3,2]
[6,2,1,8,5,3,7,4]=>[3,3,2]
[6,3,2,7,1,4,8,5]=>[4,2,1,1]
[6,3,2,1,4,7,8,5]=>[4,2,1,1]
[6,3,2,1,4,7,5,8]=>[4,2,1,1]
[3,5,2,1,7,4,6,8]=>[3,2,1,1,1]
[3,5,2,1,7,8,4,6]=>[3,2,1,1,1]
[5,8,4,2,1,7,3,6]=>[4,2,1,1]
[4,6,2,1,8,3,7,5]=>[3,3,1,1]
[2,4,1,7,3,8,6,5]=>[3,2,2,1]
[3,2,7,1,4,8,6,5]=>[3,3,1,1]
[3,5,8,2,1,7,4,6]=>[3,2,1,1,1]
[4,8,3,7,2,1,5,6]=>[4,1,1,1,1]
[4,3,7,2,8,1,5,6]=>[4,1,1,1,1]
[4,3,7,2,1,5,6,8]=>[4,1,1,1,1]
[4,8,3,2,7,1,5,6]=>[4,1,1,1,1]
[3,5,2,8,1,7,4,6]=>[3,2,1,1,1]
[6,3,2,8,1,4,7,5]=>[4,2,1,1]
[3,2,1,4,7,5,8,6]=>[3,2,2,1]
[5,3,2,1,8,4,6,7]=>[4,2,1,1]
[4,8,3,2,1,5,6,7]=>[4,1,1,1,1]
[4,3,8,2,1,5,6,7]=>[4,1,1,1,1]
[6,2,3,1,5,4,8,7]=>[3,2,2,1]
[8,4,5,2,3,1,7,6]=>[4,2,1,1]
[8,6,7,2,5,3,4,1]=>[5,1,1,1]
[8,2,5,3,4,1,7,6]=>[4,2,1,1]
[6,2,5,3,4,1,8,7]=>[4,2,1,1]
[6,1,5,2,4,3,8,7]=>[4,2,1,1]
[6,4,5,1,3,2,8,7]=>[4,2,1,1]
[6,1,5,3,4,2,8,7]=>[4,2,1,1]
[6,3,5,1,4,2,8,7]=>[4,2,1,1]
[8,3,5,2,4,1,7,6]=>[4,2,1,1]
[8,3,7,5,6,2,4,1]=>[5,1,1,1]
[8,3,7,2,4,1,6,5]=>[4,2,1,1]
[8,3,5,1,4,2,7,6]=>[4,2,1,1]
[8,1,5,3,4,2,7,6]=>[4,2,1,1]
[8,4,5,1,3,2,7,6]=>[4,2,1,1]
[2,1,8,4,5,3,7,6]=>[3,2,2,1]
[8,6,7,4,5,1,3,2]=>[5,1,1,1]
[8,6,7,1,5,3,4,2]=>[5,1,1,1]
[8,6,7,3,5,1,4,2]=>[5,1,1,1]
[8,3,7,5,6,1,4,2]=>[5,1,1,1]
[8,5,7,3,6,1,4,2]=>[5,1,1,1]
[8,3,7,4,6,2,5,1]=>[5,1,1,1]
[8,3,7,4,6,1,5,2]=>[5,1,1,1]
[8,3,7,1,6,4,5,2]=>[5,1,1,1]
[8,1,7,3,6,4,5,2]=>[5,1,1,1]
[8,1,7,5,6,3,4,2]=>[5,1,1,1]
[8,4,7,5,6,1,3,2]=>[5,1,1,1]
[2,1,8,4,7,5,6,3]=>[4,2,1,1]
[8,1,7,3,4,2,6,5]=>[4,2,1,1]
[8,1,7,3,6,2,5,4]=>[5,1,1,1]
[8,3,7,1,6,2,5,4]=>[5,1,1,1]
[8,3,7,2,6,4,5,1]=>[5,1,1,1]
[8,2,7,3,6,4,5,1]=>[5,1,1,1]
[8,2,7,3,6,1,5,4]=>[5,1,1,1]
[8,2,7,1,6,3,5,4]=>[5,1,1,1]
[8,1,7,2,4,3,6,5]=>[4,2,1,1]
[8,1,3,2,7,4,6,5]=>[4,2,1,1]
[2,1,8,3,7,4,6,5]=>[4,2,1,1]
[8,1,5,2,4,3,7,6]=>[4,2,1,1]
[8,2,7,1,4,3,6,5]=>[4,2,1,1]
[8,2,7,3,4,1,6,5]=>[4,2,1,1]
[8,2,7,5,6,3,4,1]=>[5,1,1,1]
[8,4,7,5,6,2,3,1]=>[5,1,1,1]
[8,4,7,2,3,1,6,5]=>[4,2,1,1]
[8,2,3,1,7,4,6,5]=>[4,2,1,1]
[8,2,3,1,5,4,7,6]=>[3,2,2,1]
[4,2,3,1,8,5,7,6]=>[3,3,1,1]
[4,1,3,2,8,6,7,5]=>[3,3,1,1]
[8,6,7,2,3,1,5,4]=>[4,2,1,1]
[8,2,3,1,7,5,6,4]=>[4,2,1,1]
[8,5,7,2,6,3,4,1]=>[5,1,1,1]
[8,5,7,2,6,1,4,3]=>[5,1,1,1]
[8,2,7,5,6,1,4,3]=>[5,1,1,1]
[8,6,7,2,5,1,4,3]=>[5,1,1,1]
[8,6,7,1,5,2,4,3]=>[5,1,1,1]
[8,6,7,1,3,2,5,4]=>[4,2,1,1]
[2,1,8,6,7,3,5,4]=>[4,2,1,1]
[2,1,8,3,7,5,6,4]=>[4,2,1,1]
[8,1,3,2,7,5,6,4]=>[4,2,1,1]
[8,1,7,5,6,2,4,3]=>[5,1,1,1]
[8,1,7,2,6,4,5,3]=>[5,1,1,1]
[8,2,7,1,6,4,5,3]=>[5,1,1,1]
[8,2,7,4,6,1,5,3]=>[5,1,1,1]
[8,2,7,4,6,3,5,1]=>[5,1,1,1]
[8,4,7,2,6,3,5,1]=>[5,1,1,1]
[8,4,7,2,6,1,5,3]=>[5,1,1,1]
[8,4,7,1,6,2,5,3]=>[5,1,1,1]
[8,1,7,4,6,2,5,3]=>[5,1,1,1]
[8,5,7,1,6,2,4,3]=>[5,1,1,1]
[2,1,8,5,7,3,6,4]=>[4,2,1,1]
[8,5,7,4,6,1,3,2]=>[5,1,1,1]
[8,5,7,1,6,3,4,2]=>[5,1,1,1]
[8,1,7,4,6,3,5,2]=>[5,1,1,1]
[8,4,7,1,6,3,5,2]=>[5,1,1,1]
[8,4,7,3,6,1,5,2]=>[5,1,1,1]
[2,4,8,3,6,1,7,5]=>[3,2,1,1,1]
[6,5,8,1,3,2,7,4]=>[4,2,1,1]
[4,5,8,6,3,2,7,1]=>[5,1,1,1]
[6,5,8,7,3,1,2,4]=>[4,2,1,1]
[1,5,8,7,3,6,2,4]=>[4,1,1,1,1]
[1,7,2,8,4,6,5,3]=>[4,2,1,1]
[6,7,2,8,4,1,5,3]=>[3,2,2,1]
[3,6,2,8,4,5,7,1]=>[3,2,1,1,1]
[2,6,1,8,4,5,7,3]=>[3,2,1,1,1]
[2,8,4,6,1,5,7,3]=>[4,1,1,1,1]
[6,3,1,8,4,5,7,2]=>[3,3,1,1]
[3,1,6,8,4,5,7,2]=>[3,2,1,1,1]
[2,3,6,8,4,5,7,1]=>[3,1,1,1,1,1]
[6,3,7,8,4,1,5,2]=>[3,2,2,1]
[1,3,7,8,4,6,5,2]=>[4,1,1,1,1]
[1,5,7,8,2,4,6,3]=>[3,1,1,1,1,1]
[5,1,7,8,2,4,6,3]=>[3,2,1,1,1]
[3,6,7,8,4,2,5,1]=>[4,1,1,1,1]
[7,6,1,8,4,2,5,3]=>[4,2,2]
[5,6,8,7,3,2,1,4]=>[5,1,1,1]
[2,8,3,7,1,6,5,4]=>[5,1,1,1]
[5,2,8,7,3,6,1,4]=>[4,2,1,1]
[7,2,1,8,4,6,5,3]=>[4,3,1]
[3,2,7,8,4,6,5,1]=>[4,2,1,1]
[5,2,7,8,1,4,6,3]=>[3,2,1,1,1]
[1,2,7,8,5,4,6,3]=>[4,1,1,1,1]
[4,2,1,3,8,5,6,7]=>[3,2,1,1,1]
[7,2,5,8,3,4,6,1]=>[4,1,1,1,1]
[6,2,8,5,4,3,1,7]=>[5,2,1]
[2,8,3,5,4,1,6,7]=>[4,1,1,1,1]
[2,8,4,5,3,1,6,7]=>[4,1,1,1,1]
[6,4,8,5,2,3,1,7]=>[4,2,1,1]
[7,3,5,8,2,4,6,1]=>[4,1,1,1,1]
[4,3,1,2,8,5,6,7]=>[3,2,1,1,1]
[3,4,2,1,8,5,6,7]=>[3,2,1,1,1]
[2,7,6,8,4,3,5,1]=>[5,1,1,1]
[5,7,1,8,3,4,6,2]=>[3,2,1,1,1]
[3,7,5,8,1,4,6,2]=>[4,1,1,1,1]
[1,7,5,8,3,4,6,2]=>[4,1,1,1,1]
[1,6,8,5,4,3,2,7]=>[5,1,1,1]
[4,6,8,5,1,3,2,7]=>[4,1,1,1,1]
[5,6,8,1,4,3,2,7]=>[4,1,1,1,1]
[7,5,8,6,3,4,2,1]=>[5,2,1]
[2,4,8,3,6,5,1,7]=>[4,1,1,1,1]
[2,8,4,1,5,6,3,7]=>[3,2,1,1,1]
[4,1,8,3,5,6,2,7]=>[3,2,1,1,1]
[5,6,8,4,1,3,2,7]=>[4,1,1,1,1]
[4,6,8,1,5,3,2,7]=>[4,1,1,1,1]
[1,6,8,4,5,3,2,7]=>[4,1,1,1,1]
[1,7,3,8,5,4,6,2]=>[4,2,1,1]
[3,7,1,8,5,4,6,2]=>[4,2,1,1]
[2,7,3,8,4,6,5,1]=>[4,2,1,1]
[7,1,3,8,4,6,5,2]=>[4,2,1,1]
[5,7,8,4,3,6,1,2]=>[4,1,1,1,1]
[2,8,7,4,1,6,5,3]=>[5,2,1]
[2,8,5,4,3,1,6,7]=>[5,1,1,1]
[6,5,8,4,2,3,1,7]=>[5,1,1,1]
[4,1,3,2,8,5,6,7]=>[3,2,1,1,1]
[1,4,3,2,8,5,6,7]=>[3,2,1,1,1]
[7,3,2,8,5,4,6,1]=>[4,3,1]
[6,4,8,2,5,3,1,7]=>[4,2,1,1]
[2,8,4,3,5,1,6,7]=>[4,1,1,1,1]
[2,8,3,4,5,1,6,7]=>[3,1,1,1,1,1]
[6,2,8,4,5,3,1,7]=>[4,2,1,1]
[7,2,3,8,5,4,6,1]=>[4,2,1,1]
[4,2,3,1,8,5,6,7]=>[3,2,1,1,1]
[3,2,1,4,8,5,6,7]=>[3,2,1,1,1]
[5,1,3,2,4,8,6,7]=>[3,2,1,1,1]
[2,8,1,5,3,4,7,6]=>[3,2,1,1,1]
[1,2,8,4,5,3,7,6]=>[3,2,1,1,1]
[1,4,2,8,5,3,6,7]=>[3,2,1,1,1]
[1,8,4,2,5,3,6,7]=>[3,2,1,1,1]
[8,1,5,3,2,4,6,7]=>[4,1,1,1,1]
[3,8,1,5,2,4,6,7]=>[3,1,1,1,1,1]
[3,5,1,4,8,2,6,7]=>[3,1,1,1,1,1]
[1,5,2,8,4,3,6,7]=>[3,2,1,1,1]
[1,2,8,5,4,3,6,7]=>[4,1,1,1,1]
[1,2,5,4,3,8,6,7]=>[3,2,1,1,1]
[1,2,4,8,5,3,7,6]=>[3,2,1,1,1]
[1,2,7,4,8,5,3,6]=>[3,2,1,1,1]
[1,5,2,7,8,4,3,6]=>[3,2,1,1,1]
[5,1,2,7,4,8,3,6]=>[3,2,1,1,1]
[8,3,5,1,4,7,2,6]=>[4,1,1,1,1]
[2,8,1,5,4,7,3,6]=>[4,1,1,1,1]
[1,2,8,5,7,4,3,6]=>[4,1,1,1,1]
[1,2,4,8,7,5,3,6]=>[4,1,1,1,1]
[2,8,1,4,3,7,6,5]=>[4,2,1,1]
[6,1,2,8,7,4,3,5]=>[4,2,1,1]
[6,4,1,2,8,7,3,5]=>[3,3,1,1]
[3,6,4,8,1,7,2,5]=>[3,2,1,1,1]
[7,6,1,4,2,8,3,5]=>[4,2,1,1]
[7,1,6,2,8,4,3,5]=>[4,2,1,1]
[1,6,7,2,8,4,3,5]=>[3,2,1,1,1]
[6,7,1,4,2,8,3,5]=>[3,2,1,1,1]
[6,3,7,1,4,8,2,5]=>[3,2,1,1,1]
[3,7,8,1,5,2,4,6]=>[3,1,1,1,1,1]
[7,1,2,8,5,3,4,6]=>[3,2,1,1,1]
[1,7,2,8,4,5,3,6]=>[3,2,1,1,1]
[1,4,2,7,8,5,3,6]=>[3,2,1,1,1]
[6,1,2,8,4,3,7,5]=>[3,2,2,1]
[6,4,1,2,8,3,7,5]=>[3,3,1,1]
[7,6,1,3,2,4,8,5]=>[4,2,1,1]
[6,7,1,3,2,4,8,5]=>[3,2,1,1,1]
[1,2,7,3,5,8,4,6]=>[3,1,1,1,1,1]
[1,2,7,5,8,3,4,6]=>[3,1,1,1,1,1]
[5,8,1,3,7,2,4,6]=>[3,1,1,1,1,1]
[1,2,5,8,7,3,4,6]=>[3,1,1,1,1,1]
[1,2,5,8,3,7,4,6]=>[3,1,1,1,1,1]
[2,8,1,7,3,5,4,6]=>[4,1,1,1,1]
[8,6,1,3,2,4,7,5]=>[4,2,1,1]
[4,2,8,1,7,3,6,5]=>[4,2,1,1]
[2,8,1,7,4,3,6,5]=>[4,2,1,1]
[7,1,2,8,4,3,6,5]=>[3,2,2,1]
[1,2,8,4,7,5,3,6]=>[4,1,1,1,1]
[1,2,8,7,4,5,3,6]=>[4,1,1,1,1]
[2,8,1,7,5,3,4,6]=>[4,1,1,1,1]
[8,3,7,1,5,2,4,6]=>[4,1,1,1,1]
[3,8,6,1,4,7,2,5]=>[4,1,1,1,1]
[8,6,1,4,2,7,3,5]=>[4,2,1,1]
[8,1,6,2,7,4,3,5]=>[4,2,1,1]
[7,1,2,8,6,4,3,5]=>[4,2,1,1]
[7,4,1,2,8,6,3,5]=>[3,3,1,1]
[3,7,4,8,1,6,2,5]=>[3,2,1,1,1]
[3,4,8,7,1,6,2,5]=>[4,1,1,1,1]
[4,2,8,1,7,6,3,5]=>[4,2,1,1]
[2,8,1,7,6,4,3,5]=>[5,1,1,1]
[7,8,3,4,1,5,2,6]=>[3,2,1,1,1]
[7,8,3,4,1,6,2,5]=>[3,2,1,1,1]
[6,8,3,4,1,7,2,5]=>[3,2,1,1,1]
[6,7,3,4,1,8,2,5]=>[3,2,1,1,1]
[5,7,3,4,1,8,2,6]=>[3,2,1,1,1]
[5,8,3,4,1,7,2,6]=>[3,2,1,1,1]
[5,8,3,4,1,6,2,7]=>[3,2,1,1,1]
[6,8,3,4,1,5,2,7]=>[3,2,1,1,1]
[6,7,3,4,1,5,2,8]=>[3,2,1,1,1]
[5,7,3,4,1,6,2,8]=>[3,2,1,1,1]
[5,6,2,8,3,4,1,7]=>[3,2,1,1,1]
[5,6,2,7,3,4,1,8]=>[3,2,1,1,1]
[4,6,2,8,3,5,1,7]=>[3,2,1,1,1]
[4,7,3,5,1,6,2,8]=>[3,2,1,1,1]
[4,8,3,5,1,6,2,7]=>[3,2,1,1,1]
[4,8,3,5,1,7,2,6]=>[3,2,1,1,1]
[4,7,3,5,1,8,2,6]=>[3,2,1,1,1]
[5,6,2,3,1,7,4,8]=>[3,2,1,1,1]
[5,6,2,4,1,8,3,7]=>[3,2,1,1,1]
[5,6,2,4,1,7,3,8]=>[3,2,1,1,1]
[4,6,2,5,1,7,3,8]=>[3,2,1,1,1]
[4,6,2,5,1,8,3,7]=>[3,2,1,1,1]
[4,5,1,8,3,7,2,6]=>[3,2,1,1,1]
[4,5,1,7,3,8,2,6]=>[3,2,1,1,1]
[4,6,2,7,3,8,1,5]=>[3,2,1,1,1]
[5,6,2,7,3,8,1,4]=>[3,2,1,1,1]
[5,6,2,7,4,8,1,3]=>[3,2,1,1,1]
[5,6,3,8,4,7,1,2]=>[3,2,1,1,1]
[5,6,2,8,4,7,1,3]=>[3,2,1,1,1]
[5,6,2,8,3,7,1,4]=>[3,2,1,1,1]
[4,6,2,8,3,7,1,5]=>[3,2,1,1,1]
[4,5,1,7,3,6,2,8]=>[3,2,1,1,1]
[4,5,1,8,3,6,2,7]=>[3,2,1,1,1]
[6,5,3,2,1,4,8,7]=>[5,2,1]
[4,6,3,5,2,1,8,7]=>[4,2,1,1]
[8,7,3,5,2,4,1,6]=>[5,1,1,1]
[6,8,2,4,5,7,3,1]=>[4,1,1,1,1]
[8,7,2,4,5,3,1,6]=>[5,1,1,1]
[3,6,1,4,5,2,8,7]=>[3,2,1,1,1]
[8,3,7,4,5,2,1,6]=>[5,1,1,1]
[6,3,8,4,5,7,2,1]=>[4,2,1,1]
[5,8,7,4,3,6,2,1]=>[6,1,1]
[2,8,7,4,3,6,1,5]=>[5,1,1,1]
[8,1,7,4,3,6,2,5]=>[5,1,1,1]
[8,7,3,5,1,4,2,6]=>[5,1,1,1]
[2,1,6,8,5,7,4,3]=>[4,2,1,1]
[6,8,3,5,1,7,4,2]=>[4,2,1,1]
[5,1,8,4,7,6,3,2]=>[5,2,1]
[2,5,8,4,7,6,3,1]=>[5,1,1,1]
[4,3,8,1,5,6,7,2]=>[3,2,1,1,1]
[4,8,1,3,5,6,7,2]=>[3,1,1,1,1,1]
[5,8,7,4,1,6,3,2]=>[5,2,1]
[5,8,3,6,1,4,7,2]=>[4,1,1,1,1]
[4,8,3,6,1,2,7,5]=>[3,2,1,1,1]
[3,8,7,4,1,6,2,5]=>[4,2,1,1]
[3,8,1,2,5,6,7,4]=>[3,1,1,1,1,1]
[8,7,1,4,2,6,3,5]=>[4,2,1,1]
[8,6,3,1,2,4,7,5]=>[4,2,1,1]
[8,1,7,4,5,2,3,6]=>[4,1,1,1,1]
[2,8,7,4,5,1,3,6]=>[4,1,1,1,1]
[8,7,2,4,1,6,3,5]=>[4,2,1,1]
[5,8,3,6,2,4,7,1]=>[4,1,1,1,1]
[8,6,3,2,1,4,7,5]=>[5,2,1]
[8,7,3,5,2,1,4,6]=>[5,1,1,1]
[5,8,3,6,2,1,7,4]=>[4,2,1,1]
[5,8,7,4,2,6,1,3]=>[5,1,1,1]
[2,6,8,4,5,7,1,3]=>[3,1,1,1,1,1]
[6,1,8,4,5,7,2,3]=>[3,2,1,1,1]
[6,8,3,5,1,7,2,4]=>[3,2,1,1,1]
[2,1,5,8,3,6,7,4]=>[3,2,1,1,1]
[5,8,3,6,1,2,7,4]=>[3,2,1,1,1]
[4,1,8,2,5,6,7,3]=>[3,2,1,1,1]
[2,4,8,1,5,6,7,3]=>[3,1,1,1,1,1]
[4,8,2,1,5,6,7,3]=>[3,2,1,1,1]
[3,4,8,2,5,6,7,1]=>[3,1,1,1,1,1]
[5,8,1,4,7,6,2,3]=>[4,1,1,1,1]
[5,8,3,1,6,2,7,4]=>[3,2,2,1]
[4,5,3,8,6,1,7,2]=>[3,2,2,1]
[3,4,1,8,5,6,7,2]=>[3,2,1,1,1]
[4,5,7,6,2,3,8,1]=>[4,1,1,1,1]
[3,5,7,2,6,4,8,1]=>[4,1,1,1,1]
[2,5,7,3,6,4,8,1]=>[4,1,1,1,1]
[8,4,3,7,6,1,5,2]=>[5,2,1]
[8,2,4,7,1,6,5,3]=>[5,1,1,1]
[6,7,1,3,5,8,4,2]=>[4,1,1,1,1]
[5,8,7,3,6,1,4,2]=>[5,1,1,1]
[4,8,3,7,6,1,5,2]=>[5,1,1,1]
[3,8,4,7,6,1,5,2]=>[5,1,1,1]
[2,8,4,7,1,6,5,3]=>[5,1,1,1]
[8,1,4,7,2,6,5,3]=>[5,1,1,1]
[8,1,3,2,7,6,5,4]=>[5,2,1]
[3,8,2,1,7,6,5,4]=>[5,2,1]
[6,7,1,2,8,5,4,3]=>[4,2,1,1]
[8,3,2,1,7,6,5,4]=>[5,3]
[1,4,2,7,8,6,5,3]=>[4,2,1,1]
[8,4,2,7,1,6,5,3]=>[5,2,1]
[8,5,7,2,1,6,4,3]=>[5,2,1]
[1,5,7,2,8,6,4,3]=>[4,2,1,1]
[5,4,7,6,8,1,3,2]=>[4,2,1,1]
[1,4,8,7,2,6,5,3]=>[5,1,1,1]
[4,3,8,7,6,1,5,2]=>[5,2,1]
[5,3,7,8,6,1,4,2]=>[4,2,1,1]
[6,7,2,8,1,5,4,3]=>[4,2,1,1]
[5,2,7,8,1,6,4,3]=>[4,2,1,1]
[4,2,8,7,1,6,5,3]=>[5,2,1]
[3,2,8,1,7,6,5,4]=>[5,2,1]
[1,3,8,2,7,6,5,4]=>[5,1,1,1]
[1,2,8,3,7,6,5,4]=>[5,1,1,1]
[2,1,8,3,7,6,5,4]=>[5,2,1]
[5,1,7,8,2,6,4,3]=>[4,2,1,1]
[4,8,1,7,2,6,5,3]=>[5,1,1,1]
[3,8,1,2,7,6,5,4]=>[5,1,1,1]
[2,8,1,3,7,6,5,4]=>[5,1,1,1]
[1,8,2,3,7,6,5,4]=>[5,1,1,1]
[8,1,2,3,7,6,5,4]=>[5,1,1,1]
[6,7,1,8,4,5,2,3]=>[3,2,1,1,1]
[3,7,1,5,8,2,6,4]=>[3,2,1,1,1]
[2,7,1,5,8,3,6,4]=>[3,2,1,1,1]
[2,6,5,1,8,3,7,4]=>[3,3,1,1]
[3,6,5,1,8,2,7,4]=>[3,3,1,1]
[4,6,5,1,8,7,2,3]=>[3,3,1,1]
[5,6,4,1,8,7,2,3]=>[3,3,1,1]
[8,1,4,5,7,6,2,3]=>[4,1,1,1,1]
[6,4,5,1,8,7,2,3]=>[3,3,1,1]
[5,4,6,1,8,7,2,3]=>[3,3,1,1]
[4,5,6,1,8,7,2,3]=>[3,2,1,1,1]
[3,5,6,1,8,2,7,4]=>[3,2,1,1,1]
[2,5,6,1,8,3,7,4]=>[3,2,1,1,1]
[2,4,6,1,3,8,7,5]=>[3,2,1,1,1]
[3,4,6,1,2,8,7,5]=>[3,2,1,1,1]
[4,3,6,1,2,8,7,5]=>[3,3,1,1]
[5,3,6,1,8,2,7,4]=>[3,3,1,1]
[7,3,1,5,8,2,6,4]=>[3,3,1,1]
[8,1,3,5,7,2,6,4]=>[4,1,1,1,1]
[8,1,2,5,7,3,6,4]=>[4,1,1,1,1]
[7,2,1,5,8,3,6,4]=>[3,3,1,1]
[6,2,5,1,8,3,7,4]=>[3,3,1,1]
[4,2,6,1,3,8,7,5]=>[3,3,1,1]
[2,3,6,1,4,8,7,5]=>[3,2,1,1,1]
[4,2,5,3,1,8,7,6]=>[3,3,2]
[6,2,4,1,3,8,7,5]=>[3,3,1,1]
[7,2,1,4,3,8,6,5]=>[3,3,2]
[8,1,2,4,3,7,6,5]=>[4,2,1,1]
[8,1,3,4,2,7,6,5]=>[4,2,1,1]
[7,3,1,4,2,8,6,5]=>[3,3,2]
[6,3,4,1,2,8,7,5]=>[3,3,1,1]
[4,6,3,1,2,8,7,5]=>[3,3,1,1]
[3,6,4,1,2,8,7,5]=>[3,3,1,1]
[2,6,4,1,3,8,7,5]=>[3,3,1,1]
[2,7,1,4,3,8,6,5]=>[3,3,1,1]
[3,7,1,4,2,8,6,5]=>[3,3,1,1]
[4,7,1,3,2,8,6,5]=>[3,3,1,1]
[8,1,6,7,2,3,5,4]=>[4,1,1,1,1]
[4,7,1,2,3,8,6,5]=>[3,2,1,1,1]
[3,7,1,2,4,8,6,5]=>[3,2,1,1,1]
[2,7,1,3,4,8,6,5]=>[3,2,1,1,1]
[2,6,3,1,4,8,7,5]=>[3,3,1,1]
[3,6,2,1,4,8,7,5]=>[3,3,1,1]
[5,6,2,1,8,3,7,4]=>[3,3,1,1]
[6,5,2,1,8,3,7,4]=>[4,3,1]
[8,1,5,2,7,3,6,4]=>[4,2,1,1]
[8,1,4,2,3,7,6,5]=>[4,2,1,1]
[7,4,1,2,3,8,6,5]=>[3,3,1,1]
[6,4,2,1,3,8,7,5]=>[4,3,1]
[5,4,2,3,1,8,7,6]=>[4,3,1]
[3,5,2,4,1,8,7,6]=>[3,3,1,1]
[6,3,2,1,4,8,7,5]=>[4,3,1]
[7,3,1,2,4,8,6,5]=>[3,3,1,1]
[8,1,3,2,4,7,6,5]=>[4,2,1,1]
[8,1,2,3,4,7,6,5]=>[4,1,1,1,1]
[7,2,1,3,4,8,6,5]=>[3,3,1,1]
[6,2,3,1,4,8,7,5]=>[3,3,1,1]
[2,4,3,6,1,5,8,7]=>[3,2,1,1,1]
[2,4,3,6,5,8,1,7]=>[3,2,1,1,1]
[2,4,6,3,5,8,7,1]=>[3,2,1,1,1]
[2,4,6,3,5,8,1,7]=>[3,1,1,1,1,1]
[2,4,6,3,5,1,8,7]=>[3,2,1,1,1]
[2,4,6,3,1,5,8,7]=>[3,2,1,1,1]
[2,4,1,6,5,3,8,7]=>[3,2,2,1]
[2,4,6,1,5,3,8,7]=>[3,2,1,1,1]
[4,2,6,5,3,1,8,7]=>[4,2,2]
[4,2,6,5,1,3,8,7]=>[3,2,2,1]
[4,2,6,5,1,8,7,3]=>[3,3,2]
[4,2,6,5,8,1,7,3]=>[3,2,2,1]
[4,2,6,5,8,1,3,7]=>[3,2,1,1,1]
[4,2,6,5,8,3,1,7]=>[4,2,1,1]
[2,4,6,1,5,8,3,7]=>[3,1,1,1,1,1]
[2,4,1,6,5,8,3,7]=>[3,2,1,1,1]
[2,1,4,6,5,8,3,7]=>[3,2,1,1,1]
[2,4,1,6,5,8,7,3]=>[3,2,2,1]
[2,4,6,1,5,8,7,3]=>[3,2,1,1,1]
[4,2,6,5,3,8,7,1]=>[4,2,2]
[4,2,6,5,8,3,7,1]=>[4,2,1,1]
[2,6,4,3,8,7,1,5]=>[4,2,1,1]
[2,6,4,3,8,7,5,1]=>[4,3,1]
[4,2,6,8,5,3,7,1]=>[4,2,1,1]
[2,4,6,8,1,5,7,3]=>[3,1,1,1,1,1]
[2,4,6,1,8,5,7,3]=>[3,2,1,1,1]
[2,4,1,6,8,5,7,3]=>[3,2,1,1,1]
[2,1,4,6,8,5,7,3]=>[3,2,1,1,1]
[2,1,4,6,8,5,3,7]=>[3,2,1,1,1]
[2,4,1,6,8,5,3,7]=>[3,2,1,1,1]
[2,4,6,1,8,5,3,7]=>[3,2,1,1,1]
[2,4,6,8,1,5,3,7]=>[3,1,1,1,1,1]
[4,2,6,8,5,3,1,7]=>[4,2,1,1]
[4,2,6,8,5,1,3,7]=>[3,2,1,1,1]
[4,2,6,8,5,1,7,3]=>[3,2,2,1]
[2,4,6,8,3,5,7,1]=>[3,1,1,1,1,1]
[2,4,6,8,3,5,1,7]=>[3,1,1,1,1,1]
[2,4,6,8,3,1,5,7]=>[3,1,1,1,1,1]
[2,4,6,3,1,8,5,7]=>[3,2,1,1,1]
[2,4,6,3,8,1,5,7]=>[3,1,1,1,1,1]
[2,4,6,3,8,5,1,7]=>[3,2,1,1,1]
[2,4,6,3,8,5,7,1]=>[3,2,1,1,1]
[2,4,3,6,8,5,7,1]=>[3,2,1,1,1]
[2,4,3,6,8,5,1,7]=>[3,2,1,1,1]
[2,4,3,6,8,1,5,7]=>[3,1,1,1,1,1]
[2,4,3,6,1,8,5,7]=>[3,2,1,1,1]
[2,4,3,1,6,8,5,7]=>[3,2,1,1,1]
[2,4,1,3,6,8,7,5]=>[3,2,1,1,1]
[2,4,3,6,1,8,7,5]=>[3,3,1,1]
[2,4,3,6,8,1,7,5]=>[3,2,1,1,1]
[4,6,5,2,8,7,3,1]=>[4,3,1]
[4,6,5,2,8,7,1,3]=>[4,2,1,1]
[4,6,2,5,8,7,1,3]=>[3,2,1,1,1]
[4,6,2,5,8,7,3,1]=>[4,2,1,1]
[2,4,6,3,8,1,7,5]=>[3,2,1,1,1]
[2,4,6,3,1,8,7,5]=>[3,3,1,1]
[2,4,1,6,3,8,7,5]=>[3,2,2,1]
[2,1,4,6,3,8,7,5]=>[3,2,2,1]
[2,1,4,6,8,3,7,5]=>[3,2,1,1,1]
[2,4,1,6,8,3,7,5]=>[3,2,1,1,1]
[2,4,6,1,8,3,7,5]=>[3,2,1,1,1]
[2,4,6,8,1,3,7,5]=>[3,1,1,1,1,1]
[2,4,6,8,3,1,7,5]=>[3,2,1,1,1]
[4,6,2,8,5,7,3,1]=>[4,2,1,1]
[4,6,2,8,5,7,1,3]=>[3,2,1,1,1]
[6,2,4,8,7,1,3,5]=>[3,2,1,1,1]
[6,4,2,8,7,5,3,1]=>[5,3]
[2,6,4,8,1,7,5,3]=>[4,2,1,1]
[2,6,4,1,8,7,5,3]=>[4,3,1]
[2,6,1,4,8,7,5,3]=>[4,2,1,1]
[2,1,6,4,8,7,5,3]=>[4,2,2]
[2,1,6,4,8,7,3,5]=>[3,2,2,1]
[2,6,1,4,8,7,3,5]=>[3,2,1,1,1]
[2,6,4,1,8,7,3,5]=>[3,3,1,1]
[2,6,4,8,1,7,3,5]=>[3,2,1,1,1]
[6,4,2,8,7,5,1,3]=>[4,3,1]
[6,2,4,8,7,3,5,1]=>[4,2,1,1]
[6,2,4,8,7,3,1,5]=>[4,2,1,1]
[1,6,4,7,3,8,2,5]=>[4,1,1,1,1]
[1,3,7,4,5,8,2,6]=>[3,1,1,1,1,1]
[5,2,4,7,3,6,8,1]=>[4,1,1,1,1]
[1,7,6,3,4,8,2,5]=>[4,1,1,1,1]
[8,1,6,3,7,2,4,5]=>[4,1,1,1,1]
[7,1,6,3,8,2,4,5]=>[4,1,1,1,1]
[1,2,7,4,8,3,5,6]=>[3,1,1,1,1,1]
[6,1,7,3,4,8,2,5]=>[3,2,1,1,1]
[2,1,7,4,5,8,3,6]=>[3,2,1,1,1]
[5,1,4,7,3,8,2,6]=>[4,1,1,1,1]
[4,3,1,7,5,8,2,6]=>[3,3,1,1]
[2,8,6,3,7,1,4,5]=>[4,1,1,1,1]
[6,8,1,3,7,2,4,5]=>[3,1,1,1,1,1]
[5,8,2,1,7,3,4,6]=>[3,2,1,1,1]
[5,7,2,1,8,3,4,6]=>[3,2,1,1,1]
[6,7,1,3,8,2,4,5]=>[3,1,1,1,1,1]
[5,1,2,4,8,3,6,7]=>[3,1,1,1,1,1]
[4,3,6,1,5,8,2,7]=>[3,2,1,1,1]
[2,6,1,4,5,8,3,7]=>[3,1,1,1,1,1]
[6,5,1,3,4,8,2,7]=>[4,1,1,1,1]
[1,6,2,4,8,3,5,7]=>[3,1,1,1,1,1]
[8,5,1,3,7,2,4,6]=>[4,1,1,1,1]
[1,5,3,2,8,4,6,7]=>[3,2,1,1,1]
[6,4,2,1,5,8,3,7]=>[4,2,1,1]
[2,5,3,4,1,8,6,7]=>[3,2,1,1,1]
[4,3,5,2,1,8,6,7]=>[4,2,1,1]
[2,6,4,8,7,1,3,5]=>[3,2,1,1,1]
[1,6,4,8,7,2,3,5]=>[3,2,1,1,1]
[2,7,8,3,6,1,4,5]=>[3,1,1,1,1,1]
[4,3,2,8,7,1,5,6]=>[4,2,1,1]
[5,2,4,8,7,1,3,6]=>[3,2,1,1,1]
[6,2,8,3,7,1,4,5]=>[3,2,1,1,1]
[5,1,4,8,7,2,3,6]=>[3,2,1,1,1]
[4,8,2,5,1,3,7,6]=>[3,2,1,1,1]
[4,7,2,5,1,3,8,6]=>[3,2,1,1,1]
[3,7,2,1,5,4,8,6]=>[3,2,2,1]
[3,8,2,1,5,4,7,6]=>[3,2,2,1]
[8,3,2,1,5,4,6,7]=>[4,2,1,1]
[8,3,2,1,6,4,5,7]=>[4,2,1,1]
[8,4,2,5,1,6,3,7]=>[4,2,1,1]
[8,3,2,1,5,6,4,7]=>[4,2,1,1]
[8,3,2,1,4,6,5,7]=>[4,2,1,1]
[3,8,2,1,4,5,7,6]=>[3,2,1,1,1]
[3,7,2,1,4,5,8,6]=>[3,2,1,1,1]
[3,2,7,1,4,6,8,5]=>[3,2,1,1,1]
[3,2,8,1,4,6,7,5]=>[3,2,1,1,1]
[3,2,8,1,4,7,6,5]=>[4,2,1,1]
[3,8,2,1,4,7,5,6]=>[3,2,1,1,1]
[3,8,2,1,5,7,4,6]=>[3,2,1,1,1]
[4,8,2,5,1,7,3,6]=>[3,2,1,1,1]
[4,7,2,5,1,8,3,6]=>[3,2,1,1,1]
[3,7,2,1,5,8,4,6]=>[3,2,1,1,1]
[3,7,2,1,4,8,5,6]=>[3,2,1,1,1]
[3,2,1,7,5,8,6,4]=>[3,3,2]
[3,2,7,1,6,8,4,5]=>[3,2,1,1,1]
[4,2,7,6,1,8,3,5]=>[3,2,2,1]
[4,3,7,6,8,1,2,5]=>[3,2,1,1,1]
[4,3,8,6,7,1,2,5]=>[3,2,1,1,1]
[4,2,8,6,1,7,3,5]=>[3,2,2,1]
[3,2,8,1,6,7,4,5]=>[3,2,1,1,1]
[3,2,1,8,7,5,6,4]=>[4,3,1]
[3,8,2,1,7,4,5,6]=>[3,2,1,1,1]
[3,2,8,1,7,4,6,5]=>[4,2,1,1]
[3,2,8,1,6,4,7,5]=>[3,2,2,1]
[3,2,7,1,6,4,8,5]=>[3,2,2,1]
[4,2,7,6,1,3,8,5]=>[3,2,2,1]
[4,2,8,6,1,3,7,5]=>[3,2,2,1]
[4,2,8,7,1,3,6,5]=>[4,2,1,1]
[5,7,8,3,4,1,2,6]=>[3,1,1,1,1,1]
[4,2,7,8,1,3,6,5]=>[3,2,1,1,1]
[4,2,6,8,1,3,7,5]=>[3,2,1,1,1]
[4,2,6,7,1,3,8,5]=>[3,2,1,1,1]
[3,2,6,1,8,4,7,5]=>[3,3,1,1]
[3,7,2,1,8,4,5,6]=>[3,2,1,1,1]
[3,7,2,1,8,5,4,6]=>[3,3,1,1]
[4,7,3,8,5,1,2,6]=>[3,2,1,1,1]
[4,3,7,8,6,1,2,5]=>[3,2,1,1,1]
[3,2,7,1,8,6,4,5]=>[3,3,1,1]
[3,2,1,6,8,5,7,4]=>[3,3,1,1]
[3,2,6,1,8,7,4,5]=>[3,3,1,1]
[4,2,6,8,1,7,3,5]=>[3,2,1,1,1]
[4,3,6,8,7,1,2,5]=>[3,2,1,1,1]
[4,2,6,7,1,8,3,5]=>[3,2,1,1,1]
[3,2,6,1,7,8,4,5]=>[3,2,1,1,1]
[3,4,6,8,7,5,1,2]=>[4,1,1,1,1]
[5,3,6,4,8,7,1,2]=>[3,2,2,1]
[1,4,6,2,7,8,5,3]=>[3,2,1,1,1]
[1,2,7,5,4,8,6,3]=>[4,2,1,1]
[6,3,7,5,4,8,1,2]=>[4,2,1,1]
[7,3,8,5,4,6,1,2]=>[4,2,1,1]
[3,8,7,5,4,6,1,2]=>[5,1,1,1]
[4,3,6,7,8,5,1,2]=>[3,2,1,1,1]
[4,5,6,3,8,7,1,2]=>[3,2,1,1,1]
[3,6,8,5,4,7,1,2]=>[4,1,1,1,1]
[6,8,3,5,4,7,1,2]=>[4,1,1,1,1]
[7,6,3,5,4,8,1,2]=>[5,1,1,1]
[1,6,2,5,4,8,7,3]=>[4,2,1,1]
[7,1,2,5,8,3,6,4]=>[3,2,1,1,1]
[1,8,2,5,7,3,6,4]=>[4,1,1,1,1]
[6,2,1,5,4,8,7,3]=>[4,2,2]
[4,1,6,2,8,7,5,3]=>[4,2,2]
[7,8,1,2,4,6,5,3]=>[4,1,1,1,1]
[4,3,6,1,8,2,7,5]=>[3,3,1,1]
[2,3,8,5,4,1,6,7]=>[4,1,1,1,1]
[4,8,1,5,2,3,7,6]=>[3,2,1,1,1]
[7,5,1,6,4,3,2,8]=>[5,2,1]
[5,8,1,6,4,3,2,7]=>[5,1,1,1]
[6,1,5,7,4,3,2,8]=>[5,1,1,1]
[1,5,8,6,4,3,2,7]=>[5,1,1,1]
[3,4,6,1,5,8,2,7]=>[3,1,1,1,1,1]
[7,8,4,1,5,3,2,6]=>[4,2,1,1]
[7,8,5,1,6,3,2,4]=>[4,2,1,1]
[2,6,1,5,7,3,8,4]=>[3,2,1,1,1]
[1,6,8,7,4,3,2,5]=>[5,1,1,1]
[6,8,1,7,4,3,2,5]=>[5,1,1,1]
[5,6,1,7,4,3,2,8]=>[4,2,1,1]
[5,1,7,6,4,3,2,8]=>[5,2,1]
[6,1,7,8,4,3,2,5]=>[4,2,1,1]
[7,1,8,6,4,3,2,5]=>[5,2,1]
[1,8,7,6,4,3,2,5]=>[6,1,1]
[2,1,7,5,6,3,8,4]=>[3,2,2,1]
[3,1,6,7,5,8,2,4]=>[3,2,1,1,1]
[7,8,1,6,5,3,2,4]=>[5,1,1,1]
[7,8,2,1,4,5,6,3]=>[3,2,1,1,1]
[2,8,1,5,4,6,7,3]=>[4,1,1,1,1]
[7,2,1,5,4,6,8,3]=>[4,2,1,1]
[1,2,8,5,6,3,7,4]=>[3,2,1,1,1]
[6,1,2,5,7,3,8,4]=>[3,2,1,1,1]
[4,2,1,5,6,3,7,8]=>[3,2,1,1,1]
[4,3,6,1,5,7,2,8]=>[3,2,1,1,1]
[1,3,6,8,5,7,2,4]=>[3,1,1,1,1,1]
[2,4,6,3,7,1,8,5]=>[3,2,1,1,1]
[1,3,6,4,8,7,2,5]=>[3,2,1,1,1]
[5,4,6,1,3,7,2,8]=>[4,1,1,1,1]
[6,4,1,5,2,3,7,8]=>[3,2,1,1,1]
[4,1,7,5,2,3,8,6]=>[3,2,2,1]
[1,2,4,5,8,3,7,6]=>[3,1,1,1,1,1]
[7,2,3,5,4,1,8,6]=>[4,2,1,1]
[2,8,3,5,4,1,7,6]=>[4,2,1,1]
[4,2,6,3,8,1,7,5]=>[3,2,2,1]
[7,8,2,3,4,1,6,5]=>[3,2,1,1,1]
[7,8,1,4,6,3,2,5]=>[4,1,1,1,1]
[3,1,6,4,7,8,2,5]=>[3,2,1,1,1]
[1,8,5,7,4,3,2,6]=>[5,1,1,1]
[7,1,5,8,4,3,2,6]=>[5,1,1,1]
[5,1,8,7,4,3,2,6]=>[5,2,1]
[6,5,1,8,4,3,2,7]=>[5,2,1]
[6,5,7,1,4,3,2,8]=>[5,1,1,1]
[7,5,8,1,4,3,2,6]=>[5,1,1,1]
[5,8,7,1,4,3,2,6]=>[5,1,1,1]
[1,5,7,8,4,3,2,6]=>[4,1,1,1,1]
[2,4,7,5,1,3,8,6]=>[3,2,1,1,1]
[7,8,4,6,1,3,2,5]=>[4,1,1,1,1]
[7,8,5,4,1,3,2,6]=>[5,1,1,1]
[3,5,6,4,1,8,2,7]=>[3,2,1,1,1]
[2,6,4,5,1,3,8,7]=>[3,2,1,1,1]
[1,6,5,8,4,3,2,7]=>[5,1,1,1]
[6,8,5,1,4,3,2,7]=>[5,1,1,1]
[7,6,5,1,4,3,2,8]=>[6,1,1]
[3,4,6,2,7,1,5,8]=>[3,1,1,1,1,1]
[3,6,2,5,4,1,7,8]=>[4,1,1,1,1]
[3,2,7,5,4,1,6,8]=>[4,2,1,1]
[4,3,6,2,8,1,5,7]=>[4,1,1,1,1]
[6,1,2,5,4,7,8,3]=>[4,1,1,1,1]
[6,2,4,5,1,3,7,8]=>[3,1,1,1,1,1]
[4,2,8,5,1,3,7,6]=>[3,2,2,1]
[4,3,6,8,1,7,2,5]=>[3,2,1,1,1]
[5,3,6,4,1,7,2,8]=>[3,2,2,1]
[6,2,1,5,8,3,7,4]=>[3,3,1,1]
[1,6,7,4,8,3,5,2]=>[4,1,1,1,1]
[1,4,6,3,7,5,8,2]=>[3,2,1,1,1]
[4,6,7,2,5,8,1,3]=>[3,1,1,1,1,1]
[2,4,6,1,7,5,3,8]=>[3,2,1,1,1]
[2,7,5,4,1,6,3,8]=>[4,2,1,1]
[7,5,4,6,2,8,1,3]=>[5,1,1,1]
[1,7,5,4,3,8,6,2]=>[5,2,1]
[1,4,6,3,5,8,7,2]=>[3,2,1,1,1]
[1,5,8,4,3,6,7,2]=>[4,1,1,1,1]
[5,4,6,2,7,8,1,3]=>[4,1,1,1,1]
[2,5,4,1,6,7,3,8]=>[3,2,1,1,1]
[5,6,3,2,7,1,4,8]=>[4,1,1,1,1]
[5,6,3,2,7,1,8,4]=>[4,2,1,1]
[8,5,6,3,2,7,1,4]=>[5,1,1,1]
[2,4,1,7,8,5,3,6]=>[3,2,1,1,1]
[2,5,4,1,6,3,8,7]=>[3,2,2,1]
[3,5,2,1,6,4,7,8]=>[3,2,1,1,1]
[6,8,4,3,2,1,5,7]=>[5,1,1,1]
[5,3,8,2,1,6,4,7]=>[4,2,1,1]
[3,7,5,8,2,1,4,6]=>[4,1,1,1,1]
[8,6,4,3,2,1,7,5]=>[6,2]
[7,6,4,3,2,1,8,5]=>[6,2]
[7,8,4,3,2,1,6,5]=>[5,2,1]
[7,5,8,3,2,6,1,4]=>[5,1,1,1]
[6,3,7,2,5,1,8,4]=>[4,2,1,1]
[6,7,8,3,5,2,1,4]=>[4,1,1,1,1]
[6,2,5,7,8,4,1,3]=>[4,1,1,1,1]
[2,1,5,7,8,6,3,4]=>[3,2,1,1,1]
[3,6,7,2,8,1,4,5]=>[3,1,1,1,1,1]
[6,3,7,2,8,1,4,5]=>[4,1,1,1,1]
[3,2,6,1,7,4,5,8]=>[3,2,1,1,1]
[3,5,2,1,4,7,6,8]=>[3,2,1,1,1]
[7,3,5,2,1,8,4,6]=>[4,2,1,1]
[2,5,4,1,3,7,8,6]=>[3,2,1,1,1]
[2,5,8,4,1,3,7,6]=>[3,2,1,1,1]
[2,4,1,7,8,3,6,5]=>[3,2,1,1,1]
[3,7,2,8,6,1,4,5]=>[3,2,1,1,1]
[5,3,8,2,1,4,7,6]=>[4,2,1,1]
[4,8,7,3,2,1,5,6]=>[5,1,1,1]
[4,7,3,2,1,5,6,8]=>[4,1,1,1,1]
[8,4,7,3,2,1,5,6]=>[5,1,1,1]
[8,3,5,2,1,4,7,6]=>[4,2,1,1]
[7,3,2,8,6,1,4,5]=>[4,2,1,1]
[3,5,2,1,4,6,8,7]=>[3,2,1,1,1]
[7,8,3,5,4,6,1,2]=>[4,1,1,1,1]
[8,6,3,7,5,2,4,1]=>[5,2,1]
[5,4,1,6,3,2,8,7]=>[4,2,2]
[5,4,1,6,2,3,8,7]=>[3,2,2,1]
[5,7,1,6,2,8,3,4]=>[3,2,1,1,1]
[5,7,1,6,2,8,4,3]=>[4,2,1,1]
[2,7,6,5,1,8,3,4]=>[4,2,1,1]
[2,7,6,5,1,8,4,3]=>[5,2,1]
[2,3,6,5,1,4,8,7]=>[3,2,1,1,1]
[2,3,6,4,1,5,8,7]=>[3,2,1,1,1]
[2,3,6,1,5,4,8,7]=>[3,2,1,1,1]
[2,7,6,1,4,8,5,3]=>[4,2,1,1]
[2,7,6,1,4,8,3,5]=>[4,1,1,1,1]
[7,3,5,1,8,4,2,6]=>[4,2,1,1]
[7,3,5,1,8,6,4,2]=>[4,3,1]
[2,7,6,1,5,8,4,3]=>[5,1,1,1]
[2,7,6,4,1,8,5,3]=>[4,3,1]
[2,1,7,6,3,8,5,4]=>[4,2,2]
[2,1,7,6,3,8,4,5]=>[3,2,2,1]
[5,7,3,6,2,8,4,1]=>[4,2,1,1]
[2,7,6,4,1,8,3,5]=>[4,2,1,1]
[7,3,5,1,8,6,2,4]=>[3,3,1,1]
[6,3,5,1,8,2,4,7]=>[3,2,1,1,1]
[2,3,4,8,7,6,1,5]=>[4,1,1,1,1]
[2,3,4,8,5,7,1,6]=>[3,1,1,1,1,1]
[7,3,5,4,8,1,2,6]=>[4,1,1,1,1]
[6,4,3,5,8,7,2,1]=>[5,2,1]
[2,1,4,5,8,7,3,6]=>[3,2,1,1,1]
[6,4,3,5,8,7,1,2]=>[4,2,1,1]
[7,3,5,4,8,1,6,2]=>[4,2,1,1]
[2,3,4,8,7,5,6,1]=>[4,1,1,1,1]
[2,3,4,8,7,5,1,6]=>[4,1,1,1,1]
[2,7,6,5,4,8,1,3]=>[5,1,1,1]
[7,3,5,6,8,4,1,2]=>[4,1,1,1,1]
[7,3,5,6,8,1,4,2]=>[4,1,1,1,1]
[7,3,5,6,8,1,2,4]=>[3,1,1,1,1,1]
[6,4,1,5,8,7,2,3]=>[3,3,1,1]
[6,4,1,5,8,7,3,2]=>[4,3,1]
[6,4,1,5,8,3,7,2]=>[4,2,1,1]
[5,7,1,6,3,8,2,4]=>[4,1,1,1,1]
[6,4,1,5,8,3,2,7]=>[4,2,1,1]
[7,4,1,5,8,2,3,6]=>[3,2,1,1,1]
[7,4,1,5,8,2,6,3]=>[3,3,1,1]
[6,3,5,7,8,2,1,4]=>[4,1,1,1,1]
[6,3,5,7,8,2,4,1]=>[4,1,1,1,1]
[2,7,6,4,5,8,3,1]=>[5,1,1,1]
[5,7,3,6,1,8,4,2]=>[4,2,1,1]
[2,1,4,5,8,6,3,7]=>[3,2,1,1,1]
[7,3,5,4,8,6,2,1]=>[5,2,1]
[2,3,4,8,5,6,1,7]=>[3,1,1,1,1,1]
[2,3,4,8,7,1,6,5]=>[4,1,1,1,1]
[2,3,4,8,1,7,6,5]=>[4,1,1,1,1]
[2,3,4,8,1,6,7,5]=>[3,1,1,1,1,1]
[2,3,4,8,5,1,7,6]=>[3,2,1,1,1]
[6,3,5,4,8,2,7,1]=>[5,1,1,1]
[7,4,3,5,8,2,1,6]=>[5,1,1,1]
[2,1,4,5,8,3,7,6]=>[3,2,1,1,1]
[7,4,3,5,8,2,6,1]=>[5,1,1,1]
[6,3,5,4,8,2,1,7]=>[5,1,1,1]
[2,3,4,8,5,1,6,7]=>[3,1,1,1,1,1]
[2,3,4,8,1,6,5,7]=>[3,1,1,1,1,1]
[2,3,4,8,1,5,7,6]=>[3,1,1,1,1,1]
[7,8,2,6,1,5,3,4]=>[4,1,1,1,1]
[7,8,1,6,2,5,3,4]=>[4,1,1,1,1]
[1,8,6,7,2,5,3,4]=>[4,1,1,1,1]
[1,8,5,7,2,6,3,4]=>[4,1,1,1,1]
[5,8,1,7,2,6,3,4]=>[4,1,1,1,1]
[5,8,2,7,1,6,3,4]=>[4,1,1,1,1]
[2,8,6,7,1,5,3,4]=>[4,1,1,1,1]
[2,8,5,7,1,6,3,4]=>[4,1,1,1,1]
[2,8,1,7,5,6,3,4]=>[4,1,1,1,1]
[1,8,2,7,5,6,3,4]=>[4,1,1,1,1]
[1,8,2,7,4,6,3,5]=>[4,1,1,1,1]
[2,8,1,7,4,6,3,5]=>[4,1,1,1,1]
[2,8,4,7,1,6,3,5]=>[4,1,1,1,1]
[4,8,2,7,1,6,3,5]=>[4,1,1,1,1]
[4,8,1,7,2,6,3,5]=>[4,1,1,1,1]
[1,8,4,7,2,6,3,5]=>[4,1,1,1,1]
[4,8,1,7,5,6,2,3]=>[4,1,1,1,1]
[1,8,4,7,5,6,2,3]=>[4,1,1,1,1]
[1,8,3,7,5,6,2,4]=>[4,1,1,1,1]
[3,8,1,7,5,6,2,4]=>[4,1,1,1,1]
[3,8,1,7,4,6,2,5]=>[4,1,1,1,1]
[1,8,3,7,4,6,2,5]=>[4,1,1,1,1]
[1,8,3,7,2,6,4,5]=>[4,1,1,1,1]
[3,8,1,7,2,6,4,5]=>[4,1,1,1,1]
[3,8,2,7,1,6,4,5]=>[4,1,1,1,1]
[3,8,2,7,4,6,1,5]=>[4,1,1,1,1]
[3,8,2,7,5,6,1,4]=>[4,1,1,1,1]
[4,8,2,7,5,6,1,3]=>[4,1,1,1,1]
[4,8,3,7,5,6,1,2]=>[4,1,1,1,1]
[3,8,4,7,5,6,1,2]=>[4,1,1,1,1]
[2,8,4,7,5,6,1,3]=>[4,1,1,1,1]
[2,8,3,7,5,6,1,4]=>[4,1,1,1,1]
[2,8,3,7,4,6,1,5]=>[4,1,1,1,1]
[2,8,3,7,1,6,4,5]=>[4,1,1,1,1]
[2,8,1,7,3,6,4,5]=>[4,1,1,1,1]
[7,5,2,8,6,4,1,3]=>[4,3,1]
[7,5,1,8,6,2,3,4]=>[3,3,1,1]
[7,4,8,6,1,5,2,3]=>[4,2,1,1]
[7,1,8,4,5,2,6,3]=>[3,2,2,1]
[1,6,7,4,2,8,5,3]=>[3,3,1,1]
[1,6,7,3,8,5,2,4]=>[3,2,1,1,1]
[7,1,8,3,5,6,2,4]=>[3,2,1,1,1]
[7,3,8,6,2,5,1,4]=>[4,2,1,1]
[7,4,2,8,6,1,3,5]=>[4,2,1,1]
[7,3,1,8,4,2,5,6]=>[3,3,1,1]
[7,2,8,3,5,1,6,4]=>[3,2,2,1]
[1,5,7,8,2,6,3,4]=>[3,1,1,1,1,1]
[2,6,3,7,8,5,4,1]=>[4,2,1,1]
[2,6,3,7,8,4,5,1]=>[3,2,1,1,1]
[2,4,7,3,5,6,8,1]=>[3,1,1,1,1,1]
[2,5,3,7,8,1,6,4]=>[3,2,1,1,1]
[3,1,5,4,7,8,2,6]=>[3,2,1,1,1]
[5,3,1,4,8,2,6,7]=>[3,2,1,1,1]
[5,2,4,8,6,1,3,7]=>[3,2,1,1,1]
[5,2,3,8,4,6,7,1]=>[3,2,1,1,1]
[4,8,2,3,5,7,1,6]=>[3,1,1,1,1,1]
[1,4,7,8,3,6,2,5]=>[3,1,1,1,1,1]
[4,8,1,3,6,7,2,5]=>[3,1,1,1,1,1]
[6,4,2,8,1,3,7,5]=>[4,2,1,1]
[6,3,8,1,4,7,2,5]=>[3,2,1,1,1]
[5,8,1,3,6,2,7,4]=>[3,2,1,1,1]
[1,5,7,4,2,6,8,3]=>[3,2,1,1,1]
[5,8,1,4,2,6,3,7]=>[3,2,1,1,1]
[5,8,4,1,2,7,6,3]=>[4,2,1,1]
[6,5,1,2,8,7,3,4]=>[3,3,1,1]
[6,5,3,1,4,2,8,7]=>[4,2,2]
[5,3,1,6,4,2,7,8]=>[3,3,1,1]
[4,2,5,7,1,8,6,3]=>[3,3,1,1]
[3,4,7,2,8,6,1,5]=>[3,2,1,1,1]
[3,4,5,8,2,7,1,6]=>[3,1,1,1,1,1]
[3,4,6,2,8,1,5,7]=>[3,1,1,1,1,1]
[3,5,2,6,8,1,7,4]=>[3,2,1,1,1]
[4,2,5,6,1,3,8,7]=>[3,2,1,1,1]
[5,3,6,8,4,7,2,1]=>[4,2,1,1]
[3,7,2,5,4,8,6,1]=>[4,2,1,1]
[8,4,2,5,7,3,6,1]=>[4,2,1,1]
[3,1,6,5,4,8,2,7]=>[4,2,1,1]
[4,1,6,5,8,3,2,7]=>[4,2,1,1]
[5,1,6,8,4,3,2,7]=>[4,2,1,1]
[8,5,4,7,6,3,2,1]=>[6,2]
[2,7,1,5,4,3,8,6]=>[4,2,1,1]
[8,2,1,5,4,3,7,6]=>[4,2,2]
[8,4,1,5,7,3,2,6]=>[4,2,1,1]
[8,3,6,1,4,7,2,5]=>[4,1,1,1,1]
[2,7,6,1,4,3,8,5]=>[4,2,1,1]
[6,7,8,5,1,3,2,4]=>[4,1,1,1,1]
[6,7,8,2,4,3,5,1]=>[4,1,1,1,1]
[4,7,6,2,8,3,5,1]=>[4,2,1,1]
[8,3,6,2,4,7,5,1]=>[4,2,1,1]
[3,7,6,2,4,8,5,1]=>[4,2,1,1]
[5,7,3,8,4,6,2,1]=>[4,2,1,1]
[4,7,3,5,8,6,2,1]=>[4,2,1,1]
[8,7,2,1,4,3,6,5]=>[4,2,2]
[8,7,3,1,4,6,2,5]=>[4,2,1,1]
[8,7,6,3,2,5,4,1]=>[6,2]
[8,7,3,5,1,6,2,4]=>[4,2,1,1]
[8,7,2,5,1,3,6,4]=>[4,2,1,1]
[8,4,6,5,7,1,2,3]=>[4,1,1,1,1]
[4,7,6,5,8,1,2,3]=>[4,1,1,1,1]
[3,7,6,5,1,8,2,4]=>[4,2,1,1]
[3,6,4,8,7,5,1,2]=>[4,2,1,1]
[5,6,4,3,8,7,1,2]=>[4,2,1,1]
[1,6,2,4,7,8,5,3]=>[3,2,1,1,1]
[3,6,2,4,8,1,5,7]=>[3,1,1,1,1,1]
[3,4,7,2,8,1,6,5]=>[3,2,1,1,1]
[1,4,7,2,5,8,6,3]=>[3,2,1,1,1]
[7,3,8,4,5,6,1,2]=>[3,2,1,1,1]
[3,5,6,4,8,7,1,2]=>[3,2,1,1,1]
[4,6,8,5,3,7,1,2]=>[4,1,1,1,1]
[6,8,5,3,4,7,1,2]=>[4,1,1,1,1]
[1,6,5,4,2,8,7,3]=>[4,3,1]
[1,8,5,2,7,3,6,4]=>[4,2,1,1]
[4,2,7,5,1,8,6,3]=>[3,3,2]
[7,8,1,4,2,6,5,3]=>[4,2,1,1]
[1,3,6,4,8,2,5,7]=>[3,1,1,1,1,1]
[6,5,1,3,4,2,8,7]=>[4,2,1,1]
[7,4,5,3,2,8,1,6]=>[5,1,1,1]
[5,8,3,6,1,4,2,7]=>[4,1,1,1,1]
[2,5,8,6,4,1,3,7]=>[4,1,1,1,1]
[1,4,6,2,5,8,3,7]=>[3,1,1,1,1,1]
[3,6,2,5,8,1,7,4]=>[3,2,1,1,1]
[1,6,8,7,4,2,3,5]=>[4,1,1,1,1]
[6,1,7,8,2,4,3,5]=>[3,2,1,1,1]
[7,1,8,6,3,4,2,5]=>[4,2,1,1]
[7,2,1,4,5,6,8,3]=>[3,2,1,1,1]
[1,2,8,3,6,5,7,4]=>[4,1,1,1,1]
[6,1,3,2,7,5,8,4]=>[3,3,1,1]
[1,6,3,8,5,7,2,4]=>[3,2,1,1,1]
[2,6,4,1,7,5,8,3]=>[3,3,1,1]
[7,6,5,8,1,4,2,3]=>[5,1,1,1]
[5,8,6,7,3,2,1,4]=>[5,1,1,1]
[1,6,4,3,7,2,8,5]=>[4,2,1,1]
[2,6,3,4,8,7,1,5]=>[3,2,1,1,1]
[7,1,3,4,5,2,8,6]=>[3,2,1,1,1]
[1,8,3,5,4,2,7,6]=>[4,2,1,1]
[4,1,6,3,8,2,7,5]=>[3,2,2,1]
[7,8,2,4,6,3,1,5]=>[4,1,1,1,1]
[3,2,6,4,7,8,1,5]=>[3,2,1,1,1]
[2,8,5,7,4,3,1,6]=>[5,1,1,1]
[7,2,5,8,3,4,1,6]=>[4,1,1,1,1]
[5,3,8,7,1,2,6,4]=>[4,2,1,1]
[6,5,3,8,2,1,7,4]=>[5,2,1]
[7,5,8,4,1,2,3,6]=>[4,1,1,1,1]
[5,8,7,4,1,3,2,6]=>[5,1,1,1]
[3,5,7,8,4,1,2,6]=>[3,1,1,1,1,1]
[1,4,7,5,3,8,2,6]=>[4,1,1,1,1]
[2,4,6,7,3,1,8,5]=>[3,2,1,1,1]
[7,8,4,6,3,1,2,5]=>[4,1,1,1,1]
[2,6,4,5,3,8,1,7]=>[4,1,1,1,1]
[3,6,5,8,4,2,1,7]=>[5,1,1,1]
[5,6,8,4,2,3,1,7]=>[4,1,1,1,1]
[6,8,5,4,3,1,2,7]=>[5,1,1,1]
[6,1,4,2,8,5,7,3]=>[3,3,1,1]
[4,8,6,5,3,2,7,1]=>[6,1,1]
[8,6,5,1,2,4,7,3]=>[5,1,1,1]
[6,7,5,8,2,1,4,3]=>[4,2,1,1]
[1,7,5,8,2,6,4,3]=>[4,2,1,1]
[1,3,8,5,7,6,2,4]=>[4,1,1,1,1]
[6,3,8,5,7,1,2,4]=>[3,2,1,1,1]
[8,3,1,5,6,2,7,4]=>[3,2,2,1]
[6,8,5,2,1,4,7,3]=>[4,2,1,1]
[3,8,2,5,6,1,7,4]=>[3,2,1,1,1]
[2,8,1,5,6,3,7,4]=>[3,2,1,1,1]
[8,1,2,5,6,3,7,4]=>[3,2,1,1,1]
[1,8,2,5,7,6,3,4]=>[4,1,1,1,1]
[5,1,8,6,2,7,3,4]=>[3,2,2,1]
[2,5,8,6,1,7,3,4]=>[3,2,1,1,1]
[8,6,1,5,7,2,3,4]=>[4,1,1,1,1]
[3,8,6,5,7,1,2,4]=>[4,1,1,1,1]
[7,6,5,8,1,2,4,3]=>[5,1,1,1]
[5,1,7,6,8,4,2,3]=>[4,2,1,1]
[5,1,3,7,8,6,2,4]=>[3,2,1,1,1]
[7,2,5,8,1,6,4,3]=>[4,2,1,1]
[3,2,8,5,7,6,1,4]=>[4,2,1,1]
[8,2,1,5,7,6,3,4]=>[4,2,1,1]
[5,2,8,6,1,7,3,4]=>[3,2,2,1]
[1,2,8,6,5,7,3,4]=>[4,1,1,1,1]
[4,2,1,3,6,7,8,5]=>[3,2,1,1,1]
[8,2,5,6,3,7,1,4]=>[4,1,1,1,1]
[7,2,6,5,4,1,8,3]=>[5,2,1]
[6,1,3,5,4,7,8,2]=>[4,1,1,1,1]
[6,1,5,3,4,7,8,2]=>[4,1,1,1,1]
[7,5,6,2,4,1,8,3]=>[4,2,1,1]
[8,5,2,6,3,7,1,4]=>[4,2,1,1]
[4,3,1,2,6,7,8,5]=>[3,2,1,1,1]
[8,1,6,5,7,3,2,4]=>[5,1,1,1]
[3,5,8,6,2,7,1,4]=>[4,1,1,1,1]
[5,8,1,6,3,7,2,4]=>[4,1,1,1,1]
[1,8,5,6,3,7,2,4]=>[4,1,1,1,1]
[1,7,6,5,4,2,8,3]=>[5,2,1]
[5,7,6,1,4,2,8,3]=>[4,2,1,1]
[7,1,4,2,6,5,8,3]=>[4,2,1,1]
[4,1,7,3,5,6,8,2]=>[3,2,1,1,1]
[2,7,4,1,5,6,8,3]=>[3,2,1,1,1]
[5,7,6,4,1,2,8,3]=>[4,2,1,1]
[4,7,6,1,5,2,8,3]=>[4,2,1,1]
[1,7,6,4,5,2,8,3]=>[4,2,1,1]
[1,8,3,6,5,7,2,4]=>[4,1,1,1,1]
[3,8,1,6,5,7,2,4]=>[4,1,1,1,1]
[8,1,3,5,7,6,2,4]=>[4,1,1,1,1]
[7,8,5,4,1,6,2,3]=>[4,2,1,1]
[6,1,5,4,3,7,8,2]=>[5,1,1,1]
[7,5,6,4,2,1,8,3]=>[5,2,1]
[8,3,2,6,5,7,1,4]=>[4,2,1,1]
[7,4,6,2,5,1,8,3]=>[4,2,1,1]
[6,1,4,3,5,7,8,2]=>[4,1,1,1,1]
[6,1,3,4,5,7,8,2]=>[3,1,1,1,1,1]
[7,2,6,4,5,1,8,3]=>[4,2,1,1]
[8,2,3,6,5,7,1,4]=>[4,1,1,1,1]
[5,4,7,3,6,8,1,2]=>[4,1,1,1,1]
[3,4,7,8,5,6,1,2]=>[3,1,1,1,1,1]
[3,4,7,2,5,1,6,8]=>[3,1,1,1,1,1]
[1,4,7,2,5,8,3,6]=>[3,1,1,1,1,1]
[3,6,2,4,7,1,5,8]=>[3,1,1,1,1,1]
[6,8,3,4,5,7,1,2]=>[3,1,1,1,1,1]
[4,3,6,7,5,8,1,2]=>[3,2,1,1,1]
[6,3,7,5,8,4,1,2]=>[4,2,1,1]
[7,3,8,6,4,5,1,2]=>[4,2,1,1]
[3,2,7,6,5,1,4,8]=>[4,2,1,1]
[4,8,2,6,1,5,3,7]=>[4,1,1,1,1]
[4,3,6,2,5,1,8,7]=>[4,2,1,1]
[7,8,3,2,5,1,4,6]=>[4,1,1,1,1]
[7,8,1,2,5,6,3,4]=>[3,1,1,1,1,1]
[4,1,6,2,5,7,3,8]=>[3,2,1,1,1]
[2,1,8,6,4,7,3,5]=>[4,2,1,1]
[1,8,3,6,7,4,5,2]=>[4,1,1,1,1]
[7,1,5,8,3,6,2,4]=>[4,1,1,1,1]
[6,1,5,7,4,2,8,3]=>[4,2,1,1]
[3,1,6,4,7,2,5,8]=>[3,2,1,1,1]
[6,5,7,1,4,2,3,8]=>[4,1,1,1,1]
[5,6,8,1,3,2,4,7]=>[3,1,1,1,1,1]
[6,8,5,1,3,4,2,7]=>[4,1,1,1,1]
[2,8,3,4,5,1,7,6]=>[3,2,1,1,1]
[6,2,4,3,1,5,7,8]=>[4,1,1,1,1]
[4,2,8,3,1,7,5,6]=>[3,2,2,1]
[1,3,7,4,8,2,5,6]=>[3,1,1,1,1,1]
[5,3,7,4,1,6,2,8]=>[3,2,2,1]
[2,4,7,3,6,1,8,5]=>[3,2,1,1,1]
[5,8,7,6,3,1,2,4]=>[5,1,1,1]
[7,5,6,8,1,4,3,2]=>[5,1,1,1]
[2,4,7,1,6,5,3,8]=>[4,1,1,1,1]
[1,2,7,8,5,4,3,6]=>[4,1,1,1,1]
[6,3,1,2,8,4,5,7]=>[3,2,1,1,1]
[4,2,1,3,6,5,8,7]=>[3,2,2,1]
[2,8,1,4,5,6,3,7]=>[3,1,1,1,1,1]
[7,2,1,5,4,6,3,8]=>[4,2,1,1]
[4,2,6,1,8,5,3,7]=>[3,3,1,1]
[7,8,2,1,4,5,3,6]=>[3,2,1,1,1]
[7,8,4,1,5,3,6,2]=>[4,2,1,1]
[3,4,6,1,5,8,7,2]=>[3,2,1,1,1]
[7,5,1,6,4,3,8,2]=>[5,2,1]
[5,8,1,6,3,4,7,2]=>[4,1,1,1,1]
[6,5,1,8,2,7,4,3]=>[4,3,1]
[6,8,1,7,5,2,3,4]=>[4,1,1,1,1]
[7,6,1,8,5,3,2,4]=>[5,2,1]
[5,6,1,7,4,8,2,3]=>[3,2,1,1,1]
[3,6,1,5,7,4,2,8]=>[4,1,1,1,1]
[2,5,6,1,7,4,8,3]=>[3,2,1,1,1]
[3,1,7,5,6,4,8,2]=>[4,2,1,1]
[5,1,7,6,4,8,3,2]=>[5,2,1]
[6,1,7,8,5,3,4,2]=>[4,2,1,1]
[7,1,8,6,5,4,2,3]=>[5,2,1]
[2,6,5,7,3,4,8,1]=>[4,1,1,1,1]
[1,6,4,7,5,8,2,3]=>[3,2,1,1,1]
[8,5,3,6,2,7,4,1]=>[5,2,1]
[1,3,7,4,6,8,2,5]=>[3,1,1,1,1,1]
[4,7,5,6,3,2,8,1]=>[5,1,1,1]
[1,7,6,5,4,8,2,3]=>[5,1,1,1]
[8,1,6,5,7,2,4,3]=>[5,1,1,1]
[1,2,7,6,8,3,4,5]=>[3,1,1,1,1,1]
[6,1,7,5,3,8,2,4]=>[4,2,1,1]
[2,1,7,5,6,8,3,4]=>[3,2,1,1,1]
[5,4,1,7,6,8,2,3]=>[3,3,1,1]
[4,8,5,6,2,7,3,1]=>[4,2,1,1]
[3,8,6,4,2,7,5,1]=>[5,2,1]
[7,8,5,2,4,6,3,1]=>[5,1,1,1]
[2,8,6,3,7,4,5,1]=>[4,2,1,1]
[7,8,1,6,2,4,5,3]=>[4,1,1,1,1]
[6,8,1,4,7,2,5,3]=>[4,1,1,1,1]
[3,8,4,1,7,2,6,5]=>[4,2,1,1]
[5,4,7,1,8,3,2,6]=>[4,2,1,1]
[3,7,4,1,8,5,2,6]=>[3,3,1,1]
[6,7,1,4,8,3,2,5]=>[4,1,1,1,1]
[2,7,1,8,4,5,3,6]=>[3,2,1,1,1]
[6,1,2,8,4,3,5,7]=>[3,2,1,1,1]
[6,5,1,4,3,8,2,7]=>[5,1,1,1]
[1,6,2,5,8,3,4,7]=>[3,1,1,1,1,1]
[8,5,1,3,7,2,6,4]=>[4,2,1,1]
[8,4,2,1,7,3,6,5]=>[4,3,1]
[7,4,2,1,8,5,3,6]=>[4,3,1]
[1,5,4,2,8,3,6,7]=>[3,2,1,1,1]
[6,4,3,1,5,8,2,7]=>[4,2,1,1]
[3,7,6,8,4,5,2,1]=>[5,1,1,1]
[2,7,6,8,5,3,4,1]=>[5,1,1,1]
[1,7,6,8,5,4,2,3]=>[5,1,1,1]
[1,4,8,6,7,5,2,3]=>[4,1,1,1,1]
[2,4,8,6,7,3,5,1]=>[4,1,1,1,1]
[7,3,8,5,4,6,2,1]=>[5,2,1]
[3,4,8,5,6,7,2,1]=>[4,1,1,1,1]
[6,3,5,8,4,7,2,1]=>[5,1,1,1]
[5,4,3,8,6,7,2,1]=>[5,2,1]
[5,4,2,8,7,3,6,1]=>[4,3,1]
[6,2,5,8,7,3,4,1]=>[4,2,1,1]
[3,2,8,5,7,4,6,1]=>[4,2,1,1]
[1,3,8,7,5,6,2,4]=>[4,1,1,1,1]
[2,1,8,7,4,6,3,5]=>[4,2,1,1]
[3,1,8,5,7,6,2,4]=>[4,2,1,1]
[6,1,5,8,7,4,2,3]=>[4,2,1,1]
[5,4,1,8,7,6,2,3]=>[4,3,1]
[5,8,6,7,4,3,2,1]=>[6,1,1]
[4,8,7,5,6,3,2,1]=>[6,1,1]
[4,2,1,6,3,5,8,7]=>[3,2,2,1]
[6,2,1,4,3,5,8,7]=>[3,2,2,1]
[6,2,1,4,3,8,5,7]=>[3,2,2,1]
[8,2,1,4,3,6,5,7]=>[3,2,2,1]
[8,2,4,1,3,6,5,7]=>[3,2,1,1,1]
[6,2,4,1,3,8,5,7]=>[3,2,1,1,1]
[6,2,4,1,3,5,8,7]=>[3,2,1,1,1]
[4,2,6,1,3,5,8,7]=>[3,2,1,1,1]
[2,1,6,4,3,5,8,7]=>[3,2,2,1]
[2,6,1,4,3,5,8,7]=>[3,2,1,1,1]
[2,6,4,1,3,5,8,7]=>[3,2,1,1,1]
[4,6,2,1,3,5,8,7]=>[3,2,1,1,1]
[6,4,2,1,3,5,8,7]=>[4,2,1,1]
[8,4,2,1,3,6,5,7]=>[4,2,1,1]
[8,4,2,1,6,3,5,7]=>[4,2,1,1]
[6,4,2,1,8,3,5,7]=>[4,2,1,1]
[4,6,2,1,8,3,5,7]=>[3,2,1,1,1]
[2,6,1,4,3,8,5,7]=>[3,2,1,1,1]
[2,1,6,4,3,8,5,7]=>[3,2,2,1]
[2,1,8,4,3,6,5,7]=>[3,2,2,1]
[2,8,1,4,3,6,5,7]=>[3,2,1,1,1]
[2,8,4,1,3,6,5,7]=>[3,2,1,1,1]
[4,8,2,1,3,6,5,7]=>[3,2,1,1,1]
[4,8,2,1,6,3,5,7]=>[3,2,1,1,1]
[6,8,2,1,4,3,5,7]=>[3,2,1,1,1]
[8,6,2,1,4,3,5,7]=>[4,2,1,1]
[2,8,1,4,6,3,5,7]=>[3,1,1,1,1,1]
[2,1,8,4,6,3,5,7]=>[3,2,1,1,1]
[2,1,6,4,8,3,5,7]=>[3,2,1,1,1]
[2,6,1,4,8,3,5,7]=>[3,1,1,1,1,1]
[2,6,4,1,8,3,5,7]=>[3,2,1,1,1]
[2,6,4,8,1,3,5,7]=>[3,1,1,1,1,1]
[4,6,2,8,1,3,5,7]=>[3,1,1,1,1,1]
[4,2,6,1,3,8,5,7]=>[3,2,1,1,1]
[4,2,6,1,8,3,5,7]=>[3,2,1,1,1]
[6,2,4,1,8,3,5,7]=>[3,2,1,1,1]
[8,2,4,1,6,3,5,7]=>[3,2,1,1,1]
[8,2,1,4,6,3,5,7]=>[3,2,1,1,1]
[6,2,1,4,8,3,5,7]=>[3,2,1,1,1]
[4,2,1,6,8,3,5,7]=>[3,2,1,1,1]
[4,2,1,6,3,8,5,7]=>[3,2,2,1]
[4,2,1,3,6,8,5,7]=>[3,2,1,1,1]
[2,1,4,3,8,6,5,7]=>[3,2,2,1]
[2,4,1,3,8,6,5,7]=>[3,2,1,1,1]
[4,2,1,3,8,6,5,7]=>[3,3,1,1]
[4,2,1,8,3,6,5,7]=>[3,3,1,1]
[4,2,1,8,6,3,5,7]=>[3,3,1,1]
[6,2,1,8,4,3,5,7]=>[3,3,1,1]
[8,2,1,6,4,3,5,7]=>[4,2,1,1]
[8,2,6,1,4,3,5,7]=>[4,1,1,1,1]
[6,2,8,1,4,3,5,7]=>[3,2,1,1,1]
[4,2,8,1,6,3,5,7]=>[3,2,1,1,1]
[4,2,8,1,3,6,5,7]=>[3,2,1,1,1]
[2,4,8,1,3,6,5,7]=>[3,1,1,1,1,1]
[2,4,1,8,3,6,5,7]=>[3,2,1,1,1]
[2,1,4,8,3,6,5,7]=>[3,2,1,1,1]
[2,1,4,8,6,3,5,7]=>[3,2,1,1,1]
[2,4,8,1,6,3,5,7]=>[3,1,1,1,1,1]
[2,4,8,6,1,3,5,7]=>[3,1,1,1,1,1]
[4,2,8,6,1,3,5,7]=>[3,2,1,1,1]
[6,2,8,4,1,3,5,7]=>[3,2,1,1,1]
[8,2,6,4,1,3,5,7]=>[4,1,1,1,1]
[8,4,6,2,1,3,5,7]=>[4,1,1,1,1]
[6,4,8,2,1,3,5,7]=>[4,1,1,1,1]
[4,6,8,2,1,3,5,7]=>[3,1,1,1,1,1]
[2,6,8,4,1,3,5,7]=>[3,1,1,1,1,1]
[2,6,8,1,4,3,5,7]=>[3,1,1,1,1,1]
[2,6,1,8,4,3,5,7]=>[3,2,1,1,1]
[2,1,6,8,4,3,5,7]=>[3,2,1,1,1]
[2,1,8,6,4,3,5,7]=>[4,2,1,1]
[2,8,1,6,4,3,5,7]=>[4,1,1,1,1]
[2,8,6,4,1,3,5,7]=>[4,1,1,1,1]
[4,8,6,2,1,3,5,7]=>[4,1,1,1,1]
[6,8,4,2,1,3,5,7]=>[4,1,1,1,1]
[3,2,6,1,5,4,8,7]=>[3,2,2,1]
[5,2,4,3,8,1,7,6]=>[4,2,1,1]
[6,2,4,1,5,3,8,7]=>[3,2,2,1]
[4,3,6,1,5,2,8,7]=>[3,2,2,1]
[4,3,5,2,8,1,7,6]=>[4,2,1,1]
[4,3,7,2,6,5,8,1]=>[4,2,1,1]
[4,3,8,2,6,1,7,5]=>[4,2,1,1]
[4,3,8,1,7,2,6,5]=>[4,2,1,1]
[4,3,8,1,5,2,7,6]=>[3,2,2,1]
[5,1,8,3,4,2,7,6]=>[3,2,2,1]
[5,4,8,1,3,2,7,6]=>[4,2,1,1]
[2,1,5,4,8,3,7,6]=>[3,2,2,1]
[5,1,7,6,8,3,4,2]=>[4,2,1,1]
[4,3,7,6,8,1,5,2]=>[4,2,1,1]
[4,3,7,1,8,5,6,2]=>[3,3,1,1]
[4,3,6,5,8,1,7,2]=>[3,2,2,1]
[6,3,5,4,7,2,8,1]=>[5,1,1,1]
[6,3,5,4,8,1,7,2]=>[4,2,1,1]
[7,1,6,3,8,4,5,2]=>[4,2,1,1]
[7,4,6,5,8,1,3,2]=>[5,1,1,1]
[2,1,8,4,6,3,7,5]=>[3,2,2,1]
[8,4,6,1,3,2,7,5]=>[4,2,1,1]
[8,1,6,3,4,2,7,5]=>[4,2,1,1]
[8,1,6,3,7,2,5,4]=>[4,2,1,1]
[8,3,5,1,7,2,6,4]=>[4,2,1,1]
[8,3,5,2,6,1,7,4]=>[4,2,1,1]
[7,3,5,2,6,4,8,1]=>[4,2,1,1]
[8,2,6,3,5,1,7,4]=>[4,2,1,1]
[8,2,7,1,5,3,6,4]=>[4,2,1,1]
[8,2,4,1,5,3,7,6]=>[3,2,2,1]
[8,2,4,1,7,3,6,5]=>[4,2,1,1]
[8,2,4,3,6,1,7,5]=>[4,2,1,1]
[3,2,8,4,6,1,7,5]=>[3,2,2,1]
[3,2,8,1,5,4,7,6]=>[3,2,2,1]
[3,2,7,6,8,1,5,4]=>[4,2,1,1]
[3,2,7,1,8,5,6,4]=>[3,3,1,1]
[3,2,6,5,8,1,7,4]=>[3,2,2,1]
[6,5,7,2,4,3,8,1]=>[5,1,1,1]
[6,5,8,2,4,1,7,3]=>[4,2,1,1]
[7,2,4,1,8,5,6,3]=>[3,3,1,1]
[7,6,8,2,4,1,5,3]=>[4,2,1,1]
[7,6,8,1,5,2,4,3]=>[5,1,1,1]
[2,1,7,3,8,5,6,4]=>[3,2,2,1]
[7,1,3,2,8,5,6,4]=>[3,3,1,1]
[7,1,8,5,6,2,4,3]=>[4,2,1,1]
[7,1,8,2,6,4,5,3]=>[4,2,1,1]
[7,2,8,1,5,4,6,3]=>[4,2,1,1]
[6,2,7,4,5,3,8,1]=>[4,2,1,1]
[5,4,7,2,6,3,8,1]=>[4,2,1,1]
[5,4,8,2,6,1,7,3]=>[4,2,1,1]
[6,5,8,1,7,2,4,3]=>[4,2,1,1]
[2,1,6,5,8,3,7,4]=>[3,2,2,1]
[6,5,7,4,8,1,3,2]=>[5,1,1,1]
[6,5,7,1,8,3,4,2]=>[4,2,1,1]
[6,1,7,4,8,3,5,2]=>[4,2,1,1]
[5,4,7,1,8,3,6,2]=>[4,2,1,1]
[5,4,6,3,8,1,7,2]=>[4,2,1,1]
[2,8,3,1,5,4,6,7]=>[3,2,1,1,1]
[2,5,3,4,7,1,8,6]=>[3,2,1,1,1]
[2,4,8,3,5,7,6,1]=>[4,1,1,1,1]
[4,2,5,3,1,8,6,7]=>[3,2,2,1]
[4,2,1,8,5,3,6,7]=>[3,3,1,1]
[5,4,1,3,8,2,6,7]=>[4,1,1,1,1]
[5,1,4,8,3,2,6,7]=>[4,1,1,1,1]
[1,5,8,4,3,2,6,7]=>[4,1,1,1,1]
[1,8,5,4,3,2,6,7]=>[5,1,1,1]
[1,7,4,3,8,5,2,6]=>[4,2,1,1]
[1,5,7,3,8,4,2,6]=>[3,2,1,1,1]
[5,1,4,7,8,3,2,6]=>[4,1,1,1,1]
[4,8,1,5,7,3,6,2]=>[4,1,1,1,1]
[8,1,5,3,7,4,6,2]=>[4,2,1,1]
[3,8,4,7,6,5,2,1]=>[6,1,1]
[1,6,8,5,3,7,4,2]=>[4,2,1,1]
[6,8,1,7,4,3,5,2]=>[5,1,1,1]
[6,4,8,1,7,3,5,2]=>[4,2,1,1]
[6,4,8,7,1,5,2,3]=>[4,2,1,1]
[7,6,4,1,3,8,2,5]=>[5,1,1,1]
[1,7,5,6,3,2,8,4]=>[4,2,1,1]
[4,2,1,7,8,5,3,6]=>[3,3,1,1]
[2,7,4,6,3,1,8,5]=>[4,2,1,1]
[2,6,8,4,3,7,5,1]=>[4,2,1,1]
[6,2,4,8,3,7,5,1]=>[4,2,1,1]
[7,2,6,3,4,1,8,5]=>[4,2,1,1]
[2,6,7,3,1,4,8,5]=>[3,2,1,1,1]
[2,7,1,8,3,5,4,6]=>[3,2,1,1,1]
[2,1,7,3,5,8,4,6]=>[3,2,1,1,1]
[8,7,1,3,6,2,4,5]=>[4,1,1,1,1]
[8,2,1,7,3,5,6,4]=>[4,2,1,1]
[7,8,2,6,3,1,5,4]=>[4,2,1,1]
[8,7,2,6,3,5,4,1]=>[6,1,1]
[1,2,8,7,4,5,6,3]=>[4,1,1,1,1]
[8,3,7,1,5,6,2,4]=>[4,1,1,1,1]
[8,6,1,2,7,5,3,4]=>[4,2,1,1]
[8,1,6,2,7,4,5,3]=>[4,2,1,1]
[1,8,5,2,6,7,4,3]=>[4,2,1,1]
[5,2,1,8,6,7,4,3]=>[4,3,1]
[2,8,5,7,6,4,3,1]=>[6,1,1]
[1,7,8,5,2,6,4,3]=>[4,2,1,1]
[7,8,1,6,4,2,5,3]=>[4,2,1,1]
[7,8,6,1,5,3,2,4]=>[5,1,1,1]
[7,3,8,6,1,5,2,4]=>[4,2,1,1]
[8,7,6,1,5,3,4,2]=>[6,1,1]
[8,7,1,6,4,5,3,2]=>[6,1,1]
[8,1,7,5,6,4,3,2]=>[6,1,1]
[1,8,6,7,5,4,3,2]=>[6,1,1]
[6,3,5,2,1,4,8,7]=>[4,2,1,1]
[6,3,5,7,2,8,4,1]=>[4,2,1,1]
[8,5,2,7,4,3,1,6]=>[5,2,1]
[4,5,3,6,1,2,8,7]=>[3,2,1,1,1]
[3,5,1,4,6,2,8,7]=>[3,2,1,1,1]
[8,3,4,5,7,2,1,6]=>[4,1,1,1,1]
[5,7,4,6,3,8,2,1]=>[5,1,1,1]
[2,8,4,6,3,7,1,5]=>[4,1,1,1,1]
[8,1,4,7,3,6,2,5]=>[4,1,1,1,1]
[8,3,4,7,5,1,2,6]=>[4,1,1,1,1]
[8,5,1,4,7,3,2,6]=>[5,1,1,1]
[8,5,3,7,1,4,2,6]=>[4,2,1,1]
[2,1,8,5,7,4,3,6]=>[4,2,1,1]
[6,5,3,7,1,8,4,2]=>[4,3,1]
[6,5,1,4,7,8,3,2]=>[5,1,1,1]
[6,3,4,7,5,8,1,2]=>[3,2,1,1,1]
[5,1,4,6,8,3,7,2]=>[4,1,1,1,1]
[4,7,1,3,5,8,6,2]=>[3,2,1,1,1]
[4,8,3,7,1,2,6,5]=>[4,1,1,1,1]
[3,8,6,4,1,7,2,5]=>[4,2,1,1]
[3,8,1,2,5,7,6,4]=>[4,1,1,1,1]
[2,8,7,5,4,1,3,6]=>[5,1,1,1]
[8,7,2,6,4,1,3,5]=>[5,1,1,1]
[3,8,6,7,4,2,1,5]=>[5,1,1,1]
[5,7,6,8,4,2,3,1]=>[5,1,1,1]
[5,3,7,8,2,4,6,1]=>[4,1,1,1,1]
[8,3,6,2,1,4,7,5]=>[4,2,1,1]
[5,3,7,6,2,1,8,4]=>[4,2,2]
[5,3,6,2,8,7,1,4]=>[4,2,1,1]
[5,7,8,6,4,2,1,3]=>[5,1,1,1]
[2,6,7,5,4,8,1,3]=>[4,1,1,1,1]
[6,1,7,4,5,8,2,3]=>[3,2,1,1,1]
[6,7,3,5,1,8,2,4]=>[3,2,1,1,1]
[2,1,6,7,5,8,3,4]=>[3,2,1,1,1]
[2,1,5,7,3,6,8,4]=>[3,2,1,1,1]
[5,7,3,6,1,2,8,4]=>[3,2,1,1,1]
[4,1,7,2,5,6,8,3]=>[3,2,1,1,1]
[2,4,7,1,6,5,8,3]=>[4,1,1,1,1]
[4,6,2,1,8,7,5,3]=>[4,3,1]
[3,4,6,2,7,8,5,1]=>[3,2,1,1,1]
[4,6,1,2,5,8,7,3]=>[3,2,1,1,1]
[5,6,1,4,8,2,7,3]=>[3,2,1,1,1]
[5,6,3,1,8,7,2,4]=>[3,3,1,1]
[3,5,6,4,7,1,8,2]=>[3,2,1,1,1]
[3,4,6,1,5,7,8,2]=>[3,1,1,1,1,1]
[3,4,1,5,7,6,8,2]=>[3,2,1,1,1]
[3,8,2,7,1,6,5,4]=>[5,1,1,1]
[3,8,2,7,6,1,5,4]=>[5,1,1,1]
[3,8,2,7,6,5,1,4]=>[5,1,1,1]
[3,8,2,7,6,5,4,1]=>[6,1,1]
[4,8,7,2,6,5,3,1]=>[6,1,1]
[4,8,7,2,6,5,1,3]=>[5,1,1,1]
[4,8,7,2,6,1,5,3]=>[5,1,1,1]
[4,8,7,2,1,6,5,3]=>[5,2,1]
[4,8,7,3,1,6,5,2]=>[5,2,1]
[4,8,7,3,2,1,6,5]=>[5,2,1]
[4,8,7,3,2,6,1,5]=>[5,1,1,1]
[4,8,7,3,2,6,5,1]=>[5,2,1]
[4,8,7,3,6,2,5,1]=>[5,1,1,1]
[4,8,7,3,6,2,1,5]=>[5,1,1,1]
[4,8,7,3,6,1,5,2]=>[5,1,1,1]
[4,8,7,3,6,5,1,2]=>[5,1,1,1]
[4,8,7,3,6,5,2,1]=>[6,1,1]
[5,8,7,6,3,4,2,1]=>[6,1,1]
[5,8,7,6,3,1,4,2]=>[5,2,1]
[5,8,7,6,3,2,4,1]=>[6,1,1]
[5,8,7,6,2,4,3,1]=>[6,1,1]
[5,8,7,6,2,1,4,3]=>[5,2,1]
[5,8,7,6,4,2,3,1]=>[6,1,1]
[5,8,7,6,4,2,1,3]=>[6,1,1]
[5,8,7,6,4,1,3,2]=>[6,1,1]
[5,8,7,6,4,3,1,2]=>[6,1,1]
[7,3,4,2,1,6,5,8]=>[4,2,1,1]
[7,3,5,2,6,1,4,8]=>[4,1,1,1,1]
[7,3,5,2,6,4,1,8]=>[4,2,1,1]
[6,3,5,2,7,4,8,1]=>[4,2,1,1]
[7,2,1,5,6,4,3,8]=>[4,2,1,1]
[7,3,5,1,6,4,2,8]=>[4,2,1,1]
[7,4,5,6,1,3,2,8]=>[4,1,1,1,1]
[1,4,5,7,3,2,8,6]=>[3,2,1,1,1]
[1,4,6,7,3,8,2,5]=>[3,1,1,1,1,1]
[6,4,5,7,3,1,8,2]=>[4,2,1,1]
[6,4,5,7,1,3,8,2]=>[4,1,1,1,1]
[6,3,5,1,7,4,8,2]=>[4,2,1,1]
[6,2,1,5,7,4,8,3]=>[4,2,1,1]
[3,2,1,5,7,4,8,6]=>[3,2,2,1]
[2,4,6,7,3,8,1,5]=>[3,1,1,1,1,1]
[1,4,6,7,3,8,5,2]=>[3,2,1,1,1]
[1,5,6,7,8,3,4,2]=>[3,1,1,1,1,1]
[2,5,6,7,8,3,1,4]=>[3,1,1,1,1,1]
[3,2,1,6,7,8,4,5]=>[3,2,1,1,1]
[5,2,1,6,7,8,4,3]=>[3,3,1,1]
[5,3,6,1,7,8,4,2]=>[3,3,1,1]
[5,4,6,7,1,8,3,2]=>[4,2,1,1]
[1,5,6,7,8,3,2,4]=>[3,1,1,1,1,1]
[6,4,5,7,2,1,8,3]=>[4,2,1,1]
[5,4,6,7,2,8,3,1]=>[4,2,1,1]
[5,3,6,2,7,8,4,1]=>[4,2,1,1]
[5,3,6,2,7,8,1,4]=>[4,1,1,1,1]
[6,3,5,2,7,1,8,4]=>[4,2,1,1]
[6,3,4,2,1,7,8,5]=>[4,2,1,1]
[5,3,4,1,2,7,8,6]=>[3,2,1,1,1]
[4,3,6,2,7,8,1,5]=>[4,1,1,1,1]
[4,3,6,2,7,8,5,1]=>[4,2,1,1]
[1,3,6,2,7,8,5,4]=>[3,2,1,1,1]
[1,4,6,7,2,8,5,3]=>[3,2,1,1,1]
[3,4,6,7,2,8,5,1]=>[3,2,1,1,1]
[3,4,5,7,2,1,8,6]=>[3,2,1,1,1]
[4,2,1,5,7,3,8,6]=>[3,2,2,1]
[4,2,1,6,7,8,3,5]=>[3,2,1,1,1]
[4,3,6,1,7,8,2,5]=>[3,2,1,1,1]
[1,5,6,7,8,2,4,3]=>[3,1,1,1,1,1]
[1,5,6,7,8,4,2,3]=>[3,1,1,1,1,1]
[3,4,6,7,1,8,5,2]=>[3,2,1,1,1]
[4,3,6,1,7,8,5,2]=>[3,3,1,1]
[4,2,1,6,7,8,5,3]=>[3,3,1,1]
[2,3,6,1,7,8,5,4]=>[3,2,1,1,1]
[2,4,6,7,1,8,5,3]=>[3,2,1,1,1]
[2,5,6,7,8,1,4,3]=>[3,1,1,1,1,1]
[1,4,3,6,2,5,7,8]=>[3,1,1,1,1,1]
[1,4,3,7,2,5,6,8]=>[3,1,1,1,1,1]
[1,4,3,7,6,8,2,5]=>[3,2,1,1,1]
[1,4,3,7,5,8,2,6]=>[3,2,1,1,1]
[1,4,3,7,2,6,5,8]=>[3,2,1,1,1]
[1,5,3,7,4,8,2,6]=>[3,2,1,1,1]
[1,3,2,6,5,8,4,7]=>[3,2,1,1,1]
[1,5,4,8,2,6,3,7]=>[3,2,1,1,1]
[1,5,4,8,3,7,2,6]=>[4,1,1,1,1]
[1,2,3,6,5,8,4,7]=>[3,1,1,1,1,1]
[6,8,2,4,5,7,1,3]=>[3,1,1,1,1,1]
[3,7,8,4,5,2,6,1]=>[4,1,1,1,1]
[7,8,1,4,5,3,6,2]=>[4,1,1,1,1]
[3,8,7,4,1,6,5,2]=>[5,2,1]
[4,8,3,6,1,5,7,2]=>[4,1,1,1,1]
[5,8,3,1,6,4,7,2]=>[4,2,1,1]
[5,8,1,4,7,6,3,2]=>[5,1,1,1]
[7,5,1,8,6,2,4,3]=>[4,3,1]
[7,4,1,8,2,6,3,5]=>[3,3,1,1]
[7,1,8,4,2,6,3,5]=>[3,2,2,1]
[1,6,3,8,5,2,4,7]=>[3,2,1,1,1]
[6,1,3,8,5,2,4,7]=>[3,2,1,1,1]
[7,1,8,3,6,2,5,4]=>[4,2,1,1]
[7,2,8,4,1,6,5,3]=>[4,2,2]
[7,2,8,3,6,5,1,4]=>[4,2,1,1]
[7,2,8,3,6,1,5,4]=>[4,2,1,1]
[7,1,8,2,3,6,5,4]=>[4,2,1,1]
[1,5,2,3,8,4,7,6]=>[3,2,1,1,1]
[5,1,2,3,8,4,7,6]=>[3,2,1,1,1]
[6,2,8,1,3,5,4,7]=>[3,2,1,1,1]
[6,3,1,4,2,8,5,7]=>[3,2,2,1]
[3,1,6,4,2,8,5,7]=>[3,2,2,1]
[2,6,3,8,7,1,5,4]=>[4,2,1,1]
[2,6,3,8,5,1,4,7]=>[3,2,1,1,1]
[2,5,1,3,8,4,7,6]=>[3,2,1,1,1]
[1,2,4,8,3,7,6,5]=>[4,1,1,1,1]
[2,4,8,1,3,7,6,5]=>[4,1,1,1,1]
[2,4,8,3,7,1,6,5]=>[4,1,1,1,1]
[2,4,8,3,7,6,1,5]=>[4,1,1,1,1]
[2,5,4,1,3,8,7,6]=>[3,3,1,1]
[4,8,2,3,7,6,1,5]=>[4,1,1,1,1]
[4,8,2,3,7,1,6,5]=>[4,1,1,1,1]
[4,8,1,2,3,7,6,5]=>[4,1,1,1,1]
[1,4,8,2,3,7,6,5]=>[4,1,1,1,1]
[1,4,8,3,7,2,6,5]=>[4,1,1,1,1]
[6,3,8,1,5,2,4,7]=>[3,2,1,1,1]
[5,3,8,1,2,4,7,6]=>[3,2,1,1,1]
[5,1,3,8,2,4,7,6]=>[3,2,1,1,1]
[1,5,4,8,2,7,6,3]=>[4,2,1,1]
[6,5,1,2,8,7,4,3]=>[4,3,1]
[5,3,1,6,4,2,8,7]=>[3,3,2]
[5,1,6,2,8,7,4,3]=>[4,2,2]
[1,4,2,5,8,7,6,3]=>[4,2,1,1]
[1,3,5,2,8,7,4,6]=>[3,2,1,1,1]
[3,6,2,8,7,5,1,4]=>[4,2,1,1]
[4,2,6,1,8,7,3,5]=>[3,3,1,1]
[4,3,1,5,8,2,7,6]=>[3,3,1,1]
[3,4,8,7,2,6,1,5]=>[4,1,1,1,1]
[3,4,8,7,1,2,6,5]=>[4,1,1,1,1]
[3,4,8,1,7,2,6,5]=>[4,1,1,1,1]
[1,3,4,8,7,2,6,5]=>[4,1,1,1,1]
[1,3,4,8,2,7,6,5]=>[4,1,1,1,1]
[3,4,8,1,2,7,6,5]=>[4,1,1,1,1]
[3,4,8,2,7,1,6,5]=>[4,1,1,1,1]
[3,4,8,2,7,6,1,5]=>[4,1,1,1,1]
[7,8,2,1,5,3,6,4]=>[3,2,2,1]
[6,4,1,2,7,3,5,8]=>[3,2,1,1,1]
[2,3,7,5,4,1,8,6]=>[4,2,1,1]
[6,3,1,5,4,2,7,8]=>[4,2,1,1]
[7,8,1,5,4,2,6,3]=>[4,2,1,1]
[7,8,3,5,4,1,6,2]=>[4,2,1,1]
[7,8,2,5,4,1,3,6]=>[4,1,1,1,1]
[7,8,2,5,4,6,1,3]=>[4,1,1,1,1]
[6,2,1,5,4,7,3,8]=>[4,2,1,1]
[5,3,6,1,4,7,8,2]=>[3,2,1,1,1]
[5,3,6,2,4,7,1,8]=>[4,1,1,1,1]
[6,4,2,1,7,3,8,5]=>[4,2,2]
[4,3,7,5,8,6,1,2]=>[3,2,2,1]
[4,2,7,1,8,3,6,5]=>[3,3,1,1]
[3,2,6,7,4,8,1,5]=>[3,2,1,1,1]
[3,1,6,7,4,8,5,2]=>[3,2,2,1]
[1,7,6,5,3,8,4,2]=>[5,2,1]
[2,7,6,5,3,8,1,4]=>[5,1,1,1]
[1,7,6,5,2,4,8,3]=>[5,1,1,1]
[2,7,6,5,3,1,4,8]=>[5,1,1,1]
[2,7,1,4,8,3,5,6]=>[3,1,1,1,1,1]
[3,7,6,4,8,5,1,2]=>[4,2,1,1]
[5,7,6,3,8,4,1,2]=>[4,2,1,1]
[5,1,6,2,4,8,3,7]=>[3,2,1,1,1]
[4,7,6,5,2,1,3,8]=>[5,1,1,1]
[4,7,6,5,2,8,1,3]=>[5,1,1,1]
[4,7,6,5,1,8,3,2]=>[5,2,1]
[1,7,6,5,2,8,3,4]=>[4,2,1,1]
[1,7,6,5,3,2,8,4]=>[5,2,1]
[4,7,6,5,1,2,8,3]=>[4,2,1,1]
[4,7,6,5,3,1,8,2]=>[5,2,1]
[6,1,3,5,4,8,7,2]=>[4,2,1,1]
[5,2,6,3,4,1,7,8]=>[3,2,1,1,1]
[5,1,6,2,4,7,8,3]=>[3,2,1,1,1]
[1,2,6,3,4,8,7,5]=>[3,2,1,1,1]
[1,7,2,4,8,3,6,5]=>[3,2,1,1,1]
[6,1,4,2,8,3,5,7]=>[3,2,1,1,1]
[4,1,8,2,6,3,5,7]=>[3,2,1,1,1]
[4,7,2,1,5,3,6,8]=>[3,2,1,1,1]
[4,7,1,6,2,3,8,5]=>[3,2,1,1,1]
[1,7,2,6,8,3,5,4]=>[4,1,1,1,1]
[1,2,6,7,4,8,5,3]=>[3,2,1,1,1]
[3,1,6,7,4,2,8,5]=>[3,2,2,1]
[3,2,8,5,4,6,1,7]=>[4,2,1,1]
[4,7,6,3,5,8,1,2]=>[4,1,1,1,1]
[4,7,1,2,5,3,8,6]=>[3,2,1,1,1]
[3,7,6,5,2,4,1,8]=>[5,1,1,1]
[3,7,6,5,1,4,8,2]=>[5,1,1,1]
[3,7,6,5,2,1,8,4]=>[5,2,1]
[1,7,6,5,8,2,4,3]=>[5,1,1,1]
[3,7,6,5,8,1,4,2]=>[5,1,1,1]
[3,7,6,5,1,2,4,8]=>[4,1,1,1,1]
[3,1,6,8,4,2,5,7]=>[3,2,1,1,1]
[4,7,6,8,3,5,1,2]=>[4,1,1,1,1]
[2,7,6,5,1,4,3,8]=>[5,1,1,1]
[2,7,6,5,8,1,3,4]=>[4,1,1,1,1]
[2,7,6,5,8,4,1,3]=>[5,1,1,1]
[6,3,2,1,7,4,8,5]=>[4,2,2]
[4,2,1,7,3,5,8,6]=>[3,2,2,1]
[7,3,1,5,4,2,8,6]=>[4,2,2]
[8,4,1,5,2,7,6,3]=>[4,2,2]
[8,2,5,1,3,7,6,4]=>[4,2,1,1]
[4,3,7,2,1,5,8,6]=>[4,2,1,1]
[6,3,7,4,2,1,8,5]=>[4,2,2]
[4,7,2,5,3,1,8,6]=>[4,2,1,1]
[2,7,5,4,1,3,8,6]=>[4,2,1,1]
[7,5,4,3,2,1,8,6]=>[6,2]
[8,5,3,2,1,7,6,4]=>[5,3]
[6,5,2,1,8,4,3,7]=>[4,3,1]
[4,6,3,2,8,1,5,7]=>[4,1,1,1,1]
[5,7,4,3,2,8,1,6]=>[5,1,1,1]
[1,7,6,2,4,8,3,5]=>[4,1,1,1,1]
[2,7,3,6,4,8,1,5]=>[4,1,1,1,1]
[6,2,7,5,3,8,1,4]=>[4,2,1,1]
[7,1,8,5,3,6,4,2]=>[4,2,2]
[5,8,1,6,2,7,4,3]=>[4,2,1,1]
[1,8,6,2,3,7,5,4]=>[4,2,1,1]
[1,8,6,3,2,7,5,4]=>[4,3,1]
[5,8,3,2,7,1,6,4]=>[4,2,1,1]
[8,7,3,1,6,5,4,2]=>[6,2]
[8,7,2,6,1,5,4,3]=>[6,1,1]
[1,8,5,7,4,3,6,2]=>[5,1,1,1]
[1,8,5,7,2,4,6,3]=>[4,1,1,1,1]
[3,8,6,1,7,2,5,4]=>[4,2,1,1]
[5,8,4,6,7,1,3,2]=>[4,1,1,1,1]
[7,2,8,5,6,1,4,3]=>[4,2,1,1]
[6,3,7,5,8,2,1,4]=>[4,2,1,1]
[3,7,2,6,8,4,1,5]=>[4,1,1,1,1]
[3,6,5,8,1,4,2,7]=>[4,1,1,1,1]
[2,6,5,8,4,1,3,7]=>[4,1,1,1,1]
[6,5,4,8,3,2,1,7]=>[6,1,1]
[8,4,3,7,2,1,6,5]=>[5,2,1]
[8,2,4,7,1,3,6,5]=>[4,1,1,1,1]
[6,2,5,8,1,4,3,7]=>[4,1,1,1,1]
[4,3,6,8,2,1,5,7]=>[4,1,1,1,1]
[6,3,5,1,8,4,2,7]=>[4,2,1,1]
[8,4,1,5,7,3,6,2]=>[4,2,1,1]
[6,4,2,5,8,3,1,7]=>[4,2,1,1]
[5,4,1,6,8,2,3,7]=>[3,2,1,1,1]
[6,5,2,1,7,8,3,4]=>[4,2,1,1]
[6,3,7,4,8,5,2,1]=>[4,2,2]
[4,7,2,5,8,6,3,1]=>[4,2,1,1]
[6,3,1,8,4,7,5,2]=>[4,3,1]
[6,4,2,8,7,3,5,1]=>[4,3,1]
[6,5,3,8,7,4,1,2]=>[4,3,1]
[8,5,3,7,6,4,2,1]=>[6,2]
[5,4,8,1,7,6,2,3]=>[4,2,1,1]
[5,2,8,1,7,3,6,4]=>[4,2,1,1]
[6,4,8,2,1,7,5,3]=>[4,3,1]
[3,6,8,1,4,7,5,2]=>[4,1,1,1,1]
[5,7,3,8,1,6,4,2]=>[4,2,1,1]
[6,4,7,8,1,5,3,2]=>[4,2,1,1]
[6,3,7,8,5,2,4,1]=>[4,2,1,1]
[2,5,8,7,1,3,6,4]=>[4,1,1,1,1]
[5,3,8,7,2,1,6,4]=>[4,2,2]
[8,3,7,6,1,5,4,2]=>[6,1,1]
[8,2,7,6,5,1,4,3]=>[6,1,1]
[4,3,8,7,6,2,1,5]=>[5,2,1]
[2,4,8,7,6,1,3,5]=>[4,1,1,1,1]
[3,5,8,7,2,6,1,4]=>[4,1,1,1,1]
[4,7,3,8,6,5,1,2]=>[4,2,1,1]
[7,5,8,6,4,3,2,1]=>[6,2]
[5,8,7,3,6,4,2,1]=>[6,1,1]
[4,8,7,6,2,5,3,1]=>[6,1,1]
[3,8,7,6,5,1,4,2]=>[6,1,1]
[2,8,7,6,5,4,1,3]=>[6,1,1]
[3,6,5,1,2,4,8,7]=>[3,2,1,1,1]
[3,7,5,8,2,4,1,6]=>[4,1,1,1,1]
[3,8,5,7,2,4,1,6]=>[4,1,1,1,1]
[5,1,7,8,4,3,2,6]=>[4,2,1,1]
[5,1,2,6,4,3,8,7]=>[3,2,2,1]
[6,1,2,5,4,3,8,7]=>[4,2,1,1]
[5,1,2,4,6,3,8,7]=>[3,2,1,1,1]
[4,1,2,6,5,3,8,7]=>[3,2,2,1]
[4,1,5,7,8,3,2,6]=>[3,2,1,1,1]
[4,1,5,8,7,3,2,6]=>[4,2,1,1]
[4,7,1,8,3,6,2,5]=>[3,2,1,1,1]
[4,1,7,8,5,2,3,6]=>[3,2,1,1,1]
[5,1,7,4,8,2,3,6]=>[3,2,1,1,1]
[7,5,3,8,1,4,2,6]=>[4,2,1,1]
[2,1,5,8,7,3,4,6]=>[3,2,1,1,1]
[5,1,8,4,7,2,3,6]=>[3,2,1,1,1]
[4,1,8,7,5,2,3,6]=>[4,2,1,1]
[4,7,1,6,3,2,8,5]=>[4,2,1,1]
[6,1,2,3,7,5,8,4]=>[3,2,1,1,1]
[7,1,2,3,8,6,5,4]=>[4,2,1,1]
[7,1,2,3,5,8,6,4]=>[3,2,1,1,1]
[6,8,1,4,3,7,2,5]=>[4,1,1,1,1]
[8,7,3,2,4,1,6,5]=>[5,2,1]
[2,1,7,3,4,8,6,5]=>[3,2,2,1]
[7,8,3,2,4,1,6,5]=>[4,2,1,1]
[6,7,1,4,3,8,2,5]=>[4,1,1,1,1]
[8,1,2,3,5,7,6,4]=>[4,1,1,1,1]
[8,1,2,3,6,7,5,4]=>[4,1,1,1,1]
[7,1,2,3,6,8,5,4]=>[4,1,1,1,1]
[7,1,2,3,8,5,6,4]=>[3,2,1,1,1]
[8,1,2,3,7,5,6,4]=>[4,1,1,1,1]
[8,1,2,3,6,5,7,4]=>[4,1,1,1,1]
[7,1,8,5,4,3,2,6]=>[5,2,1]
[7,8,2,6,3,4,1,5]=>[4,1,1,1,1]
[6,8,2,7,3,4,1,5]=>[4,1,1,1,1]
[6,7,2,8,3,4,1,5]=>[3,2,1,1,1]
[3,8,7,1,4,2,6,5]=>[4,2,1,1]
[3,7,8,1,4,2,6,5]=>[3,2,1,1,1]
[3,6,8,1,4,2,7,5]=>[3,2,1,1,1]
[3,5,7,8,2,4,1,6]=>[3,1,1,1,1,1]
[3,6,7,1,4,2,8,5]=>[3,2,1,1,1]
[7,6,2,8,3,1,4,5]=>[4,2,1,1]
[8,6,2,7,3,1,4,5]=>[4,2,1,1]
[8,1,7,5,4,3,2,6]=>[6,1,1]
[8,1,7,4,5,3,2,6]=>[5,1,1,1]
[5,8,3,7,1,4,2,6]=>[4,1,1,1,1]
[2,1,7,3,4,6,8,5]=>[3,2,1,1,1]
[6,7,3,2,4,1,8,5]=>[4,2,1,1]
[8,7,2,4,3,6,1,5]=>[5,1,1,1]
[7,1,2,3,5,6,8,4]=>[3,1,1,1,1,1]
[6,1,2,3,8,7,4,5]=>[3,2,1,1,1]
[5,1,2,3,7,8,6,4]=>[3,2,1,1,1]
[5,1,2,3,8,7,6,4]=>[4,2,1,1]
[5,1,2,3,8,6,7,4]=>[3,2,1,1,1]
[6,1,2,3,5,8,7,4]=>[3,2,1,1,1]
[8,6,2,4,3,1,7,5]=>[5,2,1]
[7,6,3,2,4,8,1,5]=>[5,1,1,1]
[2,1,6,3,4,8,7,5]=>[3,2,2,1]
[8,6,3,2,4,7,1,5]=>[5,1,1,1]
[7,6,2,4,3,1,8,5]=>[5,2,1]
[6,1,2,3,5,7,8,4]=>[3,1,1,1,1,1]
[5,1,2,3,6,8,7,4]=>[3,2,1,1,1]
[7,8,1,2,6,3,5,4]=>[4,1,1,1,1]
[1,4,8,2,7,3,5,6]=>[3,1,1,1,1,1]
[1,2,8,5,4,7,3,6]=>[4,1,1,1,1]
[1,3,8,5,4,2,7,6]=>[4,2,1,1]
[2,3,6,8,4,7,1,5]=>[3,1,1,1,1,1]
[1,3,6,8,4,7,5,2]=>[4,1,1,1,1]
[2,4,8,1,7,3,6,5]=>[4,1,1,1,1]
[3,4,8,5,7,6,1,2]=>[4,1,1,1,1]
[1,2,6,8,4,5,7,3]=>[3,1,1,1,1,1]
[7,5,1,2,4,3,6,8]=>[4,1,1,1,1]
[7,4,6,1,5,2,3,8]=>[4,1,1,1,1]
[7,1,4,2,6,3,5,8]=>[3,2,1,1,1]
[6,8,1,4,7,2,3,5]=>[3,1,1,1,1,1]
[1,6,4,2,8,3,5,7]=>[3,2,1,1,1]
[1,6,3,8,5,4,2,7]=>[4,2,1,1]
[6,8,1,7,3,5,4,2]=>[5,1,1,1]
[7,1,3,6,5,4,2,8]=>[5,1,1,1]
[7,3,1,6,5,4,2,8]=>[5,2,1]
[7,2,1,4,6,3,5,8]=>[3,2,1,1,1]
[7,2,3,6,5,1,4,8]=>[4,1,1,1,1]
[7,1,2,3,6,5,4,8]=>[4,1,1,1,1]
[6,8,1,2,7,3,5,4]=>[4,1,1,1,1]
[1,6,2,3,8,5,4,7]=>[3,2,1,1,1]
[1,5,8,2,7,6,3,4]=>[4,1,1,1,1]
[5,1,8,2,7,6,3,4]=>[4,2,1,1]
[5,8,2,7,6,3,4,1]=>[5,1,1,1]
[6,2,8,1,7,3,5,4]=>[4,2,1,1]
[6,8,2,1,7,4,3,5]=>[4,2,1,1]
[3,6,4,1,2,8,5,7]=>[3,2,1,1,1]
[2,1,6,3,8,5,4,7]=>[3,2,2,1]
[2,5,1,8,7,6,3,4]=>[4,2,1,1]
[2,5,3,8,7,4,6,1]=>[4,2,1,1]
[1,2,5,3,8,7,4,6]=>[3,2,1,1,1]
[2,4,8,7,6,5,1,3]=>[5,1,1,1]
[2,5,3,8,7,1,6,4]=>[4,2,1,1]
[2,5,8,4,1,7,6,3]=>[4,2,1,1]
[3,5,8,7,1,4,2,6]=>[4,1,1,1,1]
[5,3,8,4,1,7,6,2]=>[4,2,2]
[4,2,8,7,6,3,5,1]=>[5,2,1]
[4,2,8,7,6,5,3,1]=>[6,2]
[4,1,8,7,6,5,3,2]=>[6,2]
[4,3,8,7,6,5,1,2]=>[5,2,1]
[6,3,1,8,7,2,5,4]=>[4,3,1]
[5,8,3,7,6,1,4,2]=>[5,1,1,1]
[5,1,3,8,7,6,2,4]=>[4,2,1,1]
[1,5,3,8,7,6,2,4]=>[4,2,1,1]
[1,5,8,4,7,2,6,3]=>[4,1,1,1,1]
[5,1,8,4,7,2,6,3]=>[4,2,1,1]
[5,8,7,4,6,1,2,3]=>[4,1,1,1,1]
[6,8,5,1,2,4,7,3]=>[4,1,1,1,1]
[5,6,3,1,2,4,8,7]=>[3,2,1,1,1]
[5,6,2,4,3,1,8,7]=>[4,2,1,1]
[5,6,1,2,4,3,8,7]=>[3,2,1,1,1]
[4,5,8,1,7,2,3,6]=>[3,1,1,1,1,1]
[4,5,8,1,7,2,6,3]=>[4,1,1,1,1]
[1,3,2,5,8,7,4,6]=>[3,2,1,1,1]
[3,5,1,8,7,4,6,2]=>[4,2,1,1]
[3,5,1,8,7,2,6,4]=>[4,2,1,1]
[4,3,6,1,2,8,5,7]=>[3,2,1,1,1]
[4,5,8,3,1,7,2,6]=>[3,2,1,1,1]
[4,5,2,8,7,1,3,6]=>[3,2,1,1,1]
[3,2,5,8,7,1,6,4]=>[4,2,1,1]
[3,4,8,7,6,2,1,5]=>[5,1,1,1]
[3,1,4,8,7,6,2,5]=>[4,2,1,1]
[3,4,8,7,6,5,1,2]=>[5,1,1,1]
[1,3,4,8,7,6,2,5]=>[4,1,1,1,1]
[3,4,8,7,6,2,5,1]=>[5,1,1,1]
[3,2,5,8,7,4,6,1]=>[4,2,1,1]
[4,5,8,3,1,7,6,2]=>[4,2,1,1]
[2,1,3,5,8,7,4,6]=>[3,2,1,1,1]
[1,2,7,5,8,6,4,3]=>[4,2,1,1]
[7,1,4,8,2,6,5,3]=>[4,2,1,1]
[6,8,1,3,7,5,2,4]=>[4,1,1,1,1]
[3,7,8,1,2,6,5,4]=>[4,1,1,1,1]
[1,3,7,8,2,6,5,4]=>[4,1,1,1,1]
[2,3,7,8,1,6,5,4]=>[4,1,1,1,1]
[2,7,8,1,3,6,5,4]=>[4,1,1,1,1]
[8,1,2,6,7,3,5,4]=>[4,1,1,1,1]
[8,1,2,6,7,5,3,4]=>[4,1,1,1,1]
[8,2,5,7,1,3,6,4]=>[4,1,1,1,1]
[2,8,1,6,7,3,5,4]=>[4,1,1,1,1]
[2,6,8,3,7,1,5,4]=>[4,1,1,1,1]
[2,8,6,4,7,1,5,3]=>[4,2,1,1]
[6,8,3,4,1,7,5,2]=>[4,2,1,1]
[6,8,3,7,4,1,5,2]=>[4,2,1,1]
[2,6,8,3,7,5,1,4]=>[4,1,1,1,1]
[2,8,1,6,7,5,3,4]=>[4,1,1,1,1]
[8,2,5,7,1,6,3,4]=>[4,1,1,1,1]
[8,4,7,2,3,6,1,5]=>[4,1,1,1,1]
[8,5,7,4,2,6,1,3]=>[5,1,1,1]
[8,3,5,7,4,1,6,2]=>[4,2,1,1]
[8,5,2,4,7,1,6,3]=>[4,2,1,1]
[8,2,3,5,7,1,6,4]=>[4,1,1,1,1]
[8,2,4,7,3,6,1,5]=>[4,1,1,1,1]
[8,2,7,1,4,6,3,5]=>[4,1,1,1,1]
[8,7,1,2,4,6,3,5]=>[4,1,1,1,1]
[8,7,1,4,6,2,3,5]=>[4,1,1,1,1]
[8,4,7,1,3,6,2,5]=>[4,1,1,1,1]
[1,6,8,3,7,2,5,4]=>[4,1,1,1,1]
[8,3,5,7,1,2,6,4]=>[4,1,1,1,1]
[5,8,7,1,3,6,2,4]=>[4,1,1,1,1]
[8,5,4,7,1,6,2,3]=>[4,2,1,1]
[8,5,4,7,1,2,6,3]=>[4,2,1,1]
[8,5,1,4,7,2,6,3]=>[4,2,1,1]
[1,4,6,8,2,7,5,3]=>[4,1,1,1,1]
[1,6,5,8,2,7,4,3]=>[4,2,1,1]
[8,5,6,3,1,7,4,2]=>[4,3,1]
[5,6,2,8,1,7,4,3]=>[4,2,1,1]
[1,8,4,5,7,2,6,3]=>[4,1,1,1,1]
[5,8,7,3,6,1,2,4]=>[4,1,1,1,1]
[8,3,5,7,1,6,2,4]=>[4,1,1,1,1]
[1,6,8,3,7,5,2,4]=>[4,1,1,1,1]
[6,3,8,2,7,5,1,4]=>[4,2,1,1]
[6,8,4,2,7,1,5,3]=>[4,2,1,1]
[8,6,4,7,3,1,5,2]=>[5,2,1]
[8,4,5,7,3,1,6,2]=>[4,2,1,1]
[8,4,2,5,7,1,6,3]=>[4,2,1,1]
[8,3,4,7,2,6,1,5]=>[4,1,1,1,1]
[8,7,1,3,4,6,2,5]=>[4,1,1,1,1]
[8,3,7,2,4,6,1,5]=>[4,1,1,1,1]
[2,8,4,5,7,1,6,3]=>[4,1,1,1,1]
[8,7,3,4,5,1,6,2]=>[4,2,1,1]
[8,7,4,5,2,6,1,3]=>[5,1,1,1]
[5,8,7,2,3,6,1,4]=>[4,1,1,1,1]
[8,7,2,3,4,6,1,5]=>[4,1,1,1,1]
[8,7,2,3,6,1,4,5]=>[4,1,1,1,1]
[1,3,2,8,5,4,7,6]=>[3,2,2,1]
[4,2,8,5,3,7,1,6]=>[4,2,1,1]
[5,2,1,8,4,3,7,6]=>[3,3,2]
[6,2,8,4,3,7,5,1]=>[4,2,2]
[7,2,8,4,3,1,6,5]=>[4,2,2]
[7,3,4,8,2,1,6,5]=>[4,2,1,1]
[6,3,4,8,2,7,5,1]=>[4,2,1,1]
[5,3,4,1,8,2,7,6]=>[3,3,1,1]
[8,1,4,5,2,3,7,6]=>[3,2,1,1,1]
[8,1,5,4,3,2,7,6]=>[5,2,1]
[3,5,4,2,8,1,7,6]=>[4,2,1,1]
[4,5,3,2,8,7,1,6]=>[4,2,1,1]
[6,4,3,2,8,7,5,1]=>[5,3]
[6,5,3,2,1,7,8,4]=>[5,2,1]
[5,6,3,2,7,8,4,1]=>[4,2,1,1]
[4,1,6,3,2,7,8,5]=>[3,2,2,1]
[3,6,4,2,7,8,1,5]=>[4,1,1,1,1]
[8,1,6,4,3,7,2,5]=>[5,1,1,1]
[8,1,7,4,3,6,5,2]=>[5,2,1]
[2,7,4,1,3,6,5,8]=>[3,2,1,1,1]
[3,7,4,2,6,1,5,8]=>[4,1,1,1,1]
[4,1,7,3,2,6,5,8]=>[3,2,2,1]
[5,7,3,2,6,4,8,1]=>[4,2,1,1]
[6,7,3,2,5,4,1,8]=>[4,2,1,1]
[7,6,3,2,1,5,4,8]=>[5,2,1]
[4,7,5,6,2,3,8,1]=>[4,1,1,1,1]
[3,1,7,5,6,2,4,8]=>[3,2,1,1,1]
[2,7,5,6,1,3,4,8]=>[3,1,1,1,1,1]
[2,6,5,7,1,3,8,4]=>[3,2,1,1,1]
[4,6,5,7,2,8,1,3]=>[4,1,1,1,1]
[5,6,4,7,2,8,3,1]=>[4,2,1,1]
[6,5,4,1,7,2,8,3]=>[4,2,2]
[7,5,4,6,2,1,8,3]=>[5,2,1]
[6,4,5,7,1,8,2,3]=>[3,2,1,1,1]
[5,4,6,1,7,8,2,3]=>[3,2,1,1,1]
[8,1,5,6,7,2,3,4]=>[3,1,1,1,1,1]
[2,1,4,6,8,7,3,5]=>[3,2,1,1,1]
[3,4,6,8,7,1,2,5]=>[3,1,1,1,1,1]
[4,3,1,6,8,7,2,5]=>[3,3,1,1]
[5,3,6,8,7,2,4,1]=>[4,2,1,1]
[6,3,5,1,8,7,2,4]=>[3,3,1,1]
[7,3,5,8,6,2,1,4]=>[4,2,1,1]
[7,2,8,5,6,3,1,4]=>[4,2,1,1]
[6,2,8,5,1,7,3,4]=>[3,2,2,1]
[4,2,1,8,6,7,3,5]=>[3,3,1,1]
[1,3,2,8,6,7,4,5]=>[3,2,1,1,1]
[2,3,8,6,7,1,4,5]=>[3,1,1,1,1,1]
[8,1,3,2,6,7,4,5]=>[3,2,1,1,1]
[2,3,8,7,1,6,5,4]=>[5,1,1,1]
[4,2,8,7,6,1,5,3]=>[5,2,1]
[5,2,8,7,6,4,1,3]=>[5,2,1]
[7,2,1,8,6,5,4,3]=>[5,3]
[7,3,6,1,8,5,4,2]=>[5,2,1]
[6,3,7,8,5,4,2,1]=>[5,2,1]
[5,3,7,8,6,4,1,2]=>[4,2,1,1]
[4,3,1,7,8,6,5,2]=>[4,3,1]
[3,4,7,8,6,1,5,2]=>[4,1,1,1,1]
[8,1,5,7,6,2,4,3]=>[5,1,1,1]
[3,5,7,6,8,1,4,2]=>[4,1,1,1,1]
[4,5,7,6,8,3,1,2]=>[4,1,1,1,1]
[5,4,1,7,6,8,3,2]=>[4,3,1]
[6,4,7,5,8,3,2,1]=>[5,2,1]
[7,4,6,5,1,8,3,2]=>[5,2,1]
[7,5,6,4,3,1,8,2]=>[5,2,1]
[6,5,1,7,4,3,8,2]=>[5,2,1]
[4,6,7,5,3,8,1,2]=>[4,1,1,1,1]
[3,6,7,5,1,4,8,2]=>[4,1,1,1,1]
[8,1,6,7,5,4,2,3]=>[5,1,1,1]
[8,1,7,6,5,4,3,2]=>[7,1]
[2,7,6,1,5,4,3,8]=>[5,1,1,1]
[3,7,6,5,1,4,2,8]=>[5,1,1,1]
[4,7,6,5,3,1,2,8]=>[5,1,1,1]
[8,6,4,3,1,5,7,2]=>[5,2,1]
[8,6,4,1,5,2,7,3]=>[4,2,2]
[8,6,5,1,3,2,7,4]=>[5,2,1]
[8,6,3,1,7,2,4,5]=>[4,2,1,1]
[8,7,3,1,5,2,4,6]=>[4,2,1,1]
[5,3,1,7,2,4,6,8]=>[3,2,1,1,1]
[8,7,1,2,4,5,3,6]=>[4,1,1,1,1]
[8,6,1,2,4,7,3,5]=>[4,1,1,1,1]
[8,5,1,2,6,7,3,4]=>[3,2,1,1,1]
[8,5,1,6,4,2,7,3]=>[4,2,2]
[8,5,1,3,6,4,7,2]=>[4,2,1,1]
[8,6,1,5,3,4,7,2]=>[5,1,1,1]
[8,6,1,5,2,4,7,3]=>[5,1,1,1]
[8,6,1,2,5,7,3,4]=>[4,1,1,1,1]
[8,6,1,2,7,4,3,5]=>[4,2,1,1]
[8,7,1,2,5,4,3,6]=>[5,1,1,1]
[5,1,4,2,3,8,6,7]=>[3,2,1,1,1]
[5,1,4,2,7,3,6,8]=>[3,2,1,1,1]
[7,1,5,8,2,6,3,4]=>[3,2,1,1,1]
[5,7,8,1,2,4,6,3]=>[3,1,1,1,1,1]
[5,7,8,1,3,4,6,2]=>[3,1,1,1,1,1]
[5,8,1,7,3,4,6,2]=>[4,1,1,1,1]
[8,1,5,7,2,4,6,3]=>[4,1,1,1,1]
[8,4,1,2,7,6,3,5]=>[4,2,1,1]
[1,4,2,3,8,7,5,6]=>[3,2,1,1,1]
[1,4,2,7,6,3,5,8]=>[3,2,1,1,1]
[6,1,2,8,7,5,3,4]=>[4,2,1,1]
[6,1,2,4,8,7,5,3]=>[4,2,1,1]
[3,1,8,4,6,7,5,2]=>[4,2,1,1]
[3,1,7,6,4,8,5,2]=>[4,2,2]
[7,1,2,4,6,8,5,3]=>[4,1,1,1,1]
[7,1,2,6,8,5,3,4]=>[4,1,1,1,1]
[6,1,2,7,8,5,3,4]=>[3,2,1,1,1]
[6,1,2,7,4,8,5,3]=>[3,2,2,1]
[3,1,6,4,7,8,5,2]=>[3,2,2,1]
[5,7,1,3,8,4,6,2]=>[3,2,1,1,1]
[5,7,1,8,4,2,6,3]=>[3,2,2,1]
[7,1,5,3,2,8,6,4]=>[4,3,1]
[7,1,4,5,2,8,6,3]=>[3,3,1,1]
[4,7,3,1,5,8,6,2]=>[3,3,1,1]
[4,8,7,3,1,5,6,2]=>[4,2,1,1]
[8,1,7,4,5,2,6,3]=>[4,2,1,1]
[8,1,7,5,3,2,6,4]=>[5,2,1]
[8,3,7,1,2,6,4,5]=>[4,1,1,1,1]
[3,1,2,8,4,7,5,6]=>[3,2,1,1,1]
[3,1,2,8,6,4,5,7]=>[3,2,1,1,1]
[3,1,7,2,6,4,5,8]=>[3,2,1,1,1]
[1,4,2,3,8,6,5,7]=>[3,2,1,1,1]
[1,4,2,3,8,5,7,6]=>[3,2,1,1,1]
[5,8,1,7,2,4,6,3]=>[4,1,1,1,1]
[5,8,1,3,4,7,6,2]=>[4,1,1,1,1]
[3,1,8,6,4,7,5,2]=>[4,2,2]
[8,1,2,6,7,4,5,3]=>[4,1,1,1,1]
[6,1,2,8,7,3,5,4]=>[4,2,1,1]
[1,2,3,5,8,4,7,6]=>[3,1,1,1,1,1]
[1,2,3,5,8,6,4,7]=>[3,1,1,1,1,1]
[7,1,2,8,3,6,5,4]=>[4,2,1,1]
[7,1,2,8,6,4,5,3]=>[4,2,1,1]
[3,1,7,8,4,6,5,2]=>[4,2,1,1]
[3,1,8,7,6,4,5,2]=>[5,2,1]
[8,1,2,7,4,6,5,3]=>[5,1,1,1]
[8,1,2,7,3,6,5,4]=>[5,1,1,1]
[1,2,3,5,8,7,4,6]=>[3,1,1,1,1,1]
[1,2,3,6,8,5,4,7]=>[3,1,1,1,1,1]
[7,8,5,6,3,1,4,2]=>[4,2,1,1]
[7,8,5,3,6,1,2,4]=>[4,1,1,1,1]
[7,5,6,3,1,4,2,8]=>[4,2,1,1]
[7,5,8,3,1,4,2,6]=>[4,2,1,1]
[7,8,5,3,1,4,2,6]=>[4,2,1,1]
[7,8,5,3,1,6,2,4]=>[4,2,1,1]
[7,8,5,3,1,6,4,2]=>[4,3,1]
[7,8,5,3,6,1,4,2]=>[4,2,1,1]
[7,8,5,3,6,4,1,2]=>[4,2,1,1]
[7,8,5,3,4,1,6,2]=>[4,2,1,1]
[7,8,5,3,1,4,6,2]=>[4,2,1,1]
[7,5,8,3,4,1,6,2]=>[4,2,1,1]
[7,5,8,3,4,6,1,2]=>[4,1,1,1,1]
[7,5,6,3,4,1,8,2]=>[4,2,1,1]
[7,5,6,3,1,4,8,2]=>[4,2,1,1]
[7,5,6,3,1,2,8,4]=>[4,2,1,1]
[7,5,3,6,1,2,8,4]=>[4,2,1,1]
[7,5,3,1,4,2,6,8]=>[4,2,1,1]
[7,5,3,1,6,4,8,2]=>[4,3,1]
[7,5,3,6,1,4,8,2]=>[4,2,1,1]
[7,5,3,6,4,1,8,2]=>[4,2,2]
[7,5,3,6,4,8,1,2]=>[4,2,1,1]
[7,5,3,8,4,6,1,2]=>[4,2,1,1]
[7,5,3,8,1,4,6,2]=>[4,2,1,1]
[7,5,3,1,8,4,6,2]=>[4,3,1]
[7,5,3,1,8,2,6,4]=>[4,3,1]
[7,5,3,1,6,2,4,8]=>[4,2,1,1]
[7,5,3,1,6,4,2,8]=>[4,3,1]
[7,5,3,1,8,4,2,6]=>[4,3,1]
[7,5,3,1,8,6,2,4]=>[4,3,1]
[7,5,3,8,1,6,4,2]=>[4,3,1]
[7,5,3,8,6,1,4,2]=>[4,3,1]
[7,5,3,8,6,4,1,2]=>[4,3,1]
[7,5,8,3,6,4,1,2]=>[4,2,1,1]
[7,5,8,3,6,1,4,2]=>[4,2,1,1]
[7,5,8,3,1,6,4,2]=>[4,3,1]
[7,5,8,3,1,6,2,4]=>[4,2,1,1]
[7,5,3,6,1,4,2,8]=>[4,2,1,1]
[7,5,3,6,4,1,2,8]=>[4,2,1,1]
[7,5,3,8,4,1,2,6]=>[4,2,1,1]
[7,5,8,6,3,1,2,4]=>[4,2,1,1]
[7,5,8,6,3,1,4,2]=>[4,2,2]
[7,5,8,6,3,4,1,2]=>[4,2,1,1]
[7,5,6,8,3,1,4,2]=>[4,2,1,1]
[7,5,6,3,8,1,2,4]=>[4,1,1,1,1]
[7,5,3,4,1,8,2,6]=>[4,2,1,1]
[7,5,6,3,1,8,2,4]=>[4,2,1,1]
[7,5,6,3,1,8,4,2]=>[4,3,1]
[7,5,6,3,8,1,4,2]=>[4,2,1,1]
[7,5,6,3,8,4,1,2]=>[4,2,1,1]
[7,5,3,6,8,4,1,2]=>[4,2,1,1]
[7,5,3,6,8,1,4,2]=>[4,2,1,1]
[7,5,3,6,1,8,4,2]=>[4,3,1]
[7,5,3,1,6,8,4,2]=>[4,3,1]
[7,5,3,1,6,8,2,4]=>[4,2,1,1]
[7,5,3,1,2,8,4,6]=>[4,2,1,1]
[7,5,3,1,2,8,6,4]=>[4,3,1]
[7,5,3,1,4,8,6,2]=>[4,3,1]
[7,5,3,4,8,1,6,2]=>[4,2,1,1]
[7,5,3,4,1,6,8,2]=>[4,2,1,1]
[7,5,3,1,4,6,8,2]=>[4,2,1,1]
[3,6,2,5,4,1,8,7]=>[4,2,1,1]
[3,5,2,8,4,7,6,1]=>[4,2,1,1]
[5,4,7,3,2,8,6,1]=>[5,2,1]
[5,4,8,3,2,7,6,1]=>[5,2,1]
[6,4,5,3,2,1,8,7]=>[5,2,1]
[5,3,2,6,4,1,8,7]=>[4,2,2]
[4,5,8,3,2,7,6,1]=>[4,2,1,1]
[4,7,6,3,8,5,2,1]=>[5,2,1]
[4,8,6,3,7,5,2,1]=>[5,2,1]
[4,8,5,3,2,7,6,1]=>[5,2,1]
[5,8,4,3,2,7,6,1]=>[5,2,1]
[5,3,2,8,4,7,6,1]=>[4,3,1]
[2,1,5,8,4,7,6,3]=>[4,2,1,1]
[5,3,2,7,4,8,6,1]=>[4,2,2]
[5,7,4,3,2,8,6,1]=>[5,2,1]
[4,7,5,3,2,8,6,1]=>[5,2,1]
[4,7,8,3,6,5,2,1]=>[5,1,1,1]
[4,6,8,3,7,5,2,1]=>[5,1,1,1]
[7,6,4,3,8,5,2,1]=>[6,2]
[7,3,2,6,8,5,4,1]=>[5,2,1]
[2,1,8,6,7,5,4,3]=>[5,2,1]
[8,3,2,6,7,5,4,1]=>[5,2,1]
[8,6,4,3,7,5,2,1]=>[6,2]
[8,5,7,6,4,3,2,1]=>[7,1]
[8,4,5,3,2,7,6,1]=>[5,2,1]
[8,4,7,3,6,5,2,1]=>[6,1,1]
[8,4,6,3,7,5,2,1]=>[5,2,1]
[7,4,6,3,8,5,2,1]=>[5,2,1]
[3,7,2,6,8,5,4,1]=>[5,1,1,1]
[3,8,2,6,7,5,4,1]=>[5,1,1,1]
[3,8,2,5,4,7,6,1]=>[4,2,1,1]
[3,7,2,8,6,5,4,1]=>[5,2,1]
[3,6,2,8,7,5,4,1]=>[5,2,1]
[6,4,7,3,8,5,2,1]=>[5,2,1]
[6,4,8,3,7,5,2,1]=>[5,2,1]
[7,4,8,3,6,5,2,1]=>[5,2,1]
[7,4,5,3,2,8,6,1]=>[5,2,1]
[7,5,4,3,2,8,6,1]=>[6,2]
[7,3,2,5,4,8,6,1]=>[4,2,2]
[2,1,7,5,4,8,6,3]=>[4,2,2]
[7,3,2,8,6,5,4,1]=>[5,3]
[7,8,4,3,6,5,2,1]=>[5,2,1]
[6,8,5,7,4,3,2,1]=>[6,1,1]
[6,8,4,3,7,5,2,1]=>[5,2,1]
[6,3,2,8,7,5,4,1]=>[5,3]
[6,3,2,7,8,5,4,1]=>[4,3,1]
[6,7,4,3,8,5,2,1]=>[5,2,1]
[4,6,8,3,5,7,1,2]=>[3,1,1,1,1,1]
[6,8,1,2,4,5,7,3]=>[3,1,1,1,1,1]
[3,5,8,2,4,7,1,6]=>[3,1,1,1,1,1]
[8,3,5,2,4,1,6,7]=>[4,1,1,1,1]
[4,2,5,7,3,6,1,8]=>[3,2,1,1,1]
[4,5,2,8,3,1,6,7]=>[3,2,1,1,1]
[4,2,5,8,3,7,1,6]=>[3,2,1,1,1]
[2,1,6,8,4,7,3,5]=>[3,2,1,1,1]
[1,2,5,8,3,6,7,4]=>[3,1,1,1,1,1]
[5,3,6,8,4,7,1,2]=>[3,2,1,1,1]
[1,6,5,8,2,4,7,3]=>[4,1,1,1,1]
[3,1,2,6,8,5,7,4]=>[3,2,1,1,1]
[1,4,3,8,2,6,7,5]=>[3,2,1,1,1]
[5,4,8,3,2,1,6,7]=>[5,1,1,1]
[5,4,3,7,2,6,1,8]=>[5,1,1,1]
[4,3,6,2,7,5,1,8]=>[4,2,1,1]
[4,6,3,2,1,8,5,7]=>[4,2,1,1]
[4,1,7,3,2,5,8,6]=>[3,2,2,1]
[4,3,1,7,8,2,6,5]=>[3,3,1,1]
[3,5,1,2,7,8,6,4]=>[3,2,1,1,1]
[7,5,1,4,8,2,6,3]=>[4,2,1,1]
[5,4,7,3,8,6,1,2]=>[4,2,1,1]
[5,8,4,7,6,3,1,2]=>[5,1,1,1]
[5,8,7,1,4,2,6,3]=>[4,2,1,1]
[8,3,5,1,2,7,6,4]=>[4,2,1,1]
[4,8,3,1,7,2,6,5]=>[4,2,1,1]
[1,8,4,3,5,2,7,6]=>[4,2,1,1]
[4,6,3,1,5,2,8,7]=>[3,2,2,1]
[4,7,3,6,5,2,1,8]=>[5,1,1,1]
[5,3,7,6,4,2,1,8]=>[5,2,1]
[1,6,3,4,2,8,7,5]=>[3,3,1,1]
[1,8,3,6,2,7,5,4]=>[4,2,1,1]
[1,6,8,7,4,2,5,3]=>[4,2,1,1]
[6,4,8,7,5,3,1,2]=>[5,2,1]
[7,6,4,3,8,5,1,2]=>[5,2,1]
[1,7,6,2,8,4,5,3]=>[4,2,1,1]
[7,1,3,2,6,8,5,4]=>[4,2,1,1]
[1,5,3,2,7,4,8,6]=>[3,2,2,1]
[6,3,2,1,8,5,4,7]=>[4,3,1]
[6,5,3,2,7,4,1,8]=>[5,2,1]
[5,2,6,3,7,4,1,8]=>[3,2,2,1]
[2,8,5,3,1,6,4,7]=>[4,2,1,1]
[2,1,7,3,8,5,4,6]=>[3,2,2,1]
[1,6,2,3,7,8,5,4]=>[3,2,1,1,1]
[1,6,7,2,8,4,5,3]=>[3,2,1,1,1]
[5,7,1,8,2,4,6,3]=>[3,2,1,1,1]
[5,1,2,7,8,3,6,4]=>[3,2,1,1,1]
[2,4,1,7,8,6,3,5]=>[3,2,1,1,1]
[4,2,1,7,3,8,5,6]=>[3,2,2,1]
[6,2,8,4,3,1,5,7]=>[4,2,1,1]
[7,3,2,1,8,4,5,6]=>[4,2,1,1]
[7,8,3,2,5,6,1,4]=>[4,1,1,1,1]
[7,1,8,2,4,5,6,3]=>[3,2,1,1,1]
[8,7,6,1,2,4,5,3]=>[5,1,1,1]
[8,3,7,6,2,1,4,5]=>[5,1,1,1]
[3,2,8,7,5,1,4,6]=>[4,2,1,1]
[8,3,6,5,2,1,4,7]=>[5,1,1,1]
[7,6,3,5,2,4,1,8]=>[5,1,1,1]
[7,4,6,2,5,3,1,8]=>[5,1,1,1]
[8,2,4,1,6,5,3,7]=>[4,2,1,1]
[4,2,8,1,7,5,3,6]=>[4,2,1,1]
[8,2,4,1,7,6,3,5]=>[4,2,1,1]
[8,7,1,5,6,2,4,3]=>[5,1,1,1]
[8,5,7,3,6,4,1,2]=>[5,1,1,1]
[6,8,3,7,5,4,1,2]=>[5,1,1,1]
[8,1,6,7,5,2,4,3]=>[5,1,1,1]
[8,1,2,6,4,3,7,5]=>[4,2,1,1]
[2,8,1,7,5,4,3,6]=>[5,1,1,1]
[2,5,1,8,6,4,3,7]=>[4,2,1,1]
[5,7,2,6,4,3,1,8]=>[5,1,1,1]
[6,2,7,5,4,3,1,8]=>[5,2,1]
[2,1,8,6,5,4,3,7]=>[5,2,1]
[1,2,7,5,4,3,8,6]=>[4,2,1,1]
[1,7,2,4,3,8,6,5]=>[3,3,1,1]
[1,7,2,8,3,6,5,4]=>[4,2,1,1]
[1,7,8,6,5,2,4,3]=>[5,1,1,1]
[7,3,8,6,5,4,1,2]=>[5,2,1]
[1,8,7,6,5,2,4,3]=>[6,1,1]
[8,1,7,3,2,6,5,4]=>[5,2,1]
[5,1,4,3,2,8,7,6]=>[4,3,1]
[8,6,5,3,2,1,7,4]=>[6,2]
[8,6,3,2,1,7,4,5]=>[5,2,1]
[8,6,5,4,1,7,2,3]=>[5,2,1]
[8,6,5,1,7,3,2,4]=>[5,2,1]
[8,6,1,7,4,3,2,5]=>[5,2,1]
[4,6,3,2,7,5,1,8]=>[4,2,1,1]
[1,4,3,7,2,5,8,6]=>[3,2,1,1,1]
[7,4,8,3,1,6,2,5]=>[4,2,1,1]
[7,1,5,8,3,2,6,4]=>[4,2,1,1]
[5,7,4,1,8,2,6,3]=>[3,3,1,1]
[5,7,4,3,1,8,6,2]=>[4,3,1]
[1,8,7,2,5,4,6,3]=>[5,1,1,1]
[1,8,5,3,7,2,6,4]=>[4,2,1,1]
[4,3,1,8,7,5,2,6]=>[4,3,1]
[1,4,8,6,3,5,2,7]=>[4,1,1,1,1]
[7,4,6,3,5,2,1,8]=>[5,1,1,1]
[1,3,5,6,8,4,2,7]=>[3,1,1,1,1,1]
[3,5,4,8,7,1,2,6]=>[3,2,1,1,1]
[3,1,4,6,8,7,2,5]=>[3,2,1,1,1]
[1,6,3,8,7,2,5,4]=>[4,2,1,1]
[1,6,2,4,8,7,5,3]=>[4,2,1,1]
[8,4,1,6,7,5,3,2]=>[5,2,1]
[7,1,6,4,8,5,2,3]=>[4,2,1,1]
[7,3,6,8,5,1,2,4]=>[4,1,1,1,1]
[1,3,7,2,6,8,4,5]=>[3,1,1,1,1,1]
[3,6,5,2,8,1,4,7]=>[4,1,1,1,1]
[3,6,5,7,2,4,1,8]=>[4,1,1,1,1]
[4,2,6,3,8,1,5,7]=>[3,2,1,1,1]
[4,2,6,7,3,5,1,8]=>[3,2,1,1,1]
[3,6,2,4,7,5,1,8]=>[3,2,1,1,1]
[3,6,2,4,1,8,5,7]=>[3,2,1,1,1]
[7,3,8,2,1,6,4,5]=>[4,2,1,1]
[7,3,5,2,1,8,6,4]=>[4,3,1]
[8,7,6,4,3,1,5,2]=>[6,2]
[8,7,6,4,1,5,2,3]=>[5,2,1]
[3,8,7,2,1,4,6,5]=>[4,2,1,1]
[3,8,2,7,1,5,4,6]=>[4,1,1,1,1]
[3,6,8,2,1,5,4,7]=>[3,2,1,1,1]
[2,4,8,1,6,5,3,7]=>[4,1,1,1,1]
[4,2,8,1,5,7,3,6]=>[3,2,1,1,1]
[8,5,7,6,1,4,2,3]=>[5,1,1,1]
[8,6,1,7,3,5,4,2]=>[5,2,1]
[8,6,1,7,5,4,2,3]=>[5,2,1]
[1,6,2,8,7,3,5,4]=>[4,2,1,1]
[1,8,2,4,6,7,3,5]=>[3,1,1,1,1,1]
[2,8,5,4,7,1,3,6]=>[4,1,1,1,1]
[2,1,5,8,6,4,3,7]=>[4,2,1,1]
[7,2,5,6,4,3,1,8]=>[5,1,1,1]
[1,2,5,7,8,4,3,6]=>[3,1,1,1,1,1]
[1,2,7,4,8,6,3,5]=>[3,2,1,1,1]
[1,2,7,8,3,6,5,4]=>[4,1,1,1,1]
[7,1,8,6,3,5,4,2]=>[5,2,1]
[1,8,7,6,3,5,2,4]=>[5,1,1,1]
[1,8,7,4,6,3,2,5]=>[5,1,1,1]
[7,1,6,4,2,3,5,8]=>[4,1,1,1,1]
[8,6,2,4,7,3,5,1]=>[5,1,1,1]
[8,6,2,4,5,7,3,1]=>[5,1,1,1]
[7,1,4,6,5,8,3,2]=>[5,1,1,1]
[7,1,2,3,8,5,4,6]=>[3,2,1,1,1]
[7,1,5,4,3,8,2,6]=>[5,1,1,1]
[7,1,5,4,6,2,8,3]=>[4,2,1,1]
[3,5,1,4,8,6,2,7]=>[3,2,1,1,1]
[3,6,2,4,7,8,1,5]=>[3,1,1,1,1,1]
[5,6,2,4,8,7,1,3]=>[3,2,1,1,1]
[6,5,8,7,2,3,1,4]=>[4,2,1,1]
[6,5,7,8,2,4,1,3]=>[4,1,1,1,1]
[3,4,7,2,5,8,1,6]=>[3,1,1,1,1,1]
[4,3,8,1,2,7,5,6]=>[3,2,1,1,1]
[2,8,3,1,5,6,4,7]=>[3,2,1,1,1]
[3,8,7,1,5,4,2,6]=>[5,1,1,1]
[3,4,1,5,7,6,2,8]=>[3,2,1,1,1]
[4,7,8,1,2,3,6,5]=>[3,1,1,1,1,1]
[2,8,6,1,5,3,7,4]=>[4,2,1,1]
[7,6,5,1,3,8,2,4]=>[5,1,1,1]
[6,7,5,2,1,3,8,4]=>[4,2,1,1]
[8,4,5,3,7,2,6,1]=>[5,1,1,1]
[4,7,5,2,8,1,6,3]=>[4,2,1,1]
[7,3,8,4,1,5,2,6]=>[3,2,2,1]
[7,2,3,4,1,6,5,8]=>[3,2,1,1,1]
[4,2,8,3,6,1,5,7]=>[3,2,1,1,1]
[6,8,5,7,2,1,3,4]=>[4,1,1,1,1]
[4,8,5,2,7,1,3,6]=>[4,1,1,1,1]
[6,3,5,2,1,7,4,8]=>[4,2,1,1]
[3,6,5,4,2,8,1,7]=>[5,1,1,1]
[1,6,4,7,2,5,3,8]=>[3,2,1,1,1]
[1,6,4,8,2,5,3,7]=>[3,2,1,1,1]
[1,6,5,8,2,4,3,7]=>[4,1,1,1,1]
[1,6,8,2,4,3,7,5]=>[3,2,1,1,1]
[1,6,2,4,3,7,8,5]=>[3,2,1,1,1]
[1,5,6,2,4,7,3,8]=>[3,1,1,1,1,1]
[1,5,6,2,4,7,8,3]=>[3,1,1,1,1,1]
[1,5,8,2,4,7,3,6]=>[3,1,1,1,1,1]
[1,5,7,2,4,8,3,6]=>[3,1,1,1,1,1]
[1,6,5,7,2,4,3,8]=>[4,1,1,1,1]
[1,6,7,2,4,3,8,5]=>[3,2,1,1,1]
[1,5,6,7,2,4,8,3]=>[3,1,1,1,1,1]
[1,5,8,2,4,6,7,3]=>[3,1,1,1,1,1]
[1,5,7,2,4,6,8,3]=>[3,1,1,1,1,1]
[1,5,7,8,3,2,4,6]=>[3,1,1,1,1,1]
[1,5,8,3,2,4,6,7]=>[3,1,1,1,1,1]
[1,5,6,2,4,8,3,7]=>[3,1,1,1,1,1]
[1,7,6,2,8,3,4,5]=>[3,2,1,1,1]
[1,7,3,4,2,8,6,5]=>[3,3,1,1]
[1,6,2,4,3,8,7,5]=>[3,3,1,1]
[1,5,6,2,4,8,7,3]=>[3,2,1,1,1]
[1,5,8,7,3,2,4,6]=>[4,1,1,1,1]
[1,4,2,3,5,8,7,6]=>[3,2,1,1,1]
[1,5,2,3,4,8,7,6]=>[3,2,1,1,1]
[1,6,5,2,3,8,7,4]=>[3,3,1,1]
[1,7,4,2,8,6,5,3]=>[4,3,1]
[1,7,6,5,2,8,4,3]=>[5,2,1]
[1,6,7,5,2,3,8,4]=>[3,2,1,1,1]
[1,7,5,2,8,4,3,6]=>[4,2,1,1]
[1,7,5,6,2,8,3,4]=>[3,2,1,1,1]
[1,5,7,6,2,4,8,3]=>[4,1,1,1,1]
[1,5,8,3,2,4,7,6]=>[3,2,1,1,1]
[1,6,5,2,3,7,4,8]=>[3,2,1,1,1]
[1,6,5,2,3,7,8,4]=>[3,2,1,1,1]
[1,6,8,4,2,3,7,5]=>[3,2,1,1,1]
[1,7,4,6,2,8,3,5]=>[3,2,1,1,1]
[1,7,3,5,2,8,4,6]=>[3,2,1,1,1]
[1,6,8,5,2,3,7,4]=>[3,2,1,1,1]
[1,6,4,2,3,7,8,5]=>[3,2,1,1,1]
[1,6,4,2,3,7,5,8]=>[3,2,1,1,1]
[1,5,8,6,2,4,7,3]=>[4,1,1,1,1]
[1,5,7,3,2,4,8,6]=>[3,2,1,1,1]
[1,7,3,4,2,8,5,6]=>[3,2,1,1,1]
[1,7,4,2,8,5,3,6]=>[3,3,1,1]
[1,6,7,4,2,3,8,5]=>[3,2,1,1,1]
[1,6,4,2,3,8,5,7]=>[3,2,1,1,1]
[1,7,6,4,2,8,5,3]=>[4,3,1]
[1,7,5,2,8,6,4,3]=>[4,3,1]
[1,6,4,2,3,8,7,5]=>[3,3,1,1]
[7,3,5,6,1,4,8,2]=>[4,1,1,1,1]
[3,7,5,6,1,4,8,2]=>[4,1,1,1,1]
[8,2,4,1,6,7,5,3]=>[4,2,1,1]
[8,6,1,4,2,7,5,3]=>[4,3,1]
[3,6,1,4,2,8,5,7]=>[3,2,1,1,1]
[1,6,7,4,3,5,8,2]=>[4,1,1,1,1]
[6,7,1,4,3,5,8,2]=>[4,1,1,1,1]
[7,6,1,4,3,5,8,2]=>[5,1,1,1]
[3,5,4,1,6,7,8,2]=>[3,2,1,1,1]
[4,7,1,6,3,5,8,2]=>[4,1,1,1,1]
[3,1,4,7,6,5,8,2]=>[4,2,1,1]
[6,1,7,4,3,5,8,2]=>[4,2,1,1]
[7,1,6,4,3,5,8,2]=>[5,1,1,1]
[1,7,6,4,3,5,8,2]=>[5,1,1,1]
[8,1,6,4,2,7,5,3]=>[4,3,1]
[8,4,1,3,7,2,5,6]=>[4,1,1,1,1]
[4,7,1,3,8,2,5,6]=>[3,1,1,1,1,1]
[7,4,1,3,8,2,5,6]=>[4,1,1,1,1]
[1,3,6,4,2,8,5,7]=>[3,2,1,1,1]
[4,7,3,1,2,8,5,6]=>[3,2,1,1,1]
[4,7,8,1,2,6,5,3]=>[4,1,1,1,1]
[6,8,1,4,2,7,5,3]=>[4,2,1,1]
[1,8,6,4,2,7,5,3]=>[4,3,1]
[4,8,1,3,7,2,5,6]=>[3,1,1,1,1,1]
[8,7,1,3,6,2,5,4]=>[5,1,1,1]
[6,8,5,7,3,2,1,4]=>[5,1,1,1]
[1,8,4,3,7,2,5,6]=>[4,1,1,1,1]
[2,8,3,4,7,6,1,5]=>[4,1,1,1,1]
[3,7,8,4,6,2,1,5]=>[4,1,1,1,1]
[3,7,4,6,8,2,1,5]=>[4,1,1,1,1]
[2,4,3,7,8,6,1,5]=>[3,2,1,1,1]
[1,4,7,3,8,2,5,6]=>[3,1,1,1,1,1]
[5,7,6,8,3,2,1,4]=>[5,1,1,1]
[2,5,3,4,8,6,1,7]=>[3,2,1,1,1]
[3,7,5,4,8,2,1,6]=>[5,1,1,1]
[7,1,3,4,2,8,5,6]=>[3,2,1,1,1]
[6,1,4,3,8,2,5,7]=>[4,1,1,1,1]
[4,1,7,3,8,2,5,6]=>[3,2,1,1,1]
[8,1,4,3,7,2,5,6]=>[4,1,1,1,1]
[8,2,3,4,7,6,1,5]=>[4,1,1,1,1]
[4,2,3,7,8,6,1,5]=>[3,2,1,1,1]
[5,2,3,4,8,6,1,7]=>[3,2,1,1,1]
[2,7,5,6,3,8,1,4]=>[4,1,1,1,1]
[5,7,2,6,3,8,1,4]=>[4,1,1,1,1]
[5,7,2,6,8,4,1,3]=>[4,1,1,1,1]
[7,2,5,6,8,4,1,3]=>[4,1,1,1,1]
[4,2,3,8,5,6,1,7]=>[3,2,1,1,1]
[5,2,3,8,7,6,1,4]=>[4,2,1,1]
[8,2,3,7,5,6,1,4]=>[4,1,1,1,1]
[6,1,8,3,7,2,5,4]=>[4,2,1,1]
[1,7,8,4,2,6,5,3]=>[4,2,1,1]
[4,7,1,8,2,5,6,3]=>[3,2,1,1,1]
[3,7,4,8,5,2,1,6]=>[4,2,1,1]
[2,4,3,8,5,6,1,7]=>[3,2,1,1,1]
[1,4,8,3,6,2,5,7]=>[3,1,1,1,1,1]
[7,5,8,6,3,2,1,4]=>[5,2,1]
[6,5,8,7,3,2,1,4]=>[5,2,1]
[8,5,7,6,3,2,1,4]=>[6,1,1]
[2,5,3,8,7,6,1,4]=>[4,2,1,1]
[3,7,5,8,6,2,1,4]=>[4,2,1,1]
[3,7,8,6,5,2,1,4]=>[5,1,1,1]
[1,8,7,3,6,2,5,4]=>[5,1,1,1]
[6,8,7,5,3,2,1,4]=>[6,1,1]
[5,7,6,8,3,4,1,2]=>[4,1,1,1,1]
[1,5,4,7,6,8,2,3]=>[3,2,1,1,1]
[1,7,4,6,5,8,2,3]=>[4,1,1,1,1]
[3,6,4,7,5,8,1,2]=>[3,2,1,1,1]
[1,6,2,7,5,8,3,4]=>[3,2,1,1,1]
[1,8,4,6,5,7,2,3]=>[4,1,1,1,1]
[7,8,1,5,2,4,3,6]=>[4,1,1,1,1]
[1,7,2,8,5,6,3,4]=>[3,2,1,1,1]
[5,7,6,8,1,4,2,3]=>[4,1,1,1,1]
[7,8,5,6,1,3,2,4]=>[4,1,1,1,1]
[5,8,6,7,1,3,2,4]=>[4,1,1,1,1]
[1,3,2,7,6,8,4,5]=>[3,2,1,1,1]
[1,7,6,8,2,4,3,5]=>[4,1,1,1,1]
[7,8,1,6,2,4,3,5]=>[4,1,1,1,1]
[7,8,1,4,2,6,3,5]=>[3,2,1,1,1]
[7,8,1,4,2,5,3,6]=>[3,2,1,1,1]
[7,8,2,1,4,3,6,5]=>[3,2,2,1]
[7,8,1,2,4,3,5,6]=>[3,1,1,1,1,1]
[4,3,6,5,8,7,1,2]=>[3,2,2,1]
[3,4,6,5,7,8,1,2]=>[3,1,1,1,1,1]
[1,6,2,3,8,7,4,5]=>[3,2,1,1,1]
[1,7,4,3,2,8,6,5]=>[4,3,1]
[1,4,7,6,2,5,8,3]=>[4,1,1,1,1]
[1,2,6,5,3,7,4,8]=>[3,2,1,1,1]
[1,2,6,5,3,7,8,4]=>[3,2,1,1,1]
[1,3,7,5,2,6,8,4]=>[3,2,1,1,1]
[1,3,7,4,2,6,8,5]=>[3,2,1,1,1]
[1,2,6,4,3,7,8,5]=>[3,2,1,1,1]
[1,2,6,4,3,7,5,8]=>[3,2,1,1,1]
[1,4,7,3,2,5,8,6]=>[3,2,1,1,1]
[1,4,3,2,5,8,6,7]=>[3,2,1,1,1]
[1,5,3,2,4,8,6,7]=>[3,2,1,1,1]
[1,7,5,3,2,8,6,4]=>[4,3,1]
[1,5,3,2,4,8,7,6]=>[3,3,1,1]
[7,6,5,4,3,1,8,2]=>[6,2]
[6,8,5,4,3,2,1,7]=>[6,1,1]
[7,1,5,4,3,8,6,2]=>[5,2,1]
[2,8,5,4,3,7,1,6]=>[5,1,1,1]
[7,6,1,4,3,8,5,2]=>[5,2,1]
[3,8,5,4,7,2,1,6]=>[5,1,1,1]
[7,6,5,1,3,8,4,2]=>[5,2,1]
[6,8,5,4,1,2,7,3]=>[4,2,1,1]
[6,8,2,4,3,7,1,5]=>[4,1,1,1,1]
[1,8,3,4,7,2,6,5]=>[4,1,1,1,1]
[7,5,8,4,3,2,1,6]=>[6,1,1]
[4,8,5,7,3,2,1,6]=>[5,1,1,1]
[5,1,7,6,8,4,3,2]=>[5,2,1]
[6,4,8,5,2,7,1,3]=>[4,2,1,1]
[5,1,8,6,7,4,3,2]=>[5,2,1]
[8,4,7,5,2,6,1,3]=>[5,1,1,1]
[5,4,6,8,2,1,7,3]=>[4,2,1,1]
[6,4,5,8,1,2,7,3]=>[3,2,1,1,1]
[7,4,6,5,2,1,8,3]=>[5,2,1]
[8,4,6,5,2,1,7,3]=>[5,2,1]
[4,8,7,5,6,1,3,2]=>[5,1,1,1]
[2,7,5,1,8,4,3,6]=>[4,2,1,1]
[5,1,8,7,4,2,3,6]=>[4,2,1,1]
[2,8,6,7,4,3,5,1]=>[5,1,1,1]
[3,6,5,2,4,1,8,7]=>[4,2,1,1]
[5,2,3,6,4,1,8,7]=>[3,2,2,1]
[6,1,4,5,3,2,8,7]=>[4,2,1,1]
[3,8,7,1,4,6,5,2]=>[5,1,1,1]
[5,7,1,2,4,3,8,6]=>[3,2,1,1,1]
[4,3,7,6,8,2,5,1]=>[4,2,1,1]
[5,3,6,8,1,7,2,4]=>[3,2,1,1,1]
[3,2,6,8,5,7,1,4]=>[3,2,1,1,1]
[6,3,7,2,4,8,5,1]=>[4,2,1,1]
[7,4,8,6,5,2,1,3]=>[5,2,1]
[7,1,8,2,5,4,3,6]=>[4,2,1,1]
[2,5,3,7,4,1,8,6]=>[3,2,2,1]
[3,6,4,7,5,1,8,2]=>[3,2,2,1]
[8,4,7,6,2,3,1,5]=>[5,1,1,1]
[8,4,7,1,2,5,6,3]=>[4,1,1,1,1]
[4,2,8,7,3,5,6,1]=>[4,2,1,1]
[8,1,7,4,2,5,6,3]=>[4,2,1,1]
[7,4,3,8,2,5,6,1]=>[5,1,1,1]
[6,4,1,5,8,2,7,3]=>[3,3,1,1]
[2,5,8,7,3,6,1,4]=>[4,1,1,1,1]
[2,1,5,8,7,4,6,3]=>[4,2,1,1]
[8,3,5,6,7,4,1,2]=>[4,1,1,1,1]
[7,4,3,2,8,5,6,1]=>[5,2,1]
[4,2,7,1,8,5,6,3]=>[3,3,1,1]
[4,1,7,2,8,5,6,3]=>[3,2,2,1]
[2,4,8,7,3,5,6,1]=>[4,1,1,1,1]
[4,7,8,3,1,5,6,2]=>[3,2,1,1,1]
[3,4,7,2,8,5,6,1]=>[3,2,1,1,1]
[3,7,1,4,8,5,6,2]=>[3,2,1,1,1]
[7,2,3,4,8,5,6,1]=>[3,2,1,1,1]
[6,1,8,5,2,7,4,3]=>[4,2,2]
[2,1,7,4,5,8,6,3]=>[3,2,2,1]
[2,1,8,3,6,7,5,4]=>[4,2,1,1]
[8,2,1,6,4,7,5,3]=>[4,2,2]
[7,8,2,6,4,1,5,3]=>[4,2,1,1]
[2,6,3,5,8,7,1,4]=>[3,2,1,1,1]
[7,6,2,1,5,8,4,3]=>[5,2,1]
[4,5,2,7,6,1,8,3]=>[3,2,2,1]
[5,1,6,8,4,7,2,3]=>[3,2,1,1,1]
[3,6,8,7,5,2,1,4]=>[5,1,1,1]
[7,4,8,6,5,2,3,1]=>[5,2,1]
[8,1,6,4,7,3,2,5]=>[5,1,1,1]
[7,6,4,1,2,3,8,5]=>[4,2,1,1]
[2,6,4,8,5,3,7,1]=>[4,2,1,1]
[7,3,5,8,4,2,1,6]=>[5,1,1,1]
[3,2,5,8,4,1,7,6]=>[3,2,2,1]
[8,4,7,1,5,2,3,6]=>[4,1,1,1,1]
[4,8,7,5,6,1,2,3]=>[4,1,1,1,1]
[6,1,4,8,7,3,5,2]=>[4,2,1,1]
[7,2,8,4,3,5,6,1]=>[4,2,1,1]
[4,7,8,1,3,5,6,2]=>[3,1,1,1,1,1]
[8,7,3,4,1,5,6,2]=>[4,2,1,1]
[4,8,2,7,3,5,6,1]=>[4,1,1,1,1]
[3,1,8,7,2,5,6,4]=>[4,2,1,1]
[3,8,1,7,2,5,6,4]=>[4,1,1,1,1]
[8,2,3,7,1,5,6,4]=>[4,1,1,1,1]
[6,4,8,7,1,3,2,5]=>[4,2,1,1]
[2,8,4,6,7,3,1,5]=>[4,1,1,1,1]
[4,3,8,2,7,6,1,5]=>[4,2,1,1]
[6,8,4,2,1,3,7,5]=>[4,2,1,1]
[7,8,2,4,3,5,6,1]=>[4,1,1,1,1]
[2,8,3,7,1,5,6,4]=>[4,1,1,1,1]
[8,1,2,7,3,5,6,4]=>[4,1,1,1,1]
[6,4,1,3,2,8,5,7]=>[4,2,1,1]
[5,3,8,6,2,1,4,7]=>[4,2,1,1]
[4,6,5,2,8,3,1,7]=>[4,2,1,1]
[4,3,7,5,1,8,2,6]=>[3,2,2,1]
[6,8,5,2,7,4,3,1]=>[5,2,1]
[7,2,5,4,3,8,1,6]=>[5,1,1,1]
[3,6,8,1,4,5,2,7]=>[3,1,1,1,1,1]
[6,8,1,2,4,5,3,7]=>[3,1,1,1,1,1]
[8,1,6,2,4,5,3,7]=>[4,1,1,1,1]
[3,8,6,1,2,5,4,7]=>[4,1,1,1,1]
[5,8,1,6,2,3,4,7]=>[3,1,1,1,1,1]
[4,1,6,5,8,2,3,7]=>[3,2,1,1,1]
[4,3,8,6,2,5,1,7]=>[4,2,1,1]
[8,3,6,1,4,5,2,7]=>[4,1,1,1,1]
[2,3,6,8,4,5,1,7]=>[3,1,1,1,1,1]
[2,7,5,4,3,8,1,6]=>[5,1,1,1]
[6,3,8,7,4,2,5,1]=>[5,2,1]
[5,8,4,3,7,6,1,2]=>[4,2,1,1]
[8,7,4,3,1,6,2,5]=>[5,2,1]
[1,7,4,3,8,6,2,5]=>[4,2,1,1]
[7,1,5,3,4,8,2,6]=>[4,1,1,1,1]
[2,8,6,1,7,4,5,3]=>[4,2,1,1]
[4,8,6,5,7,2,1,3]=>[5,1,1,1]
[4,7,6,8,2,1,5,3]=>[4,2,1,1]
[6,1,8,7,4,3,5,2]=>[5,2,1]
[8,5,4,3,1,6,7,2]=>[5,2,1]
[1,5,8,6,3,4,7,2]=>[4,1,1,1,1]
[2,5,8,6,3,4,7,1]=>[4,1,1,1,1]
[4,1,3,8,5,6,7,2]=>[3,2,1,1,1]
[6,5,8,4,3,1,7,2]=>[5,2,1]
[4,6,5,2,8,1,7,3]=>[4,2,1,1]
[7,2,8,1,3,6,4,5]=>[3,2,1,1,1]
[1,8,5,2,3,6,7,4]=>[3,2,1,1,1]
[1,8,3,2,5,6,7,4]=>[3,2,1,1,1]
[2,8,3,1,5,6,7,4]=>[3,2,1,1,1]
[4,8,3,2,5,6,7,1]=>[4,1,1,1,1]
[8,2,3,1,5,6,7,4]=>[3,2,1,1,1]
[2,1,8,3,5,6,7,4]=>[3,2,1,1,1]
[1,4,8,2,3,6,7,5]=>[3,1,1,1,1,1]
[3,1,2,7,8,6,4,5]=>[3,2,1,1,1]
[7,5,1,8,2,4,3,6]=>[4,2,1,1]
[3,5,8,1,2,4,7,6]=>[3,1,1,1,1,1]
[4,5,8,1,2,3,7,6]=>[3,1,1,1,1,1]
[4,2,7,1,8,6,3,5]=>[3,3,1,1]
[3,8,4,1,2,6,7,5]=>[3,2,1,1,1]
[5,4,8,2,3,6,7,1]=>[4,1,1,1,1]
[5,8,3,6,7,4,1,2]=>[4,1,1,1,1]
[2,3,1,6,8,4,7,5]=>[3,2,1,1,1]
[2,4,3,7,1,8,5,6]=>[3,2,1,1,1]
[1,4,7,3,2,8,5,6]=>[3,2,1,1,1]
[2,7,1,4,3,8,5,6]=>[3,2,1,1,1]
[2,4,1,8,6,3,7,5]=>[3,2,2,1]
[8,4,1,3,6,2,7,5]=>[4,2,1,1]
[6,8,5,1,7,2,3,4]=>[3,2,1,1,1]
[7,3,6,5,8,2,1,4]=>[5,1,1,1]
[7,6,3,5,8,2,1,4]=>[5,1,1,1]
[4,5,8,7,3,6,1,2]=>[4,1,1,1,1]
[3,5,2,8,6,1,7,4]=>[3,2,2,1]
[8,2,5,6,1,4,7,3]=>[4,1,1,1,1]
[8,6,5,4,1,2,7,3]=>[5,2,1]
[2,6,1,8,3,7,5,4]=>[4,2,1,1]
[4,7,1,6,2,8,5,3]=>[4,2,1,1]
[6,1,5,3,8,7,2,4]=>[4,2,1,1]
[2,8,6,3,7,1,5,4]=>[4,2,1,1]
[7,6,1,5,8,2,3,4]=>[4,1,1,1,1]
[3,6,8,5,1,2,7,4]=>[3,2,1,1,1]
[6,5,2,4,8,1,7,3]=>[4,2,1,1]
[5,1,4,8,2,6,7,3]=>[3,2,1,1,1]
[4,8,2,5,1,6,7,3]=>[3,2,1,1,1]
[3,4,8,5,2,6,7,1]=>[4,1,1,1,1]
[4,2,1,8,5,6,7,3]=>[3,3,1,1]
[1,5,4,8,2,6,7,3]=>[3,2,1,1,1]
[7,2,1,5,8,6,3,4]=>[3,3,1,1]
[2,8,4,5,1,6,7,3]=>[3,2,1,1,1]
[5,4,8,3,7,6,1,2]=>[4,2,1,1]
[3,1,5,8,6,2,7,4]=>[3,2,2,1]
[6,3,4,8,5,1,7,2]=>[3,2,2,1]
[5,3,4,8,1,6,7,2]=>[3,2,1,1,1]
[7,6,1,2,8,3,5,4]=>[4,2,1,1]
[7,5,8,4,1,2,6,3]=>[4,2,1,1]
[7,5,8,4,6,1,3,2]=>[5,1,1,1]
[6,5,4,8,7,1,3,2]=>[5,2,1]
[6,5,4,8,1,2,7,3]=>[4,2,1,1]
[7,5,1,6,2,3,8,4]=>[3,2,2,1]
[7,5,1,6,8,2,4,3]=>[4,2,1,1]
[6,5,4,1,8,2,7,3]=>[4,3,1]
[6,5,4,7,1,2,8,3]=>[4,2,1,1]
[6,5,4,7,8,1,3,2]=>[5,1,1,1]
[6,5,3,7,1,4,2,8]=>[4,2,1,1]
[6,5,3,1,8,4,2,7]=>[4,3,1]
[7,5,1,4,8,3,2,6]=>[5,1,1,1]
[8,1,6,4,7,3,5,2]=>[5,1,1,1]
[7,5,1,4,8,3,6,2]=>[5,1,1,1]
[6,5,3,7,1,4,8,2]=>[4,2,1,1]
[6,4,3,1,5,8,7,2]=>[4,3,1]
[7,4,1,5,3,8,6,2]=>[4,2,2]
[8,1,5,4,3,7,6,2]=>[5,2,1]
[8,1,5,4,3,7,2,6]=>[5,1,1,1]
[7,4,1,5,3,8,2,6]=>[4,2,1,1]
[7,4,1,5,3,2,6,8]=>[4,2,1,1]
[8,1,5,4,3,2,6,7]=>[5,1,1,1]
[8,1,6,4,2,5,3,7]=>[4,2,1,1]
[6,5,3,1,2,7,4,8]=>[4,2,1,1]
[6,5,3,8,1,4,2,7]=>[4,2,1,1]
[7,6,8,1,4,3,2,5]=>[5,1,1,1]
[8,1,7,2,5,4,3,6]=>[5,1,1,1]
[8,1,7,2,5,4,6,3]=>[5,1,1,1]
[7,6,1,2,5,4,8,3]=>[5,1,1,1]
[6,5,3,8,1,4,7,2]=>[4,2,1,1]
[6,5,3,1,2,7,8,4]=>[4,2,1,1]
[7,5,1,4,2,6,8,3]=>[4,2,1,1]
[8,1,6,4,2,5,7,3]=>[4,2,1,1]
[7,4,1,5,3,2,8,6]=>[4,2,2]
[6,4,3,1,5,2,8,7]=>[4,2,2]
[6,4,3,1,5,7,2,8]=>[4,2,1,1]
[7,4,1,5,3,6,2,8]=>[4,2,1,1]
[8,1,5,4,3,6,2,7]=>[5,1,1,1]
[8,1,5,4,3,6,7,2]=>[5,1,1,1]
[7,4,1,5,3,6,8,2]=>[4,2,1,1]
[6,4,3,1,5,7,8,2]=>[4,2,1,1]
[6,7,3,8,4,5,1,2]=>[3,2,1,1,1]
[6,7,4,5,1,8,2,3]=>[3,2,1,1,1]
[4,7,5,6,1,8,2,3]=>[3,2,1,1,1]
[4,7,5,6,3,8,1,2]=>[4,1,1,1,1]
[4,5,3,8,6,7,1,2]=>[3,2,1,1,1]
[4,8,3,6,5,7,1,2]=>[4,1,1,1,1]
[5,6,4,7,1,8,2,3]=>[3,2,1,1,1]
[5,6,1,8,2,7,3,4]=>[3,2,1,1,1]
[5,6,1,8,4,7,2,3]=>[3,2,1,1,1]
[4,5,1,8,6,7,2,3]=>[3,2,1,1,1]
[7,8,4,5,1,6,2,3]=>[3,2,1,1,1]
[3,6,4,5,2,7,1,8]=>[4,1,1,1,1]
[3,6,4,5,1,8,2,7]=>[3,2,1,1,1]
[2,6,4,8,1,5,3,7]=>[3,2,1,1,1]
[2,8,3,6,1,5,4,7]=>[4,1,1,1,1]
[7,8,1,5,3,6,2,4]=>[4,1,1,1,1]
[1,8,3,6,2,7,4,5]=>[3,2,1,1,1]
[2,6,4,7,3,5,1,8]=>[4,1,1,1,1]
[2,7,3,6,4,5,1,8]=>[4,1,1,1,1]
[1,7,3,6,4,8,2,5]=>[4,1,1,1,1]
[6,7,1,5,3,8,2,4]=>[4,1,1,1,1]
[6,7,5,8,1,4,2,3]=>[4,1,1,1,1]
[5,8,6,7,2,3,1,4]=>[4,1,1,1,1]
[6,7,2,3,1,8,4,5]=>[3,2,1,1,1]
[6,7,2,8,1,4,3,5]=>[3,2,1,1,1]
[3,4,2,7,5,6,1,8]=>[3,2,1,1,1]
[2,3,1,8,4,7,5,6]=>[3,2,1,1,1]
[7,8,2,3,1,6,4,5]=>[3,2,1,1,1]
[7,8,2,6,1,4,3,5]=>[4,1,1,1,1]
[2,8,6,7,1,4,3,5]=>[4,1,1,1,1]
[2,8,1,4,3,7,5,6]=>[3,2,1,1,1]
[3,7,2,5,4,6,1,8]=>[4,1,1,1,1]
[4,5,2,7,3,6,1,8]=>[3,2,1,1,1]
[4,5,1,8,2,7,3,6]=>[3,2,1,1,1]
[3,4,1,8,6,7,2,5]=>[3,2,1,1,1]
[3,4,2,5,1,8,6,7]=>[3,2,1,1,1]
[3,4,2,8,1,6,5,7]=>[3,2,1,1,1]
[4,5,2,8,1,6,3,7]=>[3,2,1,1,1]
[4,5,3,6,1,8,2,7]=>[3,2,1,1,1]
[8,6,3,7,5,1,2,4]=>[4,2,1,1]
[7,6,2,8,3,5,1,4]=>[4,2,1,1]
[7,6,2,3,8,5,1,4]=>[4,2,1,1]
[8,7,1,5,2,6,3,4]=>[4,2,1,1]
[8,7,1,5,2,3,6,4]=>[4,2,1,1]
[8,5,2,3,1,7,6,4]=>[4,3,1]
[8,6,2,3,7,1,5,4]=>[4,2,1,1]
[8,6,2,7,3,1,5,4]=>[4,2,2]
[8,7,2,5,1,6,3,4]=>[4,2,1,1]
[8,4,2,1,7,6,3,5]=>[4,3,1]
[8,5,7,2,1,4,3,6]=>[4,2,1,1]
[5,8,7,3,1,4,2,6]=>[4,2,1,1]
[5,8,7,3,1,4,6,2]=>[4,2,1,1]
[8,5,7,2,1,4,6,3]=>[4,2,1,1]
[8,4,2,1,3,7,6,5]=>[4,3,1]
[8,4,3,1,7,2,6,5]=>[4,3,1]
[8,6,1,3,7,2,5,4]=>[4,2,1,1]
[8,5,1,3,2,7,6,4]=>[4,3,1]
[6,1,5,8,4,2,7,3]=>[4,2,1,1]
[5,2,8,6,4,1,3,7]=>[4,2,1,1]
[8,4,7,5,1,6,2,3]=>[4,2,1,1]
[8,4,7,5,1,2,3,6]=>[4,1,1,1,1]
[8,7,3,5,1,2,6,4]=>[4,2,1,1]
[8,3,2,6,5,1,4,7]=>[4,2,1,1]
[4,8,6,3,5,1,2,7]=>[4,1,1,1,1]
[4,8,7,3,1,5,2,6]=>[4,2,1,1]
[8,4,7,2,1,5,3,6]=>[4,2,1,1]
[8,7,3,1,4,2,6,5]=>[4,2,2]
[8,7,3,1,2,6,4,5]=>[4,2,1,1]
[8,7,3,1,2,4,6,5]=>[4,2,1,1]
[8,3,2,1,4,7,6,5]=>[4,3,1]
[8,3,2,1,7,4,6,5]=>[4,3,1]
[8,4,7,2,1,5,6,3]=>[4,2,1,1]
[8,7,2,1,6,3,4,5]=>[4,2,1,1]
[3,6,5,4,1,2,8,7]=>[4,2,1,1]
[3,8,5,6,7,4,1,2]=>[4,1,1,1,1]
[4,7,5,8,6,2,1,3]=>[4,2,1,1]
[2,5,7,8,6,3,4,1]=>[4,1,1,1,1]
[4,8,5,7,6,3,1,2]=>[5,1,1,1]
[4,6,3,2,1,5,8,7]=>[4,2,1,1]
[6,2,1,5,3,4,8,7]=>[3,2,2,1]
[5,8,1,3,7,6,4,2]=>[5,1,1,1]
[4,7,2,3,6,1,8,5]=>[3,2,1,1,1]
[3,7,4,2,8,1,5,6]=>[4,1,1,1,1]
[4,2,6,8,5,7,3,1]=>[4,2,1,1]
[6,4,2,7,3,8,5,1]=>[4,2,2]
[8,1,6,7,5,3,4,2]=>[5,1,1,1]
[2,1,5,8,7,6,3,4]=>[4,2,1,1]
[2,1,4,7,6,3,8,5]=>[3,2,2,1]
[6,4,7,8,5,3,2,1]=>[5,2,1]
[4,1,3,7,6,2,8,5]=>[3,2,2,1]
[8,5,1,6,3,2,7,4]=>[4,2,2]
[6,3,7,1,5,2,8,4]=>[3,2,2,1]
[3,2,6,8,4,7,5,1]=>[4,2,1,1]
[8,4,6,1,3,2,5,7]=>[4,1,1,1,1]
[4,2,8,6,7,3,1,5]=>[4,2,1,1]
[7,4,3,8,2,1,5,6]=>[5,1,1,1]
[4,7,5,8,1,6,3,2]=>[4,2,1,1]
[6,4,3,2,7,8,1,5]=>[5,1,1,1]
[4,2,5,1,6,7,8,3]=>[3,2,1,1,1]
[2,4,8,5,7,1,3,6]=>[3,1,1,1,1,1]
[3,7,1,4,6,8,5,2]=>[4,1,1,1,1]
[7,8,2,5,6,1,4,3]=>[4,1,1,1,1]
[2,4,3,8,7,5,6,1]=>[4,2,1,1]
[2,6,7,3,5,1,8,4]=>[3,2,1,1,1]
[7,6,8,4,2,5,3,1]=>[5,2,1]
[8,5,7,1,6,3,2,4]=>[5,1,1,1]
[6,5,7,2,8,4,3,1]=>[5,2,1]
[3,4,8,6,5,2,1,7]=>[5,1,1,1]
[2,7,6,1,4,5,8,3]=>[4,1,1,1,1]
[6,5,8,2,1,7,3,4]=>[4,2,1,1]
[7,4,3,5,1,6,8,2]=>[4,2,1,1]
[4,1,6,3,5,8,7,2]=>[3,2,2,1]
[6,2,5,8,4,3,7,1]=>[5,1,1,1]
[8,6,7,1,5,4,3,2]=>[6,1,1]
[2,1,6,5,8,4,7,3]=>[4,2,1,1]
[2,1,6,8,5,4,3,7]=>[4,2,1,1]
[4,1,8,5,6,2,3,7]=>[3,2,1,1,1]
[2,6,4,8,7,3,5,1]=>[4,2,1,1]
[6,2,8,4,3,5,1,7]=>[4,2,1,1]
[4,8,2,7,6,1,3,5]=>[4,1,1,1,1]
[3,1,8,2,7,5,4,6]=>[4,2,1,1]
[3,8,1,2,6,7,4,5]=>[3,1,1,1,1,1]
[5,8,4,3,2,7,1,6]=>[5,1,1,1]
[7,4,8,6,3,2,5,1]=>[5,2,1]
[5,8,4,7,2,1,3,6]=>[4,1,1,1,1]
[2,1,8,4,3,7,5,6]=>[3,2,2,1]
[6,3,8,2,4,5,7,1]=>[4,1,1,1,1]
[5,8,4,2,3,6,1,7]=>[4,1,1,1,1]
[5,8,2,4,3,1,6,7]=>[4,1,1,1,1]
[2,8,3,1,6,4,5,7]=>[3,2,1,1,1]
[8,2,1,3,4,7,5,6]=>[3,2,1,1,1]
[1,4,8,2,6,3,5,7]=>[3,1,1,1,1,1]
[1,2,7,3,5,4,8,6]=>[3,2,1,1,1]
[1,2,3,8,4,5,7,6]=>[3,1,1,1,1,1]
[1,2,8,3,4,5,7,6]=>[3,1,1,1,1,1]
[1,3,8,2,6,4,5,7]=>[3,1,1,1,1,1]
[1,5,7,2,3,6,4,8]=>[3,1,1,1,1,1]
[1,7,2,3,5,4,8,6]=>[3,2,1,1,1]
[1,3,8,2,4,5,7,6]=>[3,1,1,1,1,1]
[1,2,3,8,4,6,7,5]=>[3,1,1,1,1,1]
[1,8,2,3,5,4,6,7]=>[3,1,1,1,1,1]
[1,7,8,2,3,6,4,5]=>[3,1,1,1,1,1]
[1,6,7,8,2,3,5,4]=>[3,1,1,1,1,1]
[1,7,8,2,5,3,6,4]=>[3,2,1,1,1]
[1,7,8,2,4,5,3,6]=>[3,1,1,1,1,1]
[1,2,8,3,6,4,5,7]=>[3,1,1,1,1,1]
[1,8,2,3,6,4,5,7]=>[3,1,1,1,1,1]
[1,2,8,3,5,4,6,7]=>[3,1,1,1,1,1]
[1,2,7,8,3,6,4,5]=>[3,1,1,1,1,1]
[1,5,2,7,8,3,6,4]=>[3,2,1,1,1]
[1,3,2,8,4,6,7,5]=>[3,2,1,1,1]
[1,8,2,3,4,6,7,5]=>[3,1,1,1,1,1]
[1,7,8,2,4,3,6,5]=>[3,2,1,1,1]
[7,6,3,1,5,2,4,8]=>[4,2,1,1]
[6,7,3,1,5,2,8,4]=>[3,2,2,1]
[6,8,3,1,5,2,7,4]=>[3,2,2,1]
[6,8,4,5,1,2,7,3]=>[3,2,1,1,1]
[6,7,4,5,1,2,8,3]=>[3,2,1,1,1]
[7,2,1,6,5,3,4,8]=>[4,2,1,1]
[7,3,6,1,5,2,4,8]=>[4,1,1,1,1]
[7,4,6,5,1,2,3,8]=>[4,1,1,1,1]
[6,7,5,4,1,2,8,3]=>[4,2,1,1]
[5,8,6,4,1,7,2,3]=>[4,2,1,1]
[5,7,6,4,1,8,2,3]=>[4,2,1,1]
[5,6,7,4,1,8,2,3]=>[3,2,1,1,1]
[6,5,7,4,1,2,8,3]=>[4,2,1,1]
[6,4,7,5,1,2,8,3]=>[3,2,2,1]
[6,2,1,7,5,3,8,4]=>[3,3,2]
[6,3,8,1,5,2,7,4]=>[3,2,2,1]
[6,4,8,5,1,2,7,3]=>[3,2,2,1]
[6,5,8,4,1,2,7,3]=>[4,2,1,1]
[5,6,8,4,1,7,2,3]=>[3,2,1,1,1]
[4,6,8,5,7,1,2,3]=>[3,1,1,1,1,1]
[4,5,8,6,7,1,2,3]=>[3,1,1,1,1,1]
[5,4,8,6,1,7,2,3]=>[3,2,2,1]
[5,3,8,1,6,7,2,4]=>[3,2,1,1,1]
[5,2,1,8,6,7,3,4]=>[3,3,1,1]
[5,2,1,7,6,8,3,4]=>[3,3,1,1]
[5,4,7,6,1,8,2,3]=>[3,2,2,1]
[4,5,7,6,8,1,2,3]=>[3,1,1,1,1,1]
[4,6,7,5,8,1,2,3]=>[3,1,1,1,1,1]
[4,8,6,5,7,1,2,3]=>[4,1,1,1,1]
[4,8,5,6,7,1,2,3]=>[3,1,1,1,1,1]
[4,7,5,6,8,1,2,3]=>[3,1,1,1,1,1]
[4,6,5,7,8,1,2,3]=>[3,1,1,1,1,1]
[5,7,4,6,1,8,2,3]=>[3,2,1,1,1]
[5,8,4,6,1,7,2,3]=>[3,2,1,1,1]
[5,8,3,1,6,7,2,4]=>[3,2,1,1,1]
[5,7,3,1,6,8,2,4]=>[3,2,1,1,1]
[5,6,3,1,7,8,2,4]=>[3,2,1,1,1]
[6,2,1,4,3,8,7,5]=>[3,3,2]
[5,8,3,1,7,6,2,4]=>[4,2,1,1]
[5,7,4,8,1,6,2,3]=>[3,2,1,1,1]
[5,2,1,6,8,7,3,4]=>[3,3,1,1]
[5,4,6,8,1,7,2,3]=>[3,2,1,1,1]
[4,5,6,8,7,1,2,3]=>[3,1,1,1,1,1]
[4,7,5,8,6,1,2,3]=>[3,2,1,1,1]
[4,8,5,7,6,1,2,3]=>[4,1,1,1,1]
[4,8,6,7,5,1,2,3]=>[4,1,1,1,1]
[4,7,6,8,5,1,2,3]=>[4,1,1,1,1]
[4,6,7,8,5,1,2,3]=>[3,1,1,1,1,1]
[4,5,7,8,6,1,2,3]=>[3,1,1,1,1,1]
[5,4,7,8,1,6,2,3]=>[3,2,1,1,1]
[5,3,7,1,8,6,2,4]=>[3,3,1,1]
[5,2,1,7,8,6,3,4]=>[3,3,1,1]
[5,3,8,1,7,6,2,4]=>[4,2,1,1]
[5,4,8,7,1,6,2,3]=>[4,2,1,1]
[4,6,8,7,5,1,2,3]=>[4,1,1,1,1]
[4,7,8,6,5,1,2,3]=>[4,1,1,1,1]
[4,8,7,6,5,1,2,3]=>[5,1,1,1]
[2,5,4,7,3,6,1,8]=>[4,1,1,1,1]
[2,4,6,3,7,5,1,8]=>[3,2,1,1,1]
[4,2,7,3,6,5,1,8]=>[4,2,1,1]
[4,2,6,3,1,5,8,7]=>[3,2,2,1]
[2,5,3,1,6,4,8,7]=>[3,2,2,1]
[2,5,3,7,6,4,1,8]=>[4,2,1,1]
[2,6,5,3,7,4,1,8]=>[4,2,1,1]
[4,2,7,6,3,5,1,8]=>[4,2,1,1]
[2,7,5,3,6,4,1,8]=>[4,2,1,1]
[2,6,3,7,5,4,1,8]=>[4,2,1,1]
[1,7,5,2,3,8,4,6]=>[3,2,1,1,1]
[2,1,3,7,5,4,8,6]=>[3,2,2,1]
[2,3,1,8,6,5,4,7]=>[4,2,1,1]
[2,5,3,1,8,6,4,7]=>[3,3,1,1]
[4,2,8,3,1,6,5,7]=>[3,2,2,1]
[8,3,2,6,4,1,5,7]=>[4,2,1,1]
[3,6,8,2,1,4,5,7]=>[3,1,1,1,1,1]
[1,5,2,8,3,4,7,6]=>[3,2,1,1,1]
[1,2,6,3,8,7,4,5]=>[3,2,1,1,1]
[1,2,8,3,6,4,7,5]=>[3,2,1,1,1]
[1,2,7,6,3,4,8,5]=>[3,2,1,1,1]
[2,1,3,8,7,5,4,6]=>[4,2,1,1]
[1,2,3,8,6,4,7,5]=>[3,2,1,1,1]
[1,2,3,7,4,8,6,5]=>[3,2,1,1,1]
[1,2,7,6,3,8,4,5]=>[3,2,1,1,1]
[1,2,3,6,4,8,7,5]=>[3,2,1,1,1]
[1,2,3,7,6,4,8,5]=>[3,2,1,1,1]
[2,6,3,1,8,5,4,7]=>[3,3,1,1]
[2,1,3,8,5,4,7,6]=>[3,2,2,1]
[7,1,8,4,2,3,5,6]=>[3,2,1,1,1]
[2,1,8,4,3,5,7,6]=>[3,2,2,1]
[4,2,6,3,1,8,5,7]=>[3,2,2,1]
[5,4,2,8,3,1,6,7]=>[4,2,1,1]
[3,5,8,2,4,1,6,7]=>[3,1,1,1,1,1]
[2,5,4,8,3,1,6,7]=>[4,1,1,1,1]
[4,2,1,8,3,5,7,6]=>[3,3,1,1]
[1,8,7,4,2,3,5,6]=>[4,1,1,1,1]
[1,5,2,8,7,3,4,6]=>[3,2,1,1,1]
[1,2,7,3,6,4,8,5]=>[3,2,1,1,1]
[1,2,8,6,3,7,4,5]=>[3,2,1,1,1]
[1,2,7,3,8,6,4,5]=>[3,2,1,1,1]
[1,2,3,8,4,7,6,5]=>[4,1,1,1,1]
[1,2,7,3,4,8,6,5]=>[3,2,1,1,1]
[1,2,6,3,8,4,7,5]=>[3,2,1,1,1]
[1,5,2,3,8,7,4,6]=>[3,2,1,1,1]
[4,2,1,8,3,7,5,6]=>[3,3,1,1]
[8,3,2,1,7,4,5,6]=>[4,2,1,1]
[1,8,4,2,7,3,5,6]=>[3,2,1,1,1]
[1,2,8,6,3,4,7,5]=>[3,2,1,1,1]
[1,2,7,3,8,4,6,5]=>[3,2,1,1,1]
[1,2,3,8,7,4,6,5]=>[4,1,1,1,1]
[1,2,3,8,7,6,4,5]=>[4,1,1,1,1]
[2,5,3,8,1,6,4,7]=>[3,2,1,1,1]
[2,6,4,7,1,5,3,8]=>[3,2,1,1,1]
[2,6,5,7,1,4,3,8]=>[4,1,1,1,1]
[3,8,5,7,1,2,6,4]=>[4,1,1,1,1]
[3,8,5,7,2,6,4,1]=>[5,1,1,1]
[3,4,8,6,2,5,7,1]=>[4,1,1,1,1]
[3,4,8,6,1,2,5,7]=>[3,1,1,1,1,1]
[2,5,7,1,4,8,6,3]=>[3,2,1,1,1]
[2,4,8,1,5,7,6,3]=>[4,1,1,1,1]
[2,4,3,8,1,6,5,7]=>[3,2,1,1,1]
[2,8,1,7,5,6,4,3]=>[5,1,1,1]
[2,3,8,1,6,5,7,4]=>[4,1,1,1,1]
[2,4,8,1,3,5,7,6]=>[3,1,1,1,1,1]
[3,5,7,6,1,2,4,8]=>[3,1,1,1,1,1]
[3,5,7,6,2,4,8,1]=>[4,1,1,1,1]
[4,8,6,7,2,3,5,1]=>[4,1,1,1,1]
[4,8,6,7,1,2,3,5]=>[3,1,1,1,1,1]
[4,8,6,7,1,3,5,2]=>[4,1,1,1,1]
[3,4,8,6,1,5,7,2]=>[4,1,1,1,1]
[3,8,5,7,1,6,4,2]=>[5,1,1,1]
[3,2,8,5,6,1,7,4]=>[3,2,2,1]
[3,8,5,7,2,1,6,4]=>[4,2,1,1]
[3,4,8,6,2,1,5,7]=>[4,1,1,1,1]
[3,5,7,6,2,1,4,8]=>[4,1,1,1,1]
[4,8,6,7,2,1,3,5]=>[4,1,1,1,1]
[4,8,6,7,3,5,2,1]=>[5,1,1,1]
[5,8,6,7,3,4,2,1]=>[5,1,1,1]
[5,8,6,7,2,1,3,4]=>[4,1,1,1,1]
[5,8,6,7,2,1,4,3]=>[4,2,1,1]
[4,8,6,7,2,1,5,3]=>[4,2,1,1]
[4,3,1,7,5,2,8,6]=>[3,3,2]
[4,3,2,8,5,1,7,6]=>[4,2,2]
[4,3,8,5,1,6,7,2]=>[3,2,2,1]
[4,8,6,7,1,5,3,2]=>[5,1,1,1]
[5,8,6,7,1,4,3,2]=>[5,1,1,1]
[5,8,6,7,2,3,4,1]=>[4,1,1,1,1]
[5,8,6,7,2,4,3,1]=>[5,1,1,1]
[5,8,6,7,1,2,4,3]=>[4,1,1,1,1]
[4,2,3,8,5,1,6,7]=>[3,2,1,1,1]
[4,2,8,5,1,7,6,3]=>[4,2,2]
[3,4,2,8,5,6,1,7]=>[3,2,1,1,1]
[3,2,4,8,6,1,5,7]=>[3,2,1,1,1]
[3,2,5,7,6,1,4,8]=>[3,2,1,1,1]
[4,8,6,7,1,3,2,5]=>[4,1,1,1,1]
[4,8,6,7,1,2,5,3]=>[4,1,1,1,1]
[4,8,6,7,2,5,3,1]=>[5,1,1,1]
[4,3,8,5,2,6,7,1]=>[4,2,1,1]
[4,3,8,5,1,2,6,7]=>[3,2,1,1,1]
[4,2,6,7,5,1,3,8]=>[3,2,1,1,1]
[3,8,5,7,1,4,2,6]=>[4,1,1,1,1]
[3,8,4,7,1,5,2,6]=>[4,1,1,1,1]
[3,5,2,8,4,6,1,7]=>[3,2,1,1,1]
[3,5,1,7,4,6,2,8]=>[3,2,1,1,1]
[3,8,4,7,2,5,1,6]=>[4,1,1,1,1]
[4,1,3,8,5,2,6,7]=>[3,2,1,1,1]
[4,1,2,6,7,5,3,8]=>[3,2,1,1,1]
[4,2,6,7,5,3,8,1]=>[4,2,1,1]
[4,8,6,7,3,2,5,1]=>[5,1,1,1]
[4,8,6,7,3,1,2,5]=>[4,1,1,1,1]
[3,1,5,7,6,2,4,8]=>[3,2,1,1,1]
[3,4,1,7,5,6,2,8]=>[3,2,1,1,1]
[4,1,7,5,2,8,6,3]=>[3,3,2]
[4,1,6,7,5,2,3,8]=>[3,2,1,1,1]
[4,8,6,7,2,3,1,5]=>[4,1,1,1,1]
[5,8,6,7,3,2,4,1]=>[5,1,1,1]
[5,8,6,7,4,2,3,1]=>[5,1,1,1]
[5,8,6,7,4,1,2,3]=>[4,1,1,1,1]
[5,8,6,7,4,1,3,2]=>[5,1,1,1]
[5,8,6,7,3,1,4,2]=>[4,2,1,1]
[4,8,6,7,3,1,5,2]=>[4,2,1,1]
[4,1,6,7,5,3,8,2]=>[4,2,1,1]
[4,1,7,5,3,2,8,6]=>[4,2,2]
[4,2,8,5,3,1,7,6]=>[4,2,2]
[4,2,1,6,7,5,3,8]=>[3,3,1,1]
[4,8,6,7,3,2,1,5]=>[5,1,1,1]
[5,8,6,7,4,2,1,3]=>[5,1,1,1]
[5,8,6,7,4,3,1,2]=>[5,1,1,1]
[3,8,7,6,1,4,2,5]=>[5,1,1,1]
[5,1,8,3,6,7,2,4]=>[3,2,1,1,1]
[1,4,7,8,5,6,2,3]=>[3,1,1,1,1,1]
[3,6,1,4,7,8,5,2]=>[3,2,1,1,1]
[1,6,8,4,7,5,2,3]=>[4,1,1,1,1]
[6,8,1,3,5,7,2,4]=>[3,1,1,1,1,1]
[3,8,1,6,5,4,2,7]=>[5,1,1,1]
[6,1,7,3,8,4,2,5]=>[3,2,2,1]
[3,1,7,6,5,8,4,2]=>[5,2,1]
[8,4,2,6,7,5,3,1]=>[5,2,1]
[7,4,1,6,8,2,5,3]=>[4,2,1,1]
[6,1,3,2,7,8,4,5]=>[3,2,1,1,1]
[1,8,6,2,5,3,4,7]=>[4,1,1,1,1]
[4,7,2,6,8,1,5,3]=>[4,1,1,1,1]
[8,7,3,6,4,5,2,1]=>[6,1,1]
[5,7,8,6,2,1,4,3]=>[4,2,1,1]
[2,7,4,1,6,8,3,5]=>[3,2,1,1,1]
[1,8,6,4,5,2,3,7]=>[4,1,1,1,1]
[2,5,4,3,6,8,1,7]=>[4,1,1,1,1]
[6,4,1,2,7,5,8,3]=>[3,3,1,1]
[8,3,7,4,5,2,6,1]=>[5,1,1,1]
[4,3,7,8,5,1,6,2]=>[3,2,2,1]
[5,4,8,2,7,6,1,3]=>[4,2,1,1]
[5,8,2,6,3,4,1,7]=>[4,1,1,1,1]
[4,1,7,5,8,6,2,3]=>[3,2,2,1]
[5,1,7,8,4,3,6,2]=>[4,2,1,1]
[1,4,3,5,7,8,2,6]=>[3,1,1,1,1,1]
[6,5,8,7,1,3,4,2]=>[4,2,1,1]
[3,6,7,2,4,8,1,5]=>[3,1,1,1,1,1]
[1,5,2,7,4,3,8,6]=>[3,2,2,1]
[2,8,5,6,4,3,1,7]=>[5,1,1,1]
[1,8,6,5,4,3,2,7]=>[6,1,1]
[6,1,5,2,8,4,7,3]=>[4,2,1,1]
[4,6,1,8,5,7,2,3]=>[3,2,1,1,1]
[4,7,1,2,8,5,6,3]=>[3,2,1,1,1]
[1,4,7,2,8,5,6,3]=>[3,2,1,1,1]
[1,7,3,5,8,6,2,4]=>[3,2,1,1,1]
[7,3,5,8,6,1,2,4]=>[3,2,1,1,1]
[3,6,8,1,5,7,2,4]=>[3,1,1,1,1,1]
[3,4,6,5,8,1,7,2]=>[3,2,1,1,1]
[6,8,1,5,7,2,3,4]=>[3,1,1,1,1,1]
[7,1,2,5,8,6,3,4]=>[3,2,1,1,1]
[1,7,2,5,8,6,3,4]=>[3,2,1,1,1]
[1,7,6,8,2,3,5,4]=>[4,1,1,1,1]
[7,6,8,1,2,3,5,4]=>[4,1,1,1,1]
[2,7,1,5,8,6,3,4]=>[3,2,1,1,1]
[2,4,7,1,8,5,6,3]=>[3,2,1,1,1]
[4,7,5,8,3,1,6,2]=>[4,2,1,1]
[4,7,2,1,8,5,6,3]=>[3,3,1,1]
[7,6,8,2,1,3,5,4]=>[4,2,1,1]
[1,2,7,6,8,3,5,4]=>[4,1,1,1,1]
[3,7,6,8,2,1,5,4]=>[4,2,1,1]
[7,4,2,1,6,8,5,3]=>[4,3,1]
[6,7,4,1,8,5,3,2]=>[4,3,1]
[6,7,4,3,1,8,5,2]=>[4,3,1]
[2,7,4,1,6,8,5,3]=>[4,2,1,1]
[2,3,7,6,8,1,5,4]=>[4,1,1,1,1]
[7,4,2,6,8,5,1,3]=>[4,2,1,1]
[7,3,2,5,8,6,1,4]=>[4,2,1,1]
[3,1,7,6,8,2,5,4]=>[4,2,1,1]
[3,7,6,8,1,2,5,4]=>[4,1,1,1,1]
[1,3,7,6,8,2,5,4]=>[4,1,1,1,1]
[1,7,4,2,6,8,5,3]=>[4,2,1,1]
[7,4,1,2,6,8,5,3]=>[4,2,1,1]
[7,1,4,2,8,5,6,3]=>[3,3,1,1]
[7,1,8,2,5,4,6,3]=>[4,2,1,1]
[7,3,8,4,6,1,5,2]=>[4,2,1,1]
[7,2,8,1,6,4,5,3]=>[4,2,1,1]
[7,1,6,8,5,4,2,3]=>[5,1,1,1]
[7,1,2,6,8,5,4,3]=>[5,1,1,1]
[1,7,2,6,8,5,4,3]=>[5,1,1,1]
[1,7,6,8,3,2,5,4]=>[4,2,1,1]
[7,6,8,3,1,2,5,4]=>[4,2,1,1]
[7,1,5,8,6,3,2,4]=>[4,2,1,1]
[7,2,5,8,6,3,1,4]=>[4,2,1,1]
[3,6,7,1,8,5,4,2]=>[4,2,1,1]
[7,2,6,8,5,4,1,3]=>[5,1,1,1]
[7,6,8,2,3,1,5,4]=>[4,2,1,1]
[2,7,6,8,3,1,5,4]=>[4,2,1,1]
[2,7,1,6,8,5,4,3]=>[5,1,1,1]
[6,7,3,1,8,5,4,2]=>[4,3,1]
[6,7,1,8,5,4,3,2]=>[5,2,1]
[7,2,1,6,8,5,4,3]=>[5,2,1]
[7,6,8,3,2,1,5,4]=>[5,2,1]
[4,7,8,5,6,1,3,2]=>[4,1,1,1,1]
[4,6,5,8,7,1,3,2]=>[4,2,1,1]
[5,6,4,8,1,2,7,3]=>[3,2,1,1,1]
[8,1,5,6,7,2,4,3]=>[4,1,1,1,1]
[6,4,5,1,8,2,7,3]=>[3,3,1,1]
[5,4,6,7,1,2,8,3]=>[3,2,1,1,1]
[4,3,6,7,2,1,5,8]=>[4,1,1,1,1]
[5,3,6,7,1,4,2,8]=>[3,2,1,1,1]
[8,1,4,6,7,3,2,5]=>[4,1,1,1,1]
[8,1,3,6,7,4,5,2]=>[4,1,1,1,1]
[7,2,1,6,8,4,5,3]=>[4,2,1,1]
[5,2,6,7,1,4,8,3]=>[3,2,1,1,1]
[4,2,6,7,3,1,8,5]=>[3,2,2,1]
[6,2,4,1,5,8,7,3]=>[3,3,1,1]
[7,2,1,5,4,8,6,3]=>[4,2,2]
[8,1,4,5,3,7,2,6]=>[4,1,1,1,1]
[7,3,1,5,4,8,2,6]=>[4,2,1,1]
[6,3,4,1,5,8,2,7]=>[3,2,1,1,1]
[5,3,4,2,1,8,6,7]=>[4,2,1,1]
[4,3,5,2,7,1,6,8]=>[4,1,1,1,1]
[5,6,3,8,1,4,2,7]=>[3,2,1,1,1]
[8,1,7,2,4,5,6,3]=>[4,1,1,1,1]
[7,6,1,2,4,5,8,3]=>[4,1,1,1,1]
[4,7,8,2,3,1,6,5]=>[3,2,1,1,1]
[5,6,2,8,1,4,7,3]=>[3,2,1,1,1]
[6,5,2,1,3,7,8,4]=>[4,2,1,1]
[7,5,1,3,2,6,8,4]=>[4,2,1,1]
[8,1,6,3,2,5,7,4]=>[4,2,1,1]
[7,4,1,3,5,2,8,6]=>[4,2,1,1]
[5,4,2,3,1,6,8,7]=>[4,2,1,1]
[7,3,1,4,5,6,2,8]=>[3,2,1,1,1]
[8,1,4,3,5,6,2,7]=>[4,1,1,1,1]
[6,2,3,1,5,7,8,4]=>[3,2,1,1,1]
[7,8,4,2,1,6,5,3]=>[4,3,1]
[7,8,4,2,1,5,6,3]=>[4,2,1,1]
[6,2,3,4,8,7,1,5]=>[3,2,1,1,1]
[6,2,3,4,7,8,1,5]=>[3,1,1,1,1,1]
[7,8,3,4,6,2,1,5]=>[4,1,1,1,1]
[7,8,3,6,4,2,1,5]=>[5,1,1,1]
[7,8,3,5,6,2,1,4]=>[4,1,1,1,1]
[6,2,3,8,7,5,1,4]=>[4,2,1,1]
[6,2,3,7,8,5,1,4]=>[3,2,1,1,1]
[5,2,6,3,8,1,7,4]=>[3,2,2,1]
[6,3,2,5,8,7,1,4]=>[4,2,1,1]
[6,3,2,8,4,7,1,5]=>[4,2,1,1]
[6,4,3,8,7,5,1,2]=>[4,3,1]
[6,4,3,7,8,5,1,2]=>[4,2,1,1]
[6,2,4,1,7,3,5,8]=>[3,2,1,1,1]
[6,3,2,7,4,8,1,5]=>[4,2,1,1]
[6,3,2,5,7,8,1,4]=>[4,1,1,1,1]
[5,7,2,3,6,1,8,4]=>[3,2,1,1,1]
[5,8,2,3,6,1,7,4]=>[3,2,1,1,1]
[4,7,5,8,3,2,1,6]=>[5,1,1,1]
[4,5,6,8,3,2,1,7]=>[4,1,1,1,1]
[4,6,8,5,3,2,1,7]=>[5,1,1,1]
[5,6,1,4,2,3,7,8]=>[3,1,1,1,1,1]
[5,6,8,4,3,7,1,2]=>[4,1,1,1,1]
[5,6,1,4,2,3,8,7]=>[3,2,1,1,1]
[5,2,8,3,4,1,7,6]=>[3,2,2,1]
[4,5,8,6,3,2,1,7]=>[5,1,1,1]
[4,6,5,8,3,2,1,7]=>[5,1,1,1]
[4,7,5,6,3,2,1,8]=>[5,1,1,1]
[6,2,3,4,5,8,1,7]=>[3,1,1,1,1,1]
[5,1,4,3,6,2,8,7]=>[4,2,1,1]
[5,1,4,3,7,2,8,6]=>[4,2,1,1]
[5,1,4,3,8,2,7,6]=>[4,2,1,1]
[5,6,2,4,1,7,8,3]=>[3,2,1,1,1]
[5,6,2,4,1,8,7,3]=>[3,3,1,1]
[5,7,2,4,1,8,6,3]=>[3,3,1,1]
[6,1,4,2,8,7,5,3]=>[4,3,1]
[6,1,4,2,7,8,5,3]=>[3,3,1,1]
[5,8,2,4,1,7,6,3]=>[4,2,1,1]
[5,2,7,4,1,6,8,3]=>[3,2,2,1]
[5,4,1,3,7,2,6,8]=>[4,1,1,1,1]
[5,1,4,3,6,2,7,8]=>[4,1,1,1,1]
[5,8,6,4,3,7,1,2]=>[5,1,1,1]
[5,8,1,4,2,3,7,6]=>[3,2,1,1,1]
[5,1,6,3,4,2,7,8]=>[3,2,1,1,1]
[4,8,6,5,3,2,1,7]=>[6,1,1]
[4,8,5,6,3,2,1,7]=>[5,1,1,1]
[5,4,7,8,3,2,1,6]=>[5,1,1,1]
[5,4,8,7,3,2,1,6]=>[5,2,1]
[4,6,8,7,3,2,1,5]=>[5,1,1,1]
[4,6,7,8,3,2,1,5]=>[4,1,1,1,1]
[4,7,6,8,3,2,1,5]=>[5,1,1,1]
[4,7,8,5,3,2,1,6]=>[5,1,1,1]
[5,7,1,3,4,2,6,8]=>[3,1,1,1,1,1]
[5,1,8,4,2,3,6,7]=>[3,2,1,1,1]
[5,1,7,4,2,3,6,8]=>[3,2,1,1,1]
[5,8,1,3,4,2,6,7]=>[3,1,1,1,1,1]
[4,8,7,5,3,2,1,6]=>[6,1,1]
[4,7,8,6,3,2,1,5]=>[5,1,1,1]
[4,8,7,6,3,2,1,5]=>[6,1,1]
[4,8,2,6,3,7,5,1]=>[4,2,1,1]
[4,8,2,3,6,7,5,1]=>[4,1,1,1,1]
[4,8,3,1,6,7,5,2]=>[4,2,1,1]
[4,3,8,1,6,2,5,7]=>[3,2,1,1,1]
[1,4,8,7,3,5,2,6]=>[4,1,1,1,1]
[4,3,8,7,2,5,1,6]=>[4,2,1,1]
[5,8,4,3,7,1,6,2]=>[4,2,1,1]
[5,8,1,4,7,2,6,3]=>[4,1,1,1,1]
[5,8,1,7,4,2,3,6]=>[4,1,1,1,1]
[6,8,1,2,4,3,5,7]=>[3,1,1,1,1,1]
[5,8,7,1,3,4,2,6]=>[4,1,1,1,1]
[4,8,7,6,3,1,2,5]=>[5,1,1,1]
[5,8,4,7,3,1,2,6]=>[4,1,1,1,1]
[4,3,8,2,7,5,6,1]=>[4,2,1,1]
[1,4,8,3,7,5,6,2]=>[4,1,1,1,1]
[1,4,3,8,2,6,5,7]=>[3,2,1,1,1]
[4,3,2,8,1,6,5,7]=>[4,2,1,1]
[4,1,3,8,2,6,5,7]=>[3,2,1,1,1]
[4,1,8,3,7,5,6,2]=>[4,2,1,1]
[4,1,8,7,3,5,2,6]=>[4,2,1,1]
[3,7,8,1,5,4,2,6]=>[4,1,1,1,1]
[7,3,8,1,5,4,6,2]=>[4,2,1,1]
[3,4,8,1,6,2,5,7]=>[3,1,1,1,1,1]
[3,4,8,7,2,5,1,6]=>[4,1,1,1,1]
[3,4,8,2,7,5,6,1]=>[4,1,1,1,1]
[1,2,4,8,3,6,5,7]=>[3,1,1,1,1,1]
[1,2,4,3,8,6,5,7]=>[3,2,1,1,1]
[3,4,2,1,8,6,5,7]=>[3,3,1,1]
[3,4,1,8,2,6,5,7]=>[3,2,1,1,1]
[3,6,7,8,4,1,2,5]=>[3,1,1,1,1,1]
[4,1,7,8,5,3,2,6]=>[4,2,1,1]
[4,1,2,8,3,6,5,7]=>[3,2,1,1,1]
[1,4,3,2,8,6,5,7]=>[3,3,1,1]
[4,2,3,1,8,6,5,7]=>[3,3,1,1]
[3,7,6,8,4,2,1,5]=>[5,1,1,1]
[4,7,1,8,5,2,3,6]=>[3,2,1,1,1]
[2,6,8,7,4,3,1,5]=>[5,1,1,1]
[3,7,8,6,2,4,1,5]=>[4,1,1,1,1]
[3,7,8,2,6,4,5,1]=>[4,1,1,1,1]
[4,2,3,8,1,6,5,7]=>[3,2,1,1,1]
[4,3,1,8,2,6,5,7]=>[3,3,1,1]
[1,4,7,8,5,3,2,6]=>[4,1,1,1,1]
[4,3,7,8,5,2,1,6]=>[4,2,1,1]
[3,7,2,8,4,6,5,1]=>[4,2,1,1]
[4,2,8,6,3,1,5,7]=>[4,2,1,1]
[2,6,8,4,7,3,1,5]=>[4,1,1,1,1]
[2,4,8,6,3,1,5,7]=>[4,1,1,1,1]
[7,3,6,8,4,2,1,5]=>[5,1,1,1]
[7,6,2,8,3,5,4,1]=>[5,2,1]
[1,7,3,8,4,6,5,2]=>[4,2,1,1]
[1,3,4,8,2,6,5,7]=>[3,1,1,1,1,1]
[3,2,4,8,1,6,5,7]=>[3,2,1,1,1]
[7,3,8,6,2,4,1,5]=>[4,2,1,1]
[7,3,8,2,6,4,5,1]=>[4,2,1,1]
[2,4,8,3,6,1,5,7]=>[3,1,1,1,1,1]
[6,2,8,7,4,3,5,1]=>[5,2,1]
[7,4,1,8,5,2,6,3]=>[3,3,2]
[7,3,2,8,4,6,5,1]=>[4,3,1]
[2,4,3,1,8,6,5,7]=>[3,3,1,1]
[1,3,4,2,8,6,5,7]=>[3,2,1,1,1]
[1,3,2,4,8,6,5,7]=>[3,2,1,1,1]
[3,2,1,4,8,6,5,7]=>[3,3,1,1]
[3,1,2,4,8,6,5,7]=>[3,2,1,1,1]
[3,1,4,2,8,6,5,7]=>[3,2,2,1]
[3,1,4,8,2,6,5,7]=>[3,2,1,1,1]
[7,3,4,8,5,1,6,2]=>[3,2,2,1]
[3,7,4,8,5,1,2,6]=>[3,2,1,1,1]
[6,7,2,8,3,5,4,1]=>[4,2,1,1]
[2,3,1,4,8,6,5,7]=>[3,2,1,1,1]
[2,1,3,4,8,6,5,7]=>[3,2,1,1,1]
[1,2,3,4,8,6,5,7]=>[3,1,1,1,1,1]
[4,8,3,6,2,1,5,7]=>[4,1,1,1,1]
[3,5,8,2,6,1,4,7]=>[3,1,1,1,1,1]
[3,6,5,8,2,4,1,7]=>[4,1,1,1,1]
[5,3,8,7,2,4,6,1]=>[4,2,1,1]
[2,8,4,5,7,3,6,1]=>[4,1,1,1,1]
[2,4,5,7,3,8,1,6]=>[3,1,1,1,1,1]
[6,2,4,5,8,3,1,7]=>[4,1,1,1,1]
[4,8,1,2,5,6,3,7]=>[3,1,1,1,1,1]
[8,1,3,5,2,6,4,7]=>[3,2,1,1,1]
[5,2,1,6,3,8,4,7]=>[3,2,2,1]
[6,2,5,1,8,4,3,7]=>[4,2,1,1]
[3,6,1,5,8,4,2,7]=>[4,1,1,1,1]
[6,1,4,5,8,3,2,7]=>[4,1,1,1,1]
[5,6,4,8,1,3,2,7]=>[4,1,1,1,1]
[6,5,4,3,8,2,1,7]=>[6,1,1]
[5,4,3,7,2,8,1,6]=>[5,1,1,1]
[5,8,4,3,7,2,6,1]=>[5,1,1,1]
[4,6,8,3,7,2,5,1]=>[4,1,1,1,1]
[7,4,6,3,2,8,1,5]=>[5,1,1,1]
[1,4,3,6,2,7,8,5]=>[3,2,1,1,1]
[1,5,4,3,7,2,8,6]=>[4,2,1,1]
[4,7,8,5,3,1,2,6]=>[4,1,1,1,1]
[5,7,3,4,1,2,8,6]=>[3,2,1,1,1]
[8,5,4,7,6,2,1,3]=>[5,2,1]
[8,5,7,4,3,6,1,2]=>[5,1,1,1]
[4,3,8,1,6,7,5,2]=>[4,2,1,1]
[4,7,8,3,6,1,5,2]=>[4,1,1,1,1]
[5,3,8,6,7,4,1,2]=>[4,2,1,1]
[1,3,8,6,4,7,5,2]=>[4,2,1,1]
[8,6,2,7,4,1,5,3]=>[4,2,2]
[7,6,2,1,4,3,8,5]=>[4,2,2]
[7,6,1,3,4,2,8,5]=>[4,2,1,1]
[1,5,7,3,2,6,8,4]=>[3,2,1,1,1]
[1,6,7,3,2,5,8,4]=>[3,2,1,1,1]
[3,2,6,8,5,7,4,1]=>[4,2,1,1]
[5,8,2,3,6,7,4,1]=>[4,1,1,1,1]
[7,5,2,3,1,6,8,4]=>[4,2,1,1]
[1,6,4,7,2,3,8,5]=>[3,2,1,1,1]
[3,1,7,5,2,8,4,6]=>[3,2,2,1]
[2,5,7,4,1,8,3,6]=>[3,2,1,1,1]
[4,2,6,1,7,8,3,5]=>[3,2,1,1,1]
[4,2,7,6,3,8,1,5]=>[4,2,1,1]
[6,4,8,7,2,3,5,1]=>[4,2,1,1]
[3,2,6,8,7,4,5,1]=>[4,2,1,1]
[3,2,7,4,1,6,8,5]=>[3,2,2,1]
[6,3,2,1,7,8,4,5]=>[4,2,1,1]
[3,7,1,8,4,2,5,6]=>[3,2,1,1,1]
[4,2,1,3,7,5,8,6]=>[3,2,2,1]
[8,1,3,7,4,2,6,5]=>[4,2,1,1]
[8,4,3,7,6,2,1,5]=>[5,2,1]
[8,3,5,2,7,6,1,4]=>[4,2,1,1]
[3,6,2,8,7,1,5,4]=>[4,2,1,1]
[7,3,2,8,1,6,5,4]=>[4,3,1]
[3,8,7,2,6,5,4,1]=>[6,1,1]
[4,2,7,8,6,1,5,3]=>[4,2,1,1]
[6,8,2,4,7,1,5,3]=>[4,1,1,1,1]
[5,2,1,8,7,3,6,4]=>[4,3,1]
[8,2,1,6,3,7,5,4]=>[4,2,2]
[6,8,3,1,7,5,2,4]=>[4,2,1,1]
[5,8,1,6,7,2,4,3]=>[4,1,1,1,1]
[6,2,8,1,5,7,4,3]=>[4,2,1,1]
[5,7,8,2,6,1,4,3]=>[4,1,1,1,1]
[8,7,2,5,6,4,3,1]=>[6,1,1]
[8,6,7,5,2,4,3,1]=>[6,1,1]
[7,2,6,8,1,5,4,3]=>[5,1,1,1]
[1,2,7,8,5,6,4,3]=>[4,1,1,1,1]
[7,4,8,1,6,2,5,3]=>[4,2,1,1]
[3,7,1,8,2,6,5,4]=>[4,2,1,1]
[2,1,7,3,8,6,5,4]=>[4,2,2]
[8,2,1,7,6,5,4,3]=>[6,2]
[8,1,4,7,6,5,3,2]=>[6,1,1]
[8,6,7,5,1,4,3,2]=>[6,1,1]
[7,8,6,5,4,1,3,2]=>[6,1,1]
[5,8,4,3,2,1,6,7]=>[5,1,1,1]
[6,4,7,3,2,1,8,5]=>[5,2,1]
[5,4,7,3,2,1,6,8]=>[5,1,1,1]
[6,5,3,7,2,1,4,8]=>[5,1,1,1]
[5,8,3,6,2,1,4,7]=>[4,1,1,1,1]
[6,3,7,8,2,1,4,5]=>[4,1,1,1,1]
[5,3,7,6,2,1,4,8]=>[4,2,1,1]
[3,8,7,6,2,1,4,5]=>[5,1,1,1]
[5,8,4,2,6,1,3,7]=>[4,1,1,1,1]
[4,8,7,2,5,1,3,6]=>[4,1,1,1,1]
[5,8,3,2,6,1,4,7]=>[4,1,1,1,1]
[4,8,3,2,5,1,7,6]=>[4,2,1,1]
[4,3,7,2,5,1,8,6]=>[4,2,1,1]
[3,8,7,2,5,1,4,6]=>[4,1,1,1,1]
[6,4,2,7,5,1,3,8]=>[4,2,1,1]
[6,3,2,7,5,1,4,8]=>[4,2,1,1]
[5,3,2,6,7,1,4,8]=>[4,1,1,1,1]
[3,8,2,6,5,1,4,7]=>[4,1,1,1,1]
[6,2,7,8,5,1,3,4]=>[3,2,1,1,1]
[5,2,7,6,8,1,3,4]=>[3,2,1,1,1]
[4,2,7,6,5,1,3,8]=>[4,2,1,1]
[2,8,7,6,5,1,3,4]=>[5,1,1,1]
[6,5,4,3,1,7,8,2]=>[5,2,1]
[6,4,7,3,1,5,8,2]=>[4,2,1,1]
[5,4,7,3,1,8,6,2]=>[4,3,1]
[6,4,3,7,1,5,8,2]=>[4,2,1,1]
[5,4,3,6,1,8,7,2]=>[4,3,1]
[6,3,7,8,1,4,5,2]=>[3,2,1,1,1]
[5,3,7,6,1,4,8,2]=>[4,2,1,1]
[4,3,7,6,1,5,8,2]=>[4,2,1,1]
[3,8,7,6,1,4,5,2]=>[5,1,1,1]
[6,5,4,2,1,7,3,8]=>[5,2,1]
[6,4,7,2,1,5,3,8]=>[4,2,1,1]
[4,8,7,2,1,5,3,6]=>[4,2,1,1]
[5,8,3,2,1,4,7,6]=>[4,2,1,1]
[4,8,3,2,1,5,7,6]=>[4,2,1,1]
[5,3,7,2,1,4,8,6]=>[4,2,1,1]
[3,8,7,2,1,4,5,6]=>[4,1,1,1,1]
[6,5,2,7,1,4,3,8]=>[4,2,1,1]
[5,8,2,6,1,4,3,7]=>[4,1,1,1,1]
[6,4,2,7,1,5,3,8]=>[4,2,1,1]
[5,4,2,6,1,8,3,7]=>[4,2,1,1]
[4,3,2,6,1,5,8,7]=>[4,2,1,1]
[6,2,7,8,1,4,3,5]=>[3,2,1,1,1]
[4,2,7,6,1,5,3,8]=>[4,2,1,1]
[3,2,7,6,1,4,5,8]=>[3,2,1,1,1]
[6,5,4,1,8,7,3,2]=>[5,3]
[5,8,4,1,6,7,3,2]=>[4,2,1,1]
[6,4,7,1,5,8,3,2]=>[4,2,1,1]
[5,4,7,1,6,8,3,2]=>[4,2,1,1]
[4,8,7,1,5,6,3,2]=>[5,1,1,1]
[5,4,3,1,6,8,7,2]=>[4,3,1]
[4,8,3,1,5,6,7,2]=>[3,2,1,1,1]
[3,8,7,1,5,4,6,2]=>[5,1,1,1]
[5,8,2,1,6,4,3,7]=>[4,2,1,1]
[6,3,2,1,5,4,8,7]=>[4,2,2]
[5,3,2,1,6,4,8,7]=>[4,2,2]
[3,8,2,1,5,4,6,7]=>[3,2,1,1,1]
[6,2,7,1,5,4,3,8]=>[4,2,1,1]
[5,2,7,1,6,4,3,8]=>[4,2,1,1]
[4,2,7,1,5,6,3,8]=>[3,2,1,1,1]
[3,2,7,1,5,4,6,8]=>[3,2,1,1,1]
[2,8,7,1,5,4,3,6]=>[5,1,1,1]
[6,5,1,7,8,4,3,2]=>[5,2,1]
[5,8,1,6,7,4,3,2]=>[5,1,1,1]
[6,4,1,7,5,8,3,2]=>[4,3,1]
[5,4,1,6,7,8,3,2]=>[4,2,1,1]
[4,8,1,6,5,7,3,2]=>[5,1,1,1]
[6,3,1,7,5,4,8,2]=>[4,3,1]
[5,3,1,6,7,4,8,2]=>[3,3,1,1]
[4,3,1,6,5,7,8,2]=>[3,3,1,1]
[3,8,1,6,5,4,7,2]=>[5,1,1,1]
[5,2,1,6,7,4,3,8]=>[3,3,1,1]
[4,2,1,6,5,7,3,8]=>[3,3,1,1]
[2,8,1,6,5,4,3,7]=>[5,1,1,1]
[6,1,7,8,5,4,3,2]=>[5,2,1]
[4,1,7,6,5,8,3,2]=>[5,2,1]
[3,1,7,6,5,4,8,2]=>[5,2,1]
[4,5,8,1,2,6,3,7]=>[3,1,1,1,1,1]
[1,4,5,7,2,6,3,8]=>[3,1,1,1,1,1]
[1,7,3,5,6,2,4,8]=>[3,1,1,1,1,1]
[8,1,3,5,7,2,4,6]=>[3,1,1,1,1,1]
[3,6,8,1,7,2,4,5]=>[3,1,1,1,1,1]
[3,4,5,6,8,1,7,2]=>[3,1,1,1,1,1]
[4,5,8,2,6,7,1,3]=>[3,1,1,1,1,1]
[8,2,3,5,6,7,1,4]=>[3,1,1,1,1,1]
[1,7,2,3,5,4,6,8]=>[3,1,1,1,1,1]
[8,1,2,3,5,4,6,7]=>[3,1,1,1,1,1]
[2,7,8,1,3,5,4,6]=>[3,1,1,1,1,1]
[2,7,8,3,5,6,1,4]=>[3,1,1,1,1,1]
[2,4,5,7,8,1,6,3]=>[3,1,1,1,1,1]
[4,5,8,1,7,6,3,2]=>[5,1,1,1]
[4,5,8,7,2,1,6,3]=>[4,2,1,1]
[8,7,3,5,6,2,1,4]=>[5,1,1,1]
[8,7,2,1,3,5,4,6]=>[4,2,1,1]
[3,6,8,7,2,1,5,4]=>[4,2,1,1]
[8,6,4,1,7,5,3,2]=>[5,3]
[7,6,4,3,1,8,5,2]=>[5,3]
[2,3,6,7,8,1,5,4]=>[3,1,1,1,1,1]
[3,6,8,1,2,5,4,7]=>[3,1,1,1,1,1]
[1,3,6,7,2,5,4,8]=>[3,1,1,1,1,1]
[7,4,1,8,5,2,3,6]=>[3,3,1,1]
[7,1,4,2,8,3,6,5]=>[3,3,1,1]
[7,1,8,2,5,3,6,4]=>[3,2,2,1]
[8,1,7,5,4,2,3,6]=>[5,1,1,1]
[1,7,2,6,5,4,3,8]=>[5,1,1,1]
[1,7,6,3,2,5,4,8]=>[4,2,1,1]
[8,6,3,1,2,5,4,7]=>[4,2,1,1]
[8,1,7,6,3,2,4,5]=>[5,1,1,1]
[8,2,5,7,6,3,1,4]=>[5,1,1,1]
[3,6,8,1,7,5,4,2]=>[5,1,1,1]
[8,2,6,7,5,4,1,3]=>[5,1,1,1]
[2,7,8,6,3,1,5,4]=>[4,2,1,1]
[2,7,8,1,6,5,4,3]=>[5,1,1,1]
[7,3,1,8,6,5,4,2]=>[5,3]
[8,7,2,1,6,5,4,3]=>[6,2]
[8,7,6,3,2,1,5,4]=>[6,2]
[2,1,8,6,3,7,4,5]=>[3,2,2,1]
[8,6,1,5,2,7,4,3]=>[5,2,1]
[8,5,1,7,4,2,6,3]=>[4,2,2]
[2,1,7,5,4,3,8,6]=>[4,2,2]
[2,1,7,8,3,6,5,4]=>[4,2,1,1]
[2,1,4,8,5,7,3,6]=>[3,2,1,1,1]
[8,5,3,1,6,2,4,7]=>[4,2,1,1]
[6,4,1,5,2,3,8,7]=>[3,2,2,1]
[8,3,7,5,2,6,1,4]=>[5,1,1,1]
[5,3,7,4,6,8,1,2]=>[3,2,1,1,1]
[5,8,3,7,6,2,1,4]=>[5,1,1,1]
[4,2,6,3,8,5,1,7]=>[3,2,2,1]
[5,8,2,1,7,6,4,3]=>[5,2,1]
[8,3,2,4,1,7,5,6]=>[4,2,1,1]
[7,2,8,1,4,6,5,3]=>[4,2,1,1]
[6,2,3,1,4,5,8,7]=>[3,2,1,1,1]
[6,8,1,4,5,3,2,7]=>[4,1,1,1,1]
[8,2,6,1,4,7,3,5]=>[4,1,1,1,1]
[8,3,5,6,1,7,4,2]=>[4,2,1,1]
[6,3,5,4,1,2,8,7]=>[4,2,1,1]
[8,7,3,6,5,1,4,2]=>[6,1,1]
[2,7,4,3,6,1,8,5]=>[4,2,1,1]
[3,4,7,2,8,1,5,6]=>[3,1,1,1,1,1]
[4,2,3,5,8,1,6,7]=>[3,1,1,1,1,1]
[3,8,4,7,1,6,5,2]=>[5,1,1,1]
[3,2,4,6,1,5,8,7]=>[3,2,1,1,1]
[8,3,4,5,7,6,1,2]=>[4,1,1,1,1]
[3,2,4,5,6,8,1,7]=>[3,1,1,1,1,1]
[5,6,8,1,4,2,7,3]=>[3,2,1,1,1]
[1,5,7,8,4,6,2,3]=>[3,1,1,1,1,1]
[1,3,5,7,8,6,2,4]=>[3,1,1,1,1,1]
[3,5,7,8,6,1,2,4]=>[3,1,1,1,1,1]
[3,5,1,6,8,2,7,4]=>[3,2,1,1,1]
[3,1,5,6,8,2,7,4]=>[3,2,1,1,1]
[2,3,5,6,8,1,7,4]=>[3,1,1,1,1,1]
[5,6,4,8,2,1,7,3]=>[4,2,1,1]
[5,1,6,3,8,4,7,2]=>[3,2,2,1]
[2,5,1,6,8,3,7,4]=>[3,2,1,1,1]
[5,1,2,6,8,3,7,4]=>[3,2,1,1,1]
[5,7,1,8,6,2,3,4]=>[3,2,1,1,1]
[1,5,2,7,8,6,3,4]=>[3,2,1,1,1]
[1,6,7,5,2,8,3,4]=>[3,2,1,1,1]
[6,1,7,5,2,8,3,4]=>[3,2,2,1]
[2,6,7,5,1,8,3,4]=>[3,2,1,1,1]
[5,7,2,8,6,1,3,4]=>[3,2,1,1,1]
[3,5,7,8,6,2,1,4]=>[4,1,1,1,1]
[5,1,7,8,6,3,4,2]=>[4,2,1,1]
[5,1,3,7,8,6,4,2]=>[4,2,1,1]
[5,2,7,8,4,6,1,3]=>[3,2,1,1,1]
[3,2,5,7,8,6,1,4]=>[3,2,1,1,1]
[6,2,7,5,1,8,3,4]=>[3,2,2,1]
[1,2,6,7,5,8,3,4]=>[3,1,1,1,1,1]
[6,2,7,5,4,1,8,3]=>[4,2,2]
[6,7,5,2,4,1,8,3]=>[4,2,1,1]
[6,7,2,5,3,8,1,4]=>[4,1,1,1,1]
[6,7,4,5,2,1,8,3]=>[4,2,1,1]
[5,1,7,8,6,4,3,2]=>[5,2,1]
[2,5,7,8,6,3,1,4]=>[4,1,1,1,1]
[5,1,7,8,6,3,2,4]=>[4,2,1,1]
[6,3,7,5,1,8,2,4]=>[3,2,2,1]
[1,6,7,5,3,8,2,4]=>[4,1,1,1,1]
[1,6,7,5,4,2,8,3]=>[4,2,1,1]
[6,7,5,1,4,2,8,3]=>[4,2,1,1]
[5,7,8,6,4,1,2,3]=>[4,1,1,1,1]
[4,1,7,2,6,5,8,3]=>[4,2,1,1]
[2,4,7,1,5,6,8,3]=>[3,1,1,1,1,1]
[6,7,4,1,5,2,8,3]=>[3,2,2,1]
[1,6,7,4,5,2,8,3]=>[3,2,1,1,1]
[1,6,3,7,5,8,2,4]=>[3,2,1,1,1]
[6,3,1,7,5,8,2,4]=>[3,3,1,1]
[2,5,3,7,8,6,1,4]=>[3,2,1,1,1]
[6,7,5,4,2,1,8,3]=>[5,2,1]
[6,3,2,7,5,8,1,4]=>[4,2,1,1]
[6,7,4,2,5,1,8,3]=>[4,2,1,1]
[6,2,7,4,5,1,8,3]=>[3,2,2,1]
[6,2,3,7,5,8,1,4]=>[3,2,1,1,1]
[4,5,1,6,3,2,8,7]=>[3,2,2,1]
[7,5,1,6,3,8,2,4]=>[4,2,1,1]
[7,5,1,6,3,8,4,2]=>[4,2,2]
[2,7,6,1,3,8,4,5]=>[3,2,1,1,1]
[2,7,6,1,3,8,5,4]=>[4,2,1,1]
[7,3,5,1,8,2,6,4]=>[3,3,1,1]
[7,3,5,1,8,2,4,6]=>[3,2,1,1,1]
[3,7,5,1,8,6,2,4]=>[3,3,1,1]
[2,6,7,1,5,8,3,4]=>[3,1,1,1,1,1]
[2,6,7,4,1,8,3,5]=>[3,2,1,1,1]
[2,1,6,7,3,8,5,4]=>[3,2,2,1]
[2,6,7,4,1,8,5,3]=>[3,3,1,1]
[2,6,7,1,5,8,4,3]=>[4,1,1,1,1]
[3,6,5,1,8,4,7,2]=>[4,2,1,1]
[3,6,5,1,8,4,2,7]=>[4,2,1,1]
[3,7,5,4,8,1,6,2]=>[4,2,1,1]
[3,7,5,4,8,1,2,6]=>[4,1,1,1,1]
[4,6,1,5,8,7,3,2]=>[4,2,1,1]
[4,6,1,5,8,7,2,3]=>[3,2,1,1,1]
[4,6,1,5,8,2,7,3]=>[3,2,1,1,1]
[7,5,1,6,2,8,3,4]=>[3,2,2,1]
[7,5,1,6,2,8,4,3]=>[4,2,2]
[4,6,1,5,8,2,3,7]=>[3,1,1,1,1,1]
[4,7,1,5,8,3,6,2]=>[4,1,1,1,1]
[2,3,4,7,8,1,6,5]=>[3,1,1,1,1,1]
[6,8,5,4,3,2,7,1]=>[6,1,1]
[6,8,5,4,3,7,2,1]=>[6,1,1]
[5,8,4,3,2,1,7,6]=>[5,2,1]
[6,5,4,3,1,8,7,2]=>[5,3]
[8,7,5,4,3,1,6,2]=>[6,2]
[8,3,4,6,2,1,5,7]=>[4,1,1,1,1]
[3,5,6,2,1,8,4,7]=>[3,2,1,1,1]
[3,5,2,6,8,4,1,7]=>[3,2,1,1,1]
[7,5,3,2,8,4,1,6]=>[5,2,1]
[7,5,3,2,8,4,6,1]=>[5,2,1]
[2,4,5,7,3,8,6,1]=>[3,2,1,1,1]
[4,2,5,6,8,3,1,7]=>[3,2,1,1,1]
[4,2,8,1,5,6,3,7]=>[3,2,1,1,1]
[2,5,6,1,8,4,3,7]=>[3,2,1,1,1]
[5,3,6,8,1,4,2,7]=>[3,2,1,1,1]
[4,5,6,8,1,3,2,7]=>[3,1,1,1,1,1]
[1,4,5,6,8,3,2,7]=>[3,1,1,1,1,1]
[4,5,6,3,8,2,1,7]=>[4,1,1,1,1]
[4,5,3,7,2,8,6,1]=>[4,2,1,1]
[6,4,7,3,2,8,5,1]=>[5,2,1]
[6,1,4,7,3,2,8,5]=>[4,2,1,1]
[1,7,8,4,5,3,2,6]=>[4,1,1,1,1]
[5,1,7,3,8,4,2,6]=>[3,2,2,1]
[2,5,1,7,4,3,8,6]=>[3,2,2,1]
[2,5,7,4,1,8,6,3]=>[3,3,1,1]
[5,3,7,1,4,8,6,2]=>[3,3,1,1]
[6,4,3,1,7,8,5,2]=>[4,3,1]
[6,4,1,7,3,8,5,2]=>[4,2,2]
[5,6,3,7,8,4,2,1]=>[4,2,1,1]
[5,1,6,3,7,8,4,2]=>[3,2,2,1]
[5,6,1,3,7,8,4,2]=>[3,2,1,1,1]
[5,6,1,7,8,3,4,2]=>[3,2,1,1,1]
[1,6,3,7,4,8,5,2]=>[3,2,2,1]
[6,7,2,4,1,8,5,3]=>[3,3,1,1]
[6,7,2,1,4,3,8,5]=>[3,2,2,1]
[6,4,7,3,1,2,8,5]=>[4,2,1,1]
[5,6,3,1,2,7,8,4]=>[3,2,1,1,1]
[5,6,1,3,2,7,8,4]=>[3,2,1,1,1]
[5,6,3,2,1,7,8,4]=>[4,2,1,1]
[2,5,6,3,7,8,4,1]=>[3,2,1,1,1]
[2,5,6,3,1,7,8,4]=>[3,2,1,1,1]
[2,6,4,7,3,1,8,5]=>[4,2,1,1]
[6,3,7,2,8,4,5,1]=>[4,2,1,1]
[6,3,7,2,8,4,1,5]=>[4,2,1,1]
[6,3,2,7,1,8,4,5]=>[4,2,1,1]
[7,5,3,2,1,8,4,6]=>[5,2,1]
[7,3,8,4,2,1,5,6]=>[4,2,1,1]
[4,7,2,1,3,8,6,5]=>[3,3,1,1]
[1,3,7,8,6,4,2,5]=>[4,1,1,1,1]
[7,3,8,4,6,2,1,5]=>[4,2,1,1]
[5,7,3,8,2,1,6,4]=>[4,2,1,1]
[6,3,7,8,5,2,1,4]=>[4,2,1,1]
[4,6,2,7,8,5,3,1]=>[4,2,1,1]
[4,6,2,1,7,8,5,3]=>[3,3,1,1]
[7,4,5,8,1,2,6,3]=>[3,2,1,1,1]
[2,5,1,7,3,8,6,4]=>[3,2,2,1]
[6,7,2,1,3,8,5,4]=>[3,3,1,1]
[5,1,6,7,8,2,4,3]=>[3,2,1,1,1]
[6,3,7,1,8,5,2,4]=>[3,3,1,1]
[6,2,1,7,3,8,5,4]=>[3,3,2]
[6,2,7,1,8,5,4,3]=>[4,3,1]
[6,3,1,7,8,5,4,2]=>[4,3,1]
[4,1,3,6,8,2,5,7]=>[3,1,1,1,1,1]
[4,2,3,6,8,1,5,7]=>[3,1,1,1,1,1]
[5,3,2,1,8,4,7,6]=>[4,3,1]
[3,6,5,8,2,1,7,4]=>[4,2,1,1]
[4,5,2,1,3,8,7,6]=>[3,3,1,1]
[3,2,6,4,5,8,1,7]=>[3,2,1,1,1]
[2,4,6,5,8,1,3,7]=>[3,1,1,1,1,1]
[1,6,2,4,5,8,3,7]=>[3,1,1,1,1,1]
[5,3,2,1,6,8,4,7]=>[4,2,1,1]
[6,2,4,5,8,1,3,7]=>[3,1,1,1,1,1]
[1,3,4,6,5,8,2,7]=>[3,1,1,1,1,1]
[1,6,3,4,5,8,2,7]=>[3,1,1,1,1,1]
[3,4,1,8,5,2,7,6]=>[3,2,2,1]
[2,8,4,1,7,6,3,5]=>[4,2,1,1]
[8,1,4,2,7,3,6,5]=>[4,2,1,1]
[1,5,3,2,8,7,4,6]=>[3,3,1,1]
[8,2,1,7,5,3,4,6]=>[4,2,1,1]
[1,7,6,4,5,8,3,2]=>[5,1,1,1]
[5,8,7,4,1,2,6,3]=>[4,2,1,1]
[5,8,7,4,6,2,1,3]=>[5,1,1,1]
[3,4,2,5,8,6,7,1]=>[3,2,1,1,1]
[4,1,3,5,6,8,7,2]=>[3,2,1,1,1]
[2,4,8,6,7,1,3,5]=>[3,1,1,1,1,1]
[4,3,6,2,8,1,7,5]=>[4,2,1,1]
[3,7,4,8,2,1,6,5]=>[4,2,1,1]
[2,3,5,8,6,7,1,4]=>[3,1,1,1,1,1]
[3,2,5,6,8,7,1,4]=>[3,2,1,1,1]
[2,1,8,5,6,7,3,4]=>[3,2,1,1,1]
[1,2,8,3,5,6,7,4]=>[3,1,1,1,1,1]
[4,2,3,7,1,8,6,5]=>[3,3,1,1]
[3,2,6,4,8,1,7,5]=>[3,2,2,1]
[8,2,1,6,7,3,4,5]=>[3,2,1,1,1]
[2,7,8,5,4,1,3,6]=>[4,1,1,1,1]
[1,7,5,3,8,4,2,6]=>[4,2,1,1]
[4,7,5,3,1,2,8,6]=>[4,2,1,1]
[7,2,4,8,5,3,1,6]=>[4,2,1,1]
[4,8,3,1,2,7,6,5]=>[4,2,1,1]
[3,5,2,7,4,1,8,6]=>[3,2,2,1]
[8,4,2,3,7,1,5,6]=>[4,1,1,1,1]
[2,8,4,7,1,3,5,6]=>[3,1,1,1,1,1]
[8,2,4,6,7,1,3,5]=>[3,1,1,1,1,1]
[4,8,2,3,6,7,1,5]=>[3,1,1,1,1,1]
[3,5,2,7,6,1,8,4]=>[3,2,2,1]
[1,6,3,2,5,8,7,4]=>[3,3,1,1]
[5,8,3,2,1,6,7,4]=>[4,2,1,1]
[5,8,7,3,4,6,2,1]=>[5,1,1,1]
[5,8,2,7,4,1,6,3]=>[4,2,1,1]
[5,1,4,2,8,7,6,3]=>[4,3,1]
[4,7,6,5,8,2,1,3]=>[5,1,1,1]
[5,3,7,1,6,2,8,4]=>[3,2,2,1]
[5,2,6,8,7,1,3,4]=>[3,2,1,1,1]
[6,3,2,1,8,5,7,4]=>[4,3,1]
[2,7,5,4,1,8,6,3]=>[4,3,1]
[4,2,5,6,8,7,1,3]=>[3,2,1,1,1]
[1,8,4,2,5,6,7,3]=>[3,2,1,1,1]
[3,8,4,1,5,6,7,2]=>[3,2,1,1,1]
[4,2,8,5,6,7,1,3]=>[3,2,1,1,1]
[5,2,4,7,1,8,6,3]=>[3,3,1,1]
[5,3,4,7,1,8,6,2]=>[3,3,1,1]
[8,6,4,1,3,2,5,7]=>[5,1,1,1]
[8,1,3,6,5,2,4,7]=>[4,1,1,1,1]
[8,1,4,3,6,5,2,7]=>[4,2,1,1]
[3,6,5,2,1,8,7,4]=>[4,3,1]
[8,3,2,4,6,5,1,7]=>[4,2,1,1]
[8,4,2,1,6,5,3,7]=>[4,3,1]
[8,4,1,2,6,5,3,7]=>[4,2,1,1]
[8,6,4,2,1,5,3,7]=>[5,2,1]
[8,3,6,4,1,5,2,7]=>[4,2,1,1]
[8,2,6,3,4,5,1,7]=>[4,1,1,1,1]
[1,3,4,8,5,7,2,6]=>[3,1,1,1,1,1]
[5,8,4,7,6,2,3,1]=>[5,1,1,1]
[1,3,4,7,5,8,2,6]=>[3,1,1,1,1,1]
[1,3,5,2,4,8,7,6]=>[3,2,1,1,1]
[2,6,5,1,3,8,7,4]=>[3,3,1,1]
[4,7,1,6,5,8,3,2]=>[5,1,1,1]
[5,4,8,7,6,3,1,2]=>[5,2,1]
[2,8,5,1,4,7,6,3]=>[4,2,1,1]
[4,3,1,5,8,6,7,2]=>[3,3,1,1]
[4,1,3,5,8,6,7,2]=>[3,2,1,1,1]
[6,5,3,8,4,7,1,2]=>[4,2,1,1]
[5,4,2,1,6,8,7,3]=>[4,3,1]
[6,8,4,3,2,7,1,5]=>[5,1,1,1]
[3,4,7,8,2,1,6,5]=>[3,2,1,1,1]
[5,1,3,2,8,6,7,4]=>[3,3,1,1]
[5,3,1,2,8,6,7,4]=>[3,3,1,1]
[5,2,3,1,6,8,7,4]=>[3,3,1,1]
[5,3,2,1,8,6,7,4]=>[4,3,1]
[5,2,1,3,6,8,7,4]=>[3,3,1,1]
[2,4,7,3,8,1,6,5]=>[3,2,1,1,1]
[6,3,8,2,7,4,1,5]=>[4,2,1,1]
[8,2,1,3,6,4,7,5]=>[3,2,2,1]
[3,5,1,7,8,4,2,6]=>[3,2,1,1,1]
[2,7,4,5,8,3,1,6]=>[4,1,1,1,1]
[1,8,4,3,7,2,6,5]=>[4,2,1,1]
[3,4,8,7,2,1,6,5]=>[4,2,1,1]
[5,4,7,8,3,6,2,1]=>[5,1,1,1]
[6,4,3,8,7,2,1,5]=>[5,2,1]
[6,3,8,7,4,1,2,5]=>[4,2,1,1]
[3,5,7,2,4,8,1,6]=>[3,1,1,1,1,1]
[8,4,7,2,3,1,5,6]=>[4,1,1,1,1]
[8,4,7,1,3,2,5,6]=>[4,1,1,1,1]
[8,4,7,2,1,3,5,6]=>[4,1,1,1,1]
[8,6,4,2,1,3,7,5]=>[5,2,1]
[8,6,4,1,3,2,7,5]=>[5,2,1]
[8,6,4,2,3,1,7,5]=>[5,2,1]
[3,5,7,2,6,1,8,4]=>[3,2,1,1,1]
[6,1,3,8,5,7,2,4]=>[3,2,1,1,1]
[5,8,3,2,6,7,1,4]=>[4,1,1,1,1]
[4,8,5,3,6,2,7,1]=>[5,1,1,1]
[2,8,1,5,4,7,6,3]=>[4,2,1,1]
[1,5,8,7,4,6,2,3]=>[4,1,1,1,1]
[2,1,7,6,4,5,8,3]=>[4,2,1,1]
[1,7,2,4,6,5,8,3]=>[4,1,1,1,1]
[3,5,1,7,6,8,2,4]=>[3,2,1,1,1]
[5,8,2,6,1,3,7,4]=>[3,2,1,1,1]
[6,3,5,8,7,2,1,4]=>[4,2,1,1]
[2,5,7,8,4,1,6,3]=>[3,2,1,1,1]
[4,2,8,1,5,6,7,3]=>[3,2,1,1,1]
[4,1,5,2,6,8,7,3]=>[3,2,2,1]
[3,4,5,1,6,8,7,2]=>[3,2,1,1,1]
[4,2,8,5,1,6,7,3]=>[3,2,2,1]
[4,1,8,5,2,6,7,3]=>[3,2,2,1]
[2,7,1,8,5,4,6,3]=>[4,2,1,1]
[5,8,6,2,1,3,7,4]=>[4,2,1,1]
[8,2,4,1,5,6,7,3]=>[3,2,1,1,1]
[4,6,3,5,8,1,7,2]=>[3,2,1,1,1]
[1,7,8,3,5,4,6,2]=>[4,1,1,1,1]
[3,4,5,1,8,6,7,2]=>[3,2,1,1,1]
[3,8,1,4,5,6,7,2]=>[3,1,1,1,1,1]
[3,4,5,7,8,2,6,1]=>[3,1,1,1,1,1]
[3,4,6,2,8,5,1,7]=>[3,2,1,1,1]
[3,4,6,8,1,5,2,7]=>[3,1,1,1,1,1]
[3,4,7,2,1,8,6,5]=>[3,3,1,1]
[3,4,7,8,1,5,6,2]=>[3,1,1,1,1,1]
[3,4,8,2,1,5,6,7]=>[3,1,1,1,1,1]
[3,5,2,7,8,4,6,1]=>[3,2,1,1,1]
[3,5,6,2,8,4,1,7]=>[3,2,1,1,1]
[3,5,6,8,4,1,2,7]=>[3,1,1,1,1,1]
[3,5,7,2,4,8,6,1]=>[3,2,1,1,1]
[3,5,7,2,8,4,6,1]=>[3,2,1,1,1]
[3,5,7,8,4,1,6,2]=>[3,2,1,1,1]
[3,6,2,1,7,8,5,4]=>[3,3,1,1]
[3,6,2,1,8,5,4,7]=>[3,3,1,1]
[3,6,7,2,8,5,4,1]=>[4,2,1,1]
[3,6,8,2,4,5,1,7]=>[3,1,1,1,1,1]
[3,7,2,1,4,8,6,5]=>[3,3,1,1]
[3,7,2,8,4,5,6,1]=>[3,2,1,1,1]
[3,8,2,1,4,5,6,7]=>[3,1,1,1,1,1]
[4,1,5,6,7,8,3,2]=>[3,2,1,1,1]
[4,1,6,3,7,8,5,2]=>[3,2,2,1]
[4,1,6,3,8,5,2,7]=>[3,2,2,1]
[4,1,6,7,3,8,5,2]=>[3,2,2,1]
[4,1,6,7,8,5,2,3]=>[3,2,1,1,1]
[4,1,6,8,3,5,2,7]=>[3,2,1,1,1]
[4,1,7,3,2,8,6,5]=>[3,3,2]
[4,1,8,3,2,5,6,7]=>[3,2,1,1,1]
[4,5,2,6,8,1,3,7]=>[3,1,1,1,1,1]
[4,5,7,3,8,1,6,2]=>[3,2,1,1,1]
[4,5,8,3,2,1,6,7]=>[4,1,1,1,1]
[4,6,2,3,7,8,5,1]=>[3,2,1,1,1]
[4,6,2,3,8,5,1,7]=>[3,2,1,1,1]
[4,6,2,7,8,5,1,3]=>[3,2,1,1,1]
[4,6,7,3,2,8,5,1]=>[4,2,1,1]
[4,7,2,8,3,5,6,1]=>[3,2,1,1,1]
[4,7,8,3,2,5,6,1]=>[4,1,1,1,1]
[4,8,2,3,1,5,6,7]=>[3,1,1,1,1,1]
[5,1,2,6,8,4,3,7]=>[3,2,1,1,1]
[5,1,2,7,4,8,6,3]=>[3,2,2,1]
[5,1,6,3,8,4,2,7]=>[3,2,2,1]
[5,1,6,7,4,8,2,3]=>[3,2,1,1,1]
[5,6,2,3,8,4,1,7]=>[3,2,1,1,1]
[5,6,2,7,8,4,1,3]=>[3,2,1,1,1]
[5,6,8,3,4,2,1,7]=>[4,1,1,1,1]
[5,7,2,3,4,8,6,1]=>[3,2,1,1,1]
[5,7,8,3,4,2,6,1]=>[4,1,1,1,1]
[5,8,2,3,4,1,6,7]=>[3,1,1,1,1,1]
[6,1,2,3,7,8,5,4]=>[3,2,1,1,1]
[6,1,2,3,8,5,4,7]=>[3,2,1,1,1]
[6,1,2,7,8,5,4,3]=>[4,2,1,1]
[6,1,7,3,8,5,4,2]=>[4,2,2]
[6,1,7,8,4,5,3,2]=>[4,2,1,1]
[6,1,8,3,4,5,2,7]=>[3,2,1,1,1]
[6,7,2,3,8,5,4,1]=>[4,2,1,1]
[6,7,2,8,4,5,3,1]=>[4,2,1,1]
[7,1,2,3,4,8,6,5]=>[3,2,1,1,1]
[7,1,2,8,4,5,6,3]=>[3,2,1,1,1]
[7,1,8,3,4,5,6,2]=>[3,2,1,1,1]
[6,4,1,8,2,3,7,5]=>[3,3,1,1]
[5,8,1,2,4,3,7,6]=>[3,2,1,1,1]
[1,3,5,7,2,6,4,8]=>[3,1,1,1,1,1]
[3,5,8,6,1,2,4,7]=>[3,1,1,1,1,1]
[3,1,6,8,2,4,7,5]=>[3,2,1,1,1]
[3,6,2,8,1,5,7,4]=>[3,2,1,1,1]
[2,6,1,3,8,4,7,5]=>[3,2,1,1,1]
[1,7,5,2,3,4,6,8]=>[3,1,1,1,1,1]
[2,7,5,1,3,8,4,6]=>[3,2,1,1,1]
[8,2,5,7,4,6,1,3]=>[4,1,1,1,1]
[8,2,1,3,7,6,4,5]=>[4,2,1,1]
[8,2,5,1,3,7,4,6]=>[3,2,1,1,1]
[8,2,7,5,3,1,6,4]=>[5,2,1]
[8,2,6,5,4,7,1,3]=>[5,1,1,1]
[7,6,5,2,4,8,1,3]=>[5,1,1,1]
[7,8,2,5,3,1,6,4]=>[4,2,1,1]
[7,1,8,6,3,2,4,5]=>[4,2,1,1]
[6,8,1,5,3,2,4,7]=>[4,1,1,1,1]
[1,6,7,5,3,2,4,8]=>[4,1,1,1,1]
[6,5,1,2,4,8,3,7]=>[4,1,1,1,1]
[7,8,1,6,4,2,3,5]=>[4,1,1,1,1]
[8,4,1,2,5,6,3,7]=>[3,2,1,1,1]
[1,7,3,6,5,2,4,8]=>[4,1,1,1,1]
[8,1,3,7,2,6,4,5]=>[4,1,1,1,1]
[7,3,2,6,5,1,8,4]=>[4,2,2]
[7,8,4,2,5,6,1,3]=>[4,1,1,1,1]
[8,2,7,4,5,6,1,3]=>[4,1,1,1,1]
[8,2,3,6,5,1,7,4]=>[4,2,1,1]
[4,8,5,6,7,3,2,1]=>[5,1,1,1]
[1,8,7,6,5,3,2,4]=>[6,1,1]
[2,8,7,6,3,4,5,1]=>[5,1,1,1]
[1,8,7,6,5,2,3,4]=>[5,1,1,1]
[7,2,8,6,5,4,1,3]=>[5,2,1]
[7,2,8,5,4,6,1,3]=>[4,2,1,1]
[6,3,2,8,5,1,7,4]=>[4,2,2]
[8,4,7,2,5,6,3,1]=>[5,1,1,1]
[6,8,5,4,3,1,7,2]=>[5,2,1]
[5,8,6,4,1,3,7,2]=>[5,1,1,1]
[4,8,6,1,5,3,7,2]=>[5,1,1,1]
[3,6,1,8,5,2,7,4]=>[3,2,2,1]
[3,4,1,2,8,6,7,5]=>[3,2,1,1,1]
[6,8,3,5,4,1,7,2]=>[4,2,1,1]
[7,2,5,8,3,6,1,4]=>[4,1,1,1,1]
[1,7,5,6,3,4,2,8]=>[4,1,1,1,1]
[7,2,6,8,5,3,1,4]=>[5,1,1,1]
[7,6,3,8,5,2,1,4]=>[5,2,1]
[7,2,6,4,8,3,1,5]=>[5,1,1,1]
[1,5,7,4,2,6,3,8]=>[3,2,1,1,1]
[4,2,3,1,7,8,5,6]=>[3,2,1,1,1]
[5,2,8,4,1,7,6,3]=>[4,2,2]
[8,6,3,4,7,2,5,1]=>[5,1,1,1]
[6,8,3,4,5,1,7,2]=>[3,2,1,1,1]
[1,6,3,2,5,8,4,7]=>[3,2,1,1,1]
[8,3,2,1,5,4,7,6]=>[4,2,2]
[6,3,7,1,5,8,4,2]=>[4,2,1,1]
[2,5,1,8,4,3,7,6]=>[3,2,2,1]
[6,2,5,4,8,1,3,7]=>[4,1,1,1,1]
[4,3,1,6,5,8,2,7]=>[3,3,1,1]
[1,3,5,4,6,8,2,7]=>[3,1,1,1,1,1]
[6,1,3,4,5,8,2,7]=>[3,1,1,1,1,1]
[8,3,4,1,5,2,7,6]=>[3,2,2,1]
[7,5,4,2,6,8,3,1]=>[5,2,1]
[8,2,6,4,1,7,3,5]=>[4,2,1,1]
[7,3,8,4,5,2,1,6]=>[4,2,1,1]
[7,2,5,1,8,4,3,6]=>[4,2,1,1]
[1,7,3,2,5,4,8,6]=>[3,2,2,1]
[8,7,2,1,5,3,4,6]=>[4,2,1,1]
[3,6,1,5,8,7,4,2]=>[4,2,1,1]
[8,3,6,4,5,1,7,2]=>[4,2,1,1]
[5,4,6,8,1,2,7,3]=>[3,2,1,1,1]
[6,4,7,2,3,5,8,1]=>[4,1,1,1,1]
[6,8,4,1,3,5,7,2]=>[4,1,1,1,1]
[3,4,7,8,6,2,5,1]=>[4,1,1,1,1]
[4,1,3,5,7,8,6,2]=>[3,2,1,1,1]
[6,5,1,8,4,7,3,2]=>[5,2,1]
[5,3,1,8,4,7,6,2]=>[4,3,1]
[8,2,7,4,6,1,3,5]=>[4,1,1,1,1]
[4,7,3,2,8,1,6,5]=>[4,2,1,1]
[6,3,1,4,7,2,8,5]=>[3,2,2,1]
[8,7,3,6,1,5,2,4]=>[5,1,1,1]
[7,4,3,6,8,2,5,1]=>[5,1,1,1]
[2,4,7,3,8,5,6,1]=>[3,2,1,1,1]
[2,8,6,1,5,7,3,4]=>[4,1,1,1,1]
[7,8,2,5,4,3,1,6]=>[5,1,1,1]
[1,8,3,4,2,7,6,5]=>[4,2,1,1]
[8,5,3,7,4,2,6,1]=>[5,2,1]
[5,7,3,2,4,1,8,6]=>[4,2,1,1]
[2,8,3,4,7,1,5,6]=>[3,1,1,1,1,1]
[4,1,3,6,7,8,2,5]=>[3,1,1,1,1,1]
[1,7,6,3,2,5,8,4]=>[4,2,1,1]
[3,8,1,5,6,2,7,4]=>[3,2,1,1,1]
[8,2,5,6,1,7,4,3]=>[4,2,1,1]
[7,1,5,2,8,6,4,3]=>[4,3,1]
[6,5,4,8,7,2,1,3]=>[5,2,1]
[1,8,6,4,5,2,7,3]=>[4,2,1,1]
[1,8,5,3,6,2,7,4]=>[4,2,1,1]
[3,6,2,1,7,5,8,4]=>[3,3,1,1]
[2,5,4,1,8,7,6,3]=>[4,3,1]
[4,7,2,6,5,8,1,3]=>[4,1,1,1,1]
[6,8,1,4,2,7,3,5]=>[3,2,1,1,1]
[6,3,4,7,1,8,2,5]=>[3,2,1,1,1]
[3,4,7,8,2,5,6,1]=>[3,1,1,1,1,1]
[1,8,2,4,5,6,7,3]=>[3,1,1,1,1,1]
[5,2,4,1,6,8,7,3]=>[3,3,1,1]
[3,2,5,7,6,1,8,4]=>[3,2,2,1]
[4,3,5,6,1,8,7,2]=>[3,3,1,1]
[5,3,4,1,7,6,8,2]=>[3,3,1,1]
[3,1,4,6,5,7,8,2]=>[3,2,1,1,1]
[1,4,7,3,5,6,8,2]=>[3,1,1,1,1,1]
[1,3,2,7,5,8,6,4]=>[3,2,2,1]
[1,4,2,5,8,3,7,6]=>[3,2,1,1,1]
[4,1,2,6,8,5,3,7]=>[3,2,1,1,1]
[1,5,2,4,8,7,6,3]=>[4,2,1,1]
[1,2,6,4,8,7,5,3]=>[4,2,1,1]
[1,2,7,4,8,6,5,3]=>[4,2,1,1]
[1,3,2,7,5,8,4,6]=>[3,2,1,1,1]
[1,3,2,8,5,7,4,6]=>[3,2,1,1,1]
[1,4,2,5,8,7,3,6]=>[3,2,1,1,1]
[1,5,2,4,8,7,3,6]=>[3,2,1,1,1]
[1,2,6,4,8,7,3,5]=>[3,2,1,1,1]
[1,2,7,8,5,6,3,4]=>[3,1,1,1,1,1]
[1,3,8,2,6,7,4,5]=>[3,1,1,1,1,1]
[1,6,7,8,2,5,3,4]=>[3,1,1,1,1,1]
[1,5,7,8,2,3,6,4]=>[3,1,1,1,1,1]
[1,5,2,7,8,4,6,3]=>[3,2,1,1,1]
[1,4,7,2,8,3,6,5]=>[3,2,1,1,1]
[1,3,6,2,4,8,7,5]=>[3,2,1,1,1]
[1,6,7,3,4,8,5,2]=>[3,2,1,1,1]
[1,5,3,7,4,8,6,2]=>[3,2,2,1]
[2,8,4,1,5,3,7,6]=>[3,2,2,1]
[3,8,4,1,5,7,2,6]=>[3,2,1,1,1]
[1,3,8,4,2,7,6,5]=>[4,2,1,1]
[1,2,7,4,8,3,6,5]=>[3,2,1,1,1]
[1,2,6,4,8,3,7,5]=>[3,2,1,1,1]
[1,5,2,4,8,3,7,6]=>[3,2,1,1,1]
[1,8,3,5,2,7,4,6]=>[3,2,1,1,1]
[1,3,8,6,2,7,4,5]=>[3,2,1,1,1]
[1,4,8,6,7,2,3,5]=>[3,1,1,1,1,1]
[1,2,6,8,5,3,7,4]=>[3,2,1,1,1]
[1,2,7,8,6,3,5,4]=>[4,1,1,1,1]
[1,6,7,8,5,2,3,4]=>[3,1,1,1,1,1]
[1,5,7,8,6,2,3,4]=>[3,1,1,1,1,1]
[1,4,7,6,8,2,3,5]=>[3,1,1,1,1,1]
[1,3,7,6,2,8,4,5]=>[3,2,1,1,1]
[2,3,8,7,4,1,6,5]=>[4,2,1,1]
[1,2,5,8,7,6,3,4]=>[4,1,1,1,1]
[1,2,7,8,6,5,3,4]=>[4,1,1,1,1]
[5,2,6,7,3,4,8,1]=>[3,2,1,1,1]
[5,2,4,7,6,3,8,1]=>[4,2,1,1]
[5,6,2,1,7,8,3,4]=>[3,2,1,1,1]
[5,6,2,1,4,8,7,3]=>[3,3,1,1]
[2,6,1,4,5,8,7,3]=>[3,2,1,1,1]
[5,4,2,7,6,3,8,1]=>[4,3,1]
[2,3,7,6,4,5,8,1]=>[4,1,1,1,1]
[2,6,1,7,5,8,3,4]=>[3,2,1,1,1]
[2,6,1,7,4,8,5,3]=>[3,2,2,1]
[5,1,2,7,8,4,3,6]=>[3,2,1,1,1]
[2,6,1,7,4,8,3,5]=>[3,2,1,1,1]
[3,6,4,1,7,8,2,5]=>[3,2,1,1,1]
[5,4,6,1,3,8,7,2]=>[4,2,1,1]
[3,6,4,1,5,8,7,2]=>[3,3,1,1]
[2,6,1,5,4,8,7,3]=>[4,2,1,1]
[2,6,1,4,7,8,5,3]=>[3,2,1,1,1]
[5,1,2,4,8,6,7,3]=>[3,2,1,1,1]
[5,1,2,4,8,7,3,6]=>[3,2,1,1,1]
[5,1,2,4,8,7,6,3]=>[4,2,1,1]
[1,2,3,8,5,4,7,6]=>[3,2,1,1,1]
[4,3,1,2,8,5,7,6]=>[3,3,1,1]
[2,1,5,3,8,6,4,7]=>[3,2,2,1]
[1,2,3,8,5,6,4,7]=>[3,1,1,1,1,1]
[1,2,3,8,6,4,5,7]=>[3,1,1,1,1,1]
[1,2,3,8,6,5,4,7]=>[4,1,1,1,1]
[1,2,3,8,5,4,6,7]=>[3,1,1,1,1,1]
[2,6,1,5,4,8,3,7]=>[4,1,1,1,1]
[5,1,2,4,8,6,3,7]=>[3,2,1,1,1]
[5,1,2,4,8,3,7,6]=>[3,2,1,1,1]
[5,6,3,1,4,8,2,7]=>[3,2,1,1,1]
[2,5,4,3,1,8,6,7]=>[4,2,1,1]
[5,4,6,3,1,8,7,2]=>[4,3,1]
[3,6,4,5,1,8,7,2]=>[3,3,1,1]
[3,6,5,4,1,8,7,2]=>[4,3,1]
[5,2,6,1,7,8,4,3]=>[3,3,1,1]
[5,1,6,2,8,7,3,4]=>[3,2,2,1]
[2,1,3,7,8,6,4,5]=>[3,2,1,1,1]
[2,1,3,7,8,5,6,4]=>[3,2,1,1,1]
[5,2,4,1,7,8,6,3]=>[3,3,1,1]
[4,3,1,2,8,6,7,5]=>[3,3,1,1]
[5,1,4,2,8,6,7,3]=>[3,3,1,1]
[2,1,3,6,8,5,7,4]=>[3,2,1,1,1]
[1,2,3,8,6,7,4,5]=>[3,1,1,1,1,1]
[1,2,3,8,7,5,4,6]=>[4,1,1,1,1]
[1,2,3,8,7,4,5,6]=>[3,1,1,1,1,1]
[1,2,3,8,5,7,4,6]=>[3,1,1,1,1,1]
[2,1,3,6,8,7,4,5]=>[3,2,1,1,1]
[5,4,1,2,8,7,6,3]=>[4,3,1]
[3,1,6,2,8,7,5,4]=>[4,2,2]
[1,8,3,4,2,5,6,7]=>[3,1,1,1,1,1]
[1,8,4,3,2,5,6,7]=>[4,1,1,1,1]
[8,4,7,6,5,3,2,1]=>[7,1]
[8,5,7,4,6,3,2,1]=>[6,1,1]
[8,5,7,3,6,4,2,1]=>[6,1,1]
[8,1,7,4,6,5,3,2]=>[6,1,1]
[8,2,7,3,6,5,4,1]=>[6,1,1]
[8,3,7,2,6,5,4,1]=>[6,1,1]
[8,5,7,2,6,4,3,1]=>[6,1,1]
[8,4,7,1,6,5,3,2]=>[6,1,1]
[8,3,7,1,6,5,4,2]=>[6,1,1]
[8,2,7,1,6,5,4,3]=>[6,1,1]
[8,1,7,2,6,5,4,3]=>[6,1,1]
[8,1,7,6,5,3,4,2]=>[6,1,1]
[8,3,7,6,5,2,4,1]=>[6,1,1]
[8,4,7,6,5,2,3,1]=>[6,1,1]
[8,5,7,6,4,2,3,1]=>[6,1,1]
[8,6,7,5,4,1,3,2]=>[6,1,1]
[8,3,7,6,5,1,4,2]=>[6,1,1]
[8,7,6,1,5,2,4,3]=>[6,1,1]
[6,8,1,3,2,5,4,7]=>[3,2,1,1,1]
[6,8,1,4,2,5,3,7]=>[3,2,1,1,1]
[7,8,3,6,1,4,2,5]=>[4,1,1,1,1]
[7,8,2,5,3,6,1,4]=>[4,1,1,1,1]
[7,8,2,5,1,4,3,6]=>[4,1,1,1,1]
[7,8,1,4,3,6,2,5]=>[4,1,1,1,1]
[5,8,1,4,3,7,2,6]=>[4,1,1,1,1]
[6,8,2,5,1,4,3,7]=>[4,1,1,1,1]
[6,8,2,5,3,7,1,4]=>[4,1,1,1,1]
[6,8,2,5,4,7,1,3]=>[4,1,1,1,1]
[2,5,4,7,6,8,1,3]=>[3,2,1,1,1]
[2,5,3,7,6,8,1,4]=>[3,2,1,1,1]
[2,5,1,4,3,7,6,8]=>[3,2,1,1,1]
[2,6,1,4,3,7,5,8]=>[3,2,1,1,1]
[2,6,5,8,1,4,3,7]=>[4,1,1,1,1]
[2,6,1,5,3,7,4,8]=>[3,2,1,1,1]
[2,6,3,7,4,8,1,5]=>[3,2,1,1,1]
[2,6,4,7,5,8,1,3]=>[3,2,1,1,1]
[5,8,3,6,4,7,1,2]=>[4,1,1,1,1]
[5,8,2,6,4,7,1,3]=>[4,1,1,1,1]
[4,8,2,6,3,7,1,5]=>[4,1,1,1,1]
[4,8,1,5,3,7,2,6]=>[4,1,1,1,1]
[4,8,1,5,2,6,3,7]=>[3,2,1,1,1]
[4,8,3,7,1,5,2,6]=>[4,1,1,1,1]
[6,8,3,7,1,4,2,5]=>[4,1,1,1,1]
[5,8,1,3,2,6,4,7]=>[3,2,1,1,1]
[5,8,4,7,1,3,2,6]=>[4,1,1,1,1]
[6,8,4,7,1,3,2,5]=>[4,1,1,1,1]
[6,8,5,7,1,3,2,4]=>[4,1,1,1,1]
[5,7,6,8,2,4,1,3]=>[4,1,1,1,1]
[4,7,6,8,1,3,2,5]=>[4,1,1,1,1]
[4,7,5,8,1,3,2,6]=>[4,1,1,1,1]
[4,7,1,3,2,6,5,8]=>[3,2,1,1,1]
[3,7,1,4,2,6,5,8]=>[3,2,1,1,1]
[3,7,5,8,1,4,2,6]=>[4,1,1,1,1]
[3,7,6,8,1,4,2,5]=>[4,1,1,1,1]
[3,7,6,8,2,5,1,4]=>[4,1,1,1,1]
[4,7,6,8,2,5,1,3]=>[4,1,1,1,1]
[4,7,5,8,3,6,1,2]=>[4,1,1,1,1]
[4,7,5,8,2,6,1,3]=>[4,1,1,1,1]
[3,7,5,8,2,6,1,4]=>[4,1,1,1,1]
[3,7,4,8,2,6,1,5]=>[4,1,1,1,1]
[3,7,4,8,1,5,2,6]=>[3,2,1,1,1]
[3,7,1,5,2,6,4,8]=>[3,2,1,1,1]
[3,7,2,6,1,5,4,8]=>[4,1,1,1,1]
[3,7,2,6,5,8,1,4]=>[4,1,1,1,1]
[4,7,3,6,5,8,1,2]=>[4,1,1,1,1]
[3,6,5,8,4,7,1,2]=>[4,1,1,1,1]
[2,6,5,8,4,7,1,3]=>[4,1,1,1,1]
[2,6,5,8,3,7,1,4]=>[4,1,1,1,1]
[2,6,3,7,1,5,4,8]=>[3,2,1,1,1]
[7,6,4,2,8,5,3,1]=>[5,3]
[7,6,4,3,8,2,5,1]=>[6,1,1]
[7,6,4,8,5,2,3,1]=>[5,2,1]
[6,8,4,3,7,2,1,5]=>[5,1,1,1]
[6,7,4,3,5,1,8,2]=>[4,2,1,1]
[6,7,3,5,4,8,2,1]=>[5,1,1,1]
[6,8,3,7,5,2,4,1]=>[5,1,1,1]
[7,6,8,3,5,2,4,1]=>[5,1,1,1]
[7,6,3,5,8,2,4,1]=>[5,1,1,1]
[7,6,3,5,2,4,8,1]=>[5,1,1,1]
[7,6,4,2,5,1,8,3]=>[5,2,1]
[7,6,2,8,4,1,5,3]=>[4,2,2]
[7,6,3,8,2,4,1,5]=>[5,1,1,1]
[7,6,3,4,8,2,5,1]=>[5,1,1,1]
[6,8,3,7,4,5,2,1]=>[5,1,1,1]
[6,7,3,5,8,4,2,1]=>[5,1,1,1]
[5,7,8,3,6,2,1,4]=>[4,1,1,1,1]
[5,8,3,6,7,2,1,4]=>[4,1,1,1,1]
[6,3,4,8,7,2,5,1]=>[4,2,1,1]
[6,3,8,4,7,2,1,5]=>[4,2,1,1]
[6,2,8,4,1,7,5,3]=>[4,2,2]
[6,2,7,4,1,5,3,8]=>[3,2,2,1]
[6,3,4,7,5,8,2,1]=>[4,2,1,1]
[6,3,5,7,8,4,2,1]=>[5,1,1,1]
[5,7,3,6,8,2,1,4]=>[4,1,1,1,1]
[5,6,8,3,7,2,1,4]=>[4,1,1,1,1]
[5,6,7,3,4,1,8,2]=>[3,2,1,1,1]
[4,6,7,8,3,5,2,1]=>[4,1,1,1,1]
[4,6,8,3,5,7,2,1]=>[4,1,1,1,1]
[4,7,3,5,6,8,2,1]=>[4,1,1,1,1]
[4,7,3,5,8,2,6,1]=>[4,1,1,1,1]
[5,3,4,7,8,2,1,6]=>[4,1,1,1,1]
[5,3,8,2,4,1,6,7]=>[4,1,1,1,1]
[5,3,4,8,2,6,1,7]=>[4,1,1,1,1]
[4,8,3,6,2,5,7,1]=>[4,1,1,1,1]
[4,8,3,5,7,2,6,1]=>[4,1,1,1,1]
[4,8,3,5,6,7,2,1]=>[4,1,1,1,1]
[4,7,8,3,5,6,2,1]=>[4,1,1,1,1]
[4,7,8,3,6,2,5,1]=>[4,1,1,1,1]
[4,8,3,6,7,2,5,1]=>[4,1,1,1,1]
[4,8,3,7,2,5,6,1]=>[4,1,1,1,1]
[5,3,4,8,2,7,6,1]=>[4,2,1,1]
[5,3,8,2,4,1,7,6]=>[4,2,1,1]
[5,2,8,4,1,7,3,6]=>[3,2,2,1]
[6,4,2,5,1,8,7,3]=>[4,3,1]
[6,4,3,5,8,2,1,7]=>[5,1,1,1]
[6,3,5,8,7,2,4,1]=>[4,2,1,1]
[5,8,3,7,2,6,4,1]=>[5,1,1,1]
[5,7,3,4,8,2,1,6]=>[4,1,1,1,1]
[5,8,4,2,3,1,6,7]=>[4,1,1,1,1]
[5,8,4,2,3,1,7,6]=>[4,2,1,1]
[6,4,5,3,8,2,1,7]=>[5,1,1,1]
[6,4,8,5,3,7,2,1]=>[5,2,1]
[6,4,3,8,5,7,2,1]=>[5,2,1]
[6,4,2,8,5,3,1,7]=>[4,3,1]
[6,4,2,7,3,1,8,5]=>[4,2,2]
[6,4,3,7,8,5,2,1]=>[5,2,1]
[6,4,5,3,7,1,8,2]=>[4,2,1,1]
[5,7,4,2,3,1,6,8]=>[4,1,1,1,1]
[5,6,3,7,1,8,2,4]=>[3,2,1,1,1]
[5,6,3,4,7,1,8,2]=>[3,2,1,1,1]
[5,6,3,4,8,2,1,7]=>[4,1,1,1,1]
[6,3,5,7,4,8,2,1]=>[5,1,1,1]
[6,3,5,4,7,8,2,1]=>[5,1,1,1]
[6,4,3,5,7,1,8,2]=>[4,2,1,1]
[6,4,2,5,1,7,3,8]=>[4,2,1,1]
[5,3,7,2,4,1,6,8]=>[4,1,1,1,1]
[5,3,4,7,2,6,1,8]=>[4,1,1,1,1]
[4,7,3,6,2,5,8,1]=>[4,1,1,1,1]
[4,7,3,6,8,2,5,1]=>[4,1,1,1,1]
[4,6,7,3,5,8,2,1]=>[4,1,1,1,1]
[4,5,7,8,3,6,2,1]=>[4,1,1,1,1]
[4,5,8,3,6,7,2,1]=>[4,1,1,1,1]
[4,5,8,3,7,2,6,1]=>[4,1,1,1,1]
[5,3,4,6,8,2,1,7]=>[4,1,1,1,1]
[5,3,6,8,2,1,4,7]=>[4,1,1,1,1]
[5,3,6,7,1,8,2,4]=>[3,2,1,1,1]
[5,3,4,6,7,1,8,2]=>[3,2,1,1,1]
[4,6,3,5,7,8,2,1]=>[4,1,1,1,1]
[4,5,7,3,6,8,2,1]=>[4,1,1,1,1]
[4,5,6,8,3,7,2,1]=>[4,1,1,1,1]
[5,7,4,8,6,3,2,1]=>[5,2,1]
[3,5,6,7,2,8,4,1]=>[3,2,1,1,1]
[1,6,2,5,3,4,8,7]=>[3,2,1,1,1]
[1,3,8,2,4,6,5,7]=>[3,1,1,1,1,1]
[1,7,2,3,6,4,8,5]=>[3,2,1,1,1]
[1,6,8,2,5,3,7,4]=>[3,2,1,1,1]
[1,8,2,5,3,4,7,6]=>[3,2,1,1,1]
[1,8,2,3,6,4,7,5]=>[3,2,1,1,1]
[1,3,5,2,8,4,7,6]=>[3,2,1,1,1]
[1,2,7,3,5,4,6,8]=>[3,1,1,1,1,1]
[1,8,2,7,3,4,6,5]=>[4,1,1,1,1]
[1,5,8,2,3,7,4,6]=>[3,1,1,1,1,1]
[1,6,8,2,3,5,4,7]=>[3,1,1,1,1,1]
[5,3,6,1,2,4,8,7]=>[3,2,1,1,1]
[7,1,5,8,4,2,3,6]=>[4,1,1,1,1]
[8,1,5,7,4,2,3,6]=>[4,1,1,1,1]
[7,1,4,5,8,2,3,6]=>[3,1,1,1,1,1]
[7,4,1,6,2,8,3,5]=>[3,2,2,1]
[8,4,1,7,2,6,3,5]=>[4,2,1,1]
[8,1,4,7,5,2,3,6]=>[4,1,1,1,1]
[8,1,5,4,7,2,3,6]=>[4,1,1,1,1]
[2,1,7,5,8,3,4,6]=>[3,2,1,1,1]
[7,1,5,4,8,2,3,6]=>[4,1,1,1,1]
[7,1,4,8,5,2,3,6]=>[3,2,1,1,1]
[6,4,1,7,2,3,8,5]=>[3,2,2,1]
[7,8,3,1,2,4,6,5]=>[3,2,1,1,1]
[8,7,1,6,4,2,3,5]=>[5,1,1,1]
[8,6,1,7,4,2,3,5]=>[4,2,1,1]
[7,6,1,8,4,2,3,5]=>[4,2,1,1]
[7,3,8,1,2,4,6,5]=>[3,2,1,1,1]
[8,3,7,1,2,4,6,5]=>[4,1,1,1,1]
[8,3,6,1,2,4,7,5]=>[3,2,1,1,1]
[8,3,7,5,1,2,4,6]=>[4,1,1,1,1]
[7,3,6,1,2,4,8,5]=>[3,2,1,1,1]
[6,7,1,8,4,2,3,5]=>[3,2,1,1,1]
[6,8,1,7,4,2,3,5]=>[4,1,1,1,1]
[7,1,8,5,4,2,3,6]=>[4,2,1,1]
[7,1,8,4,5,2,3,6]=>[3,2,1,1,1]
[2,1,7,8,5,3,4,6]=>[3,2,1,1,1]
[7,6,3,1,2,4,8,5]=>[4,2,1,1]
[6,1,2,3,8,7,5,4]=>[4,2,1,1]
[6,8,1,4,2,3,7,5]=>[3,2,1,1,1]
[6,8,3,1,2,7,4,5]=>[3,2,1,1,1]
[6,7,3,1,2,8,4,5]=>[3,2,1,1,1]
[6,7,1,4,2,3,8,5]=>[3,2,1,1,1]
[4,3,6,8,5,7,1,2]=>[3,2,1,1,1]
[6,1,2,5,4,8,3,7]=>[4,1,1,1,1]
[3,2,8,5,4,1,7,6]=>[4,2,2]
[7,8,2,1,4,6,3,5]=>[3,2,1,1,1]
[7,2,1,5,8,3,4,6]=>[3,2,1,1,1]
[2,4,8,5,1,3,6,7]=>[3,1,1,1,1,1]
[3,5,6,1,8,4,2,7]=>[3,2,1,1,1]
[1,3,6,8,7,4,2,5]=>[4,1,1,1,1]
[1,2,8,5,7,3,4,6]=>[3,1,1,1,1,1]
[2,6,1,5,8,3,4,7]=>[3,1,1,1,1,1]
[5,7,1,6,8,4,3,2]=>[5,1,1,1]
[4,8,1,2,5,7,3,6]=>[3,1,1,1,1,1]
[8,4,6,2,5,7,3,1]=>[5,1,1,1]
[8,3,6,4,7,2,5,1]=>[5,1,1,1]
[3,8,1,4,7,2,5,6]=>[3,1,1,1,1,1]
[1,7,8,4,6,2,5,3]=>[4,1,1,1,1]
[3,7,4,8,5,1,6,2]=>[3,2,2,1]
[3,7,1,6,5,4,8,2]=>[5,1,1,1]
[2,7,3,1,5,8,4,6]=>[3,2,1,1,1]
[2,7,4,6,8,1,3,5]=>[3,1,1,1,1,1]
[2,7,5,8,6,4,1,3]=>[4,2,1,1]
[8,2,6,7,5,4,3,1]=>[6,1,1]
[3,8,7,1,6,4,5,2]=>[5,1,1,1]
[3,6,8,2,7,4,1,5]=>[4,1,1,1,1]
[1,5,2,8,7,4,6,3]=>[4,2,1,1]
[3,4,2,7,8,1,6,5]=>[3,2,1,1,1]
[4,1,3,7,5,6,8,2]=>[3,2,1,1,1]
[6,3,8,1,7,4,2,5]=>[4,2,1,1]
[6,5,8,7,1,4,2,3]=>[4,2,1,1]
[4,1,7,3,8,5,2,6]=>[3,2,2,1]
[3,6,1,4,5,8,2,7]=>[3,1,1,1,1,1]
[1,6,7,4,5,3,8,2]=>[4,1,1,1,1]
[6,1,7,3,5,4,8,2]=>[4,2,1,1]
[6,3,1,2,5,8,4,7]=>[3,2,1,1,1]
[1,4,7,2,8,5,3,6]=>[3,2,1,1,1]
[5,6,8,7,2,4,1,3]=>[4,1,1,1,1]
[6,8,5,7,1,2,4,3]=>[4,1,1,1,1]
[2,8,4,1,7,5,6,3]=>[4,2,1,1]
[8,2,4,3,7,5,6,1]=>[4,2,1,1]
[6,8,2,1,5,7,3,4]=>[3,2,1,1,1]
[7,2,8,4,1,6,3,5]=>[3,2,2,1]
[1,2,4,8,6,5,3,7]=>[4,1,1,1,1]
[7,1,5,6,8,4,3,2]=>[5,1,1,1]
[2,7,8,1,4,6,3,5]=>[3,1,1,1,1,1]
[4,8,2,5,7,1,6,3]=>[4,1,1,1,1]
[4,1,6,8,5,3,7,2]=>[4,2,1,1]
[5,2,6,4,8,3,1,7]=>[4,2,1,1]
[6,7,1,3,4,5,8,2]=>[3,1,1,1,1,1]
[1,7,3,2,4,8,5,6]=>[3,2,1,1,1]
[1,3,6,5,2,8,4,7]=>[3,2,1,1,1]
[7,1,6,5,3,4,8,2]=>[5,1,1,1]
[6,3,4,2,8,7,5,1]=>[4,3,1]
[4,3,8,7,5,2,6,1]=>[5,2,1]
[6,8,7,4,2,3,5,1]=>[5,1,1,1]
[3,6,4,5,2,8,7,1]=>[4,2,1,1]
[8,6,1,3,5,4,2,7]=>[5,1,1,1]
[5,3,8,6,1,2,4,7]=>[3,2,1,1,1]
[2,5,6,3,4,8,7,1]=>[3,2,1,1,1]
[2,5,3,6,8,7,4,1]=>[4,2,1,1]
[4,8,7,3,5,2,6,1]=>[5,1,1,1]
[3,8,7,2,6,4,5,1]=>[5,1,1,1]
[6,3,5,4,8,7,2,1]=>[5,2,1]
[4,3,8,6,1,5,2,7]=>[4,2,1,1]
[4,7,6,2,5,3,8,1]=>[5,1,1,1]
[7,5,2,6,8,1,4,3]=>[4,2,1,1]
[8,5,2,7,1,4,3,6]=>[4,2,1,1]
[1,8,5,3,6,2,4,7]=>[4,1,1,1,1]
[5,1,7,2,4,3,8,6]=>[3,2,2,1]
[1,5,3,4,8,6,2,7]=>[3,2,1,1,1]
[5,4,1,3,8,6,2,7]=>[4,2,1,1]
[5,1,8,6,3,4,2,7]=>[4,2,1,1]
[4,5,2,8,3,7,6,1]=>[4,2,1,1]
[8,2,3,7,6,4,5,1]=>[5,1,1,1]
[5,8,2,4,7,6,3,1]=>[5,1,1,1]
[6,8,2,5,3,4,7,1]=>[4,1,1,1,1]
[7,2,5,6,4,8,1,3]=>[4,1,1,1,1]
[1,6,7,4,8,2,3,5]=>[3,1,1,1,1,1]
[7,1,3,5,8,2,6,4]=>[3,2,1,1,1]
[8,2,1,3,5,6,7,4]=>[3,2,1,1,1]
[6,3,1,4,7,5,8,2]=>[3,3,1,1]
[4,1,3,8,2,6,7,5]=>[3,2,1,1,1]
[2,8,3,6,7,5,4,1]=>[5,1,1,1]
[3,1,7,2,8,5,4,6]=>[3,2,2,1]
[3,6,1,4,7,2,8,5]=>[3,2,1,1,1]
[1,5,8,4,7,2,3,6]=>[3,1,1,1,1,1]
[7,1,3,6,2,8,4,5]=>[3,2,1,1,1]
[6,2,7,4,5,8,1,3]=>[3,2,1,1,1]
[2,1,8,4,5,7,3,6]=>[3,2,1,1,1]
[1,8,5,7,3,2,4,6]=>[4,1,1,1,1]
[2,1,8,5,4,3,6,7]=>[4,2,1,1]
[2,7,4,1,5,3,8,6]=>[3,2,2,1]
[7,4,8,6,2,3,1,5]=>[4,2,1,1]
[2,7,1,4,6,3,8,5]=>[3,2,1,1,1]
[4,7,5,6,8,1,3,2]=>[4,1,1,1,1]
[7,1,3,2,8,5,4,6]=>[3,3,1,1]
[2,8,5,4,1,3,6,7]=>[4,1,1,1,1]
[5,1,7,4,2,3,8,6]=>[3,2,2,1]
[3,8,6,5,1,4,2,7]=>[5,1,1,1]
[1,3,4,8,6,5,2,7]=>[4,1,1,1,1]
[4,1,8,6,5,3,2,7]=>[5,2,1]
[4,8,5,2,7,3,6,1]=>[4,2,1,1]
[7,2,8,5,3,6,4,1]=>[4,2,2]
[5,2,8,4,3,7,6,1]=>[4,2,2]
[8,4,7,5,2,3,6,1]=>[5,1,1,1]
[7,5,2,8,4,6,1,3]=>[4,2,1,1]
[5,7,4,3,6,2,8,1]=>[5,1,1,1]
[6,7,5,1,2,8,3,4]=>[3,2,1,1,1]
[5,2,6,8,3,4,7,1]=>[3,2,1,1,1]
[7,6,2,4,5,8,3,1]=>[5,1,1,1]
[3,6,8,4,7,2,5,1]=>[4,1,1,1,1]
[7,6,3,8,4,2,5,1]=>[5,2,1]
[2,6,3,8,4,7,5,1]=>[4,2,1,1]
[7,2,3,6,5,8,4,1]=>[5,1,1,1]
[6,2,7,5,8,3,1,4]=>[4,2,1,1]
[2,8,3,6,4,5,7,1]=>[4,1,1,1,1]
[2,1,5,6,8,3,7,4]=>[3,2,1,1,1]
[5,8,1,2,6,4,7,3]=>[4,1,1,1,1]
[1,6,8,3,2,7,4,5]=>[3,2,1,1,1]
[6,5,7,2,8,4,1,3]=>[4,2,1,1]
[7,5,1,2,8,4,6,3]=>[4,2,1,1]
[5,4,8,3,6,2,7,1]=>[5,1,1,1]
[5,8,2,7,4,3,6,1]=>[5,1,1,1]
[6,4,5,8,2,7,3,1]=>[4,2,1,1]
[5,7,3,6,4,8,2,1]=>[5,1,1,1]
[1,5,6,4,8,2,7,3]=>[3,2,1,1,1]
[3,1,5,6,4,8,7,2]=>[3,2,2,1]
[1,3,6,2,5,7,8,4]=>[3,1,1,1,1,1]
[1,4,6,3,5,7,8,2]=>[3,1,1,1,1,1]
[3,5,1,6,4,7,8,2]=>[3,2,1,1,1]
[3,6,1,4,2,7,8,5]=>[3,2,1,1,1]
[2,4,6,3,1,7,8,5]=>[3,2,1,1,1]
[1,3,6,5,2,7,8,4]=>[3,2,1,1,1]
[1,2,6,4,3,8,5,7]=>[3,2,1,1,1]
[1,2,6,3,5,8,7,4]=>[3,2,1,1,1]
[2,3,5,1,8,4,7,6]=>[3,2,1,1,1]
[2,3,6,1,8,5,4,7]=>[3,2,1,1,1]
[1,2,7,4,6,8,3,5]=>[3,1,1,1,1,1]
[2,3,7,5,1,8,4,6]=>[3,2,1,1,1]
[4,7,2,5,3,8,6,1]=>[4,2,1,1]
[3,1,7,5,4,8,6,2]=>[4,2,2]
[1,2,7,6,4,8,5,3]=>[4,2,1,1]
[1,2,7,3,6,8,5,4]=>[4,1,1,1,1]
[2,3,6,1,8,5,7,4]=>[3,2,1,1,1]
[3,1,5,4,8,7,6,2]=>[4,2,2]
[1,2,5,8,4,7,3,6]=>[3,1,1,1,1,1]
[1,2,6,8,5,4,7,3]=>[4,1,1,1,1]
[1,3,6,8,5,2,7,4]=>[3,2,1,1,1]
[3,5,7,4,8,2,1,6]=>[4,1,1,1,1]
[2,4,7,6,8,3,1,5]=>[4,1,1,1,1]
[1,4,6,8,3,5,2,7]=>[3,1,1,1,1,1]
[1,3,6,8,5,2,4,7]=>[3,1,1,1,1,1]
[1,2,6,8,5,4,3,7]=>[4,1,1,1,1]
[1,2,5,8,4,3,7,6]=>[3,2,1,1,1]
[1,3,5,8,2,4,7,6]=>[3,1,1,1,1,1]
[1,3,6,8,2,5,4,7]=>[3,1,1,1,1,1]
[1,4,6,8,3,2,5,7]=>[3,1,1,1,1,1]
[3,5,7,4,8,1,2,6]=>[3,1,1,1,1,1]
[4,6,1,7,5,8,2,3]=>[3,2,1,1,1]
[2,3,6,7,5,8,1,4]=>[3,1,1,1,1,1]
[1,3,7,5,6,8,2,4]=>[3,1,1,1,1,1]
[2,3,6,5,8,1,7,4]=>[3,2,1,1,1]
[3,4,6,2,8,1,7,5]=>[3,2,1,1,1]
[3,5,4,6,8,2,1,7]=>[4,1,1,1,1]
[3,5,4,6,8,1,2,7]=>[3,1,1,1,1,1]
[1,2,4,7,5,8,3,6]=>[3,1,1,1,1,1]
[1,2,6,7,4,8,3,5]=>[3,1,1,1,1,1]
[3,6,4,7,1,8,5,2]=>[3,3,1,1]
[1,2,6,7,3,8,5,4]=>[3,2,1,1,1]
[1,2,5,7,3,8,6,4]=>[3,2,1,1,1]
[3,1,5,7,6,8,4,2]=>[4,2,1,1]
[3,5,4,6,8,2,7,1]=>[4,1,1,1,1]
[4,2,6,1,8,7,5,3]=>[4,3,1]
[3,1,6,5,8,7,4,2]=>[4,2,2]
[2,3,6,5,8,7,1,4]=>[3,2,1,1,1]
[1,2,7,4,6,8,5,3]=>[4,1,1,1,1]
[1,2,7,5,6,8,4,3]=>[4,1,1,1,1]
[3,1,6,7,5,8,4,2]=>[4,2,1,1]
[4,6,2,7,5,8,3,1]=>[4,2,1,1]
[3,5,7,4,8,2,6,1]=>[4,1,1,1,1]
[2,4,7,6,8,3,5,1]=>[4,1,1,1,1]
[1,4,6,8,3,5,7,2]=>[3,1,1,1,1,1]
[1,3,6,8,2,5,7,4]=>[3,1,1,1,1,1]
[1,3,5,8,2,7,4,6]=>[3,1,1,1,1,1]
[1,2,5,8,4,7,6,3]=>[4,1,1,1,1]
[1,2,4,8,7,3,6,5]=>[4,1,1,1,1]
[1,2,5,8,7,4,3,6]=>[4,1,1,1,1]
[1,3,5,8,7,2,4,6]=>[3,1,1,1,1,1]
[2,3,7,6,8,5,1,4]=>[4,1,1,1,1]
[5,7,1,2,8,6,4,3]=>[4,2,1,1]
[3,1,7,6,8,5,4,2]=>[5,2,1]
[1,2,6,8,5,7,4,3]=>[4,1,1,1,1]
[1,2,5,8,7,4,6,3]=>[4,1,1,1,1]
[1,2,4,8,7,6,3,5]=>[4,1,1,1,1]
[6,4,5,7,2,8,1,3]=>[4,1,1,1,1]
[5,3,4,7,2,8,1,6]=>[4,1,1,1,1]
[3,2,7,4,6,8,1,5]=>[3,2,1,1,1]
[5,3,6,2,7,1,4,8]=>[4,1,1,1,1]
[2,6,3,4,7,1,5,8]=>[3,1,1,1,1,1]
[2,7,3,4,5,8,1,6]=>[3,1,1,1,1,1]
[3,7,4,5,6,8,1,2]=>[3,1,1,1,1,1]
[2,5,7,3,6,8,1,4]=>[3,1,1,1,1,1]
[4,7,6,2,3,8,1,5]=>[4,1,1,1,1]
[7,3,5,2,4,8,1,6]=>[4,1,1,1,1]
[7,6,2,4,5,8,1,3]=>[4,1,1,1,1]
[6,5,2,3,4,8,1,7]=>[4,1,1,1,1]
[5,3,1,2,8,4,7,6]=>[3,3,1,1]
[6,5,2,3,7,1,4,8]=>[4,1,1,1,1]
[5,2,1,7,3,4,6,8]=>[3,2,1,1,1]
[5,2,1,8,3,4,6,7]=>[3,2,1,1,1]
[6,3,2,8,4,5,7,1]=>[4,2,1,1]
[7,3,1,2,8,4,6,5]=>[3,3,1,1]
[6,4,1,3,8,5,7,2]=>[4,2,1,1]
[6,2,3,1,8,4,7,5]=>[3,3,1,1]
[8,3,5,2,7,1,4,6]=>[4,1,1,1,1]
[8,6,2,4,7,1,5,3]=>[4,2,1,1]
[8,5,2,3,6,1,4,7]=>[4,1,1,1,1]
[8,2,1,7,3,4,5,6]=>[3,2,1,1,1]
[8,6,3,7,2,4,5,1]=>[5,1,1,1]
[7,1,6,2,3,4,5,8]=>[3,1,1,1,1,1]
[8,2,7,3,4,5,6,1]=>[4,1,1,1,1]
[8,1,6,2,3,4,5,7]=>[3,1,1,1,1,1]
[8,1,7,3,4,5,6,2]=>[4,1,1,1,1]
[8,6,1,7,2,4,5,3]=>[4,2,1,1]
[8,1,5,7,2,3,6,4]=>[4,1,1,1,1]
[1,7,5,8,2,3,6,4]=>[3,2,1,1,1]
[7,2,1,8,3,4,5,6]=>[3,2,1,1,1]
[7,3,8,2,4,5,6,1]=>[4,1,1,1,1]
[7,2,8,3,4,5,6,1]=>[3,2,1,1,1]
[1,7,8,3,4,5,6,2]=>[3,1,1,1,1,1]
[1,4,5,8,3,6,7,2]=>[3,1,1,1,1,1]
[2,5,7,1,8,3,6,4]=>[3,2,1,1,1]
[6,2,7,1,8,4,5,3]=>[3,3,1,1]
[4,7,1,3,8,5,6,2]=>[3,2,1,1,1]
[1,6,2,8,4,5,7,3]=>[3,2,1,1,1]
[4,1,3,6,8,2,7,5]=>[3,2,1,1,1]
[5,3,4,6,8,2,7,1]=>[4,1,1,1,1]
[4,6,3,8,7,1,2,5]=>[3,2,1,1,1]
[6,4,5,8,7,1,2,3]=>[3,2,1,1,1]
[5,3,4,8,7,1,2,6]=>[3,2,1,1,1]
[3,2,8,7,1,4,6,5]=>[4,2,1,1]
[3,1,8,7,2,4,6,5]=>[4,2,1,1]
[5,3,7,6,1,2,4,8]=>[3,2,1,1,1]
[1,8,3,7,2,4,5,6]=>[3,1,1,1,1,1]
[3,8,1,7,2,4,5,6]=>[3,1,1,1,1,1]
[6,8,2,3,5,1,4,7]=>[3,1,1,1,1,1]
[4,7,8,2,6,1,3,5]=>[3,1,1,1,1,1]
[6,2,8,7,1,4,5,3]=>[4,2,1,1]
[3,8,7,1,4,5,6,2]=>[4,1,1,1,1]
[2,8,6,1,3,4,5,7]=>[3,1,1,1,1,1]
[2,7,6,1,3,4,5,8]=>[3,1,1,1,1,1]
[1,7,6,2,3,4,5,8]=>[3,1,1,1,1,1]
[1,8,6,2,3,4,5,7]=>[3,1,1,1,1,1]
[2,8,7,3,4,5,6,1]=>[4,1,1,1,1]
[3,8,7,2,4,5,6,1]=>[4,1,1,1,1]
[7,8,3,6,2,4,5,1]=>[4,1,1,1,1]
[1,5,8,7,2,3,6,4]=>[4,1,1,1,1]
[8,7,6,1,3,4,5,2]=>[5,1,1,1]
[3,4,7,2,5,1,8,6]=>[3,2,1,1,1]
[2,1,6,4,8,5,3,7]=>[3,2,2,1]
[1,2,8,3,7,5,4,6]=>[4,1,1,1,1]
[1,6,3,8,7,4,2,5]=>[4,2,1,1]
[4,3,8,1,2,6,7,5]=>[3,2,1,1,1]
[3,6,8,7,1,2,5,4]=>[4,1,1,1,1]
[6,2,8,5,4,7,1,3]=>[4,2,1,1]
[6,5,7,2,4,8,1,3]=>[4,1,1,1,1]
[3,4,1,6,5,8,7,2]=>[3,2,2,1]
[3,5,1,2,4,8,7,6]=>[3,2,1,1,1]
[3,7,5,2,1,4,6,8]=>[4,1,1,1,1]
[3,8,5,2,7,4,1,6]=>[4,2,1,1]
[5,2,8,4,7,3,1,6]=>[4,2,1,1]
[5,2,7,4,1,3,6,8]=>[3,2,1,1,1]
[4,3,5,1,2,8,7,6]=>[3,3,1,1]
[3,1,4,6,2,8,7,5]=>[3,2,2,1]
[1,4,6,5,2,8,7,3]=>[3,3,1,1]
[3,4,5,6,1,8,7,2]=>[3,2,1,1,1]
[3,4,5,8,7,2,1,6]=>[4,1,1,1,1]
[1,4,7,2,6,3,5,8]=>[3,1,1,1,1,1]
[8,4,7,5,2,1,6,3]=>[5,2,1]
[8,1,4,7,2,3,6,5]=>[4,1,1,1,1]
[1,8,5,7,3,4,6,2]=>[4,1,1,1,1]
[6,3,5,1,7,4,2,8]=>[4,2,1,1]
[6,1,4,8,7,3,2,5]=>[4,2,1,1]
[6,4,8,5,7,1,2,3]=>[3,2,1,1,1]
[5,4,8,1,6,3,2,7]=>[4,2,1,1]
[1,4,8,6,3,7,2,5]=>[4,1,1,1,1]
[5,4,7,6,3,8,1,2]=>[4,2,1,1]
[4,6,3,7,5,8,1,2]=>[3,2,1,1,1]
[4,1,3,5,8,6,2,7]=>[3,2,1,1,1]
[5,7,4,3,8,1,2,6]=>[4,1,1,1,1]
[1,4,8,3,7,6,5,2]=>[5,1,1,1]
[4,3,8,2,1,6,5,7]=>[4,2,1,1]
[3,8,4,2,7,1,5,6]=>[4,1,1,1,1]
[3,1,2,5,7,6,4,8]=>[3,2,1,1,1]
[1,8,2,7,6,5,4,3]=>[6,1,1]
[3,8,1,6,7,5,4,2]=>[5,1,1,1]
[3,7,2,6,8,5,1,4]=>[4,1,1,1,1]
[7,2,3,8,5,6,1,4]=>[3,2,1,1,1]
[8,2,1,7,5,6,4,3]=>[5,2,1]
[8,1,3,6,5,7,4,2]=>[5,1,1,1]
[8,2,4,3,6,1,5,7]=>[4,1,1,1,1]
[1,7,8,5,4,3,6,2]=>[5,1,1,1]
[1,8,4,5,3,2,6,7]=>[4,1,1,1,1]
[7,8,5,4,3,1,6,2]=>[5,2,1]
[7,1,6,3,4,2,5,8]=>[4,1,1,1,1]
[6,8,7,1,4,2,5,3]=>[4,2,1,1]
[3,6,1,4,2,7,5,8]=>[3,2,1,1,1]
[3,4,1,8,5,7,6,2]=>[4,2,1,1]
[3,6,5,1,2,8,4,7]=>[3,2,1,1,1]
[3,8,5,6,7,2,1,4]=>[4,1,1,1,1]
[8,1,7,6,2,4,3,5]=>[5,1,1,1]
[8,5,6,1,4,2,3,7]=>[4,1,1,1,1]
[8,6,5,4,7,1,3,2]=>[6,1,1]
[1,6,4,5,7,2,3,8]=>[3,1,1,1,1,1]
[8,3,6,1,7,2,4,5]=>[3,2,1,1,1]
[1,8,6,5,7,3,4,2]=>[5,1,1,1]
[1,7,5,3,6,8,4,2]=>[4,2,1,1]
[7,4,1,6,5,8,3,2]=>[5,2,1]
[4,1,5,8,7,6,3,2]=>[5,2,1]
[1,2,5,8,6,7,3,4]=>[3,1,1,1,1,1]
[4,2,1,5,8,7,3,6]=>[3,3,1,1]
[5,2,4,6,1,7,3,8]=>[3,2,1,1,1]
[1,5,3,6,8,7,4,2]=>[4,2,1,1]
[3,5,4,6,1,8,2,7]=>[3,2,1,1,1]
[3,1,5,7,6,8,2,4]=>[3,2,1,1,1]
[1,4,5,6,8,7,2,3]=>[3,1,1,1,1,1]
[1,4,6,3,7,2,8,5]=>[3,2,1,1,1]
[1,7,3,6,5,2,8,4]=>[4,2,1,1]
[8,6,2,5,4,1,7,3]=>[5,2,1]
[3,7,2,6,5,4,1,8]=>[5,1,1,1]
[7,6,2,5,4,3,1,8]=>[6,1,1]
[3,2,6,4,7,5,1,8]=>[3,2,2,1]
[6,2,3,7,5,4,1,8]=>[4,2,1,1]
[1,3,4,7,6,2,8,5]=>[3,2,1,1,1]
[8,7,2,5,1,6,4,3]=>[5,2,1]
[7,8,2,5,4,1,6,3]=>[4,2,1,1]
[4,5,1,3,7,2,8,6]=>[3,2,1,1,1]
[6,1,3,7,5,2,8,4]=>[3,2,2,1]
[8,1,3,6,2,7,5,4]=>[4,2,1,1]
[1,2,4,7,3,8,6,5]=>[3,2,1,1,1]
[7,1,8,2,6,5,4,3]=>[5,2,1]
[3,1,8,6,2,7,5,4]=>[4,2,2]
[5,6,1,8,2,7,4,3]=>[4,2,1,1]
[4,2,7,8,1,6,5,3]=>[4,2,1,1]
[3,2,8,6,1,7,5,4]=>[4,2,2]
[7,2,8,1,6,5,4,3]=>[5,2,1]
[1,8,7,2,6,5,4,3]=>[6,1,1]
[2,8,7,1,6,5,4,3]=>[6,1,1]
[3,8,7,1,6,5,4,2]=>[6,1,1]
[4,8,7,5,1,6,3,2]=>[5,2,1]
[6,7,8,5,1,4,3,2]=>[5,1,1,1]
[5,6,3,8,4,1,7,2]=>[3,2,2,1]
[7,3,8,5,4,1,6,2]=>[4,2,2]
[3,4,8,6,5,1,7,2]=>[4,2,1,1]
[3,4,6,5,1,2,8,7]=>[3,2,1,1,1]
[1,4,6,2,3,8,7,5]=>[3,2,1,1,1]
[1,3,2,7,4,8,6,5]=>[3,2,2,1]
[2,3,1,7,6,4,8,5]=>[3,2,2,1]
[4,5,2,1,7,3,8,6]=>[3,2,2,1]
[5,6,7,1,2,8,4,3]=>[3,2,1,1,1]
[7,6,1,2,8,5,4,3]=>[5,2,1]
[2,7,1,3,8,6,5,4]=>[4,2,1,1]
[8,6,1,2,7,5,4,3]=>[5,2,1]
[1,7,2,3,8,6,5,4]=>[4,2,1,1]
[8,7,1,2,6,5,4,3]=>[6,1,1]
[7,8,1,2,6,5,4,3]=>[5,1,1,1]
[3,8,1,6,2,7,5,4]=>[4,2,1,1]
[5,6,8,1,2,7,4,3]=>[4,1,1,1,1]
[2,1,3,7,4,8,6,5]=>[3,2,2,1]
[4,2,7,3,6,8,1,5]=>[3,2,1,1,1]
[5,3,6,4,2,8,1,7]=>[4,2,1,1]
[4,1,5,3,8,2,7,6]=>[3,2,2,1]
[5,2,6,4,7,3,1,8]=>[4,2,1,1]
[2,6,3,4,7,5,1,8]=>[3,2,1,1,1]
[2,6,3,5,4,8,1,7]=>[4,1,1,1,1]
[2,7,4,3,5,8,1,6]=>[4,1,1,1,1]
[7,3,6,4,2,8,1,5]=>[5,1,1,1]
[7,6,4,5,2,8,1,3]=>[5,1,1,1]
[5,4,3,1,8,2,7,6]=>[4,3,1]
[6,5,4,2,7,3,1,8]=>[5,2,1]
[5,4,1,7,2,6,3,8]=>[3,3,1,1]
[5,4,1,8,3,2,6,7]=>[4,2,1,1]
[6,5,2,8,3,4,7,1]=>[4,2,1,1]
[7,4,2,1,8,3,6,5]=>[4,3,1]
[6,5,3,4,8,2,7,1]=>[5,1,1,1]
[6,1,5,3,8,2,7,4]=>[4,2,1,1]
[4,6,3,1,8,2,7,5]=>[3,3,1,1]
[5,8,4,2,7,3,1,6]=>[4,2,1,1]
[8,2,6,4,7,3,1,5]=>[5,1,1,1]
[8,6,2,5,7,4,1,3]=>[5,1,1,1]
[8,5,3,2,6,4,1,7]=>[5,2,1]
[8,3,1,7,2,5,4,6]=>[4,2,1,1]
[7,5,2,6,4,3,1,8]=>[5,2,1]
[7,1,6,2,5,4,3,8]=>[5,1,1,1]
[8,1,7,3,5,6,4,2]=>[5,1,1,1]
[8,6,1,7,4,5,2,3]=>[4,2,1,1]
[8,1,3,7,2,6,5,4]=>[5,1,1,1]
[1,7,6,8,3,2,4,5]=>[4,1,1,1,1]
[7,1,5,8,4,2,6,3]=>[4,2,1,1]
[7,3,8,4,5,2,6,1]=>[4,2,1,1]
[7,2,8,5,3,4,6,1]=>[4,2,1,1]
[6,1,8,4,3,2,5,7]=>[4,2,1,1]
[6,1,7,4,2,5,3,8]=>[3,2,2,1]
[1,2,7,3,4,6,5,8]=>[3,1,1,1,1,1]
[1,7,8,4,3,5,6,2]=>[4,1,1,1,1]
[1,6,2,8,3,5,7,4]=>[3,2,1,1,1]
[2,6,1,7,3,5,4,8]=>[3,2,1,1,1]
[3,1,5,8,4,2,6,7]=>[3,2,1,1,1]
[4,3,1,6,8,2,7,5]=>[3,3,1,1]
[5,7,4,8,3,2,1,6]=>[5,1,1,1]
[5,4,8,2,7,3,1,6]=>[4,2,1,1]
[5,2,8,7,3,4,1,6]=>[4,2,1,1]
[6,4,7,5,3,2,1,8]=>[5,2,1]
[1,8,3,7,6,2,4,5]=>[4,1,1,1,1]
[5,8,3,2,6,4,1,7]=>[4,2,1,1]
[6,8,2,4,7,5,1,3]=>[4,1,1,1,1]
[7,3,8,2,6,4,1,5]=>[4,2,1,1]
[4,6,8,2,7,3,1,5]=>[4,1,1,1,1]
[2,6,8,7,3,4,1,5]=>[4,1,1,1,1]
[7,2,8,6,3,5,1,4]=>[4,2,1,1]
[6,8,1,7,2,5,4,3]=>[5,1,1,1]
[3,8,7,4,5,6,1,2]=>[4,1,1,1,1]
[2,8,6,4,3,5,1,7]=>[5,1,1,1]
[2,7,6,3,5,4,1,8]=>[5,1,1,1]
[1,7,6,5,2,4,3,8]=>[5,1,1,1]
[1,8,6,5,3,2,4,7]=>[5,1,1,1]
[3,8,7,4,6,2,5,1]=>[5,1,1,1]
[5,8,3,7,6,2,4,1]=>[5,1,1,1]
[7,1,8,6,5,2,3,4]=>[4,2,1,1]
[8,4,7,5,3,2,1,6]=>[6,1,1]
[8,7,2,5,4,3,1,6]=>[6,1,1]
[6,8,3,2,5,4,7,1]=>[4,2,1,1]
[6,8,4,5,2,3,7,1]=>[4,1,1,1,1]
[1,5,7,8,4,3,6,2]=>[4,1,1,1,1]
[6,3,8,1,5,4,7,2]=>[4,2,1,1]
[6,2,1,8,5,4,7,3]=>[4,3,1]
[2,6,3,1,7,5,4,8]=>[3,3,1,1]
[2,6,5,7,4,1,3,8]=>[4,1,1,1,1]
[2,5,6,8,4,3,7,1]=>[4,1,1,1,1]
[2,4,7,5,8,1,6,3]=>[3,2,1,1,1]
[2,5,4,7,1,8,6,3]=>[3,3,1,1]
[5,2,1,8,7,6,4,3]=>[5,3]
[4,8,5,7,6,1,3,2]=>[5,1,1,1]
[4,8,6,7,5,3,1,2]=>[5,1,1,1]
[4,8,7,5,6,2,3,1]=>[5,1,1,1]
[6,5,4,8,2,1,7,3]=>[5,2,1]
[5,8,4,7,2,6,3,1]=>[5,1,1,1]
[1,5,7,4,8,2,6,3]=>[3,2,1,1,1]
[1,5,7,3,2,8,6,4]=>[3,3,1,1]
[5,8,3,2,7,6,4,1]=>[5,2,1]
[5,2,1,4,3,6,7,8]=>[3,2,1,1,1]
[3,5,7,4,2,6,1,8]=>[4,1,1,1,1]
[3,6,4,5,1,2,7,8]=>[3,1,1,1,1,1]
[4,2,1,6,5,3,7,8]=>[3,3,1,1]
[4,2,1,5,7,6,3,8]=>[3,3,1,1]
[4,3,5,1,7,6,2,8]=>[3,3,1,1]
[3,5,4,7,1,6,2,8]=>[3,2,1,1,1]
[3,4,7,5,6,1,2,8]=>[3,1,1,1,1,1]
[3,4,5,8,6,7,1,2]=>[3,1,1,1,1,1]
[3,5,4,6,1,8,7,2]=>[3,3,1,1]
[4,3,5,1,6,8,7,2]=>[3,3,1,1]
[4,2,1,5,6,8,7,3]=>[3,3,1,1]
[2,1,7,3,8,4,6,5]=>[3,2,2,1]
[4,1,8,2,7,3,6,5]=>[4,2,1,1]
[4,1,7,2,8,3,6,5]=>[3,2,2,1]
[7,1,3,2,8,4,6,5]=>[3,3,1,1]
[7,1,8,2,4,3,6,5]=>[3,2,2,1]
[8,1,7,2,5,3,6,4]=>[4,2,1,1]
[7,1,5,2,8,3,6,4]=>[3,3,1,1]
[5,1,7,2,8,3,6,4]=>[3,2,2,1]
[5,1,8,2,7,3,6,4]=>[4,2,1,1]
[5,1,8,2,4,3,7,6]=>[3,2,2,1]
[8,1,6,2,4,3,7,5]=>[4,2,1,1]
[6,1,8,2,4,3,7,5]=>[3,2,2,1]
[6,1,8,2,5,3,7,4]=>[3,2,2,1]
[8,1,6,2,5,3,7,4]=>[4,2,1,1]
[8,1,6,2,7,3,5,4]=>[4,2,1,1]
[6,1,8,2,7,3,5,4]=>[4,2,1,1]
[6,1,7,2,8,3,5,4]=>[3,2,2,1]
[6,1,7,2,5,3,8,4]=>[3,2,2,1]
[6,1,7,2,4,3,8,5]=>[3,2,2,1]
[5,1,6,2,4,3,8,7]=>[3,2,2,1]
[7,1,5,2,4,3,8,6]=>[4,2,1,1]
[7,1,6,2,4,3,8,5]=>[4,2,1,1]
[7,1,6,2,5,3,8,4]=>[4,2,1,1]
[7,1,6,2,8,3,5,4]=>[4,2,1,1]
[7,1,8,2,6,3,5,4]=>[4,2,1,1]
[1,8,2,7,5,4,6,3]=>[5,1,1,1]
[1,8,2,7,4,3,5,6]=>[4,1,1,1,1]
[1,8,6,4,7,2,3,5]=>[4,1,1,1,1]
[1,8,4,2,6,3,5,7]=>[3,2,1,1,1]
[7,4,8,1,5,2,3,6]=>[3,2,1,1,1]
[4,1,7,2,6,3,5,8]=>[3,2,1,1,1]
[5,1,7,4,3,6,2,8]=>[4,2,1,1]
[7,5,8,3,2,4,1,6]=>[5,1,1,1]
[1,8,5,4,3,6,2,7]=>[5,1,1,1]
[1,8,5,4,3,7,2,6]=>[5,1,1,1]
[1,8,5,4,7,2,6,3]=>[4,2,1,1]
[1,8,4,2,5,3,7,6]=>[3,2,2,1]
[1,8,5,4,2,6,7,3]=>[4,2,1,1]
[7,4,8,2,1,3,5,6]=>[4,1,1,1,1]
[4,1,7,3,2,5,6,8]=>[3,2,1,1,1]
[7,5,4,8,2,3,6,1]=>[5,1,1,1]
[3,1,7,2,6,8,4,5]=>[3,2,1,1,1]
[5,1,7,4,2,6,8,3]=>[3,2,2,1]
[4,1,6,3,2,5,8,7]=>[3,2,2,1]
[4,3,1,6,2,5,7,8]=>[3,2,1,1,1]
[6,5,4,3,7,1,8,2]=>[5,2,1]
[6,5,1,7,3,8,2,4]=>[4,2,1,1]
[6,3,2,8,5,7,1,4]=>[4,2,1,1]
[6,5,4,3,8,2,7,1]=>[6,1,1]
[6,5,4,3,8,7,1,2]=>[5,2,1]
[7,5,4,8,6,1,3,2]=>[5,2,1]
[7,6,3,8,5,4,1,2]=>[5,2,1]
[6,3,8,1,7,5,2,4]=>[4,2,1,1]
[6,5,8,3,1,7,4,2]=>[4,3,1]
[5,4,8,2,1,7,3,6]=>[4,2,1,1]
[6,4,2,8,5,1,3,7]=>[4,2,1,1]
[7,6,4,8,5,1,2,3]=>[4,2,1,1]
[7,2,8,6,3,1,4,5]=>[4,2,1,1]
[7,2,8,6,1,5,3,4]=>[4,2,1,1]
[2,1,7,8,3,6,4,5]=>[3,2,1,1,1]
[6,4,1,7,8,2,3,5]=>[3,2,1,1,1]
[4,2,1,6,7,3,5,8]=>[3,2,1,1,1]
[4,3,1,5,2,7,6,8]=>[3,2,2,1]
[5,4,2,7,3,8,1,6]=>[4,2,1,1]
[4,1,5,3,2,8,6,7]=>[3,2,2,1]
[3,1,6,2,8,7,4,5]=>[3,2,2,1]
[6,3,1,7,8,5,2,4]=>[3,3,1,1]
[6,5,4,1,7,8,3,2]=>[5,2,1]
[5,4,3,1,6,7,2,8]=>[4,2,1,1]
[6,5,4,2,7,8,3,1]=>[5,2,1]
[5,4,2,6,3,8,7,1]=>[4,2,2]
[4,3,1,5,2,6,8,7]=>[3,2,2,1]
[5,4,2,1,6,7,8,3]=>[4,2,1,1]
[5,4,3,1,6,7,8,2]=>[4,2,1,1]
[6,3,8,1,2,5,7,4]=>[3,2,1,1,1]
[3,6,7,1,2,5,8,4]=>[3,1,1,1,1,1]
[7,8,3,1,2,5,6,4]=>[3,2,1,1,1]
[7,8,1,3,2,4,6,5]=>[3,2,1,1,1]
[7,8,2,1,3,5,4,6]=>[3,2,1,1,1]
[5,2,3,7,1,8,6,4]=>[3,3,1,1]
[2,5,3,6,1,8,7,4]=>[3,3,1,1]
[2,6,7,3,1,8,4,5]=>[3,2,1,1,1]
[2,6,7,1,3,5,4,8]=>[3,1,1,1,1,1]
[6,2,8,3,1,7,4,5]=>[3,2,2,1]
[3,2,5,7,1,8,4,6]=>[3,2,1,1,1]
[4,3,1,2,7,8,6,5]=>[3,3,1,1]
[5,1,2,7,3,6,4,8]=>[3,2,1,1,1]
[5,1,4,7,8,2,3,6]=>[3,1,1,1,1,1]
[5,3,4,7,8,6,1,2]=>[3,2,1,1,1]
[3,5,4,6,8,7,1,2]=>[3,2,1,1,1]
[1,5,4,6,8,2,3,7]=>[3,1,1,1,1,1]
[1,6,7,3,2,4,8,5]=>[3,2,1,1,1]
[1,5,3,6,2,7,8,4]=>[3,2,1,1,1]
[5,1,3,7,2,6,8,4]=>[3,2,1,1,1]
[5,2,4,7,8,1,6,3]=>[3,2,1,1,1]
[4,2,5,7,6,1,8,3]=>[3,2,2,1]
[4,5,2,8,6,1,7,3]=>[3,2,2,1]
[5,3,1,8,2,6,7,4]=>[3,3,1,1]
[6,1,8,3,2,4,7,5]=>[3,2,2,1]
[4,3,5,7,6,8,1,2]=>[3,2,1,1,1]
[4,1,5,7,6,2,3,8]=>[3,2,1,1,1]
[4,5,1,8,6,2,3,7]=>[3,2,1,1,1]
[5,2,1,8,3,6,4,7]=>[3,3,1,1]
[3,4,2,1,8,7,5,6]=>[3,3,1,1]
[7,6,5,4,2,1,8,3]=>[6,2]
[7,6,5,8,2,1,4,3]=>[5,2,1]
[8,5,4,3,2,1,7,6]=>[6,2]
[7,6,5,4,1,8,3,2]=>[6,2]
[7,6,5,8,4,1,3,2]=>[6,1,1]
[7,6,8,5,2,1,4,3]=>[5,2,1]
[7,8,2,4,5,1,3,6]=>[3,1,1,1,1,1]
[4,6,7,2,5,1,3,8]=>[3,1,1,1,1,1]
[7,8,1,3,2,4,5,6]=>[3,1,1,1,1,1]
[7,8,4,1,5,2,3,6]=>[3,2,1,1,1]
[3,6,7,2,1,4,5,8]=>[3,1,1,1,1,1]
[5,2,3,6,1,4,7,8]=>[3,1,1,1,1,1]
[2,5,3,6,1,4,7,8]=>[3,1,1,1,1,1]
[2,6,7,3,1,4,5,8]=>[3,1,1,1,1,1]
[4,6,7,1,5,2,3,8]=>[3,1,1,1,1,1]
[4,6,7,3,5,8,1,2]=>[3,1,1,1,1,1]
[6,4,7,1,5,2,3,8]=>[3,2,1,1,1]
[6,2,7,3,1,4,5,8]=>[3,2,1,1,1]
[3,2,5,6,1,4,7,8]=>[3,1,1,1,1,1]
[3,5,2,6,1,4,7,8]=>[3,1,1,1,1,1]
[5,1,4,6,7,2,3,8]=>[3,1,1,1,1,1]
[3,5,4,6,7,8,1,2]=>[3,1,1,1,1,1]
[1,5,4,6,7,2,3,8]=>[3,1,1,1,1,1]
[1,6,7,3,2,4,5,8]=>[3,1,1,1,1,1]
[1,5,3,6,2,4,7,8]=>[3,1,1,1,1,1]
[5,1,3,6,2,4,7,8]=>[3,1,1,1,1,1]
[5,2,4,6,7,1,3,8]=>[3,1,1,1,1,1]
[2,5,4,6,7,1,3,8]=>[3,1,1,1,1,1]
[2,6,7,4,5,1,3,8]=>[3,1,1,1,1,1]
[6,2,7,4,5,1,3,8]=>[3,2,1,1,1]
[4,2,5,6,7,1,3,8]=>[3,1,1,1,1,1]
[4,5,2,6,7,1,3,8]=>[3,1,1,1,1,1]
[5,3,1,6,2,4,7,8]=>[3,2,1,1,1]
[6,1,7,3,2,4,5,8]=>[3,2,1,1,1]
[6,1,7,4,5,2,3,8]=>[3,2,1,1,1]
[6,3,7,4,5,8,1,2]=>[3,2,1,1,1]
[5,4,1,6,7,2,3,8]=>[3,2,1,1,1]
[5,2,1,6,3,4,7,8]=>[3,2,1,1,1]
[7,3,2,5,4,1,6,8]=>[4,2,1,1]
[7,3,5,4,2,1,6,8]=>[5,1,1,1]
[7,3,5,2,4,1,6,8]=>[4,1,1,1,1]
[7,6,5,2,1,4,3,8]=>[5,2,1]
[1,3,6,7,5,2,8,4]=>[3,2,1,1,1]
[7,3,4,1,6,2,5,8]=>[3,2,1,1,1]
[7,3,4,1,6,5,2,8]=>[4,2,1,1]
[7,3,4,1,5,6,2,8]=>[3,2,1,1,1]
[7,3,2,5,1,6,4,8]=>[4,2,1,1]
[7,6,5,4,1,3,2,8]=>[6,1,1]
[7,3,4,1,5,2,6,8]=>[3,2,1,1,1]
[1,3,6,7,2,5,8,4]=>[3,1,1,1,1,1]
[1,7,4,6,2,8,5,3]=>[4,2,1,1]
[4,3,1,7,2,6,8,5]=>[3,3,1,1]
[5,6,1,4,7,3,8,2]=>[4,1,1,1,1]
[5,3,2,1,7,4,8,6]=>[4,2,2]
[1,3,4,5,8,7,2,6]=>[3,1,1,1,1,1]
[6,3,4,5,8,1,7,2]=>[3,2,1,1,1]
[2,4,5,1,6,8,7,3]=>[3,2,1,1,1]
[3,1,2,5,6,8,7,4]=>[3,2,1,1,1]
[4,3,2,5,6,8,1,7]=>[4,1,1,1,1]
[3,7,5,4,6,8,1,2]=>[4,1,1,1,1]
[3,1,4,6,5,8,2,7]=>[3,2,1,1,1]
[2,3,4,5,8,6,1,7]=>[3,1,1,1,1,1]
[2,3,4,5,8,1,7,6]=>[3,1,1,1,1,1]
[3,1,4,6,5,8,7,2]=>[3,2,2,1]
[3,7,5,4,6,8,2,1]=>[5,1,1,1]
[5,6,1,4,7,2,8,3]=>[3,2,1,1,1]
[4,3,1,7,5,6,8,2]=>[3,3,1,1]
[4,3,1,7,6,5,8,2]=>[4,3,1]
[3,1,4,6,7,8,5,2]=>[3,2,1,1,1]
[1,4,5,2,6,8,7,3]=>[3,2,1,1,1]
[3,7,5,2,6,8,1,4]=>[4,1,1,1,1]
[3,7,5,2,6,8,4,1]=>[4,2,1,1]
[5,6,1,2,7,4,8,3]=>[3,2,1,1,1]
[6,3,5,2,4,7,8,1]=>[4,1,1,1,1]
[5,3,2,1,4,7,8,6]=>[4,2,1,1]
[5,3,1,4,2,7,8,6]=>[3,2,2,1]
[5,3,1,2,4,7,8,6]=>[3,2,1,1,1]
[7,1,5,2,6,8,4,3]=>[4,2,1,1]
[7,1,5,2,6,8,3,4]=>[3,2,1,1,1]
[1,7,4,6,5,8,3,2]=>[5,1,1,1]
[2,7,4,6,1,8,3,5]=>[3,2,1,1,1]
[2,7,4,6,1,8,5,3]=>[4,2,1,1]
[2,3,6,7,1,5,8,4]=>[3,1,1,1,1,1]
[2,3,6,7,5,1,8,4]=>[3,2,1,1,1]
[4,3,2,6,7,1,8,5]=>[4,2,1,1]
[7,3,2,5,6,8,1,4]=>[4,1,1,1,1]
[7,1,5,4,6,8,2,3]=>[4,1,1,1,1]
[2,7,4,6,5,8,1,3]=>[4,1,1,1,1]
[7,3,4,5,8,6,1,2]=>[3,2,1,1,1]
[7,3,4,5,8,1,6,2]=>[3,2,1,1,1]
[7,3,4,5,8,1,2,6]=>[3,1,1,1,1,1]
[1,3,4,5,8,6,2,7]=>[3,1,1,1,1,1]
[1,3,4,5,8,2,7,6]=>[3,1,1,1,1,1]
[6,3,4,5,8,2,1,7]=>[4,1,1,1,1]
[6,3,4,5,8,2,7,1]=>[4,1,1,1,1]
[7,3,4,5,8,6,2,1]=>[4,2,1,1]
[2,7,4,6,5,8,3,1]=>[5,1,1,1]
[7,1,5,4,6,8,3,2]=>[5,1,1,1]
[7,3,2,5,6,8,4,1]=>[4,2,1,1]
[5,7,4,6,1,8,3,2]=>[4,2,1,1]
[6,3,4,5,8,1,2,7]=>[3,1,1,1,1,1]
[7,3,4,5,8,2,1,6]=>[4,1,1,1,1]
[7,3,4,5,8,2,6,1]=>[4,1,1,1,1]
[4,7,6,1,8,2,5,3]=>[4,2,1,1]
[4,8,6,1,7,5,2,3]=>[4,2,1,1]
[4,7,8,2,6,1,5,3]=>[4,1,1,1,1]
[7,6,4,2,8,3,5,1]=>[5,2,1]
[8,6,4,2,7,5,3,1]=>[5,3]
[8,4,7,3,6,5,1,2]=>[5,1,1,1]
[8,4,6,1,7,5,3,2]=>[5,2,1]
[6,4,7,1,8,3,2,5]=>[4,2,1,1]
[7,4,8,3,6,1,5,2]=>[4,2,1,1]
[7,8,4,3,6,2,5,1]=>[5,1,1,1]
[6,2,1,7,3,5,4,8]=>[3,3,1,1]
[2,1,8,6,3,5,4,7]=>[4,2,1,1]
[2,1,7,3,5,8,6,4]=>[3,2,2,1]
[2,7,3,1,5,4,6,8]=>[3,2,1,1,1]
[2,6,3,1,4,8,5,7]=>[3,2,1,1,1]
[4,2,1,8,3,6,7,5]=>[3,3,1,1]
[2,1,8,6,3,5,7,4]=>[4,2,1,1]
[6,2,1,7,3,5,8,4]=>[3,3,1,1]
[2,7,3,1,4,8,5,6]=>[3,2,1,1,1]
[3,2,1,6,4,5,7,8]=>[3,2,1,1,1]
[3,2,1,5,7,8,4,6]=>[3,2,1,1,1]
[2,1,7,3,6,8,4,5]=>[3,2,1,1,1]
[2,7,3,1,5,6,8,4]=>[3,2,1,1,1]
[2,4,7,5,1,6,8,3]=>[3,2,1,1,1]
[4,3,7,5,6,1,8,2]=>[3,2,2,1]
[4,3,6,8,5,1,7,2]=>[3,2,2,1]
[2,6,1,8,3,5,7,4]=>[3,2,1,1,1]
[2,1,6,8,3,7,4,5]=>[3,2,1,1,1]
[2,1,8,3,5,7,4,6]=>[3,2,1,1,1]
[3,2,1,5,6,8,4,7]=>[3,2,1,1,1]
[3,2,1,5,7,4,6,8]=>[3,2,1,1,1]
[2,1,7,3,6,4,5,8]=>[3,2,1,1,1]
[2,1,6,3,5,8,4,7]=>[3,2,1,1,1]
[8,2,4,1,7,5,6,3]=>[4,2,1,1]
[3,8,4,7,5,1,6,2]=>[4,2,1,1]
[8,4,3,6,1,7,5,2]=>[4,3,1]
[8,2,1,7,3,5,4,6]=>[4,2,1,1]
[2,6,1,8,3,5,4,7]=>[3,2,1,1,1]
[2,7,3,1,5,6,4,8]=>[3,2,1,1,1]
[2,4,7,5,1,6,3,8]=>[3,2,1,1,1]
[8,2,4,1,7,5,3,6]=>[4,2,1,1]
[5,8,6,3,1,7,4,2]=>[4,3,1]
[2,4,7,1,8,5,3,6]=>[3,2,1,1,1]
[2,4,8,5,1,6,3,7]=>[3,2,1,1,1]
[6,2,1,7,3,4,8,5]=>[3,2,2,1]
[6,2,1,7,8,3,5,4]=>[3,3,1,1]
[2,7,1,8,3,5,6,4]=>[3,2,1,1,1]
[2,1,8,3,6,4,5,7]=>[3,2,1,1,1]
[3,2,1,6,7,4,5,8]=>[3,2,1,1,1]
[3,2,1,7,4,5,6,8]=>[3,2,1,1,1]
[3,2,1,6,8,4,5,7]=>[3,2,1,1,1]
[2,1,8,3,7,4,5,6]=>[3,2,1,1,1]
[2,1,8,3,6,7,4,5]=>[3,2,1,1,1]
[2,4,8,5,1,6,7,3]=>[3,2,1,1,1]
[4,3,8,5,6,1,7,2]=>[3,2,2,1]
[3,2,1,8,4,5,6,7]=>[3,2,1,1,1]
[1,6,8,3,7,2,4,5]=>[3,1,1,1,1,1]
[3,8,1,5,7,2,4,6]=>[3,1,1,1,1,1]
[1,2,6,8,4,7,3,5]=>[3,1,1,1,1,1]
[6,1,5,8,2,4,7,3]=>[4,1,1,1,1]
[1,2,4,8,3,6,7,5]=>[3,1,1,1,1,1]
[4,1,2,7,8,3,6,5]=>[3,2,1,1,1]
[3,5,7,4,8,6,1,2]=>[3,2,1,1,1]
[5,3,8,4,7,6,1,2]=>[4,2,1,1]
[8,7,1,2,5,4,6,3]=>[5,1,1,1]
[5,8,1,2,3,7,6,4]=>[4,1,1,1,1]
[1,2,8,4,3,5,7,6]=>[3,2,1,1,1]
[1,2,5,3,7,6,4,8]=>[3,2,1,1,1]
[6,1,2,8,7,4,5,3]=>[4,2,1,1]
[7,1,6,2,8,4,5,3]=>[4,2,1,1]
[1,2,6,3,8,5,4,7]=>[3,2,1,1,1]
[1,2,8,5,3,6,4,7]=>[3,2,1,1,1]
[1,2,7,3,8,5,4,6]=>[3,2,1,1,1]
[4,1,2,7,8,6,3,5]=>[3,2,1,1,1]
[1,6,2,8,4,3,5,7]=>[3,2,1,1,1]
[1,6,4,2,7,3,5,8]=>[3,2,1,1,1]
[1,8,6,3,2,4,5,7]=>[4,1,1,1,1]
[1,7,3,2,8,4,5,6]=>[3,2,1,1,1]
[3,1,7,8,6,2,4,5]=>[3,2,1,1,1]
[1,8,7,2,4,5,6,3]=>[4,1,1,1,1]
[1,8,7,3,5,6,2,4]=>[4,1,1,1,1]
[1,3,2,8,7,4,5,6]=>[3,2,1,1,1]
[1,8,3,2,6,4,5,7]=>[3,2,1,1,1]
[1,7,6,3,2,4,5,8]=>[4,1,1,1,1]
[1,2,8,4,3,7,5,6]=>[3,2,1,1,1]
[8,5,1,7,2,4,6,3]=>[4,2,1,1]
[5,3,8,7,4,6,1,2]=>[4,2,1,1]
[3,8,6,4,7,5,1,2]=>[4,2,1,1]
[6,1,8,2,7,4,5,3]=>[4,2,1,1]
[1,2,5,3,8,6,4,7]=>[3,2,1,1,1]
[1,2,7,5,3,6,4,8]=>[3,2,1,1,1]
[1,2,6,3,7,5,4,8]=>[3,2,1,1,1]
[1,2,3,7,5,4,8,6]=>[3,2,1,1,1]
[3,7,4,8,6,5,1,2]=>[4,2,1,1]
[1,8,2,7,6,4,5,3]=>[5,1,1,1]
[2,8,7,6,5,1,4,3]=>[6,1,1]
[7,1,6,3,2,5,4,8]=>[4,2,1,1]
[2,7,6,3,1,5,8,4]=>[4,2,1,1]
[1,8,4,3,6,5,2,7]=>[4,2,1,1]
[1,8,4,6,5,3,2,7]=>[5,1,1,1]
[7,4,2,1,6,5,3,8]=>[4,3,1]
[7,6,1,4,3,5,2,8]=>[5,1,1,1]
[7,4,1,3,5,2,6,8]=>[4,1,1,1,1]
[7,3,1,2,4,6,5,8]=>[3,2,1,1,1]
[1,8,6,3,4,5,2,7]=>[4,1,1,1,1]
[1,8,6,7,4,2,5,3]=>[4,2,1,1]
[3,6,2,1,4,8,5,7]=>[3,2,1,1,1]
[3,1,7,2,4,6,8,5]=>[3,2,1,1,1]
[3,4,7,1,5,2,8,6]=>[3,2,1,1,1]
[3,6,7,4,1,5,8,2]=>[3,2,1,1,1]
[4,3,2,7,1,5,8,6]=>[4,2,1,1]
[3,1,2,8,6,5,4,7]=>[4,2,1,1]
[5,4,8,6,1,2,3,7]=>[3,2,1,1,1]
[5,6,8,7,4,3,1,2]=>[5,1,1,1]
[1,8,2,7,4,3,6,5]=>[4,2,1,1]
[6,5,8,2,3,7,1,4]=>[4,1,1,1,1]
[6,4,8,5,3,1,7,2]=>[4,2,2]
[5,7,8,6,1,3,2,4]=>[4,1,1,1,1]
[2,4,8,1,6,3,7,5]=>[3,2,1,1,1]
[3,1,2,8,6,4,7,5]=>[3,2,2,1]
[5,3,2,6,4,8,1,7]=>[4,2,1,1]
[4,1,6,3,5,8,2,7]=>[3,2,1,1,1]
[2,4,5,3,8,6,1,7]=>[3,2,1,1,1]
[1,8,5,3,2,7,6,4]=>[4,3,1]
[1,8,4,5,2,6,7,3]=>[3,2,1,1,1]
[4,1,2,7,6,5,8,3]=>[4,2,1,1]
[2,4,1,6,7,8,5,3]=>[3,2,1,1,1]
[1,8,4,3,6,2,7,5]=>[4,2,1,1]
[5,6,7,3,2,8,1,4]=>[4,1,1,1,1]
[2,5,7,3,6,8,4,1]=>[4,1,1,1,1]
[5,3,2,1,4,8,6,7]=>[4,2,1,1]
[5,3,1,4,2,8,6,7]=>[3,2,2,1]
[7,6,1,3,8,5,4,2]=>[5,2,1]
[3,4,7,8,1,2,6,5]=>[3,1,1,1,1,1]
[3,6,7,8,1,4,5,2]=>[3,1,1,1,1,1]
[3,6,2,8,1,5,4,7]=>[3,2,1,1,1]
[2,3,6,8,5,1,4,7]=>[3,1,1,1,1,1]
[3,1,6,4,8,2,5,7]=>[3,2,1,1,1]
[7,3,2,6,8,5,1,4]=>[4,2,1,1]
[7,3,5,8,4,6,1,2]=>[4,1,1,1,1]
[7,5,2,8,4,1,6,3]=>[4,2,2]
[7,4,5,8,2,1,3,6]=>[4,1,1,1,1]
[1,8,5,2,4,6,3,7]=>[4,1,1,1,1]
[1,8,4,2,3,5,7,6]=>[3,2,1,1,1]
[6,4,2,8,3,5,1,7]=>[4,2,1,1]
[6,3,4,8,2,5,7,1]=>[4,1,1,1,1]
[7,5,4,8,3,6,2,1]=>[6,1,1]
[2,7,4,8,5,3,6,1]=>[4,2,1,1]
[7,1,5,4,8,3,6,2]=>[5,1,1,1]
[7,3,2,5,8,4,6,1]=>[4,2,1,1]
[8,4,6,3,7,2,5,1]=>[5,1,1,1]
[7,4,6,3,8,5,1,2]=>[4,2,1,1]
[2,5,6,8,3,4,1,7]=>[3,1,1,1,1,1]
[8,4,6,2,7,5,3,1]=>[5,2,1]
[8,5,6,7,2,4,3,1]=>[5,1,1,1]
[2,5,6,8,4,3,1,7]=>[4,1,1,1,1]
[2,5,7,8,4,1,3,6]=>[3,1,1,1,1,1]
[6,5,7,8,4,1,3,2]=>[5,1,1,1]
[7,5,6,8,2,4,1,3]=>[4,1,1,1,1]
[7,4,6,2,8,5,1,3]=>[4,2,1,1]
[4,3,2,6,8,5,1,7]=>[4,2,1,1]
[3,5,6,8,2,4,1,7]=>[3,1,1,1,1,1]
[3,5,6,8,4,2,1,7]=>[4,1,1,1,1]
[2,6,7,8,1,4,5,3]=>[3,1,1,1,1,1]
[3,6,7,8,1,4,2,5]=>[3,1,1,1,1,1]
[3,5,7,8,2,1,4,6]=>[3,1,1,1,1,1]
[2,6,7,8,1,4,3,5]=>[3,1,1,1,1,1]
[6,5,7,8,3,1,4,2]=>[4,2,1,1]
[2,5,7,8,3,1,4,6]=>[3,1,1,1,1,1]
[2,4,7,3,8,1,5,6]=>[3,1,1,1,1,1]
[6,4,7,3,8,1,5,2]=>[4,2,1,1]
[6,4,7,3,8,1,2,5]=>[4,1,1,1,1]
[7,4,6,3,8,2,1,5]=>[5,1,1,1]
[6,3,2,5,4,8,1,7]=>[4,2,1,1]
[6,4,5,2,3,8,1,7]=>[4,1,1,1,1]
[6,4,5,3,2,8,1,7]=>[5,1,1,1]
[5,4,6,3,8,2,1,7]=>[5,1,1,1]
[5,4,7,3,8,1,6,2]=>[4,2,1,1]
[2,5,7,8,3,1,6,4]=>[3,2,1,1,1]
[4,5,7,8,3,1,2,6]=>[3,1,1,1,1,1]
[4,5,6,8,2,3,1,7]=>[3,1,1,1,1,1]
[5,4,6,2,8,3,1,7]=>[4,2,1,1]
[5,3,2,6,8,4,1,7]=>[4,2,1,1]
[5,4,7,2,8,1,3,6]=>[4,1,1,1,1]
[4,5,7,8,2,1,3,6]=>[3,1,1,1,1,1]
[4,6,7,8,1,3,2,5]=>[3,1,1,1,1,1]
[4,6,7,8,1,3,5,2]=>[3,1,1,1,1,1]
[2,6,7,8,1,3,5,4]=>[3,1,1,1,1,1]
[2,6,7,8,1,5,3,4]=>[3,1,1,1,1,1]
[4,6,7,8,1,5,2,3]=>[3,1,1,1,1,1]
[4,6,7,8,1,2,5,3]=>[3,1,1,1,1,1]
[4,5,7,8,2,1,6,3]=>[3,2,1,1,1]
[5,4,7,2,8,1,6,3]=>[4,2,1,1]
[5,3,2,7,8,1,6,4]=>[4,2,1,1]
[4,3,2,7,8,1,6,5]=>[4,2,1,1]
[3,5,7,8,2,1,6,4]=>[3,2,1,1,1]
[3,6,7,8,1,2,5,4]=>[3,1,1,1,1,1]
[3,6,7,8,1,5,2,4]=>[3,1,1,1,1,1]
[3,6,7,8,1,5,4,2]=>[4,1,1,1,1]
[2,6,7,8,1,5,4,3]=>[4,1,1,1,1]
[4,2,7,1,5,3,8,6]=>[3,2,2,1]
[4,2,8,6,1,5,3,7]=>[4,2,1,1]
[3,2,6,7,5,1,4,8]=>[3,2,1,1,1]
[2,7,1,3,5,4,8,6]=>[3,2,1,1,1]
[4,7,2,1,5,8,6,3]=>[3,3,1,1]
[7,2,1,3,5,8,6,4]=>[3,3,1,1]
[2,3,6,4,7,1,5,8]=>[3,1,1,1,1,1]
[1,3,4,8,2,7,5,6]=>[3,1,1,1,1,1]
[3,1,4,8,2,6,7,5]=>[3,2,1,1,1]
[8,3,1,6,2,5,7,4]=>[4,2,1,1]
[4,8,6,2,1,5,7,3]=>[4,2,1,1]
[4,8,3,6,5,1,7,2]=>[4,2,1,1]
[6,4,7,3,5,1,8,2]=>[4,2,1,1]
[6,4,7,5,1,8,2,3]=>[3,2,2,1]
[3,6,1,7,5,8,2,4]=>[3,2,1,1,1]
[7,3,5,1,6,8,2,4]=>[3,2,1,1,1]
[4,7,3,5,6,1,8,2]=>[3,2,1,1,1]
[3,4,6,8,5,1,7,2]=>[3,2,1,1,1]
[4,6,8,2,1,5,7,3]=>[3,2,1,1,1]
[6,8,2,1,3,5,7,4]=>[3,2,1,1,1]
[1,8,2,3,5,7,4,6]=>[3,1,1,1,1,1]
[2,7,3,6,1,4,5,8]=>[3,1,1,1,1,1]
[2,6,1,3,5,8,4,7]=>[3,1,1,1,1,1]
[7,3,2,5,6,1,4,8]=>[4,1,1,1,1]
[4,7,5,2,6,1,3,8]=>[4,1,1,1,1]
[4,6,2,8,1,5,3,7]=>[3,2,1,1,1]
[8,4,1,2,7,5,3,6]=>[4,2,1,1]
[4,5,6,2,7,1,3,8]=>[3,1,1,1,1,1]
[8,5,1,2,6,3,4,7]=>[3,2,1,1,1]
[1,6,2,7,4,8,3,5]=>[3,2,1,1,1]
[6,2,1,7,8,5,3,4]=>[3,3,1,1]
[6,7,3,8,4,1,5,2]=>[3,2,2,1]
[2,7,8,4,1,5,6,3]=>[3,2,1,1,1]
[2,7,1,8,5,6,3,4]=>[3,2,1,1,1]
[8,2,5,1,6,7,3,4]=>[3,2,1,1,1]
[8,2,4,5,1,6,7,3]=>[3,2,1,1,1]
[3,8,4,5,6,1,7,2]=>[3,2,1,1,1]
[4,5,8,3,6,7,1,2]=>[3,1,1,1,1,1]
[4,5,8,3,7,6,1,2]=>[4,1,1,1,1]
[4,2,8,3,7,1,6,5]=>[4,2,1,1]
[7,2,3,4,8,1,6,5]=>[3,2,1,1,1]
[7,2,3,8,5,1,4,6]=>[3,2,1,1,1]
[7,2,3,8,5,1,6,4]=>[3,2,2,1]
[7,2,3,5,8,1,4,6]=>[3,1,1,1,1,1]
[7,8,2,3,6,1,4,5]=>[3,1,1,1,1,1]
[7,8,2,3,6,1,5,4]=>[4,1,1,1,1]
[4,2,6,3,7,1,5,8]=>[3,2,1,1,1]
[2,6,4,8,1,3,7,5]=>[3,2,1,1,1]
[7,6,5,1,2,3,8,4]=>[4,2,1,1]
[2,6,4,5,1,8,7,3]=>[3,3,1,1]
[7,8,5,4,1,2,6,3]=>[4,2,1,1]
[7,6,5,1,2,4,8,3]=>[5,1,1,1]
[7,6,5,1,3,2,8,4]=>[5,2,1]
[7,6,5,1,3,4,2,8]=>[5,1,1,1]
[7,2,3,4,5,1,8,6]=>[3,2,1,1,1]
[2,6,4,3,1,5,8,7]=>[4,2,1,1]
[3,5,8,4,1,2,7,6]=>[3,2,1,1,1]
[4,2,8,3,6,1,7,5]=>[3,2,2,1]
[3,5,8,4,1,6,7,2]=>[3,2,1,1,1]
[2,5,8,4,1,7,3,6]=>[3,2,1,1,1]
[3,6,4,2,1,7,8,5]=>[4,2,1,1]
[2,6,4,5,1,3,7,8]=>[3,1,1,1,1,1]
[7,6,5,1,8,2,4,3]=>[5,2,1]
[7,6,5,1,8,3,2,4]=>[5,2,1]
[7,6,5,1,4,8,2,3]=>[5,1,1,1]
[3,6,4,5,1,7,2,8]=>[3,2,1,1,1]
[2,5,6,4,1,7,8,3]=>[3,2,1,1,1]
[7,8,5,4,1,6,3,2]=>[5,2,1]
[2,5,6,4,1,7,3,8]=>[3,2,1,1,1]
[7,6,5,1,8,3,4,2]=>[5,2,1]
[7,6,5,1,8,4,2,3]=>[5,2,1]
[4,1,7,6,2,8,5,3]=>[4,2,2]
[7,8,6,2,1,3,5,4]=>[4,2,1,1]
[3,7,6,1,2,8,4,5]=>[3,2,1,1,1]
[2,6,5,3,1,4,8,7]=>[4,2,1,1]
[4,6,1,5,3,2,8,7]=>[4,2,1,1]
[3,6,1,4,2,5,8,7]=>[3,2,1,1,1]
[2,6,4,5,7,8,1,3]=>[3,1,1,1,1,1]
[8,7,1,6,5,2,4,3]=>[6,1,1]
[7,2,5,6,8,1,3,4]=>[3,1,1,1,1,1]
[6,1,3,4,2,8,7,5]=>[3,3,1,1]
[2,4,5,6,1,8,7,3]=>[3,2,1,1,1]
[8,4,1,6,5,7,3,2]=>[5,2,1]
[2,8,3,4,7,5,1,6]=>[4,1,1,1,1]
[6,8,2,7,4,3,5,1]=>[5,1,1,1]
[4,7,8,5,1,6,3,2]=>[4,2,1,1]
[8,2,6,4,7,3,5,1]=>[5,1,1,1]
[4,8,6,1,7,3,2,5]=>[4,2,1,1]
[8,7,3,2,1,5,4,6]=>[5,2,1]
[3,8,5,1,7,2,4,6]=>[3,2,1,1,1]
[6,8,7,1,3,2,4,5]=>[4,1,1,1,1]
[2,5,1,8,7,4,6,3]=>[4,2,1,1]
[3,7,1,8,4,5,6,2]=>[3,2,1,1,1]
[6,2,3,8,4,7,5,1]=>[4,2,1,1]
[8,6,4,3,1,7,2,5]=>[5,2,1]
[8,3,7,4,6,1,2,5]=>[4,1,1,1,1]
[7,1,3,8,6,4,5,2]=>[4,2,1,1]
[2,3,5,8,6,7,4,1]=>[4,1,1,1,1]
[7,4,2,1,8,6,5,3]=>[4,4]
[4,6,7,2,5,8,3,1]=>[4,1,1,1,1]
[7,6,2,5,3,8,1,4]=>[5,1,1,1]
[6,2,1,3,4,8,7,5]=>[3,3,1,1]
[6,5,4,2,8,3,1,7]=>[5,2,1]
[5,4,3,1,8,7,2,6]=>[4,3,1]
[6,1,4,3,8,5,2,7]=>[4,2,1,1]
[4,7,6,2,8,1,5,3]=>[4,2,1,1]
[6,4,5,1,7,8,3,2]=>[4,2,1,1]
[4,2,3,1,7,8,6,5]=>[3,3,1,1]
[3,4,2,1,8,6,7,5]=>[3,3,1,1]
[2,7,6,8,1,5,3,4]=>[4,1,1,1,1]
[6,4,5,8,3,1,2,7]=>[4,1,1,1,1]
[8,1,3,2,5,6,7,4]=>[3,2,1,1,1]
[3,6,8,1,5,2,4,7]=>[3,1,1,1,1,1]
[3,2,8,7,4,5,1,6]=>[4,2,1,1]
[6,3,8,5,7,4,2,1]=>[5,2,1]
[7,4,6,8,5,1,2,3]=>[4,1,1,1,1]
[2,1,4,8,7,5,3,6]=>[4,2,1,1]
[2,1,6,8,3,7,5,4]=>[4,2,1,1]
[3,6,8,2,4,1,5,7]=>[3,1,1,1,1,1]
[6,2,8,1,7,5,4,3]=>[5,2,1]
[2,6,5,4,8,1,3,7]=>[4,1,1,1,1]
[6,5,3,4,8,1,7,2]=>[4,2,1,1]
[8,4,3,2,5,1,7,6]=>[5,2,1]
[4,2,8,1,5,3,6,7]=>[3,2,1,1,1]
[5,1,8,2,6,4,3,7]=>[4,2,1,1]
[7,4,8,6,2,1,3,5]=>[4,2,1,1]
[4,6,2,8,3,7,5,1]=>[4,2,1,1]
[2,1,5,8,3,6,4,7]=>[3,2,1,1,1]
[2,8,5,3,6,7,1,4]=>[4,1,1,1,1]
[7,8,5,6,4,1,3,2]=>[5,1,1,1]
[5,8,4,1,6,3,7,2]=>[4,2,1,1]
[4,8,1,3,5,7,6,2]=>[4,1,1,1,1]
[3,8,1,4,5,6,2,7]=>[3,1,1,1,1,1]
[7,6,8,3,5,1,4,2]=>[5,1,1,1]
[7,8,6,3,5,1,4,2]=>[5,1,1,1]
[5,3,8,7,6,1,4,2]=>[5,2,1]
[6,5,8,4,7,1,3,2]=>[5,1,1,1]
[6,7,4,2,5,3,1,8]=>[4,2,1,1]
[7,6,4,8,3,1,5,2]=>[5,2,1]
[7,4,8,5,6,1,3,2]=>[4,2,1,1]
[7,4,2,5,6,3,1,8]=>[4,2,1,1]
[4,2,7,5,6,3,1,8]=>[4,2,1,1]
[3,4,7,5,6,2,1,8]=>[4,1,1,1,1]
[4,7,3,5,6,2,1,8]=>[4,1,1,1,1]
[3,7,2,5,6,4,1,8]=>[4,1,1,1,1]
[7,8,3,5,6,1,4,2]=>[4,1,1,1,1]
[1,6,8,5,2,7,4,3]=>[4,2,1,1]
[6,2,8,5,1,7,4,3]=>[4,2,2]
[6,7,4,8,2,1,5,3]=>[4,2,1,1]
[3,2,7,8,6,1,5,4]=>[4,2,1,1]
[6,8,4,1,2,3,7,5]=>[3,2,1,1,1]
[4,1,8,5,6,3,2,7]=>[4,2,1,1]
[1,8,2,5,6,4,3,7]=>[4,1,1,1,1]
[6,1,8,5,3,7,4,2]=>[4,2,2]
[3,8,1,5,2,7,6,4]=>[4,2,1,1]
[8,2,1,5,3,7,6,4]=>[4,2,2]
[1,5,2,4,6,7,8,3]=>[3,1,1,1,1,1]
[4,1,5,3,6,7,8,2]=>[3,2,1,1,1]
[8,1,6,5,3,7,2,4]=>[5,1,1,1]
[7,1,4,6,3,2,8,5]=>[4,2,1,1]
[3,2,6,4,1,7,8,5]=>[3,2,2,1]
[7,6,4,3,1,2,8,5]=>[5,2,1]
[8,6,3,5,1,7,2,4]=>[4,2,1,1]
[4,5,3,1,6,7,8,2]=>[3,2,1,1,1]
[3,5,2,1,6,7,8,4]=>[3,2,1,1,1]
[5,2,3,1,6,7,8,4]=>[3,2,1,1,1]
[1,5,3,2,6,7,8,4]=>[3,2,1,1,1]
[8,4,6,5,1,7,2,3]=>[4,2,1,1]
[7,5,4,6,1,2,8,3]=>[4,2,1,1]
[3,2,5,6,1,7,8,4]=>[3,2,1,1,1]
[3,2,8,7,6,1,4,5]=>[4,2,1,1]
[6,8,4,7,2,1,3,5]=>[4,1,1,1,1]
[3,8,7,5,6,1,2,4]=>[4,1,1,1,1]
[8,2,7,5,6,1,3,4]=>[4,1,1,1,1]
[4,8,6,5,1,7,3,2]=>[5,2,1]
[1,7,4,6,2,3,8,5]=>[3,2,1,1,1]
[7,6,4,2,1,5,8,3]=>[5,2,1]
[5,7,4,6,1,3,8,2]=>[4,1,1,1,1]
[8,6,4,7,3,1,2,5]=>[5,1,1,1]
[5,2,4,3,7,1,8,6]=>[4,2,1,1]
[3,5,4,2,7,1,8,6]=>[4,2,1,1]
[8,6,4,1,3,5,2,7]=>[5,1,1,1]
[6,7,4,1,5,3,8,2]=>[4,2,1,1]
[7,5,4,1,2,6,8,3]=>[4,2,1,1]
[1,7,4,2,3,6,8,5]=>[3,2,1,1,1]
[1,8,2,5,3,7,6,4]=>[4,2,1,1]
[6,8,1,5,4,7,3,2]=>[5,1,1,1]
[8,2,1,5,6,4,3,7]=>[4,2,1,1]
[3,8,1,5,6,4,2,7]=>[4,1,1,1,1]
[6,8,4,1,2,5,3,7]=>[3,2,1,1,1]
[3,2,8,1,6,5,4,7]=>[4,2,1,1]
[3,2,6,1,5,7,8,4]=>[3,2,1,1,1]
[7,6,4,1,5,2,8,3]=>[4,2,2]
[8,6,1,5,4,7,2,3]=>[5,1,1,1]
[3,5,1,4,6,7,8,2]=>[3,1,1,1,1,1]
[5,2,1,4,6,7,8,3]=>[3,2,1,1,1]
[5,4,1,3,6,7,8,2]=>[4,1,1,1,1]
[8,4,1,5,3,7,2,6]=>[4,2,1,1]
[7,5,4,1,3,2,8,6]=>[5,2,1]
[3,2,5,1,4,7,8,6]=>[3,2,1,1,1]
[7,1,4,3,5,2,8,6]=>[4,2,1,1]
[8,1,3,5,4,7,2,6]=>[4,1,1,1,1]
[5,1,3,4,6,7,8,2]=>[3,1,1,1,1,1]
[3,1,8,2,5,7,4,6]=>[3,2,1,1,1]
[8,3,2,6,1,4,7,5]=>[4,2,1,1]
[2,6,1,3,8,7,5,4]=>[4,2,1,1]
[2,5,7,1,3,8,6,4]=>[3,2,1,1,1]
[2,6,8,1,5,7,4,3]=>[4,1,1,1,1]
[2,7,1,6,4,8,3,5]=>[4,1,1,1,1]
[2,8,1,7,6,5,4,3]=>[6,1,1]
[8,3,2,7,1,6,5,4]=>[5,2,1]
[3,7,1,8,6,5,4,2]=>[5,2,1]
[3,6,8,5,1,4,7,2]=>[4,1,1,1,1]
[7,3,5,8,2,1,4,6]=>[4,1,1,1,1]
[7,3,6,2,1,4,5,8]=>[4,1,1,1,1]
[7,3,6,2,1,5,4,8]=>[4,2,1,1]
[7,4,2,8,1,6,5,3]=>[4,3,1]
[8,7,5,3,2,1,6,4]=>[6,2]
[7,5,2,6,3,1,4,8]=>[4,2,1,1]
[7,4,6,2,1,8,3,5]=>[4,2,1,1]
[6,8,4,5,2,1,7,3]=>[4,2,1,1]
[4,6,8,5,1,7,3,2]=>[4,2,1,1]
[4,7,5,1,3,8,6,2]=>[4,2,1,1]
[5,1,7,6,4,2,8,3]=>[4,2,2]
[5,1,8,7,6,4,3,2]=>[6,2]
[8,5,2,1,7,6,4,3]=>[5,3]
[8,5,2,1,6,3,7,4]=>[4,2,2]
[5,1,8,6,3,2,7,4]=>[4,2,2]
[3,6,1,7,4,8,2,5]=>[3,2,1,1,1]
[8,4,2,5,7,3,1,6]=>[4,2,1,1]
[3,4,6,8,5,7,1,2]=>[3,1,1,1,1,1]
[5,4,8,2,7,3,6,1]=>[4,2,1,1]
[5,4,8,7,3,6,1,2]=>[4,2,1,1]
[8,5,4,7,3,6,2,1]=>[6,1,1]
[6,3,7,2,4,8,1,5]=>[4,1,1,1,1]
[5,7,4,2,8,1,3,6]=>[4,1,1,1,1]
[6,5,2,7,1,3,8,4]=>[4,2,1,1]
[8,6,5,4,2,1,7,3]=>[6,2]
[6,4,7,3,1,8,2,5]=>[4,2,1,1]
[7,5,8,4,6,3,2,1]=>[6,1,1]
[7,6,5,3,8,2,4,1]=>[6,1,1]
[5,6,3,7,4,2,1,8]=>[4,2,1,1]
[7,6,3,8,5,1,4,2]=>[5,2,1]
[6,4,8,1,3,2,5,7]=>[4,1,1,1,1]
[7,4,8,6,3,1,5,2]=>[4,2,2]
[4,2,7,6,5,3,1,8]=>[5,2,1]
[3,7,2,4,6,5,1,8]=>[4,1,1,1,1]
[8,1,3,4,5,2,6,7]=>[3,1,1,1,1,1]
[1,6,8,4,2,5,3,7]=>[3,2,1,1,1]
[6,2,8,4,1,5,7,3]=>[3,2,2,1]
[6,7,4,8,5,1,2,3]=>[3,2,1,1,1]
[3,2,7,8,5,1,6,4]=>[3,2,2,1]
[3,2,8,1,5,4,6,7]=>[3,2,1,1,1]
[6,1,4,8,5,3,7,2]=>[4,2,1,1]
[1,4,8,5,2,6,7,3]=>[3,2,1,1,1]
[6,1,8,4,3,7,2,5]=>[4,2,1,1]
[3,7,1,4,2,5,8,6]=>[3,2,1,1,1]
[7,2,1,4,3,5,6,8]=>[3,2,1,1,1]
[4,1,5,3,6,8,2,7]=>[3,2,1,1,1]
[6,1,8,5,3,2,7,4]=>[4,2,2]
[7,1,4,6,3,8,5,2]=>[4,2,1,1]
[3,2,6,4,1,8,7,5]=>[3,3,2]
[7,6,4,3,1,8,2,5]=>[5,2,1]
[3,5,2,1,8,7,6,4]=>[4,3,1]
[1,5,3,2,8,6,4,7]=>[3,3,1,1]
[5,4,2,1,7,8,6,3]=>[4,3,1]
[8,2,7,6,5,1,3,4]=>[5,1,1,1]
[8,6,2,7,1,4,5,3]=>[4,2,1,1]
[1,7,3,6,2,8,5,4]=>[4,2,1,1]
[7,6,3,2,1,8,5,4]=>[5,3]
[8,6,3,7,4,1,2,5]=>[4,2,1,1]
[5,2,3,4,7,1,8,6]=>[3,2,1,1,1]
[8,6,3,1,4,5,7,2]=>[4,2,1,1]
[6,7,3,1,5,4,2,8]=>[4,2,1,1]
[5,8,3,1,2,4,7,6]=>[3,2,1,1,1]
[8,1,3,2,4,5,6,7]=>[3,1,1,1,1,1]
[8,4,1,7,2,3,6,5]=>[4,2,1,1]
[8,2,1,6,5,4,7,3]=>[5,2,1]
[3,8,1,5,6,4,7,2]=>[4,1,1,1,1]
[6,8,4,1,2,5,7,3]=>[3,2,1,1,1]
[3,2,8,1,6,5,7,4]=>[4,2,1,1]
[7,6,4,1,5,2,3,8]=>[4,2,1,1]
[8,6,1,5,4,7,3,2]=>[6,1,1]
[3,5,1,4,6,7,2,8]=>[3,1,1,1,1,1]
[5,2,1,4,7,6,3,8]=>[3,3,1,1]
[4,5,8,2,1,3,7,6]=>[3,2,1,1,1]
[5,8,2,3,1,4,6,7]=>[3,1,1,1,1,1]
[4,2,1,3,5,8,7,6]=>[3,3,1,1]
[5,4,1,3,6,2,8,7]=>[4,2,1,1]
[8,5,4,1,3,6,2,7]=>[5,1,1,1]
[3,2,5,1,4,6,8,7]=>[3,2,1,1,1]
[8,1,4,3,5,6,7,2]=>[4,1,1,1,1]
[7,1,3,5,4,6,2,8]=>[4,1,1,1,1]
[5,1,3,4,6,2,7,8]=>[3,1,1,1,1,1]
[4,1,3,2,5,7,6,8]=>[3,2,1,1,1]
[6,8,2,4,5,1,3,7]=>[3,1,1,1,1,1]
[3,6,7,2,5,1,4,8]=>[3,1,1,1,1,1]
[4,6,7,3,1,5,2,8]=>[3,2,1,1,1]
[5,8,1,2,4,7,3,6]=>[3,1,1,1,1,1]
[6,8,1,3,5,2,7,4]=>[3,2,1,1,1]
[6,8,3,1,4,5,7,2]=>[3,2,1,1,1]
[7,5,1,8,2,3,6,4]=>[3,3,1,1]
[6,1,8,2,3,4,7,5]=>[3,2,1,1,1]
[5,3,8,4,2,6,7,1]=>[4,2,1,1]
[5,1,8,4,6,3,7,2]=>[4,2,1,1]
[4,1,8,3,5,7,2,6]=>[3,2,1,1,1]
[3,4,7,2,6,1,8,5]=>[3,2,1,1,1]
[4,5,7,3,2,6,8,1]=>[4,1,1,1,1]
[4,5,7,2,3,6,8,1]=>[3,1,1,1,1,1]
[2,6,3,4,7,5,8,1]=>[3,2,1,1,1]
[3,6,4,2,7,5,8,1]=>[4,2,1,1]
[4,5,2,7,1,6,8,3]=>[3,2,1,1,1]
[3,4,1,6,5,8,2,7]=>[3,2,1,1,1]
[4,1,2,8,5,7,3,6]=>[3,2,1,1,1]
[5,1,4,8,6,2,7,3]=>[3,2,2,1]
[7,3,1,4,8,5,6,2]=>[3,3,1,1]
[5,6,3,1,7,4,2,8]=>[3,3,1,1]
[7,3,4,1,8,5,2,6]=>[3,3,1,1]
[6,4,2,8,7,1,5,3]=>[4,3,1]
[7,2,4,8,1,5,3,6]=>[3,2,1,1,1]
[2,6,3,7,5,1,4,8]=>[3,2,1,1,1]
[7,1,3,8,5,2,4,6]=>[3,2,1,1,1]
[1,5,3,7,8,2,4,6]=>[3,1,1,1,1,1]
[3,2,6,7,1,8,4,5]=>[3,2,1,1,1]
[4,6,3,1,7,8,5,2]=>[3,3,1,1]
[5,3,1,6,7,8,4,2]=>[3,3,1,1]
[4,1,6,2,7,8,5,3]=>[3,2,2,1]
[2,1,3,4,8,7,5,6]=>[3,2,1,1,1]
[4,8,3,7,6,5,1,2]=>[5,1,1,1]
[6,3,8,7,5,4,1,2]=>[5,2,1]
[5,3,8,7,6,4,1,2]=>[5,2,1]
[2,8,7,6,1,5,4,3]=>[6,1,1]
[5,2,8,7,6,1,4,3]=>[5,2,1]
[6,2,8,7,5,1,4,3]=>[5,2,1]
[7,8,2,6,5,1,4,3]=>[5,1,1,1]
[6,1,8,7,5,4,3,2]=>[6,2]
[3,1,8,7,6,5,4,2]=>[6,2]
[7,8,2,6,1,5,4,3]=>[5,1,1,1]
[6,2,8,7,1,5,4,3]=>[5,2,1]
[4,2,8,1,7,6,5,3]=>[5,2,1]
[4,8,2,7,6,1,5,3]=>[5,1,1,1]
[3,8,7,2,1,6,5,4]=>[5,2,1]
[6,5,8,7,1,4,3,2]=>[5,2,1]
[4,8,1,7,6,5,3,2]=>[6,1,1]
[5,4,1,8,7,6,3,2]=>[5,3]
[6,4,8,1,7,5,3,2]=>[5,2,1]
[7,8,4,1,6,5,3,2]=>[5,2,1]
[7,8,3,1,6,5,4,2]=>[5,2,1]
[6,3,8,1,7,5,4,2]=>[5,2,1]
[5,3,1,8,7,6,4,2]=>[5,3]
[7,8,2,1,6,5,4,3]=>[5,2,1]
[6,5,3,1,8,7,4,2]=>[4,4]
[6,4,3,1,8,7,5,2]=>[4,4]
[7,5,2,1,8,6,4,3]=>[4,4]
[5,4,2,1,8,7,6,3]=>[4,4]
[7,3,2,1,8,6,5,4]=>[4,4]
[6,3,2,1,8,7,5,4]=>[4,4]
[6,1,4,2,3,5,8,7]=>[3,2,1,1,1]
[8,6,1,4,2,3,5,7]=>[4,1,1,1,1]
[6,8,1,4,2,3,5,7]=>[3,1,1,1,1,1]
[8,1,4,2,3,6,5,7]=>[3,2,1,1,1]
[4,1,8,2,3,6,5,7]=>[3,2,1,1,1]
[8,2,3,6,1,4,5,7]=>[3,1,1,1,1,1]
[6,2,3,8,1,4,5,7]=>[3,1,1,1,1,1]
[4,6,2,3,8,1,5,7]=>[3,1,1,1,1,1]
[4,8,2,3,6,1,5,7]=>[3,1,1,1,1,1]
[8,2,3,6,4,1,5,7]=>[4,1,1,1,1]
[8,4,3,6,2,1,5,7]=>[5,1,1,1]
[6,2,3,8,4,1,5,7]=>[3,2,1,1,1]
[8,4,2,3,6,1,5,7]=>[4,1,1,1,1]
[6,4,2,3,8,1,5,7]=>[4,1,1,1,1]
[2,6,4,3,8,1,5,7]=>[4,1,1,1,1]
[2,8,4,3,6,1,5,7]=>[4,1,1,1,1]
[2,6,3,8,4,1,5,7]=>[3,2,1,1,1]
[6,3,8,4,2,1,5,7]=>[4,2,1,1]
[2,6,3,8,1,4,5,7]=>[3,1,1,1,1,1]
[2,8,3,6,1,4,5,7]=>[3,1,1,1,1,1]
[8,3,6,4,2,1,5,7]=>[5,1,1,1]
[2,8,3,6,4,1,5,7]=>[4,1,1,1,1]
[8,3,6,2,4,1,5,7]=>[4,1,1,1,1]
[8,3,6,2,1,4,5,7]=>[4,1,1,1,1]
[6,2,1,3,8,4,5,7]=>[3,2,1,1,1]
[8,2,1,3,6,4,5,7]=>[3,2,1,1,1]
[6,3,8,2,4,1,5,7]=>[4,1,1,1,1]
[6,2,4,3,8,1,5,7]=>[4,1,1,1,1]
[3,6,4,7,8,5,1,2]=>[3,2,1,1,1]
[6,4,8,5,3,7,1,2]=>[4,2,1,1]
[1,6,5,4,2,7,8,3]=>[4,2,1,1]
[1,6,5,2,4,8,7,3]=>[4,2,1,1]
[7,8,1,4,2,5,6,3]=>[3,2,1,1,1]
[4,8,5,3,1,6,2,7]=>[4,2,1,1]
[6,1,8,7,4,2,3,5]=>[4,2,1,1]
[1,3,6,8,7,5,2,4]=>[4,1,1,1,1]
[1,8,2,5,4,7,6,3]=>[4,2,1,1]
[7,1,2,4,5,8,6,3]=>[3,2,1,1,1]
[1,6,3,7,8,5,2,4]=>[3,2,1,1,1]
[4,6,2,3,7,8,1,5]=>[3,1,1,1,1,1]
[4,6,3,7,1,2,8,5]=>[3,2,1,1,1]
[4,2,1,3,5,7,8,6]=>[3,2,1,1,1]
[7,3,2,4,5,1,8,6]=>[4,2,1,1]
[7,8,4,2,6,3,1,5]=>[4,2,1,1]
[4,2,6,3,8,7,1,5]=>[3,2,2,1]
[5,8,2,7,4,3,1,6]=>[5,1,1,1]
[4,3,6,8,1,2,7,5]=>[3,2,1,1,1]
[6,4,3,5,2,8,1,7]=>[5,1,1,1]
[3,8,1,7,5,6,4,2]=>[5,1,1,1]
[8,2,5,7,3,6,4,1]=>[5,1,1,1]
[1,8,6,7,5,3,4,2]=>[5,1,1,1]
[8,2,6,7,5,3,4,1]=>[5,1,1,1]
[1,5,8,7,2,6,4,3]=>[5,1,1,1]
[5,4,8,6,2,3,7,1]=>[4,2,1,1]
[2,7,6,1,3,5,4,8]=>[4,1,1,1,1]
[6,4,1,8,2,5,7,3]=>[3,3,1,1]
[2,8,6,1,3,5,4,7]=>[4,1,1,1,1]
[4,1,3,6,5,8,7,2]=>[3,2,2,1]
[2,1,6,3,5,8,7,4]=>[3,2,2,1]
[2,4,1,3,8,5,7,6]=>[3,2,1,1,1]
[2,4,1,3,5,8,7,6]=>[3,2,1,1,1]
[2,6,1,3,5,8,7,4]=>[3,2,1,1,1]
[4,6,1,3,5,8,7,2]=>[3,2,1,1,1]
[6,1,4,3,5,8,7,2]=>[4,2,1,1]
[6,4,1,3,5,8,7,2]=>[4,2,1,1]
[6,2,1,3,5,8,7,4]=>[3,3,1,1]
[4,2,1,3,6,5,7,8]=>[3,2,1,1,1]
[4,2,1,6,3,5,7,8]=>[3,2,1,1,1]
[6,2,1,8,3,5,7,4]=>[3,3,1,1]
[6,2,1,3,8,5,7,4]=>[3,3,1,1]
[6,1,4,3,8,5,7,2]=>[4,2,1,1]
[1,6,4,3,8,5,7,2]=>[4,2,1,1]
[8,1,4,3,6,5,7,2]=>[4,2,1,1]
[8,4,1,3,6,5,7,2]=>[4,2,1,1]
[8,2,1,3,6,5,7,4]=>[4,2,1,1]
[8,2,1,6,3,5,7,4]=>[4,2,1,1]
[8,2,1,4,3,5,7,6]=>[3,2,2,1]
[6,2,1,4,3,5,7,8]=>[3,2,1,1,1]
[8,2,4,1,3,5,7,6]=>[3,2,1,1,1]
[8,2,6,1,3,5,7,4]=>[4,1,1,1,1]
[8,4,6,1,3,5,7,2]=>[4,1,1,1,1]
[8,4,1,6,3,5,7,2]=>[4,2,1,1]
[8,1,4,6,3,5,7,2]=>[4,1,1,1,1]
[1,8,4,6,3,5,7,2]=>[4,1,1,1,1]
[1,6,4,8,3,5,7,2]=>[4,1,1,1,1]
[6,4,1,8,3,5,7,2]=>[4,2,1,1]
[6,4,8,1,3,5,7,2]=>[4,1,1,1,1]
[6,2,8,1,3,5,7,4]=>[3,2,1,1,1]
[4,2,8,1,3,5,7,6]=>[3,2,1,1,1]
[2,6,8,1,3,5,7,4]=>[3,1,1,1,1,1]
[4,6,8,1,3,5,7,2]=>[3,1,1,1,1,1]
[4,6,1,8,3,5,7,2]=>[3,2,1,1,1]
[4,1,6,8,3,5,7,2]=>[3,2,1,1,1]
[1,4,6,3,8,5,7,2]=>[3,2,1,1,1]
[4,6,1,3,8,5,7,2]=>[3,2,1,1,1]
[2,4,1,8,3,5,7,6]=>[3,2,1,1,1]
[2,1,6,8,3,5,7,4]=>[3,2,1,1,1]
[4,1,3,6,8,5,7,2]=>[3,2,1,1,1]
[1,4,3,6,8,5,7,2]=>[3,2,1,1,1]
[4,1,3,8,6,5,7,2]=>[4,2,1,1]
[2,1,8,3,6,5,7,4]=>[4,2,1,1]
[2,1,6,4,3,5,7,8]=>[3,2,1,1,1]
[2,6,1,4,3,5,7,8]=>[3,1,1,1,1,1]
[2,8,1,4,3,5,7,6]=>[3,2,1,1,1]
[2,8,1,6,3,5,7,4]=>[4,1,1,1,1]
[4,8,1,3,6,5,7,2]=>[4,1,1,1,1]
[1,4,8,3,6,5,7,2]=>[4,1,1,1,1]
[1,4,8,6,3,5,7,2]=>[4,1,1,1,1]
[4,1,8,6,3,5,7,2]=>[4,2,1,1]
[4,8,1,6,3,5,7,2]=>[4,1,1,1,1]
[4,8,6,1,3,5,7,2]=>[4,1,1,1,1]
[2,8,6,1,3,5,7,4]=>[4,1,1,1,1]
[2,8,4,1,3,5,7,6]=>[3,2,1,1,1]
[2,6,4,1,3,5,7,8]=>[3,1,1,1,1,1]
[4,6,2,1,3,5,7,8]=>[3,1,1,1,1,1]
[6,8,1,4,3,5,7,2]=>[4,1,1,1,1]
[6,1,8,4,3,5,7,2]=>[4,2,1,1]
[1,6,8,4,3,5,7,2]=>[4,1,1,1,1]
[1,8,6,4,3,5,7,2]=>[5,1,1,1]
[8,1,6,4,3,5,7,2]=>[5,1,1,1]
[8,6,1,4,3,5,7,2]=>[5,1,1,1]
[8,6,4,1,3,5,7,2]=>[5,1,1,1]
[8,6,2,1,3,5,7,4]=>[4,2,1,1]
[8,4,2,1,3,5,7,6]=>[4,2,1,1]
[7,8,6,5,2,1,4,3]=>[5,2,1]
[5,7,4,1,8,6,3,2]=>[4,3,1]
[5,6,4,2,8,3,7,1]=>[4,2,1,1]
[5,6,4,2,7,3,1,8]=>[4,2,1,1]
[5,7,1,4,6,3,2,8]=>[4,1,1,1,1]
[5,8,1,4,6,3,7,2]=>[4,1,1,1,1]
[3,6,7,4,5,8,2,1]=>[4,1,1,1,1]
[3,5,7,4,6,8,2,1]=>[4,1,1,1,1]
[6,8,4,1,7,2,5,3]=>[4,2,1,1]
[5,4,6,1,7,8,3,2]=>[4,2,1,1]
[5,6,4,1,8,7,3,2]=>[4,3,1]
[3,5,8,4,6,7,2,1]=>[4,1,1,1,1]
[3,6,8,4,5,7,2,1]=>[4,1,1,1,1]
[3,7,8,4,5,6,2,1]=>[4,1,1,1,1]
[6,8,1,4,5,3,7,2]=>[4,1,1,1,1]
[6,7,1,4,5,3,2,8]=>[4,1,1,1,1]
[3,7,1,5,4,6,2,8]=>[4,1,1,1,1]
[3,8,1,5,4,6,7,2]=>[4,1,1,1,1]
[3,7,1,5,4,6,8,2]=>[4,1,1,1,1]
[6,7,1,4,5,3,8,2]=>[4,1,1,1,1]
[5,7,1,4,6,3,8,2]=>[4,1,1,1,1]
[5,6,4,2,7,3,8,1]=>[4,2,1,1]
[5,4,7,2,8,3,1,6]=>[4,2,1,1]
[5,4,7,2,8,3,6,1]=>[4,2,1,1]
[5,6,4,2,8,3,1,7]=>[4,2,1,1]
[5,8,1,4,6,3,2,7]=>[4,1,1,1,1]
[3,8,1,5,4,6,2,7]=>[4,1,1,1,1]
[3,6,1,5,4,2,7,8]=>[4,1,1,1,1]
[3,6,1,5,4,8,2,7]=>[4,1,1,1,1]
[6,8,3,1,4,2,5,7]=>[3,2,1,1,1]
[7,3,8,1,4,2,5,6]=>[3,2,1,1,1]
[6,7,3,1,4,2,8,5]=>[3,2,2,1]
[3,6,1,5,4,7,8,2]=>[4,1,1,1,1]
[3,4,1,2,7,6,5,8]=>[3,2,1,1,1]
[3,4,1,2,6,8,7,5]=>[3,2,1,1,1]
[6,8,3,1,4,7,2,5]=>[3,2,1,1,1]
[6,4,7,2,8,5,1,3]=>[4,2,1,1]
[5,8,1,4,7,3,2,6]=>[4,1,1,1,1]
[7,8,1,4,5,3,2,6]=>[4,1,1,1,1]
[3,8,1,5,4,7,2,6]=>[4,1,1,1,1]
[3,6,1,5,4,8,7,2]=>[4,2,1,1]
[3,6,1,5,4,7,2,8]=>[4,1,1,1,1]
[6,7,3,1,4,2,5,8]=>[3,2,1,1,1]
[6,8,3,1,4,2,7,5]=>[3,2,2,1]
[7,8,3,1,4,6,2,5]=>[3,2,1,1,1]
[7,8,4,2,6,5,1,3]=>[4,2,1,1]
[6,5,8,7,3,4,2,1]=>[5,2,1]
[7,8,3,1,4,6,5,2]=>[4,2,1,1]
[6,7,3,1,4,5,2,8]=>[3,2,1,1,1]
[3,7,1,5,4,2,6,8]=>[4,1,1,1,1]
[3,8,1,5,4,2,7,6]=>[4,2,1,1]
[5,8,1,4,7,3,6,2]=>[4,1,1,1,1]
[6,8,4,2,7,5,3,1]=>[5,2,1]
[6,4,7,2,8,5,3,1]=>[4,3,1]
[6,3,7,1,4,8,5,2]=>[3,3,1,1]
[6,8,3,1,4,7,5,2]=>[4,2,1,1]
[3,7,1,5,4,8,6,2]=>[4,2,1,1]
[3,4,1,2,8,5,7,6]=>[3,2,1,1,1]
[3,4,1,2,5,8,7,6]=>[3,2,1,1,1]
[3,7,1,5,4,2,8,6]=>[4,2,1,1]
[6,7,3,1,4,5,8,2]=>[3,2,1,1,1]
[7,3,8,1,4,5,2,6]=>[3,2,1,1,1]
[7,3,8,1,4,5,6,2]=>[3,2,1,1,1]
[6,8,3,1,4,5,2,7]=>[3,2,1,1,1]
[3,8,1,5,4,2,6,7]=>[4,1,1,1,1]
[8,5,7,4,3,2,1,6]=>[6,1,1]
[8,7,3,6,5,2,1,4]=>[6,1,1]
[6,5,8,4,3,2,1,7]=>[6,1,1]
[8,4,7,6,3,2,1,5]=>[6,1,1]
[5,8,7,4,3,2,1,6]=>[6,1,1]
[5,8,6,2,3,4,7,1]=>[4,1,1,1,1]
[4,5,2,7,3,1,8,6]=>[3,2,2,1]
[4,8,2,6,3,5,7,1]=>[4,1,1,1,1]
[4,3,7,8,6,5,1,2]=>[4,2,1,1]
[4,1,7,2,5,8,6,3]=>[3,2,2,1]
[7,8,2,1,5,6,4,3]=>[4,2,1,1]
[1,6,2,5,8,4,3,7]=>[4,1,1,1,1]
[2,1,8,7,4,5,3,6]=>[4,2,1,1]
[7,3,1,6,8,5,2,4]=>[4,2,1,1]
[1,5,8,6,2,3,7,4]=>[3,2,1,1,1]
[2,4,8,3,1,6,5,7]=>[3,2,1,1,1]
[5,2,7,1,8,6,3,4]=>[3,3,1,1]
[2,6,1,3,8,7,4,5]=>[3,2,1,1,1]
[6,5,2,8,1,7,3,4]=>[4,2,1,1]
[8,5,4,3,7,2,6,1]=>[6,1,1]
[8,3,7,4,2,6,5,1]=>[5,2,1]
[5,4,2,8,3,1,7,6]=>[4,2,2]
[2,8,6,4,1,7,5,3]=>[4,3,1]
[8,4,7,6,2,5,3,1]=>[6,1,1]
[4,8,7,6,1,5,3,2]=>[6,1,1]
[7,4,8,6,2,1,5,3]=>[4,2,2]
[7,3,8,5,2,1,6,4]=>[4,2,2]
[7,3,8,4,2,1,6,5]=>[4,2,2]
[7,5,4,3,8,2,1,6]=>[6,1,1]
[3,7,8,4,1,2,6,5]=>[3,2,1,1,1]
[4,7,8,6,1,2,5,3]=>[4,1,1,1,1]
[8,7,4,6,3,5,2,1]=>[6,1,1]
[5,7,8,6,1,2,4,3]=>[4,1,1,1,1]
[6,4,7,8,3,1,2,5]=>[4,1,1,1,1]
[7,3,4,8,2,1,5,6]=>[4,1,1,1,1]
[7,6,4,8,3,2,1,5]=>[6,1,1]
[7,5,8,6,2,1,4,3]=>[4,2,2]
[6,5,8,7,3,1,4,2]=>[4,2,2]
[2,3,8,4,1,6,7,5]=>[3,2,1,1,1]
[6,4,8,7,3,1,5,2]=>[4,2,2]
[8,6,4,7,3,2,5,1]=>[6,1,1]
[8,3,4,7,2,5,6,1]=>[4,1,1,1,1]
[3,4,8,7,1,5,6,2]=>[4,1,1,1,1]
[2,5,8,6,1,4,7,3]=>[4,1,1,1,1]
[8,3,5,7,2,4,6,1]=>[4,1,1,1,1]
[8,4,6,7,2,3,5,1]=>[4,1,1,1,1]
[4,6,8,7,1,3,5,2]=>[4,1,1,1,1]
[2,6,8,5,1,3,7,4]=>[3,2,1,1,1]
[2,5,8,3,1,4,7,6]=>[3,2,1,1,1]
[5,6,8,7,1,3,4,2]=>[4,1,1,1,1]
[7,4,6,8,2,1,3,5]=>[4,1,1,1,1]
[2,3,5,4,1,8,6,7]=>[3,2,1,1,1]
[2,3,6,4,8,1,5,7]=>[3,1,1,1,1,1]
[1,8,4,6,3,5,2,7]=>[4,1,1,1,1]
[5,4,8,6,2,1,3,7]=>[4,2,1,1]
[2,3,6,8,1,5,4,7]=>[3,1,1,1,1,1]
[2,5,6,1,4,7,8,3]=>[3,1,1,1,1,1]
[2,5,6,1,4,7,3,8]=>[3,1,1,1,1,1]
[7,3,5,1,6,8,4,2]=>[4,2,1,1]
[2,7,6,1,8,5,4,3]=>[5,2,1]
[2,7,6,8,1,4,5,3]=>[4,1,1,1,1]
[1,8,7,6,3,2,5,4]=>[5,2,1]
[1,8,7,6,3,2,4,5]=>[5,1,1,1]
[5,7,8,6,2,3,4,1]=>[4,1,1,1,1]
[2,7,6,1,8,5,3,4]=>[4,2,1,1]
[6,3,5,1,7,2,4,8]=>[3,2,1,1,1]
[2,3,4,7,6,1,5,8]=>[3,1,1,1,1,1]
[7,3,5,8,4,1,2,6]=>[4,1,1,1,1]
[1,8,4,5,2,7,3,6]=>[3,2,1,1,1]
[1,8,4,5,2,7,6,3]=>[4,2,1,1]
[7,3,5,8,4,1,6,2]=>[4,2,1,1]
[2,7,6,4,8,5,1,3]=>[4,2,1,1]
[7,3,5,4,6,8,1,2]=>[4,1,1,1,1]
[6,3,5,4,7,1,8,2]=>[4,2,1,1]
[6,3,5,4,7,1,2,8]=>[4,1,1,1,1]
[3,4,1,5,6,8,7,2]=>[3,2,1,1,1]
[3,7,1,6,8,5,2,4]=>[4,1,1,1,1]
[2,3,1,8,6,4,7,5]=>[3,2,2,1]
[1,8,4,3,6,2,5,7]=>[4,1,1,1,1]
[2,3,1,8,6,4,5,7]=>[3,2,1,1,1]
[3,7,1,6,8,5,4,2]=>[5,1,1,1]
[6,3,5,4,7,2,1,8]=>[5,1,1,1]
[7,3,5,4,6,8,2,1]=>[5,1,1,1]
[2,7,6,4,8,5,3,1]=>[5,2,1]
[1,8,4,5,2,6,3,7]=>[3,2,1,1,1]
[6,4,8,5,3,1,2,7]=>[4,2,1,1]
[7,3,5,8,4,6,2,1]=>[5,1,1,1]
[2,3,4,6,5,8,1,7]=>[3,1,1,1,1,1]
[2,3,4,7,5,1,8,6]=>[3,2,1,1,1]
[2,3,4,7,5,1,6,8]=>[3,1,1,1,1,1]
[2,3,4,7,1,6,5,8]=>[3,1,1,1,1,1]
[2,3,4,7,1,6,8,5]=>[3,1,1,1,1,1]
[2,3,4,6,1,8,7,5]=>[3,2,1,1,1]
[6,3,5,8,4,2,7,1]=>[5,1,1,1]
[7,4,8,5,3,2,1,6]=>[5,2,1]
[1,8,4,5,2,3,6,7]=>[3,1,1,1,1,1]
[7,4,8,5,3,2,6,1]=>[5,2,1]
[6,3,5,8,4,2,1,7]=>[5,1,1,1]
[5,2,4,6,8,3,7,1]=>[4,1,1,1,1]
[1,5,7,4,6,3,2,8]=>[4,1,1,1,1]
[5,2,8,4,6,3,7,1]=>[4,2,1,1]
[3,8,5,4,6,7,2,1]=>[5,1,1,1]
[6,8,3,4,5,7,2,1]=>[4,1,1,1,1]
[2,5,7,4,6,3,8,1]=>[4,1,1,1,1]
[5,4,1,7,8,3,2,6]=>[4,2,1,1]
[5,4,2,7,8,3,6,1]=>[4,2,1,1]
[5,1,4,6,8,3,2,7]=>[4,1,1,1,1]
[5,1,8,4,6,3,2,7]=>[4,2,1,1]
[8,1,6,4,5,3,2,7]=>[5,1,1,1]
[8,1,3,5,4,6,2,7]=>[4,1,1,1,1]
[8,1,6,2,4,3,5,7]=>[4,1,1,1,1]
[8,7,1,2,4,3,5,6]=>[4,1,1,1,1]
[1,7,6,2,4,3,5,8]=>[4,1,1,1,1]
[8,7,3,2,4,6,5,1]=>[5,2,1]
[8,2,6,3,4,5,7,1]=>[4,1,1,1,1]
[1,7,6,3,4,5,2,8]=>[4,1,1,1,1]
[1,7,2,5,4,3,6,8]=>[4,1,1,1,1]
[8,7,2,4,5,3,6,1]=>[5,1,1,1]
[5,8,2,4,7,3,6,1]=>[4,1,1,1,1]
[6,8,3,2,4,7,5,1]=>[4,2,1,1]
[8,7,1,3,4,5,2,6]=>[4,1,1,1,1]
[8,1,6,3,4,5,2,7]=>[4,1,1,1,1]
[8,1,2,5,4,3,6,7]=>[4,1,1,1,1]
[3,4,8,7,5,2,6,1]=>[5,1,1,1]
[3,2,8,6,1,5,4,7]=>[4,2,1,1]
[8,6,1,2,4,3,5,7]=>[4,1,1,1,1]
[8,7,3,6,4,2,5,1]=>[6,1,1]
[3,8,7,2,5,4,6,1]=>[5,1,1,1]
[8,7,2,4,5,6,3,1]=>[5,1,1,1]
[5,3,6,2,4,8,7,1]=>[4,2,1,1]
[3,5,2,8,6,1,4,7]=>[3,2,1,1,1]
[3,7,2,5,1,4,8,6]=>[3,2,1,1,1]
[5,1,8,6,2,3,4,7]=>[3,2,1,1,1]
[2,5,4,1,8,6,3,7]=>[3,3,1,1]
[3,7,6,1,8,2,5,4]=>[4,2,1,1]
[7,6,3,1,8,2,4,5]=>[4,2,1,1]
[8,2,3,6,1,4,7,5]=>[3,2,1,1,1]
[1,8,2,6,3,4,7,5]=>[3,2,1,1,1]
[8,1,3,6,4,7,2,5]=>[4,1,1,1,1]
[7,1,3,6,4,8,2,5]=>[4,1,1,1,1]
[8,2,1,3,5,7,4,6]=>[3,2,1,1,1]
[8,2,6,3,1,4,7,5]=>[4,2,1,1]
[7,5,4,1,3,8,2,6]=>[5,1,1,1]
[2,7,5,8,3,4,1,6]=>[4,1,1,1,1]
[7,3,8,5,4,1,2,6]=>[4,2,1,1]
[7,2,3,6,1,4,8,5]=>[3,2,1,1,1]
[1,3,7,2,5,8,4,6]=>[3,1,1,1,1,1]
[1,7,2,3,5,8,4,6]=>[3,1,1,1,1,1]
[7,4,8,1,3,6,2,5]=>[4,1,1,1,1]
[8,1,2,3,5,7,4,6]=>[3,1,1,1,1,1]
[7,1,2,3,5,8,4,6]=>[3,1,1,1,1,1]
[8,6,1,4,7,3,2,5]=>[5,1,1,1]
[2,6,3,7,1,4,8,5]=>[3,2,1,1,1]
[2,6,3,8,1,4,7,5]=>[3,2,1,1,1]
[7,5,4,8,1,3,2,6]=>[5,1,1,1]
[8,5,4,7,1,3,2,6]=>[5,1,1,1]
[2,3,1,8,5,4,6,7]=>[3,2,1,1,1]
[8,6,5,1,3,4,2,7]=>[5,1,1,1]
[8,5,1,7,6,3,4,2]=>[5,2,1]
[3,4,7,6,1,8,5,2]=>[4,2,1,1]
[3,5,2,6,7,1,8,4]=>[3,2,1,1,1]
[3,2,8,4,7,5,1,6]=>[4,2,1,1]
[8,4,7,5,1,3,2,6]=>[5,1,1,1]
[3,8,1,6,5,2,7,4]=>[4,2,1,1]
[6,1,2,8,3,4,7,5]=>[3,2,1,1,1]
[6,8,3,1,7,2,4,5]=>[3,2,1,1,1]
[3,7,2,5,6,1,8,4]=>[3,2,1,1,1]
[6,8,4,2,5,1,7,3]=>[4,2,1,1]
[2,7,5,3,8,4,1,6]=>[4,2,1,1]
[8,3,1,4,7,2,6,5]=>[4,2,1,1]
[8,3,2,1,5,7,4,6]=>[4,2,1,1]
[2,8,3,6,4,7,1,5]=>[4,1,1,1,1]
[7,3,6,4,8,1,2,5]=>[4,1,1,1,1]
[8,3,6,4,7,1,2,5]=>[4,1,1,1,1]
[1,2,8,3,5,7,4,6]=>[3,1,1,1,1,1]
[1,8,3,2,5,7,4,6]=>[3,2,1,1,1]
[6,5,1,7,4,2,8,3]=>[4,2,2]
[7,3,6,4,8,2,1,5]=>[5,1,1,1]
[4,6,1,7,3,5,2,8]=>[3,2,1,1,1]
[5,6,1,7,3,4,2,8]=>[3,2,1,1,1]
[6,1,7,3,4,2,8,5]=>[3,2,2,1]
[7,3,8,1,6,5,2,4]=>[4,2,1,1]
[8,3,7,1,6,5,2,4]=>[5,1,1,1]
[5,1,7,4,2,8,6,3]=>[3,3,2]
[2,8,1,7,6,5,3,4]=>[5,1,1,1]
[4,2,8,6,5,1,7,3]=>[4,2,2]
[6,4,2,8,5,1,7,3]=>[4,2,2]
[8,6,4,7,1,5,2,3]=>[4,2,1,1]
[7,6,4,8,1,5,2,3]=>[4,2,1,1]
[5,1,6,4,2,3,8,7]=>[3,2,2,1]
[4,2,3,8,7,5,1,6]=>[4,2,1,1]
[3,8,7,1,6,5,2,4]=>[5,1,1,1]
[2,4,3,8,1,6,7,5]=>[3,2,1,1,1]
[2,4,3,7,1,6,8,5]=>[3,2,1,1,1]
[4,2,3,7,8,5,1,6]=>[3,2,1,1,1]
[5,1,6,4,2,3,7,8]=>[3,2,1,1,1]
[6,4,7,8,1,5,2,3]=>[3,2,1,1,1]
[8,7,4,6,1,5,2,3]=>[5,1,1,1]
[6,5,7,8,1,4,2,3]=>[4,1,1,1,1]
[4,7,8,6,1,5,2,3]=>[4,1,1,1,1]
[3,2,4,7,8,1,5,6]=>[3,1,1,1,1,1]
[3,2,4,8,7,1,5,6]=>[3,2,1,1,1]
[4,8,7,6,1,5,2,3]=>[5,1,1,1]
[5,8,7,6,1,4,2,3]=>[5,1,1,1]
[8,6,5,7,1,4,2,3]=>[5,1,1,1]
[5,1,6,7,4,2,3,8]=>[3,2,1,1,1]
[6,7,4,8,1,5,2,3]=>[3,2,1,1,1]
[8,4,7,6,1,5,2,3]=>[5,1,1,1]
[8,3,2,4,7,1,5,6]=>[4,1,1,1,1]
[7,3,2,4,8,1,5,6]=>[4,1,1,1,1]
[2,5,3,7,1,6,4,8]=>[3,2,1,1,1]
[8,4,6,7,1,5,2,3]=>[4,1,1,1,1]
[7,4,6,8,1,5,2,3]=>[4,1,1,1,1]
[5,1,6,8,4,2,3,7]=>[3,2,1,1,1]
[4,2,3,7,5,1,6,8]=>[3,2,1,1,1]
[3,7,5,8,1,6,2,4]=>[3,2,1,1,1]
[2,4,3,7,1,6,5,8]=>[3,2,1,1,1]
[2,4,7,1,5,8,6,3]=>[3,2,1,1,1]
[3,2,4,7,6,1,5,8]=>[3,2,1,1,1]
[4,7,6,8,1,5,2,3]=>[4,1,1,1,1]
[8,5,6,7,1,4,2,3]=>[4,1,1,1,1]
[8,6,7,5,1,4,2,3]=>[5,1,1,1]
[7,6,8,5,1,4,2,3]=>[5,1,1,1]
[6,8,7,5,1,4,2,3]=>[5,1,1,1]
[5,6,8,7,1,4,2,3]=>[4,1,1,1,1]
[4,6,8,7,1,5,2,3]=>[4,1,1,1,1]
[2,4,6,7,1,5,8,3]=>[3,1,1,1,1,1]
[3,2,4,6,1,5,7,8]=>[3,1,1,1,1,1]
[6,7,8,5,1,4,2,3]=>[4,1,1,1,1]
[7,8,6,5,1,4,2,3]=>[5,1,1,1]
[3,1,7,5,4,2,8,6]=>[4,2,2]
[4,1,8,5,2,3,6,7]=>[3,2,1,1,1]
[8,2,7,1,5,3,4,6]=>[4,1,1,1,1]
[6,3,7,1,5,4,2,8]=>[4,2,1,1]
[7,1,5,3,8,4,2,6]=>[4,2,1,1]
[4,5,1,3,6,8,2,7]=>[3,1,1,1,1,1]
[6,8,3,1,5,4,2,7]=>[4,2,1,1]
[3,6,2,1,5,8,4,7]=>[3,2,1,1,1]
[8,6,2,1,5,3,4,7]=>[4,2,1,1]
[4,8,2,1,7,5,3,6]=>[4,2,1,1]
[7,1,6,2,8,3,4,5]=>[3,2,1,1,1]
[4,7,1,2,6,3,8,5]=>[3,2,1,1,1]
[2,7,8,1,5,3,4,6]=>[3,1,1,1,1,1]
[4,7,2,1,8,5,3,6]=>[3,3,1,1]
[8,7,2,1,4,5,3,6]=>[4,2,1,1]
[8,7,5,6,1,4,3,2]=>[6,1,1]
[5,7,8,6,1,4,3,2]=>[5,1,1,1]
[3,7,1,4,5,6,8,2]=>[3,1,1,1,1,1]
[3,5,1,4,7,6,8,2]=>[3,2,1,1,1]
[5,6,8,7,1,4,3,2]=>[5,1,1,1]
[6,8,5,7,1,4,3,2]=>[5,1,1,1]
[8,6,5,7,1,4,3,2]=>[6,1,1]
[8,5,7,6,1,4,3,2]=>[6,1,1]
[6,5,7,8,1,4,3,2]=>[5,1,1,1]
[7,2,3,1,5,6,4,8]=>[3,2,1,1,1]
[5,3,1,8,4,6,7,2]=>[3,3,1,1]
[8,3,1,5,4,6,7,2]=>[4,2,1,1]
[6,2,8,1,4,5,3,7]=>[3,2,1,1,1]
[4,2,1,5,6,3,8,7]=>[3,2,2,1]
[7,1,2,5,8,3,4,6]=>[3,1,1,1,1,1]
[8,5,6,7,1,4,3,2]=>[5,1,1,1]
[7,6,8,5,1,4,3,2]=>[6,1,1]
[6,8,7,5,1,4,3,2]=>[6,1,1]
[2,7,6,1,4,5,3,8]=>[4,1,1,1,1]
[5,7,6,8,1,4,3,2]=>[5,1,1,1]
[7,8,6,5,1,4,3,2]=>[6,1,1]
[4,3,1,6,5,8,7,2]=>[3,3,2]
[5,3,1,2,4,8,7,6]=>[3,3,1,1]
[5,3,6,2,1,8,7,4]=>[4,3,1]
[5,3,7,2,1,4,6,8]=>[4,1,1,1,1]
[5,3,7,2,8,4,1,6]=>[4,2,1,1]
[7,2,4,5,8,3,1,6]=>[4,1,1,1,1]
[7,2,4,5,1,3,6,8]=>[3,1,1,1,1,1]
[6,2,4,5,1,8,7,3]=>[3,3,1,1]
[3,1,4,5,2,8,7,6]=>[3,2,2,1]
[1,6,4,5,2,8,7,3]=>[3,3,1,1]
[3,7,4,5,1,2,6,8]=>[3,1,1,1,1,1]
[3,7,4,5,8,2,1,6]=>[4,1,1,1,1]
[1,7,4,2,6,3,5,8]=>[3,2,1,1,1]
[8,7,4,5,2,1,6,3]=>[5,2,1]
[6,3,7,1,8,4,2,5]=>[3,3,1,1]
[5,7,4,1,6,3,2,8]=>[4,2,1,1]
[1,7,4,8,6,3,2,5]=>[4,2,1,1]
[5,7,4,8,6,3,1,2]=>[4,2,1,1]
[4,8,3,5,6,7,1,2]=>[3,1,1,1,1,1]
[1,8,3,5,6,7,2,4]=>[3,1,1,1,1,1]
[4,8,1,5,6,7,2,3]=>[3,1,1,1,1,1]
[4,1,3,5,6,7,2,8]=>[3,1,1,1,1,1]
[5,8,4,3,6,1,2,7]=>[4,1,1,1,1]
[5,3,8,4,1,7,2,6]=>[3,2,2,1]
[1,5,8,4,6,7,3,2]=>[4,1,1,1,1]
[1,4,8,3,6,7,5,2]=>[4,1,1,1,1]
[4,3,8,2,1,7,5,6]=>[4,2,1,1]
[3,8,4,2,6,1,5,7]=>[4,1,1,1,1]
[1,8,2,5,6,7,4,3]=>[4,1,1,1,1]
[3,8,1,5,6,7,4,2]=>[4,1,1,1,1]
[3,8,2,5,6,7,1,4]=>[3,1,1,1,1,1]
[8,2,1,5,6,7,4,3]=>[4,2,1,1]
[8,1,3,5,6,7,4,2]=>[4,1,1,1,1]
[7,1,4,3,6,2,5,8]=>[4,1,1,1,1]
[7,8,4,3,6,2,1,5]=>[5,1,1,1]
[4,3,1,8,5,7,6,2]=>[4,3,1]
[4,3,1,6,8,7,5,2]=>[4,3,1]
[6,3,1,8,2,7,4,5]=>[3,3,1,1]
[6,3,5,8,2,7,1,4]=>[4,1,1,1,1]
[7,5,4,8,6,2,1,3]=>[5,2,1]
[7,1,4,8,6,2,3,5]=>[3,2,1,1,1]
[7,5,4,1,6,2,3,8]=>[4,2,1,1]
[7,6,4,5,8,1,3,2]=>[5,1,1,1]
[1,6,4,5,8,2,3,7]=>[3,1,1,1,1,1]
[7,3,6,1,8,2,4,5]=>[3,2,1,1,1]
[1,7,6,5,8,3,4,2]=>[5,1,1,1]
[1,8,5,3,6,7,4,2]=>[4,2,1,1]
[8,3,5,2,1,7,4,6]=>[4,2,1,1]
[8,4,1,5,6,7,3,2]=>[4,2,1,1]
[8,4,2,5,6,7,1,3]=>[4,1,1,1,1]
[4,1,8,5,6,7,3,2]=>[4,2,1,1]
[1,2,8,5,6,7,3,4]=>[3,1,1,1,1,1]
[4,2,1,5,6,7,3,8]=>[3,2,1,1,1]
[1,5,3,8,6,7,4,2]=>[4,2,1,1]
[1,4,5,8,6,7,3,2]=>[4,1,1,1,1]
[4,3,5,8,1,7,2,6]=>[3,2,1,1,1]
[3,5,4,8,6,1,2,7]=>[3,2,1,1,1]
[1,4,8,5,6,7,2,3]=>[3,1,1,1,1,1]
[3,4,8,5,6,7,1,2]=>[3,1,1,1,1,1]
[2,7,1,5,6,3,4,8]=>[3,1,1,1,1,1]
[2,7,1,4,3,6,5,8]=>[3,2,1,1,1]
[4,3,7,2,5,6,8,1]=>[4,1,1,1,1]
[2,6,3,1,4,5,8,7]=>[3,2,1,1,1]
[3,7,1,4,2,6,8,5]=>[3,2,1,1,1]
[3,7,1,5,6,2,8,4]=>[3,2,1,1,1]
[4,7,1,5,6,8,2,3]=>[3,1,1,1,1,1]
[8,5,2,6,7,3,1,4]=>[4,2,1,1]
[8,4,2,6,3,7,1,5]=>[4,2,1,1]
[8,4,2,3,5,7,1,6]=>[4,1,1,1,1]
[4,7,3,2,5,6,1,8]=>[4,1,1,1,1]
[5,3,4,6,2,8,1,7]=>[4,1,1,1,1]
[5,3,7,4,2,8,1,6]=>[4,2,1,1]
[6,4,7,2,3,8,1,5]=>[4,1,1,1,1]
[6,5,7,2,8,3,1,4]=>[4,2,1,1]
[5,3,7,2,4,8,6,1]=>[4,2,1,1]
[2,6,5,1,8,3,4,7]=>[3,2,1,1,1]
[8,7,6,1,4,5,2,3]=>[5,1,1,1]
[8,7,6,1,3,2,5,4]=>[5,2,1]
[8,7,2,4,3,1,6,5]=>[5,2,1]
[8,7,4,5,1,6,2,3]=>[4,2,1,1]
[8,5,6,4,1,7,2,3]=>[4,2,1,1]
[8,5,6,3,1,2,7,4]=>[4,2,1,1]
[8,4,6,2,3,1,7,5]=>[4,2,1,1]
[8,3,5,4,2,1,7,6]=>[5,2,1]
[5,7,3,4,2,1,8,6]=>[4,2,1,1]
[6,7,4,2,3,1,8,5]=>[4,2,1,1]
[6,7,5,3,1,2,8,4]=>[4,2,1,1]
[6,7,5,4,1,8,2,3]=>[4,2,1,1]
[6,2,4,3,8,7,5,1]=>[4,3,1]
[7,3,5,4,1,8,6,2]=>[4,3,1]
[5,2,7,1,3,4,8,6]=>[3,2,1,1,1]
[2,6,5,7,3,1,4,8]=>[4,1,1,1,1]
[2,6,5,7,3,1,8,4]=>[4,2,1,1]
[6,3,1,4,7,8,5,2]=>[3,3,1,1]
[6,8,2,1,3,4,5,7]=>[3,1,1,1,1,1]
[3,7,1,8,4,5,2,6]=>[3,2,1,1,1]
[6,3,2,4,7,5,8,1]=>[4,2,1,1]
[6,3,2,4,7,5,1,8]=>[4,2,1,1]
[4,2,1,6,3,7,5,8]=>[3,2,2,1]
[4,2,1,6,3,7,8,5]=>[3,2,2,1]
[7,4,3,5,8,6,1,2]=>[4,2,1,1]
[2,7,6,8,3,1,4,5]=>[4,1,1,1,1]
[7,4,3,5,8,6,2,1]=>[5,2,1]
[4,2,1,7,3,8,6,5]=>[3,3,2]
[4,2,1,3,7,8,6,5]=>[3,3,1,1]
[5,8,1,7,4,3,6,2]=>[5,1,1,1]
[5,8,1,7,4,3,2,6]=>[5,1,1,1]
[3,7,8,6,2,1,4,5]=>[4,1,1,1,1]
[4,2,1,8,3,5,6,7]=>[3,2,1,1,1]
[4,2,1,3,6,7,5,8]=>[3,2,1,1,1]
[4,2,1,3,7,5,6,8]=>[3,2,1,1,1]
[4,2,1,3,6,8,7,5]=>[3,3,1,1]
[7,3,2,4,8,6,5,1]=>[4,3,1]
[4,2,1,6,3,8,7,5]=>[3,3,2]
[4,2,1,7,3,5,6,8]=>[3,2,1,1,1]
[3,6,7,5,2,1,4,8]=>[4,1,1,1,1]
[3,6,7,5,2,1,8,4]=>[4,2,1,1]
[7,3,4,2,6,8,5,1]=>[4,2,1,1]
[4,8,6,2,7,3,5,1]=>[4,2,1,1]
[7,3,4,2,6,8,1,5]=>[4,1,1,1,1]
[3,6,7,5,2,4,8,1]=>[4,1,1,1,1]
[3,6,7,5,2,4,1,8]=>[4,1,1,1,1]
[4,2,1,7,3,6,5,8]=>[3,3,1,1]
[4,2,1,7,3,6,8,5]=>[3,3,1,1]
[3,7,6,8,4,2,5,1]=>[5,1,1,1]
[5,8,1,7,4,2,6,3]=>[4,2,1,1]
[3,7,8,6,2,4,5,1]=>[4,1,1,1,1]
[4,2,1,3,8,6,7,5]=>[3,3,1,1]
[4,2,1,3,7,6,5,8]=>[3,3,1,1]
[4,2,1,3,5,7,6,8]=>[3,2,1,1,1]
[4,2,1,3,5,8,6,7]=>[3,2,1,1,1]
[4,8,1,7,3,6,5,2]=>[5,1,1,1]
[4,7,8,6,3,5,2,1]=>[5,1,1,1]
[4,2,1,8,3,7,6,5]=>[4,3,1]
[4,2,1,3,5,6,8,7]=>[3,2,1,1,1]
[2,6,1,5,4,7,8,3]=>[4,1,1,1,1]
[4,6,3,5,8,7,1,2]=>[3,2,1,1,1]
[3,5,6,1,4,8,7,2]=>[3,2,1,1,1]
[2,7,5,1,8,3,4,6]=>[3,2,1,1,1]
[4,7,5,2,1,3,6,8]=>[4,1,1,1,1]
[3,5,6,2,4,1,7,8]=>[3,1,1,1,1,1]
[2,5,6,1,4,8,3,7]=>[3,1,1,1,1,1]
[6,7,8,4,1,5,3,2]=>[4,2,1,1]
[7,1,6,8,4,5,3,2]=>[5,1,1,1]
[5,7,8,1,4,6,3,2]=>[4,1,1,1,1]
[1,8,4,6,7,5,3,2]=>[5,1,1,1]
[6,1,8,4,7,5,3,2]=>[5,2,1]
[4,5,8,6,1,7,3,2]=>[4,2,1,1]
[5,6,7,1,4,2,3,8]=>[3,1,1,1,1,1]
[4,8,5,2,1,6,7,3]=>[4,2,1,1]
[5,1,8,4,2,6,3,7]=>[3,2,2,1]
[1,8,4,6,2,5,3,7]=>[4,1,1,1,1]
[8,2,4,3,6,7,1,5]=>[4,1,1,1,1]
[3,2,8,5,7,1,6,4]=>[4,2,1,1]
[2,8,7,1,4,6,5,3]=>[5,1,1,1]
[8,2,7,1,5,4,6,3]=>[5,1,1,1]
[7,2,5,3,6,8,1,4]=>[4,1,1,1,1]
[7,3,1,5,6,2,4,8]=>[3,2,1,1,1]
[2,7,3,6,5,8,1,4]=>[4,1,1,1,1]
[8,7,2,4,1,6,5,3]=>[5,2,1]
[1,7,3,8,2,6,4,5]=>[3,2,1,1,1]
[1,2,7,3,6,4,5,8]=>[3,1,1,1,1,1]
[7,1,5,8,3,2,4,6]=>[4,1,1,1,1]
[1,6,2,8,4,3,7,5]=>[3,2,2,1]
[1,8,3,7,2,5,4,6]=>[4,1,1,1,1]
[8,1,4,7,3,2,5,6]=>[4,1,1,1,1]
[7,1,4,2,3,5,6,8]=>[3,1,1,1,1,1]
[2,1,3,8,4,6,7,5]=>[3,2,1,1,1]
[1,2,3,4,8,5,7,6]=>[3,1,1,1,1,1]
[2,4,7,5,6,8,3,1]=>[4,1,1,1,1]
[2,4,8,7,5,6,3,1]=>[5,1,1,1]
[2,5,3,8,4,7,6,1]=>[4,2,1,1]
[2,8,5,7,3,6,4,1]=>[5,1,1,1]
[3,1,8,5,2,7,6,4]=>[4,2,2]
[2,8,6,3,4,5,7,1]=>[4,1,1,1,1]
[2,5,7,3,4,8,6,1]=>[3,2,1,1,1]
[8,3,7,6,1,4,5,2]=>[5,1,1,1]
[3,1,7,8,2,5,6,4]=>[3,2,1,1,1]
[7,3,8,5,1,6,4,2]=>[4,2,2]
[7,5,1,2,3,4,8,6]=>[3,2,1,1,1]
[4,8,1,5,2,7,3,6]=>[3,2,1,1,1]
[4,1,2,5,3,8,7,6]=>[3,2,2,1]
[4,3,6,8,7,5,1,2]=>[4,2,1,1]
[6,4,8,1,2,5,3,7]=>[3,2,1,1,1]
[5,4,1,6,8,2,7,3]=>[3,3,1,1]
[5,4,7,1,2,8,6,3]=>[3,3,1,1]
[6,7,4,1,2,8,3,5]=>[3,2,1,1,1]
[6,5,1,2,3,7,8,4]=>[3,2,1,1,1]
[6,5,1,2,3,4,8,7]=>[3,2,1,1,1]
[6,7,4,1,2,5,3,8]=>[3,2,1,1,1]
[2,4,6,3,5,7,1,8]=>[3,1,1,1,1,1]
[1,4,6,3,7,2,5,8]=>[3,1,1,1,1,1]
[8,6,2,5,3,1,7,4]=>[5,2,1]
[8,2,3,4,5,1,7,6]=>[3,2,1,1,1]
[1,8,3,4,2,7,5,6]=>[3,2,1,1,1]
[7,8,2,4,3,1,6,5]=>[4,2,1,1]
[6,1,3,5,7,2,4,8]=>[3,1,1,1,1,1]
[8,1,3,6,2,4,7,5]=>[3,2,1,1,1]
[7,1,8,2,5,6,3,4]=>[3,2,1,1,1]
[6,1,5,8,2,7,3,4]=>[3,2,1,1,1]
[4,5,2,8,1,6,7,3]=>[3,2,1,1,1]
[6,2,5,8,1,4,7,3]=>[4,1,1,1,1]
[8,2,7,1,4,6,5,3]=>[5,1,1,1]
[1,3,8,2,5,7,4,6]=>[3,1,1,1,1,1]
[2,8,7,1,6,4,5,3]=>[5,1,1,1]
[3,4,8,5,6,1,7,2]=>[3,2,1,1,1]
[6,2,3,1,5,4,7,8]=>[3,2,1,1,1]
[8,2,3,1,4,5,7,6]=>[3,2,1,1,1]
[8,5,1,3,2,4,7,6]=>[4,2,1,1]
[7,5,1,3,2,6,4,8]=>[4,2,1,1]
[3,6,4,1,5,2,7,8]=>[3,2,1,1,1]
[4,5,7,1,2,6,3,8]=>[3,1,1,1,1,1]
[6,7,1,4,2,5,3,8]=>[3,2,1,1,1]
[2,7,1,3,5,6,4,8]=>[3,1,1,1,1,1]
[8,6,1,2,4,3,7,5]=>[4,2,1,1]
[2,8,1,3,4,6,7,5]=>[3,1,1,1,1,1]
[7,8,1,2,5,3,6,4]=>[3,2,1,1,1]
[1,2,6,7,5,3,8,4]=>[3,2,1,1,1]
[1,7,5,3,2,8,4,6]=>[4,2,1,1]
[1,6,7,5,3,8,4,2]=>[4,2,1,1]
[1,6,5,7,2,3,8,4]=>[3,2,1,1,1]
[1,3,8,2,6,5,7,4]=>[4,1,1,1,1]
[1,2,5,7,6,3,4,8]=>[3,1,1,1,1,1]
[1,3,4,8,2,5,7,6]=>[3,1,1,1,1,1]
[1,5,7,6,2,3,4,8]=>[3,1,1,1,1,1]
[1,5,3,8,2,6,4,7]=>[3,2,1,1,1]
[1,4,8,3,2,5,7,6]=>[3,2,1,1,1]
[1,4,8,3,5,7,6,2]=>[4,1,1,1,1]
[1,2,4,8,3,5,7,6]=>[3,1,1,1,1,1]
[1,3,8,4,2,6,7,5]=>[3,2,1,1,1]
[1,4,8,2,3,5,7,6]=>[3,1,1,1,1,1]
[6,5,7,3,8,2,4,1]=>[5,1,1,1]
[4,2,6,7,5,8,3,1]=>[4,2,1,1]
[6,7,5,2,1,8,4,3]=>[4,3,1]
[3,4,8,7,5,2,1,6]=>[5,1,1,1]
[1,7,5,2,8,4,6,3]=>[4,2,1,1]
[5,6,8,3,1,7,2,4]=>[3,2,1,1,1]
[6,1,4,8,3,2,7,5]=>[4,2,1,1]
[3,4,7,1,8,6,2,5]=>[3,2,1,1,1]
[3,4,6,8,2,1,5,7]=>[3,1,1,1,1,1]
[3,8,2,5,6,1,4,7]=>[3,1,1,1,1,1]
[3,5,2,8,6,4,1,7]=>[4,2,1,1]
[4,2,5,7,3,8,6,1]=>[3,2,2,1]
[7,4,2,5,3,8,1,6]=>[4,2,1,1]
[3,1,2,8,5,6,4,7]=>[3,2,1,1,1]
[5,2,1,6,8,3,4,7]=>[3,2,1,1,1]
[5,2,6,8,4,1,3,7]=>[3,2,1,1,1]
[1,5,6,8,3,4,2,7]=>[3,1,1,1,1,1]
[4,5,8,1,6,3,2,7]=>[4,1,1,1,1]
[4,5,1,6,8,3,2,7]=>[3,2,1,1,1]
[4,5,7,3,8,2,6,1]=>[4,1,1,1,1]
[6,4,3,7,8,2,5,1]=>[5,1,1,1]
[6,4,3,1,7,8,2,5]=>[4,2,1,1]
[4,5,3,1,7,8,2,6]=>[3,2,1,1,1]
[7,1,3,5,4,8,2,6]=>[4,1,1,1,1]
[7,5,2,8,1,4,3,6]=>[4,2,1,1]
[5,7,3,8,4,6,1,2]=>[3,2,1,1,1]
[1,4,5,7,3,8,6,2]=>[3,2,1,1,1]
[4,6,3,7,8,5,2,1]=>[4,2,1,1]
[5,3,6,7,8,4,2,1]=>[4,2,1,1]
[1,5,3,6,7,8,4,2]=>[3,2,1,1,1]
[4,6,1,7,3,8,5,2]=>[3,2,2,1]
[6,3,7,1,8,4,5,2]=>[3,3,1,1]
[6,7,2,4,8,1,5,3]=>[3,2,1,1,1]
[2,6,1,4,7,3,8,5]=>[3,2,1,1,1]
[3,2,5,6,7,8,1,4]=>[3,1,1,1,1,1]
[5,2,3,6,7,8,4,1]=>[3,2,1,1,1]
[6,7,1,3,2,8,4,5]=>[3,2,1,1,1]
[6,2,7,1,3,4,8,5]=>[3,2,1,1,1]
[5,2,1,7,3,8,4,6]=>[3,2,2,1]
[6,4,2,7,1,8,3,5]=>[4,2,1,1]
[4,2,6,3,7,8,1,5]=>[3,2,1,1,1]
[4,2,6,3,7,8,5,1]=>[3,2,2,1]
[6,7,3,8,2,4,5,1]=>[4,1,1,1,1]
[3,6,2,7,4,1,8,5]=>[3,2,2,1]
[6,7,3,2,1,4,8,5]=>[4,2,1,1]
[7,1,8,3,4,2,5,6]=>[3,2,1,1,1]
[7,2,4,1,8,3,5,6]=>[3,2,1,1,1]
[7,2,4,8,6,1,3,5]=>[3,2,1,1,1]
[7,3,4,8,6,2,1,5]=>[4,2,1,1]
[3,5,7,2,1,8,6,4]=>[3,3,1,1]
[6,7,8,3,2,5,1,4]=>[4,1,1,1,1]
[6,3,7,8,2,5,4,1]=>[4,2,1,1]
[2,6,7,4,8,5,3,1]=>[4,2,1,1]
[6,2,4,7,1,8,5,3]=>[3,3,1,1]
[4,6,2,7,1,8,5,3]=>[3,3,1,1]
[1,7,4,8,5,2,6,3]=>[3,2,2,1]
[1,3,7,8,5,2,6,4]=>[3,2,1,1,1]
[2,5,7,8,1,6,3,4]=>[3,1,1,1,1,1]
[6,3,7,1,8,2,5,4]=>[3,3,1,1]
[1,6,4,7,8,2,5,3]=>[3,2,1,1,1]
[2,5,6,1,7,8,4,3]=>[3,2,1,1,1]
[5,6,1,2,7,8,4,3]=>[3,2,1,1,1]
[6,7,2,1,8,5,3,4]=>[3,3,1,1]
[6,7,2,8,5,4,1,3]=>[4,2,1,1]
[1,6,7,4,8,5,3,2]=>[4,2,1,1]
[1,8,2,4,6,3,5,7]=>[3,1,1,1,1,1]
[7,2,8,3,5,1,4,6]=>[3,2,1,1,1]
[1,3,7,4,6,2,5,8]=>[3,1,1,1,1,1]
[1,5,7,4,3,6,2,8]=>[4,1,1,1,1]
[1,8,4,5,3,6,2,7]=>[4,1,1,1,1]
[1,8,5,3,4,7,2,6]=>[4,1,1,1,1]
[1,8,2,4,6,3,7,5]=>[3,2,1,1,1]
[1,8,2,5,4,6,7,3]=>[4,1,1,1,1]
[3,6,2,7,1,4,5,8]=>[3,1,1,1,1,1]
[6,3,8,1,2,4,7,5]=>[3,2,1,1,1]
[1,3,7,4,6,2,8,5]=>[3,2,1,1,1]
[1,4,7,5,2,6,8,3]=>[3,2,1,1,1]
[4,5,2,7,1,3,8,6]=>[3,2,1,1,1]
[4,5,2,3,6,1,8,7]=>[3,2,1,1,1]
[4,6,5,3,7,1,8,2]=>[4,2,1,1]
[2,5,4,7,1,6,8,3]=>[3,2,1,1,1]
[4,2,3,8,6,7,1,5]=>[3,2,1,1,1]
[6,2,4,8,5,1,7,3]=>[3,2,2,1]
[5,2,4,8,1,3,7,6]=>[3,2,1,1,1]
[6,2,5,4,8,3,7,1]=>[5,1,1,1]
[6,4,3,5,8,2,7,1]=>[5,1,1,1]
[5,2,3,4,8,1,6,7]=>[3,1,1,1,1,1]
[3,5,2,4,7,1,6,8]=>[3,1,1,1,1,1]
[5,3,4,8,1,6,2,7]=>[3,2,1,1,1]
[4,5,3,7,1,6,2,8]=>[3,2,1,1,1]
[6,2,4,8,5,1,3,7]=>[3,2,1,1,1]
[7,6,3,8,5,1,2,4]=>[4,2,1,1]
[1,4,3,7,8,2,5,6]=>[3,1,1,1,1,1]
[4,2,6,7,3,8,1,5]=>[3,2,1,1,1]
[1,5,7,4,2,8,6,3]=>[3,3,1,1]
[1,3,7,2,8,6,4,5]=>[3,2,1,1,1]
[1,4,3,7,8,6,2,5]=>[3,2,1,1,1]
[1,5,3,6,8,2,7,4]=>[3,2,1,1,1]
[4,5,2,7,1,8,6,3]=>[3,3,1,1]
[4,3,6,5,7,8,1,2]=>[3,2,1,1,1]
[4,2,3,5,6,8,1,7]=>[3,1,1,1,1,1]
[5,2,6,4,7,8,3,1]=>[4,2,1,1]
[4,2,6,7,3,8,5,1]=>[3,2,2,1]
[3,2,5,6,8,1,7,4]=>[3,2,1,1,1]
[6,4,5,2,3,8,7,1]=>[4,2,1,1]
[8,4,6,7,5,2,3,1]=>[5,1,1,1]
[4,6,5,2,3,1,8,7]=>[4,2,1,1]
[6,4,2,5,3,1,8,7]=>[4,2,2]
[6,4,2,5,3,8,7,1]=>[4,2,2]
[8,6,4,7,5,2,3,1]=>[5,2,1]
[8,6,2,7,4,5,3,1]=>[5,2,1]
[6,4,2,5,8,7,3,1]=>[4,3,1]
[4,6,2,5,3,8,7,1]=>[4,2,1,1]
[4,6,5,2,3,8,7,1]=>[4,2,1,1]
[6,8,7,4,5,2,3,1]=>[5,1,1,1]
[4,8,6,7,5,2,3,1]=>[5,1,1,1]
[6,8,4,7,5,2,3,1]=>[5,1,1,1]
[6,8,2,7,4,5,3,1]=>[5,1,1,1]
[8,6,4,7,2,5,3,1]=>[5,2,1]
[8,6,2,4,7,5,3,1]=>[5,2,1]
[6,8,2,4,7,5,3,1]=>[5,1,1,1]
[4,8,2,6,7,5,3,1]=>[5,1,1,1]
[2,8,4,6,7,5,3,1]=>[5,1,1,1]
[2,8,6,7,4,5,3,1]=>[5,1,1,1]
[6,8,7,2,4,5,3,1]=>[5,1,1,1]
[2,6,4,5,8,7,3,1]=>[4,2,1,1]
[2,6,4,8,7,5,3,1]=>[5,2,1]
[4,6,2,8,7,5,3,1]=>[5,2,1]
[8,2,4,6,7,5,3,1]=>[5,1,1,1]
[6,2,4,8,7,5,3,1]=>[5,2,1]
[4,2,6,8,7,5,3,1]=>[5,2,1]
[4,2,6,5,8,7,3,1]=>[4,2,2]
[6,2,4,5,8,7,3,1]=>[4,2,1,1]
[8,2,6,7,4,5,3,1]=>[5,1,1,1]
[8,6,7,2,4,5,3,1]=>[5,1,1,1]
[6,4,5,2,8,7,3,1]=>[4,3,1]
[4,2,3,6,8,7,5,1]=>[4,2,1,1]
[6,4,5,8,7,2,3,1]=>[4,2,1,1]
[8,6,7,4,2,5,3,1]=>[5,2,1]
[8,4,6,7,2,5,3,1]=>[5,1,1,1]
[6,4,8,7,2,5,3,1]=>[5,2,1]
[6,2,8,7,4,5,3,1]=>[5,2,1]
[6,4,8,7,5,2,3,1]=>[5,2,1]
[4,6,8,7,5,2,3,1]=>[5,1,1,1]
[4,6,5,8,7,2,3,1]=>[4,2,1,1]
[2,1,6,8,7,4,5,3]=>[4,2,1,1]
[2,6,8,7,4,5,3,1]=>[5,1,1,1]
[2,4,8,6,7,5,3,1]=>[5,1,1,1]
[4,2,8,6,7,5,3,1]=>[5,2,1]
[6,2,8,4,7,5,3,1]=>[5,2,1]
[8,2,6,4,7,5,3,1]=>[5,2,1]
[6,4,8,2,7,5,3,1]=>[5,2,1]
[4,6,8,2,7,5,3,1]=>[5,1,1,1]
[2,6,8,4,7,5,3,1]=>[5,1,1,1]
[4,6,8,7,2,5,3,1]=>[5,1,1,1]
[4,6,5,8,2,7,3,1]=>[4,2,1,1]
[2,1,6,8,4,7,5,3]=>[4,2,1,1]
[2,1,8,6,4,7,5,3]=>[4,2,2]
[6,8,7,4,2,5,3,1]=>[5,2,1]
[2,8,6,4,7,5,3,1]=>[5,2,1]
[4,8,6,2,7,5,3,1]=>[5,2,1]
[4,2,5,6,3,8,1,7]=>[3,2,1,1,1]
[6,2,5,7,4,8,3,1]=>[5,1,1,1]
[8,5,2,1,4,7,6,3]=>[4,3,1]
[6,7,3,2,5,8,4,1]=>[4,2,1,1]
[3,2,6,4,8,1,5,7]=>[3,2,1,1,1]
[2,3,6,4,7,8,5,1]=>[3,2,1,1,1]
[7,5,1,8,3,4,6,2]=>[4,2,1,1]
[5,7,8,2,6,3,4,1]=>[4,1,1,1,1]
[7,1,6,3,5,8,4,2]=>[5,1,1,1]
[6,3,1,7,8,4,5,2]=>[3,3,1,1]
[5,3,6,7,4,1,8,2]=>[3,2,2,1]
[7,3,1,2,5,8,6,4]=>[3,3,1,1]
[1,6,3,5,2,4,8,7]=>[3,2,1,1,1]
[3,4,8,2,7,5,1,6]=>[4,1,1,1,1]
[6,3,2,8,5,7,4,1]=>[4,3,1]
[3,8,4,7,2,5,6,1]=>[4,1,1,1,1]
[2,4,8,1,5,3,7,6]=>[3,2,1,1,1]
[3,4,8,1,6,2,7,5]=>[3,2,1,1,1]
[1,8,4,6,7,3,5,2]=>[4,1,1,1,1]
[8,1,6,3,4,5,7,2]=>[4,1,1,1,1]
[7,6,5,4,1,2,8,3]=>[5,2,1]
[5,7,6,8,3,4,2,1]=>[5,1,1,1]
[2,8,1,6,5,7,4,3]=>[5,1,1,1]
[4,6,8,2,5,3,7,1]=>[4,1,1,1,1]
[5,2,3,7,6,1,8,4]=>[3,2,2,1]
[8,1,2,4,6,7,3,5]=>[3,1,1,1,1,1]
[5,2,3,7,4,8,6,1]=>[3,2,2,1]
[5,2,6,8,4,3,1,7]=>[4,2,1,1]
[7,8,1,5,4,3,6,2]=>[5,1,1,1]
[7,2,4,8,5,3,6,1]=>[4,2,1,1]
[3,7,5,1,8,4,6,2]=>[4,2,1,1]
[2,7,8,5,4,6,1,3]=>[4,1,1,1,1]
[5,7,4,3,8,6,2,1]=>[5,2,1]
[4,8,1,6,3,5,2,7]=>[4,1,1,1,1]
[8,3,1,7,4,2,5,6]=>[4,2,1,1]
[3,1,8,2,4,5,7,6]=>[3,2,1,1,1]
[8,1,3,7,6,2,4,5]=>[4,1,1,1,1]
[2,3,6,8,7,1,4,5]=>[3,1,1,1,1,1]
[4,3,2,8,5,7,1,6]=>[4,2,1,1]
[3,6,4,2,8,5,7,1]=>[4,2,1,1]
[4,7,3,2,5,1,8,6]=>[4,2,1,1]
[3,2,4,7,5,8,6,1]=>[3,2,2,1]
[4,2,3,8,6,5,1,7]=>[4,2,1,1]
[2,4,3,5,1,8,6,7]=>[3,2,1,1,1]
[3,2,8,1,4,6,5,7]=>[3,2,1,1,1]
[3,7,8,5,6,1,2,4]=>[3,1,1,1,1,1]
[3,6,1,8,4,7,2,5]=>[3,2,1,1,1]
[3,1,6,8,4,7,2,5]=>[3,2,1,1,1]
[4,1,6,8,3,2,7,5]=>[3,2,2,1]
[4,6,1,8,3,2,7,5]=>[3,2,2,1]
[4,7,8,1,3,2,6,5]=>[3,2,1,1,1]
[4,7,8,3,1,2,6,5]=>[3,2,1,1,1]
[2,7,8,3,4,6,5,1]=>[4,1,1,1,1]
[4,7,8,2,1,3,6,5]=>[3,2,1,1,1]
[4,6,1,8,2,3,7,5]=>[3,2,1,1,1]
[4,1,6,8,2,3,7,5]=>[3,2,1,1,1]
[4,5,1,2,8,3,7,6]=>[3,2,1,1,1]
[4,5,2,1,8,3,7,6]=>[3,3,1,1]
[4,6,2,8,1,3,7,5]=>[3,2,1,1,1]
[3,6,2,8,4,7,1,5]=>[3,2,1,1,1]
[2,3,6,8,4,7,5,1]=>[4,1,1,1,1]
[3,2,6,8,4,7,1,5]=>[3,2,1,1,1]
[4,2,6,8,3,1,7,5]=>[3,2,2,1]
[4,2,5,1,8,3,7,6]=>[3,3,1,1]
[4,1,2,5,8,3,7,6]=>[3,2,1,1,1]
[5,1,2,4,3,8,7,6]=>[3,3,1,1]
[5,2,4,1,3,8,7,6]=>[3,3,1,1]
[4,2,5,3,8,1,7,6]=>[3,2,2,1]
[3,2,5,4,8,7,1,6]=>[3,2,2,1]
[3,5,2,4,8,7,1,6]=>[3,2,1,1,1]
[5,4,2,1,3,8,7,6]=>[4,3,1]
[5,1,4,2,3,8,7,6]=>[3,3,1,1]
[5,4,1,3,2,8,7,6]=>[4,3,1]
[5,4,3,1,2,8,7,6]=>[4,3,1]
[4,5,3,1,8,2,7,6]=>[3,3,1,1]
[4,5,1,3,8,2,7,6]=>[3,2,1,1,1]
[3,1,5,4,8,7,2,6]=>[3,2,2,1]
[3,5,1,4,8,7,2,6]=>[3,2,1,1,1]
[3,5,4,1,8,7,2,6]=>[3,3,1,1]
[3,6,5,8,7,1,2,4]=>[3,2,1,1,1]
[2,5,6,8,7,3,4,1]=>[4,1,1,1,1]
[3,4,5,1,8,7,2,6]=>[3,2,1,1,1]
[3,4,1,5,8,7,2,6]=>[3,2,1,1,1]
[4,1,3,5,8,2,7,6]=>[3,2,1,1,1]
[4,3,6,8,2,1,7,5]=>[4,2,1,1]
[2,4,6,8,3,7,5,1]=>[4,1,1,1,1]
[3,4,5,2,8,7,1,6]=>[3,2,1,1,1]
[5,3,1,4,2,8,7,6]=>[3,3,2]
[5,1,3,4,2,8,7,6]=>[3,3,1,1]
[5,1,3,2,4,8,7,6]=>[3,3,1,1]
[5,3,2,1,4,8,7,6]=>[4,3,1]
[4,3,2,5,8,1,7,6]=>[4,2,1,1]
[3,4,2,5,8,7,1,6]=>[3,2,1,1,1]
[3,2,4,5,8,7,1,6]=>[3,2,1,1,1]
[4,2,3,5,8,1,7,6]=>[3,2,1,1,1]
[5,2,3,1,4,8,7,6]=>[3,3,1,1]
[5,2,1,3,4,8,7,6]=>[3,3,1,1]
[5,1,2,3,4,8,7,6]=>[3,2,1,1,1]
[8,6,2,5,4,1,3,7]=>[5,1,1,1]
[6,5,7,4,2,8,3,1]=>[5,2,1]
[6,7,5,3,8,2,4,1]=>[5,1,1,1]
[8,2,1,6,3,4,5,7]=>[3,2,1,1,1]
[8,3,5,6,2,4,1,7]=>[4,1,1,1,1]
[8,6,2,1,3,5,4,7]=>[4,2,1,1]
[8,1,2,3,4,6,5,7]=>[3,1,1,1,1,1]
[6,2,3,7,8,4,5,1]=>[3,2,1,1,1]
[7,5,8,2,6,3,4,1]=>[4,2,1,1]
[7,3,1,6,5,8,4,2]=>[5,2,1]
[1,5,6,7,3,4,8,2]=>[3,1,1,1,1,1]
[6,7,8,2,1,4,5,3]=>[3,2,1,1,1]
[8,4,7,6,2,1,3,5]=>[5,1,1,1]
[5,3,8,4,7,2,6,1]=>[4,2,1,1]
[8,1,3,7,6,4,2,5]=>[5,1,1,1]
[5,3,1,7,8,6,2,4]=>[3,3,1,1]
[3,5,8,2,7,1,6,4]=>[4,1,1,1,1]
[6,2,8,5,3,1,7,4]=>[4,2,2]
[8,2,6,4,7,1,3,5]=>[4,1,1,1,1]
[3,4,2,8,5,1,7,6]=>[3,2,2,1]
[3,8,6,5,2,1,7,4]=>[5,2,1]
[8,3,7,4,2,5,6,1]=>[5,1,1,1]
[4,8,5,7,2,1,3,6]=>[4,1,1,1,1]
[3,4,1,8,2,6,7,5]=>[3,2,1,1,1]
[8,4,6,3,7,1,5,2]=>[4,2,1,1]
[6,8,3,4,1,5,7,2]=>[3,2,1,1,1]
[5,1,7,6,2,8,4,3]=>[4,2,2]
[6,8,2,5,7,4,1,3]=>[4,1,1,1,1]
[2,8,5,6,7,1,3,4]=>[3,1,1,1,1,1]
[2,5,7,6,3,1,8,4]=>[4,2,1,1]
[4,2,8,3,1,5,6,7]=>[3,2,1,1,1]
[2,5,7,3,8,4,6,1]=>[3,2,1,1,1]
[4,2,7,1,8,5,3,6]=>[3,3,1,1]
[4,2,1,8,7,5,6,3]=>[4,3,1]
[8,3,6,7,1,5,4,2]=>[5,1,1,1]
[1,3,7,5,8,6,4,2]=>[4,2,1,1]
[5,7,8,4,3,1,6,2]=>[4,2,1,1]
[2,7,4,5,8,3,6,1]=>[4,1,1,1,1]
[3,5,7,1,4,8,6,2]=>[3,2,1,1,1]
[7,2,8,5,1,4,6,3]=>[4,2,1,1]
[1,6,5,3,8,4,2,7]=>[4,2,1,1]
[5,7,4,8,3,6,2,1]=>[5,1,1,1]
[4,8,6,1,3,5,2,7]=>[4,1,1,1,1]
[1,8,3,2,4,7,5,6]=>[3,2,1,1,1]
[8,4,3,2,5,7,1,6]=>[5,1,1,1]
[3,6,4,8,2,5,7,1]=>[4,1,1,1,1]
[4,3,7,2,5,8,1,6]=>[4,1,1,1,1]
[3,2,4,7,8,5,6,1]=>[3,2,1,1,1]
[2,6,4,3,8,5,1,7]=>[4,2,1,1]
[3,8,2,1,6,4,5,7]=>[3,2,1,1,1]
[8,2,1,3,4,5,7,6]=>[3,2,1,1,1]
[4,6,8,3,2,1,5,7]=>[4,1,1,1,1]
[3,2,6,8,5,4,1,7]=>[4,2,1,1]
[7,3,8,2,5,4,1,6]=>[4,2,1,1]
[4,2,5,3,8,7,6,1]=>[4,2,2]
[4,8,2,6,5,3,1,7]=>[5,1,1,1]
[2,6,8,5,4,1,3,7]=>[4,1,1,1,1]
[3,1,8,6,5,4,2,7]=>[5,2,1]
[5,4,8,7,3,2,6,1]=>[5,2,1]
[6,4,8,3,7,2,5,1]=>[5,1,1,1]
[4,7,3,6,2,1,8,5]=>[4,2,1,1]
[5,4,3,7,1,8,2,6]=>[4,2,1,1]
[7,3,8,5,1,4,2,6]=>[4,2,1,1]
[5,4,8,7,6,2,1,3]=>[5,2,1]
[3,8,1,5,7,4,6,2]=>[4,1,1,1,1]
[4,8,5,7,3,1,6,2]=>[4,2,1,1]
[1,5,4,8,3,7,6,2]=>[4,2,1,1]
[4,8,3,6,7,1,5,2]=>[4,1,1,1,1]
[4,7,8,3,1,6,5,2]=>[4,2,1,1]
[8,7,5,3,6,4,2,1]=>[6,2]
[4,6,1,3,8,7,5,2]=>[4,2,1,1]
[6,8,2,1,7,4,5,3]=>[4,2,1,1]
[3,7,1,6,4,2,8,5]=>[4,2,1,1]
[3,1,2,7,5,6,8,4]=>[3,2,1,1,1]
[3,6,1,2,7,5,8,4]=>[3,2,1,1,1]
[3,7,6,2,5,8,1,4]=>[4,1,1,1,1]
[3,6,2,5,8,7,4,1]=>[4,2,1,1]
[8,5,2,3,6,7,4,1]=>[4,2,1,1]
[4,7,2,6,3,8,1,5]=>[4,1,1,1,1]
[6,3,2,4,8,7,5,1]=>[4,3,1]
[3,7,2,4,6,1,8,5]=>[3,2,1,1,1]
[5,3,7,2,8,1,4,6]=>[4,1,1,1,1]
[6,3,2,8,7,5,1,4]=>[4,3,1]
[7,3,8,2,6,5,1,4]=>[4,2,1,1]
[6,4,8,7,2,5,1,3]=>[4,2,1,1]
[2,5,4,8,1,7,6,3]=>[4,2,1,1]
[5,2,8,1,7,6,3,4]=>[4,2,1,1]
[6,2,1,3,8,7,5,4]=>[4,3,1]
[3,6,1,8,7,5,2,4]=>[4,2,1,1]
[5,6,1,2,8,7,4,3]=>[4,2,1,1]
[7,5,2,8,1,6,4,3]=>[4,3,1]
[2,7,6,8,1,5,4,3]=>[5,1,1,1]
[7,8,5,1,6,2,4,3]=>[4,2,1,1]
[7,4,8,6,1,2,5,3]=>[4,2,1,1]
[7,2,1,8,3,6,5,4]=>[4,3,1]
[5,8,7,1,6,4,3,2]=>[6,1,1]
[8,5,4,3,7,2,1,6]=>[6,1,1]
[6,5,4,8,3,2,7,1]=>[6,1,1]
[7,6,4,3,2,8,5,1]=>[6,2]
[7,3,1,4,8,2,5,6]=>[3,2,1,1,1]
[7,4,1,2,5,8,3,6]=>[3,2,1,1,1]
[6,7,4,2,5,1,3,8]=>[4,1,1,1,1]
[5,7,2,4,6,8,1,3]=>[3,1,1,1,1,1]
[4,7,5,1,6,2,8,3]=>[3,2,2,1]
[5,7,4,6,3,1,8,2]=>[4,2,1,1]
[7,5,1,4,3,2,8,6]=>[5,2,1]
[8,6,4,2,3,7,5,1]=>[5,2,1]
[6,4,7,1,3,8,5,2]=>[4,2,1,1]
[5,4,2,7,3,1,6,8]=>[4,2,1,1]
[4,5,1,2,7,6,8,3]=>[3,2,1,1,1]
[5,4,6,8,3,1,2,7]=>[4,1,1,1,1]
[6,4,8,1,3,7,2,5]=>[4,1,1,1,1]
[4,6,1,3,8,5,2,7]=>[3,2,1,1,1]
[1,3,8,4,5,7,2,6]=>[3,1,1,1,1,1]
[2,6,7,4,5,3,1,8]=>[4,1,1,1,1]
[2,6,8,4,3,5,1,7]=>[4,1,1,1,1]
[1,3,7,4,2,8,5,6]=>[3,2,1,1,1]
[4,6,1,3,7,2,5,8]=>[3,1,1,1,1,1]
[7,5,8,6,2,1,3,4]=>[4,2,1,1]
[2,8,1,3,6,5,4,7]=>[4,1,1,1,1]
[2,8,7,3,5,4,1,6]=>[5,1,1,1]
[3,4,2,6,8,7,1,5]=>[3,2,1,1,1]
[7,4,2,3,6,1,8,5]=>[4,2,1,1]
[8,4,2,3,6,5,7,1]=>[4,2,1,1]
[7,3,8,4,1,2,6,5]=>[3,2,2,1]
[6,8,3,2,7,1,5,4]=>[4,2,1,1]
[2,8,5,6,3,7,1,4]=>[4,1,1,1,1]
[7,4,2,5,8,1,6,3]=>[4,2,1,1]
[2,7,8,3,4,5,1,6]=>[3,1,1,1,1,1]
[3,7,1,2,4,6,5,8]=>[3,1,1,1,1,1]
[7,5,6,8,2,1,4,3]=>[4,2,1,1]
[3,1,6,5,2,7,4,8]=>[3,2,2,1]
[2,8,6,5,3,4,1,7]=>[5,1,1,1]
[1,7,2,3,5,6,8,4]=>[3,1,1,1,1,1]
[3,7,4,2,1,5,6,8]=>[4,1,1,1,1]
[3,4,6,2,8,5,7,1]=>[3,2,1,1,1]
[4,2,1,7,5,8,3,6]=>[3,3,1,1]
[4,7,2,6,5,1,3,8]=>[4,1,1,1,1]
[3,7,4,1,2,5,8,6]=>[3,2,1,1,1]
[4,7,1,6,5,2,8,3]=>[4,2,1,1]
[4,7,3,6,5,1,8,2]=>[4,2,1,1]
[4,3,7,1,6,8,5,2]=>[4,2,1,1]
[4,2,1,7,5,6,8,3]=>[3,3,1,1]
[3,2,4,8,6,7,1,5]=>[3,2,1,1,1]
[4,2,6,8,7,3,1,5]=>[4,2,1,1]
[3,4,6,1,8,5,2,7]=>[3,2,1,1,1]
[4,1,6,7,5,8,2,3]=>[3,2,1,1,1]
[4,3,6,7,5,1,2,8]=>[3,2,1,1,1]
[4,3,7,1,6,8,2,5]=>[3,2,1,1,1]
[4,3,7,5,6,8,2,1]=>[4,2,1,1]
[4,1,7,3,6,5,2,8]=>[4,2,1,1]
[2,8,7,4,5,3,1,6]=>[5,1,1,1]
[2,8,7,4,3,5,1,6]=>[5,1,1,1]
[3,8,1,4,2,6,5,7]=>[3,2,1,1,1]
[4,1,7,3,6,2,5,8]=>[3,2,1,1,1]
[5,8,7,6,1,2,4,3]=>[5,1,1,1]
[5,8,7,6,2,1,3,4]=>[5,1,1,1]
[4,1,7,2,6,8,5,3]=>[4,2,1,1]
[4,2,7,3,6,1,8,5]=>[3,2,2,1]
[4,2,7,3,6,5,8,1]=>[4,2,1,1]
[3,8,2,4,5,6,7,1]=>[3,1,1,1,1,1]
[3,8,2,4,1,6,7,5]=>[3,2,1,1,1]
[3,8,5,6,2,4,1,7]=>[4,1,1,1,1]
[2,8,6,5,3,7,1,4]=>[5,1,1,1]
[3,8,6,5,1,4,7,2]=>[5,1,1,1]
[3,8,2,1,4,6,7,5]=>[3,2,1,1,1]
[3,8,2,5,4,6,7,1]=>[4,1,1,1,1]
[4,2,7,5,6,3,8,1]=>[4,2,1,1]
[4,2,7,5,6,1,8,3]=>[3,2,2,1]
[4,2,6,7,5,3,1,8]=>[4,2,1,1]
[3,2,6,1,4,5,8,7]=>[3,2,1,1,1]
[2,8,7,3,4,5,1,6]=>[4,1,1,1,1]
[3,8,1,2,4,6,5,7]=>[3,1,1,1,1,1]
[5,8,7,6,1,3,4,2]=>[5,1,1,1]
[5,8,7,6,2,3,4,1]=>[5,1,1,1]
[4,1,7,5,6,2,3,8]=>[3,2,1,1,1]
[3,8,1,5,2,6,4,7]=>[3,2,1,1,1]
[2,8,7,5,3,4,1,6]=>[5,1,1,1]
[2,8,7,5,4,3,1,6]=>[6,1,1]
[4,1,7,5,6,3,2,8]=>[4,2,1,1]
[5,8,7,6,1,3,2,4]=>[5,1,1,1]
[5,8,7,6,4,1,2,3]=>[5,1,1,1]
[5,4,2,3,7,6,8,1]=>[4,2,1,1]
[7,4,3,5,2,8,1,6]=>[5,1,1,1]
[8,4,3,7,5,1,6,2]=>[4,2,2]
[8,4,7,2,5,1,6,3]=>[4,2,1,1]
[7,4,6,2,3,5,8,1]=>[4,1,1,1,1]
[5,1,7,2,4,6,8,3]=>[3,2,1,1,1]
[4,5,7,1,2,6,8,3]=>[3,1,1,1,1,1]
[5,4,1,7,3,6,8,2]=>[4,2,1,1]
[3,6,4,7,5,2,8,1]=>[4,2,1,1]
[3,4,7,6,2,5,8,1]=>[4,1,1,1,1]
[4,7,5,6,1,3,8,2]=>[4,1,1,1,1]
[5,7,6,4,3,1,8,2]=>[5,2,1]
[5,7,6,3,1,4,8,2]=>[4,2,1,1]
[7,5,2,3,4,8,1,6]=>[4,1,1,1,1]
[8,7,5,3,4,1,6,2]=>[5,2,1]
[6,7,1,3,8,4,2,5]=>[3,2,1,1,1]
[7,6,1,3,4,8,5,2]=>[4,2,1,1]
[3,6,5,2,7,8,1,4]=>[4,1,1,1,1]
[3,2,8,6,7,1,4,5]=>[3,2,1,1,1]
[4,8,3,6,5,2,1,7]=>[5,1,1,1]
[1,8,6,5,4,2,3,7]=>[5,1,1,1]
[1,8,7,2,3,5,4,6]=>[4,1,1,1,1]
[1,8,7,2,5,3,4,6]=>[4,1,1,1,1]
[3,6,8,5,1,2,4,7]=>[3,1,1,1,1,1]
[3,7,5,1,8,2,6,4]=>[3,3,1,1]
[7,1,2,8,3,5,6,4]=>[3,2,1,1,1]
[6,1,7,8,2,5,3,4]=>[3,2,1,1,1]
[6,7,5,2,8,1,4,3]=>[4,2,1,1]
[7,1,4,5,8,6,2,3]=>[3,2,1,1,1]
[5,7,6,4,2,8,1,3]=>[5,1,1,1]
[7,5,6,1,2,8,4,3]=>[4,2,1,1]
[4,1,3,7,8,6,2,5]=>[3,2,1,1,1]
[5,1,4,3,6,8,7,2]=>[4,2,1,1]
[4,5,7,6,8,2,1,3]=>[4,1,1,1,1]
[5,7,6,8,4,2,1,3]=>[5,1,1,1]
[5,1,6,8,4,2,7,3]=>[3,2,2,1]
[7,4,8,2,3,6,5,1]=>[4,2,1,1]
[5,6,8,4,7,3,2,1]=>[5,1,1,1]
[6,4,7,8,5,2,1,3]=>[4,2,1,1]
[3,6,4,8,5,1,2,7]=>[3,2,1,1,1]
[3,7,4,8,1,2,5,6]=>[3,1,1,1,1,1]
[7,4,3,8,2,6,5,1]=>[5,2,1]
[7,6,8,3,2,5,4,1]=>[5,2,1]
[8,7,1,3,5,4,6,2]=>[5,1,1,1]
[7,1,8,3,4,2,6,5]=>[3,2,2,1]
[7,6,8,3,1,4,5,2]=>[4,2,1,1]
[3,1,4,8,2,5,7,6]=>[3,2,1,1,1]
[4,8,5,2,1,3,6,7]=>[4,1,1,1,1]
[5,8,2,6,3,1,4,7]=>[4,1,1,1,1]
[6,8,2,3,7,4,1,5]=>[4,1,1,1,1]
[7,8,2,3,4,6,5,1]=>[4,1,1,1,1]
[8,1,7,2,4,5,3,6]=>[4,1,1,1,1]
[8,1,3,6,2,5,4,7]=>[4,1,1,1,1]
[7,2,1,6,3,5,4,8]=>[4,2,1,1]
[2,7,1,6,3,5,4,8]=>[4,1,1,1,1]
[2,7,1,5,4,3,6,8]=>[4,1,1,1,1]
[7,2,1,5,4,3,6,8]=>[4,2,1,1]
[8,1,3,5,4,2,6,7]=>[4,1,1,1,1]
[8,1,5,3,4,2,6,7]=>[4,1,1,1,1]
[8,1,5,6,2,3,7,4]=>[3,2,1,1,1]
[8,1,4,5,3,2,6,7]=>[4,1,1,1,1]
[8,1,4,3,5,2,6,7]=>[4,1,1,1,1]
[7,2,1,4,5,3,6,8]=>[3,2,1,1,1]
[2,7,1,4,5,3,6,8]=>[3,1,1,1,1,1]
[2,6,3,1,5,4,7,8]=>[3,2,1,1,1]
[6,3,2,1,5,4,7,8]=>[4,2,1,1]
[7,3,1,4,5,2,6,8]=>[3,2,1,1,1]
[7,3,1,5,4,2,6,8]=>[4,2,1,1]
[7,3,1,6,2,5,4,8]=>[4,2,1,1]
[3,7,1,6,2,5,4,8]=>[4,1,1,1,1]
[3,7,1,4,5,2,6,8]=>[3,1,1,1,1,1]
[3,6,2,1,5,4,7,8]=>[3,2,1,1,1]
[2,3,6,1,5,4,7,8]=>[3,1,1,1,1,1]
[3,5,2,4,1,6,7,8]=>[3,1,1,1,1,1]
[6,3,4,1,5,2,7,8]=>[3,2,1,1,1]
[6,2,4,1,5,3,7,8]=>[3,2,1,1,1]
[2,6,4,1,5,3,7,8]=>[3,2,1,1,1]
[2,6,5,1,3,7,4,8]=>[3,2,1,1,1]
[6,2,5,1,3,7,4,8]=>[3,2,1,1,1]
[6,5,2,1,3,7,4,8]=>[4,2,1,1]
[7,6,1,2,4,5,3,8]=>[4,1,1,1,1]
[6,7,1,2,8,3,5,4]=>[3,2,1,1,1]
[6,7,1,2,5,4,3,8]=>[4,1,1,1,1]
[5,6,2,1,3,7,4,8]=>[3,2,1,1,1]
[5,2,6,1,3,7,4,8]=>[3,2,1,1,1]
[2,4,6,1,5,3,7,8]=>[3,1,1,1,1,1]
[4,7,1,3,5,2,6,8]=>[3,1,1,1,1,1]
[4,7,1,5,3,2,6,8]=>[4,1,1,1,1]
[5,7,1,4,2,6,3,8]=>[3,2,1,1,1]
[5,7,1,6,2,3,8,4]=>[3,2,1,1,1]
[5,6,3,1,2,7,4,8]=>[3,2,1,1,1]
[4,2,5,3,1,6,7,8]=>[3,2,1,1,1]
[5,3,6,1,2,7,4,8]=>[3,2,1,1,1]
[3,4,6,1,5,2,7,8]=>[3,1,1,1,1,1]
[6,5,1,8,7,3,4,2]=>[4,3,1]
[8,2,7,5,4,1,3,6]=>[5,1,1,1]
[6,8,5,2,3,4,1,7]=>[4,1,1,1,1]
[2,6,8,7,1,5,3,4]=>[4,1,1,1,1]
[8,5,6,2,7,1,4,3]=>[4,2,1,1]
[6,5,1,2,7,8,4,3]=>[4,2,1,1]
[4,7,6,1,5,3,8,2]=>[5,1,1,1]
[5,7,6,4,1,3,8,2]=>[5,1,1,1]
[7,6,2,4,5,3,8,1]=>[5,1,1,1]
[6,1,7,5,3,8,4,2]=>[4,2,2]
[8,6,7,5,3,1,4,2]=>[5,2,1]
[8,5,2,7,1,6,4,3]=>[5,2,1]
[7,6,1,5,3,8,4,2]=>[5,2,1]
[5,6,2,4,7,8,1,3]=>[3,1,1,1,1,1]
[3,4,6,1,7,8,5,2]=>[3,2,1,1,1]
[3,4,8,6,7,1,5,2]=>[4,1,1,1,1]
[4,8,5,6,7,2,3,1]=>[4,1,1,1,1]
[5,8,6,4,1,2,7,3]=>[4,2,1,1]
[5,8,6,1,7,2,4,3]=>[4,2,1,1]
[5,8,7,3,2,6,4,1]=>[5,2,1]
[5,8,1,7,2,6,4,3]=>[5,1,1,1]
[8,1,5,7,2,6,4,3]=>[5,1,1,1]
[8,1,7,2,5,6,3,4]=>[4,1,1,1,1]
[6,8,7,2,5,1,3,4]=>[4,1,1,1,1]
[5,8,7,2,1,6,3,4]=>[4,2,1,1]
[4,8,1,5,2,6,7,3]=>[3,2,1,1,1]
[3,7,8,5,1,6,2,4]=>[3,2,1,1,1]
[6,5,2,7,8,1,4,3]=>[4,2,1,1]
[7,1,2,8,5,6,3,4]=>[3,2,1,1,1]
[8,7,2,1,5,6,3,4]=>[4,2,1,1]
[8,6,7,1,5,2,3,4]=>[4,1,1,1,1]
[6,1,7,8,5,2,3,4]=>[3,2,1,1,1]
[7,5,6,2,1,8,4,3]=>[4,3,1]
[8,7,5,2,1,6,4,3]=>[5,3]
[7,1,3,5,8,6,2,4]=>[3,2,1,1,1]
[5,1,3,4,6,8,7,2]=>[3,2,1,1,1]
[4,5,3,6,8,2,7,1]=>[4,1,1,1,1]
[5,6,3,4,8,1,7,2]=>[3,2,1,1,1]
[4,6,7,8,5,1,3,2]=>[4,1,1,1,1]
[8,4,3,1,2,6,7,5]=>[4,2,1,1]
[8,5,1,6,3,4,7,2]=>[4,2,1,1]
[5,1,8,6,3,4,7,2]=>[4,2,1,1]
[4,6,8,1,5,3,7,2]=>[4,1,1,1,1]
[6,4,5,8,3,2,7,1]=>[5,1,1,1]
[3,6,4,8,7,1,5,2]=>[4,2,1,1]
[6,5,8,1,3,4,7,2]=>[4,1,1,1,1]
[5,6,8,3,1,2,7,4]=>[3,2,1,1,1]
[6,1,8,3,5,2,7,4]=>[3,2,2,1]
[7,6,8,3,5,2,1,4]=>[5,1,1,1]
[8,6,1,3,5,2,7,4]=>[4,2,1,1]
[8,7,1,3,5,6,2,4]=>[4,1,1,1,1]
[6,7,8,3,5,1,2,4]=>[3,1,1,1,1,1]
[3,4,8,1,2,6,7,5]=>[3,1,1,1,1,1]
[5,8,2,4,3,6,7,1]=>[4,1,1,1,1]
[5,8,2,3,1,6,7,4]=>[3,2,1,1,1]
[6,8,2,3,5,1,7,4]=>[3,2,1,1,1]
[7,8,2,3,5,6,1,4]=>[3,1,1,1,1,1]
[8,6,5,1,4,3,7,2]=>[6,1,1]
[2,4,8,6,1,3,7,5]=>[3,2,1,1,1]
[6,7,1,8,4,3,5,2]=>[4,2,1,1]
[2,7,8,6,1,4,3,5]=>[4,1,1,1,1]
[2,7,3,8,1,6,4,5]=>[3,2,1,1,1]
[7,5,1,8,2,4,6,3]=>[4,2,1,1]
[2,7,8,4,1,6,3,5]=>[3,2,1,1,1]
[2,6,5,4,1,3,8,7]=>[4,2,1,1]
[4,1,7,6,3,8,2,5]=>[4,2,1,1]
[4,8,2,5,7,6,3,1]=>[5,1,1,1]
[3,4,6,5,1,8,2,7]=>[3,2,1,1,1]
[2,6,5,3,4,1,8,7]=>[4,2,1,1]
[4,6,1,5,2,3,8,7]=>[3,2,1,1,1]
[6,2,3,5,1,4,8,7]=>[3,2,1,1,1]
[2,6,7,5,1,8,4,3]=>[4,2,1,1]
[8,6,1,2,5,3,4,7]=>[4,1,1,1,1]
[6,2,5,1,8,3,4,7]=>[3,2,1,1,1]
[7,6,5,2,8,3,4,1]=>[5,2,1]
[2,6,3,5,1,8,7,4]=>[3,3,1,1]
[2,4,7,6,5,8,1,3]=>[4,1,1,1,1]
[2,1,4,8,7,6,3,5]=>[4,2,1,1]
[7,4,6,8,5,3,2,1]=>[6,1,1]
[8,1,3,5,7,4,6,2]=>[4,1,1,1,1]
[3,2,8,7,5,1,6,4]=>[4,2,2]
[4,8,5,1,6,7,2,3]=>[3,2,1,1,1]
[3,8,5,1,6,7,2,4]=>[3,2,1,1,1]
[7,8,6,1,3,5,2,4]=>[4,1,1,1,1]
[5,6,7,2,8,1,3,4]=>[3,1,1,1,1,1]
[2,5,1,8,6,7,4,3]=>[4,2,1,1]
[3,5,1,8,6,7,4,2]=>[4,2,1,1]
[5,2,3,8,6,7,4,1]=>[4,2,1,1]
[8,3,5,4,6,7,1,2]=>[4,1,1,1,1]
[5,1,3,8,6,7,4,2]=>[4,2,1,1]
[3,2,5,8,6,7,4,1]=>[4,2,1,1]
[6,2,1,5,3,8,7,4]=>[3,3,2]
[5,6,3,2,8,1,4,7]=>[4,1,1,1,1]
[8,1,6,3,5,2,7,4]=>[4,2,1,1]
[8,7,6,2,5,3,1,4]=>[6,1,1]
[4,7,6,8,3,2,5,1]=>[5,1,1,1]
[2,7,5,8,1,3,4,6]=>[3,1,1,1,1,1]
[7,6,2,8,5,1,4,3]=>[5,2,1]
[8,1,3,7,5,2,6,4]=>[4,2,1,1]
[3,4,8,7,5,1,6,2]=>[4,2,1,1]
[6,3,8,1,4,2,5,7]=>[3,2,1,1,1]
[6,3,8,5,7,4,1,2]=>[4,2,1,1]
[7,4,6,8,5,1,3,2]=>[5,1,1,1]
[2,1,4,8,7,5,6,3]=>[4,2,1,1]
[7,1,5,8,2,6,4,3]=>[4,2,1,1]
[3,6,8,2,4,1,7,5]=>[3,2,1,1,1]
[4,5,8,2,6,7,3,1]=>[4,1,1,1,1]
[5,2,8,1,6,7,3,4]=>[3,2,1,1,1]
[2,5,8,4,6,7,3,1]=>[4,1,1,1,1]
[5,8,3,4,6,7,2,1]=>[4,1,1,1,1]
[8,4,3,2,6,7,1,5]=>[5,1,1,1]
[4,2,8,1,6,7,3,5]=>[3,2,1,1,1]
[2,4,8,1,6,7,3,5]=>[3,1,1,1,1,1]
[5,1,8,2,6,7,3,4]=>[3,2,1,1,1]
[3,4,8,7,2,1,5,6]=>[4,1,1,1,1]
[7,8,5,3,6,4,2,1]=>[5,2,1]
[2,8,5,7,4,1,3,6]=>[4,1,1,1,1]
[5,8,4,1,6,7,2,3]=>[3,2,1,1,1]
[3,8,1,4,6,7,2,5]=>[3,1,1,1,1,1]
[8,2,3,4,6,7,1,5]=>[3,1,1,1,1,1]
[6,2,7,3,8,4,1,5]=>[3,2,2,1]
[7,4,3,2,8,5,1,6]=>[5,2,1]
[5,3,2,8,4,6,1,7]=>[4,2,1,1]
[8,4,2,6,5,3,1,7]=>[5,2,1]
[7,4,2,5,3,1,6,8]=>[4,2,1,1]
[8,3,6,2,5,4,1,7]=>[5,1,1,1]
[5,4,8,3,2,6,1,7]=>[5,1,1,1]
[3,5,8,2,4,6,1,7]=>[3,1,1,1,1,1]
[6,4,7,8,2,3,1,5]=>[4,1,1,1,1]
[5,8,3,6,4,2,1,7]=>[5,1,1,1]
[4,8,6,2,5,3,1,7]=>[5,1,1,1]
[1,6,4,3,2,8,7,5]=>[4,3,1]
[1,5,3,2,8,4,7,6]=>[3,3,1,1]
[5,7,4,3,1,2,6,8]=>[4,1,1,1,1]
[2,8,7,3,5,1,4,6]=>[4,1,1,1,1]
[7,3,8,6,4,1,2,5]=>[4,2,1,1]
[6,1,2,7,3,8,5,4]=>[3,2,2,1]
[2,1,7,4,3,8,6,5]=>[3,3,2]
[6,1,4,3,8,2,7,5]=>[4,2,1,1]
[5,1,3,2,8,7,4,6]=>[3,3,1,1]
[1,8,4,2,7,6,5,3]=>[5,2,1]
[1,8,3,7,2,6,5,4]=>[5,1,1,1]
[5,1,4,8,3,7,2,6]=>[4,1,1,1,1]
[2,1,6,8,5,4,7,3]=>[4,2,1,1]
[6,1,5,7,8,2,4,3]=>[4,1,1,1,1]
[8,3,1,6,7,2,5,4]=>[4,2,1,1]
[7,4,8,6,1,3,2,5]=>[4,2,1,1]
[4,7,6,1,2,5,3,8]=>[4,1,1,1,1]
[3,7,6,1,5,2,4,8]=>[4,1,1,1,1]
[1,5,4,8,3,2,7,6]=>[4,2,1,1]
[7,3,6,1,2,5,4,8]=>[4,1,1,1,1]
[5,4,7,1,3,2,6,8]=>[4,1,1,1,1]
[5,7,4,8,2,1,3,6]=>[4,1,1,1,1]
[4,6,8,2,5,1,3,7]=>[3,1,1,1,1,1]
[7,4,6,2,1,5,3,8]=>[4,2,1,1]
[1,2,6,3,8,5,7,4]=>[3,2,1,1,1]
[1,5,2,6,8,4,7,3]=>[3,2,1,1,1]
[5,7,2,3,8,1,4,6]=>[3,1,1,1,1,1]
[6,4,7,5,8,1,2,3]=>[3,2,1,1,1]
[7,4,8,5,1,6,3,2]=>[4,2,2]
[5,8,3,6,1,7,4,2]=>[4,2,1,1]
[8,6,4,2,1,7,5,3]=>[5,3]
[7,4,2,1,5,8,6,3]=>[4,3,1]
[7,6,4,1,8,5,2,3]=>[4,3,1]
[1,6,4,8,7,5,3,2]=>[5,2,1]
[6,3,1,2,8,4,7,5]=>[3,3,1,1]
[7,5,1,3,2,8,6,4]=>[4,3,1]
[4,7,1,2,5,8,6,3]=>[3,2,1,1,1]
[6,8,4,1,2,7,5,3]=>[4,2,1,1]
[7,5,8,1,2,6,4,3]=>[4,2,1,1]
[7,4,8,1,6,3,5,2]=>[4,2,1,1]
[5,8,2,1,7,3,6,4]=>[4,2,1,1]
[3,6,1,8,2,4,7,5]=>[3,2,1,1,1]
[1,3,8,7,6,2,5,4]=>[5,1,1,1]
[5,4,1,8,7,3,2,6]=>[4,3,1]
[3,5,1,8,7,2,4,6]=>[3,2,1,1,1]
[4,6,1,8,3,7,2,5]=>[3,2,1,1,1]
[4,7,1,2,8,6,3,5]=>[3,2,1,1,1]
[5,8,4,1,7,6,2,3]=>[4,2,1,1]
[7,6,8,1,5,4,2,3]=>[5,1,1,1]
[8,6,1,7,5,4,3,2]=>[6,2]
[7,1,5,8,6,4,3,2]=>[5,2,1]
[5,1,8,7,3,6,4,2]=>[5,2,1]
[4,1,8,7,6,2,5,3]=>[5,2,1]
[3,1,8,7,6,5,2,4]=>[5,2,1]
[1,6,4,5,2,3,7,8]=>[3,1,1,1,1,1]
[1,7,4,5,2,3,6,8]=>[3,1,1,1,1,1]
[1,7,3,5,2,4,6,8]=>[3,1,1,1,1,1]
[1,6,3,5,2,4,7,8]=>[3,1,1,1,1,1]
[1,6,3,4,2,5,7,8]=>[3,1,1,1,1,1]
[1,7,3,4,2,5,6,8]=>[3,1,1,1,1,1]
[1,8,6,7,3,4,2,5]=>[4,1,1,1,1]
[1,8,5,7,3,4,2,6]=>[4,1,1,1,1]
[1,7,3,4,2,6,5,8]=>[3,2,1,1,1]
[1,5,2,8,4,7,3,6]=>[3,2,1,1,1]
[1,4,2,8,5,7,3,6]=>[3,2,1,1,1]
[1,7,3,5,2,6,4,8]=>[3,2,1,1,1]
[1,8,4,7,3,5,2,6]=>[4,1,1,1,1]
[1,7,3,6,2,5,4,8]=>[4,1,1,1,1]
[1,7,3,6,2,4,5,8]=>[3,1,1,1,1,1]
[1,7,4,6,2,3,5,8]=>[3,1,1,1,1,1]
[1,8,5,6,2,3,4,7]=>[3,1,1,1,1,1]
[1,8,5,6,2,4,3,7]=>[4,1,1,1,1]
[1,3,2,8,5,6,4,7]=>[3,2,1,1,1]
[1,4,2,8,5,6,3,7]=>[3,2,1,1,1]
[1,5,2,8,4,6,3,7]=>[3,2,1,1,1]
[1,6,2,8,4,5,3,7]=>[3,2,1,1,1]
[8,6,4,7,2,1,3,5]=>[5,1,1,1]
[1,6,4,7,2,8,3,5]=>[3,2,1,1,1]
[1,4,7,3,5,8,2,6]=>[3,1,1,1,1,1]
[8,4,6,2,3,5,1,7]=>[4,1,1,1,1]
[5,4,8,2,3,6,1,7]=>[4,1,1,1,1]
[7,4,8,5,2,3,1,6]=>[4,2,1,1]
[3,8,6,2,4,5,1,7]=>[4,1,1,1,1]
[4,8,6,2,3,5,1,7]=>[4,1,1,1,1]
[1,7,5,3,4,8,2,6]=>[4,1,1,1,1]
[1,7,6,4,8,2,3,5]=>[4,1,1,1,1]
[5,8,7,4,1,2,3,6]=>[4,1,1,1,1]
[6,8,5,3,4,1,2,7]=>[4,1,1,1,1]
[6,8,3,7,2,1,4,5]=>[4,1,1,1,1]
[8,5,1,6,3,7,2,4]=>[4,2,1,1]
[6,1,3,7,4,8,2,5]=>[3,2,1,1,1]
[4,1,7,3,5,8,2,6]=>[3,2,1,1,1]
[7,1,6,4,8,2,3,5]=>[4,1,1,1,1]
[1,8,5,7,2,3,4,6]=>[3,1,1,1,1,1]
[6,1,5,8,2,3,4,7]=>[3,1,1,1,1,1]
[5,1,7,3,8,2,4,6]=>[3,2,1,1,1]
[6,1,5,7,8,2,3,4]=>[3,1,1,1,1,1]
[7,4,8,6,1,2,3,5]=>[3,2,1,1,1]
[3,8,7,5,1,2,4,6]=>[4,1,1,1,1]
[3,7,6,1,2,4,5,8]=>[3,1,1,1,1,1]
[4,7,6,1,2,3,5,8]=>[3,1,1,1,1,1]
[1,6,5,8,2,3,4,7]=>[3,1,1,1,1,1]
[6,5,8,4,1,2,3,7]=>[4,1,1,1,1]
[8,5,7,4,1,2,3,6]=>[4,1,1,1,1]
[1,5,7,4,8,2,3,6]=>[3,1,1,1,1,1]
[7,6,4,8,2,1,3,5]=>[5,1,1,1]
[7,6,2,3,8,1,4,5]=>[4,1,1,1,1]
[7,4,8,5,1,6,2,3]=>[3,2,2,1]
[8,6,2,3,1,7,4,5]=>[4,2,1,1]
[8,6,4,1,2,7,3,5]=>[4,2,1,1]
[1,7,2,8,6,3,4,5]=>[3,2,1,1,1]
[7,6,1,3,8,2,4,5]=>[4,1,1,1,1]
[7,5,8,1,3,6,2,4]=>[4,1,1,1,1]
[5,4,1,8,2,3,6,7]=>[3,2,1,1,1]
[1,4,8,7,2,3,5,6]=>[3,1,1,1,1,1]
[1,5,8,7,2,3,4,6]=>[3,1,1,1,1,1]
[6,5,1,8,2,3,4,7]=>[3,2,1,1,1]
[5,7,1,3,8,2,4,6]=>[3,1,1,1,1,1]
[7,6,8,1,5,2,3,4]=>[4,1,1,1,1]
[7,1,5,8,6,2,3,4]=>[3,2,1,1,1]
[6,1,8,2,7,3,4,5]=>[3,2,1,1,1]
[4,1,8,7,2,3,5,6]=>[3,2,1,1,1]
[5,1,8,7,2,3,4,6]=>[3,2,1,1,1]
[1,8,7,6,4,5,3,2]=>[6,1,1]
[1,8,7,3,6,5,4,2]=>[6,1,1]
[6,4,2,7,5,8,3,1]=>[4,3,1]
[2,4,1,7,5,8,3,6]=>[3,2,1,1,1]
[7,1,4,6,5,8,2,3]=>[4,1,1,1,1]
[7,1,4,6,3,8,2,5]=>[4,1,1,1,1]
[7,1,4,6,5,3,2,8]=>[5,1,1,1]
[6,4,2,7,5,3,8,1]=>[4,3,1]
[3,4,7,2,6,8,5,1]=>[4,1,1,1,1]
[3,4,7,1,6,8,2,5]=>[3,1,1,1,1,1]
[3,4,1,7,8,6,2,5]=>[3,2,1,1,1]
[6,4,2,7,5,3,1,8]=>[4,3,1]
[4,8,3,2,5,6,1,7]=>[4,1,1,1,1]
[4,8,7,3,5,1,2,6]=>[4,1,1,1,1]
[3,4,7,2,6,5,8,1]=>[4,1,1,1,1]
[4,8,3,1,2,6,7,5]=>[3,2,1,1,1]
[6,8,5,1,3,7,2,4]=>[4,1,1,1,1]
[5,4,7,3,6,2,8,1]=>[5,1,1,1]
[6,4,3,7,5,1,8,2]=>[4,2,2]
[6,2,4,3,1,5,8,7]=>[4,2,1,1]
[3,8,7,4,1,5,2,6]=>[4,2,1,1]
[2,4,7,3,6,1,5,8]=>[3,1,1,1,1,1]
[5,8,3,2,1,6,4,7]=>[4,2,1,1]
[5,4,7,3,6,2,1,8]=>[5,1,1,1]
[7,3,8,2,1,6,5,4]=>[4,3,1]
[7,4,3,8,5,2,1,6]=>[5,2,1]
[6,5,2,8,4,3,1,7]=>[5,2,1]
[4,3,2,8,6,5,1,7]=>[4,3,1]
[4,3,8,7,5,1,6,2]=>[4,2,2]
[3,2,5,8,6,1,4,7]=>[3,2,1,1,1]
[8,4,3,7,5,2,6,1]=>[5,2,1]
[4,3,7,8,5,1,2,6]=>[3,2,1,1,1]
[5,3,7,8,4,1,2,6]=>[3,2,1,1,1]
[6,2,5,8,3,1,4,7]=>[4,1,1,1,1]
[6,2,4,8,3,1,5,7]=>[4,1,1,1,1]
[5,2,3,8,4,1,6,7]=>[3,2,1,1,1]
[5,3,8,7,4,1,6,2]=>[4,2,2]
[5,3,2,8,6,4,1,7]=>[4,3,1]
[7,5,3,8,4,2,1,6]=>[5,2,1]
[8,7,5,3,6,2,4,1]=>[6,1,1]
[8,6,5,3,7,2,4,1]=>[6,1,1]
[7,5,4,3,8,2,6,1]=>[6,1,1]
[6,4,5,3,8,2,7,1]=>[5,1,1,1]
[7,4,6,3,8,2,5,1]=>[5,1,1,1]
[7,5,6,3,8,2,4,1]=>[5,1,1,1]
[8,5,6,3,7,2,4,1]=>[5,1,1,1]
[7,4,6,3,5,2,8,1]=>[5,1,1,1]
[8,4,6,3,5,2,7,1]=>[5,1,1,1]
[8,4,7,3,5,2,6,1]=>[5,1,1,1]
[8,5,7,3,4,2,6,1]=>[5,1,1,1]
[7,5,8,4,3,2,6,1]=>[6,1,1]
[6,5,8,4,3,2,7,1]=>[6,1,1]
[6,5,8,3,4,2,7,1]=>[5,1,1,1]
[7,5,8,3,4,2,6,1]=>[5,1,1,1]
[7,5,8,4,6,2,3,1]=>[5,1,1,1]
[7,4,8,3,6,2,5,1]=>[5,1,1,1]
[7,4,8,3,5,2,6,1]=>[5,1,1,1]
[6,4,8,3,5,2,7,1]=>[5,1,1,1]
[6,4,7,3,5,2,8,1]=>[5,1,1,1]
[5,4,8,3,7,2,6,1]=>[5,1,1,1]
[6,5,8,3,7,2,4,1]=>[5,1,1,1]
[6,5,8,4,7,2,3,1]=>[5,1,1,1]
[6,5,8,4,7,3,2,1]=>[6,1,1]
[6,4,7,3,8,2,5,1]=>[5,1,1,1]
[5,4,7,3,8,2,6,1]=>[5,1,1,1]
[5,4,6,3,8,2,7,1]=>[5,1,1,1]
[5,3,6,2,4,7,8,1]=>[4,1,1,1,1]
[5,3,7,2,4,6,8,1]=>[4,1,1,1,1]
[4,2,1,5,8,6,3,7]=>[3,3,1,1]
[4,2,1,5,8,6,7,3]=>[3,3,1,1]
[4,2,1,5,8,7,6,3]=>[4,3,1]
[4,3,1,7,5,8,6,2]=>[3,3,2]
[6,7,3,1,4,8,2,5]=>[3,2,1,1,1]
[3,2,1,8,5,4,6,7]=>[3,3,1,1]
[5,2,7,1,8,4,3,6]=>[3,3,1,1]
[4,3,1,6,7,8,5,2]=>[3,3,1,1]
[4,2,1,6,8,7,5,3]=>[4,3,1]
[4,2,1,6,8,5,3,7]=>[3,3,1,1]
[5,2,6,1,8,7,4,3]=>[4,3,1]
[5,2,6,1,8,7,3,4]=>[3,3,1,1]
[5,2,6,1,8,3,4,7]=>[3,2,1,1,1]
[4,2,1,6,8,3,7,5]=>[3,3,1,1]
[4,2,1,7,8,6,3,5]=>[3,3,1,1]
[3,2,1,8,6,4,7,5]=>[3,3,2]
[3,2,1,8,6,4,5,7]=>[3,3,1,1]
[3,2,1,8,4,6,5,7]=>[3,3,1,1]
[3,2,1,8,4,6,7,5]=>[3,3,1,1]
[3,2,1,8,4,7,6,5]=>[4,3,1]
[3,2,1,8,7,4,6,5]=>[4,3,1]
[5,2,7,1,8,3,4,6]=>[3,2,1,1,1]
[4,2,1,7,8,3,5,6]=>[3,2,1,1,1]
[3,2,1,8,4,5,7,6]=>[3,3,1,1]
[7,5,2,8,6,3,4,1]=>[4,3,1]
[7,4,8,6,2,5,3,1]=>[5,2,1]
[7,3,8,6,2,4,5,1]=>[4,2,1,1]
[7,3,8,5,2,4,6,1]=>[4,2,1,1]
[7,3,8,4,5,6,2,1]=>[4,2,1,1]
[6,3,8,2,4,5,1,7]=>[4,1,1,1,1]
[6,4,3,8,1,5,2,7]=>[4,2,1,1]
[6,3,7,8,2,4,1,5]=>[4,1,1,1,1]
[5,6,7,3,8,2,4,1]=>[4,1,1,1,1]
[5,3,8,2,4,6,7,1]=>[4,1,1,1,1]
[6,3,8,2,4,7,5,1]=>[4,2,1,1]
[6,4,8,2,7,5,1,3]=>[4,2,1,1]
[5,6,3,7,8,2,4,1]=>[4,1,1,1,1]
[6,3,7,2,5,8,4,1]=>[4,2,1,1]
[5,3,6,8,2,4,7,1]=>[4,1,1,1,1]
[5,3,6,7,8,2,4,1]=>[4,1,1,1,1]
[3,6,4,2,1,5,8,7]=>[4,2,1,1]
[3,5,8,6,4,2,1,7]=>[5,1,1,1]
[5,8,6,3,4,2,1,7]=>[5,1,1,1]
[5,6,3,4,2,1,8,7]=>[4,2,1,1]
[6,3,4,2,1,5,8,7]=>[4,2,1,1]
[5,6,4,2,1,3,8,7]=>[4,2,1,1]
[2,5,4,1,7,8,6,3]=>[3,3,1,1]
[2,7,8,5,4,1,6,3]=>[4,2,1,1]
[2,8,5,4,1,6,3,7]=>[4,2,1,1]
[2,6,3,8,5,4,1,7]=>[4,2,1,1]
[2,8,6,3,5,4,1,7]=>[5,1,1,1]
[5,8,6,4,2,1,3,7]=>[5,1,1,1]
[4,2,1,5,7,8,6,3]=>[3,3,1,1]
[2,7,8,6,3,5,4,1]=>[5,1,1,1]
[4,3,8,5,7,6,2,1]=>[5,2,1]
[7,6,2,1,8,4,3,5]=>[4,3,1]
[2,1,8,5,6,4,3,7]=>[4,2,1,1]
[4,2,1,8,5,6,3,7]=>[3,3,1,1]
[8,4,2,1,5,6,3,7]=>[4,2,1,1]
[2,5,6,3,8,4,1,7]=>[3,2,1,1,1]
[6,3,4,2,1,8,5,7]=>[4,2,1,1]
[3,7,8,5,6,4,2,1]=>[5,1,1,1]
[3,8,5,6,4,2,1,7]=>[5,1,1,1]
[3,6,4,2,1,8,5,7]=>[4,2,1,1]
[3,8,6,4,2,1,5,7]=>[5,1,1,1]
[3,7,8,6,4,2,1,5]=>[5,1,1,1]
[8,5,3,7,6,2,4,1]=>[5,2,1]
[7,6,2,4,1,8,5,3]=>[4,3,1]
[8,5,4,1,7,6,2,3]=>[4,3,1]
[7,6,2,3,8,5,4,1]=>[5,2,1]
[2,1,7,8,6,4,3,5]=>[4,2,1,1]
[2,1,6,4,3,7,8,5]=>[3,2,2,1]
[6,4,2,1,3,7,8,5]=>[4,2,1,1]
[6,3,7,8,4,2,1,5]=>[4,2,1,1]
[7,8,4,2,1,6,3,5]=>[4,2,1,1]
[5,7,6,2,3,8,4,1]=>[4,2,1,1]
[2,6,1,8,4,3,7,5]=>[3,2,2,1]
[2,6,1,7,5,8,4,3]=>[4,2,1,1]
[8,4,2,3,7,5,6,1]=>[4,2,1,1]
[8,5,7,6,2,1,4,3]=>[5,2,1]
[4,8,5,7,6,2,1,3]=>[5,1,1,1]
[4,7,6,2,1,3,8,5]=>[4,2,1,1]
[7,5,6,1,8,4,2,3]=>[4,2,1,1]
[2,7,5,8,4,3,6,1]=>[5,1,1,1]
[2,8,4,3,6,1,7,5]=>[4,2,1,1]
[6,4,7,8,3,2,1,5]=>[5,1,1,1]
[6,4,3,7,5,2,1,8]=>[5,2,1]
[6,5,3,2,8,4,1,7]=>[5,2,1]
[6,5,2,7,8,4,1,3]=>[4,2,1,1]
[6,4,3,2,5,8,1,7]=>[5,1,1,1]
[6,3,7,2,5,4,1,8]=>[4,2,1,1]
[6,3,2,7,5,4,1,8]=>[4,3,1]
[8,4,2,6,3,1,7,5]=>[4,2,2]
[1,5,3,7,4,2,8,6]=>[3,2,2,1]
[1,6,7,3,4,2,8,5]=>[3,2,1,1,1]
[8,6,5,2,3,1,7,4]=>[5,2,1]
[1,7,6,3,4,2,8,5]=>[4,2,1,1]
[1,8,6,3,2,5,7,4]=>[4,2,1,1]
[8,7,5,2,1,4,6,3]=>[5,2,1]
[7,8,5,2,1,4,6,3]=>[4,2,1,1]
[6,8,5,2,3,1,7,4]=>[4,2,1,1]
[5,8,6,2,3,1,7,4]=>[4,2,1,1]
[4,8,2,6,3,1,7,5]=>[4,2,1,1]
[3,2,8,6,4,1,7,5]=>[4,2,2]
[3,2,1,7,5,4,8,6]=>[3,3,2]
[4,1,3,7,5,2,8,6]=>[3,2,2,1]
[5,1,7,3,4,2,8,6]=>[3,2,2,1]
[7,1,6,3,2,5,8,4]=>[4,2,1,1]
[1,2,7,4,3,6,8,5]=>[3,2,1,1,1]
[6,1,8,2,4,5,7,3]=>[3,2,1,1,1]
[5,1,8,3,2,6,7,4]=>[3,2,2,1]
[3,2,8,7,1,5,6,4]=>[4,2,1,1]
[4,8,2,7,1,5,6,3]=>[4,1,1,1,1]
[5,8,7,2,1,4,6,3]=>[4,2,1,1]
[6,8,7,1,3,4,5,2]=>[4,1,1,1,1]
[7,8,6,1,3,4,5,2]=>[4,1,1,1,1]
[1,7,8,2,4,5,6,3]=>[3,1,1,1,1,1]
[8,6,7,1,3,4,5,2]=>[4,1,1,1,1]
[7,6,8,1,3,4,5,2]=>[4,1,1,1,1]
[6,5,8,2,3,1,7,4]=>[4,2,1,1]
[1,6,8,3,2,5,7,4]=>[3,2,1,1,1]
[1,5,3,8,2,6,7,4]=>[3,2,1,1,1]
[8,4,2,7,1,5,6,3]=>[4,2,1,1]
[7,4,2,8,1,5,6,3]=>[4,2,1,1]
[6,4,2,8,3,1,7,5]=>[4,2,2]
[5,4,2,3,8,1,7,6]=>[4,2,1,1]
[4,5,2,3,1,6,8,7]=>[3,2,1,1,1]
[7,4,2,1,3,6,8,5]=>[4,2,1,1]
[8,4,2,1,3,6,7,5]=>[4,2,1,1]
[1,5,3,2,4,7,8,6]=>[3,2,1,1,1]
[8,5,1,3,2,6,7,4]=>[4,2,1,1]
[5,6,1,3,4,2,8,7]=>[3,2,1,1,1]
[4,6,2,1,5,3,8,7]=>[3,2,2,1]
[4,7,2,1,3,6,8,5]=>[3,2,1,1,1]
[5,7,1,3,2,6,8,4]=>[3,2,1,1,1]
[6,7,1,2,4,5,8,3]=>[3,1,1,1,1,1]
[8,6,1,2,4,5,7,3]=>[4,1,1,1,1]
[1,8,2,3,5,6,7,4]=>[3,1,1,1,1,1]
[8,7,1,2,4,5,6,3]=>[4,1,1,1,1]
[7,8,1,2,4,5,6,3]=>[3,1,1,1,1,1]
[5,8,1,3,2,6,7,4]=>[3,2,1,1,1]
[4,8,2,1,3,6,7,5]=>[3,2,1,1,1]
[4,1,3,2,5,7,8,6]=>[3,2,1,1,1]
[5,1,2,4,3,7,8,6]=>[3,2,1,1,1]
[5,4,8,1,2,3,7,6]=>[3,2,1,1,1]
[1,4,7,6,3,2,5,8]=>[4,1,1,1,1]
[4,8,3,2,7,6,1,5]=>[4,2,1,1]
[4,3,8,2,7,1,6,5]=>[4,2,1,1]
[1,4,7,3,6,2,5,8]=>[3,1,1,1,1,1]
[4,3,2,8,1,7,6,5]=>[4,3,1]
[4,1,8,3,7,2,5,6]=>[3,2,1,1,1]
[4,1,8,7,3,2,5,6]=>[4,2,1,1]
[4,7,8,1,2,5,3,6]=>[3,1,1,1,1,1]
[3,4,7,6,2,1,8,5]=>[4,2,1,1]
[3,4,2,7,1,6,8,5]=>[3,2,1,1,1]
[2,3,6,7,4,1,8,5]=>[3,2,1,1,1]
[2,6,3,4,7,8,1,5]=>[3,1,1,1,1,1]
[2,6,7,8,3,4,1,5]=>[3,1,1,1,1,1]
[3,1,7,8,4,2,5,6]=>[3,2,1,1,1]
[4,1,3,2,8,7,5,6]=>[3,3,1,1]
[3,7,8,2,6,4,1,5]=>[4,1,1,1,1]
[4,2,3,8,1,6,7,5]=>[3,2,1,1,1]
[4,3,1,8,2,5,7,6]=>[3,3,1,1]
[1,3,6,7,4,2,5,8]=>[3,1,1,1,1,1]
[3,2,7,8,4,1,6,5]=>[3,2,2,1]
[4,2,8,6,3,1,7,5]=>[4,2,2]
[3,7,2,4,8,6,1,5]=>[3,2,1,1,1]
[3,2,7,4,8,1,6,5]=>[3,2,2,1]
[1,3,6,4,7,2,5,8]=>[3,1,1,1,1,1]
[3,2,4,7,1,8,6,5]=>[3,3,1,1]
[3,7,4,2,6,8,1,5]=>[4,1,1,1,1]
[3,7,4,6,2,8,1,5]=>[4,1,1,1,1]
[4,7,1,5,8,2,3,6]=>[3,1,1,1,1,1]
[3,7,6,4,8,2,1,5]=>[5,1,1,1]
[3,1,7,4,8,2,5,6]=>[3,2,1,1,1]
[2,6,7,3,8,4,1,5]=>[3,2,1,1,1]
[2,3,6,4,7,1,8,5]=>[3,2,1,1,1]
[8,7,5,2,6,3,4,1]=>[5,2,1]
[8,6,5,2,7,3,4,1]=>[5,2,1]
[7,4,8,5,6,3,2,1]=>[5,2,1]
[3,4,6,7,8,5,1,2]=>[3,1,1,1,1,1]
[6,3,8,5,4,7,1,2]=>[4,2,1,1]
[1,2,6,4,8,5,7,3]=>[3,2,1,1,1]
[7,8,3,1,4,2,5,6]=>[3,2,1,1,1]
[5,6,1,8,4,3,2,7]=>[4,2,1,1]
[5,1,6,3,8,7,2,4]=>[3,2,2,1]
[6,1,8,7,4,3,2,5]=>[5,2,1]
[1,2,7,5,8,3,6,4]=>[3,2,1,1,1]
[4,1,6,3,7,8,2,5]=>[3,2,1,1,1]
[3,1,6,4,8,2,7,5]=>[3,2,2,1]
[7,8,4,1,6,3,2,5]=>[4,2,1,1]
[4,1,6,3,8,7,2,5]=>[3,2,2,1]
[7,5,1,8,4,3,2,6]=>[5,2,1]
[5,4,6,1,3,8,2,7]=>[4,1,1,1,1]
[6,5,8,1,4,3,2,7]=>[5,1,1,1]
[1,3,5,7,6,8,2,4]=>[3,1,1,1,1,1]
[1,3,5,7,6,2,8,4]=>[3,2,1,1,1]
[1,3,5,7,2,6,8,4]=>[3,1,1,1,1,1]
[1,3,5,2,7,6,4,8]=>[3,2,1,1,1]
[1,3,5,7,6,2,4,8]=>[3,1,1,1,1,1]
[1,3,5,7,4,6,8,2]=>[3,1,1,1,1,1]
[1,3,5,7,4,6,2,8]=>[3,1,1,1,1,1]
[1,3,5,7,4,2,6,8]=>[3,1,1,1,1,1]
[1,3,5,4,7,2,6,8]=>[3,1,1,1,1,1]
[1,3,5,4,7,8,2,6]=>[3,1,1,1,1,1]
[1,3,5,4,7,2,8,6]=>[3,2,1,1,1]
[1,3,5,7,4,2,8,6]=>[3,2,1,1,1]
[1,3,5,7,4,8,2,6]=>[3,1,1,1,1,1]
[1,3,5,7,4,8,6,2]=>[3,2,1,1,1]
[1,3,5,7,8,4,6,2]=>[3,1,1,1,1,1]
[1,3,5,7,8,4,2,6]=>[3,1,1,1,1,1]
[1,3,5,2,7,8,6,4]=>[3,2,1,1,1]
[1,3,5,7,2,8,6,4]=>[3,2,1,1,1]
[1,3,5,7,8,2,6,4]=>[3,1,1,1,1,1]
[1,6,3,2,7,4,8,5]=>[3,2,2,1]
[3,5,1,6,2,8,7,4]=>[3,2,2,1]
[1,3,7,2,5,4,8,6]=>[3,2,1,1,1]
[2,6,1,7,4,3,8,5]=>[3,2,2,1]
[1,4,7,3,5,2,8,6]=>[3,2,1,1,1]
[1,3,7,5,2,4,8,6]=>[3,2,1,1,1]
[2,5,7,4,3,8,1,6]=>[4,1,1,1,1]
[2,5,3,7,4,8,1,6]=>[3,2,1,1,1]
[1,4,7,2,3,8,6,5]=>[3,2,1,1,1]
[2,4,7,3,1,8,6,5]=>[3,3,1,1]
[1,4,6,3,8,2,7,5]=>[3,2,1,1,1]
[1,3,5,2,8,7,6,4]=>[4,2,1,1]
[1,4,7,3,8,2,6,5]=>[3,2,1,1,1]
[2,5,1,7,8,4,6,3]=>[3,2,1,1,1]
[3,2,6,7,8,1,5,4]=>[3,2,1,1,1]
[4,3,6,7,8,2,1,5]=>[4,1,1,1,1]
[3,5,2,7,8,4,1,6]=>[3,2,1,1,1]
[1,5,7,4,8,3,2,6]=>[4,1,1,1,1]
[2,5,1,6,8,4,7,3]=>[3,2,1,1,1]
[4,6,2,1,7,8,3,5]=>[3,2,1,1,1]
[5,3,6,4,7,8,2,1]=>[4,2,1,1]
[3,5,2,6,8,4,7,1]=>[3,2,1,1,1]
[2,5,4,6,8,7,1,3]=>[3,2,1,1,1]
[1,3,6,2,8,7,5,4]=>[4,2,1,1]
[1,4,6,3,8,7,2,5]=>[3,2,1,1,1]
[2,5,7,4,3,8,6,1]=>[4,2,1,1]
[1,5,7,2,4,8,6,3]=>[3,2,1,1,1]
[4,6,3,7,2,8,5,1]=>[4,2,1,1]
[4,3,6,7,8,2,5,1]=>[4,1,1,1,1]
[1,4,7,3,8,6,2,5]=>[3,2,1,1,1]
[2,5,4,7,8,6,1,3]=>[3,2,1,1,1]
[3,2,6,7,8,5,1,4]=>[3,2,1,1,1]
[1,3,7,2,8,6,5,4]=>[4,2,1,1]
[5,3,7,8,2,4,1,6]=>[4,1,1,1,1]
[2,4,7,8,3,1,5,6]=>[3,1,1,1,1,1]
[6,3,1,5,8,2,4,7]=>[3,2,1,1,1]
[3,2,4,8,1,5,6,7]=>[3,1,1,1,1,1]
[3,2,4,6,8,1,5,7]=>[3,1,1,1,1,1]
[7,2,4,8,3,1,5,6]=>[4,1,1,1,1]
[5,3,8,7,2,4,1,6]=>[4,2,1,1]
[2,4,8,7,3,1,5,6]=>[4,1,1,1,1]
[8,7,4,6,2,3,1,5]=>[5,1,1,1]
[5,6,8,7,2,3,1,4]=>[4,1,1,1,1]
[5,7,6,8,2,3,1,4]=>[4,1,1,1,1]
[4,7,6,8,2,3,1,5]=>[4,1,1,1,1]
[8,6,4,7,2,3,1,5]=>[5,1,1,1]
[2,3,7,8,4,1,6,5]=>[3,2,1,1,1]
[3,7,4,8,2,5,1,6]=>[4,1,1,1,1]
[2,3,7,4,1,6,8,5]=>[3,2,1,1,1]
[7,5,8,6,2,3,1,4]=>[4,2,1,1]
[7,1,6,4,2,3,8,5]=>[4,2,1,1]
[3,1,7,6,4,2,8,5]=>[4,2,2]
[6,8,7,5,2,3,1,4]=>[5,1,1,1]
[4,3,6,1,5,8,7,2]=>[3,3,1,1]
[4,3,6,5,1,8,7,2]=>[3,3,2]
[4,6,3,5,1,8,7,2]=>[3,3,1,1]
[4,6,3,1,5,8,7,2]=>[3,3,1,1]
[4,1,6,5,3,8,7,2]=>[4,2,2]
[4,6,1,5,3,8,7,2]=>[4,2,1,1]
[2,6,5,3,1,8,7,4]=>[4,3,1]
[2,6,5,1,8,7,3,4]=>[3,3,1,1]
[2,6,5,8,1,7,3,4]=>[3,2,1,1,1]
[2,6,5,8,1,3,7,4]=>[3,2,1,1,1]
[2,6,5,8,3,1,7,4]=>[4,2,1,1]
[2,6,5,3,8,1,7,4]=>[4,2,1,1]
[4,6,1,5,8,3,7,2]=>[4,1,1,1,1]
[4,1,6,5,8,3,7,2]=>[4,2,1,1]
[1,4,6,5,8,3,7,2]=>[4,1,1,1,1]
[4,1,6,5,8,7,3,2]=>[4,2,2]
[2,6,5,3,8,7,1,4]=>[4,2,1,1]
[6,4,3,8,7,1,5,2]=>[4,3,1]
[6,4,8,3,7,1,5,2]=>[4,2,1,1]
[2,6,8,5,3,7,1,4]=>[4,1,1,1,1]
[4,6,8,1,5,7,3,2]=>[4,1,1,1,1]
[4,6,1,8,5,7,3,2]=>[4,2,1,1]
[4,1,6,8,5,7,3,2]=>[4,2,1,1]
[1,4,6,8,5,7,3,2]=>[4,1,1,1,1]
[1,4,6,8,5,3,7,2]=>[4,1,1,1,1]
[4,6,1,8,5,3,7,2]=>[4,2,1,1]
[2,6,8,5,3,1,7,4]=>[4,2,1,1]
[2,6,8,5,1,7,3,4]=>[3,2,1,1,1]
[4,6,8,3,5,1,7,2]=>[3,2,1,1,1]
[4,6,8,3,1,5,7,2]=>[3,2,1,1,1]
[4,6,3,1,8,5,7,2]=>[3,3,1,1]
[4,6,3,8,1,5,7,2]=>[3,2,1,1,1]
[4,6,3,8,5,7,1,2]=>[3,2,1,1,1]
[4,3,6,8,1,5,7,2]=>[3,2,1,1,1]
[4,3,6,1,8,5,7,2]=>[3,3,1,1]
[4,3,1,6,8,5,7,2]=>[3,3,1,1]
[4,1,3,6,8,7,5,2]=>[4,2,1,1]
[4,3,6,1,8,7,5,2]=>[4,3,1]
[4,3,6,8,1,7,5,2]=>[4,2,1,1]
[6,5,2,8,7,3,1,4]=>[4,3,1]
[6,5,2,8,7,1,3,4]=>[4,2,1,1]
[6,2,5,8,7,1,3,4]=>[3,2,1,1,1]
[6,2,5,8,7,3,1,4]=>[4,2,1,1]
[4,6,3,8,1,7,5,2]=>[4,2,1,1]
[4,6,3,1,8,7,5,2]=>[4,3,1]
[4,1,6,3,8,7,5,2]=>[4,2,2]
[1,4,6,3,8,7,5,2]=>[4,2,1,1]
[4,1,6,8,3,7,5,2]=>[4,2,1,1]
[4,6,1,8,3,7,5,2]=>[4,2,1,1]
[4,6,8,1,3,7,5,2]=>[4,1,1,1,1]
[6,2,8,5,7,3,1,4]=>[4,2,1,1]
[6,2,8,5,7,1,3,4]=>[3,2,1,1,1]
[2,4,8,7,1,5,3,6]=>[4,1,1,1,1]
[4,2,8,7,5,3,1,6]=>[5,2,1]
[6,4,1,8,7,5,3,2]=>[5,3]
[6,1,4,8,7,5,3,2]=>[5,2,1]
[1,6,4,8,7,3,5,2]=>[4,2,1,1]
[6,4,1,8,7,3,5,2]=>[4,3,1]
[4,2,8,7,5,1,3,6]=>[4,2,1,1]
[2,4,8,7,3,5,1,6]=>[4,1,1,1,1]
[2,3,4,7,8,5,6,1]=>[3,1,1,1,1,1]
[2,3,7,1,4,8,6,5]=>[3,2,1,1,1]
[2,6,1,3,7,8,5,4]=>[3,2,1,1,1]
[2,6,7,3,4,8,5,1]=>[3,2,1,1,1]
[1,5,3,2,6,4,7,8]=>[3,2,1,1,1]
[1,5,3,2,6,7,4,8]=>[3,2,1,1,1]
[1,7,3,2,8,5,4,6]=>[3,3,1,1]
[1,7,3,2,5,8,4,6]=>[3,2,1,1,1]
[1,3,2,7,5,4,8,6]=>[3,2,2,1]
[6,5,2,4,3,7,1,8]=>[5,1,1,1]
[6,4,2,5,3,7,1,8]=>[4,2,1,1]
[5,4,7,6,2,3,1,8]=>[4,2,1,1]
[3,6,4,8,2,1,5,7]=>[4,1,1,1,1]
[1,6,2,8,5,3,4,7]=>[3,2,1,1,1]
[4,6,2,3,7,5,1,8]=>[3,2,1,1,1]
[4,7,2,3,6,5,1,8]=>[4,1,1,1,1]
[4,7,2,3,5,6,1,8]=>[3,1,1,1,1,1]
[5,3,2,7,4,6,1,8]=>[4,2,1,1]
[5,3,2,6,4,7,1,8]=>[4,2,1,1]
[4,6,2,3,5,7,1,8]=>[3,1,1,1,1,1]
[3,5,2,1,6,8,4,7]=>[3,2,1,1,1]
[1,5,2,6,8,4,3,7]=>[3,2,1,1,1]
[1,5,7,2,8,4,3,6]=>[3,2,1,1,1]
[3,5,2,1,8,6,4,7]=>[3,3,1,1]
[3,6,8,4,2,1,5,7]=>[4,1,1,1,1]
[4,3,2,6,1,8,5,7]=>[4,2,1,1]
[1,5,8,2,7,4,3,6]=>[4,1,1,1,1]
[1,7,2,3,4,8,6,5]=>[3,2,1,1,1]
[6,8,2,3,4,1,7,5]=>[3,2,1,1,1]
[4,1,8,2,3,5,7,6]=>[3,2,1,1,1]
[2,3,1,8,4,5,7,6]=>[3,2,1,1,1]
[7,3,2,1,4,5,8,6]=>[4,2,1,1]
[7,8,1,4,3,5,2,6]=>[4,1,1,1,1]
[7,1,2,3,4,6,8,5]=>[3,1,1,1,1,1]
[6,1,2,3,4,8,7,5]=>[3,2,1,1,1]
[1,8,2,3,4,7,6,5]=>[4,1,1,1,1]
[8,1,2,3,4,6,7,5]=>[3,1,1,1,1,1]
[2,8,1,3,5,4,7,6]=>[3,2,1,1,1]
[8,7,1,4,3,5,2,6]=>[5,1,1,1]
[8,3,2,1,4,5,7,6]=>[4,2,1,1]
[3,8,2,1,5,6,4,7]=>[3,2,1,1,1]
[3,8,2,1,6,5,4,7]=>[4,2,1,1]
[1,7,8,3,5,4,2,6]=>[4,1,1,1,1]
[7,4,1,8,3,5,2,6]=>[4,2,1,1]
[8,4,1,7,3,5,2,6]=>[4,2,1,1]
[3,8,4,6,2,1,5,7]=>[4,1,1,1,1]
[8,4,2,5,3,1,6,7]=>[4,2,1,1]
[8,5,2,4,3,1,6,7]=>[5,1,1,1]
[8,3,2,5,4,1,6,7]=>[4,2,1,1]
[4,3,2,5,1,8,6,7]=>[4,2,1,1]
[3,5,2,4,1,8,6,7]=>[3,2,1,1,1]
[2,4,7,8,1,5,3,6]=>[3,1,1,1,1,1]
[1,8,7,3,5,4,2,6]=>[5,1,1,1]
[5,1,8,2,7,4,3,6]=>[4,2,1,1]
[5,1,7,2,8,4,3,6]=>[3,2,2,1]
[6,1,2,8,5,3,4,7]=>[3,2,1,1,1]
[6,3,2,1,8,4,5,7]=>[4,2,1,1]
[7,3,2,8,4,5,1,6]=>[4,2,1,1]
[2,7,8,4,3,5,1,6]=>[4,1,1,1,1]
[7,1,8,3,5,4,2,6]=>[4,2,1,1]
[7,8,2,3,4,6,1,5]=>[3,1,1,1,1,1]
[6,7,1,3,4,8,2,5]=>[3,1,1,1,1,1]
[6,8,1,3,4,7,2,5]=>[3,1,1,1,1,1]
[1,7,2,3,4,6,8,5]=>[3,1,1,1,1,1]
[1,6,2,3,4,8,7,5]=>[3,2,1,1,1]
[7,6,2,3,4,1,8,5]=>[4,2,1,1]
[8,6,2,3,4,1,7,5]=>[4,2,1,1]
[8,1,7,3,5,4,2,6]=>[5,1,1,1]
[8,3,2,7,4,5,1,6]=>[4,2,1,1]
[6,7,2,3,4,1,8,5]=>[3,2,1,1,1]
[7,6,2,3,4,8,1,5]=>[4,1,1,1,1]
[8,6,2,3,4,7,1,5]=>[4,1,1,1,1]
[6,3,4,8,7,5,1,2]=>[4,2,1,1]
[4,8,7,3,5,6,1,2]=>[4,1,1,1,1]
[5,8,4,2,1,6,7,3]=>[4,2,1,1]
[7,8,4,1,2,6,5,3]=>[4,2,1,1]
[4,8,1,5,2,7,6,3]=>[4,2,1,1]
[3,8,7,6,2,4,1,5]=>[5,1,1,1]
[2,8,7,6,4,1,3,5]=>[5,1,1,1]
[2,8,7,6,3,1,4,5]=>[5,1,1,1]
[1,8,7,6,2,4,3,5]=>[5,1,1,1]
[1,8,7,6,3,4,2,5]=>[5,1,1,1]
[2,1,7,3,6,5,8,4]=>[4,2,1,1]
[3,1,7,2,6,5,8,4]=>[4,2,1,1]
[6,1,2,8,5,7,3,4]=>[3,2,1,1,1]
[6,2,1,8,5,7,3,4]=>[3,3,1,1]
[6,4,2,1,7,5,8,3]=>[4,3,1]
[6,1,3,8,5,2,7,4]=>[3,2,2,1]
[2,3,7,1,6,8,5,4]=>[4,1,1,1,1]
[3,2,6,7,5,8,1,4]=>[3,2,1,1,1]
[3,8,7,6,2,1,5,4]=>[5,2,1]
[4,8,7,6,2,1,3,5]=>[5,1,1,1]
[4,8,7,6,1,3,2,5]=>[5,1,1,1]
[5,1,4,6,8,2,3,7]=>[3,1,1,1,1,1]
[1,7,6,3,5,4,8,2]=>[5,1,1,1]
[4,3,7,2,6,5,1,8]=>[4,2,1,1]
[3,4,6,1,5,7,2,8]=>[3,1,1,1,1,1]
[1,6,8,5,7,3,4,2]=>[4,1,1,1,1]
[2,4,1,5,8,6,3,7]=>[3,2,1,1,1]
[4,6,1,2,5,8,3,7]=>[3,1,1,1,1,1]
[5,6,7,2,1,4,8,3]=>[3,2,1,1,1]
[7,8,6,5,1,2,4,3]=>[5,1,1,1]
[1,3,6,5,7,8,2,4]=>[3,1,1,1,1,1]
[7,4,8,5,3,1,6,2]=>[4,2,2]
[6,8,5,2,4,1,7,3]=>[4,2,1,1]
[2,3,1,6,8,5,7,4]=>[3,2,1,1,1]
[7,3,2,5,1,4,8,6]=>[4,2,1,1]
[7,1,4,2,3,6,8,5]=>[3,2,1,1,1]
[1,5,8,3,4,6,7,2]=>[3,1,1,1,1,1]
[8,3,1,2,4,7,6,5]=>[4,2,1,1]
[2,3,8,1,6,5,4,7]=>[4,1,1,1,1]
[8,1,4,7,2,5,3,6]=>[4,1,1,1,1]
[3,5,2,4,1,7,8,6]=>[3,2,1,1,1]
[3,4,7,8,6,2,1,5]=>[4,1,1,1,1]
[3,4,8,6,2,7,1,5]=>[4,1,1,1,1]
[5,8,2,1,6,7,3,4]=>[3,2,1,1,1]
[5,7,2,8,6,4,3,1]=>[5,2,1]
[6,1,2,7,5,3,8,4]=>[3,2,2,1]
[7,3,2,8,6,4,1,5]=>[4,3,1]
[2,7,8,4,6,3,1,5]=>[4,1,1,1,1]
[1,4,5,7,2,6,8,3]=>[3,1,1,1,1,1]
[7,3,5,2,6,1,8,4]=>[4,2,1,1]
[8,5,2,3,6,1,7,4]=>[4,2,1,1]
[8,1,6,3,5,7,2,4]=>[4,1,1,1,1]
[2,8,6,4,3,7,1,5]=>[5,1,1,1]
[8,3,2,6,4,7,1,5]=>[4,2,1,1]
[2,3,8,7,6,5,1,4]=>[5,1,1,1]
[1,5,8,7,3,2,6,4]=>[4,2,1,1]
[4,5,8,7,3,2,1,6]=>[5,1,1,1]
[2,6,8,1,7,5,4,3]=>[5,1,1,1]
[3,6,8,4,7,2,1,5]=>[4,1,1,1,1]
[2,5,8,3,7,6,1,4]=>[4,1,1,1,1]
[3,2,8,4,7,6,1,5]=>[4,2,1,1]
[1,6,8,4,2,7,5,3]=>[4,2,1,1]
[1,5,8,4,2,7,6,3]=>[4,2,1,1]
[1,5,8,2,3,7,6,4]=>[4,1,1,1,1]
[2,1,8,4,3,7,6,5]=>[4,2,2]
[5,6,8,4,1,2,7,3]=>[3,2,1,1,1]
[1,6,8,4,3,2,7,5]=>[4,2,1,1]
[5,6,8,4,3,2,1,7]=>[5,1,1,1]
[7,1,2,8,6,5,4,3]=>[5,2,1]
[7,1,4,8,6,2,5,3]=>[4,2,1,1]
[7,3,1,8,6,2,5,4]=>[4,3,1]
[1,6,4,8,7,2,5,3]=>[4,2,1,1]
[3,2,5,8,7,6,1,4]=>[4,2,1,1]
[3,2,4,8,7,6,1,5]=>[4,2,1,1]
[3,1,4,8,7,2,6,5]=>[4,2,1,1]
[1,6,4,8,2,7,5,3]=>[4,2,1,1]
[1,4,5,8,3,2,7,6]=>[3,2,1,1,1]
[7,6,1,4,8,2,5,3]=>[4,2,1,1]
[7,6,3,4,8,2,1,5]=>[5,1,1,1]
[7,2,5,3,8,6,1,4]=>[4,2,1,1]
[7,2,1,4,8,6,5,3]=>[4,3,1]
[7,2,1,3,8,6,5,4]=>[4,3,1]
[7,2,3,4,8,6,1,5]=>[3,2,1,1,1]
[1,6,5,4,8,2,7,3]=>[4,2,1,1]
[1,3,5,4,8,2,7,6]=>[3,2,1,1,1]
[7,6,2,4,3,8,1,5]=>[5,1,1,1]
[7,1,5,2,3,8,6,4]=>[3,3,1,1]
[2,6,5,4,3,8,1,7]=>[5,1,1,1]
[3,4,2,6,7,8,1,5]=>[3,1,1,1,1,1]
[3,1,4,2,6,8,7,5]=>[3,2,2,1]
[8,3,4,2,6,1,7,5]=>[4,2,1,1]
[2,6,7,3,5,4,1,8]=>[4,1,1,1,1]
[2,7,8,3,5,4,1,6]=>[4,1,1,1,1]
[2,6,8,3,5,4,1,7]=>[4,1,1,1,1]
[4,7,1,2,8,5,3,6]=>[3,2,1,1,1]
[4,8,1,2,7,5,3,6]=>[4,1,1,1,1]
[2,1,6,3,7,5,4,8]=>[3,2,2,1]
[2,7,1,3,6,8,4,5]=>[3,1,1,1,1,1]
[6,7,3,2,8,1,4,5]=>[4,1,1,1,1]
[7,3,4,2,6,1,8,5]=>[4,2,1,1]
[7,4,1,2,8,5,3,6]=>[3,3,1,1]
[8,7,4,2,1,5,3,6]=>[5,2,1]
[7,4,1,2,6,5,3,8]=>[4,2,1,1]
[7,4,3,1,5,6,8,2]=>[4,2,1,1]
[6,7,4,1,5,8,3,2]=>[4,2,1,1]
[4,7,5,1,6,8,3,2]=>[4,2,1,1]
[4,5,3,1,7,6,8,2]=>[3,3,1,1]
[4,6,1,2,7,5,3,8]=>[3,2,1,1,1]
[2,7,1,3,6,5,4,8]=>[4,1,1,1,1]
[4,1,8,2,6,5,3,7]=>[4,2,1,1]
[4,6,1,2,8,5,3,7]=>[3,2,1,1,1]
[8,4,3,1,5,6,7,2]=>[4,2,1,1]
[4,5,3,1,8,6,7,2]=>[3,3,1,1]
[4,8,5,6,3,1,7,2]=>[4,2,1,1]
[5,1,3,4,8,6,7,2]=>[3,2,1,1,1]
[5,4,3,8,1,6,7,2]=>[4,2,1,1]
[8,5,3,4,1,6,7,2]=>[4,2,1,1]
[6,4,8,2,1,5,3,7]=>[4,2,1,1]
[6,7,3,2,5,1,4,8]=>[4,1,1,1,1]
[6,8,3,2,5,1,4,7]=>[4,1,1,1,1]
[5,7,1,4,6,8,3,2]=>[4,1,1,1,1]
[5,1,3,4,7,6,8,2]=>[3,2,1,1,1]
[6,1,4,2,7,5,3,8]=>[3,3,1,1]
[5,4,3,7,1,6,8,2]=>[4,2,1,1]
[6,7,5,4,1,8,3,2]=>[5,2,1]
[7,6,4,2,1,5,3,8]=>[5,2,1]
[8,2,7,6,5,4,1,3]=>[6,1,1]
[7,2,8,6,5,4,3,1]=>[6,2]
[3,2,8,7,6,5,1,4]=>[5,2,1]
[4,8,7,6,5,3,1,2]=>[6,1,1]
[7,8,6,1,5,4,3,2]=>[6,1,1]
[7,3,8,6,5,4,2,1]=>[6,2]
[4,8,5,7,6,3,2,1]=>[6,1,1]
[8,5,6,1,3,2,4,7]=>[4,1,1,1,1]
[8,6,1,5,3,2,4,7]=>[5,1,1,1]
[7,8,1,5,3,2,4,6]=>[4,1,1,1,1]
[8,1,7,5,3,2,4,6]=>[5,1,1,1]
[8,6,1,4,5,2,3,7]=>[4,1,1,1,1]
[8,6,3,1,5,2,4,7]=>[4,2,1,1]
[8,4,6,1,5,2,3,7]=>[4,1,1,1,1]
[8,6,2,1,5,4,3,7]=>[5,2,1]
[8,5,2,6,1,4,3,7]=>[4,2,1,1]
[8,5,2,1,7,4,3,6]=>[4,3,1]
[7,8,2,1,5,4,3,6]=>[4,2,1,1]
[7,8,3,1,5,2,4,6]=>[3,2,1,1,1]
[8,2,7,5,1,3,4,6]=>[4,1,1,1,1]
[8,4,1,7,5,2,3,6]=>[4,2,1,1]
[8,2,7,1,5,4,3,6]=>[5,1,1,1]
[8,2,6,1,7,4,3,5]=>[4,2,1,1]
[8,1,7,4,3,2,6,5]=>[5,2,1]
[8,1,5,7,3,2,6,4]=>[4,2,1,1]
[5,7,8,1,3,2,6,4]=>[3,2,1,1,1]
[8,2,6,1,5,7,3,4]=>[4,1,1,1,1]
[5,8,1,6,7,2,3,4]=>[3,1,1,1,1,1]
[5,7,6,1,8,2,3,4]=>[3,2,1,1,1]
[6,7,2,5,1,8,3,4]=>[3,2,1,1,1]
[7,5,1,6,8,2,3,4]=>[3,2,1,1,1]
[6,5,7,1,8,2,3,4]=>[3,2,1,1,1]
[6,7,3,8,1,2,4,5]=>[3,1,1,1,1,1]
[7,5,4,1,8,2,3,6]=>[4,2,1,1]
[7,6,1,4,8,2,3,5]=>[4,1,1,1,1]
[8,1,6,4,7,2,3,5]=>[4,1,1,1,1]
[7,5,8,1,3,2,4,6]=>[4,1,1,1,1]
[7,8,4,1,3,2,5,6]=>[4,1,1,1,1]
[8,3,7,4,1,2,5,6]=>[4,1,1,1,1]
[8,5,1,7,3,2,4,6]=>[4,2,1,1]
[6,8,1,7,3,2,4,5]=>[4,1,1,1,1]
[7,1,8,4,3,6,2,5]=>[4,2,1,1]
[7,3,1,8,6,4,2,5]=>[4,3,1]
[8,3,1,7,4,6,2,5]=>[4,2,1,1]
[8,4,5,1,7,2,3,6]=>[3,2,1,1,1]
[5,6,8,1,7,2,3,4]=>[3,1,1,1,1,1]
[6,5,8,1,2,7,3,4]=>[3,2,1,1,1]
[7,3,1,8,5,6,2,4]=>[3,3,1,1]
[6,2,7,8,3,1,5,4]=>[3,2,2,1]
[5,8,1,7,3,2,6,4]=>[4,2,1,1]
[8,4,1,7,3,2,6,5]=>[4,2,2]
[8,3,4,7,1,2,6,5]=>[4,1,1,1,1]
[8,2,7,4,1,3,6,5]=>[4,2,1,1]
[7,4,8,2,1,3,6,5]=>[4,2,1,1]
[7,4,3,8,1,2,6,5]=>[4,2,1,1]
[8,2,3,6,7,1,5,4]=>[4,1,1,1,1]
[2,6,8,7,1,5,4,3]=>[5,1,1,1]
[7,8,5,2,3,6,4,1]=>[4,2,1,1]
[8,7,5,2,3,1,6,4]=>[5,2,1]
[6,8,5,2,3,4,7,1]=>[4,1,1,1,1]
[3,5,2,6,8,1,4,7]=>[3,1,1,1,1,1]
[3,5,2,4,6,8,1,7]=>[3,1,1,1,1,1]
[2,4,5,7,3,6,8,1]=>[3,1,1,1,1,1]
[2,4,5,3,6,8,1,7]=>[3,1,1,1,1,1]
[5,2,4,6,8,1,3,7]=>[3,1,1,1,1,1]
[5,1,3,4,6,8,2,7]=>[3,1,1,1,1,1]
[4,3,5,2,6,8,1,7]=>[4,1,1,1,1]
[4,3,5,7,2,8,1,6]=>[4,1,1,1,1]
[4,3,5,7,2,6,8,1]=>[4,1,1,1,1]
[4,6,3,7,2,5,8,1]=>[4,1,1,1,1]
[4,6,3,1,7,8,2,5]=>[3,2,1,1,1]
[4,3,5,1,7,8,2,6]=>[3,2,1,1,1]
[5,7,1,3,4,8,2,6]=>[3,1,1,1,1,1]
[5,7,1,3,4,6,8,2]=>[3,1,1,1,1,1]
[4,5,7,1,3,6,8,2]=>[3,1,1,1,1,1]
[4,3,6,7,1,5,8,2]=>[3,2,1,1,1]
[4,6,3,5,1,7,8,2]=>[3,2,1,1,1]
[4,6,3,5,7,2,8,1]=>[4,1,1,1,1]
[3,5,6,4,1,7,8,2]=>[3,2,1,1,1]
[3,1,5,6,7,4,8,2]=>[3,2,1,1,1]
[5,1,6,7,3,4,8,2]=>[3,2,1,1,1]
[6,4,7,1,3,5,8,2]=>[4,1,1,1,1]
[1,6,7,3,4,5,8,2]=>[3,1,1,1,1,1]
[2,6,7,4,5,8,1,3]=>[3,1,1,1,1,1]
[2,6,7,4,8,1,3,5]=>[3,1,1,1,1,1]
[5,3,6,1,2,7,8,4]=>[3,2,1,1,1]
[3,5,2,6,1,7,8,4]=>[3,2,1,1,1]
[3,5,2,6,7,4,8,1]=>[3,2,1,1,1]
[5,2,3,6,7,4,8,1]=>[3,2,1,1,1]
[5,2,3,6,1,7,8,4]=>[3,2,1,1,1]
[5,2,6,1,3,7,8,4]=>[3,2,1,1,1]
[4,2,6,7,3,5,8,1]=>[3,2,1,1,1]
[6,3,7,2,4,5,8,1]=>[4,1,1,1,1]
[3,5,7,2,8,1,4,6]=>[3,1,1,1,1,1]
[3,7,2,4,8,1,5,6]=>[3,1,1,1,1,1]
[7,2,4,6,8,1,3,5]=>[3,1,1,1,1,1]
[7,1,3,4,6,8,2,5]=>[3,1,1,1,1,1]
[3,7,2,4,6,8,1,5]=>[3,1,1,1,1,1]
[3,5,7,2,6,8,1,4]=>[3,1,1,1,1,1]
[6,3,7,2,5,8,1,4]=>[4,1,1,1,1]
[6,3,5,7,2,8,1,4]=>[4,1,1,1,1]
[6,3,5,7,2,4,8,1]=>[4,1,1,1,1]
[6,2,4,5,7,3,8,1]=>[4,1,1,1,1]
[6,2,4,5,1,7,8,3]=>[3,2,1,1,1]
[4,7,1,2,5,6,8,3]=>[3,1,1,1,1,1]
[2,6,7,5,8,1,3,4]=>[3,1,1,1,1,1]
[4,6,7,1,2,5,8,3]=>[3,1,1,1,1,1]
[5,6,2,4,7,3,8,1]=>[4,1,1,1,1]
[5,4,2,6,7,3,8,1]=>[4,2,1,1]
[5,4,2,6,1,7,8,3]=>[4,2,1,1]
[1,5,4,6,2,7,8,3]=>[3,2,1,1,1]
[5,6,4,1,2,7,8,3]=>[3,2,1,1,1]
[6,4,5,1,2,7,8,3]=>[3,2,1,1,1]
[6,3,5,1,7,8,2,4]=>[3,2,1,1,1]
[6,5,7,2,8,1,3,4]=>[4,1,1,1,1]
[6,5,7,1,3,4,8,2]=>[4,1,1,1,1]
[5,6,4,7,1,3,8,2]=>[4,1,1,1,1]
[5,4,6,3,1,7,8,2]=>[4,2,1,1]
[7,5,3,2,4,8,1,6]=>[5,1,1,1]
[8,4,5,2,6,1,3,7]=>[4,1,1,1,1]
[8,5,4,2,1,6,3,7]=>[5,2,1]
[8,5,3,4,1,6,2,7]=>[4,2,1,1]
[8,4,5,3,1,6,2,7]=>[4,2,1,1]
[7,5,4,2,1,8,3,6]=>[5,2,1]
[7,5,4,2,1,6,8,3]=>[5,2,1]
[7,4,5,3,1,6,8,2]=>[4,2,1,1]
[7,4,3,5,6,1,8,2]=>[4,2,1,1]
[5,6,3,7,4,1,8,2]=>[3,2,2,1]
[5,6,7,3,1,4,8,2]=>[3,2,1,1,1]
[6,7,3,4,1,5,8,2]=>[3,2,1,1,1]
[6,7,4,2,1,5,8,3]=>[4,2,1,1]
[5,6,7,3,1,8,2,4]=>[3,2,1,1,1]
[5,6,3,7,8,1,2,4]=>[3,1,1,1,1,1]
[5,6,3,7,2,4,8,1]=>[4,1,1,1,1]
[5,6,7,2,3,8,1,4]=>[3,1,1,1,1,1]
[7,4,5,2,8,1,3,6]=>[4,1,1,1,1]
[6,7,3,2,4,8,1,5]=>[4,1,1,1,1]
[7,6,4,2,1,3,8,5]=>[5,2,1]
[7,6,3,4,1,2,8,5]=>[4,2,1,1]
[7,6,3,2,4,1,8,5]=>[5,2,1]
[6,7,3,2,5,1,8,4]=>[4,2,1,1]
[6,5,3,2,7,8,1,4]=>[5,1,1,1]
[6,5,3,2,7,4,8,1]=>[5,2,1]
[6,4,5,2,7,3,8,1]=>[4,2,1,1]
[6,4,5,2,7,8,1,3]=>[4,1,1,1,1]
[7,4,5,2,6,1,8,3]=>[4,2,1,1]
[7,4,5,6,1,2,8,3]=>[3,2,1,1,1]
[7,5,6,2,1,3,8,4]=>[4,2,1,1]
[6,7,3,5,1,2,8,4]=>[3,2,1,1,1]
[5,6,7,4,1,2,8,3]=>[3,2,1,1,1]
[5,6,7,2,4,1,8,3]=>[3,2,1,1,1]
[5,6,4,2,7,8,1,3]=>[4,1,1,1,1]
[6,5,7,2,1,8,3,4]=>[4,2,1,1]
[6,5,7,2,1,4,8,3]=>[4,2,1,1]
[5,4,6,7,3,1,8,2]=>[4,2,1,1]
[5,7,8,3,6,4,1,2]=>[4,1,1,1,1]
[3,7,8,5,6,4,1,2]=>[4,1,1,1,1]
[3,7,8,5,6,1,4,2]=>[4,1,1,1,1]
[1,7,8,5,6,3,4,2]=>[4,1,1,1,1]
[1,7,5,8,6,3,4,2]=>[4,2,1,1]
[3,7,5,8,6,1,4,2]=>[4,2,1,1]
[3,7,5,8,6,4,1,2]=>[4,2,1,1]
[5,7,3,8,6,4,1,2]=>[4,2,1,1]
[7,3,8,5,6,4,1,2]=>[4,2,1,1]
[7,3,5,8,6,4,1,2]=>[4,2,1,1]
[3,5,7,8,6,4,1,2]=>[4,1,1,1,1]
[1,5,7,8,6,3,4,2]=>[4,1,1,1,1]
[1,5,7,8,3,6,4,2]=>[4,1,1,1,1]
[3,5,7,8,1,6,4,2]=>[4,1,1,1,1]
[5,3,7,8,1,6,4,2]=>[4,2,1,1]
[7,3,5,8,6,1,4,2]=>[4,2,1,1]
[7,3,8,5,6,1,4,2]=>[4,2,1,1]
[7,8,1,5,6,3,4,2]=>[4,1,1,1,1]
[7,1,8,5,6,3,4,2]=>[4,2,1,1]
[7,1,5,8,6,3,4,2]=>[4,2,1,1]
[5,1,7,8,3,6,4,2]=>[4,2,1,1]
[3,1,7,8,5,6,4,2]=>[4,2,1,1]
[1,3,7,8,5,6,4,2]=>[4,1,1,1,1]
[3,1,7,5,8,6,4,2]=>[4,2,2]
[5,1,7,3,8,6,4,2]=>[4,2,2]
[7,1,5,3,8,6,4,2]=>[4,3,1]
[7,1,5,8,3,6,4,2]=>[4,2,1,1]
[7,8,1,5,3,6,4,2]=>[4,2,1,1]
[7,8,3,5,1,6,4,2]=>[4,2,1,1]
[7,3,5,8,1,6,4,2]=>[4,2,1,1]
[5,3,7,1,8,6,4,2]=>[4,3,1]
[3,5,7,1,8,6,4,2]=>[4,2,1,1]
[1,7,5,3,8,6,4,2]=>[4,3,1]
[5,7,3,1,8,6,4,2]=>[4,3,1]
[5,7,3,8,6,1,4,2]=>[4,2,1,1]
[3,7,5,8,1,6,4,2]=>[4,2,1,1]
[1,7,5,8,3,6,4,2]=>[4,2,1,1]
[1,7,8,5,3,6,4,2]=>[4,2,1,1]
[3,7,8,5,1,6,4,2]=>[4,2,1,1]
[5,7,8,3,6,1,4,2]=>[4,1,1,1,1]
[5,7,8,6,3,1,4,2]=>[4,2,1,1]
[7,5,8,6,1,3,4,2]=>[4,2,1,1]
[5,7,8,1,6,3,4,2]=>[4,1,1,1,1]
[5,7,8,1,3,6,4,2]=>[4,1,1,1,1]
[3,7,8,1,5,6,4,2]=>[4,1,1,1,1]
[1,7,8,3,5,6,4,2]=>[4,1,1,1,1]
[1,7,3,8,5,6,4,2]=>[4,2,1,1]
[3,7,1,8,5,6,4,2]=>[4,2,1,1]
[5,7,1,8,3,6,4,2]=>[4,2,1,1]
[5,7,1,8,6,3,4,2]=>[4,2,1,1]
[7,5,1,8,6,3,4,2]=>[4,3,1]
[7,5,8,1,6,3,4,2]=>[4,2,1,1]
[7,8,5,1,6,3,4,2]=>[4,2,1,1]
[7,8,5,1,3,6,4,2]=>[4,2,1,1]
[7,5,8,1,3,6,4,2]=>[4,2,1,1]
[7,5,1,8,3,6,4,2]=>[4,3,1]
[7,5,1,3,8,6,4,2]=>[4,3,1]
[5,7,1,3,8,6,4,2]=>[4,2,1,1]
[3,7,1,5,8,6,4,2]=>[4,2,1,1]
[1,7,3,5,8,6,4,2]=>[4,2,1,1]
[1,5,3,7,8,6,4,2]=>[4,2,1,1]
[3,5,1,7,8,6,4,2]=>[4,2,1,1]
[5,3,1,7,8,6,4,2]=>[4,3,1]
[7,3,1,5,8,6,4,2]=>[4,3,1]
[7,3,1,8,5,6,4,2]=>[4,3,1]
[7,3,8,1,5,6,4,2]=>[4,2,1,1]
[7,8,3,1,5,6,4,2]=>[4,2,1,1]
[7,8,1,3,5,6,4,2]=>[4,1,1,1,1]
[7,1,8,3,5,6,4,2]=>[4,2,1,1]
[7,1,3,8,5,6,4,2]=>[4,2,1,1]
[7,1,3,5,8,6,4,2]=>[4,2,1,1]
[3,1,5,7,8,6,4,2]=>[4,2,1,1]
[5,7,3,4,6,8,1,2]=>[3,1,1,1,1,1]
[5,7,3,4,8,6,1,2]=>[3,2,1,1,1]
[5,7,3,4,8,1,6,2]=>[3,2,1,1,1]
[5,7,3,4,1,8,6,2]=>[3,3,1,1]
[5,7,3,4,1,6,8,2]=>[3,2,1,1,1]
[5,7,3,4,6,1,2,8]=>[3,1,1,1,1,1]
[7,3,5,6,1,2,8,4]=>[3,2,1,1,1]
[5,7,3,1,4,6,2,8]=>[3,2,1,1,1]
[5,7,3,1,4,6,8,2]=>[3,2,1,1,1]
[5,7,3,1,4,8,6,2]=>[3,3,1,1]
[5,7,3,1,4,8,2,6]=>[3,2,1,1,1]
[5,3,7,4,1,2,8,6]=>[3,2,2,1]
[5,3,7,4,1,2,6,8]=>[3,2,1,1,1]
[5,3,7,1,4,2,6,8]=>[3,2,1,1,1]
[5,3,7,1,4,2,8,6]=>[3,2,2,1]
[3,7,5,1,2,8,6,4]=>[3,3,1,1]
[7,8,3,5,1,2,6,4]=>[3,2,1,1,1]
[7,3,8,5,1,2,6,4]=>[3,2,2,1]
[7,3,5,8,1,2,6,4]=>[3,2,1,1,1]
[3,7,5,1,2,6,4,8]=>[3,2,1,1,1]
[3,7,5,1,2,6,8,4]=>[3,2,1,1,1]
[6,1,4,3,5,2,8,7]=>[4,2,1,1]
[2,5,7,3,8,4,1,6]=>[3,2,1,1,1]
[5,4,7,8,6,1,3,2]=>[4,2,1,1]
[7,5,6,2,8,3,1,4]=>[4,2,1,1]
[4,7,2,5,8,3,1,6]=>[4,1,1,1,1]
[6,2,4,5,1,3,8,7]=>[3,2,1,1,1]
[5,1,4,6,3,2,8,7]=>[4,2,1,1]
[3,5,6,2,4,1,8,7]=>[3,2,1,1,1]
[3,8,6,7,5,4,1,2]=>[5,1,1,1]
[6,2,7,8,3,4,1,5]=>[3,2,1,1,1]
[2,5,3,4,8,1,7,6]=>[3,2,1,1,1]
[8,7,1,2,5,3,4,6]=>[4,1,1,1,1]
[5,1,8,2,3,4,7,6]=>[3,2,1,1,1]
[5,4,7,6,2,8,1,3]=>[4,2,1,1]
[3,7,8,1,5,4,6,2]=>[4,1,1,1,1]
[7,1,3,4,6,8,5,2]=>[4,1,1,1,1]
[8,3,6,5,7,1,4,2]=>[5,1,1,1]
[5,8,7,1,4,6,2,3]=>[4,1,1,1,1]
[4,7,6,1,8,3,5,2]=>[4,2,1,1]
[4,7,2,6,3,8,5,1]=>[4,2,1,1]
[2,1,8,4,6,7,3,5]=>[3,2,1,1,1]
[4,7,8,6,3,1,2,5]=>[4,1,1,1,1]
[3,8,1,5,6,7,2,4]=>[3,1,1,1,1,1]
[6,7,2,4,8,5,3,1]=>[4,2,1,1]
[2,8,3,6,7,5,1,4]=>[4,1,1,1,1]
[8,2,1,7,6,3,5,4]=>[5,2,1]
[3,2,4,5,8,1,7,6]=>[3,2,1,1,1]
[7,4,6,3,2,1,8,5]=>[5,2,1]
[4,7,3,2,1,8,6,5]=>[4,3,1]
[6,4,7,5,2,3,8,1]=>[4,2,1,1]
[6,4,8,1,7,3,2,5]=>[4,2,1,1]
[4,8,7,2,3,1,5,6]=>[4,1,1,1,1]
[4,2,3,1,8,7,5,6]=>[3,3,1,1]
[7,6,8,1,3,5,2,4]=>[4,1,1,1,1]
[6,7,5,2,3,1,8,4]=>[4,2,1,1]
[4,7,2,6,5,1,8,3]=>[4,2,1,1]
[6,4,2,1,8,5,7,3]=>[4,3,1]
[7,2,1,5,6,8,4,3]=>[4,2,1,1]
[8,7,2,6,4,1,5,3]=>[5,2,1]
[6,7,8,2,5,3,1,4]=>[4,1,1,1,1]
[2,1,7,3,6,8,5,4]=>[4,2,1,1]
[2,1,5,7,8,4,6,3]=>[3,2,1,1,1]
[2,5,7,8,3,6,1,4]=>[3,1,1,1,1,1]
[6,4,1,5,7,2,8,3]=>[3,2,2,1]
[7,4,8,1,2,5,6,3]=>[3,2,1,1,1]
[4,2,7,8,6,3,5,1]=>[4,2,1,1]
[6,1,7,4,3,2,8,5]=>[4,2,2]
[6,8,3,4,2,1,7,5]=>[4,2,1,1]
[4,2,6,1,5,7,8,3]=>[3,2,1,1,1]
[2,4,6,7,3,5,8,1]=>[3,1,1,1,1,1]
[6,5,8,3,7,4,1,2]=>[4,2,1,1]
[7,1,4,8,3,5,6,2]=>[4,1,1,1,1]
[6,8,7,5,3,4,1,2]=>[5,1,1,1]
[4,8,6,3,1,5,7,2]=>[4,2,1,1]
[3,4,8,2,5,7,6,1]=>[4,1,1,1,1]
[3,5,7,2,8,6,1,4]=>[3,2,1,1,1]
[2,5,7,4,8,6,1,3]=>[3,2,1,1,1]
[2,6,3,7,5,1,8,4]=>[3,2,2,1]
[2,6,4,8,7,5,1,3]=>[4,2,1,1]
[6,3,7,2,8,5,1,4]=>[4,2,1,1]
[3,6,2,5,8,7,1,4]=>[3,2,1,1,1]
[5,2,8,4,7,6,1,3]=>[4,2,1,1]
[7,2,4,8,6,5,1,3]=>[4,2,1,1]
[6,2,4,8,7,5,1,3]=>[4,2,1,1]
[2,4,5,8,7,6,1,3]=>[4,1,1,1,1]
[4,2,7,3,8,1,6,5]=>[3,2,2,1]
[6,1,3,8,7,2,5,4]=>[4,2,1,1]
[3,1,5,6,2,8,7,4]=>[3,2,2,1]
[4,1,5,2,8,7,6,3]=>[4,2,2]
[7,1,4,2,8,6,5,3]=>[4,3,1]
[4,1,5,3,2,8,7,6]=>[3,3,2]
[7,2,3,5,1,8,6,4]=>[3,3,1,1]
[3,4,5,1,8,7,6,2]=>[4,2,1,1]
[1,4,5,2,8,7,6,3]=>[4,2,1,1]
[1,6,4,2,8,7,5,3]=>[4,3,1]
[5,6,3,1,8,7,4,2]=>[4,3,1]
[7,4,2,5,1,8,6,3]=>[4,3,1]
[5,3,6,2,8,1,7,4]=>[4,2,1,1]
[4,6,2,7,5,1,8,3]=>[3,2,2,1]
[1,5,3,6,2,8,7,4]=>[3,3,1,1]
[1,5,8,3,2,7,6,4]=>[4,2,1,1]
[4,5,8,2,1,7,6,3]=>[4,2,1,1]
[3,6,2,5,1,4,8,7]=>[3,2,1,1,1]
[2,4,8,7,1,3,6,5]=>[4,1,1,1,1]
[1,3,8,2,4,7,6,5]=>[4,1,1,1,1]
[7,5,1,2,8,6,4,3]=>[4,3,1]
[1,5,2,3,8,7,6,4]=>[4,2,1,1]
[4,5,1,2,8,7,6,3]=>[4,2,1,1]
[6,4,1,2,8,7,5,3]=>[4,3,1]
[5,3,1,7,2,8,6,4]=>[3,3,2]
[5,2,8,1,3,7,6,4]=>[4,2,1,1]
[4,7,5,6,8,3,1,2]=>[4,1,1,1,1]
[8,6,4,7,5,3,1,2]=>[5,2,1]
[7,5,2,6,4,1,3,8]=>[4,2,1,1]
[1,6,3,7,5,8,4,2]=>[4,2,1,1]
[1,3,7,4,5,8,6,2]=>[3,2,1,1,1]
[7,2,6,3,4,1,5,8]=>[4,1,1,1,1]
[8,3,7,4,6,5,1,2]=>[5,1,1,1]
[6,8,4,7,5,3,1,2]=>[5,1,1,1]
[4,8,7,5,6,3,1,2]=>[5,1,1,1]
[3,8,7,6,4,5,1,2]=>[5,1,1,1]
[1,6,5,2,8,3,7,4]=>[3,3,1,1]
[8,6,5,2,1,4,3,7]=>[5,2,1]
[2,7,6,3,1,4,5,8]=>[4,1,1,1,1]
[6,8,5,3,2,1,4,7]=>[5,1,1,1]
[2,7,6,4,5,1,3,8]=>[4,1,1,1,1]
[5,7,2,6,4,1,3,8]=>[4,1,1,1,1]
[6,1,3,7,5,8,4,2]=>[4,2,1,1]
[4,1,7,3,6,8,5,2]=>[4,2,1,1]
[8,1,6,4,3,7,5,2]=>[5,2,1]
[2,1,7,4,8,6,3,5]=>[3,2,2,1]
[1,8,6,3,7,5,4,2]=>[5,2,1]
[1,8,2,7,3,6,5,4]=>[5,1,1,1]
[2,1,3,8,4,7,5,6]=>[3,2,1,1,1]
[8,1,2,7,4,3,6,5]=>[4,2,1,1]
[5,3,1,6,8,4,7,2]=>[3,3,1,1]
[6,2,8,7,1,4,3,5]=>[4,2,1,1]
[8,7,2,1,5,4,3,6]=>[5,2,1]
[8,2,3,1,4,6,5,7]=>[3,2,1,1,1]
[2,4,8,3,1,5,6,7]=>[3,1,1,1,1,1]
[3,4,2,7,1,5,6,8]=>[3,1,1,1,1,1]
[4,7,3,8,2,1,5,6]=>[4,1,1,1,1]
[5,2,7,3,1,4,6,8]=>[3,2,1,1,1]
[8,3,7,2,1,5,4,6]=>[4,2,1,1]
[1,3,7,2,8,4,6,5]=>[3,2,1,1,1]
[1,4,2,5,8,6,7,3]=>[3,2,1,1,1]
[6,5,3,8,2,1,4,7]=>[5,1,1,1]
[2,6,4,5,7,1,3,8]=>[3,1,1,1,1,1]
[5,4,6,2,7,1,3,8]=>[4,1,1,1,1]
[7,6,3,1,8,4,5,2]=>[4,3,1]
[7,6,2,1,8,5,3,4]=>[4,3,1]
[1,7,5,8,6,4,3,2]=>[5,2,1]
[6,5,1,2,8,3,7,4]=>[3,3,1,1]
[8,6,1,4,3,7,5,2]=>[5,2,1]
[6,8,4,1,3,7,5,2]=>[4,2,1,1]
[6,5,7,1,3,8,4,2]=>[4,2,1,1]
[5,8,3,1,7,4,6,2]=>[4,2,1,1]
[8,3,1,7,5,4,6,2]=>[5,2,1]
[1,3,8,7,4,6,5,2]=>[5,1,1,1]
[1,2,8,7,6,3,5,4]=>[5,1,1,1]
[8,2,1,7,6,4,3,5]=>[5,2,1]
[2,3,1,8,7,4,5,6]=>[3,2,1,1,1]
[2,4,1,8,5,7,3,6]=>[3,2,1,1,1]
[5,8,2,1,7,6,3,4]=>[4,2,1,1]
[6,2,7,1,8,5,3,4]=>[3,3,1,1]
[8,7,1,6,5,4,3,2]=>[7,1]
[7,1,8,3,6,5,4,2]=>[5,2,1]
[4,1,8,7,5,6,3,2]=>[5,2,1]
[3,5,8,7,2,6,4,1]=>[5,1,1,1]
[5,8,2,7,1,6,4,3]=>[5,1,1,1]
[2,1,6,4,5,8,3,7]=>[3,2,1,1,1]
[8,6,3,7,5,2,1,4]=>[5,2,1]
[4,6,3,8,5,2,1,7]=>[4,2,1,1]
[4,6,3,7,5,2,8,1]=>[4,2,1,1]
[3,5,7,8,2,6,1,4]=>[3,1,1,1,1,1]
[7,2,3,4,6,8,5,1]=>[4,1,1,1,1]
[4,2,3,6,1,5,8,7]=>[3,2,1,1,1]
[4,8,3,7,5,1,6,2]=>[4,2,1,1]
[5,2,3,4,8,7,1,6]=>[3,2,1,1,1]
[5,2,3,4,6,8,1,7]=>[3,1,1,1,1,1]
[4,2,8,5,7,6,1,3]=>[4,2,1,1]
[3,7,6,4,5,1,8,2]=>[4,2,1,1]
[3,8,6,4,5,1,2,7]=>[4,1,1,1,1]
[4,8,3,7,5,2,1,6]=>[5,1,1,1]
[8,7,3,6,5,1,2,4]=>[5,1,1,1]
[4,2,7,5,8,6,3,1]=>[4,2,2]
[5,8,1,7,3,6,4,2]=>[5,1,1,1]
[5,2,7,8,4,6,3,1]=>[4,2,1,1]
[5,2,8,3,7,6,1,4]=>[4,2,1,1]
[8,2,7,3,1,6,4,5]=>[4,2,1,1]
[6,2,3,4,8,5,1,7]=>[3,2,1,1,1]
[6,2,3,4,1,8,5,7]=>[3,2,1,1,1]
[7,2,3,4,1,8,6,5]=>[3,3,1,1]
[7,2,3,4,1,5,8,6]=>[3,2,1,1,1]
[1,2,3,4,8,7,5,6]=>[3,1,1,1,1,1]
[1,2,8,5,3,4,6,7]=>[3,1,1,1,1,1]
[1,8,4,2,3,5,6,7]=>[3,1,1,1,1,1]
[8,6,7,4,1,5,3,2]=>[5,2,1]
[4,8,6,7,5,1,3,2]=>[5,1,1,1]
[7,1,8,4,6,5,2,3]=>[4,2,1,1]
[8,7,1,5,4,6,2,3]=>[5,1,1,1]
[8,5,7,1,4,6,3,2]=>[5,1,1,1]
[6,4,8,5,1,7,3,2]=>[4,2,2]
[8,7,5,1,4,6,2,3]=>[5,1,1,1]
[8,7,2,5,1,4,6,3]=>[5,1,1,1]
[1,6,4,8,5,2,7,3]=>[3,2,2,1]
[8,7,1,4,2,5,6,3]=>[4,2,1,1]
[3,8,7,1,2,5,6,4]=>[4,1,1,1,1]
[2,3,8,5,7,1,6,4]=>[4,1,1,1,1]
[3,5,8,7,1,6,2,4]=>[4,1,1,1,1]
[2,3,8,6,7,5,1,4]=>[4,1,1,1,1]
[4,1,8,6,2,7,5,3]=>[4,2,2]
[5,7,1,8,2,6,3,4]=>[3,2,1,1,1]
[2,8,7,1,5,6,3,4]=>[4,1,1,1,1]
[1,3,8,5,7,2,6,4]=>[4,1,1,1,1]
[1,8,3,7,2,5,6,4]=>[4,1,1,1,1]
[2,8,7,1,3,5,6,4]=>[4,1,1,1,1]
[7,1,8,2,3,5,6,4]=>[3,2,1,1,1]
[8,6,3,7,4,1,5,2]=>[4,2,2]
[4,2,8,6,7,5,1,3]=>[4,2,1,1]
[8,4,2,7,5,6,1,3]=>[4,2,1,1]
[4,8,3,6,1,7,5,2]=>[4,2,1,1]
[8,3,4,7,5,1,6,2]=>[4,2,1,1]
[8,3,7,4,5,1,6,2]=>[4,2,1,1]
[8,7,4,2,5,6,1,3]=>[5,1,1,1]
[8,7,5,1,6,2,3,4]=>[4,2,1,1]
[8,7,2,4,1,5,6,3]=>[4,2,1,1]
[4,8,6,1,7,2,5,3]=>[4,2,1,1]
[4,7,1,8,2,6,5,3]=>[4,2,1,1]
[4,2,8,6,7,1,5,3]=>[4,2,1,1]
[8,7,4,1,2,5,6,3]=>[4,2,1,1]
[8,2,7,1,6,3,4,5]=>[4,1,1,1,1]
[8,2,7,1,3,6,4,5]=>[4,1,1,1,1]
[2,8,3,6,7,1,5,4]=>[4,1,1,1,1]
[8,7,2,1,3,5,6,4]=>[4,2,1,1]
[1,8,7,2,3,6,4,5]=>[4,1,1,1,1]
[1,8,7,2,6,3,4,5]=>[4,1,1,1,1]
[8,2,7,3,6,1,4,5]=>[4,1,1,1,1]
[1,8,7,3,6,2,4,5]=>[4,1,1,1,1]
[1,8,2,7,6,3,4,5]=>[4,1,1,1,1]
[8,2,7,4,1,5,6,3]=>[4,2,1,1]
[8,2,1,7,5,6,3,4]=>[4,2,1,1]
[8,7,3,1,5,6,2,4]=>[4,2,1,1]
[2,8,7,3,5,6,1,4]=>[4,1,1,1,1]
[8,3,1,6,7,5,2,4]=>[4,2,1,1]
[8,5,2,1,6,7,4,3]=>[4,3,1]
[1,5,2,8,6,7,4,3]=>[4,2,1,1]
[1,2,8,6,7,5,3,4]=>[4,1,1,1,1]
[1,8,3,6,7,5,2,4]=>[4,1,1,1,1]
[8,2,3,6,7,5,1,4]=>[4,1,1,1,1]
[8,3,7,2,5,6,1,4]=>[4,1,1,1,1]
[8,1,3,7,5,6,2,4]=>[4,1,1,1,1]
[8,4,1,2,7,5,6,3]=>[4,2,1,1]
[8,1,4,2,6,7,5,3]=>[4,2,1,1]
[1,2,8,6,7,3,5,4]=>[4,1,1,1,1]
[8,1,2,7,3,6,4,5]=>[4,1,1,1,1]
[8,1,7,3,6,2,4,5]=>[4,1,1,1,1]
[8,1,7,2,6,3,4,5]=>[4,1,1,1,1]
[8,1,7,2,3,6,4,5]=>[4,1,1,1,1]
[8,1,3,7,2,5,6,4]=>[4,1,1,1,1]
[1,8,3,6,7,2,5,4]=>[4,1,1,1,1]
[1,7,8,2,3,6,5,4]=>[4,1,1,1,1]
[8,3,7,1,2,5,6,4]=>[4,1,1,1,1]
[8,7,1,2,3,6,4,5]=>[4,1,1,1,1]
[2,8,5,7,4,6,3,1]=>[5,1,1,1]
[3,1,8,5,7,4,2,6]=>[4,2,1,1]
[8,3,5,7,4,2,6,1]=>[5,1,1,1]
[8,3,6,2,4,5,7,1]=>[4,1,1,1,1]
[2,8,6,4,3,5,7,1]=>[5,1,1,1]
[2,6,8,3,5,4,7,1]=>[4,1,1,1,1]
[2,7,5,8,4,6,3,1]=>[5,1,1,1]
[8,4,2,7,6,1,3,5]=>[4,2,1,1]
[4,8,1,7,6,3,2,5]=>[5,1,1,1]
[4,1,7,6,2,3,5,8]=>[3,2,1,1,1]
[3,7,1,8,6,2,5,4]=>[4,2,1,1]
[3,1,7,6,4,5,2,8]=>[4,2,1,1]
[3,1,7,5,8,4,2,6]=>[4,2,1,1]
[3,1,6,8,7,5,2,4]=>[4,2,1,1]
[6,3,8,7,5,2,4,1]=>[5,2,1]
[7,3,5,8,4,2,6,1]=>[5,1,1,1]
[7,3,6,4,2,8,5,1]=>[5,2,1]
[7,8,3,6,2,5,4,1]=>[5,1,1,1]
[7,4,8,2,1,6,3,5]=>[4,2,1,1]
[8,7,4,6,3,2,5,1]=>[6,1,1]
[7,8,5,2,1,4,3,6]=>[4,2,1,1]
[7,5,2,3,1,4,8,6]=>[4,2,1,1]
[7,4,6,2,3,8,1,5]=>[4,1,1,1,1]
[6,4,2,5,8,3,7,1]=>[4,2,1,1]
[4,6,5,8,1,3,2,7]=>[4,1,1,1,1]
[4,7,1,5,3,8,2,6]=>[4,1,1,1,1]
[4,7,8,1,3,6,2,5]=>[3,1,1,1,1,1]
[5,7,1,3,4,6,2,8]=>[3,1,1,1,1,1]
[5,7,1,4,2,3,6,8]=>[3,1,1,1,1,1]
[5,8,1,3,2,4,6,7]=>[3,1,1,1,1,1]
[4,8,6,1,3,2,7,5]=>[4,2,1,1]
[8,4,6,2,1,3,7,5]=>[4,2,1,1]
[5,4,8,7,2,3,6,1]=>[4,2,1,1]
[5,4,8,7,3,1,2,6]=>[4,2,1,1]
[6,8,3,7,2,5,4,1]=>[5,1,1,1]
[5,4,6,8,2,3,7,1]=>[4,1,1,1,1]
[5,7,4,2,8,3,6,1]=>[4,2,1,1]
[6,4,7,2,1,8,3,5]=>[4,2,1,1]
[6,5,3,4,1,2,8,7]=>[4,2,1,1]
[6,8,5,4,1,3,2,7]=>[5,1,1,1]
[6,4,3,7,1,5,2,8]=>[4,2,1,1]
[7,4,2,5,6,1,3,8]=>[4,1,1,1,1]
[6,4,2,8,1,5,7,3]=>[4,2,1,1]
[6,3,7,8,2,5,1,4]=>[4,1,1,1,1]
[7,3,5,6,4,2,1,8]=>[5,1,1,1]
[7,4,3,1,5,6,2,8]=>[4,2,1,1]
[5,3,8,2,6,7,4,1]=>[4,2,1,1]
[6,4,8,2,1,5,7,3]=>[4,2,1,1]
[4,7,8,5,6,3,2,1]=>[5,1,1,1]
[5,3,7,6,8,2,4,1]=>[4,2,1,1]
[4,8,6,7,5,3,2,1]=>[6,1,1]
[6,3,8,7,2,4,1,5]=>[4,2,1,1]
[5,3,8,7,2,6,4,1]=>[5,2,1]
[5,3,7,8,6,2,4,1]=>[4,2,1,1]
[6,5,2,4,3,7,8,1]=>[5,1,1,1]
[5,4,6,2,8,7,1,3]=>[4,2,1,1]
[5,7,4,3,6,8,1,2]=>[4,1,1,1,1]
[5,7,3,8,6,2,4,1]=>[4,2,1,1]
[5,4,6,8,2,7,1,3]=>[4,1,1,1,1]
[5,7,8,2,6,4,1,3]=>[4,1,1,1,1]
[3,6,8,5,7,1,4,2]=>[4,1,1,1,1]
[1,7,4,8,6,2,3,5]=>[3,2,1,1,1]
[3,6,2,5,7,8,1,4]=>[3,1,1,1,1,1]
[5,2,7,4,6,8,1,3]=>[3,2,1,1,1]
[5,3,6,7,1,8,4,2]=>[3,3,1,1]
[4,2,5,6,7,1,8,3]=>[3,2,1,1,1]
[8,1,3,6,7,2,4,5]=>[3,1,1,1,1,1]
[8,1,4,2,5,6,3,7]=>[3,2,1,1,1]
[8,1,4,2,7,5,3,6]=>[4,2,1,1]
[6,1,3,8,2,7,4,5]=>[3,2,1,1,1]
[7,3,4,1,5,8,6,2]=>[3,3,1,1]
[1,7,5,2,8,6,3,4]=>[3,3,1,1]
[3,7,4,1,8,5,6,2]=>[3,3,1,1]
[5,6,3,1,7,8,4,2]=>[3,3,1,1]
[1,5,8,4,2,6,3,7]=>[3,2,1,1,1]
[3,5,7,4,1,6,8,2]=>[3,2,1,1,1]
[3,5,7,1,2,6,4,8]=>[3,1,1,1,1,1]
[4,5,1,8,2,3,7,6]=>[3,2,1,1,1]
[4,7,1,8,2,6,3,5]=>[3,2,1,1,1]
[7,5,1,2,3,8,6,4]=>[3,3,1,1]
[7,8,4,5,1,3,2,6]=>[4,1,1,1,1]
[6,7,1,3,2,5,4,8]=>[3,2,1,1,1]
[6,7,1,4,3,5,2,8]=>[4,1,1,1,1]
[7,8,2,3,1,5,4,6]=>[3,2,1,1,1]
[7,8,2,4,3,5,1,6]=>[4,1,1,1,1]
[7,8,2,4,1,5,3,6]=>[3,2,1,1,1]
[1,4,2,6,5,7,3,8]=>[3,2,1,1,1]
[5,6,1,4,2,7,3,8]=>[3,2,1,1,1]
[6,7,2,4,1,5,3,8]=>[3,2,1,1,1]
[6,7,2,4,3,5,1,8]=>[4,1,1,1,1]
[6,7,2,3,1,5,4,8]=>[3,2,1,1,1]
[6,7,3,5,4,8,1,2]=>[4,1,1,1,1]
[2,4,1,6,5,7,3,8]=>[3,2,1,1,1]
[1,5,2,6,4,7,3,8]=>[3,2,1,1,1]
[2,5,1,6,4,7,3,8]=>[3,2,1,1,1]
[3,6,5,7,4,8,1,2]=>[4,1,1,1,1]
[5,6,2,4,3,7,1,8]=>[4,1,1,1,1]
[4,5,2,6,1,7,3,8]=>[3,2,1,1,1]
[4,5,1,6,3,7,2,8]=>[3,2,1,1,1]
[4,5,3,6,1,7,2,8]=>[3,2,1,1,1]
[5,6,3,4,1,7,2,8]=>[3,2,1,1,1]
[5,6,1,4,3,7,2,8]=>[4,1,1,1,1]
[5,6,1,3,2,7,4,8]=>[3,2,1,1,1]
[5,6,4,7,1,3,2,8]=>[4,1,1,1,1]
[6,7,4,5,1,3,2,8]=>[4,1,1,1,1]
[6,7,5,8,1,3,2,4]=>[4,1,1,1,1]
[4,5,1,3,2,7,6,8]=>[3,2,1,1,1]
[4,6,5,7,1,3,2,8]=>[4,1,1,1,1]
[4,6,1,3,2,7,5,8]=>[3,2,1,1,1]
[1,4,3,6,2,7,5,8]=>[3,2,1,1,1]
[3,4,1,6,5,7,2,8]=>[3,2,1,1,1]
[4,5,2,3,1,7,6,8]=>[3,2,1,1,1]
[4,5,3,7,6,8,1,2]=>[3,2,1,1,1]
[4,6,5,7,3,8,1,2]=>[4,1,1,1,1]
[4,6,5,7,2,3,1,8]=>[4,1,1,1,1]
[3,5,4,6,1,7,2,8]=>[3,2,1,1,1]
[3,5,1,6,4,7,2,8]=>[3,2,1,1,1]
[1,5,3,6,4,7,2,8]=>[3,2,1,1,1]
[1,5,3,6,2,7,4,8]=>[3,2,1,1,1]
[3,5,2,6,1,7,4,8]=>[3,2,1,1,1]
[3,5,2,6,4,7,1,8]=>[3,2,1,1,1]
[3,4,2,6,1,7,5,8]=>[3,2,1,1,1]
[4,6,2,3,1,7,5,8]=>[3,2,1,1,1]
[2,4,3,6,1,7,5,8]=>[3,2,1,1,1]
[2,5,3,6,4,7,1,8]=>[3,2,1,1,1]
[2,5,3,6,1,7,4,8]=>[3,2,1,1,1]
[4,6,2,7,3,5,8,1]=>[3,2,1,1,1]
[3,6,2,7,5,4,8,1]=>[4,2,1,1]
[4,6,1,7,3,8,2,5]=>[3,2,1,1,1]
[2,4,7,1,3,8,6,5]=>[3,2,1,1,1]
[5,2,6,7,4,3,8,1]=>[4,2,1,1]
[3,5,2,7,6,4,8,1]=>[4,2,1,1]
[1,5,7,4,3,8,2,6]=>[4,1,1,1,1]
[2,5,7,3,1,8,6,4]=>[3,3,1,1]
[1,5,7,2,8,3,6,4]=>[3,2,1,1,1]
[2,5,7,3,1,8,4,6]=>[3,2,1,1,1]
[1,5,7,3,4,8,2,6]=>[3,1,1,1,1,1]
[5,2,6,7,1,8,4,3]=>[3,3,1,1]
[1,3,7,2,8,5,6,4]=>[3,2,1,1,1]
[2,3,1,5,8,4,7,6]=>[3,2,1,1,1]
[2,1,5,6,8,4,3,7]=>[3,2,1,1,1]
[2,3,1,5,8,6,4,7]=>[3,2,1,1,1]
[2,4,7,3,1,8,5,6]=>[3,2,1,1,1]
[1,3,7,2,8,5,4,6]=>[3,2,1,1,1]
[2,3,1,6,8,5,4,7]=>[3,2,1,1,1]
[4,6,2,7,1,8,3,5]=>[3,2,1,1,1]
[1,5,4,3,6,8,2,7]=>[4,1,1,1,1]
[1,6,4,5,7,8,3,2]=>[4,1,1,1,1]
[2,5,1,7,8,6,3,4]=>[3,2,1,1,1]
[1,3,6,2,8,7,4,5]=>[3,2,1,1,1]
[2,1,5,6,8,4,7,3]=>[3,2,1,1,1]
[2,4,1,7,8,5,6,3]=>[3,2,1,1,1]
[1,3,6,2,8,4,7,5]=>[3,2,1,1,1]
[2,1,5,6,8,7,3,4]=>[3,2,1,1,1]
[3,6,5,2,7,8,4,1]=>[4,2,1,1]
[6,2,4,7,5,8,3,1]=>[4,2,1,1]
[1,5,7,8,4,2,6,3]=>[3,2,1,1,1]
[3,7,4,1,8,6,2,5]=>[3,3,1,1]
[3,4,6,8,5,7,2,1]=>[4,1,1,1,1]
[4,2,5,7,3,1,8,6]=>[3,2,2,1]
[2,5,6,8,1,7,4,3]=>[4,1,1,1,1]
[4,5,6,1,8,7,3,2]=>[4,2,1,1]
[4,5,6,3,1,8,7,2]=>[3,3,1,1]
[4,3,6,2,1,7,5,8]=>[4,2,1,1]
[4,6,3,2,1,7,5,8]=>[4,2,1,1]
[4,3,5,7,6,1,8,2]=>[3,2,2,1]
[4,3,2,6,1,7,5,8]=>[4,2,1,1]
[5,3,2,1,6,4,7,8]=>[4,2,1,1]
[5,3,1,6,2,7,4,8]=>[3,2,2,1]
[5,1,6,3,2,7,4,8]=>[3,2,2,1]
[4,6,1,7,5,3,2,8]=>[4,2,1,1]
[5,3,6,4,2,1,7,8]=>[4,2,1,1]
[5,3,2,6,4,1,7,8]=>[4,2,1,1]
[5,2,1,6,3,7,4,8]=>[3,2,2,1]
[5,2,6,3,1,7,4,8]=>[3,2,2,1]
[4,2,6,3,1,7,8,5]=>[3,2,2,1]
[3,5,7,2,8,6,4,1]=>[4,2,1,1]
[2,4,7,1,3,6,5,8]=>[3,1,1,1,1,1]
[2,6,1,3,7,5,4,8]=>[3,2,1,1,1]
[5,1,6,2,7,4,3,8]=>[3,2,2,1]
[5,2,1,6,4,3,7,8]=>[3,3,1,1]
[5,4,2,1,6,3,7,8]=>[4,2,1,1]
[5,4,2,6,3,1,7,8]=>[4,2,1,1]
[5,4,1,6,2,7,3,8]=>[3,2,2,1]
[5,1,6,4,2,7,3,8]=>[3,2,2,1]
[2,6,1,5,4,3,7,8]=>[4,1,1,1,1]
[3,1,6,2,5,4,7,8]=>[3,2,1,1,1]
[5,1,6,4,3,2,7,8]=>[4,2,1,1]
[5,4,1,6,3,2,7,8]=>[4,2,1,1]
[5,4,3,1,6,2,7,8]=>[4,2,1,1]
[7,3,1,6,5,4,8,2]=>[5,2,1]
[7,2,8,1,5,4,3,6]=>[4,2,1,1]
[4,2,7,6,5,8,1,3]=>[4,2,1,1]
[3,8,2,6,5,4,1,7]=>[5,1,1,1]
[7,3,2,1,5,4,6,8]=>[4,2,1,1]
[7,2,8,6,1,4,3,5]=>[4,2,1,1]
[5,2,7,6,8,4,1,3]=>[4,2,1,1]
[3,8,7,2,5,4,1,6]=>[5,1,1,1]
[7,5,1,6,8,4,3,2]=>[5,2,1]
[7,4,2,1,5,6,3,8]=>[4,2,1,1]
[7,2,8,6,5,1,3,4]=>[4,2,1,1]
[5,3,2,6,7,4,1,8]=>[4,2,1,1]
[4,3,7,2,5,6,1,8]=>[4,1,1,1,1]
[6,7,1,4,3,2,5,8]=>[4,1,1,1,1]
[3,4,2,6,7,1,5,8]=>[3,1,1,1,1,1]
[3,7,1,6,5,2,4,8]=>[4,1,1,1,1]
[3,5,6,2,4,7,1,8]=>[3,1,1,1,1,1]
[3,5,8,7,2,4,6,1]=>[4,1,1,1,1]
[1,7,8,2,5,4,3,6]=>[4,1,1,1,1]
[8,7,2,5,4,3,6,1]=>[6,1,1]
[2,5,6,4,7,1,3,8]=>[3,1,1,1,1,1]
[4,7,1,6,3,5,2,8]=>[4,1,1,1,1]
[4,5,3,8,7,2,6,1]=>[4,2,1,1]
[1,4,5,3,7,8,2,6]=>[3,1,1,1,1,1]
[1,4,8,2,7,6,3,5]=>[4,1,1,1,1]
[4,7,3,5,1,8,6,2]=>[3,3,1,1]
[8,7,3,6,1,5,4,2]=>[6,1,1]
[2,5,8,7,4,6,1,3]=>[4,1,1,1,1]
[5,4,2,1,7,8,3,6]=>[4,2,1,1]
[4,7,8,3,5,2,1,6]=>[4,1,1,1,1]
[4,7,6,2,1,8,3,5]=>[4,2,1,1]
[1,4,6,7,3,5,8,2]=>[3,1,1,1,1,1]
[8,3,6,2,1,7,5,4]=>[4,3,1]
[8,3,7,6,4,2,1,5]=>[6,1,1]
[2,3,1,8,4,7,6,5]=>[4,2,1,1]
[2,7,4,8,6,5,1,3]=>[4,2,1,1]
[8,6,5,1,4,7,3,2]=>[6,1,1]
[8,5,4,1,7,3,6,2]=>[5,2,1]
[6,3,7,2,8,5,4,1]=>[4,3,1]
[1,6,3,8,2,7,5,4]=>[4,2,1,1]
[1,7,5,3,8,2,6,4]=>[4,2,1,1]
[6,2,7,4,1,8,5,3]=>[3,3,2]
[8,6,3,2,7,5,1,4]=>[5,2,1]
[2,7,5,1,3,8,6,4]=>[3,3,1,1]
[1,7,6,4,3,8,2,5]=>[5,1,1,1]
[3,7,2,4,8,6,5,1]=>[4,2,1,1]
[3,4,2,8,7,6,1,5]=>[4,2,1,1]
[5,1,4,3,2,7,8,6]=>[4,2,1,1]
[3,7,8,5,2,4,1,6]=>[4,1,1,1,1]
[3,7,6,2,4,1,8,5]=>[4,2,1,1]
[1,6,8,2,5,7,4,3]=>[4,1,1,1,1]
[6,7,2,5,8,4,3,1]=>[5,1,1,1]
[5,2,7,8,4,3,1,6]=>[4,2,1,1]
[5,3,1,7,8,4,2,6]=>[3,3,1,1]
[2,7,6,4,1,3,8,5]=>[4,2,1,1]
[4,1,7,6,3,2,8,5]=>[4,2,2]
[8,4,2,7,6,3,1,5]=>[5,2,1]
[6,3,1,7,5,2,8,4]=>[3,3,2]
[6,2,7,5,3,1,8,4]=>[4,2,2]
[1,5,8,2,7,4,6,3]=>[4,1,1,1,1]
[5,7,2,8,4,6,3,1]=>[4,2,1,1]
[5,7,3,1,8,4,6,2]=>[3,3,1,1]
[8,4,7,3,1,6,5,2]=>[5,2,1]
[2,6,8,5,7,4,1,3]=>[4,1,1,1,1]
[6,5,2,1,7,4,8,3]=>[4,3,1]
[5,7,4,6,2,1,8,3]=>[4,2,1,1]
[5,6,4,8,3,7,2,1]=>[5,1,1,1]
[6,7,1,8,3,4,2,5]=>[3,2,1,1,1]
[7,8,3,5,1,4,2,6]=>[4,1,1,1,1]
[5,6,2,7,1,8,3,4]=>[3,2,1,1,1]
[6,7,2,4,3,8,1,5]=>[4,1,1,1,1]
[2,4,3,8,6,7,1,5]=>[3,2,1,1,1]
[1,8,2,7,4,5,3,6]=>[4,1,1,1,1]
[2,5,4,8,3,6,1,7]=>[4,1,1,1,1]
[2,3,1,8,5,6,4,7]=>[3,2,1,1,1]
[3,8,5,6,4,7,1,2]=>[4,1,1,1,1]
[5,7,3,6,4,8,1,2]=>[4,1,1,1,1]
[5,7,2,3,1,6,4,8]=>[3,2,1,1,1]
[5,7,2,4,3,6,1,8]=>[4,1,1,1,1]
[4,6,2,7,1,5,3,8]=>[3,2,1,1,1]
[4,7,1,6,2,5,3,8]=>[4,1,1,1,1]
[4,7,1,5,3,6,2,8]=>[4,1,1,1,1]
[4,6,3,5,1,7,2,8]=>[3,2,1,1,1]
[6,7,3,5,1,4,2,8]=>[4,1,1,1,1]
[5,6,3,7,1,4,2,8]=>[3,2,1,1,1]
[5,7,1,6,3,4,2,8]=>[4,1,1,1,1]
[1,8,5,6,3,4,2,7]=>[4,1,1,1,1]
[1,8,5,6,4,7,2,3]=>[4,1,1,1,1]
[5,7,1,6,4,8,2,3]=>[4,1,1,1,1]
[4,6,5,8,1,7,2,3]=>[3,2,1,1,1]
[3,7,1,4,2,8,5,6]=>[3,2,1,1,1]
[3,5,1,4,2,8,6,7]=>[3,2,1,1,1]
[4,6,5,8,3,7,1,2]=>[4,1,1,1,1]
[4,6,5,8,2,3,1,7]=>[4,1,1,1,1]
[3,4,2,6,5,8,1,7]=>[3,2,1,1,1]
[3,5,4,6,2,8,1,7]=>[4,1,1,1,1]
[1,8,3,5,4,7,2,6]=>[4,1,1,1,1]
[3,4,2,7,1,8,5,6]=>[3,2,1,1,1]
[4,7,2,3,1,8,5,6]=>[3,2,1,1,1]
[2,4,3,8,1,7,5,6]=>[3,2,1,1,1]
[2,5,3,8,4,7,1,6]=>[3,2,1,1,1]
[2,6,3,8,1,7,4,5]=>[3,2,1,1,1]
[2,7,1,8,3,6,4,5]=>[3,2,1,1,1]
[1,2,8,7,4,6,3,5]=>[4,1,1,1,1]
[3,7,4,8,6,1,5,2]=>[4,2,1,1]
[4,5,1,8,7,6,2,3]=>[4,2,1,1]
[1,5,2,8,7,6,3,4]=>[4,2,1,1]
[5,1,2,8,7,6,3,4]=>[4,2,1,1]
[4,1,5,8,7,6,2,3]=>[4,2,1,1]
[2,3,6,8,7,4,5,1]=>[4,1,1,1,1]
[2,3,7,8,6,4,5,1]=>[4,1,1,1,1]
[4,5,7,8,2,6,3,1]=>[4,1,1,1,1]
[4,5,6,8,2,7,3,1]=>[4,1,1,1,1]
[5,2,6,8,3,7,4,1]=>[4,2,1,1]
[3,1,6,8,7,4,5,2]=>[4,2,1,1]
[6,1,4,8,7,2,5,3]=>[4,2,1,1]
[6,1,8,4,7,3,5,2]=>[4,2,1,1]
[5,8,3,4,7,1,6,2]=>[4,1,1,1,1]
[6,8,3,5,7,1,4,2]=>[4,1,1,1,1]
[3,1,7,8,6,4,5,2]=>[4,2,1,1]
[5,2,7,8,3,6,4,1]=>[4,2,1,1]
[4,6,7,8,2,5,3,1]=>[4,1,1,1,1]
[7,4,5,2,8,6,3,1]=>[4,3,1]
[7,5,8,4,2,6,3,1]=>[5,2,1]
[6,8,4,5,2,7,3,1]=>[4,2,1,1]
[6,8,2,5,3,7,4,1]=>[4,2,1,1]
[6,3,8,4,2,7,5,1]=>[4,2,2]
[7,2,5,3,8,6,4,1]=>[4,3,1]
[3,4,7,5,8,6,2,1]=>[4,2,1,1]
[3,6,7,4,8,5,2,1]=>[4,2,1,1]
[6,7,4,2,8,5,3,1]=>[4,3,1]
[4,7,5,2,8,6,3,1]=>[4,3,1]
[2,7,5,3,8,6,4,1]=>[4,3,1]
[5,6,2,8,3,7,4,1]=>[4,2,1,1]
[5,7,8,3,2,6,4,1]=>[4,2,1,1]
[5,6,8,3,2,7,4,1]=>[4,2,1,1]
[3,6,8,4,2,7,5,1]=>[4,2,1,1]
[1,5,8,2,7,3,6,4]=>[4,1,1,1,1]
[5,8,4,7,2,3,6,1]=>[4,1,1,1,1]
[5,6,8,1,3,7,4,2]=>[4,1,1,1,1]
[6,7,4,8,1,5,3,2]=>[4,2,1,1]
[5,7,2,8,3,6,4,1]=>[4,2,1,1]
[1,7,4,8,6,2,5,3]=>[4,2,1,1]
[7,4,2,8,6,1,5,3]=>[4,3,1]
[6,8,5,3,7,2,4,1]=>[5,1,1,1]
[6,8,5,2,3,7,4,1]=>[4,2,1,1]
[7,5,3,8,2,6,4,1]=>[5,2,1]
[7,5,2,3,8,6,4,1]=>[4,3,1]
[3,7,4,5,8,6,2,1]=>[4,2,1,1]
[6,7,3,4,8,5,2,1]=>[4,2,1,1]
[3,6,4,7,8,5,2,1]=>[4,2,1,1]
[6,4,2,7,8,5,3,1]=>[4,3,1]
[7,4,2,5,8,6,3,1]=>[4,3,1]
[6,1,8,3,4,7,5,2]=>[4,2,1,1]
[6,8,4,2,5,7,3,1]=>[4,2,1,1]
[7,5,8,3,4,6,2,1]=>[5,1,1,1]
[7,4,5,8,1,6,3,2]=>[4,2,1,1]
[6,3,4,7,8,5,2,1]=>[4,2,1,1]
[6,1,2,7,4,5,8,3]=>[3,2,1,1,1]
[2,5,8,3,4,1,6,7]=>[3,1,1,1,1,1]
[5,6,2,7,4,3,8,1]=>[4,2,1,1]
[4,6,7,3,2,5,8,1]=>[4,1,1,1,1]
[2,6,7,3,8,5,4,1]=>[4,2,1,1]
[2,6,1,8,4,5,3,7]=>[3,2,1,1,1]
[2,5,7,8,4,3,6,1]=>[4,1,1,1,1]
[3,4,5,7,8,6,1,2]=>[3,1,1,1,1,1]
[3,4,5,7,6,8,1,2]=>[3,1,1,1,1,1]
[3,6,7,4,8,5,1,2]=>[3,2,1,1,1]
[3,4,5,6,8,7,1,2]=>[3,1,1,1,1,1]
[1,2,5,8,3,6,4,7]=>[3,1,1,1,1,1]
[1,2,5,8,3,4,7,6]=>[3,1,1,1,1,1]
[7,8,1,2,3,5,4,6]=>[3,1,1,1,1,1]
[1,2,5,7,3,6,8,4]=>[3,1,1,1,1,1]
[1,6,8,4,5,2,3,7]=>[3,1,1,1,1,1]
[1,6,8,4,5,2,7,3]=>[3,2,1,1,1]
[1,6,8,2,3,7,4,5]=>[3,1,1,1,1,1]
[1,4,5,7,6,2,8,3]=>[3,2,1,1,1]
[7,8,1,2,3,4,6,5]=>[3,1,1,1,1,1]
[7,8,1,2,3,6,4,5]=>[3,1,1,1,1,1]
[4,2,1,6,5,3,8,7]=>[3,3,2]
[8,2,4,3,1,6,5,7]=>[4,2,1,1]
[6,2,4,3,1,8,7,5]=>[4,3,1]
[4,2,6,3,5,1,8,7]=>[3,2,2,1]
[4,6,2,1,5,8,7,3]=>[3,3,1,1]
[4,6,5,2,1,8,7,3]=>[4,3,1]
[2,1,6,4,3,8,7,5]=>[3,3,2]
[4,8,2,1,6,7,3,5]=>[3,2,1,1,1]
[6,8,2,1,4,3,7,5]=>[3,2,2,1]
[8,6,2,4,3,1,5,7]=>[5,1,1,1]
[6,8,2,4,3,1,7,5]=>[4,2,1,1]
[6,8,7,2,4,3,1,5]=>[5,1,1,1]
[2,1,8,4,6,5,3,7]=>[4,2,1,1]
[2,1,6,4,8,5,7,3]=>[3,2,2,1]
[4,6,5,2,8,3,7,1]=>[4,2,1,1]
[2,6,4,5,8,3,7,1]=>[4,1,1,1,1]
[6,4,2,8,3,5,7,1]=>[4,2,1,1]
[8,4,2,6,3,5,1,7]=>[4,2,1,1]
[6,2,4,8,5,3,7,1]=>[4,2,1,1]
[4,2,6,3,5,8,7,1]=>[3,2,2,1]
[4,2,6,3,8,7,5,1]=>[4,2,2]
[6,2,4,3,8,5,7,1]=>[4,2,1,1]
[8,2,4,3,6,5,1,7]=>[4,2,1,1]
[8,2,1,4,6,5,3,7]=>[4,2,1,1]
[6,2,1,4,8,5,7,3]=>[3,3,1,1]
[6,2,1,8,7,4,3,5]=>[4,3,1]
[6,2,1,8,4,3,7,5]=>[3,3,2]
[8,4,6,5,2,1,3,7]=>[5,1,1,1]
[6,4,8,5,2,1,7,3]=>[4,2,2]
[6,4,8,5,7,2,1,3]=>[4,2,1,1]
[4,6,8,7,5,2,1,3]=>[5,1,1,1]
[2,1,4,8,6,7,3,5]=>[3,2,1,1,1]
[2,6,8,7,4,5,1,3]=>[4,1,1,1,1]
[2,4,8,6,7,5,1,3]=>[4,1,1,1,1]
[4,2,8,6,5,7,1,3]=>[4,2,1,1]
[8,2,6,4,5,1,3,7]=>[4,1,1,1,1]
[8,4,6,2,1,5,3,7]=>[4,2,1,1]
[4,6,8,7,2,1,5,3]=>[4,2,1,1]
[4,6,5,8,2,1,7,3]=>[4,2,1,1]
[2,1,6,8,4,3,7,5]=>[3,2,2,1]
[6,8,7,4,2,1,3,5]=>[5,1,1,1]
[2,8,6,4,7,1,3,5]=>[4,1,1,1,1]
[4,8,6,2,1,7,3,5]=>[4,2,1,1]
[2,8,5,3,1,4,6,7]=>[4,1,1,1,1]
[2,7,4,8,3,5,1,6]=>[4,1,1,1,1]
[2,7,4,8,3,5,6,1]=>[4,1,1,1,1]
[7,2,8,4,3,5,1,6]=>[4,2,1,1]
[8,4,2,1,5,3,6,7]=>[4,2,1,1]
[8,5,1,4,2,3,6,7]=>[4,1,1,1,1]
[8,4,1,5,3,2,6,7]=>[4,2,1,1]
[6,7,3,8,4,2,5,1]=>[4,2,1,1]
[6,7,3,8,4,2,1,5]=>[4,2,1,1]
[7,1,8,4,3,5,2,6]=>[4,2,1,1]
[1,7,8,4,3,5,2,6]=>[4,1,1,1,1]
[7,1,4,8,3,5,2,6]=>[4,1,1,1,1]
[7,4,8,1,5,6,2,3]=>[3,2,1,1,1]
[7,1,8,4,3,5,6,2]=>[4,2,1,1]
[6,7,3,1,8,4,5,2]=>[3,3,1,1]
[6,7,3,8,4,5,2,1]=>[4,2,1,1]
[6,7,1,4,8,3,5,2]=>[4,1,1,1,1]
[6,7,4,1,3,8,2,5]=>[4,1,1,1,1]
[1,6,7,8,4,3,2,5]=>[4,1,1,1,1]
[7,2,1,8,4,5,3,6]=>[3,3,1,1]
[6,2,7,1,8,4,3,5]=>[3,3,1,1]
[6,2,7,8,4,3,1,5]=>[4,2,1,1]
[6,2,7,8,4,3,5,1]=>[4,2,1,1]
[2,6,7,4,8,3,5,1]=>[4,1,1,1,1]
[2,6,7,4,8,3,1,5]=>[4,1,1,1,1]
[7,8,1,3,6,2,4,5]=>[3,1,1,1,1,1]
[1,2,7,8,6,3,4,5]=>[3,1,1,1,1,1]
[2,6,7,1,8,5,3,4]=>[3,2,1,1,1]
[2,6,7,8,5,3,1,4]=>[4,1,1,1,1]
[2,6,7,8,5,3,4,1]=>[4,1,1,1,1]
[6,2,7,8,4,5,3,1]=>[4,2,1,1]
[7,2,1,8,4,5,6,3]=>[3,3,1,1]
[1,7,2,8,4,5,6,3]=>[3,2,1,1,1]
[3,7,8,1,5,6,2,4]=>[3,1,1,1,1,1]
[6,3,7,8,1,5,2,4]=>[3,2,1,1,1]
[6,7,1,2,8,5,3,4]=>[3,2,1,1,1]
[1,6,7,8,4,2,5,3]=>[3,2,1,1,1]
[3,1,2,7,6,5,8,4]=>[4,2,1,1]
[6,1,2,4,7,3,8,5]=>[3,2,1,1,1]
[1,7,5,3,6,4,8,2]=>[4,2,1,1]
[5,1,2,6,7,4,8,3]=>[3,2,1,1,1]
[4,1,5,7,3,2,6,8]=>[3,2,1,1,1]
[4,6,1,7,3,2,5,8]=>[3,2,1,1,1]
[4,6,1,8,3,2,5,7]=>[3,2,1,1,1]
[4,7,1,8,3,5,2,6]=>[3,2,1,1,1]
[4,1,7,8,6,2,3,5]=>[3,2,1,1,1]
[1,6,5,7,8,3,4,2]=>[4,1,1,1,1]
[1,6,5,8,7,3,4,2]=>[4,2,1,1]
[4,1,8,7,6,2,3,5]=>[4,2,1,1]
[4,8,1,7,3,5,2,6]=>[4,1,1,1,1]
[4,8,1,6,3,2,5,7]=>[4,1,1,1,1]
[4,7,1,6,3,2,5,8]=>[4,1,1,1,1]
[6,1,2,3,7,5,4,8]=>[3,2,1,1,1]
[6,8,1,5,3,7,2,4]=>[4,1,1,1,1]
[8,7,5,2,4,1,6,3]=>[5,2,1]
[1,5,7,3,4,8,6,2]=>[3,2,1,1,1]
[1,5,8,3,4,7,6,2]=>[4,1,1,1,1]
[7,8,5,2,4,1,6,3]=>[4,2,1,1]
[7,1,2,3,5,6,4,8]=>[3,1,1,1,1,1]
[8,1,2,3,5,6,4,7]=>[3,1,1,1,1,1]
[8,1,2,3,5,4,7,6]=>[3,2,1,1,1]
[7,1,8,4,6,3,2,5]=>[4,2,1,1]
[6,8,2,4,3,1,5,7]=>[4,1,1,1,1]
[6,7,2,4,3,1,5,8]=>[4,1,1,1,1]
[3,8,1,2,4,5,7,6]=>[3,1,1,1,1,1]
[3,7,1,8,6,4,2,5]=>[4,2,1,1]
[1,6,4,3,7,5,8,2]=>[4,2,1,1]
[3,1,2,6,7,5,8,4]=>[3,2,1,1,1]
[3,8,1,7,6,4,2,5]=>[5,1,1,1]
[7,6,2,4,3,1,5,8]=>[5,1,1,1]
[8,7,2,4,3,5,1,6]=>[5,1,1,1]
[8,1,7,4,6,3,2,5]=>[5,1,1,1]
[8,1,7,6,5,3,2,4]=>[6,1,1]
[1,5,7,3,4,6,8,2]=>[3,1,1,1,1,1]
[8,7,2,5,3,6,1,4]=>[5,1,1,1]
[7,1,2,3,5,4,8,6]=>[3,2,1,1,1]
[6,1,2,3,5,8,4,7]=>[3,1,1,1,1,1]
[6,1,2,3,5,7,4,8]=>[3,1,1,1,1,1]
[5,1,2,3,7,6,4,8]=>[3,2,1,1,1]
[5,1,2,3,8,6,4,7]=>[3,2,1,1,1]
[1,5,6,3,4,7,8,2]=>[3,1,1,1,1,1]
[8,6,5,2,4,7,1,3]=>[5,1,1,1]
[7,6,2,5,3,1,8,4]=>[5,2,1]
[7,4,5,2,3,8,6,1]=>[4,2,1,1]
[8,2,3,7,4,5,1,6]=>[4,1,1,1,1]
[8,4,7,3,2,5,1,6]=>[5,1,1,1]
[5,4,6,3,1,2,8,7]=>[4,2,1,1]
[4,6,2,3,1,5,8,7]=>[3,2,1,1,1]
[7,2,3,4,5,8,6,1]=>[3,2,1,1,1]
[8,2,3,4,5,7,1,6]=>[3,1,1,1,1,1]
[7,3,4,6,8,5,1,2]=>[4,1,1,1,1]
[4,7,3,2,8,6,1,5]=>[4,2,1,1]
[3,7,4,5,1,8,6,2]=>[3,3,1,1]
[3,8,2,6,7,4,5,1]=>[4,1,1,1,1]
[4,8,1,5,6,7,3,2]=>[4,1,1,1,1]
[5,8,2,4,6,7,1,3]=>[3,1,1,1,1,1]
[6,8,1,3,4,2,7,5]=>[3,2,1,1,1]
[5,8,2,4,3,1,7,6]=>[4,2,1,1]
[2,1,7,6,8,5,3,4]=>[4,2,1,1]
[3,7,6,1,8,5,2,4]=>[4,2,1,1]
[4,7,2,3,8,5,1,6]=>[3,2,1,1,1]
[7,1,3,6,4,8,5,2]=>[4,2,1,1]
[7,6,1,4,8,5,2,3]=>[4,2,1,1]
[6,2,3,7,8,5,4,1]=>[4,2,1,1]
[6,2,3,8,4,5,1,7]=>[3,2,1,1,1]
[7,2,3,6,8,4,1,5]=>[4,1,1,1,1]
[8,2,3,5,7,1,4,6]=>[3,1,1,1,1,1]
[6,4,8,3,5,1,7,2]=>[4,2,1,1]
[5,4,8,3,6,7,1,2]=>[4,1,1,1,1]
[3,5,1,8,4,6,7,2]=>[3,2,1,1,1]
[3,6,1,8,4,5,2,7]=>[3,2,1,1,1]
[4,6,8,3,5,2,7,1]=>[4,1,1,1,1]
[5,7,8,3,2,4,1,6]=>[4,1,1,1,1]
[4,8,2,3,5,6,1,7]=>[3,1,1,1,1,1]
[6,8,2,3,1,4,5,7]=>[3,1,1,1,1,1]
[5,2,7,4,8,3,1,6]=>[4,2,1,1]
[3,7,8,2,1,4,6,5]=>[3,2,1,1,1]
[3,7,5,2,8,4,1,6]=>[4,2,1,1]
[6,3,2,4,1,8,7,5]=>[4,3,1]
[7,2,3,4,8,5,1,6]=>[3,2,1,1,1]
[5,7,3,1,4,2,6,8]=>[3,2,1,1,1]
[3,7,4,1,8,2,5,6]=>[3,2,1,1,1]
[6,3,7,4,8,1,2,5]=>[3,2,1,1,1]
[8,3,7,4,2,6,1,5]=>[5,1,1,1]
[3,7,4,1,5,6,2,8]=>[3,2,1,1,1]
[1,8,3,2,4,5,7,6]=>[3,2,1,1,1]
[8,4,1,6,3,7,5,2]=>[4,2,2]
[8,7,4,2,1,6,3,5]=>[5,2,1]
[8,3,5,2,7,4,1,6]=>[4,2,1,1]
[1,5,3,8,7,6,4,2]=>[5,2,1]
[7,2,4,8,1,3,6,5]=>[3,2,1,1,1]
[1,2,8,7,5,6,3,4]=>[4,1,1,1,1]
[3,1,8,6,7,5,2,4]=>[4,2,1,1]
[1,4,8,6,5,7,2,3]=>[4,1,1,1,1]
[1,6,5,4,8,2,3,7]=>[4,1,1,1,1]
[5,1,6,8,3,4,2,7]=>[3,2,1,1,1]
[6,2,5,1,7,4,3,8]=>[4,2,1,1]
[5,2,1,8,7,4,3,6]=>[4,3,1]
[5,2,6,3,8,1,4,7]=>[3,2,1,1,1]
[5,2,8,3,4,6,1,7]=>[3,2,1,1,1]
[6,2,8,4,3,1,7,5]=>[4,2,2]
[7,2,8,1,3,6,5,4]=>[4,2,1,1]
[7,3,8,1,4,6,2,5]=>[3,2,1,1,1]
[1,7,8,5,4,6,3,2]=>[5,1,1,1]
[1,5,8,4,6,3,7,2]=>[4,1,1,1,1]
[5,3,8,4,1,2,7,6]=>[3,2,2,1]
[5,8,4,3,6,2,1,7]=>[5,1,1,1]
[1,8,3,6,5,2,7,4]=>[4,2,1,1]
[1,8,2,4,7,6,5,3]=>[5,1,1,1]
[3,8,1,4,6,7,5,2]=>[4,1,1,1,1]
[3,8,2,5,1,7,6,4]=>[4,2,1,1]
[4,3,8,2,5,1,6,7]=>[4,1,1,1,1]
[8,2,4,3,5,1,7,6]=>[4,2,1,1]
[8,2,1,4,6,5,7,3]=>[4,2,1,1]
[8,1,3,4,5,7,6,2]=>[4,1,1,1,1]
[6,1,5,2,4,7,8,3]=>[4,1,1,1,1]
[4,1,8,5,2,7,6,3]=>[4,2,2]
[4,8,5,1,3,6,2,7]=>[4,1,1,1,1]
[3,6,1,5,7,2,8,4]=>[3,2,1,1,1]
[6,3,1,2,8,5,7,4]=>[3,3,1,1]
[4,1,8,2,3,7,5,6]=>[3,2,1,1,1]
[5,3,8,7,2,1,4,6]=>[4,2,1,1]
[6,7,3,5,1,4,8,2]=>[4,1,1,1,1]
[6,4,7,5,8,2,3,1]=>[4,2,1,1]
[5,7,8,4,2,6,3,1]=>[4,2,1,1]
[5,7,4,1,6,8,3,2]=>[4,2,1,1]
[5,8,4,6,1,7,3,2]=>[4,2,1,1]
[5,6,1,4,7,8,3,2]=>[4,1,1,1,1]
[5,6,3,7,4,8,2,1]=>[4,2,1,1]
[5,3,6,7,4,8,2,1]=>[4,2,1,1]
[5,4,8,2,6,7,3,1]=>[4,2,1,1]
[5,4,8,6,2,7,3,1]=>[4,2,2]
[7,4,8,5,6,2,1,3]=>[4,2,1,1]
[5,6,3,8,4,7,2,1]=>[4,2,1,1]
[5,6,3,8,2,7,4,1]=>[4,2,1,1]
[6,7,3,8,5,2,4,1]=>[4,2,1,1]
[6,2,7,5,1,4,8,3]=>[4,2,1,1]
[3,5,7,8,4,6,2,1]=>[4,1,1,1,1]
[5,3,7,8,4,6,2,1]=>[4,2,1,1]
[5,7,8,2,4,6,3,1]=>[4,1,1,1,1]
[2,5,8,4,3,7,6,1]=>[4,2,1,1]
[3,7,4,8,6,2,1,5]=>[4,2,1,1]
[3,6,4,8,7,2,5,1]=>[4,2,1,1]
[3,5,4,8,2,7,6,1]=>[4,2,1,1]
[4,5,7,3,8,6,2,1]=>[4,2,1,1]
[3,5,6,8,4,7,2,1]=>[4,1,1,1,1]
[6,3,1,8,7,5,4,2]=>[5,3]
[5,4,8,1,7,6,3,2]=>[5,2,1]
[5,8,4,1,7,6,3,2]=>[5,2,1]
[7,5,4,1,8,6,3,2]=>[5,3]
[8,5,4,1,7,6,3,2]=>[5,3]
[1,8,2,5,6,3,4,7]=>[3,1,1,1,1,1]
[7,2,8,4,5,1,3,6]=>[3,2,1,1,1]
[1,3,7,5,6,2,4,8]=>[3,1,1,1,1,1]
[1,6,7,4,3,5,2,8]=>[4,1,1,1,1]
[1,8,5,2,3,7,4,6]=>[3,2,1,1,1]
[1,8,2,5,3,6,7,4]=>[3,2,1,1,1]
[2,6,8,4,3,5,7,1]=>[4,1,1,1,1]
[7,5,8,3,2,1,6,4]=>[5,2,1]
[7,2,8,4,1,5,6,3]=>[3,2,2,1]
[7,5,8,1,2,6,3,4]=>[3,2,1,1,1]
[1,6,7,4,3,2,8,5]=>[4,2,1,1]
[1,5,2,6,4,7,8,3]=>[3,2,1,1,1]
[1,5,4,6,2,3,7,8]=>[3,1,1,1,1,1]
[6,2,5,7,1,4,8,3]=>[4,1,1,1,1]
[6,5,4,3,8,1,7,2]=>[5,2,1]
[7,3,6,8,5,2,4,1]=>[5,1,1,1]
[2,7,8,3,6,5,1,4]=>[4,1,1,1,1]
[2,7,8,5,4,6,3,1]=>[5,1,1,1]
[2,6,5,8,3,4,1,7]=>[4,1,1,1,1]
[2,6,5,7,3,4,1,8]=>[4,1,1,1,1]
[6,2,5,7,4,1,3,8]=>[4,1,1,1,1]
[6,2,5,8,4,1,3,7]=>[4,1,1,1,1]
[2,7,8,4,6,1,3,5]=>[3,1,1,1,1,1]
[6,1,2,8,3,7,4,5]=>[3,2,1,1,1]
[6,1,2,8,5,4,7,3]=>[4,2,1,1]
[6,2,5,7,8,1,3,4]=>[3,1,1,1,1,1]
[1,5,4,2,6,7,3,8]=>[3,2,1,1,1]
[2,6,5,7,3,8,1,4]=>[4,1,1,1,1]
[1,6,2,7,5,8,4,3]=>[4,2,1,1]
[1,3,2,7,8,5,6,4]=>[3,2,1,1,1]
[1,6,2,4,8,7,3,5]=>[3,2,1,1,1]
[6,5,2,1,8,7,3,4]=>[4,3,1]
[2,6,5,3,7,8,4,1]=>[4,2,1,1]
[6,2,5,3,8,4,7,1]=>[4,2,1,1]
[6,5,2,3,8,7,1,4]=>[4,2,1,1]
[5,4,1,2,3,8,6,7]=>[3,2,1,1,1]
[5,1,4,2,3,7,8,6]=>[3,2,1,1,1]
[1,5,4,2,6,3,8,7]=>[3,2,2,1]
[5,1,6,3,8,2,7,4]=>[3,2,2,1]
[1,8,7,6,2,5,4,3]=>[6,1,1]
[5,2,7,4,1,6,3,8]=>[3,2,2,1]
[4,7,3,1,5,6,2,8]=>[3,2,1,1,1]
[5,8,3,4,1,6,7,2]=>[3,2,1,1,1]
[1,7,8,4,5,6,2,3]=>[3,1,1,1,1,1]
[1,5,8,4,2,6,7,3]=>[3,2,1,1,1]
[1,6,3,8,5,2,7,4]=>[3,2,2,1]
[1,7,3,4,8,6,2,5]=>[3,2,1,1,1]
[8,7,3,2,1,6,5,4]=>[5,3]
[8,7,6,3,1,5,2,4]=>[5,2,1]
[8,5,1,7,2,3,4,6]=>[3,2,1,1,1]
[2,4,8,5,3,7,1,6]=>[4,1,1,1,1]
[2,4,1,8,5,3,7,6]=>[3,2,2,1]
[2,4,8,6,3,1,7,5]=>[4,2,1,1]
[3,4,6,8,2,1,7,5]=>[3,2,1,1,1]
[3,4,1,5,8,2,7,6]=>[3,2,1,1,1]
[8,1,4,5,3,2,7,6]=>[4,2,1,1]
[3,4,1,5,2,8,7,6]=>[3,2,2,1]
[3,4,6,2,1,8,7,5]=>[3,3,1,1]
[3,5,6,2,1,7,8,4]=>[3,2,1,1,1]
[3,4,6,2,7,8,1,5]=>[3,1,1,1,1,1]
[8,1,4,6,3,7,2,5]=>[4,1,1,1,1]
[8,1,4,6,3,7,5,2]=>[4,2,1,1]
[3,5,6,2,1,7,4,8]=>[3,2,1,1,1]
[8,1,5,6,7,3,4,2]=>[4,1,1,1,1]
[8,1,5,6,7,3,2,4]=>[4,1,1,1,1]
[3,4,1,6,8,7,2,5]=>[3,2,1,1,1]
[3,5,6,1,8,7,2,4]=>[3,2,1,1,1]
[2,1,3,8,6,7,4,5]=>[3,2,1,1,1]
[8,1,3,2,6,7,5,4]=>[4,2,1,1]
[2,3,8,6,7,1,5,4]=>[4,1,1,1,1]
[2,4,1,8,6,7,5,3]=>[4,2,1,1]
[2,5,8,6,1,7,4,3]=>[4,2,1,1]
[3,5,6,1,8,7,4,2]=>[4,2,1,1]
[3,4,1,6,8,7,5,2]=>[4,2,1,1]
[3,4,6,8,7,1,5,2]=>[4,1,1,1,1]
[8,1,4,6,2,7,5,3]=>[4,2,1,1]
[3,5,1,6,7,8,4,2]=>[3,2,1,1,1]
[4,5,6,1,7,8,3,2]=>[3,2,1,1,1]
[4,5,6,1,7,3,8,2]=>[3,2,1,1,1]
[3,5,1,6,7,4,8,2]=>[3,2,1,1,1]
[8,1,5,6,7,4,2,3]=>[4,1,1,1,1]
[8,1,5,6,7,4,3,2]=>[5,1,1,1]
[3,5,1,6,7,4,2,8]=>[3,2,1,1,1]
[4,5,6,1,7,3,2,8]=>[3,2,1,1,1]
[6,5,8,7,4,3,1,2]=>[5,2,1]
[6,4,2,7,8,5,1,3]=>[4,2,1,1]
[6,1,4,8,7,5,2,3]=>[4,2,1,1]
[1,6,4,8,7,5,2,3]=>[4,2,1,1]
[1,8,6,2,4,7,3,5]=>[4,1,1,1,1]
[8,1,6,2,4,7,3,5]=>[4,1,1,1,1]
[7,6,2,1,4,8,3,5]=>[4,2,1,1]
[6,4,1,7,8,5,2,3]=>[3,3,1,1]
[7,6,1,2,4,8,3,5]=>[4,1,1,1,1]
[7,6,1,3,4,8,2,5]=>[4,1,1,1,1]
[8,1,6,3,4,7,2,5]=>[4,1,1,1,1]
[1,8,6,3,4,7,2,5]=>[4,1,1,1,1]
[1,7,2,5,4,8,3,6]=>[4,1,1,1,1]
[7,1,2,5,4,8,3,6]=>[4,1,1,1,1]
[2,7,1,5,4,8,3,6]=>[4,1,1,1,1]
[2,8,6,3,4,7,1,5]=>[4,1,1,1,1]
[2,8,6,1,4,7,3,5]=>[4,1,1,1,1]
[7,2,1,5,4,8,3,6]=>[4,2,1,1]
[1,2,7,5,4,8,3,6]=>[4,1,1,1,1]
[3,2,7,5,4,8,1,6]=>[4,2,1,1]
[2,5,8,4,7,3,1,6]=>[4,1,1,1,1]
[2,3,7,5,4,8,1,6]=>[4,1,1,1,1]
[6,8,3,2,4,7,1,5]=>[4,1,1,1,1]
[3,7,2,5,4,8,1,6]=>[4,1,1,1,1]
[3,1,7,5,4,8,2,6]=>[4,2,1,1]
[1,3,7,5,4,8,2,6]=>[4,1,1,1,1]
[1,5,8,4,7,3,2,6]=>[4,1,1,1,1]
[5,1,8,4,7,3,2,6]=>[4,2,1,1]
[5,8,2,4,7,3,1,6]=>[4,1,1,1,1]
[6,8,4,3,7,5,1,2]=>[4,2,1,1]
[8,7,5,6,2,1,4,3]=>[5,2,1]
[8,5,2,4,7,3,1,6]=>[5,1,1,1]
[8,1,5,4,7,3,2,6]=>[5,1,1,1]
[1,8,5,4,7,3,2,6]=>[5,1,1,1]
[1,7,3,5,4,8,2,6]=>[4,1,1,1,1]
[8,6,3,1,4,7,2,5]=>[4,2,1,1]
[8,6,4,2,7,5,1,3]=>[5,2,1]
[8,6,4,1,7,2,5,3]=>[4,3,1]
[5,3,7,4,6,8,2,1]=>[4,2,1,1]
[4,1,3,2,7,8,5,6]=>[3,2,1,1,1]
[1,4,3,2,7,8,5,6]=>[3,2,1,1,1]
[2,4,3,1,7,8,5,6]=>[3,2,1,1,1]
[2,7,3,5,4,8,1,6]=>[4,1,1,1,1]
[2,8,5,4,7,3,1,6]=>[5,1,1,1]
[5,7,3,4,6,8,2,1]=>[4,1,1,1,1]
[8,2,5,4,7,3,1,6]=>[5,1,1,1]
[7,2,3,5,4,8,1,6]=>[4,1,1,1,1]
[3,2,1,4,7,8,5,6]=>[3,2,1,1,1]
[8,1,7,6,4,3,5,2]=>[6,1,1]
[8,6,4,5,2,7,1,3]=>[5,1,1,1]
[7,1,8,6,4,3,5,2]=>[5,2,1]
[7,4,2,5,1,6,3,8]=>[4,2,1,1]
[7,3,6,5,2,1,4,8]=>[5,1,1,1]
[8,3,6,5,2,1,7,4]=>[5,2,1]
[7,3,6,5,2,1,8,4]=>[5,2,1]
[7,5,8,6,4,2,1,3]=>[5,2,1]
[5,4,2,8,1,3,7,6]=>[4,2,1,1]
[5,8,2,6,4,1,3,7]=>[4,1,1,1,1]
[6,4,2,5,1,8,3,7]=>[4,2,1,1]
[6,3,5,2,1,4,7,8]=>[4,1,1,1,1]
[2,5,8,6,3,1,4,7]=>[4,1,1,1,1]
[2,3,5,8,1,4,7,6]=>[3,1,1,1,1,1]
[2,3,6,8,1,5,7,4]=>[3,1,1,1,1,1]
[6,3,8,5,2,7,1,4]=>[4,2,1,1]
[6,3,7,5,2,1,4,8]=>[4,2,1,1]
[2,5,7,6,3,1,4,8]=>[4,1,1,1,1]
[2,8,7,6,3,1,5,4]=>[5,2,1]
[2,5,8,7,6,3,1,4]=>[5,1,1,1]
[2,4,8,1,6,5,7,3]=>[4,1,1,1,1]
[2,8,7,3,6,1,4,5]=>[4,1,1,1,1]
[7,3,5,2,1,4,6,8]=>[4,1,1,1,1]
[8,4,2,5,1,3,7,6]=>[4,2,1,1]
[2,3,6,8,1,4,7,5]=>[3,1,1,1,1,1]
[2,7,8,6,3,1,4,5]=>[4,1,1,1,1]
[7,3,8,5,2,1,4,6]=>[4,2,1,1]
[2,3,6,1,8,4,7,5]=>[3,2,1,1,1]
[2,8,6,3,1,4,5,7]=>[4,1,1,1,1]
[8,3,5,2,1,4,6,7]=>[4,1,1,1,1]
[2,4,8,1,3,7,5,6]=>[3,1,1,1,1,1]
[2,5,8,1,7,3,6,4]=>[4,1,1,1,1]
[2,8,1,5,7,3,6,4]=>[4,1,1,1,1]
[3,8,6,1,4,7,5,2]=>[4,2,1,1]
[2,6,8,1,5,7,3,4]=>[3,1,1,1,1,1]
[2,7,1,5,8,3,4,6]=>[3,1,1,1,1,1]
[3,7,5,8,1,2,6,4]=>[3,2,1,1,1]
[7,3,6,1,2,8,4,5]=>[3,2,1,1,1]
[7,4,8,1,6,5,2,3]=>[4,2,1,1]
[7,4,5,8,6,1,2,3]=>[3,2,1,1,1]
[6,8,4,5,1,7,2,3]=>[3,2,1,1,1]
[5,1,8,7,6,2,3,4]=>[4,2,1,1]
[4,6,1,8,7,5,2,3]=>[4,2,1,1]
[4,5,1,8,7,2,3,6]=>[3,2,1,1,1]
[3,4,8,7,1,2,5,6]=>[3,1,1,1,1,1]
[6,4,8,7,1,2,5,3]=>[4,2,1,1]
[5,6,8,3,7,1,4,2]=>[4,1,1,1,1]
[6,5,1,2,7,3,8,4]=>[3,2,2,1]
[6,5,1,8,2,7,3,4]=>[3,3,1,1]
[6,5,1,8,7,2,3,4]=>[3,3,1,1]
[6,5,1,7,2,8,3,4]=>[3,2,2,1]
[6,5,1,7,2,3,8,4]=>[3,2,2,1]
[5,6,8,7,4,1,2,3]=>[4,1,1,1,1]
[6,8,5,7,4,1,2,3]=>[4,1,1,1,1]
[7,3,8,1,5,2,4,6]=>[3,2,1,1,1]
[4,1,7,5,3,6,2,8]=>[4,2,1,1]
[1,8,4,2,3,6,7,5]=>[3,2,1,1,1]
[2,5,8,3,4,6,7,1]=>[3,1,1,1,1,1]
[4,1,7,2,3,6,8,5]=>[3,2,1,1,1]
[4,6,2,1,5,7,8,3]=>[3,2,1,1,1]
[4,5,2,3,1,7,8,6]=>[3,2,1,1,1]
[3,2,6,7,4,1,8,5]=>[3,2,2,1]
[5,6,2,7,1,4,8,3]=>[3,2,1,1,1]
[6,2,3,8,1,7,4,5]=>[3,2,1,1,1]
[2,6,8,3,4,7,1,5]=>[3,1,1,1,1,1]
[4,6,2,7,5,1,3,8]=>[3,2,1,1,1]
[2,6,3,1,8,4,5,7]=>[3,2,1,1,1]
[2,4,3,7,8,1,5,6]=>[3,1,1,1,1,1]
[5,3,2,7,4,8,1,6]=>[4,2,1,1]
[5,1,2,7,6,8,4,3]=>[4,2,1,1]
[2,6,3,1,8,7,4,5]=>[3,3,1,1]
[3,5,6,4,7,8,1,2]=>[3,1,1,1,1,1]
[5,3,6,4,2,8,7,1]=>[4,2,2]
[5,4,2,3,7,8,6,1]=>[4,2,1,1]
[4,1,8,2,5,7,3,6]=>[3,2,1,1,1]
[3,1,8,4,7,2,5,6]=>[3,2,1,1,1]
[6,2,3,8,4,1,7,5]=>[3,2,2,1]
[2,6,4,1,5,3,8,7]=>[3,2,2,1]
[3,2,7,6,4,1,8,5]=>[4,2,2]
[2,5,4,1,7,6,8,3]=>[3,3,1,1]
[6,2,1,4,7,8,3,5]=>[3,2,1,1,1]
[2,6,5,1,7,8,3,4]=>[3,2,1,1,1]
[4,7,5,2,1,6,3,8]=>[4,2,1,1]
[4,2,3,7,8,1,6,5]=>[3,2,1,1,1]
[5,8,3,1,7,2,4,6]=>[3,2,1,1,1]
[6,8,3,1,5,2,4,7]=>[3,2,1,1,1]
[4,2,7,1,6,3,5,8]=>[3,2,1,1,1]
[5,1,7,4,2,6,3,8]=>[3,2,2,1]
[6,8,4,2,1,5,3,7]=>[4,2,1,1]
[6,8,5,2,1,7,3,4]=>[4,2,1,1]
[5,8,2,1,4,7,3,6]=>[3,2,1,1,1]
[6,8,3,2,5,1,7,4]=>[4,2,1,1]
[6,8,4,3,1,5,7,2]=>[4,2,1,1]
[6,8,4,2,1,5,7,3]=>[4,2,1,1]
[6,8,3,2,1,4,5,7]=>[4,1,1,1,1]
[5,1,7,3,2,4,6,8]=>[3,2,1,1,1]
[5,2,1,8,3,6,7,4]=>[3,3,1,1]
[4,3,8,1,6,2,7,5]=>[3,2,2,1]
[5,4,7,2,1,6,8,3]=>[4,2,1,1]
[5,2,1,7,3,4,8,6]=>[3,2,2,1]
[6,4,3,1,7,5,8,2]=>[4,3,1]
[5,3,1,7,2,6,8,4]=>[3,3,1,1]
[3,2,1,7,6,4,8,5]=>[3,3,2]
[4,2,1,6,5,8,3,7]=>[3,3,1,1]
[4,2,1,8,5,7,3,6]=>[3,3,1,1]
[7,4,3,1,8,5,6,2]=>[4,3,1]
[7,4,2,1,8,5,6,3]=>[4,3,1]
[6,3,2,1,7,4,5,8]=>[4,2,1,1]
[6,4,2,1,7,5,3,8]=>[4,3,1]
[7,5,2,1,8,6,3,4]=>[4,3,1]
[6,1,8,4,2,7,3,5]=>[3,2,2,1]
[6,2,1,8,3,7,4,5]=>[3,3,1,1]
[5,2,1,7,3,6,4,8]=>[3,3,1,1]
[5,3,2,7,6,1,4,8]=>[4,2,1,1]
[5,3,2,8,6,1,4,7]=>[4,2,1,1]
[6,3,2,8,7,1,4,5]=>[4,2,1,1]
[4,2,8,1,7,3,5,6]=>[3,2,1,1,1]
[4,3,8,7,2,1,5,6]=>[4,2,1,1]
[2,1,5,8,4,7,3,6]=>[3,2,1,1,1]
[4,3,2,5,8,1,6,7]=>[4,1,1,1,1]
[4,3,2,5,7,1,6,8]=>[4,1,1,1,1]
[4,3,1,6,2,7,5,8]=>[3,2,2,1]
[4,3,1,7,2,8,5,6]=>[3,2,2,1]
[5,4,1,7,2,8,6,3]=>[3,3,2]
[6,5,3,1,7,8,4,2]=>[4,3,1]
[6,4,2,1,7,8,3,5]=>[4,2,1,1]
[5,4,2,1,6,7,3,8]=>[4,2,1,1]
[5,3,2,1,6,7,4,8]=>[4,2,1,1]
[6,4,2,1,7,8,5,3]=>[4,3,1]
[5,3,2,6,8,1,7,4]=>[4,2,1,1]
[3,2,1,4,8,7,5,6]=>[3,3,1,1]
[3,2,1,4,6,8,5,7]=>[3,2,1,1,1]
[4,3,2,6,1,7,8,5]=>[4,2,1,1]
[5,3,2,1,6,7,8,4]=>[4,2,1,1]
[8,6,1,4,5,7,2,3]=>[4,1,1,1,1]
[3,8,6,4,5,7,1,2]=>[4,1,1,1,1]
[5,2,8,3,7,4,6,1]=>[4,2,1,1]
[6,2,8,5,4,7,3,1]=>[5,2,1]
[1,8,6,3,7,4,2,5]=>[4,2,1,1]
[1,8,6,5,7,2,3,4]=>[4,1,1,1,1]
[5,2,8,4,3,6,7,1]=>[4,2,1,1]
[5,4,2,7,3,6,1,8]=>[4,2,1,1]
[5,4,2,8,3,6,1,7]=>[4,2,1,1]
[6,5,3,8,4,7,2,1]=>[5,2,1]
[5,2,8,4,3,7,1,6]=>[4,2,1,1]
[6,2,8,3,7,4,1,5]=>[4,2,1,1]
[5,4,2,7,3,1,8,6]=>[4,2,2]
[6,4,3,7,1,2,8,5]=>[4,2,1,1]
[6,4,3,8,1,2,7,5]=>[4,2,1,1]
[7,6,3,8,4,2,1,5]=>[5,2,1]
[7,2,8,5,1,6,3,4]=>[3,2,2,1]
[7,2,8,4,3,1,5,6]=>[4,2,1,1]
[7,5,3,8,4,2,6,1]=>[5,2,1]
[6,4,2,7,3,1,5,8]=>[4,2,1,1]
[7,6,4,8,2,3,5,1]=>[5,1,1,1]
[7,6,8,1,2,5,3,4]=>[4,1,1,1,1]
[5,3,1,7,8,4,6,2]=>[3,3,1,1]
[5,3,2,7,8,4,6,1]=>[4,2,1,1]
[5,4,1,6,3,8,7,2]=>[4,2,2]
[6,5,1,7,8,2,3,4]=>[3,2,1,1,1]
[6,3,1,7,8,4,2,5]=>[3,3,1,1]
[5,4,1,7,3,8,2,6]=>[4,2,1,1]
[6,3,2,7,8,4,1,5]=>[4,2,1,1]
[6,1,5,4,3,2,8,7]=>[5,2,1]
[8,7,6,1,3,5,2,4]=>[5,1,1,1]
[8,1,6,5,7,3,4,2]=>[5,1,1,1]
[8,4,1,5,7,6,2,3]=>[4,2,1,1]
[7,8,6,2,5,3,1,4]=>[5,1,1,1]
[6,1,3,5,2,8,4,7]=>[3,2,1,1,1]
[8,1,3,7,4,2,5,6]=>[4,1,1,1,1]
[4,3,8,7,5,2,1,6]=>[5,2,1]
[6,7,1,8,5,3,4,2]=>[4,2,1,1]
[2,7,6,4,8,3,5,1]=>[5,1,1,1]
[6,5,2,7,1,4,8,3]=>[4,2,1,1]
[7,4,6,1,3,2,8,5]=>[4,2,1,1]
[7,5,2,1,3,8,4,6]=>[4,2,1,1]
[8,4,7,6,3,1,5,2]=>[5,2,1]
[7,4,1,5,6,3,8,2]=>[4,2,1,1]
[3,4,7,5,6,1,8,2]=>[3,2,1,1,1]
[2,4,7,5,6,3,8,1]=>[4,1,1,1,1]
[5,4,1,7,6,2,8,3]=>[3,3,2]
[3,5,6,7,1,4,8,2]=>[3,1,1,1,1,1]
[2,7,6,1,3,4,8,5]=>[3,2,1,1,1]
[5,7,2,1,6,3,8,4]=>[3,2,2,1]
[4,7,2,5,6,3,8,1]=>[4,1,1,1,1]
[8,6,2,5,7,1,4,3]=>[5,1,1,1]
[2,7,4,5,3,8,1,6]=>[4,1,1,1,1]
[6,8,7,1,3,2,5,4]=>[4,2,1,1]
[2,8,6,5,7,1,4,3]=>[5,1,1,1]
[5,8,4,3,2,6,7,1]=>[5,1,1,1]
[1,8,5,6,2,4,7,3]=>[4,1,1,1,1]
[8,1,5,6,2,4,7,3]=>[4,1,1,1,1]
[6,4,8,1,3,2,7,5]=>[4,2,1,1]
[1,4,5,2,8,6,7,3]=>[3,2,1,1,1]
[2,3,1,7,8,6,4,5]=>[3,2,1,1,1]
[3,5,7,6,2,8,1,4]=>[4,1,1,1,1]
[4,5,6,1,2,8,7,3]=>[3,2,1,1,1]
[5,4,1,2,8,6,7,3]=>[3,3,1,1]
[8,4,5,2,1,6,7,3]=>[4,2,1,1]
[3,1,2,6,8,4,7,5]=>[3,2,1,1,1]
[5,1,3,2,7,8,4,6]=>[3,2,1,1,1]
[1,5,4,2,7,8,3,6]=>[3,2,1,1,1]
[4,6,7,8,3,1,5,2]=>[3,2,1,1,1]
[7,6,2,8,4,3,1,5]=>[5,2,1]
[5,2,8,6,3,4,7,1]=>[4,2,1,1]
[5,6,8,4,3,2,7,1]=>[5,1,1,1]
[5,3,8,1,7,2,4,6]=>[3,2,1,1,1]
[3,6,7,8,4,2,1,5]=>[4,1,1,1,1]
[6,5,1,8,4,3,7,2]=>[5,2,1]
[6,3,8,4,2,1,7,5]=>[4,2,2]
[2,5,8,3,1,6,7,4]=>[3,2,1,1,1]
[3,5,8,1,2,6,7,4]=>[3,1,1,1,1,1]
[3,2,8,1,5,6,7,4]=>[3,2,1,1,1]
[1,5,8,3,2,6,7,4]=>[3,2,1,1,1]
[1,3,8,6,2,4,7,5]=>[3,2,1,1,1]
[3,2,7,8,4,6,1,5]=>[3,2,1,1,1]
[5,1,8,3,4,6,7,2]=>[3,2,1,1,1]
[4,8,7,2,1,6,3,5]=>[4,2,1,1]
[2,8,1,6,3,4,7,5]=>[3,2,1,1,1]
[8,3,4,2,1,6,5,7]=>[4,2,1,1]
[6,4,7,2,5,8,1,3]=>[4,1,1,1,1]
[8,4,5,2,6,3,1,7]=>[4,2,1,1]
[2,4,5,8,3,6,1,7]=>[3,1,1,1,1,1]
[3,5,8,1,2,6,4,7]=>[3,1,1,1,1,1]
[8,6,1,3,5,2,4,7]=>[4,1,1,1,1]
[8,5,1,2,6,4,3,7]=>[4,2,1,1]
[5,8,6,1,3,4,2,7]=>[4,1,1,1,1]
[5,8,4,6,1,3,2,7]=>[4,1,1,1,1]
[7,3,4,5,2,8,1,6]=>[4,1,1,1,1]
[5,7,4,3,6,1,8,2]=>[4,2,1,1]
[2,6,4,3,7,8,5,1]=>[4,2,1,1]
[7,4,1,8,3,2,5,6]=>[4,2,1,1]
[6,2,1,7,8,4,5,3]=>[3,3,1,1]
[7,6,3,1,5,4,8,2]=>[5,2,1]
[2,4,6,5,1,7,8,3]=>[3,2,1,1,1]
[1,4,7,5,6,8,2,3]=>[3,1,1,1,1,1]
[1,4,7,6,5,8,2,3]=>[4,1,1,1,1]
[3,7,5,2,4,6,8,1]=>[4,1,1,1,1]
[5,6,1,7,4,2,8,3]=>[3,2,2,1]
[3,7,4,8,1,2,6,5]=>[3,2,1,1,1]
[6,3,5,7,8,1,4,2]=>[4,1,1,1,1]
[3,6,5,7,1,8,4,2]=>[4,2,1,1]
[6,4,7,8,2,1,3,5]=>[4,1,1,1,1]
[6,7,3,8,4,1,2,5]=>[3,2,1,1,1]
[2,7,8,3,4,6,1,5]=>[3,1,1,1,1,1]
[7,5,8,4,1,3,2,6]=>[5,1,1,1]
[4,7,5,8,3,1,2,6]=>[4,1,1,1,1]
[3,6,7,4,8,1,2,5]=>[3,1,1,1,1,1]
[5,7,3,1,6,8,4,2]=>[4,2,1,1]
[2,7,3,1,8,6,4,5]=>[3,3,1,1]
[2,8,4,3,1,5,7,6]=>[4,2,1,1]
[4,8,1,2,3,5,7,6]=>[3,1,1,1,1,1]
[7,6,8,1,2,4,3,5]=>[4,1,1,1,1]
[7,6,8,5,1,3,2,4]=>[5,1,1,1]
[2,8,5,4,6,1,7,3]=>[4,2,1,1]
[8,4,5,2,7,6,1,3]=>[4,2,1,1]
[8,7,6,4,1,2,5,3]=>[5,2,1]
[6,7,1,3,5,2,8,4]=>[3,2,1,1,1]
[5,7,2,3,6,8,1,4]=>[3,1,1,1,1,1]
[8,5,3,2,7,6,1,4]=>[5,2,1]
[3,4,6,7,5,8,1,2]=>[3,1,1,1,1,1]
[3,4,5,7,6,1,8,2]=>[3,2,1,1,1]
[2,6,4,5,7,8,3,1]=>[4,1,1,1,1]
[3,8,5,1,6,2,7,4]=>[3,2,2,1]
[2,5,1,3,6,8,7,4]=>[3,2,1,1,1]
[5,4,6,1,3,7,8,2]=>[4,1,1,1,1]
[6,3,5,7,1,4,8,2]=>[4,1,1,1,1]
[7,3,4,6,8,1,5,2]=>[4,1,1,1,1]
[7,5,2,8,4,1,3,6]=>[4,2,1,1]
[3,7,6,4,1,8,2,5]=>[4,2,1,1]
[3,7,8,4,1,5,6,2]=>[3,2,1,1,1]
[8,7,5,4,2,1,6,3]=>[6,2]
[3,5,8,6,7,4,2,1]=>[5,1,1,1]
[5,8,1,6,7,3,4,2]=>[4,1,1,1,1]
[6,7,2,5,1,8,4,3]=>[4,2,1,1]
[5,8,2,1,6,7,4,3]=>[4,2,1,1]
[4,5,2,8,6,3,7,1]=>[4,2,1,1]
[3,6,1,2,5,8,4,7]=>[3,1,1,1,1,1]
[1,4,5,8,2,3,7,6]=>[3,1,1,1,1,1]
[1,2,6,4,5,8,3,7]=>[3,1,1,1,1,1]
[1,5,2,4,6,8,3,7]=>[3,1,1,1,1,1]
[3,6,1,5,8,2,4,7]=>[3,1,1,1,1,1]
[2,6,5,1,4,8,3,7]=>[4,1,1,1,1]
[5,2,6,1,4,8,3,7]=>[3,2,1,1,1]
[2,5,1,8,4,7,3,6]=>[3,2,1,1,1]
[2,7,1,4,3,6,8,5]=>[3,2,1,1,1]
[1,3,7,5,8,2,4,6]=>[3,1,1,1,1,1]
[8,2,1,5,7,3,4,6]=>[3,2,1,1,1]
[2,5,4,8,1,3,7,6]=>[3,2,1,1,1]
[2,4,1,3,8,6,7,5]=>[3,2,1,1,1]
[8,4,3,7,1,2,6,5]=>[4,2,1,1]
[1,7,3,5,8,2,6,4]=>[3,2,1,1,1]
[1,8,4,2,6,7,3,5]=>[3,2,1,1,1]
[3,1,6,8,7,2,4,5]=>[3,2,1,1,1]
[7,2,1,6,8,3,4,5]=>[3,2,1,1,1]
[3,1,7,6,8,2,4,5]=>[3,2,1,1,1]
[4,1,7,2,6,8,3,5]=>[3,2,1,1,1]
[5,1,7,2,3,6,8,4]=>[3,2,1,1,1]
[7,2,1,6,3,5,8,4]=>[4,2,1,1]
[2,6,1,7,3,5,8,4]=>[3,2,1,1,1]
[7,1,2,5,3,6,8,4]=>[3,2,1,1,1]
[5,4,1,2,7,8,3,6]=>[3,2,1,1,1]
[8,1,3,2,4,6,7,5]=>[3,2,1,1,1]
[7,3,1,2,4,6,8,5]=>[3,2,1,1,1]
[1,8,3,4,7,2,5,6]=>[3,1,1,1,1,1]
[3,5,8,1,2,7,4,6]=>[3,1,1,1,1,1]
[3,6,8,1,2,4,7,5]=>[3,1,1,1,1,1]
[4,1,3,8,7,2,6,5]=>[4,2,1,1]
[1,3,7,4,8,2,6,5]=>[3,2,1,1,1]
[1,4,6,8,2,3,7,5]=>[3,1,1,1,1,1]
[3,5,8,1,7,2,4,6]=>[3,1,1,1,1,1]
[2,6,8,1,7,3,4,5]=>[3,1,1,1,1,1]
[6,1,5,8,2,3,7,4]=>[3,2,1,1,1]
[1,8,3,2,7,5,6,4]=>[4,2,1,1]
[3,1,7,2,8,5,6,4]=>[3,2,2,1]
[2,6,7,3,8,1,5,4]=>[3,2,1,1,1]
[8,4,1,7,3,6,2,5]=>[4,2,1,1]
[3,7,2,8,6,1,5,4]=>[4,2,1,1]
[6,2,3,8,7,1,5,4]=>[4,2,1,1]
[5,1,7,8,4,2,6,3]=>[3,2,2,1]
[5,1,8,7,4,2,6,3]=>[4,2,2]
[4,7,2,8,3,6,5,1]=>[4,2,1,1]
[4,1,7,8,5,3,6,2]=>[4,2,1,1]
[5,1,7,4,8,3,6,2]=>[4,2,1,1]
[4,1,8,7,5,3,6,2]=>[5,2,1]
[4,8,2,7,3,6,5,1]=>[5,1,1,1]
[4,7,2,6,3,5,8,1]=>[4,1,1,1,1]
[6,8,2,4,3,7,5,1]=>[4,2,1,1]
[6,7,2,4,3,8,5,1]=>[4,2,1,1]
[6,8,2,7,3,5,4,1]=>[5,1,1,1]
[3,8,7,2,4,1,5,6]=>[4,1,1,1,1]
[3,7,8,2,4,1,5,6]=>[3,1,1,1,1,1]
[3,6,8,2,4,5,7,1]=>[3,1,1,1,1,1]
[3,6,7,2,4,5,8,1]=>[3,1,1,1,1,1]
[6,5,1,4,2,3,8,7]=>[4,2,1,1]
[8,6,1,7,2,5,4,3]=>[5,2,1]
[8,7,6,1,2,3,5,4]=>[5,1,1,1]
[5,4,3,1,6,2,8,7]=>[4,2,2]
[8,3,4,7,1,6,2,5]=>[4,1,1,1,1]
[6,3,4,1,8,5,2,7]=>[3,3,1,1]
[3,8,5,2,7,1,6,4]=>[4,2,1,1]
[2,8,6,7,5,3,4,1]=>[5,1,1,1]
[2,1,8,7,3,6,4,5]=>[4,2,1,1]
[3,6,5,8,2,4,7,1]=>[4,1,1,1,1]
[5,2,1,8,7,3,4,6]=>[3,3,1,1]
[6,5,2,7,4,3,8,1]=>[5,2,1]
[4,6,5,2,7,3,8,1]=>[4,2,1,1]
[6,2,7,1,8,3,5,4]=>[3,3,1,1]
[2,7,5,4,8,3,6,1]=>[5,1,1,1]
[8,7,5,1,2,6,4,3]=>[5,2,1]
[8,4,3,2,7,1,6,5]=>[5,2,1]
[7,1,6,2,3,8,5,4]=>[4,2,1,1]
[4,8,1,3,2,7,5,6]=>[3,2,1,1,1]
[3,8,1,4,7,5,2,6]=>[4,1,1,1,1]
[6,3,8,7,4,5,1,2]=>[4,2,1,1]
[6,1,4,8,5,2,3,7]=>[3,2,1,1,1]
[8,5,7,4,6,2,1,3]=>[5,1,1,1]
[4,6,7,8,2,3,5,1]=>[3,1,1,1,1,1]
[8,7,4,6,2,1,5,3]=>[5,2,1]
[7,6,1,3,5,2,8,4]=>[4,2,1,1]
[5,8,3,2,4,6,1,7]=>[4,1,1,1,1]
[8,2,6,5,3,1,7,4]=>[5,2,1]
[4,8,7,6,5,2,3,1]=>[6,1,1]
[2,1,8,6,4,3,7,5]=>[4,2,2]
[2,1,7,6,5,3,8,4]=>[4,2,2]
[2,7,6,1,3,5,8,4]=>[4,1,1,1,1]
[7,2,5,4,6,1,8,3]=>[4,2,1,1]
[4,7,6,1,2,5,8,3]=>[4,1,1,1,1]
[2,4,1,7,6,8,5,3]=>[4,2,1,1]
[3,4,1,7,8,5,6,2]=>[3,2,1,1,1]
[7,5,4,3,1,8,6,2]=>[5,3]
[8,5,6,2,7,3,1,4]=>[4,2,1,1]
[8,4,2,5,6,1,7,3]=>[4,2,1,1]
[6,3,5,4,1,7,8,2]=>[4,2,1,1]
[4,1,3,6,7,5,8,2]=>[3,2,1,1,1]
[1,7,5,3,8,2,4,6]=>[4,1,1,1,1]
[1,7,2,4,5,8,3,6]=>[3,1,1,1,1,1]
[8,2,5,3,1,6,4,7]=>[4,2,1,1]
[1,7,4,5,8,3,2,6]=>[4,1,1,1,1]
[2,6,4,7,8,3,5,1]=>[4,1,1,1,1]
[2,6,4,7,8,3,1,5]=>[4,1,1,1,1]
[1,2,6,4,7,8,3,5]=>[3,1,1,1,1,1]
[2,7,4,5,8,1,3,6]=>[3,1,1,1,1,1]
[2,7,5,3,1,8,4,6]=>[4,2,1,1]
[6,1,4,7,8,3,5,2]=>[4,1,1,1,1]
[3,6,4,7,8,1,5,2]=>[3,2,1,1,1]
[4,3,6,7,1,8,5,2]=>[3,3,1,1]
[4,3,6,7,1,8,2,5]=>[3,2,1,1,1]
[3,6,4,7,8,1,2,5]=>[3,1,1,1,1,1]
[2,3,6,4,1,7,8,5]=>[3,2,1,1,1]
[4,7,2,1,5,3,8,6]=>[3,2,2,1]
[3,7,4,5,2,1,8,6]=>[4,2,1,1]
[1,3,6,4,7,2,8,5]=>[3,2,1,1,1]
[3,6,4,7,2,8,5,1]=>[4,2,1,1]
[5,1,3,4,2,7,8,6]=>[3,2,1,1,1]
[5,4,2,1,3,7,8,6]=>[4,2,1,1]
[6,1,7,3,8,2,5,4]=>[3,2,2,1]
[1,6,7,3,8,2,5,4]=>[3,2,1,1,1]
[6,1,4,7,8,5,2,3]=>[3,2,1,1,1]
[6,3,2,1,7,8,5,4]=>[4,3,1]
[6,2,7,3,1,8,5,4]=>[3,3,2]
[6,2,4,7,8,1,5,3]=>[3,2,1,1,1]
[2,6,7,3,1,8,5,4]=>[3,3,1,1]
[8,6,5,1,3,2,4,7]=>[5,1,1,1]
[6,4,7,8,3,2,5,1]=>[5,1,1,1]
[3,8,4,7,1,2,5,6]=>[3,1,1,1,1,1]
[8,6,1,2,5,4,3,7]=>[5,1,1,1]
[4,8,6,1,5,3,2,7]=>[5,1,1,1]
[5,8,6,4,1,3,2,7]=>[5,1,1,1]
[8,3,6,4,5,2,1,7]=>[5,1,1,1]
[6,8,5,7,4,2,3,1]=>[5,1,1,1]
[2,3,8,7,1,6,4,5]=>[4,1,1,1,1]
[4,3,7,8,1,6,2,5]=>[3,2,1,1,1]
[3,5,8,7,4,1,2,6]=>[4,1,1,1,1]
[7,3,8,4,1,2,5,6]=>[3,2,1,1,1]
[4,8,1,2,7,3,5,6]=>[3,1,1,1,1,1]
[6,8,1,2,7,4,5,3]=>[4,1,1,1,1]
[5,6,8,4,1,3,7,2]=>[4,1,1,1,1]
[8,5,4,7,1,6,3,2]=>[5,2,1]
[2,5,8,7,3,6,4,1]=>[5,1,1,1]
[2,4,8,7,5,6,1,3]=>[4,1,1,1,1]
[3,7,4,8,5,6,2,1]=>[4,2,1,1]
[6,4,8,7,5,1,2,3]=>[4,2,1,1]
[3,8,5,2,4,6,7,1]=>[4,1,1,1,1]
[5,7,1,8,4,6,2,3]=>[3,2,1,1,1]
[6,3,8,7,2,1,4,5]=>[4,2,1,1]
[2,3,7,8,5,6,1,4]=>[3,1,1,1,1,1]
[3,7,6,8,5,1,2,4]=>[4,1,1,1,1]
[2,6,7,8,5,1,3,4]=>[3,1,1,1,1,1]
[2,4,7,8,1,6,3,5]=>[3,1,1,1,1,1]
[5,4,7,8,2,6,3,1]=>[4,2,1,1]
[2,8,3,4,1,5,7,6]=>[3,2,1,1,1]
[6,8,3,4,1,2,7,5]=>[3,2,1,1,1]
[6,8,7,1,5,2,3,4]=>[4,1,1,1,1]
[5,8,3,2,7,6,1,4]=>[4,2,1,1]
[2,5,3,1,8,6,7,4]=>[3,3,1,1]
[4,5,3,2,8,6,7,1]=>[4,2,1,1]
[3,5,8,6,1,4,7,2]=>[4,1,1,1,1]
[2,8,5,6,1,4,7,3]=>[4,1,1,1,1]
[4,8,6,1,5,2,7,3]=>[4,2,1,1]
[5,8,2,3,7,6,1,4]=>[4,1,1,1,1]
[4,6,8,5,3,2,7,1]=>[5,1,1,1]
[2,6,4,8,5,1,7,3]=>[3,2,2,1]
[7,6,4,8,5,2,1,3]=>[5,2,1]
[3,4,8,6,5,2,7,1]=>[5,1,1,1]
[3,4,8,7,5,6,2,1]=>[5,1,1,1]
[7,5,3,2,8,6,1,4]=>[5,2,1]
[2,5,1,3,8,6,7,4]=>[3,2,1,1,1]
[4,5,1,2,8,6,7,3]=>[3,2,1,1,1]
[5,4,8,1,3,6,7,2]=>[4,1,1,1,1]
[8,3,5,4,1,6,7,2]=>[4,2,1,1]
[7,3,4,8,5,6,1,2]=>[3,2,1,1,1]
[6,1,5,7,2,4,8,3]=>[4,1,1,1,1]
[7,4,5,1,2,3,8,6]=>[3,2,1,1,1]
[7,4,3,1,2,8,5,6]=>[4,2,1,1]
[8,4,7,6,2,1,5,3]=>[5,2,1]
[8,4,6,5,7,1,3,2]=>[5,1,1,1]
[7,2,1,4,5,8,3,6]=>[3,2,1,1,1]
[7,4,1,6,3,5,8,2]=>[4,2,1,1]
[3,5,7,6,4,1,8,2]=>[4,2,1,1]
[4,7,5,2,1,3,8,6]=>[4,2,1,1]
[5,7,2,3,6,4,8,1]=>[4,1,1,1,1]
[8,6,2,3,7,1,4,5]=>[4,1,1,1,1]
[5,7,2,4,8,3,6,1]=>[4,1,1,1,1]
[1,7,2,4,8,6,3,5]=>[3,2,1,1,1]
[7,6,1,5,4,8,3,2]=>[6,1,1]
[4,7,3,2,1,8,5,6]=>[4,2,1,1]
[3,1,7,2,5,8,4,6]=>[3,2,1,1,1]
[4,8,7,6,1,2,5,3]=>[5,1,1,1]
[7,8,6,1,3,2,5,4]=>[4,2,1,1]
[2,8,6,7,4,1,3,5]=>[4,1,1,1,1]
[5,8,6,4,2,3,1,7]=>[5,1,1,1]
[2,8,3,1,6,5,4,7]=>[4,2,1,1]
[3,8,1,2,5,7,4,6]=>[3,1,1,1,1,1]
[6,8,5,4,2,7,3,1]=>[5,2,1]
[6,8,3,1,2,4,5,7]=>[3,1,1,1,1,1]
[4,6,8,7,3,1,5,2]=>[4,2,1,1]
[6,5,3,7,8,4,1,2]=>[4,2,1,1]
[4,1,3,8,7,5,6,2]=>[4,2,1,1]
[6,2,7,4,8,1,3,5]=>[3,2,1,1,1]
[8,4,5,2,1,6,3,7]=>[4,2,1,1]
[4,3,2,6,8,1,7,5]=>[4,2,1,1]
[7,1,5,6,3,8,2,4]=>[4,1,1,1,1]
[5,1,2,4,7,8,3,6]=>[3,1,1,1,1,1]
[3,5,4,2,8,1,6,7]=>[4,1,1,1,1]
[5,1,3,8,4,2,7,6]=>[3,2,2,1]
[6,2,8,7,3,5,4,1]=>[5,2,1]
[7,1,8,4,3,6,5,2]=>[4,2,2]
[3,6,8,7,4,1,2,5]=>[4,1,1,1,1]
[5,6,8,1,7,3,2,4]=>[4,1,1,1,1]
[3,1,6,8,7,4,2,5]=>[4,2,1,1]
[7,4,6,8,2,1,5,3]=>[4,2,1,1]
[6,5,8,4,3,1,2,7]=>[5,1,1,1]
[2,5,8,3,6,7,4,1]=>[4,1,1,1,1]
[8,5,1,3,7,4,6,2]=>[4,2,1,1]
[1,5,8,3,7,4,2,6]=>[4,1,1,1,1]
[3,8,2,7,1,5,6,4]=>[4,1,1,1,1]
[5,8,2,3,6,4,1,7]=>[4,1,1,1,1]
[6,8,2,3,4,7,5,1]=>[4,1,1,1,1]
[7,5,1,8,4,2,6,3]=>[4,2,2]
[3,6,8,5,2,7,4,1]=>[4,2,1,1]
[2,1,6,5,4,8,3,7]=>[4,2,1,1]
[2,1,7,8,4,6,5,3]=>[4,2,1,1]
[2,1,7,4,3,5,8,6]=>[3,2,2,1]
[7,5,2,8,4,6,3,1]=>[5,2,1]
[7,8,2,4,3,1,5,6]=>[4,1,1,1,1]
[7,6,3,8,1,5,4,2]=>[5,2,1]
[8,4,3,1,7,5,2,6]=>[4,3,1]
[7,3,1,4,6,8,5,2]=>[4,2,1,1]
[4,3,8,7,1,6,5,2]=>[5,2,1]
[4,7,1,8,5,2,6,3]=>[3,2,2,1]
[5,2,4,3,6,8,1,7]=>[4,1,1,1,1]
[3,8,6,5,4,1,2,7]=>[5,1,1,1]
[4,7,5,6,3,8,2,1]=>[5,1,1,1]
[4,2,7,5,8,3,6,1]=>[4,2,1,1]
[5,8,2,7,3,4,6,1]=>[4,1,1,1,1]
[6,7,2,4,5,3,8,1]=>[4,1,1,1,1]
[6,3,2,1,4,8,5,7]=>[4,2,1,1]
[6,2,3,1,4,7,8,5]=>[3,2,1,1,1]
[5,2,1,3,6,4,8,7]=>[3,2,2,1]
[7,1,8,3,5,4,6,2]=>[4,2,1,1]
[7,1,2,4,8,5,6,3]=>[3,2,1,1,1]
[7,2,1,3,4,5,8,6]=>[3,2,1,1,1]
[8,7,3,5,4,2,1,6]=>[6,1,1]
[5,1,6,4,3,2,8,7]=>[4,2,2]
[8,3,7,1,4,6,5,2]=>[5,1,1,1]
[2,8,3,6,4,7,5,1]=>[4,2,1,1]
[6,2,1,7,5,8,3,4]=>[3,3,1,1]
[6,3,8,7,5,2,1,4]=>[5,2,1]
[6,7,2,1,5,8,4,3]=>[4,2,1,1]
[7,6,8,1,5,4,3,2]=>[6,1,1]
[5,4,8,7,6,1,3,2]=>[5,2,1]
[7,6,1,8,5,4,3,2]=>[6,2]
[6,5,8,1,7,4,3,2]=>[5,2,1]
[6,5,8,7,4,1,3,2]=>[5,2,1]
[1,6,4,8,3,2,5,7]=>[4,1,1,1,1]
[1,8,3,5,6,2,4,7]=>[3,1,1,1,1,1]
[1,4,8,5,6,2,3,7]=>[3,1,1,1,1,1]
[1,2,8,5,3,7,4,6]=>[3,2,1,1,1]
[6,1,4,8,2,3,5,7]=>[3,1,1,1,1,1]
[8,7,2,5,6,1,4,3]=>[5,1,1,1]
[1,8,2,5,4,7,3,6]=>[4,1,1,1,1]
[5,7,4,1,2,3,8,6]=>[3,2,1,1,1]
[1,7,4,2,5,3,8,6]=>[3,2,2,1]
[6,7,4,2,1,3,8,5]=>[4,2,1,1]
[6,4,3,8,5,7,1,2]=>[4,2,1,1]
[7,4,3,6,2,1,5,8]=>[5,1,1,1]
[7,2,5,3,4,1,6,8]=>[4,1,1,1,1]
[8,3,7,4,5,6,1,2]=>[4,1,1,1,1]
[2,7,4,3,1,5,6,8]=>[4,1,1,1,1]
[6,8,4,2,3,1,5,7]=>[4,1,1,1,1]
[3,7,5,2,4,1,6,8]=>[4,1,1,1,1]
[7,1,3,2,8,4,5,6]=>[3,2,1,1,1]
[2,1,7,4,8,3,5,6]=>[3,2,1,1,1]
[5,2,8,6,1,3,4,7]=>[3,2,1,1,1]
[2,8,3,1,4,5,6,7]=>[3,1,1,1,1,1]
[7,4,8,2,3,1,5,6]=>[4,1,1,1,1]
[4,2,7,3,1,5,6,8]=>[3,2,1,1,1]
[8,3,7,2,1,4,5,6]=>[4,1,1,1,1]
[6,5,2,4,7,1,3,8]=>[4,1,1,1,1]
[6,5,7,4,1,8,2,3]=>[4,2,1,1]
[7,6,4,5,1,8,2,3]=>[4,2,1,1]
[8,6,4,1,3,7,2,5]=>[5,1,1,1]
[6,4,3,1,8,2,5,7]=>[4,2,1,1]
[7,4,1,2,8,3,5,6]=>[3,2,1,1,1]
[4,8,1,3,5,7,2,6]=>[3,1,1,1,1,1]
[7,8,4,1,3,6,2,5]=>[4,1,1,1,1]
[6,5,8,1,3,7,2,4]=>[4,1,1,1,1]
[5,3,6,1,8,2,4,7]=>[3,2,1,1,1]
[4,7,3,1,8,2,5,6]=>[3,2,1,1,1]
[8,3,1,7,2,4,5,6]=>[3,2,1,1,1]
[2,8,1,4,7,3,5,6]=>[3,1,1,1,1,1]
[3,1,8,5,4,7,6,2]=>[4,2,2]
[4,1,5,8,3,7,6,2]=>[4,2,1,1]
[4,1,5,3,8,7,6,2]=>[4,2,2]
[4,5,1,8,2,7,6,3]=>[4,2,1,1]
[4,8,5,3,1,7,6,2]=>[4,3,1]
[4,5,2,8,1,7,6,3]=>[4,2,1,1]
[4,5,2,1,8,7,6,3]=>[4,3,1]
[5,6,2,7,8,1,4,3]=>[3,2,1,1,1]
[4,6,2,8,7,1,5,3]=>[4,2,1,1]
[4,8,6,3,7,1,5,2]=>[4,2,1,1]
[4,8,6,3,7,5,1,2]=>[4,2,1,1]
[4,6,8,2,7,5,1,3]=>[4,1,1,1,1]
[4,6,2,8,7,5,1,3]=>[4,2,1,1]
[5,6,2,7,4,1,8,3]=>[3,2,2,1]
[5,6,7,2,3,1,8,4]=>[3,2,1,1,1]
[5,6,7,2,8,3,1,4]=>[3,2,1,1,1]
[5,6,7,2,1,8,3,4]=>[3,2,1,1,1]
[5,6,7,2,1,3,8,4]=>[3,2,1,1,1]
[5,6,1,7,8,2,4,3]=>[3,2,1,1,1]
[5,6,1,7,2,4,8,3]=>[3,2,1,1,1]
[5,1,6,7,8,3,4,2]=>[3,2,1,1,1]
[4,1,6,8,7,3,5,2]=>[4,2,1,1]
[3,1,8,6,7,5,4,2]=>[5,2,1]
[4,1,6,8,7,5,3,2]=>[5,2,1]
[5,1,6,7,4,8,3,2]=>[4,2,1,1]
[5,6,1,7,8,4,2,3]=>[3,2,1,1,1]
[4,6,8,1,7,5,2,3]=>[4,1,1,1,1]
[4,8,6,1,7,5,3,2]=>[5,2,1]
[5,6,7,1,8,3,2,4]=>[3,2,1,1,1]
[5,6,7,1,3,8,2,4]=>[3,1,1,1,1,1]
[5,6,7,1,3,2,8,4]=>[3,2,1,1,1]
[5,6,7,3,1,2,8,4]=>[3,2,1,1,1]
[5,6,7,3,8,1,2,4]=>[3,1,1,1,1,1]
[5,6,8,7,4,2,1,3]=>[5,1,1,1]
[5,6,7,3,8,2,1,4]=>[4,1,1,1,1]
[7,4,6,2,3,5,1,8]=>[4,1,1,1,1]
[1,4,8,6,3,2,5,7]=>[4,1,1,1,1]
[7,4,1,6,3,8,5,2]=>[4,2,2]
[7,6,3,1,5,8,4,2]=>[5,2,1]
[6,4,2,5,7,3,1,8]=>[4,2,1,1]
[4,2,5,7,6,3,1,8]=>[4,2,1,1]
[7,4,5,6,1,8,3,2]=>[4,2,1,1]
[4,1,5,8,6,3,2,7]=>[4,2,1,1]
[3,2,7,6,1,8,5,4]=>[4,2,2]
[4,7,5,1,6,8,2,3]=>[3,2,1,1,1]
[8,6,5,1,2,7,4,3]=>[5,2,1]
[3,2,5,1,4,8,7,6]=>[3,3,1,1]
[8,5,4,1,3,2,7,6]=>[5,2,1]
[1,4,2,3,6,8,7,5]=>[3,2,1,1,1]
[5,4,8,3,7,1,6,2]=>[4,2,1,1]
[4,7,1,8,2,5,3,6]=>[3,2,1,1,1]
[6,4,1,8,5,3,7,2]=>[4,3,1]
[8,4,6,1,3,5,2,7]=>[4,1,1,1,1]
[3,2,5,4,7,8,1,6]=>[3,2,1,1,1]
[5,2,4,3,7,8,1,6]=>[4,1,1,1,1]
[8,1,6,7,2,5,3,4]=>[4,1,1,1,1]
[3,1,7,6,5,8,2,4]=>[4,2,1,1]
[1,2,7,5,6,8,3,4]=>[3,1,1,1,1,1]
[6,1,4,7,2,8,3,5]=>[3,2,1,1,1]
[3,2,1,7,6,8,4,5]=>[3,3,1,1]
[3,2,8,6,4,7,1,5]=>[4,2,1,1]
[7,8,4,6,3,2,1,5]=>[5,1,1,1]
[1,8,6,5,3,7,2,4]=>[5,1,1,1]
[8,2,5,3,6,7,1,4]=>[4,1,1,1,1]
[3,8,5,2,7,6,1,4]=>[4,2,1,1]
[4,7,5,3,1,8,6,2]=>[4,3,1]
[4,5,3,6,8,1,7,2]=>[3,2,1,1,1]
[3,5,2,6,1,8,7,4]=>[3,3,1,1]
[1,6,3,5,7,2,8,4]=>[3,2,1,1,1]
[1,5,4,6,7,8,2,3]=>[3,1,1,1,1,1]
[8,4,6,5,7,2,1,3]=>[5,1,1,1]
[7,4,5,2,6,8,1,3]=>[4,1,1,1,1]
[5,4,2,6,8,7,1,3]=>[4,2,1,1]
[6,5,1,4,3,2,8,7]=>[5,2,1]
[3,6,4,5,2,1,8,7]=>[4,2,1,1]
[7,5,4,2,3,8,1,6]=>[5,1,1,1]
[7,8,1,3,5,6,2,4]=>[3,1,1,1,1,1]
[7,8,3,1,5,6,2,4]=>[3,2,1,1,1]
[1,7,8,3,5,6,2,4]=>[3,1,1,1,1,1]
[1,5,7,8,3,4,6,2]=>[3,1,1,1,1,1]
[1,3,7,8,2,5,6,4]=>[3,1,1,1,1,1]
[3,1,7,8,5,2,6,4]=>[3,2,2,1]
[1,3,7,5,8,2,6,4]=>[3,2,1,1,1]
[3,1,7,5,8,2,6,4]=>[3,2,2,1]
[3,5,7,1,8,4,6,2]=>[3,2,1,1,1]
[3,5,7,8,1,4,6,2]=>[3,1,1,1,1,1]
[5,3,7,8,4,6,1,2]=>[3,2,1,1,1]
[5,3,7,1,8,4,6,2]=>[3,3,1,1]
[1,5,3,7,8,4,2,6]=>[3,2,1,1,1]
[3,6,2,1,4,5,8,7]=>[3,2,1,1,1]
[4,6,2,5,1,3,8,7]=>[3,2,1,1,1]
[6,4,2,5,1,3,8,7]=>[4,2,1,1]
[8,6,1,7,3,2,4,5]=>[4,2,1,1]
[2,5,8,1,7,3,4,6]=>[3,1,1,1,1,1]
[6,8,2,7,3,1,4,5]=>[4,1,1,1,1]
[6,8,2,3,7,1,4,5]=>[3,1,1,1,1,1]
[8,6,2,7,4,5,1,3]=>[4,2,1,1]
[5,2,8,1,7,3,4,6]=>[3,2,1,1,1]
[4,2,3,8,1,5,6,7]=>[3,1,1,1,1,1]
[5,2,8,3,7,1,4,6]=>[3,2,1,1,1]
[5,2,8,4,6,1,3,7]=>[3,2,1,1,1]
[2,1,5,8,4,3,6,7]=>[3,2,1,1,1]
[5,8,3,2,7,1,4,6]=>[4,1,1,1,1]
[4,1,3,8,2,5,6,7]=>[3,1,1,1,1,1]
[3,5,8,2,7,1,4,6]=>[3,1,1,1,1,1]
[4,5,8,2,6,1,3,7]=>[3,1,1,1,1,1]
[2,6,8,3,7,1,4,5]=>[3,1,1,1,1,1]
[5,1,8,3,7,2,4,6]=>[3,2,1,1,1]
[5,1,8,4,6,2,3,7]=>[3,2,1,1,1]
[5,8,4,1,6,2,3,7]=>[3,2,1,1,1]
[4,5,8,1,6,2,3,7]=>[3,1,1,1,1,1]
[5,4,8,1,6,2,3,7]=>[3,2,1,1,1]
[4,8,5,1,6,2,3,7]=>[3,2,1,1,1]
[2,1,5,4,8,3,6,7]=>[3,2,1,1,1]
[2,4,3,8,1,5,6,7]=>[3,1,1,1,1,1]
[3,1,8,4,2,5,6,7]=>[3,2,1,1,1]
[3,8,4,2,1,5,6,7]=>[4,1,1,1,1]
[2,3,8,4,1,5,6,7]=>[3,1,1,1,1,1]
[3,4,2,8,1,5,6,7]=>[3,1,1,1,1,1]
[3,8,5,2,7,1,4,6]=>[4,1,1,1,1]
[4,8,5,2,6,1,3,7]=>[4,1,1,1,1]
[2,1,4,8,5,3,6,7]=>[3,2,1,1,1]
[3,2,8,4,1,5,6,7]=>[3,2,1,1,1]
[2,8,4,3,1,5,6,7]=>[4,1,1,1,1]
[5,7,4,3,8,2,6,1]=>[5,1,1,1]
[3,8,4,2,6,7,5,1]=>[4,2,1,1]
[6,1,7,5,2,8,4,3]=>[4,2,2]
[2,6,7,5,3,8,4,1]=>[4,2,1,1]
[6,7,4,8,2,5,3,1]=>[4,2,1,1]
[2,1,6,7,5,3,8,4]=>[3,2,2,1]
[3,8,4,2,1,6,7,5]=>[4,2,1,1]
[6,7,5,8,1,2,4,3]=>[4,1,1,1,1]
[3,4,8,1,2,5,7,6]=>[3,1,1,1,1,1]
[6,1,3,4,8,2,5,7]=>[3,1,1,1,1,1]
[6,2,3,4,8,1,5,7]=>[3,1,1,1,1,1]
[6,7,4,8,2,3,5,1]=>[4,1,1,1,1]
[2,6,7,5,1,3,8,4]=>[3,2,1,1,1]
[6,7,4,8,1,3,2,5]=>[4,1,1,1,1]
[6,7,5,8,4,1,3,2]=>[5,1,1,1]
[6,7,4,8,2,1,3,5]=>[4,1,1,1,1]
[1,4,3,6,5,8,2,7]=>[3,2,1,1,1]
[6,7,8,2,3,5,4,1]=>[4,1,1,1,1]
[5,8,6,2,3,7,4,1]=>[4,2,1,1]
[1,8,3,4,7,6,2,5]=>[4,1,1,1,1]
[8,7,2,3,6,5,4,1]=>[6,1,1]
[3,8,1,7,5,2,6,4]=>[4,2,1,1]
[4,8,1,6,7,2,5,3]=>[4,1,1,1,1]
[2,1,3,8,4,6,5,7]=>[3,2,1,1,1]
[1,3,2,8,5,4,6,7]=>[3,2,1,1,1]
[8,3,1,5,7,2,6,4]=>[4,2,1,1]
[1,5,6,8,7,4,2,3]=>[4,1,1,1,1]
[2,4,8,5,7,3,6,1]=>[4,1,1,1,1]
[4,3,8,6,5,7,2,1]=>[5,2,1]
[4,2,8,6,7,3,5,1]=>[4,2,1,1]
[3,1,8,7,5,6,2,4]=>[4,2,1,1]
[5,1,7,8,6,4,2,3]=>[4,2,1,1]
[7,8,3,2,6,1,4,5]=>[4,1,1,1,1]
[3,4,8,2,6,1,7,5]=>[3,2,1,1,1]
[7,8,4,1,5,6,3,2]=>[4,2,1,1]
[7,8,1,4,5,6,3,2]=>[4,1,1,1,1]
[7,8,1,2,6,3,4,5]=>[3,1,1,1,1,1]
[7,8,5,1,4,6,3,2]=>[5,1,1,1]
[7,8,4,5,1,6,3,2]=>[4,2,1,1]
[5,3,8,4,1,6,7,2]=>[3,2,2,1]
[6,2,4,8,1,5,3,7]=>[3,2,1,1,1]
[3,4,8,5,1,6,7,2]=>[3,2,1,1,1]
[3,5,8,1,4,6,7,2]=>[3,1,1,1,1,1]
[1,4,8,2,6,3,7,5]=>[3,2,1,1,1]
[5,3,8,1,4,6,7,2]=>[3,2,1,1,1]
[4,2,6,8,1,5,3,7]=>[3,2,1,1,1]
[7,4,2,8,1,5,3,6]=>[4,2,1,1]
[6,1,7,5,8,4,3,2]=>[5,2,1]
[6,2,1,8,4,5,3,7]=>[3,3,1,1]
[1,2,7,8,5,3,4,6]=>[3,1,1,1,1,1]
[6,3,7,8,5,4,1,2]=>[4,2,1,1]
[6,1,5,7,8,4,3,2]=>[5,1,1,1]
[1,7,5,6,8,4,3,2]=>[5,1,1,1]
[3,1,8,4,5,6,7,2]=>[3,2,1,1,1]
[2,1,4,8,6,5,3,7]=>[4,2,1,1]
[2,4,1,8,6,5,3,7]=>[4,2,1,1]
[4,2,1,8,6,5,3,7]=>[4,3,1]
[3,2,7,8,5,1,4,6]=>[3,2,1,1,1]
[2,3,7,8,5,1,4,6]=>[3,1,1,1,1,1]
[2,7,3,8,5,1,4,6]=>[3,2,1,1,1]
[3,6,2,8,5,1,4,7]=>[3,2,1,1,1]
[4,1,2,8,7,5,3,6]=>[4,2,1,1]
[1,4,2,8,7,5,3,6]=>[4,2,1,1]
[7,3,6,8,5,4,1,2]=>[5,1,1,1]
[7,2,1,8,5,3,4,6]=>[3,3,1,1]
[1,2,6,8,4,5,3,7]=>[3,1,1,1,1,1]
[7,1,6,5,8,4,3,2]=>[6,1,1]
[6,5,7,1,8,4,3,2]=>[5,2,1]
[5,7,6,1,8,4,3,2]=>[5,2,1]
[6,7,1,5,8,4,3,2]=>[5,1,1,1]
[6,7,3,8,5,4,1,2]=>[4,2,1,1]
[7,1,2,8,4,5,3,6]=>[3,2,1,1,1]
[7,6,1,5,8,4,3,2]=>[6,1,1]
[7,5,6,1,8,4,3,2]=>[5,2,1]
[7,1,6,5,3,2,4,8]=>[5,1,1,1]
[1,8,7,5,3,2,4,6]=>[5,1,1,1]
[1,8,7,4,2,5,3,6]=>[4,2,1,1]
[8,7,4,2,5,3,6,1]=>[5,2,1]
[7,1,6,4,2,5,3,8]=>[4,2,1,1]
[2,6,5,4,7,1,3,8]=>[4,1,1,1,1]
[7,1,5,3,6,4,2,8]=>[4,2,1,1]
[5,3,7,1,6,4,2,8]=>[4,2,1,1]
[5,3,6,4,2,7,1,8]=>[4,2,1,1]
[1,5,3,8,7,4,2,6]=>[4,2,1,1]
[7,4,2,8,6,3,5,1]=>[4,3,1]
[5,3,6,1,8,7,4,2]=>[4,3,1]
[6,1,5,3,8,7,4,2]=>[4,3,1]
[2,8,7,5,4,6,1,3]=>[5,1,1,1]
[2,3,1,8,7,5,4,6]=>[4,2,1,1]
[5,3,8,7,4,2,1,6]=>[5,2,1]
[7,4,2,1,8,6,3,5]=>[4,3,1]
[8,6,3,5,7,4,2,1]=>[6,1,1]
[1,8,6,3,5,7,4,2]=>[5,1,1,1]
[6,3,8,5,2,1,7,4]=>[4,2,2]
[8,6,3,7,4,2,1,5]=>[5,2,1]
[2,8,6,4,7,5,1,3]=>[4,2,1,1]
[5,1,8,6,3,7,4,2]=>[4,2,2]
[6,3,7,4,1,8,5,2]=>[3,3,2]
[8,5,2,6,3,7,4,1]=>[4,2,2]
[6,1,8,7,4,2,5,3]=>[4,2,2]
[8,6,3,7,4,2,5,1]=>[5,2,1]
[1,8,6,3,2,4,7,5]=>[4,2,1,1]
[8,6,3,2,4,7,5,1]=>[5,2,1]
[7,5,1,8,6,3,2,4]=>[4,3,1]
[6,1,8,7,5,3,2,4]=>[5,2,1]
[4,3,2,8,7,6,1,5]=>[4,3,1]
[2,4,5,1,3,8,7,6]=>[3,2,1,1,1]
[7,5,8,6,3,2,4,1]=>[5,2,1]
[1,7,5,8,6,3,2,4]=>[4,2,1,1]
[1,7,4,2,5,8,6,3]=>[3,3,1,1]
[8,6,3,1,7,4,2,5]=>[4,3,1]
[8,7,4,2,5,3,1,6]=>[5,2,1]
[5,3,1,8,7,4,2,6]=>[4,3,1]
[4,1,8,7,5,3,2,6]=>[5,2,1]
[2,8,6,4,1,3,7,5]=>[4,2,1,1]
[4,1,8,6,3,2,7,5]=>[4,2,2]
[7,4,2,8,6,3,1,5]=>[4,3,1]
[6,3,1,8,5,2,7,4]=>[3,3,2]
[8,5,2,6,3,1,7,4]=>[4,2,2]
[7,4,8,5,2,6,3,1]=>[4,2,2]
[1,8,5,2,7,4,6,3]=>[4,2,1,1]
[8,5,2,7,4,6,3,1]=>[5,2,1]
[7,4,6,3,1,8,5,2]=>[4,3,1]
[6,3,1,7,4,8,5,2]=>[3,3,2]
[8,6,3,1,5,7,4,2]=>[5,2,1]
[4,1,7,5,8,6,3,2]=>[4,2,2]
[2,3,1,7,5,8,6,4]=>[3,2,2,1]
[7,4,8,5,2,1,6,3]=>[4,2,2]
[8,5,2,1,7,4,6,3]=>[4,3,1]
[1,7,4,6,3,8,5,2]=>[4,2,1,1]
[3,6,5,2,1,4,8,7]=>[4,2,1,1]
[3,5,6,2,1,4,8,7]=>[3,2,1,1,1]
[3,5,7,8,1,4,2,6]=>[3,1,1,1,1,1]
[4,1,8,5,7,3,2,6]=>[4,2,1,1]
[4,1,7,5,8,3,2,6]=>[4,2,1,1]
[2,1,5,8,7,4,3,6]=>[4,2,1,1]
[2,1,5,7,8,4,3,6]=>[3,2,1,1,1]
[5,1,7,4,8,3,2,6]=>[4,2,1,1]
[4,7,2,8,3,6,1,5]=>[3,2,1,1,1]
[4,6,2,7,3,1,8,5]=>[3,2,2,1]
[3,7,8,2,4,1,6,5]=>[3,2,1,1,1]
[3,8,7,2,4,1,6,5]=>[4,2,1,1]
[3,8,6,2,4,1,7,5]=>[4,2,1,1]
[6,2,8,4,1,7,3,5]=>[3,2,2,1]
[6,3,4,8,1,7,2,5]=>[3,2,1,1,1]
[1,8,5,4,2,3,7,6]=>[4,2,1,1]
[3,5,4,8,1,2,7,6]=>[3,2,1,1,1]
[5,6,3,8,7,1,2,4]=>[3,2,1,1,1]
[2,6,8,4,1,7,3,5]=>[3,2,1,1,1]
[1,8,7,4,2,6,3,5]=>[4,2,1,1]
[5,7,3,8,6,1,2,4]=>[3,2,1,1,1]
[1,8,7,5,6,2,3,4]=>[4,1,1,1,1]
[6,3,5,8,7,1,2,4]=>[3,2,1,1,1]
[5,2,8,6,7,1,3,4]=>[3,2,1,1,1]
[6,2,8,7,5,1,3,4]=>[4,2,1,1]
[1,8,5,7,6,2,3,4]=>[4,1,1,1,1]
[3,6,7,8,5,1,2,4]=>[3,1,1,1,1,1]
[1,8,6,7,5,2,3,4]=>[4,1,1,1,1]
[5,7,6,4,8,1,2,3]=>[4,1,1,1,1]
[6,3,8,7,5,1,2,4]=>[4,2,1,1]
[2,8,7,4,1,3,5,6]=>[4,1,1,1,1]
[5,4,8,7,1,3,2,6]=>[4,2,1,1]
[4,8,6,1,3,2,5,7]=>[4,1,1,1,1]
[5,4,2,7,6,8,1,3]=>[4,2,1,1]
[2,8,7,1,4,5,3,6]=>[4,1,1,1,1]
[4,2,1,8,7,3,5,6]=>[3,3,1,1]
[5,1,6,3,2,8,7,4]=>[3,3,2]
[4,6,1,8,7,3,2,5]=>[4,2,1,1]
[8,7,2,3,5,4,1,6]=>[5,1,1,1]
[5,3,1,4,8,7,2,6]=>[3,3,1,1]
[4,3,5,2,8,7,1,6]=>[4,2,1,1]
[3,4,2,8,6,1,5,7]=>[3,2,1,1,1]
[3,7,6,8,1,5,2,4]=>[4,1,1,1,1]
[8,1,4,2,3,6,7,5]=>[3,2,1,1,1]
[3,7,2,1,8,6,4,5]=>[3,3,1,1]
[2,8,6,1,7,3,5,4]=>[4,2,1,1]
[1,7,6,3,5,8,2,4]=>[4,1,1,1,1]
[3,7,5,1,6,8,2,4]=>[3,2,1,1,1]
[3,6,5,8,1,4,7,2]=>[4,1,1,1,1]
[8,1,5,6,4,7,2,3]=>[4,1,1,1,1]
[3,6,7,4,1,8,2,5]=>[3,2,1,1,1]
[1,7,4,6,8,2,5,3]=>[4,1,1,1,1]
[7,5,8,2,6,3,1,4]=>[4,2,1,1]
[2,7,1,6,5,4,8,3]=>[5,1,1,1]
[7,3,2,6,1,8,5,4]=>[4,3,1]
[6,4,7,2,3,1,8,5]=>[4,2,1,1]
[5,3,1,8,4,6,2,7]=>[3,3,1,1]
[3,8,1,6,7,4,2,5]=>[4,1,1,1,1]
[2,7,4,3,6,8,1,5]=>[4,1,1,1,1]
[2,8,4,6,1,5,3,7]=>[4,1,1,1,1]
[8,4,1,6,3,2,5,7]=>[4,2,1,1]
[4,7,3,8,5,2,1,6]=>[4,2,1,1]
[3,1,7,4,8,5,2,6]=>[3,2,2,1]
[7,4,1,6,3,2,8,5]=>[4,2,2]
[3,8,6,2,7,4,1,5]=>[4,2,1,1]
[7,3,1,4,5,2,8,6]=>[3,2,2,1]
[6,1,4,8,5,3,2,7]=>[4,2,1,1]
[8,1,2,4,6,7,5,3]=>[4,1,1,1,1]
[8,1,3,6,7,5,4,2]=>[5,1,1,1]
[7,5,2,3,8,6,1,4]=>[4,2,1,1]
[8,6,2,4,1,3,7,5]=>[4,2,1,1]
[4,7,5,1,8,6,3,2]=>[4,3,1]
[4,7,3,2,8,5,6,1]=>[4,2,1,1]
[8,4,5,7,6,1,3,2]=>[5,1,1,1]
[7,5,8,4,2,3,6,1]=>[5,1,1,1]
[3,8,4,6,1,7,5,2]=>[4,2,1,1]
[3,7,4,6,5,2,8,1]=>[5,1,1,1]
[4,2,7,6,1,5,8,3]=>[4,2,1,1]
[8,3,1,4,5,7,6,2]=>[4,2,1,1]
[3,5,1,6,8,4,7,2]=>[3,2,1,1,1]
[6,1,5,7,3,8,4,2]=>[4,2,1,1]
[5,8,4,7,3,2,6,1]=>[5,1,1,1]
[7,2,6,5,8,4,1,3]=>[5,1,1,1]
[8,3,2,5,1,6,7,4]=>[4,2,1,1]
[2,6,8,3,7,4,1,5]=>[4,1,1,1,1]
[8,1,5,6,4,7,3,2]=>[5,1,1,1]
[2,5,8,1,6,4,7,3]=>[4,1,1,1,1]
[7,4,1,8,3,2,6,5]=>[4,2,2]
[8,3,7,4,2,1,6,5]=>[5,2,1]
[5,2,6,8,3,1,7,4]=>[3,2,2,1]
[3,6,5,8,4,1,7,2]=>[4,2,1,1]
[7,3,6,1,8,4,5,2]=>[4,2,1,1]
[8,2,7,3,4,6,5,1]=>[5,1,1,1]
[7,3,8,2,5,6,4,1]=>[4,2,1,1]
[5,7,3,1,6,4,8,2]=>[4,2,1,1]
[6,1,3,2,4,8,7,5]=>[3,3,1,1]
[8,7,4,2,3,6,1,5]=>[5,1,1,1]
[8,7,1,5,4,2,3,6]=>[5,1,1,1]
[3,7,1,5,2,8,6,4]=>[3,3,1,1]
[8,7,2,5,4,1,3,6]=>[5,1,1,1]
[8,7,2,5,3,1,4,6]=>[5,1,1,1]
[5,2,8,7,1,4,3,6]=>[4,2,1,1]
[7,1,8,6,2,4,3,5]=>[4,2,1,1]
[8,1,6,2,7,5,3,4]=>[4,2,1,1]
[7,1,6,2,8,5,3,4]=>[4,2,1,1]
[6,3,4,1,7,2,8,5]=>[3,2,2,1]
[7,2,4,3,5,1,8,6]=>[4,2,1,1]
[5,1,7,2,3,8,6,4]=>[3,2,2,1]
[8,2,3,5,1,7,6,4]=>[4,2,1,1]
[7,6,3,1,4,8,2,5]=>[4,2,1,1]
[6,1,8,2,7,5,3,4]=>[4,2,1,1]
[7,2,8,1,6,5,3,4]=>[4,2,1,1]
[7,2,6,4,3,8,1,5]=>[5,1,1,1]
[5,1,7,4,3,8,2,6]=>[4,2,1,1]
[5,3,1,7,4,8,2,6]=>[3,3,1,1]
[7,4,8,2,1,5,3,6]=>[4,2,1,1]
[8,2,4,1,6,3,7,5]=>[3,2,2,1]
[8,2,7,5,1,6,4,3]=>[5,2,1]
[6,1,7,3,2,8,5,4]=>[3,3,2]
[4,7,2,1,6,3,8,5]=>[3,2,2,1]
[6,2,1,5,3,8,4,7]=>[3,2,2,1]
[5,3,1,6,2,8,4,7]=>[3,2,2,1]
[6,1,5,2,8,4,3,7]=>[4,2,1,1]
[7,4,3,8,1,5,2,6]=>[4,2,1,1]
[7,4,8,1,5,3,2,6]=>[4,2,1,1]
[6,1,5,3,2,8,4,7]=>[4,2,1,1]
[6,3,2,8,4,1,5,7]=>[4,2,1,1]
[7,3,4,2,8,5,1,6]=>[4,2,1,1]
[7,1,6,3,4,2,8,5]=>[4,2,1,1]
[8,5,1,3,7,4,2,6]=>[4,2,1,1]
[3,8,6,1,5,2,7,4]=>[4,2,1,1]
[8,6,1,3,7,5,2,4]=>[4,2,1,1]
[4,8,5,6,1,7,3,2]=>[4,2,1,1]
[6,7,1,3,8,5,2,4]=>[3,2,1,1,1]
[3,6,7,1,5,2,8,4]=>[3,2,1,1,1]
[7,1,3,8,4,2,6,5]=>[3,2,2,1]
[5,6,2,7,1,3,8,4]=>[3,2,1,1,1]
[5,6,2,8,1,3,7,4]=>[3,2,1,1,1]
[6,1,8,3,7,5,2,4]=>[4,2,1,1]
[7,4,2,1,5,8,3,6]=>[4,2,1,1]
[7,4,1,5,8,3,2,6]=>[4,2,1,1]
[7,3,2,6,4,8,1,5]=>[4,2,1,1]
[6,4,2,7,3,8,1,5]=>[4,2,1,1]
[5,1,8,3,7,4,2,6]=>[4,2,1,1]
[7,4,8,3,1,5,2,6]=>[4,2,1,1]
[5,2,1,7,4,8,3,6]=>[3,3,1,1]
[6,1,8,4,5,2,7,3]=>[3,2,2,1]
[7,1,6,4,5,2,8,3]=>[4,2,1,1]
[3,5,2,7,1,6,8,4]=>[3,2,1,1,1]
[4,5,7,3,1,6,8,2]=>[3,2,1,1,1]
[4,5,7,2,8,6,1,3]=>[3,2,1,1,1]
[3,5,1,7,2,6,8,4]=>[3,2,1,1,1]
[4,5,7,2,8,1,3,6]=>[3,1,1,1,1,1]
[4,6,7,2,1,5,8,3]=>[3,2,1,1,1]
[4,6,7,1,3,8,5,2]=>[3,2,1,1,1]
[3,6,1,5,7,8,4,2]=>[4,1,1,1,1]
[4,6,7,1,5,8,3,2]=>[4,1,1,1,1]
[6,1,3,7,4,8,5,2]=>[3,2,2,1]
[3,2,1,7,4,8,5,6]=>[3,2,2,1]
[4,1,5,2,7,6,3,8]=>[3,2,2,1]
[2,5,1,3,7,6,4,8]=>[3,2,1,1,1]
[2,5,1,4,3,8,6,7]=>[3,2,1,1,1]
[3,7,2,1,5,8,6,4]=>[3,3,1,1]
[6,2,7,1,4,8,5,3]=>[3,3,1,1]
[3,7,4,2,1,8,5,6]=>[4,2,1,1]
[7,2,5,3,1,8,6,4]=>[4,3,1]
[7,5,1,4,2,8,6,3]=>[4,3,1]
[7,5,4,1,3,8,6,2]=>[5,2,1]
[5,3,2,1,7,6,4,8]=>[4,3,1]
[6,3,2,8,1,5,7,4]=>[4,2,1,1]
[7,4,3,2,8,1,6,5]=>[5,2,1]
[7,6,2,4,8,3,5,1]=>[5,1,1,1]
[7,3,6,4,8,1,5,2]=>[4,2,1,1]
[2,7,5,3,8,1,4,6]=>[4,1,1,1,1]
[1,8,5,3,6,4,2,7]=>[4,2,1,1]
[8,6,2,3,7,5,4,1]=>[5,2,1]
[8,6,3,2,7,5,4,1]=>[5,3]
[8,3,2,7,1,6,4,5]=>[4,2,1,1]
[7,2,6,1,5,4,3,8]=>[5,1,1,1]
[8,5,7,4,3,6,2,1]=>[6,1,1]
[8,5,7,2,4,6,3,1]=>[5,1,1,1]
[8,4,6,7,1,3,2,5]=>[4,1,1,1,1]
[2,8,5,6,1,4,3,7]=>[4,1,1,1,1]
[7,2,6,8,4,1,5,3]=>[4,2,1,1]
[7,6,4,8,3,2,5,1]=>[6,1,1]
[6,5,8,1,4,2,7,3]=>[4,2,1,1]
[6,5,8,4,1,3,7,2]=>[5,1,1,1]
[5,4,8,3,2,1,7,6]=>[5,2,1]
[4,3,7,2,1,6,5,8]=>[4,2,1,1]
[2,5,8,1,4,3,7,6]=>[3,2,1,1,1]
[3,6,8,2,1,5,7,4]=>[3,2,1,1,1]
[5,7,4,8,1,3,6,2]=>[4,1,1,1,1]
[5,7,1,4,8,2,6,3]=>[3,2,1,1,1]
[2,7,4,1,8,3,6,5]=>[3,3,1,1]
[3,5,1,8,4,2,7,6]=>[3,2,2,1]
[4,1,5,7,3,6,2,8]=>[3,2,1,1,1]
[4,2,5,8,3,1,7,6]=>[3,2,2,1]
[6,1,2,7,8,3,5,4]=>[3,2,1,1,1]
[5,3,1,8,6,4,2,7]=>[4,3,1]
[3,1,8,4,7,5,2,6]=>[4,2,1,1]
[4,2,8,7,3,5,1,6]=>[4,2,1,1]
[4,8,1,7,6,2,3,5]=>[4,1,1,1,1]
[6,8,1,4,7,5,2,3]=>[4,1,1,1,1]
[7,3,8,1,6,4,2,5]=>[4,2,1,1]
[4,7,8,1,5,3,2,6]=>[4,1,1,1,1]
[7,1,8,6,2,5,3,4]=>[4,2,1,1]
[5,8,7,1,3,6,4,2]=>[5,1,1,1]
[3,8,7,2,1,6,4,5]=>[4,2,1,1]
[2,8,7,1,6,3,5,4]=>[5,1,1,1]
[3,7,6,1,5,4,2,8]=>[5,1,1,1]
[4,8,7,6,1,3,5,2]=>[5,1,1,1]
[5,8,7,2,6,1,4,3]=>[5,1,1,1]
[6,8,1,7,5,2,4,3]=>[5,1,1,1]
[7,3,8,6,5,1,2,4]=>[4,2,1,1]
[5,7,8,4,3,1,2,6]=>[4,1,1,1,1]
[5,8,6,4,3,2,1,7]=>[6,1,1]
[8,7,3,6,4,2,1,5]=>[6,1,1]
[6,1,4,2,5,3,7,8]=>[3,2,1,1,1]
[1,3,7,5,4,2,8,6]=>[4,2,1,1]
[6,1,3,5,4,2,7,8]=>[4,1,1,1,1]
[6,1,2,5,4,7,3,8]=>[4,1,1,1,1]
[5,1,6,3,4,7,8,2]=>[3,2,1,1,1]
[5,2,6,3,4,7,1,8]=>[3,2,1,1,1]
[3,4,7,5,8,6,1,2]=>[3,2,1,1,1]
[2,4,7,1,5,3,8,6]=>[3,2,1,1,1]
[2,3,6,7,4,8,1,5]=>[3,1,1,1,1,1]
[1,3,6,7,4,8,5,2]=>[3,2,1,1,1]
[2,7,6,5,3,1,8,4]=>[5,2,1]
[5,2,6,1,4,7,8,3]=>[3,2,1,1,1]
[4,7,6,5,2,1,8,3]=>[5,2,1]
[5,3,6,2,4,1,7,8]=>[4,1,1,1,1]
[5,7,4,2,1,3,6,8]=>[4,1,1,1,1]
[6,3,1,5,4,7,8,2]=>[4,2,1,1]
[5,3,6,1,4,2,7,8]=>[3,2,1,1,1]
[1,7,4,2,6,3,8,5]=>[3,2,2,1]
[5,7,4,1,2,3,6,8]=>[3,1,1,1,1,1]
[6,4,1,2,5,3,7,8]=>[3,2,1,1,1]
[4,7,6,3,8,5,1,2]=>[4,2,1,1]
[3,7,6,5,2,8,1,4]=>[5,1,1,1]
[3,7,6,5,1,2,8,4]=>[4,2,1,1]
[4,7,2,6,1,3,8,5]=>[3,2,1,1,1]
[2,7,1,6,8,3,5,4]=>[4,1,1,1,1]
[2,7,6,5,8,1,4,3]=>[5,1,1,1]
[5,2,8,7,6,4,3,1]=>[6,2]
[8,2,7,6,1,5,4,3]=>[6,1,1]
[8,4,1,7,6,5,3,2]=>[6,2]
[4,5,6,2,3,8,1,7]=>[3,1,1,1,1,1]
[4,5,3,2,7,8,1,6]=>[4,1,1,1,1]
[6,5,7,3,8,4,2,1]=>[5,2,1]
[6,8,7,2,4,3,5,1]=>[5,1,1,1]
[3,2,7,4,5,8,1,6]=>[3,2,1,1,1]
[6,8,1,5,2,4,3,7]=>[4,1,1,1,1]
[8,3,4,6,1,5,2,7]=>[4,1,1,1,1]
[2,3,4,7,5,8,1,6]=>[3,1,1,1,1,1]
[6,3,4,7,8,2,5,1]=>[4,1,1,1,1]
[5,3,7,4,8,6,1,2]=>[3,2,2,1]
[8,3,6,4,1,7,2,5]=>[4,2,1,1]
[1,3,7,4,8,6,2,5]=>[3,2,1,1,1]
[3,7,8,5,4,1,2,6]=>[4,1,1,1,1]
[5,4,3,1,7,8,2,6]=>[4,2,1,1]
[5,7,6,2,8,4,1,3]=>[4,2,1,1]
[6,1,7,5,8,3,4,2]=>[4,2,1,1]
[7,5,6,4,1,3,8,2]=>[5,1,1,1]
[1,5,6,8,4,7,3,2]=>[4,1,1,1,1]
[4,1,3,7,6,5,8,2]=>[4,2,1,1]
[3,4,1,7,5,8,6,2]=>[3,2,2,1]
[8,5,7,4,3,1,6,2]=>[5,2,1]
[6,8,5,1,7,2,4,3]=>[4,2,1,1]
[8,2,4,1,3,7,6,5]=>[4,2,1,1]
[7,8,3,6,2,1,4,5]=>[4,1,1,1,1]
[8,1,7,4,2,3,6,5]=>[4,2,1,1]
[1,8,7,2,3,5,6,4]=>[4,1,1,1,1]
[2,8,3,1,6,7,5,4]=>[4,2,1,1]
[8,2,3,1,5,7,6,4]=>[4,2,1,1]
[3,8,4,1,2,7,6,5]=>[4,2,1,1]
[5,4,7,2,3,6,8,1]=>[4,1,1,1,1]
[6,3,2,1,8,4,7,5]=>[4,3,1]
[2,3,7,4,1,8,5,6]=>[3,2,1,1,1]
[6,4,1,3,2,7,8,5]=>[4,2,1,1]
[2,7,8,5,1,3,6,4]=>[3,2,1,1,1]
[8,2,5,6,7,1,3,4]=>[3,1,1,1,1,1]
[2,8,5,4,7,6,1,3]=>[4,2,1,1]
[6,7,1,5,8,2,4,3]=>[4,1,1,1,1]
[4,8,7,6,2,3,5,1]=>[5,1,1,1]
[7,8,1,5,3,2,6,4]=>[4,2,1,1]
[6,5,7,3,8,2,1,4]=>[5,1,1,1]
[8,1,4,7,2,5,6,3]=>[4,1,1,1,1]
[7,3,4,6,1,5,8,2]=>[4,1,1,1,1]
[8,3,4,5,7,1,6,2]=>[4,1,1,1,1]
[4,2,6,8,3,1,5,7]=>[3,2,1,1,1]
[3,7,6,2,4,5,1,8]=>[4,1,1,1,1]
[2,3,6,5,8,1,4,7]=>[3,1,1,1,1,1]
[2,3,5,8,6,1,4,7]=>[3,1,1,1,1,1]
[4,2,3,8,6,1,5,7]=>[3,2,1,1,1]
[6,4,1,2,8,3,5,7]=>[3,2,1,1,1]
[1,2,3,7,4,6,8,5]=>[3,1,1,1,1,1]
[3,2,7,1,4,5,8,6]=>[3,2,1,1,1]
[2,1,5,3,8,7,4,6]=>[3,2,2,1]
[5,8,3,2,4,1,6,7]=>[4,1,1,1,1]
[4,2,7,1,8,3,5,6]=>[3,2,1,1,1]
[4,1,8,2,7,3,5,6]=>[3,2,1,1,1]
[1,2,7,5,3,8,4,6]=>[3,2,1,1,1]
[3,2,7,1,4,8,5,6]=>[3,2,1,1,1]
[1,2,3,7,6,8,4,5]=>[3,1,1,1,1,1]
[1,2,3,6,8,7,4,5]=>[3,1,1,1,1,1]
[1,2,3,7,8,4,6,5]=>[3,1,1,1,1,1]
[1,2,3,6,8,4,7,5]=>[3,1,1,1,1,1]
[1,2,3,7,8,6,4,5]=>[3,1,1,1,1,1]
[6,2,8,3,7,5,1,4]=>[4,2,1,1]
[4,2,8,3,7,5,6,1]=>[4,2,1,1]
[7,3,4,8,6,5,1,2]=>[4,2,1,1]
[5,3,4,8,7,2,6,1]=>[4,2,1,1]
[4,3,5,8,7,2,6,1]=>[4,2,1,1]
[4,6,3,8,5,7,2,1]=>[4,2,1,1]
[7,5,3,8,6,2,4,1]=>[5,2,1]
[2,6,8,3,7,4,5,1]=>[4,1,1,1,1]
[1,8,4,3,7,5,6,2]=>[4,2,1,1]
[2,5,8,3,7,4,6,1]=>[4,1,1,1,1]
[7,4,3,8,6,2,5,1]=>[5,2,1]
[3,5,4,8,7,2,6,1]=>[4,2,1,1]
[4,5,3,8,6,7,2,1]=>[4,2,1,1]
[3,6,7,8,4,5,2,1]=>[4,1,1,1,1]
[2,6,8,5,4,7,3,1]=>[5,1,1,1]
[1,8,5,6,4,7,3,2]=>[5,1,1,1]
[2,5,8,6,4,7,3,1]=>[5,1,1,1]
[7,4,6,5,8,3,2,1]=>[6,1,1]
[6,3,7,8,4,5,2,1]=>[4,2,1,1]
[4,3,7,8,5,6,2,1]=>[4,2,1,1]
[5,2,8,6,4,7,3,1]=>[5,2,1]
[4,2,8,6,5,7,3,1]=>[5,2,1]
[3,2,8,6,7,4,5,1]=>[4,2,1,1]
[2,3,8,7,5,4,6,1]=>[5,1,1,1]
[1,8,2,7,4,5,6,3]=>[4,1,1,1,1]
[7,2,8,6,3,4,5,1]=>[4,2,1,1]
[6,2,8,4,5,7,3,1]=>[4,2,1,1]
[5,2,8,4,6,7,3,1]=>[4,2,1,1]
[4,2,8,5,6,7,3,1]=>[4,2,1,1]
[4,3,6,8,5,7,2,1]=>[4,2,1,1]
[3,4,6,8,7,2,5,1]=>[4,1,1,1,1]
[7,3,5,8,6,2,4,1]=>[4,2,1,1]
[1,8,3,5,7,4,6,2]=>[4,1,1,1,1]
[2,7,8,4,5,6,3,1]=>[4,1,1,1,1]
[3,7,5,8,4,6,2,1]=>[5,1,1,1]
[5,7,4,6,8,3,2,1]=>[5,1,1,1]
[3,6,5,8,4,7,2,1]=>[5,1,1,1]
[2,6,8,4,5,7,3,1]=>[4,1,1,1,1]
[4,2,7,1,3,8,5,6]=>[3,2,1,1,1]
[4,2,5,1,3,8,6,7]=>[3,2,1,1,1]
[5,3,6,1,7,2,4,8]=>[3,2,1,1,1]
[3,7,1,2,5,8,6,4]=>[3,2,1,1,1]
[3,7,4,1,2,8,5,6]=>[3,2,1,1,1]
[7,5,1,3,4,8,6,2]=>[4,2,1,1]
[7,5,1,2,4,8,6,3]=>[4,2,1,1]
[6,4,2,3,7,1,5,8]=>[4,1,1,1,1]
[7,6,3,8,1,2,5,4]=>[4,2,1,1]
[7,4,2,3,8,1,6,5]=>[4,2,1,1]
[4,7,5,2,8,1,3,6]=>[4,1,1,1,1]
[8,2,6,3,7,1,4,5]=>[4,1,1,1,1]
[8,6,1,2,7,4,5,3]=>[4,2,1,1]
[8,4,7,1,2,3,6,5]=>[4,1,1,1,1]
[8,5,7,1,2,4,6,3]=>[4,1,1,1,1]
[8,5,7,1,3,4,6,2]=>[4,1,1,1,1]
[8,6,2,7,1,3,5,4]=>[4,2,1,1]
[3,8,5,6,1,2,4,7]=>[3,1,1,1,1,1]
[3,7,5,8,1,2,4,6]=>[3,1,1,1,1,1]
[7,6,4,8,1,3,5,2]=>[5,1,1,1]
[6,5,8,1,2,4,7,3]=>[4,1,1,1,1]
[3,6,8,1,2,5,7,4]=>[3,1,1,1,1,1]
[3,7,2,4,8,1,6,5]=>[3,2,1,1,1]
[4,6,3,8,1,2,5,7]=>[3,1,1,1,1,1]
[4,6,3,7,1,2,5,8]=>[3,1,1,1,1,1]
[4,1,7,8,2,3,6,5]=>[3,2,1,1,1]
[5,1,2,8,6,3,4,7]=>[3,2,1,1,1]
[5,3,8,1,6,2,4,7]=>[3,2,1,1,1]
[6,1,8,5,2,3,4,7]=>[3,2,1,1,1]
[6,1,7,5,2,3,4,8]=>[3,2,1,1,1]
[6,8,1,3,7,4,5,2]=>[4,1,1,1,1]
[7,2,8,1,6,3,4,5]=>[3,2,1,1,1]
[4,7,8,2,5,1,3,6]=>[3,1,1,1,1,1]
[6,8,2,7,1,4,5,3]=>[4,1,1,1,1]
[4,8,7,1,3,5,6,2]=>[4,1,1,1,1]
[3,8,7,1,2,4,6,5]=>[4,1,1,1,1]
[4,8,7,1,2,3,6,5]=>[4,1,1,1,1]
[5,8,7,1,2,4,6,3]=>[4,1,1,1,1]
[5,8,7,1,3,4,6,2]=>[4,1,1,1,1]
[7,1,8,6,2,3,5,4]=>[4,2,1,1]
[5,8,6,4,1,2,3,7]=>[4,1,1,1,1]
[7,8,4,1,2,5,3,6]=>[3,2,1,1,1]
[7,8,1,2,6,5,3,4]=>[4,1,1,1,1]
[1,4,8,2,7,5,3,6]=>[4,1,1,1,1]
[6,1,3,4,7,2,5,8]=>[3,1,1,1,1,1]
[7,8,2,1,6,3,5,4]=>[4,2,1,1]
[6,1,2,7,5,4,3,8]=>[4,2,1,1]
[1,2,8,7,5,4,3,6]=>[5,1,1,1]
[5,1,7,3,6,4,8,2]=>[4,2,1,1]
[6,2,1,5,7,4,3,8]=>[4,2,1,1]
[6,2,3,7,4,1,5,8]=>[3,2,1,1,1]
[3,4,8,7,5,6,1,2]=>[4,1,1,1,1]
[2,3,8,7,4,1,5,6]=>[4,1,1,1,1]
[2,7,3,8,6,4,1,5]=>[4,2,1,1]
[1,8,3,7,6,4,5,2]=>[5,1,1,1]
[5,2,7,1,4,6,8,3]=>[3,2,1,1,1]
[4,6,7,5,2,1,8,3]=>[4,2,1,1]
[6,3,1,4,5,7,8,2]=>[3,2,1,1,1]
[5,3,1,4,6,2,7,8]=>[3,2,1,1,1]
[5,1,2,4,7,6,8,3]=>[3,2,1,1,1]
[5,7,4,1,2,6,3,8]=>[3,2,1,1,1]
[4,8,1,2,6,7,3,5]=>[3,1,1,1,1,1]
[4,1,7,8,2,6,3,5]=>[3,2,1,1,1]
[1,2,8,7,6,5,3,4]=>[5,1,1,1]
[3,1,2,4,6,8,7,5]=>[3,2,1,1,1]
[3,1,8,4,5,7,6,2]=>[4,2,1,1]
[3,2,8,5,4,7,1,6]=>[4,2,1,1]
[4,2,8,1,5,3,7,6]=>[3,2,2,1]
[4,3,8,5,7,6,1,2]=>[4,2,1,1]
[4,8,2,1,6,3,7,5]=>[3,2,2,1]
[3,8,6,5,2,7,1,4]=>[5,1,1,1]
[3,8,5,6,1,7,4,2]=>[4,2,1,1]
[3,5,7,8,1,2,6,4]=>[3,1,1,1,1,1]
[3,7,8,5,2,1,6,4]=>[4,2,1,1]
[3,7,2,8,4,1,6,5]=>[3,2,2,1]
[2,8,1,7,4,6,5,3]=>[5,1,1,1]
[2,8,7,5,1,6,4,3]=>[5,2,1]
[2,8,6,7,5,1,4,3]=>[5,1,1,1]
[8,2,4,1,7,3,5,6]=>[3,2,1,1,1]
[3,6,1,4,2,8,7,5]=>[3,3,1,1]
[6,1,7,4,3,8,2,5]=>[4,2,1,1]
[4,8,2,3,1,5,7,6]=>[3,2,1,1,1]
[2,7,4,1,8,3,5,6]=>[3,2,1,1,1]
[1,7,8,4,2,3,6,5]=>[3,2,1,1,1]
[4,7,1,3,8,2,6,5]=>[3,2,1,1,1]
[2,4,3,7,5,8,1,6]=>[3,2,1,1,1]
[1,8,3,4,2,6,7,5]=>[3,2,1,1,1]
[6,4,1,3,7,2,8,5]=>[4,2,1,1]
[8,1,4,3,6,2,7,5]=>[4,2,1,1]
[7,2,5,8,4,3,1,6]=>[5,1,1,1]
[6,1,8,3,4,2,7,5]=>[3,2,2,1]
[6,3,1,4,2,8,7,5]=>[3,3,2]
[7,3,8,1,2,6,4,5]=>[3,2,1,1,1]
[7,1,4,5,3,2,6,8]=>[4,1,1,1,1]
[1,8,4,2,6,5,3,7]=>[4,2,1,1]
[5,1,4,8,6,3,2,7]=>[4,2,1,1]
[5,3,1,8,4,7,2,6]=>[3,3,1,1]
[4,3,8,1,5,7,2,6]=>[3,2,1,1,1]
[6,3,1,2,5,7,4,8]=>[3,2,1,1,1]
[7,1,4,2,6,5,3,8]=>[4,2,1,1]
[3,8,4,1,6,5,2,7]=>[4,2,1,1]
[7,5,3,6,4,8,2,1]=>[5,2,1]
[7,3,6,4,5,8,2,1]=>[5,1,1,1]
[8,7,2,4,5,1,6,3]=>[4,2,1,1]
[7,1,5,4,8,6,3,2]=>[5,2,1]
[2,7,5,4,8,6,3,1]=>[5,2,1]
[2,1,8,7,5,3,6,4]=>[4,2,2]
[5,8,3,7,4,1,6,2]=>[4,2,1,1]
[8,1,7,4,2,6,5,3]=>[5,2,1]
[5,6,3,1,8,4,7,2]=>[3,3,1,1]
[5,7,1,4,8,6,3,2]=>[4,2,1,1]
[3,5,7,4,8,6,2,1]=>[4,2,1,1]
[2,6,7,4,5,8,3,1]=>[4,1,1,1,1]
[6,1,7,4,5,8,3,2]=>[4,2,1,1]
[5,3,7,4,8,6,2,1]=>[4,2,2]
[8,5,3,6,1,4,7,2]=>[4,2,1,1]
[5,4,3,6,8,2,7,1]=>[5,1,1,1]
[6,5,3,7,4,8,2,1]=>[5,2,1]
[7,5,8,4,1,6,3,2]=>[5,2,1]
[2,7,8,4,5,1,6,3]=>[3,2,1,1,1]
[5,7,3,8,4,1,6,2]=>[3,2,2,1]
[5,6,3,8,1,4,7,2]=>[3,2,1,1,1]
[8,4,1,2,5,6,7,3]=>[3,2,1,1,1]
[3,7,8,4,1,6,5,2]=>[4,2,1,1]
[6,8,3,1,2,5,7,4]=>[3,2,1,1,1]
[8,7,1,4,5,2,6,3]=>[4,2,1,1]
[8,7,3,1,5,4,2,6]=>[5,2,1]
[3,6,2,1,5,4,8,7]=>[3,2,2,1]
[5,4,2,6,1,3,8,7]=>[4,2,1,1]
[3,2,6,5,1,4,8,7]=>[3,2,2,1]
[2,5,8,1,7,4,3,6]=>[4,1,1,1,1]
[6,8,2,7,4,3,1,5]=>[5,1,1,1]
[6,8,2,3,7,5,1,4]=>[4,1,1,1,1]
[7,6,2,5,4,8,1,3]=>[5,1,1,1]
[2,6,5,1,8,4,3,7]=>[4,2,1,1]
[4,2,7,3,1,8,5,6]=>[3,2,2,1]
[4,2,3,7,1,5,8,6]=>[3,2,1,1,1]
[5,2,7,3,8,6,1,4]=>[3,2,2,1]
[2,1,5,8,4,3,7,6]=>[3,2,2,1]
[5,8,4,2,6,7,1,3]=>[4,1,1,1,1]
[3,2,4,8,1,5,7,6]=>[3,2,1,1,1]
[2,4,8,3,1,7,5,6]=>[3,2,1,1,1]
[4,8,3,2,1,7,6,5]=>[4,3,1]
[4,1,3,7,2,6,8,5]=>[3,2,1,1,1]
[3,4,8,2,1,6,5,7]=>[3,2,1,1,1]
[6,8,3,7,2,1,5,4]=>[4,2,1,1]
[3,5,8,1,7,2,6,4]=>[4,1,1,1,1]
[5,1,7,4,6,8,3,2]=>[4,2,1,1]
[7,6,4,8,1,5,3,2]=>[5,2,1]
[5,3,7,1,8,2,6,4]=>[3,3,1,1]
[2,7,6,3,8,1,4,5]=>[4,1,1,1,1]
[2,1,7,6,4,8,3,5]=>[4,2,1,1]
[2,1,5,4,8,7,3,6]=>[3,2,2,1]
[5,4,8,7,2,6,1,3]=>[4,2,1,1]
[2,4,3,8,7,1,5,6]=>[3,2,1,1,1]
[3,4,1,8,6,2,7,5]=>[3,2,2,1]
[3,8,5,4,2,1,7,6]=>[5,2,1]
[4,8,6,5,2,7,1,3]=>[5,1,1,1]
[3,2,8,7,5,4,1,6]=>[5,2,1]
[2,8,6,5,4,3,1,7]=>[6,1,1]
[5,4,2,6,3,1,8,7]=>[4,2,2]
[6,5,2,1,3,4,8,7]=>[4,2,1,1]
[8,5,2,7,3,1,4,6]=>[4,2,1,1]
[7,3,6,5,2,8,4,1]=>[5,2,1]
[7,6,2,3,4,8,5,1]=>[4,2,1,1]
[8,7,5,3,1,4,2,6]=>[5,2,1]
[7,1,5,3,8,4,6,2]=>[4,2,1,1]
[6,7,2,3,5,8,4,1]=>[4,1,1,1,1]
[3,7,6,4,2,8,5,1]=>[5,2,1]
[2,1,7,6,4,8,5,3]=>[4,2,2]
[2,1,8,7,4,3,5,6]=>[4,2,1,1]
[5,8,3,7,2,1,4,6]=>[4,1,1,1,1]
[3,8,7,4,2,1,5,6]=>[5,1,1,1]
[7,8,2,3,5,1,4,6]=>[3,1,1,1,1,1]
[2,8,6,3,1,4,7,5]=>[4,2,1,1]
[8,1,6,3,2,4,5,7]=>[4,1,1,1,1]
[5,7,1,4,8,3,6,2]=>[4,1,1,1,1]
[6,1,7,5,4,8,3,2]=>[5,2,1]
[6,3,7,5,8,4,2,1]=>[5,2,1]
[7,6,1,5,8,3,4,2]=>[5,1,1,1]
[8,6,7,5,1,3,2,4]=>[5,1,1,1]
[8,5,2,6,1,7,3,4]=>[4,2,1,1]
[5,4,2,6,8,3,7,1]=>[4,2,1,1]
[6,5,2,8,1,4,3,7]=>[4,2,1,1]
[7,4,2,8,1,3,6,5]=>[4,2,1,1]
[2,7,8,4,5,1,3,6]=>[3,1,1,1,1,1]
[5,7,3,8,4,1,2,6]=>[3,2,1,1,1]
[2,4,8,1,5,6,3,7]=>[3,1,1,1,1,1]
[3,4,8,1,5,2,7,6]=>[3,2,1,1,1]
[3,6,8,4,1,2,7,5]=>[3,2,1,1,1]
[4,8,1,2,5,3,6,7]=>[3,1,1,1,1,1]
[5,8,7,4,6,3,2,1]=>[6,1,1]
[4,8,7,6,3,5,2,1]=>[6,1,1]
[3,8,7,6,5,2,4,1]=>[6,1,1]
[5,8,4,7,6,3,2,1]=>[6,1,1]
[6,8,5,4,7,3,2,1]=>[6,1,1]
[3,8,7,6,2,5,4,1]=>[6,1,1]
[4,8,7,6,3,2,5,1]=>[6,1,1]
[3,8,7,6,5,2,1,4]=>[6,1,1]
[3,5,2,4,7,6,1,8]=>[3,2,1,1,1]
[3,5,4,7,2,6,1,8]=>[4,1,1,1,1]
[3,5,4,7,6,1,2,8]=>[3,2,1,1,1]
[3,5,4,7,6,1,8,2]=>[3,2,2,1]
[3,5,7,4,6,1,8,2]=>[3,2,1,1,1]
[3,5,7,4,6,1,2,8]=>[3,1,1,1,1,1]
[3,5,7,4,6,2,1,8]=>[4,1,1,1,1]
[3,2,5,7,4,6,1,8]=>[3,2,1,1,1]
[3,5,2,7,6,4,1,8]=>[4,2,1,1]
[3,5,7,2,6,4,1,8]=>[4,1,1,1,1]
[5,3,7,6,2,4,1,8]=>[4,2,1,1]
[5,3,7,6,1,2,8,4]=>[3,2,2,1]
[5,3,7,6,1,4,2,8]=>[4,2,1,1]
[5,3,7,6,4,1,2,8]=>[4,2,1,1]
[3,5,7,2,6,1,4,8]=>[3,1,1,1,1,1]
[3,5,2,7,6,1,4,8]=>[3,2,1,1,1]
[5,3,7,6,4,1,8,2]=>[4,2,2]
[3,7,5,4,1,8,2,6]=>[4,2,1,1]
[3,7,5,4,1,8,6,2]=>[4,3,1]
[3,7,5,1,4,8,6,2]=>[4,2,1,1]
[3,7,5,1,4,8,2,6]=>[4,1,1,1,1]
[3,5,7,1,2,6,8,4]=>[3,1,1,1,1,1]
[3,5,7,2,1,6,8,4]=>[3,2,1,1,1]
[3,5,2,7,1,6,4,8]=>[3,2,1,1,1]
[3,5,7,2,1,6,4,8]=>[3,2,1,1,1]
[5,3,7,1,6,2,4,8]=>[3,2,1,1,1]
[3,5,7,1,4,6,8,2]=>[3,1,1,1,1,1]
[3,5,7,1,4,6,2,8]=>[3,1,1,1,1,1]
[3,5,7,1,4,2,6,8]=>[3,1,1,1,1,1]
[3,5,7,2,1,4,6,8]=>[3,1,1,1,1,1]
[3,5,2,7,1,4,6,8]=>[3,1,1,1,1,1]
[3,2,5,7,4,1,6,8]=>[3,2,1,1,1]
[3,5,2,7,4,1,6,8]=>[3,2,1,1,1]
[3,5,7,4,2,1,6,8]=>[4,1,1,1,1]
[3,5,7,4,1,2,6,8]=>[3,1,1,1,1,1]
[3,5,4,7,1,6,8,2]=>[3,2,1,1,1]
[3,5,4,7,1,2,6,8]=>[3,1,1,1,1,1]
[3,5,4,7,2,1,6,8]=>[4,1,1,1,1]
[3,5,4,2,7,1,6,8]=>[4,1,1,1,1]
[3,2,5,4,7,1,6,8]=>[3,2,1,1,1]
[3,5,4,7,2,1,8,6]=>[4,2,1,1]
[3,5,4,7,1,2,8,6]=>[3,2,1,1,1]
[5,7,6,3,1,8,4,2]=>[4,3,1]
[5,7,6,3,1,8,2,4]=>[4,2,1,1]
[3,5,7,4,1,2,8,6]=>[3,2,1,1,1]
[3,5,7,4,2,1,8,6]=>[4,2,1,1]
[3,2,5,7,4,1,8,6]=>[3,2,2,1]
[3,2,5,7,1,4,8,6]=>[3,2,1,1,1]
[3,5,2,7,1,4,8,6]=>[3,2,1,1,1]
[3,5,7,2,1,4,8,6]=>[3,2,1,1,1]
[3,5,7,1,4,2,8,6]=>[3,2,1,1,1]
[3,7,5,2,1,8,6,4]=>[4,3,1]
[3,7,2,5,1,8,6,4]=>[3,3,1,1]
[3,2,7,5,1,8,6,4]=>[3,3,2]
[3,2,7,5,1,8,4,6]=>[3,2,2,1]
[3,7,2,5,1,8,4,6]=>[3,2,1,1,1]
[3,7,5,2,1,8,4,6]=>[4,2,1,1]
[2,1,7,5,8,4,6,3]=>[4,2,1,1]
[5,8,3,4,1,7,6,2]=>[4,2,1,1]
[5,8,7,2,4,1,6,3]=>[4,2,1,1]
[3,8,6,4,1,7,5,2]=>[4,3,1]
[4,3,5,6,8,1,7,2]=>[3,2,1,1,1]
[3,7,6,4,1,8,5,2]=>[4,3,1]
[3,7,4,1,8,6,5,2]=>[4,3,1]
[3,8,4,1,7,6,5,2]=>[5,2,1]
[3,2,7,6,1,5,4,8]=>[4,2,1,1]
[3,2,8,7,6,1,5,4]=>[5,2,1]
[5,7,8,2,4,1,6,3]=>[3,2,1,1,1]
[4,2,5,8,1,6,7,3]=>[3,2,1,1,1]
[4,2,5,8,1,7,3,6]=>[3,2,1,1,1]
[5,8,2,4,1,6,3,7]=>[3,2,1,1,1]
[8,4,2,6,5,1,3,7]=>[4,2,1,1]
[3,2,6,8,1,5,4,7]=>[3,2,1,1,1]
[8,3,2,5,6,1,4,7]=>[4,1,1,1,1]
[3,2,8,6,7,1,5,4]=>[4,2,1,1]
[3,2,6,8,7,1,5,4]=>[4,2,1,1]
[3,2,6,7,1,5,4,8]=>[3,2,1,1,1]
[8,7,3,2,5,6,1,4]=>[5,1,1,1]
[7,2,8,1,5,3,6,4]=>[3,2,2,1]
[8,4,2,7,5,1,3,6]=>[4,2,1,1]
[7,4,2,8,5,1,3,6]=>[4,2,1,1]
[7,2,4,1,8,3,6,5]=>[3,3,1,1]
[3,2,8,5,7,1,4,6]=>[3,2,1,1,1]
[2,6,5,7,1,8,3,4]=>[3,2,1,1,1]
[2,5,1,8,7,4,3,6]=>[4,2,1,1]
[8,1,4,6,3,5,2,7]=>[4,1,1,1,1]
[8,3,5,4,1,6,2,7]=>[4,2,1,1]
[8,6,3,4,1,5,2,7]=>[4,2,1,1]
[5,4,7,6,8,2,3,1]=>[4,2,1,1]
[4,1,8,2,3,7,6,5]=>[4,2,1,1]
[2,1,8,5,3,4,7,6]=>[3,2,2,1]
[5,2,4,6,8,7,3,1]=>[4,2,1,1]
[1,6,8,3,4,5,7,2]=>[3,1,1,1,1,1]
[5,7,4,8,6,1,3,2]=>[4,2,1,1]
[5,4,2,6,7,8,1,3]=>[4,1,1,1,1]
[6,4,2,7,3,5,8,1]=>[4,2,1,1]
[7,4,1,8,3,5,6,2]=>[4,2,1,1]
[6,5,4,8,7,3,1,2]=>[5,2,1]
[8,7,4,2,1,3,6,5]=>[5,2,1]
[8,7,1,3,2,5,6,4]=>[4,2,1,1]
[6,8,2,3,1,7,5,4]=>[4,2,1,1]
[7,4,3,2,6,8,5,1]=>[5,2,1]
[2,7,4,3,8,5,6,1]=>[4,2,1,1]
[8,3,7,2,1,5,6,4]=>[4,2,1,1]
[5,7,8,2,4,3,1,6]=>[4,1,1,1,1]
[8,4,7,3,2,6,1,5]=>[5,1,1,1]
[8,3,1,6,7,4,2,5]=>[4,2,1,1]
[3,2,5,7,4,8,1,6]=>[3,2,1,1,1]
[8,2,7,3,4,1,5,6]=>[4,1,1,1,1]
[7,1,6,3,5,8,2,4]=>[4,1,1,1,1]
[2,8,5,6,7,1,4,3]=>[4,1,1,1,1]
[1,5,2,7,8,6,4,3]=>[4,2,1,1]
[2,6,8,5,1,4,7,3]=>[4,1,1,1,1]
[1,4,2,8,6,5,7,3]=>[4,2,1,1]
[3,5,1,6,8,7,2,4]=>[3,2,1,1,1]
[5,7,6,2,1,3,8,4]=>[4,2,1,1]
[2,5,8,7,4,1,6,3]=>[4,2,1,1]
[4,1,7,5,2,6,8,3]=>[3,2,2,1]
[7,6,2,4,5,1,8,3]=>[4,2,1,1]
[7,3,4,2,5,8,6,1]=>[4,2,1,1]
[8,7,4,2,5,1,6,3]=>[5,2,1]
[8,1,4,5,2,6,7,3]=>[3,2,1,1,1]
[5,2,4,8,6,7,1,3]=>[3,2,1,1,1]
[8,5,6,2,1,3,7,4]=>[4,2,1,1]
[4,2,1,5,6,7,8,3]=>[3,2,1,1,1]
[3,4,6,5,1,7,8,2]=>[3,2,1,1,1]
[7,3,5,2,4,6,1,8]=>[4,1,1,1,1]
[5,3,7,2,4,6,1,8]=>[4,1,1,1,1]
[3,7,5,2,4,6,1,8]=>[4,1,1,1,1]
[5,7,3,2,4,6,1,8]=>[4,1,1,1,1]
[1,5,3,2,4,7,6,8]=>[3,2,1,1,1]
[1,5,3,2,7,4,6,8]=>[3,2,1,1,1]
[5,7,3,2,1,4,6,8]=>[4,1,1,1,1]
[5,7,3,2,4,1,6,8]=>[4,1,1,1,1]
[3,7,2,5,4,1,6,8]=>[4,1,1,1,1]
[5,1,3,2,4,7,6,8]=>[3,2,1,1,1]
[5,1,3,2,7,4,6,8]=>[3,2,1,1,1]
[7,1,3,2,5,4,6,8]=>[3,2,1,1,1]
[1,7,3,2,5,4,6,8]=>[3,2,1,1,1]
[7,1,3,5,2,4,6,8]=>[3,1,1,1,1,1]
[5,1,3,7,2,4,6,8]=>[3,1,1,1,1,1]
[3,2,7,5,1,4,6,8]=>[3,2,1,1,1]
[3,7,5,1,2,4,6,8]=>[3,1,1,1,1,1]
[5,7,3,1,2,4,6,8]=>[3,1,1,1,1,1]
[1,5,3,7,2,4,6,8]=>[3,1,1,1,1,1]
[5,3,2,7,4,1,6,8]=>[4,2,1,1]
[5,3,2,4,7,1,6,8]=>[4,1,1,1,1]
[5,3,2,1,4,7,6,8]=>[4,2,1,1]
[5,3,2,1,7,4,6,8]=>[4,2,1,1]
[1,3,2,7,5,4,6,8]=>[3,2,1,1,1]
[1,3,7,2,5,4,6,8]=>[3,1,1,1,1,1]
[7,3,1,2,5,4,6,8]=>[3,2,1,1,1]
[5,3,1,2,7,4,6,8]=>[3,2,1,1,1]
[5,3,1,2,4,7,6,8]=>[3,2,1,1,1]
[3,2,5,1,4,7,6,8]=>[3,2,1,1,1]
[7,3,1,5,2,4,6,8]=>[3,2,1,1,1]
[1,3,7,5,2,4,6,8]=>[3,1,1,1,1,1]
[7,5,1,3,2,4,6,8]=>[4,1,1,1,1]
[5,7,1,3,2,4,6,8]=>[3,1,1,1,1,1]
[3,7,1,5,2,4,6,8]=>[3,1,1,1,1,1]
[3,7,1,2,5,4,6,8]=>[3,1,1,1,1,1]
[3,7,2,1,5,4,6,8]=>[3,2,1,1,1]
[3,2,1,7,5,4,6,8]=>[3,3,1,1]
[3,1,2,7,5,4,6,8]=>[3,2,1,1,1]
[3,1,7,2,5,4,6,8]=>[3,2,1,1,1]
[3,1,7,5,2,4,6,8]=>[3,2,1,1,1]
[7,1,5,3,2,4,6,8]=>[4,1,1,1,1]
[1,7,5,3,2,4,6,8]=>[4,1,1,1,1]
[1,8,5,4,2,7,6,3]=>[4,3,1]
[7,5,3,4,2,8,1,6]=>[5,1,1,1]
[8,5,6,2,7,4,3,1]=>[5,2,1]
[1,7,2,3,6,8,5,4]=>[4,1,1,1,1]
[3,5,6,4,8,2,7,1]=>[4,1,1,1,1]
[3,5,1,4,8,2,7,6]=>[3,2,1,1,1]
[1,7,5,4,8,2,6,3]=>[4,2,1,1]
[3,7,5,1,6,4,8,2]=>[4,2,1,1]
[2,7,5,4,8,1,3,6]=>[4,1,1,1,1]
[2,7,5,4,8,6,1,3]=>[4,2,1,1]
[1,7,5,4,8,6,3,2]=>[5,2,1]
[2,5,1,4,8,7,3,6]=>[3,2,1,1,1]
[3,6,4,2,8,7,1,5]=>[4,2,1,1]
[3,5,2,4,8,1,6,7]=>[3,1,1,1,1,1]
[3,5,6,4,8,1,2,7]=>[3,1,1,1,1,1]
[1,5,6,4,8,7,2,3]=>[3,2,1,1,1]
[3,6,4,1,8,7,2,5]=>[3,3,1,1]
[3,6,4,5,8,7,2,1]=>[4,2,1,1]
[1,6,4,3,8,5,2,7]=>[4,2,1,1]
[7,1,3,4,5,8,2,6]=>[3,1,1,1,1,1]
[7,6,1,4,5,3,8,2]=>[5,1,1,1]
[7,6,1,3,5,4,8,2]=>[5,1,1,1]
[7,1,3,2,5,8,4,6]=>[3,2,1,1,1]
[1,6,4,2,8,5,3,7]=>[3,3,1,1]
[7,6,5,8,2,4,3,1]=>[6,1,1]
[7,6,5,8,3,1,4,2]=>[5,2,1]
[2,6,4,3,8,1,7,5]=>[4,2,1,1]
[2,6,4,3,8,5,7,1]=>[4,2,1,1]
[7,2,3,1,5,8,6,4]=>[3,3,1,1]
[7,1,5,6,3,8,4,2]=>[4,2,1,1]
[7,3,6,5,1,4,8,2]=>[5,1,1,1]
[7,2,6,5,3,8,1,4]=>[5,1,1,1]
[7,2,3,1,4,8,6,5]=>[3,3,1,1]
[7,2,3,5,4,8,6,1]=>[4,2,1,1]
[2,6,4,5,8,1,7,3]=>[3,2,1,1,1]
[1,5,6,4,8,3,7,2]=>[4,1,1,1,1]
[2,5,6,4,8,3,1,7]=>[4,1,1,1,1]
[3,5,6,1,4,7,8,2]=>[3,1,1,1,1,1]
[7,6,1,3,4,5,8,2]=>[4,1,1,1,1]
[7,1,3,2,4,8,5,6]=>[3,2,1,1,1]
[7,6,1,5,3,4,8,2]=>[5,1,1,1]
[7,6,1,5,4,3,8,2]=>[6,1,1]
[1,6,4,5,8,3,2,7]=>[4,1,1,1,1]
[7,6,5,8,1,3,2,4]=>[5,1,1,1]
[3,4,6,8,7,2,1,5]=>[4,1,1,1,1]
[3,5,6,8,2,1,7,4]=>[3,2,1,1,1]
[4,2,1,5,3,7,8,6]=>[3,2,2,1]
[4,2,5,6,3,1,8,7]=>[3,2,2,1]
[3,5,6,8,1,7,2,4]=>[3,1,1,1,1,1]
[4,1,5,6,3,2,8,7]=>[3,2,2,1]
[4,5,3,1,7,2,8,6]=>[3,2,2,1]
[4,1,3,5,2,7,8,6]=>[3,2,1,1,1]
[2,5,4,7,3,8,6,1]=>[4,2,1,1]
[3,5,7,1,8,4,2,6]=>[3,2,1,1,1]
[4,1,5,3,2,7,8,6]=>[3,2,2,1]
[4,5,3,7,1,2,8,6]=>[3,2,1,1,1]
[4,3,6,1,2,7,5,8]=>[3,2,1,1,1]
[5,1,3,2,4,6,7,8]=>[3,1,1,1,1,1]
[3,6,1,7,4,5,2,8]=>[3,2,1,1,1]
[5,1,3,4,2,6,7,8]=>[3,1,1,1,1,1]
[5,3,1,4,2,6,7,8]=>[3,2,1,1,1]
[4,5,2,3,7,1,8,6]=>[3,2,1,1,1]
[4,2,6,1,3,7,5,8]=>[3,2,1,1,1]
[4,6,2,1,3,7,5,8]=>[3,2,1,1,1]
[3,6,2,1,7,4,8,5]=>[3,2,2,1]
[3,1,4,7,6,5,2,8]=>[4,2,1,1]
[3,6,2,7,1,5,8,4]=>[3,2,1,1,1]
[4,6,2,7,1,3,5,8]=>[3,1,1,1,1,1]
[3,5,7,1,8,2,6,4]=>[3,2,1,1,1]
[5,1,4,2,3,6,7,8]=>[3,1,1,1,1,1]
[3,6,1,7,2,5,8,4]=>[3,2,1,1,1]
[2,6,5,3,4,7,8,1]=>[4,1,1,1,1]
[3,6,1,7,5,4,2,8]=>[4,2,1,1]
[5,1,4,3,2,6,7,8]=>[4,1,1,1,1]
[5,4,1,3,2,6,7,8]=>[4,1,1,1,1]
[6,4,2,5,3,8,1,7]=>[4,2,1,1]
[4,6,2,3,5,1,8,7]=>[3,2,1,1,1]
[6,2,4,5,1,8,3,7]=>[3,2,1,1,1]
[8,2,6,7,1,4,5,3]=>[4,1,1,1,1]
[8,2,6,7,4,1,5,3]=>[4,2,1,1]
[4,6,2,3,5,8,1,7]=>[3,1,1,1,1,1]
[2,6,4,1,5,8,3,7]=>[3,2,1,1,1]
[2,8,1,6,7,4,5,3]=>[4,1,1,1,1]
[6,8,4,5,7,2,3,1]=>[4,1,1,1,1]
[2,8,6,1,4,7,5,3]=>[4,2,1,1]
[2,8,1,6,4,7,5,3]=>[4,2,1,1]
[2,6,1,4,8,5,3,7]=>[3,2,1,1,1]
[6,4,5,2,8,3,1,7]=>[4,2,1,1]
[4,2,3,6,1,8,5,7]=>[3,2,1,1,1]
[4,2,3,1,6,8,5,7]=>[3,2,1,1,1]
[4,2,3,8,6,1,7,5]=>[3,2,2,1]
[6,4,5,8,2,3,7,1]=>[4,1,1,1,1]
[8,6,7,2,4,5,1,3]=>[4,1,1,1,1]
[6,4,8,5,2,3,7,1]=>[4,2,1,1]
[4,2,8,3,1,6,7,5]=>[3,2,2,1]
[2,4,8,1,3,6,7,5]=>[3,1,1,1,1,1]
[2,4,1,8,3,6,7,5]=>[3,2,1,1,1]
[2,1,4,8,6,3,7,5]=>[3,2,2,1]
[6,4,8,2,5,3,7,1]=>[4,2,1,1]
[8,6,2,4,7,5,1,3]=>[4,2,1,1]
[4,6,8,2,3,5,7,1]=>[3,1,1,1,1,1]
[2,6,8,4,1,5,7,3]=>[3,2,1,1,1]
[2,6,8,1,4,5,7,3]=>[3,1,1,1,1,1]
[2,1,6,8,4,5,7,3]=>[3,2,1,1,1]
[2,8,1,4,6,7,3,5]=>[3,1,1,1,1,1]
[4,8,6,2,3,7,5,1]=>[4,2,1,1]
[8,4,2,6,7,3,1,5]=>[4,2,1,1]
[7,6,4,5,1,3,8,2]=>[5,1,1,1]
[1,6,7,5,3,4,8,2]=>[4,1,1,1,1]
[7,6,2,3,8,4,1,5]=>[4,2,1,1]
[1,6,7,5,8,2,3,4]=>[3,1,1,1,1,1]
[6,2,5,8,3,4,7,1]=>[4,1,1,1,1]
[6,2,3,8,7,4,1,5]=>[4,2,1,1]
[2,4,7,3,5,8,6,1]=>[3,2,1,1,1]
[2,5,3,7,1,8,4,6]=>[3,2,1,1,1]
[5,2,8,3,1,4,6,7]=>[3,2,1,1,1]
[4,8,2,3,6,5,7,1]=>[4,1,1,1,1]
[5,8,1,3,6,4,7,2]=>[4,1,1,1,1]
[5,8,1,4,3,6,2,7]=>[4,1,1,1,1]
[5,8,4,1,3,7,6,2]=>[4,2,1,1]
[6,4,5,3,8,1,7,2]=>[4,2,1,1]
[4,6,5,3,7,1,2,8]=>[4,1,1,1,1]
[4,5,1,3,6,2,8,7]=>[3,2,1,1,1]
[4,2,6,5,1,7,3,8]=>[3,2,2,1]
[4,3,5,7,2,1,6,8]=>[4,1,1,1,1]
[3,4,7,6,8,1,2,5]=>[3,1,1,1,1,1]
[3,4,6,2,5,8,7,1]=>[3,2,1,1,1]
[3,5,2,4,6,1,8,7]=>[3,2,1,1,1]
[4,2,5,1,6,8,3,7]=>[3,2,1,1,1]
[1,8,2,3,6,5,7,4]=>[4,1,1,1,1]
[4,2,8,3,5,7,1,6]=>[3,2,1,1,1]
[4,3,8,6,5,7,1,2]=>[4,2,1,1]
[1,3,7,2,6,5,8,4]=>[4,1,1,1,1]
[1,3,6,4,2,5,8,7]=>[3,2,1,1,1]
[1,5,4,7,3,6,8,2]=>[4,1,1,1,1]
[5,2,3,8,4,1,7,6]=>[3,2,2,1]
[7,5,3,4,8,2,1,6]=>[5,1,1,1]
[7,2,8,3,4,1,5,6]=>[3,2,1,1,1]
[7,4,3,8,5,2,6,1]=>[5,2,1]
[4,6,2,7,3,1,5,8]=>[3,2,1,1,1]
[7,6,3,8,2,4,5,1]=>[5,1,1,1]
[7,2,8,5,1,3,4,6]=>[3,2,1,1,1]
[1,5,3,7,6,8,4,2]=>[4,2,1,1]
[1,6,3,7,8,2,4,5]=>[3,1,1,1,1,1]
[1,4,3,7,8,5,2,6]=>[3,2,1,1,1]
[4,2,6,5,7,8,3,1]=>[4,2,1,1]
[4,2,6,7,5,8,1,3]=>[3,2,1,1,1]
[3,2,4,7,8,5,1,6]=>[3,2,1,1,1]
[3,2,6,7,8,1,4,5]=>[3,1,1,1,1,1]
[5,1,8,3,6,4,7,2]=>[4,2,1,1]
[3,6,8,5,7,2,1,4]=>[4,1,1,1,1]
[5,1,3,8,7,6,4,2]=>[5,2,1]
[3,8,5,6,1,7,2,4]=>[3,2,1,1,1]
[3,4,8,1,7,6,2,5]=>[4,1,1,1,1]
[4,7,6,8,5,1,3,2]=>[5,1,1,1]
[6,7,4,8,5,1,3,2]=>[4,2,1,1]
[5,3,6,8,7,1,4,2]=>[4,2,1,1]
[1,8,4,6,7,2,5,3]=>[4,1,1,1,1]
[5,2,8,3,7,1,6,4]=>[4,2,1,1]
[7,4,5,8,6,1,3,2]=>[4,2,1,1]
[4,3,6,8,7,1,5,2]=>[4,2,1,1]
[6,4,8,3,1,7,5,2]=>[4,3,1]
[3,6,5,8,7,1,4,2]=>[4,2,1,1]
[5,7,4,8,2,6,3,1]=>[4,2,1,1]
[5,6,4,8,2,7,3,1]=>[4,2,1,1]
[5,6,8,3,1,7,4,2]=>[4,2,1,1]
[4,6,3,8,2,7,5,1]=>[4,2,1,1]
[5,3,8,1,7,2,6,4]=>[4,2,1,1]
[6,5,8,1,3,7,4,2]=>[4,2,1,1]
[6,5,3,8,2,7,4,1]=>[5,2,1]
[6,4,8,1,3,7,5,2]=>[4,2,1,1]
[6,2,8,3,4,7,5,1]=>[4,2,1,1]
[7,6,3,1,4,2,5,8]=>[4,2,1,1]
[1,5,4,3,7,8,2,6]=>[4,1,1,1,1]
[7,8,4,2,5,3,1,6]=>[4,2,1,1]
[4,2,7,8,5,3,1,6]=>[4,2,1,1]
[4,2,5,3,1,7,8,6]=>[3,2,2,1]
[4,2,8,7,6,3,1,5]=>[5,2,1]
[4,2,7,6,3,1,5,8]=>[4,2,1,1]
[6,3,1,7,5,2,4,8]=>[3,3,1,1]
[6,3,1,8,7,5,2,4]=>[4,3,1]
[8,6,3,1,7,5,2,4]=>[4,3,1]
[4,2,7,6,3,1,8,5]=>[4,2,2]
[7,6,3,1,8,4,2,5]=>[4,3,1]
[7,6,4,2,1,8,3,5]=>[5,2,1]
[1,8,2,7,6,4,3,5]=>[5,1,1,1]
[8,3,5,7,6,4,2,1]=>[6,1,1]
[8,4,2,5,7,6,3,1]=>[5,2,1]
[7,5,2,4,8,6,3,1]=>[5,2,1]
[8,7,5,2,4,6,3,1]=>[6,1,1]
[7,5,2,4,6,3,1,8]=>[5,1,1,1]
[5,2,8,6,3,7,4,1]=>[4,2,2]
[8,4,7,5,2,6,3,1]=>[5,2,1]
[8,3,6,4,7,5,2,1]=>[5,2,1]
[1,8,2,7,5,3,6,4]=>[4,2,1,1]
[7,5,2,1,8,3,6,4]=>[4,3,1]
[7,5,2,6,3,1,8,4]=>[4,2,2]
[5,2,7,4,1,8,6,3]=>[3,3,2]
[5,2,8,7,4,1,6,3]=>[4,2,2]
[8,7,4,1,5,2,6,3]=>[4,2,2]
[7,4,1,5,2,8,6,3]=>[3,3,2]
[7,6,3,1,4,2,8,5]=>[4,2,2]
[7,5,2,8,6,3,1,4]=>[4,3,1]
[8,7,5,2,6,3,1,4]=>[5,2,1]
[7,5,2,1,3,6,4,8]=>[4,2,1,1]
[8,7,5,2,1,3,6,4]=>[5,2,1]
[7,5,2,1,3,8,6,4]=>[4,3,1]
[1,3,7,6,5,8,2,4]=>[4,1,1,1,1]
[8,6,4,7,5,2,1,3]=>[5,2,1]
[6,4,8,7,5,2,1,3]=>[5,2,1]
[6,4,7,5,2,1,3,8]=>[4,2,1,1]
[6,3,1,4,7,5,2,8]=>[3,3,1,1]
[6,3,1,4,8,7,5,2]=>[4,3,1]
[8,6,3,1,4,7,5,2]=>[4,3,1]
[8,5,7,6,3,1,4,2]=>[5,2,1]
[1,8,2,5,7,6,4,3]=>[5,1,1,1]
[1,8,2,6,4,7,5,3]=>[4,2,1,1]
[7,5,2,1,6,4,8,3]=>[4,3,1]
[6,3,8,7,4,1,5,2]=>[4,2,2]
[6,3,7,4,1,5,2,8]=>[3,2,2,1]
[7,4,1,6,3,5,2,8]=>[4,2,1,1]
[7,4,1,8,6,3,5,2]=>[4,3,1]
[8,4,6,3,1,7,5,2]=>[4,3,1]
[6,4,7,5,2,1,8,3]=>[4,2,2]
[1,6,4,7,5,3,8,2]=>[4,2,1,1]
[8,6,3,5,2,7,4,1]=>[5,2,1]
[6,3,5,2,8,7,4,1]=>[4,3,1]
[6,3,5,2,7,4,1,8]=>[4,2,1,1]
[4,5,7,2,6,3,1,8]=>[4,1,1,1,1]
[3,5,8,4,6,1,7,2]=>[3,2,1,1,1]
[1,4,7,3,5,2,6,8]=>[3,1,1,1,1,1]
[5,7,4,2,6,3,1,8]=>[4,2,1,1]
[4,2,6,3,5,7,1,8]=>[3,2,1,1,1]
[1,4,5,8,2,7,3,6]=>[3,1,1,1,1,1]
[2,4,5,8,1,6,7,3]=>[3,1,1,1,1,1]
[8,3,4,7,1,6,5,2]=>[5,1,1,1]
[4,2,5,7,8,1,6,3]=>[3,2,1,1,1]
[8,3,4,6,5,1,7,2]=>[4,2,1,1]
[4,1,7,3,5,2,6,8]=>[3,2,1,1,1]
[6,1,3,7,4,2,5,8]=>[3,2,1,1,1]
[3,1,6,8,2,7,4,5]=>[3,2,1,1,1]
[6,1,3,8,2,5,4,7]=>[3,2,1,1,1]
[4,8,2,3,1,6,7,5]=>[3,2,1,1,1]
[3,2,6,8,1,5,7,4]=>[3,2,1,1,1]
[8,2,6,1,5,4,7,3]=>[5,1,1,1]
[8,6,2,7,1,5,4,3]=>[5,2,1]
[7,6,8,3,1,5,4,2]=>[5,2,1]
[5,7,4,2,8,1,6,3]=>[4,2,1,1]
[6,3,7,2,8,1,5,4]=>[4,2,1,1]
[7,5,2,8,6,1,4,3]=>[4,3,1]
[2,7,3,8,1,5,6,4]=>[3,2,1,1,1]
[1,6,8,5,2,4,3,7]=>[4,1,1,1,1]
[4,5,7,2,8,1,6,3]=>[3,2,1,1,1]
[4,5,6,8,3,1,7,2]=>[3,2,1,1,1]
[8,4,6,5,3,1,7,2]=>[5,2,1]
[5,6,4,8,3,1,7,2]=>[4,2,1,1]
[3,4,7,1,2,6,5,8]=>[3,1,1,1,1,1]
[4,8,1,6,2,3,7,5]=>[3,2,1,1,1]
[4,5,3,1,7,2,6,8]=>[3,2,1,1,1]
[4,7,3,1,2,6,5,8]=>[3,2,1,1,1]
[5,2,7,1,3,6,4,8]=>[3,2,1,1,1]
[7,8,1,2,4,3,6,5]=>[3,2,1,1,1]
[8,4,1,6,2,3,7,5]=>[3,2,2,1]
[4,8,3,1,2,5,7,6]=>[3,2,1,1,1]
[4,1,3,6,5,7,8,2]=>[3,2,1,1,1]
[6,1,3,4,2,8,5,7]=>[3,2,1,1,1]
[8,1,4,2,5,7,6,3]=>[4,2,1,1]
[8,1,4,3,5,7,6,2]=>[4,2,1,1]
[5,2,4,1,3,7,8,6]=>[3,2,1,1,1]
[2,6,5,3,1,7,8,4]=>[4,2,1,1]
[8,3,2,1,5,7,6,4]=>[4,3,1]
[1,7,4,3,6,8,2,5]=>[4,1,1,1,1]
[2,7,6,3,1,8,4,5]=>[4,2,1,1]
[2,8,4,6,3,7,5,1]=>[4,2,1,1]
[8,7,1,3,6,5,4,2]=>[6,1,1]
[1,8,5,7,4,2,6,3]=>[4,2,1,1]
[3,8,6,5,7,1,4,2]=>[5,1,1,1]
[4,8,6,2,7,1,5,3]=>[4,2,1,1]
[4,7,5,3,8,2,1,6]=>[5,1,1,1]
[1,6,5,8,3,4,2,7]=>[4,1,1,1,1]
[6,1,5,3,8,4,2,7]=>[4,2,1,1]
[8,1,5,4,7,2,6,3]=>[4,2,1,1]
[2,1,4,7,5,8,3,6]=>[3,2,1,1,1]
[6,3,5,8,7,4,1,2]=>[4,2,1,1]
[4,7,2,8,5,6,3,1]=>[4,2,1,1]
[1,4,8,7,3,5,6,2]=>[4,1,1,1,1]
[8,1,7,6,3,5,4,2]=>[6,1,1]
[3,6,8,5,7,4,1,2]=>[4,1,1,1,1]
[4,7,6,8,5,3,1,2]=>[5,1,1,1]
[5,7,2,8,6,4,1,3]=>[4,2,1,1]
[3,8,7,5,6,4,2,1]=>[6,1,1]
[2,8,7,6,4,5,3,1]=>[6,1,1]
[1,8,7,6,5,3,4,2]=>[6,1,1]
[4,6,7,2,5,3,1,8]=>[4,1,1,1,1]
[3,6,7,4,8,1,5,2]=>[3,2,1,1,1]
[3,8,5,7,6,1,4,2]=>[5,1,1,1]
[1,4,7,8,2,6,5,3]=>[4,1,1,1,1]
[2,4,7,8,1,6,5,3]=>[4,1,1,1,1]
[4,2,6,8,7,1,5,3]=>[4,2,1,1]
[3,1,7,8,2,6,5,4]=>[4,2,1,1]
[6,1,3,8,2,7,5,4]=>[4,2,1,1]
[5,1,8,4,2,7,6,3]=>[4,2,2]
[8,2,6,1,7,5,4,3]=>[5,2,1]
[6,8,3,7,1,5,4,2]=>[5,1,1,1]
[2,7,3,8,1,6,5,4]=>[4,2,1,1]
[1,7,3,8,2,6,5,4]=>[4,2,1,1]
[2,6,8,4,1,7,5,3]=>[4,2,1,1]
[4,5,8,6,3,1,7,2]=>[4,2,1,1]
[4,6,7,1,2,8,5,3]=>[3,2,1,1,1]
[3,6,1,8,2,7,5,4]=>[4,2,1,1]
[5,7,4,1,2,8,6,3]=>[3,3,1,1]
[6,3,7,1,2,8,5,4]=>[3,3,1,1]
[6,2,1,8,3,7,5,4]=>[4,3,1]
[8,1,5,6,3,2,4,7]=>[4,1,1,1,1]
[1,7,8,3,5,2,4,6]=>[3,1,1,1,1,1]
[8,5,3,7,2,4,6,1]=>[5,1,1,1]
[1,7,2,4,8,5,3,6]=>[3,2,1,1,1]
[1,7,8,5,4,3,2,6]=>[5,1,1,1]
[2,6,8,7,4,3,5,1]=>[5,1,1,1]
[1,2,6,7,8,4,3,5]=>[3,1,1,1,1,1]
[2,7,5,8,4,1,3,6]=>[4,1,1,1,1]
[2,1,7,8,4,5,3,6]=>[3,2,1,1,1]
[3,7,8,2,1,5,4,6]=>[3,2,1,1,1]
[8,5,1,4,7,3,6,2]=>[5,1,1,1]
[8,4,7,5,3,6,1,2]=>[5,1,1,1]
[8,1,4,6,7,3,5,2]=>[4,1,1,1,1]
[3,5,8,6,7,4,1,2]=>[4,1,1,1,1]
[3,6,8,4,7,1,5,2]=>[4,1,1,1,1]
[4,7,1,3,6,8,2,5]=>[3,1,1,1,1,1]
[3,7,6,4,8,1,2,5]=>[4,1,1,1,1]
[3,1,7,5,6,8,2,4]=>[3,2,1,1,1]
[2,3,6,5,7,1,8,4]=>[3,2,1,1,1]
[3,7,5,4,2,1,8,6]=>[5,2,1]
[1,3,6,7,4,2,8,5]=>[3,2,1,1,1]
[3,6,4,8,2,7,5,1]=>[4,2,1,1]
[1,4,6,3,2,7,8,5]=>[3,2,1,1,1]
[8,7,1,5,6,3,2,4]=>[5,1,1,1]
[8,1,6,7,5,3,2,4]=>[5,1,1,1]
[1,7,8,6,5,3,2,4]=>[5,1,1,1]
[8,7,2,4,6,5,3,1]=>[6,1,1]
[1,7,8,2,6,4,5,3]=>[4,1,1,1,1]
[8,7,2,5,4,6,1,3]=>[5,1,1,1]
[8,7,2,5,3,1,6,4]=>[5,2,1]
[8,7,3,2,1,5,6,4]=>[5,2,1]
[8,2,6,7,3,1,5,4]=>[4,2,1,1]
[1,7,2,8,5,6,4,3]=>[4,2,1,1]
[2,7,1,8,4,6,5,3]=>[4,2,1,1]
[3,7,8,2,1,6,5,4]=>[4,2,1,1]
[8,7,6,1,4,5,3,2]=>[6,1,1]
[1,8,5,4,6,2,3,7]=>[4,1,1,1,1]
[1,8,5,4,6,3,2,7]=>[5,1,1,1]
[2,5,8,4,7,3,6,1]=>[4,1,1,1,1]
[3,6,4,2,7,8,5,1]=>[4,2,1,1]
[4,5,8,1,7,6,2,3]=>[4,1,1,1,1]
[3,5,8,4,7,1,6,2]=>[4,1,1,1,1]
[1,5,8,4,7,3,6,2]=>[4,1,1,1,1]
[3,6,4,1,7,8,5,2]=>[3,3,1,1]
[1,6,4,3,7,8,5,2]=>[4,2,1,1]
[7,1,3,4,8,6,5,2]=>[4,2,1,1]
[2,6,4,3,7,1,8,5]=>[4,2,1,1]
[2,6,4,1,7,8,3,5]=>[3,2,1,1,1]
[7,2,3,4,8,6,5,1]=>[4,2,1,1]
[7,2,3,1,8,6,4,5]=>[3,3,1,1]
[7,2,3,4,1,6,8,5]=>[3,2,1,1,1]
[7,2,3,1,5,6,8,4]=>[3,2,1,1,1]
[7,2,3,8,1,6,5,4]=>[4,2,1,1]
[1,5,8,4,7,6,2,3]=>[4,1,1,1,1]
[7,1,3,2,5,6,8,4]=>[3,2,1,1,1]
[7,1,3,8,2,6,5,4]=>[4,2,1,1]
[7,6,1,8,5,4,2,3]=>[5,2,1]
[3,2,6,5,8,4,7,1]=>[4,2,1,1]
[4,3,7,1,6,5,8,2]=>[4,2,1,1]
[5,2,6,4,8,3,7,1]=>[4,2,1,1]
[4,3,7,5,8,2,6,1]=>[4,2,1,1]
[5,3,7,4,8,2,6,1]=>[4,2,1,1]
[5,3,7,4,8,1,6,2]=>[3,2,2,1]
[5,4,8,1,6,2,7,3]=>[3,2,2,1]
[4,3,7,1,5,2,8,6]=>[3,2,2,1]
[5,4,8,2,6,3,7,1]=>[4,2,1,1]
[5,4,8,1,6,3,7,2]=>[4,2,1,1]
[4,1,7,5,2,3,6,8]=>[3,2,1,1,1]
[4,1,7,8,6,3,2,5]=>[4,2,1,1]
[4,7,2,8,3,5,1,6]=>[3,2,1,1,1]
[6,8,3,2,1,4,7,5]=>[4,2,1,1]
[7,2,4,1,6,5,8,3]=>[4,2,1,1]
[7,5,8,4,3,1,6,2]=>[5,2,1]
[6,8,2,4,1,3,7,5]=>[3,2,1,1,1]
[2,8,4,7,6,3,5,1]=>[5,1,1,1]
[4,2,7,3,8,5,6,1]=>[3,2,2,1]
[4,5,2,6,8,3,7,1]=>[3,2,1,1,1]
[4,8,3,2,5,7,6,1]=>[4,2,1,1]
[6,8,5,3,4,7,2,1]=>[5,1,1,1]
[6,8,4,1,5,3,7,2]=>[4,2,1,1]
[6,8,3,5,1,4,7,2]=>[4,1,1,1,1]
[6,8,5,4,2,3,7,1]=>[5,1,1,1]
[5,8,2,4,3,7,6,1]=>[4,2,1,1]
[8,2,1,3,5,6,4,7]=>[3,2,1,1,1]
[8,2,1,3,5,4,7,6]=>[3,2,2,1]
[8,2,1,3,4,6,7,5]=>[3,2,1,1,1]
[8,1,3,4,2,6,5,7]=>[3,2,1,1,1]
[8,1,3,4,2,5,7,6]=>[3,2,1,1,1]
[8,1,3,2,5,6,4,7]=>[3,2,1,1,1]
[8,1,2,4,5,3,7,6]=>[3,2,1,1,1]
[8,1,2,4,3,6,7,5]=>[3,2,1,1,1]
[6,5,3,8,4,2,7,1]=>[5,2,1]
[7,4,5,1,6,2,8,3]=>[3,2,2,1]
[4,7,3,5,6,2,8,1]=>[4,1,1,1,1]
[6,7,8,4,1,3,5,2]=>[4,1,1,1,1]
[3,1,6,8,4,7,5,2]=>[4,2,1,1]
[8,3,6,1,5,7,4,2]=>[5,1,1,1]
[3,2,7,5,8,6,1,4]=>[3,2,2,1]
[2,5,4,7,8,1,6,3]=>[3,2,1,1,1]
[2,4,6,7,8,1,5,3]=>[3,1,1,1,1,1]
[2,4,6,8,1,7,5,3]=>[4,1,1,1,1]
[7,4,3,8,6,2,1,5]=>[5,2,1]
[2,4,7,8,3,5,6,1]=>[3,1,1,1,1,1]
[3,2,7,6,1,8,4,5]=>[3,2,2,1]
[3,2,6,8,1,7,4,5]=>[3,2,1,1,1]
[4,3,6,2,1,8,5,7]=>[4,2,1,1]
[3,6,4,2,5,8,1,7]=>[4,1,1,1,1]
[4,6,2,3,7,5,8,1]=>[3,2,1,1,1]
[5,8,4,2,3,6,7,1]=>[4,1,1,1,1]
[8,4,5,3,2,1,7,6]=>[5,2,1]
[5,8,3,4,2,1,7,6]=>[4,2,1,1]
[6,8,4,2,3,7,5,1]=>[4,2,1,1]
[6,4,8,3,2,7,1,5]=>[5,1,1,1]
[5,8,3,7,2,1,6,4]=>[4,2,1,1]
[2,5,6,4,7,1,8,3]=>[3,2,1,1,1]
[2,5,4,8,1,6,7,3]=>[3,2,1,1,1]
[6,4,7,3,8,2,1,5]=>[5,1,1,1]
[6,7,4,3,2,1,8,5]=>[5,2,1]
[8,4,3,7,2,1,5,6]=>[5,1,1,1]
[1,2,6,5,8,7,3,4]=>[3,2,1,1,1]
[1,5,2,8,4,6,7,3]=>[3,2,1,1,1]
[1,5,2,7,4,6,8,3]=>[3,2,1,1,1]
[5,1,2,7,3,6,8,4]=>[3,2,1,1,1]
[5,1,2,8,3,6,7,4]=>[3,2,1,1,1]
[5,6,3,4,8,7,2,1]=>[4,2,1,1]
[6,5,3,4,8,7,2,1]=>[5,2,1]
[4,1,2,8,3,6,7,5]=>[3,2,1,1,1]
[4,1,2,7,3,6,8,5]=>[3,2,1,1,1]
[7,5,3,8,4,6,2,1]=>[5,2,1]
[8,5,3,7,4,6,2,1]=>[5,2,1]
[5,8,1,2,3,4,7,6]=>[3,1,1,1,1,1]
[7,1,2,8,3,6,4,5]=>[3,2,1,1,1]
[6,1,8,2,3,5,7,4]=>[3,2,1,1,1]
[6,1,7,2,3,5,8,4]=>[3,2,1,1,1]
[1,6,8,2,4,5,7,3]=>[3,1,1,1,1,1]
[4,3,8,7,5,6,2,1]=>[5,2,1]
[1,8,2,7,4,6,5,3]=>[5,1,1,1]
[7,1,6,2,3,5,8,4]=>[4,1,1,1,1]
[8,1,6,2,3,5,7,4]=>[4,1,1,1,1]
[8,1,7,2,3,5,6,4]=>[4,1,1,1,1]
[5,8,3,7,4,6,2,1]=>[5,1,1,1]
[6,8,7,3,4,5,2,1]=>[5,1,1,1]
[1,8,7,2,4,5,3,6]=>[4,1,1,1,1]
[8,7,1,2,3,4,6,5]=>[4,1,1,1,1]
[8,6,1,2,3,4,7,5]=>[3,2,1,1,1]
[8,1,6,2,3,5,4,7]=>[4,1,1,1,1]
[1,7,6,2,4,5,3,8]=>[4,1,1,1,1]
[1,8,7,4,6,3,5,2]=>[5,1,1,1]
[6,3,7,5,1,4,8,2]=>[4,2,1,1]
[1,8,3,5,7,2,6,4]=>[4,1,1,1,1]
[2,3,4,6,8,5,7,1]=>[3,1,1,1,1,1]
[2,3,5,7,4,8,6,1]=>[3,2,1,1,1]
[2,4,6,3,7,8,5,1]=>[3,2,1,1,1]
[2,5,7,1,8,6,3,4]=>[3,2,1,1,1]
[1,3,8,5,2,4,6,7]=>[3,1,1,1,1,1]
[2,6,7,1,8,4,5,3]=>[3,2,1,1,1]
[5,8,3,1,4,2,6,7]=>[3,2,1,1,1]
[3,8,4,2,6,7,1,5]=>[4,1,1,1,1]
[2,4,1,8,5,6,3,7]=>[3,2,1,1,1]
[1,6,2,7,8,5,3,4]=>[3,2,1,1,1]
[3,5,2,6,7,8,4,1]=>[3,2,1,1,1]
[4,5,1,6,7,3,8,2]=>[3,2,1,1,1]
[2,8,4,1,7,5,3,6]=>[4,2,1,1]
[8,5,3,1,7,4,2,6]=>[4,3,1]
[4,2,8,7,1,5,3,6]=>[4,2,1,1]
[5,2,6,8,1,7,4,3]=>[4,2,1,1]
[5,7,3,2,6,8,1,4]=>[4,1,1,1,1]
[8,4,7,3,1,6,2,5]=>[4,2,1,1]
[6,7,1,2,3,5,8,4]=>[3,1,1,1,1,1]
[3,1,6,7,8,4,2,5]=>[3,2,1,1,1]
[3,1,4,8,5,6,2,7]=>[3,2,1,1,1]
[8,3,1,4,5,7,2,6]=>[3,2,1,1,1]
[8,6,2,3,5,1,4,7]=>[4,1,1,1,1]
[8,2,4,5,7,3,1,6]=>[4,1,1,1,1]
[2,6,3,8,7,5,4,1]=>[5,2,1]
[8,2,3,7,5,4,1,6]=>[5,1,1,1]
[8,2,6,3,5,4,1,7]=>[5,1,1,1]
[8,6,1,5,2,4,3,7]=>[5,1,1,1]
[8,6,2,4,1,5,3,7]=>[4,2,1,1]
[8,4,1,6,5,3,2,7]=>[5,2,1]
[8,3,6,1,5,4,2,7]=>[5,1,1,1]
[8,3,2,6,5,4,1,7]=>[5,2,1]
[8,3,2,5,7,4,1,6]=>[4,2,1,1]
[8,3,1,7,5,4,2,6]=>[5,2,1]
[8,2,7,4,1,5,3,6]=>[4,2,1,1]
[6,1,3,8,7,5,4,2]=>[5,2,1]
[3,6,1,8,7,5,4,2]=>[5,2,1]
[3,8,1,5,7,6,4,2]=>[5,1,1,1]
[3,5,2,8,7,6,4,1]=>[5,2,1]
[3,4,8,2,7,6,5,1]=>[5,1,1,1]
[3,4,8,7,1,6,5,2]=>[5,1,1,1]
[8,1,3,5,7,6,4,2]=>[5,1,1,1]
[4,1,8,5,7,6,3,2]=>[5,2,1]
[8,2,7,1,4,5,6,3]=>[4,1,1,1,1]
[8,1,7,3,4,6,2,5]=>[4,1,1,1,1]
[8,3,1,7,2,6,5,4]=>[5,2,1]
[3,8,2,4,7,6,5,1]=>[5,1,1,1]
[2,8,3,7,4,6,5,1]=>[5,1,1,1]
[8,2,3,7,1,6,5,4]=>[5,1,1,1]
[8,2,7,1,3,6,5,4]=>[5,1,1,1]
[8,1,7,2,6,4,3,5]=>[5,1,1,1]
[8,1,7,5,2,4,3,6]=>[5,1,1,1]
[8,2,3,7,4,6,1,5]=>[4,1,1,1,1]
[2,4,8,5,7,6,3,1]=>[5,1,1,1]
[8,2,4,3,7,6,1,5]=>[4,2,1,1]
[8,2,7,3,5,1,4,6]=>[4,1,1,1,1]
[8,2,7,4,3,1,5,6]=>[5,1,1,1]
[8,2,7,3,1,5,6,4]=>[4,2,1,1]
[8,2,1,5,7,6,4,3]=>[5,2,1]
[6,2,1,8,7,5,4,3]=>[5,3]
[6,1,8,2,7,5,4,3]=>[5,2,1]
[8,1,7,3,5,2,6,4]=>[4,2,1,1]
[8,1,5,2,7,6,4,3]=>[5,2,1]
[8,1,7,2,4,6,5,3]=>[5,1,1,1]
[8,2,4,1,7,6,5,3]=>[5,2,1]
[4,2,8,3,7,6,5,1]=>[5,2,1]
[4,8,2,1,7,6,5,3]=>[5,2,1]
[5,1,8,7,2,6,4,3]=>[5,2,1]
[5,8,1,3,7,6,2,4]=>[4,1,1,1,1]
[8,2,5,4,1,7,6,3]=>[4,3,1]
[5,1,4,8,7,6,3,2]=>[5,2,1]
[8,1,4,3,7,6,5,2]=>[5,2,1]
[4,8,1,3,7,6,5,2]=>[5,1,1,1]
[4,3,8,1,7,6,5,2]=>[5,2,1]
[5,8,6,3,2,1,7,4]=>[5,2,1]
[5,7,6,3,2,4,1,8]=>[5,1,1,1]
[6,5,7,2,4,3,1,8]=>[5,1,1,1]
[5,7,1,3,2,8,6,4]=>[3,3,1,1]
[5,8,1,3,2,7,4,6]=>[3,2,1,1,1]
[8,5,1,3,2,4,6,7]=>[4,1,1,1,1]
[7,5,1,3,2,4,8,6]=>[4,2,1,1]
[7,5,8,2,1,4,3,6]=>[4,2,1,1]
[6,7,1,2,5,4,8,3]=>[4,1,1,1,1]
[6,8,1,2,5,7,4,3]=>[4,1,1,1,1]
[7,1,2,3,8,6,4,5]=>[3,2,1,1,1]
[8,1,6,4,2,3,5,7]=>[4,1,1,1,1]
[1,5,4,8,2,3,7,6]=>[3,2,1,1,1]
[1,7,8,2,3,5,6,4]=>[3,1,1,1,1,1]
[7,5,8,2,3,1,4,6]=>[4,1,1,1,1]
[7,4,1,2,6,8,3,5]=>[3,2,1,1,1]
[6,2,8,1,5,7,3,4]=>[3,2,1,1,1]
[7,2,5,4,1,8,6,3]=>[4,3,1]
[7,3,5,4,2,1,8,6]=>[5,2,1]
[7,3,2,8,5,6,1,4]=>[4,2,1,1]
[1,7,4,3,6,8,5,2]=>[4,2,1,1]
[4,7,6,5,2,3,8,1]=>[5,1,1,1]
[4,7,6,5,1,3,8,2]=>[5,1,1,1]
[5,4,6,8,7,2,1,3]=>[4,2,1,1]
[6,7,4,2,1,8,5,3]=>[4,3,1]
[6,5,8,1,7,3,4,2]=>[4,2,1,1]
[6,5,8,2,3,7,4,1]=>[4,2,1,1]
[6,5,8,3,4,1,7,2]=>[4,2,1,1]
[4,1,2,8,5,3,6,7]=>[3,2,1,1,1]
[3,5,8,2,6,1,7,4]=>[3,2,1,1,1]
[3,7,6,1,5,2,8,4]=>[4,2,1,1]
[1,7,6,2,5,8,4,3]=>[5,1,1,1]
[1,7,6,5,8,4,2,3]=>[5,1,1,1]
[3,7,6,2,8,4,5,1]=>[4,2,1,1]
[4,3,6,8,5,1,2,7]=>[3,2,1,1,1]
[2,7,6,1,8,4,3,5]=>[4,2,1,1]
[7,1,2,6,3,5,4,8]=>[4,1,1,1,1]
[7,2,6,3,4,5,1,8]=>[4,1,1,1,1]
[6,1,2,5,7,8,4,3]=>[4,1,1,1,1]
[4,1,2,7,8,5,3,6]=>[3,2,1,1,1]
[4,7,3,1,2,6,8,5]=>[3,2,1,1,1]
[3,7,6,1,5,8,2,4]=>[4,1,1,1,1]
[3,8,5,6,4,2,7,1]=>[5,1,1,1]
[3,2,6,4,7,8,5,1]=>[3,2,2,1]
[4,2,7,5,8,3,1,6]=>[4,2,1,1]
[5,2,1,4,7,8,3,6]=>[3,2,1,1,1]
[5,6,2,7,3,4,8,1]=>[3,2,1,1,1]
[6,1,3,8,5,4,7,2]=>[4,2,1,1]
[2,7,6,8,5,1,3,4]=>[4,1,1,1,1]
[2,7,6,8,5,3,1,4]=>[5,1,1,1]
[1,5,8,6,4,2,3,7]=>[4,1,1,1,1]
[2,5,8,6,4,1,7,3]=>[4,2,1,1]
[1,6,2,3,5,8,7,4]=>[3,2,1,1,1]
[4,7,2,3,1,6,8,5]=>[3,2,1,1,1]
[6,7,3,1,5,4,8,2]=>[4,2,1,1]
[7,4,6,2,8,3,5,1]=>[4,2,1,1]
[7,3,5,1,4,8,2,6]=>[4,1,1,1,1]
[3,4,6,5,1,2,7,8]=>[3,1,1,1,1,1]
[7,5,4,3,8,6,2,1]=>[6,2]
[4,3,8,2,6,7,5,1]=>[4,2,1,1]
[4,3,8,2,5,7,1,6]=>[4,1,1,1,1]
[4,1,6,2,5,3,7,8]=>[3,2,1,1,1]
[5,1,8,6,4,7,2,3]=>[4,2,1,1]
[4,2,6,1,5,3,8,7]=>[3,2,2,1]
[6,7,2,3,1,5,8,4]=>[3,2,1,1,1]
[7,5,2,3,8,1,6,4]=>[4,2,1,1]
[7,5,2,3,8,4,1,6]=>[4,2,1,1]
[4,5,1,7,6,3,8,2]=>[4,2,1,1]
[8,1,7,5,2,3,4,6]=>[4,1,1,1,1]
[8,6,3,1,4,2,5,7]=>[4,2,1,1]
[4,5,1,6,2,8,7,3]=>[3,2,2,1]
[6,2,7,8,3,4,5,1]=>[3,2,1,1,1]
[1,2,4,6,8,5,7,3]=>[3,1,1,1,1,1]
[2,1,7,5,8,6,3,4]=>[3,2,2,1]
[4,7,3,8,6,5,2,1]=>[5,2,1]
[3,8,7,4,6,5,1,2]=>[5,1,1,1]
[7,3,8,4,6,5,1,2]=>[4,2,1,1]
[7,4,3,6,5,8,1,2]=>[4,2,1,1]
[4,5,8,7,2,6,1,3]=>[4,1,1,1,1]
[3,8,6,7,5,1,4,2]=>[5,1,1,1]
[4,2,7,6,5,8,3,1]=>[5,2,1]
[4,6,7,8,5,2,3,1]=>[4,1,1,1,1]
[4,5,3,8,2,7,6,1]=>[4,2,1,1]
[3,8,5,4,1,7,6,2]=>[4,3,1]
[6,4,7,2,5,8,3,1]=>[4,2,1,1]
[6,3,8,7,5,1,4,2]=>[5,2,1]
[5,3,6,4,1,2,8,7]=>[3,2,2,1]
[6,8,4,3,5,7,1,2]=>[4,1,1,1,1]
[5,2,4,8,7,6,1,3]=>[4,2,1,1]
[4,2,5,1,7,8,3,6]=>[3,2,1,1,1]
[2,5,4,1,3,8,6,7]=>[3,2,1,1,1]
[1,4,5,3,8,2,6,7]=>[3,1,1,1,1,1]
[5,1,8,2,4,3,6,7]=>[3,2,1,1,1]
[1,5,4,8,2,3,6,7]=>[3,1,1,1,1,1]
[3,5,1,4,7,8,2,6]=>[3,1,1,1,1,1]
[4,8,3,1,6,7,2,5]=>[3,2,1,1,1]
[3,4,8,2,6,5,7,1]=>[4,1,1,1,1]
[3,6,2,4,8,7,1,5]=>[3,2,1,1,1]
[4,7,3,2,6,8,1,5]=>[4,1,1,1,1]
[7,3,4,6,8,1,2,5]=>[3,1,1,1,1,1]
[3,6,7,2,5,8,1,4]=>[3,1,1,1,1,1]
[1,5,6,8,3,7,2,4]=>[3,1,1,1,1,1]
[6,1,5,8,3,4,7,2]=>[4,1,1,1,1]
[5,6,8,1,3,4,7,2]=>[3,1,1,1,1,1]
[2,8,5,6,3,4,7,1]=>[4,1,1,1,1]
[6,8,1,3,5,4,7,2]=>[4,1,1,1,1]
[8,1,6,3,5,4,7,2]=>[5,1,1,1]
[7,1,2,5,8,4,6,3]=>[4,1,1,1,1]
[6,2,4,8,1,7,3,5]=>[3,2,1,1,1]
[3,1,7,8,5,4,6,2]=>[4,2,1,1]
[1,6,2,7,4,8,5,3]=>[3,2,2,1]
[2,7,1,8,4,3,5,6]=>[3,2,1,1,1]
[6,7,1,8,3,2,4,5]=>[3,2,1,1,1]
[2,7,6,3,5,8,1,4]=>[4,1,1,1,1]
[2,7,5,6,8,1,3,4]=>[3,1,1,1,1,1]
[6,7,2,8,1,3,4,5]=>[3,1,1,1,1,1]
[5,1,6,8,7,2,3,4]=>[3,2,1,1,1]
[1,5,7,6,8,2,3,4]=>[3,1,1,1,1,1]
[7,4,6,8,5,3,1,2]=>[5,1,1,1]
[2,1,5,7,8,3,6,4]=>[3,2,1,1,1]
[3,8,6,7,5,1,2,4]=>[4,1,1,1,1]
[4,7,5,8,6,3,1,2]=>[4,2,1,1]
[1,6,8,3,2,5,4,7]=>[3,2,1,1,1]
[7,8,5,1,3,2,6,4]=>[4,2,1,1]
[2,6,8,1,5,4,7,3]=>[4,1,1,1,1]
[1,5,4,7,6,2,8,3]=>[3,2,2,1]
[6,1,5,8,3,2,7,4]=>[4,2,1,1]
[3,1,2,4,8,5,7,6]=>[3,2,1,1,1]
[7,1,5,4,8,3,2,6]=>[5,1,1,1]
[6,4,1,7,5,3,2,8]=>[4,3,1]
[2,7,6,4,8,1,5,3]=>[4,2,1,1]
[7,2,5,4,8,1,6,3]=>[4,2,1,1]
[1,7,2,5,3,8,6,4]=>[3,3,1,1]
[7,2,3,8,6,1,5,4]=>[4,2,1,1]
[5,3,8,4,1,2,6,7]=>[3,2,1,1,1]
[2,4,8,3,7,1,5,6]=>[3,1,1,1,1,1]
[5,2,8,4,1,6,3,7]=>[3,2,2,1]
[7,6,5,2,1,8,4,3]=>[5,3]
[2,7,5,1,8,3,6,4]=>[3,3,1,1]
[5,1,8,7,4,3,6,2]=>[5,2,1]
[3,8,7,2,4,6,1,5]=>[4,1,1,1,1]
[5,7,1,3,2,4,8,6]=>[3,2,1,1,1]
[4,2,7,6,3,5,8,1]=>[4,2,1,1]
[8,4,7,6,3,5,1,2]=>[5,1,1,1]
[8,1,7,4,2,3,5,6]=>[4,1,1,1,1]
[6,5,1,3,8,7,4,2]=>[4,3,1]
[4,7,8,3,2,5,1,6]=>[4,1,1,1,1]
[6,1,8,5,3,7,2,4]=>[4,2,1,1]
[5,1,6,8,3,7,4,2]=>[4,2,1,1]
[8,6,5,1,7,4,3,2]=>[6,2]
[7,6,4,1,3,5,8,2]=>[5,1,1,1]
[8,2,3,7,1,4,5,6]=>[3,1,1,1,1,1]
[2,8,3,7,1,4,5,6]=>[3,1,1,1,1,1]
[5,6,2,7,4,3,1,8]=>[4,2,1,1]
[8,6,2,7,4,1,3,5]=>[4,2,1,1]
[3,7,8,2,6,1,4,5]=>[3,1,1,1,1,1]
[3,7,8,5,2,1,4,6]=>[4,1,1,1,1]
[6,8,4,7,3,1,5,2]=>[4,2,1,1]
[4,8,6,5,1,2,7,3]=>[4,2,1,1]
[4,8,6,5,1,2,3,7]=>[4,1,1,1,1]
[3,4,5,1,7,6,8,2]=>[3,2,1,1,1]
[3,8,7,6,5,1,2,4]=>[5,1,1,1]
[8,4,6,7,1,2,5,3]=>[4,1,1,1,1]
[5,7,2,6,1,8,4,3]=>[4,2,1,1]
[5,7,2,6,1,3,8,4]=>[3,2,1,1,1]
[5,8,2,6,1,4,7,3]=>[4,1,1,1,1]
[3,8,7,5,6,1,4,2]=>[5,1,1,1]
[6,8,4,7,2,1,5,3]=>[4,2,1,1]
[7,4,6,5,1,3,8,2]=>[5,1,1,1]
[1,7,3,4,5,2,8,6]=>[3,2,1,1,1]
[1,7,2,5,4,3,8,6]=>[4,2,1,1]
[2,6,7,3,4,8,1,5]=>[3,1,1,1,1,1]
[2,1,5,7,4,3,8,6]=>[3,2,2,1]
[6,4,1,3,8,7,5,2]=>[4,3,1]
[2,1,7,4,6,8,3,5]=>[3,2,1,1,1]
[8,6,4,2,7,3,5,1]=>[5,2,1]
[2,1,8,3,5,7,6,4]=>[4,2,1,1]
[3,5,8,1,7,6,2,4]=>[4,1,1,1,1]
[7,2,4,8,6,1,5,3]=>[4,2,1,1]
[6,4,3,2,8,1,7,5]=>[5,2,1]
[6,2,4,3,8,1,7,5]=>[4,2,1,1]
[5,8,4,3,1,6,7,2]=>[4,2,1,1]
[4,2,8,1,5,7,6,3]=>[4,2,1,1]
[6,3,7,2,5,4,8,1]=>[4,2,1,1]
[5,4,7,3,2,6,8,1]=>[5,1,1,1]
[5,7,2,6,3,4,8,1]=>[4,1,1,1,1]
[3,7,5,4,6,2,8,1]=>[5,1,1,1]
[6,8,3,2,1,7,4,5]=>[4,2,1,1]
[4,8,1,7,5,3,2,6]=>[5,1,1,1]
[5,4,3,7,2,8,6,1]=>[5,2,1]
[3,6,5,7,2,8,4,1]=>[4,2,1,1]
[4,6,5,3,8,2,1,7]=>[5,1,1,1]
[2,6,5,8,7,3,1,4]=>[4,2,1,1]
[6,3,8,4,1,7,2,5]=>[3,2,2,1]
[7,2,8,1,6,4,3,5]=>[4,2,1,1]
[3,2,8,7,6,4,1,5]=>[5,2,1]
[8,2,6,4,3,5,1,7]=>[5,1,1,1]
[5,4,2,8,6,3,7,1]=>[4,3,1]
[2,8,7,5,3,1,4,6]=>[5,1,1,1]
[2,5,6,3,1,4,8,7]=>[3,2,1,1,1]
[2,4,7,8,5,3,1,6]=>[4,1,1,1,1]
[6,5,3,2,4,1,8,7]=>[5,2,1]
[6,5,8,7,3,2,4,1]=>[5,2,1]
[2,1,4,7,8,5,3,6]=>[3,2,1,1,1]
[8,5,6,7,3,1,4,2]=>[4,2,1,1]
[8,7,5,3,2,6,4,1]=>[6,2]
[8,5,3,1,4,6,7,2]=>[4,2,1,1]
[8,5,1,6,4,3,7,2]=>[5,2,1]
[6,1,4,3,7,8,2,5]=>[4,1,1,1,1]
[6,1,2,7,5,8,3,4]=>[3,2,1,1,1]
[2,7,3,1,4,6,8,5]=>[3,2,1,1,1]
[2,8,3,1,6,5,7,4]=>[4,2,1,1]
[3,8,5,6,7,1,2,4]=>[3,1,1,1,1,1]
[2,5,8,1,4,6,7,3]=>[3,1,1,1,1,1]
[2,1,8,7,5,4,6,3]=>[5,2,1]
[7,8,3,4,1,6,5,2]=>[4,2,1,1]
[8,7,3,4,2,6,5,1]=>[5,2,1]
[8,4,5,2,3,7,1,6]=>[4,1,1,1,1]
[4,7,2,8,6,3,1,5]=>[4,2,1,1]
[4,7,5,2,3,8,1,6]=>[4,1,1,1,1]
[6,4,7,5,2,8,3,1]=>[4,2,2]
[7,5,1,3,6,4,8,2]=>[4,2,1,1]
[6,5,2,3,7,8,4,1]=>[4,2,1,1]
[7,2,6,3,1,5,8,4]=>[4,2,1,1]
[1,8,4,2,5,7,6,3]=>[4,2,1,1]
[1,8,5,2,4,7,6,3]=>[4,2,1,1]
[1,4,6,2,8,7,5,3]=>[4,2,1,1]
[2,4,6,1,8,7,5,3]=>[4,2,1,1]
[2,1,6,8,7,5,3,4]=>[4,2,1,1]
[1,2,8,3,5,7,6,4]=>[4,1,1,1,1]
[2,3,8,1,5,7,6,4]=>[4,1,1,1,1]
[2,6,1,8,7,5,3,4]=>[4,2,1,1]
[2,6,3,8,7,5,1,4]=>[4,2,1,1]
[3,2,8,1,5,7,6,4]=>[4,2,1,1]
[2,8,1,4,5,7,6,3]=>[4,1,1,1,1]
[7,8,2,1,4,6,5,3]=>[4,2,1,1]
[2,3,6,8,7,5,1,4]=>[4,1,1,1,1]
[3,8,4,5,1,6,2,7]=>[3,2,1,1,1]
[6,1,4,5,7,2,3,8]=>[3,1,1,1,1,1]
[8,1,4,7,6,3,2,5]=>[5,1,1,1]
[8,3,1,6,4,7,2,5]=>[4,2,1,1]
[5,3,8,6,2,7,1,4]=>[4,2,1,1]
[8,3,6,1,5,7,2,4]=>[4,1,1,1,1]
[8,4,6,3,1,2,5,7]=>[4,1,1,1,1]
[6,8,1,4,5,2,3,7]=>[3,1,1,1,1,1]
[1,5,8,4,6,2,3,7]=>[3,1,1,1,1,1]
[2,1,6,5,3,8,4,7]=>[3,2,2,1]
[5,6,8,1,4,2,3,7]=>[3,1,1,1,1,1]
[5,7,4,8,1,2,3,6]=>[3,1,1,1,1,1]
[8,2,1,5,3,7,4,6]=>[3,2,2,1]
[4,7,8,1,2,6,3,5]=>[3,1,1,1,1,1]
[8,7,1,5,6,2,3,4]=>[4,1,1,1,1]
[1,6,5,8,7,2,3,4]=>[3,2,1,1,1]
[5,1,2,7,6,8,3,4]=>[3,2,1,1,1]
[6,1,7,2,5,8,3,4]=>[3,2,1,1,1]
[1,7,6,5,8,2,3,4]=>[4,1,1,1,1]
[1,6,8,5,7,2,3,4]=>[3,1,1,1,1,1]
[7,5,1,2,6,8,3,4]=>[3,2,1,1,1]
[6,1,5,2,7,8,3,4]=>[3,2,1,1,1]
[1,6,3,8,7,2,4,5]=>[3,2,1,1,1]
[1,7,3,2,4,6,8,5]=>[3,2,1,1,1]
[8,3,1,4,2,5,7,6]=>[3,2,2,1]
[3,1,2,7,8,4,6,5]=>[3,2,1,1,1]
[5,1,2,6,8,7,3,4]=>[3,2,1,1,1]
[1,8,6,2,5,7,3,4]=>[4,1,1,1,1]
[5,7,8,1,2,6,3,4]=>[3,1,1,1,1,1]
[8,1,5,7,6,2,3,4]=>[4,1,1,1,1]
[7,1,6,8,5,2,3,4]=>[4,1,1,1,1]
[3,7,1,2,8,4,6,5]=>[3,2,1,1,1]
[8,3,1,2,7,6,4,5]=>[4,2,1,1]
[1,5,8,7,6,2,3,4]=>[4,1,1,1,1]
[7,8,6,1,5,2,3,4]=>[4,1,1,1,1]
[7,8,6,3,1,5,2,4]=>[4,2,1,1]
[7,8,1,3,4,5,2,6]=>[3,1,1,1,1,1]
[1,7,4,8,2,5,3,6]=>[3,2,1,1,1]
[3,8,6,1,4,2,7,5]=>[4,2,1,1]
[7,1,8,2,4,6,3,5]=>[3,2,1,1,1]
[7,6,8,4,1,5,3,2]=>[5,2,1]
[7,3,2,8,1,5,4,6]=>[4,2,1,1]
[3,5,4,1,7,2,6,8]=>[3,2,1,1,1]
[6,4,7,3,2,5,1,8]=>[5,1,1,1]
[7,6,5,3,8,4,1,2]=>[5,2,1]
[6,4,5,7,8,1,3,2]=>[4,1,1,1,1]
[3,7,4,1,6,8,5,2]=>[4,2,1,1]
[3,1,2,7,6,8,5,4]=>[4,2,1,1]
[6,3,2,8,4,5,1,7]=>[4,2,1,1]
[6,1,8,3,5,4,2,7]=>[4,2,1,1]
[3,8,5,2,4,6,1,7]=>[4,1,1,1,1]
[1,6,4,8,3,5,2,7]=>[4,1,1,1,1]
[1,5,4,8,6,3,7,2]=>[4,2,1,1]
[4,8,2,5,3,7,1,6]=>[4,1,1,1,1]
[3,8,4,5,2,6,7,1]=>[4,1,1,1,1]
[4,1,8,6,5,3,7,2]=>[5,2,1]
[5,7,8,4,6,3,2,1]=>[5,1,1,1]
[5,3,2,8,6,4,7,1]=>[4,3,1]
[6,8,1,2,7,4,3,5]=>[4,1,1,1,1]
[5,8,7,3,6,2,4,1]=>[5,1,1,1]
[7,5,2,3,4,8,6,1]=>[4,2,1,1]
[7,3,5,4,2,8,6,1]=>[5,2,1]
[5,6,1,3,2,4,7,8]=>[3,1,1,1,1,1]
[2,5,1,3,7,8,6,4]=>[3,2,1,1,1]
[4,3,7,2,1,8,6,5]=>[4,3,1]
[4,6,7,2,1,3,5,8]=>[3,1,1,1,1,1]
[4,6,2,3,1,5,7,8]=>[3,1,1,1,1,1]
[3,6,4,2,5,1,7,8]=>[4,1,1,1,1]
[3,1,6,4,7,5,2,8]=>[3,2,2,1]
[3,6,2,7,5,4,1,8]=>[4,2,1,1]
[2,4,7,5,3,6,1,8]=>[4,1,1,1,1]
[2,5,7,3,4,1,6,8]=>[3,1,1,1,1,1]
[2,3,5,8,6,4,7,1]=>[4,1,1,1,1]
[2,4,7,3,8,6,5,1]=>[4,2,1,1]
[3,4,2,7,5,8,6,1]=>[3,2,2,1]
[3,1,5,4,7,8,6,2]=>[3,2,2,1]
[4,5,7,2,3,1,8,6]=>[3,2,1,1,1]
[3,7,8,1,4,6,5,2]=>[4,1,1,1,1]
[2,5,8,7,4,1,3,6]=>[4,1,1,1,1]
[2,6,4,7,5,3,8,1]=>[4,2,1,1]
[6,2,4,7,1,3,8,5]=>[3,2,1,1,1]
[7,3,5,1,4,2,8,6]=>[4,2,1,1]
[5,4,7,1,3,2,8,6]=>[4,2,1,1]
[6,1,4,7,5,3,8,2]=>[4,2,1,1]
[8,7,4,3,1,5,6,2]=>[5,2,1]
[8,7,1,4,3,5,6,2]=>[5,1,1,1]
[6,1,8,4,7,3,2,5]=>[4,2,1,1]
[4,7,3,6,1,2,8,5]=>[3,2,1,1,1]
[5,2,1,7,4,3,8,6]=>[3,3,2]
[4,7,6,2,3,1,8,5]=>[4,2,1,1]
[7,6,8,2,5,3,4,1]=>[5,1,1,1]
[2,3,6,1,8,7,5,4]=>[4,2,1,1]
[2,6,8,7,5,3,1,4]=>[5,1,1,1]
[6,4,1,7,5,2,8,3]=>[3,3,2]
[5,7,8,2,3,6,1,4]=>[3,1,1,1,1,1]
[4,8,7,1,2,5,6,3]=>[4,1,1,1,1]
[2,8,7,4,1,5,6,3]=>[4,2,1,1]
[8,6,2,1,5,7,4,3]=>[5,2,1]
[3,8,6,7,5,2,1,4]=>[5,1,1,1]
[6,1,3,7,5,8,2,4]=>[3,2,1,1,1]
[4,7,3,1,8,5,6,2]=>[3,3,1,1]
[2,6,7,5,3,4,8,1]=>[4,1,1,1,1]
[2,6,4,5,7,3,8,1]=>[4,1,1,1,1]
[6,1,4,5,8,3,7,2]=>[4,1,1,1,1]
[6,1,8,5,3,4,7,2]=>[4,2,1,1]
[4,1,5,6,8,3,7,2]=>[3,2,1,1,1]
[6,4,1,8,7,2,5,3]=>[4,3,1]
[1,3,8,5,2,7,4,6]=>[3,2,1,1,1]
[1,3,8,6,7,2,4,5]=>[3,1,1,1,1,1]
[2,8,3,7,6,1,4,5]=>[4,1,1,1,1]
[4,2,7,8,6,1,3,5]=>[3,2,1,1,1]
[1,3,8,7,6,2,4,5]=>[4,1,1,1,1]
[7,4,6,8,5,2,3,1]=>[5,1,1,1]
[7,5,3,6,8,2,1,4]=>[5,1,1,1]
[5,2,6,7,8,1,3,4]=>[3,1,1,1,1,1]
[4,5,6,8,1,2,7,3]=>[3,1,1,1,1,1]
[3,5,8,6,1,2,7,4]=>[3,2,1,1,1]
[4,2,6,8,7,1,3,5]=>[3,2,1,1,1]
[1,4,6,8,7,2,3,5]=>[3,1,1,1,1,1]
[4,5,3,8,1,7,2,6]=>[3,2,1,1,1]
[3,5,8,4,1,7,2,6]=>[3,2,1,1,1]
[1,6,5,7,8,2,3,4]=>[3,1,1,1,1,1]
[5,6,4,8,2,3,7,1]=>[4,1,1,1,1]
[6,5,4,8,1,3,7,2]=>[5,1,1,1]
[7,6,4,8,5,1,3,2]=>[5,2,1]
[7,2,6,5,8,1,3,4]=>[4,1,1,1,1]
[6,3,7,5,2,4,8,1]=>[4,2,1,1]
[8,1,2,7,4,5,3,6]=>[4,1,1,1,1]
[2,5,7,4,6,1,3,8]=>[3,1,1,1,1,1]
[6,1,7,4,5,3,8,2]=>[4,2,1,1]
[8,2,7,3,1,5,4,6]=>[4,2,1,1]
[8,1,3,7,5,6,4,2]=>[5,1,1,1]
[1,2,5,3,8,6,7,4]=>[3,2,1,1,1]
[4,1,6,5,7,8,2,3]=>[3,2,1,1,1]
[6,1,3,7,4,2,8,5]=>[3,2,2,1]
[6,7,2,4,1,3,8,5]=>[3,2,1,1,1]
[7,3,8,4,2,6,5,1]=>[4,2,2]
[8,5,3,4,2,7,1,6]=>[5,1,1,1]
[1,3,8,2,5,6,7,4]=>[3,1,1,1,1,1]
[1,8,6,7,2,5,4,3]=>[5,1,1,1]
[8,7,2,4,6,1,5,3]=>[5,1,1,1]
[7,8,6,5,2,4,3,1]=>[6,1,1]
[3,6,7,5,2,8,4,1]=>[4,2,1,1]
[5,4,6,7,8,1,3,2]=>[4,1,1,1,1]
[5,3,6,7,8,1,4,2]=>[3,2,1,1,1]
[5,3,7,6,8,4,1,2]=>[4,2,1,1]
[7,5,3,2,8,6,4,1]=>[5,3]
[5,4,8,6,7,2,3,1]=>[4,2,1,1]
[5,4,8,6,3,1,2,7]=>[4,2,1,1]
[4,5,7,3,6,2,8,1]=>[4,1,1,1,1]
[4,5,6,3,8,2,7,1]=>[4,1,1,1,1]
[5,4,8,7,2,1,3,6]=>[4,2,1,1]
[2,5,4,7,8,1,3,6]=>[3,1,1,1,1,1]
[5,3,6,4,8,2,7,1]=>[4,2,1,1]
[5,3,7,4,6,2,8,1]=>[4,2,1,1]
[8,2,4,7,3,5,6,1]=>[4,1,1,1,1]
[4,5,6,2,7,3,8,1]=>[3,2,1,1,1]
[5,4,6,2,8,3,7,1]=>[4,2,1,1]
[8,4,6,1,7,2,5,3]=>[4,2,1,1]
[5,2,1,6,3,8,7,4]=>[3,3,2]
[4,5,6,3,7,1,8,2]=>[3,2,1,1,1]
[6,3,2,8,5,4,1,7]=>[4,3,1]
[4,3,1,5,2,8,6,7]=>[3,2,2,1]
[8,5,4,1,3,2,6,7]=>[5,1,1,1]
[3,8,4,1,5,2,6,7]=>[3,2,1,1,1]
[2,5,4,3,8,1,6,7]=>[4,1,1,1,1]
[2,5,7,4,3,1,6,8]=>[4,1,1,1,1]
[5,3,4,2,7,1,6,8]=>[4,1,1,1,1]
[3,7,5,4,1,2,6,8]=>[4,1,1,1,1]
[4,2,5,1,3,8,7,6]=>[3,3,1,1]
[4,3,5,1,2,7,6,8]=>[3,2,1,1,1]
[5,3,4,1,7,2,6,8]=>[3,2,1,1,1]
[4,1,6,3,5,2,7,8]=>[3,2,1,1,1]
[4,2,1,8,6,3,7,5]=>[3,3,2]
[3,1,7,2,5,6,4,8]=>[3,2,1,1,1]
[3,7,5,4,2,1,6,8]=>[5,1,1,1]
[3,7,2,4,1,6,5,8]=>[3,2,1,1,1]
[7,3,2,1,6,4,5,8]=>[4,2,1,1]
[2,8,6,1,7,4,3,5]=>[4,2,1,1]
[2,5,4,6,1,3,7,8]=>[3,1,1,1,1,1]
[2,5,6,4,1,3,7,8]=>[3,1,1,1,1,1]
[8,5,2,6,1,3,7,4]=>[4,2,1,1]
[7,1,5,6,3,2,4,8]=>[4,1,1,1,1]
[7,1,2,5,4,6,3,8]=>[4,1,1,1,1]
[2,4,1,6,5,3,7,8]=>[3,2,1,1,1]
[4,1,2,7,5,6,3,8]=>[3,2,1,1,1]
[7,1,2,6,5,4,3,8]=>[5,1,1,1]
[8,2,1,5,6,3,7,4]=>[3,2,2,1]
[6,1,4,5,3,2,7,8]=>[4,1,1,1,1]
[3,1,6,5,4,2,7,8]=>[4,2,1,1]
[3,1,4,6,5,2,7,8]=>[3,2,1,1,1]
[6,4,1,5,3,2,8,7]=>[4,2,2]
[2,1,8,6,3,7,5,4]=>[4,2,2]
[5,8,3,1,7,6,4,2]=>[5,2,1]
[7,6,3,2,8,5,1,4]=>[5,2,1]
[5,6,3,8,7,4,1,2]=>[4,2,1,1]
[5,2,6,8,7,4,1,3]=>[4,2,1,1]
[6,3,8,5,4,1,2,7]=>[4,2,1,1]
[6,3,8,4,5,1,2,7]=>[3,2,1,1,1]
[5,2,3,1,4,8,6,7]=>[3,2,1,1,1]
[5,4,1,3,2,8,6,7]=>[4,2,1,1]
[5,1,3,4,2,8,6,7]=>[3,2,1,1,1]
[4,2,7,3,8,5,1,6]=>[3,2,2,1]
[4,3,7,2,8,5,6,1]=>[4,2,1,1]
[5,3,1,2,4,8,6,7]=>[3,2,1,1,1]
[5,4,3,1,2,8,6,7]=>[4,2,1,1]
[5,3,4,1,2,8,6,7]=>[3,2,1,1,1]
[5,2,3,4,1,8,6,7]=>[3,2,1,1,1]
[5,1,7,3,4,6,8,2]=>[3,2,1,1,1]
[5,8,7,4,3,1,6,2]=>[5,2,1]
[6,8,1,3,4,5,7,2]=>[3,1,1,1,1,1]
[3,5,2,8,1,6,7,4]=>[3,2,1,1,1]
[3,1,7,8,2,5,4,6]=>[3,2,1,1,1]
[6,2,3,7,4,1,8,5]=>[3,2,2,1]
[6,3,7,4,1,2,5,8]=>[3,2,1,1,1]
[3,7,2,8,6,5,1,4]=>[4,2,1,1]
[3,6,7,5,1,2,4,8]=>[3,1,1,1,1,1]
[7,4,5,1,8,2,3,6]=>[3,2,1,1,1]
[7,2,3,1,8,4,5,6]=>[3,2,1,1,1]
[2,1,4,8,3,7,5,6]=>[3,2,1,1,1]
[1,2,7,8,4,3,6,5]=>[3,2,1,1,1]
[5,8,1,4,3,2,7,6]=>[4,2,1,1]
[4,8,1,3,5,6,2,7]=>[3,1,1,1,1,1]
[5,3,7,8,4,2,6,1]=>[4,2,1,1]
[6,3,7,8,2,4,5,1]=>[4,1,1,1,1]
[8,5,2,4,3,1,7,6]=>[5,2,1]
[7,5,4,2,3,1,8,6]=>[5,2,1]
[3,5,6,4,8,1,7,2]=>[3,2,1,1,1]
[3,5,4,6,7,1,8,2]=>[3,2,1,1,1]
[1,4,2,6,5,8,7,3]=>[3,2,2,1]
[1,3,2,6,4,8,7,5]=>[3,2,2,1]
[1,4,2,5,3,8,7,6]=>[3,2,2,1]
[1,5,2,6,4,8,7,3]=>[3,2,2,1]
[1,6,2,5,3,8,7,4]=>[3,3,1,1]
[2,5,1,4,3,8,7,6]=>[3,3,1,1]
[1,7,3,5,4,8,6,2]=>[4,2,1,1]
[1,8,3,6,4,7,5,2]=>[4,2,1,1]
[1,7,2,6,4,8,5,3]=>[4,2,1,1]
[1,5,2,7,4,8,6,3]=>[3,2,2,1]
[1,4,2,8,5,7,6,3]=>[4,2,1,1]
[4,8,1,3,2,6,5,7]=>[3,2,1,1,1]
[1,5,3,8,4,7,6,2]=>[4,2,1,1]
[1,8,4,7,3,6,5,2]=>[5,1,1,1]
[2,6,3,8,1,5,4,7]=>[3,2,1,1,1]
[8,3,1,4,2,6,5,7]=>[3,2,2,1]
[4,8,7,3,5,2,1,6]=>[5,1,1,1]
[6,8,7,3,5,2,4,1]=>[5,1,1,1]
[8,3,5,1,2,6,4,7]=>[3,2,1,1,1]
[8,6,3,1,5,4,2,7]=>[5,2,1]
[8,6,4,1,5,3,2,7]=>[5,2,1]
[8,6,5,4,1,3,2,7]=>[6,1,1]
[5,3,8,7,4,6,2,1]=>[5,2,1]
[2,3,8,7,4,6,1,5]=>[4,1,1,1,1]
[8,3,5,7,4,1,2,6]=>[4,1,1,1,1]
[4,8,5,3,1,2,7,6]=>[4,2,1,1]
[6,8,7,3,1,5,4,2]=>[5,2,1]
[6,8,5,4,1,3,7,2]=>[5,1,1,1]
[2,5,8,7,4,6,3,1]=>[5,1,1,1]
[4,8,7,6,5,1,3,2]=>[6,1,1]
[3,8,7,5,1,6,2,4]=>[4,2,1,1]
[2,3,8,7,5,6,1,4]=>[4,1,1,1,1]
[2,8,7,1,3,6,4,5]=>[4,1,1,1,1]
[8,5,4,7,2,1,3,6]=>[5,1,1,1]
[6,8,7,3,5,2,1,4]=>[5,1,1,1]
[3,5,8,6,4,2,7,1]=>[5,1,1,1]
[6,8,4,1,5,2,7,3]=>[3,2,2,1]
[6,8,2,1,7,5,3,4]=>[4,2,1,1]
[5,8,4,6,1,2,7,3]=>[3,2,1,1,1]
[2,4,8,6,5,1,7,3]=>[4,2,1,1]
[4,8,7,6,5,2,1,3]=>[6,1,1]
[4,8,7,5,1,6,2,3]=>[4,2,1,1]
[4,5,2,1,8,6,7,3]=>[3,3,1,1]
[4,5,8,3,1,6,7,2]=>[3,2,1,1,1]
[5,7,2,8,4,6,1,3]=>[3,2,1,1,1]
[7,2,8,6,4,5,1,3]=>[4,2,1,1]
[8,7,2,6,5,1,3,4]=>[5,1,1,1]
[5,2,7,8,4,1,3,6]=>[3,2,1,1,1]
[5,1,6,3,4,8,2,7]=>[3,2,1,1,1]
[3,5,2,6,4,8,1,7]=>[3,2,1,1,1]
[6,3,8,2,4,1,7,5]=>[4,2,1,1]
[6,3,8,7,5,4,2,1]=>[6,2]
[6,8,4,2,1,7,5,3]=>[4,3,1]
[5,2,6,4,3,8,1,7]=>[4,2,1,1]
[6,5,3,1,4,8,2,7]=>[4,2,1,1]
[3,8,1,7,6,2,5,4]=>[5,1,1,1]
[8,1,7,6,4,2,5,3]=>[5,2,1]
[7,2,6,3,8,5,4,1]=>[5,2,1]
[7,3,8,6,4,1,5,2]=>[4,2,2]
[1,7,5,8,2,4,3,6]=>[4,1,1,1,1]
[6,1,5,2,4,8,3,7]=>[4,1,1,1,1]
[2,6,7,4,3,8,5,1]=>[4,2,1,1]
[5,2,4,7,3,8,6,1]=>[4,2,1,1]
[8,3,7,2,5,1,6,4]=>[4,2,1,1]
[3,7,2,8,1,5,4,6]=>[3,2,1,1,1]
[7,2,8,1,4,3,6,5]=>[3,2,2,1]
[1,7,5,4,8,3,2,6]=>[5,1,1,1]
[6,1,5,4,3,8,2,7]=>[5,1,1,1]
[1,7,4,5,6,8,2,3]=>[3,1,1,1,1,1]
[1,6,4,2,3,5,7,8]=>[3,1,1,1,1,1]
[1,8,7,2,3,4,5,6]=>[3,1,1,1,1,1]
[1,5,8,6,2,3,4,7]=>[3,1,1,1,1,1]
[1,6,5,7,2,3,4,8]=>[3,1,1,1,1,1]
[1,7,5,6,2,3,4,8]=>[3,1,1,1,1,1]
[1,3,2,7,6,4,5,8]=>[3,2,1,1,1]
[1,2,3,7,6,4,5,8]=>[3,1,1,1,1,1]
[1,5,4,2,3,7,6,8]=>[3,2,1,1,1]
[1,5,4,2,3,8,6,7]=>[3,2,1,1,1]
[1,3,2,8,6,4,5,7]=>[3,2,1,1,1]
[1,7,5,8,2,3,4,6]=>[3,1,1,1,1,1]
[1,8,7,5,2,3,4,6]=>[4,1,1,1,1]
[2,1,5,8,6,3,7,4]=>[3,2,2,1]
[2,5,8,4,6,1,7,3]=>[3,2,1,1,1]
[2,5,3,8,6,1,7,4]=>[3,2,2,1]
[2,6,3,5,8,1,7,4]=>[3,2,1,1,1]
[6,3,2,5,8,1,7,4]=>[4,2,1,1]
[5,3,2,8,6,1,7,4]=>[4,2,2]
[5,8,4,6,1,3,7,2]=>[4,1,1,1,1]
[5,3,8,6,1,4,7,2]=>[4,2,1,1]
[2,6,5,4,8,1,7,3]=>[4,2,1,1]
[8,3,5,7,2,6,4,1]=>[5,1,1,1]
[2,4,6,8,5,3,7,1]=>[4,1,1,1,1]
[2,4,8,1,7,6,5,3]=>[5,1,1,1]
[4,3,8,1,5,7,6,2]=>[4,2,1,1]
[3,8,4,1,5,7,6,2]=>[4,2,1,1]
[4,3,6,8,5,2,7,1]=>[4,2,1,1]
[8,5,4,7,2,6,3,1]=>[5,2,1]
[3,6,8,5,4,2,7,1]=>[5,1,1,1]
[3,6,4,8,5,2,7,1]=>[4,2,1,1]
[3,6,4,1,8,2,7,5]=>[3,3,1,1]
[3,6,4,1,5,2,8,7]=>[3,2,2,1]
[4,8,6,5,1,3,7,2]=>[5,1,1,1]
[2,8,3,5,6,7,1,4]=>[3,1,1,1,1,1]
[5,6,2,4,7,1,8,3]=>[3,2,1,1,1]
[2,7,5,4,6,1,8,3]=>[4,2,1,1]
[2,3,7,4,6,1,8,5]=>[3,2,1,1,1]
[2,6,7,4,1,3,8,5]=>[3,2,1,1,1]
[6,5,7,4,1,3,8,2]=>[5,1,1,1]
[2,4,6,3,5,7,8,1]=>[3,1,1,1,1,1]
[4,1,6,3,5,7,8,2]=>[3,2,1,1,1]
[3,6,4,2,5,7,8,1]=>[4,1,1,1,1]
[2,3,6,1,5,7,8,4]=>[3,1,1,1,1,1]
[4,3,6,2,5,7,8,1]=>[4,1,1,1,1]
[4,6,1,2,5,7,8,3]=>[3,1,1,1,1,1]
[2,6,4,1,5,7,8,3]=>[3,2,1,1,1]
[2,4,1,6,5,7,8,3]=>[3,2,1,1,1]
[7,5,4,2,6,1,8,3]=>[5,2,1]
[4,7,3,1,8,6,5,2]=>[4,3,1]
[5,6,4,2,7,1,8,3]=>[4,2,1,1]
[4,2,7,5,3,1,8,6]=>[4,2,2]
[5,3,6,4,8,2,1,7]=>[4,2,1,1]
[7,3,2,5,4,1,8,6]=>[4,2,2]
[7,3,2,5,1,8,6,4]=>[4,3,1]
[4,6,3,8,7,2,1,5]=>[4,2,1,1]
[4,7,6,3,8,2,1,5]=>[5,1,1,1]
[4,7,3,8,6,2,1,5]=>[4,2,1,1]
[5,7,3,2,6,1,8,4]=>[4,2,1,1]
[5,7,3,2,6,4,1,8]=>[4,2,1,1]
[2,7,5,3,1,8,6,4]=>[4,3,1]
[7,3,2,4,1,8,6,5]=>[4,3,1]
[4,3,7,5,8,2,1,6]=>[4,2,1,1]
[8,4,5,3,7,2,1,6]=>[5,1,1,1]
[4,3,5,2,8,6,1,7]=>[4,2,1,1]
[4,5,3,6,8,2,1,7]=>[4,1,1,1,1]
[1,2,8,6,4,5,7,3]=>[4,1,1,1,1]
[1,8,5,3,4,6,7,2]=>[4,1,1,1,1]
[7,8,4,1,6,3,5,2]=>[4,2,1,1]
[8,7,5,6,1,3,4,2]=>[5,1,1,1]
[3,2,6,4,1,8,5,7]=>[3,2,2,1]
[2,8,6,5,3,1,4,7]=>[5,1,1,1]
[5,4,8,6,2,3,1,7]=>[4,2,1,1]
[4,8,7,5,2,3,1,6]=>[5,1,1,1]
[5,2,4,7,6,8,3,1]=>[4,2,1,1]
[3,4,2,8,7,5,1,6]=>[4,2,1,1]
[8,5,7,6,3,2,4,1]=>[6,1,1]
[6,4,1,8,7,3,2,5]=>[4,3,1]
[1,8,5,4,2,7,3,6]=>[4,2,1,1]
[3,7,6,1,5,8,4,2]=>[5,1,1,1]
[3,6,5,8,2,7,4,1]=>[4,2,1,1]
[8,3,2,7,4,6,5,1]=>[5,2,1]
[7,5,8,4,1,3,6,2]=>[5,1,1,1]
[7,1,6,2,3,8,4,5]=>[3,2,1,1,1]
[6,4,7,1,3,2,8,5]=>[4,2,1,1]
[5,1,3,8,7,2,6,4]=>[4,2,1,1]
[8,7,1,6,2,5,3,4]=>[5,1,1,1]
[3,8,5,2,4,7,6,1]=>[4,2,1,1]
[7,1,5,2,4,8,3,6]=>[4,1,1,1,1]
[3,8,5,1,4,7,2,6]=>[4,1,1,1,1]
[7,2,5,4,1,3,8,6]=>[4,2,1,1]
[7,5,8,1,6,3,2,4]=>[4,2,1,1]
[7,1,4,8,5,6,2,3]=>[3,2,1,1,1]
[7,4,6,1,3,2,5,8]=>[4,1,1,1,1]
[1,4,5,8,6,3,2,7]=>[4,1,1,1,1]
[8,4,5,7,2,6,1,3]=>[4,1,1,1,1]
[4,5,2,6,7,3,1,8]=>[3,2,1,1,1]
[8,1,7,5,3,6,2,4]=>[5,1,1,1]
[5,2,8,3,6,1,4,7]=>[3,2,1,1,1]
[5,2,6,3,1,7,8,4]=>[3,2,2,1]
[4,3,5,1,6,7,8,2]=>[3,2,1,1,1]
[5,7,6,1,2,3,8,4]=>[3,2,1,1,1]
[3,6,7,5,1,2,8,4]=>[3,2,1,1,1]
[1,7,6,8,5,2,4,3]=>[5,1,1,1]
[5,7,6,8,1,2,4,3]=>[4,1,1,1,1]
[5,6,3,7,1,4,8,2]=>[3,2,1,1,1]
[5,3,2,1,8,6,4,7]=>[4,3,1]
[7,8,6,1,4,5,2,3]=>[4,1,1,1,1]
[1,8,5,4,6,7,2,3]=>[4,1,1,1,1]
[6,5,8,3,7,2,1,4]=>[5,1,1,1]
[7,8,5,3,6,2,1,4]=>[5,1,1,1]
[7,8,5,3,6,2,4,1]=>[5,1,1,1]
[7,8,4,3,2,6,5,1]=>[5,2,1]
[1,8,4,3,2,6,7,5]=>[4,2,1,1]
[5,4,3,8,2,1,7,6]=>[5,2,1]
[6,4,8,3,2,1,7,5]=>[5,2,1]
[1,8,4,3,2,7,6,5]=>[4,3,1]
[6,5,8,3,1,2,7,4]=>[4,2,1,1]
[1,8,6,7,3,2,4,5]=>[4,1,1,1,1]
[7,8,6,1,3,2,4,5]=>[4,1,1,1,1]
[5,4,3,8,2,1,6,7]=>[5,1,1,1]
[1,8,4,3,2,5,7,6]=>[4,2,1,1]
[5,4,3,8,2,6,7,1]=>[5,1,1,1]
[6,4,2,3,5,1,8,7]=>[4,2,1,1]
[5,2,3,6,1,4,8,7]=>[3,2,1,1,1]
[5,2,3,8,6,4,7,1]=>[4,2,1,1]
[5,2,3,7,4,8,1,6]=>[3,2,1,1,1]
[8,6,3,2,5,4,7,1]=>[5,2,1]
[7,2,3,4,5,8,1,6]=>[3,1,1,1,1,1]
[7,2,8,1,5,3,4,6]=>[3,2,1,1,1]
[3,8,6,4,7,2,5,1]=>[5,1,1,1]
[2,1,8,6,4,5,7,3]=>[4,2,1,1]
[4,8,2,5,7,3,1,6]=>[4,1,1,1,1]
[5,8,2,3,4,7,1,6]=>[3,1,1,1,1,1]
[6,3,4,7,8,2,1,5]=>[4,1,1,1,1]
[3,8,5,1,4,7,6,2]=>[4,2,1,1]
[4,8,5,1,3,6,7,2]=>[4,1,1,1,1]
[4,6,8,5,2,7,3,1]=>[4,2,1,1]
[3,7,8,5,2,6,4,1]=>[4,2,1,1]
[3,8,6,2,7,4,5,1]=>[4,2,1,1]
[8,5,4,7,1,3,6,2]=>[5,1,1,1]
[7,3,6,2,8,1,5,4]=>[4,2,1,1]
[8,1,5,2,3,7,6,4]=>[4,2,1,1]
[6,4,2,3,7,8,5,1]=>[4,2,1,1]
[8,4,2,3,6,7,1,5]=>[4,1,1,1,1]
[4,5,8,3,7,2,1,6]=>[4,1,1,1,1]
[3,7,2,8,4,5,1,6]=>[3,2,1,1,1]
[3,5,1,8,4,6,2,7]=>[3,2,1,1,1]
[4,2,1,5,6,8,3,7]=>[3,2,1,1,1]
[4,1,2,6,5,8,3,7]=>[3,2,1,1,1]
[4,1,8,3,2,6,7,5]=>[3,2,2,1]
[4,2,7,5,8,1,3,6]=>[3,2,1,1,1]
[4,6,2,7,8,3,1,5]=>[3,2,1,1,1]
[4,6,1,3,8,2,5,7]=>[3,1,1,1,1,1]
[4,3,6,2,1,8,7,5]=>[4,3,1]
[3,7,4,5,1,6,2,8]=>[3,2,1,1,1]
[3,6,4,5,8,2,1,7]=>[4,1,1,1,1]
[6,1,4,5,2,8,7,3]=>[3,3,1,1]
[7,2,4,5,1,6,3,8]=>[3,2,1,1,1]
[7,5,4,1,6,3,2,8]=>[5,2,1]
[1,5,4,8,6,3,2,7]=>[4,2,1,1]
[7,5,4,8,6,3,1,2]=>[5,2,1]
[1,8,7,5,3,6,4,2]=>[5,2,1]
[8,3,7,4,1,6,2,5]=>[4,2,1,1]
[8,5,4,1,6,3,2,7]=>[5,2,1]
[1,7,4,2,6,5,3,8]=>[4,2,1,1]
[8,2,1,5,6,7,3,4]=>[3,2,1,1,1]
[6,3,1,8,4,7,2,5]=>[3,3,1,1]
[7,1,4,8,6,3,2,5]=>[4,2,1,1]
[4,1,8,5,6,7,2,3]=>[3,2,1,1,1]
[5,7,4,8,6,2,1,3]=>[4,2,1,1]
[5,3,6,8,2,7,1,4]=>[4,1,1,1,1]
[6,3,7,4,8,2,1,5]=>[4,2,1,1]
[5,3,6,1,4,7,2,8]=>[3,2,1,1,1]
[4,3,6,8,2,7,1,5]=>[4,1,1,1,1]
[5,3,7,4,8,2,1,6]=>[4,2,1,1]
[5,3,8,4,1,6,2,7]=>[3,2,2,1]
[5,3,8,1,4,7,2,6]=>[3,2,1,1,1]
[5,8,4,1,6,3,2,7]=>[4,2,1,1]
[7,3,8,4,1,6,2,5]=>[3,2,2,1]
[1,5,8,3,6,7,4,2]=>[4,1,1,1,1]
[1,8,2,5,6,7,3,4]=>[3,1,1,1,1,1]
[7,8,4,1,6,5,2,3]=>[4,2,1,1]
[6,3,8,1,5,7,2,4]=>[3,2,1,1,1]
[8,3,1,2,5,7,4,6]=>[3,2,1,1,1]
[8,1,4,2,6,5,3,7]=>[4,2,1,1]
[5,1,3,7,4,8,2,6]=>[3,2,1,1,1]
[5,1,3,4,7,8,2,6]=>[3,1,1,1,1,1]
[2,5,8,7,4,3,6,1]=>[5,1,1,1]
[5,1,7,8,3,4,2,6]=>[3,2,1,1,1]
[2,5,4,8,3,7,6,1]=>[4,2,1,1]
[5,6,8,2,3,4,1,7]=>[3,1,1,1,1,1]
[2,3,5,7,4,6,8,1]=>[3,1,1,1,1,1]
[3,7,4,5,8,1,2,6]=>[3,1,1,1,1,1]
[3,7,8,1,4,5,2,6]=>[3,1,1,1,1,1]
[5,8,2,1,6,3,4,7]=>[3,2,1,1,1]
[4,8,1,3,7,5,2,6]=>[4,1,1,1,1]
[2,4,7,8,5,3,6,1]=>[4,1,1,1,1]
[5,3,1,4,7,2,8,6]=>[3,2,2,1]
[4,3,8,5,1,2,7,6]=>[3,2,2,1]
[2,4,7,5,8,3,6,1]=>[4,1,1,1,1]
[4,3,5,8,2,1,7,6]=>[4,2,1,1]
[4,8,5,3,7,1,2,6]=>[4,1,1,1,1]
[4,8,5,7,3,1,2,6]=>[4,1,1,1,1]
[4,8,7,5,1,3,2,6]=>[5,1,1,1]
[4,2,8,5,1,3,6,7]=>[3,2,1,1,1]
[3,7,8,4,1,5,2,6]=>[3,2,1,1,1]
[3,4,7,5,8,2,1,6]=>[4,1,1,1,1]
[1,8,5,7,2,4,3,6]=>[4,1,1,1,1]
[1,8,5,4,2,3,6,7]=>[4,1,1,1,1]
[1,3,6,8,5,4,2,7]=>[4,1,1,1,1]
[1,6,3,8,2,7,4,5]=>[3,2,1,1,1]
[1,3,6,8,2,7,5,4]=>[4,1,1,1,1]
[1,6,5,4,3,8,2,7]=>[5,1,1,1]
[1,8,3,4,5,6,2,7]=>[3,1,1,1,1,1]
[1,8,3,6,2,4,5,7]=>[3,1,1,1,1,1]
[1,4,5,8,3,6,2,7]=>[3,1,1,1,1,1]
[1,2,7,8,4,5,3,6]=>[3,1,1,1,1,1]
[7,2,8,5,6,3,4,1]=>[4,2,1,1]
[7,6,3,8,5,4,2,1]=>[6,2]
[6,2,8,7,5,4,1,3]=>[5,2,1]
[6,2,8,4,3,7,1,5]=>[4,2,1,1]
[5,2,8,4,3,1,7,6]=>[4,2,2]
[1,5,7,3,6,2,8,4]=>[3,2,1,1,1]
[1,2,5,4,8,3,7,6]=>[3,2,1,1,1]
[1,4,3,6,8,7,2,5]=>[3,2,1,1,1]
[3,2,5,7,6,8,1,4]=>[3,2,1,1,1]
[5,3,2,6,8,4,7,1]=>[4,2,1,1]
[3,1,8,6,4,7,2,5]=>[4,2,1,1]
[5,3,2,8,7,6,4,1]=>[5,3]
[5,3,8,2,7,6,1,4]=>[4,2,1,1]
[6,5,4,8,3,7,2,1]=>[6,1,1]
[4,8,5,1,3,7,2,6]=>[4,1,1,1,1]
[4,3,8,7,2,6,5,1]=>[5,2,1]
[2,7,5,1,8,4,6,3]=>[4,2,1,1]
[7,8,5,2,1,6,4,3]=>[4,3,1]
[7,6,4,8,1,2,5,3]=>[4,2,1,1]
[7,5,4,8,3,2,6,1]=>[6,1,1]
[8,6,4,7,3,2,1,5]=>[6,1,1]
[3,8,5,6,2,7,1,4]=>[4,1,1,1,1]
[2,4,5,8,7,3,1,6]=>[4,1,1,1,1]
[2,4,5,8,6,7,1,3]=>[3,1,1,1,1,1]
[4,3,1,5,6,2,8,7]=>[3,2,2,1]
[4,1,5,8,6,7,2,3]=>[3,2,1,1,1]
[4,3,7,6,1,2,8,5]=>[3,2,2,1]
[4,7,5,6,1,2,8,3]=>[3,2,1,1,1]
[4,3,7,5,6,2,8,1]=>[4,2,1,1]
[4,5,1,8,6,7,3,2]=>[4,2,1,1]
[3,4,5,8,6,7,2,1]=>[4,1,1,1,1]
[2,1,5,8,6,7,4,3]=>[4,2,1,1]
[3,4,5,8,7,1,2,6]=>[3,1,1,1,1,1]
[4,7,1,5,6,2,8,3]=>[3,2,1,1,1]
[2,6,4,7,1,3,8,5]=>[3,2,1,1,1]
[5,3,8,6,4,7,2,1]=>[5,2,1]
[6,4,1,5,7,8,3,2]=>[4,2,1,1]
[3,6,4,7,2,1,8,5]=>[4,2,1,1]
[3,8,4,6,1,7,2,5]=>[3,2,1,1,1]
[3,8,5,6,4,7,2,1]=>[5,1,1,1]
[3,8,4,5,6,7,2,1]=>[4,1,1,1,1]
[3,8,6,5,2,7,4,1]=>[5,2,1]
[3,8,7,5,2,1,4,6]=>[5,1,1,1]
[3,8,6,5,1,7,2,4]=>[4,2,1,1]
[6,4,1,7,3,2,8,5]=>[4,2,2]
[5,1,4,6,7,2,8,3]=>[3,2,1,1,1]
[6,5,4,7,1,3,8,2]=>[5,1,1,1]
[2,1,6,5,3,7,8,4]=>[3,2,2,1]
[6,1,4,7,2,3,8,5]=>[3,2,1,1,1]
[1,6,2,5,4,8,3,7]=>[4,1,1,1,1]
[6,1,3,5,8,2,4,7]=>[3,1,1,1,1,1]
[4,1,7,5,8,3,6,2]=>[4,2,1,1]
[6,7,3,2,1,8,4,5]=>[4,2,1,1]
[2,5,7,3,1,4,8,6]=>[3,2,1,1,1]
[1,2,6,7,4,3,8,5]=>[3,2,1,1,1]
[2,7,5,8,1,6,3,4]=>[3,2,1,1,1]
[8,2,5,7,1,4,6,3]=>[4,1,1,1,1]
[8,3,5,7,6,1,4,2]=>[5,1,1,1]
[8,7,3,6,2,1,5,4]=>[5,2,1]
[8,6,5,2,7,4,3,1]=>[6,2]
[8,4,3,7,6,5,1,2]=>[5,2,1]
[8,4,2,7,5,1,6,3]=>[4,2,2]
[8,3,4,2,7,5,6,1]=>[4,2,1,1]
[8,4,7,6,5,1,2,3]=>[5,1,1,1]
[8,3,5,2,7,4,6,1]=>[4,2,1,1]
[8,6,2,4,7,3,1,5]=>[5,1,1,1]
[8,5,2,3,7,4,1,6]=>[4,2,1,1]
[8,5,3,2,7,6,4,1]=>[5,3]
[8,6,1,5,4,3,2,7]=>[6,1,1]
[2,4,5,8,3,1,6,7]=>[3,1,1,1,1,1]
[2,7,4,6,1,5,8,3]=>[4,1,1,1,1]
[2,4,3,8,5,1,6,7]=>[3,2,1,1,1]
[7,8,3,2,5,4,6,1]=>[4,2,1,1]
[1,5,6,7,3,8,2,4]=>[3,1,1,1,1,1]
[1,6,5,4,8,3,2,7]=>[5,1,1,1]
[1,7,3,5,8,4,6,2]=>[4,1,1,1,1]
[7,2,1,6,4,8,5,3]=>[4,2,2]
[7,5,8,3,2,4,6,1]=>[5,1,1,1]
[3,8,7,2,4,6,5,1]=>[5,1,1,1]
[1,3,7,6,4,8,5,2]=>[4,2,1,1]
[3,1,8,7,6,4,2,5]=>[5,2,1]
[3,1,8,7,5,4,2,6]=>[5,2,1]
[3,1,7,6,5,4,2,8]=>[5,2,1]
[4,7,1,6,5,3,2,8]=>[5,1,1,1]
[4,8,1,6,5,3,2,7]=>[5,1,1,1]
[8,4,1,7,6,3,2,5]=>[5,2,1]
[5,4,1,8,6,3,2,7]=>[4,3,1]
[5,4,1,7,6,3,2,8]=>[4,3,1]
[6,4,1,8,5,3,2,7]=>[4,3,1]
[8,4,1,7,5,3,2,6]=>[5,2,1]
[7,4,1,6,5,3,2,8]=>[5,2,1]
[7,5,6,1,4,3,2,8]=>[5,1,1,1]
[8,5,6,1,4,3,2,7]=>[5,1,1,1]
[8,5,7,1,4,3,2,6]=>[5,1,1,1]
[5,7,6,1,4,3,2,8]=>[5,1,1,1]
[5,8,6,1,4,3,2,7]=>[5,1,1,1]
[6,7,5,1,4,3,2,8]=>[5,1,1,1]
[8,7,5,1,4,3,2,6]=>[6,1,1]
[8,6,5,1,4,3,2,7]=>[6,1,1]
[8,6,1,7,2,5,3,4]=>[4,2,1,1]
[1,8,6,3,4,2,5,7]=>[4,1,1,1,1]
[3,1,6,4,5,8,2,7]=>[3,2,1,1,1]
[3,1,6,4,5,7,2,8]=>[3,2,1,1,1]
[7,6,3,8,4,5,2,1]=>[5,2,1]
[8,2,7,6,1,4,3,5]=>[5,1,1,1]
[5,6,3,8,4,1,2,7]=>[3,2,1,1,1]
[8,2,7,6,1,4,5,3]=>[5,1,1,1]
[5,2,3,4,7,1,6,8]=>[3,1,1,1,1,1]
[5,2,3,7,1,6,8,4]=>[3,2,1,1,1]
[8,7,5,3,1,6,4,2]=>[5,3]
[1,4,7,8,5,2,3,6]=>[3,1,1,1,1,1]
[5,8,3,7,6,4,1,2]=>[5,1,1,1]
[6,5,1,7,2,4,8,3]=>[4,2,1,1]
[3,6,7,1,4,2,5,8]=>[3,1,1,1,1,1]
[8,1,2,7,5,4,3,6]=>[5,1,1,1]
[6,5,1,8,3,7,2,4]=>[4,2,1,1]
[1,8,7,5,3,2,6,4]=>[5,2,1]
[7,8,1,5,4,2,3,6]=>[4,1,1,1,1]
[2,7,5,1,4,6,3,8]=>[4,1,1,1,1]
[6,8,1,7,5,4,2,3]=>[5,1,1,1]
[7,6,3,1,2,8,5,4]=>[4,3,1]
[6,3,5,7,1,4,2,8]=>[4,1,1,1,1]
[5,2,6,7,4,8,1,3]=>[3,2,1,1,1]
[1,7,5,2,6,4,8,3]=>[4,2,1,1]
[7,1,3,6,8,2,4,5]=>[3,1,1,1,1,1]
[1,2,5,7,8,4,6,3]=>[3,1,1,1,1,1]
[3,1,2,7,5,4,8,6]=>[3,2,2,1]
[6,7,4,1,3,2,8,5]=>[4,2,1,1]
[1,7,2,8,4,3,5,6]=>[3,2,1,1,1]
[1,6,3,5,7,8,2,4]=>[3,1,1,1,1,1]
[8,6,1,7,5,2,4,3]=>[5,2,1]
[7,6,4,1,8,3,2,5]=>[5,2,1]
[8,4,1,6,5,2,7,3]=>[4,2,2]
[1,5,3,4,7,8,2,6]=>[3,1,1,1,1,1]
[4,2,1,5,7,8,3,6]=>[3,2,1,1,1]
[5,4,1,6,7,8,2,3]=>[3,2,1,1,1]
[5,1,4,6,7,8,2,3]=>[3,1,1,1,1,1]
[4,1,5,3,7,8,2,6]=>[3,2,1,1,1]
[8,1,4,6,5,2,7,3]=>[4,2,1,1]
[7,1,5,4,6,3,2,8]=>[5,1,1,1]
[8,2,1,6,7,5,4,3]=>[5,2,1]
[1,2,4,7,6,3,8,5]=>[3,2,1,1,1]
[6,7,4,1,8,5,2,3]=>[3,3,1,1]
[8,6,4,1,5,7,3,2]=>[5,2,1]
[5,2,4,3,7,1,6,8]=>[4,1,1,1,1]
[6,1,5,4,8,3,2,7]=>[5,1,1,1]
[1,2,8,7,4,3,6,5]=>[4,2,1,1]
[3,2,1,7,5,8,4,6]=>[3,3,1,1]
[1,3,6,4,7,8,2,5]=>[3,1,1,1,1,1]
[4,5,1,3,7,8,2,6]=>[3,1,1,1,1,1]
[5,2,3,1,7,8,4,6]=>[3,2,1,1,1]
[1,6,4,3,7,8,2,5]=>[4,1,1,1,1]
[7,6,4,3,1,5,2,8]=>[5,2,1]
[7,5,4,6,1,3,2,8]=>[5,1,1,1]
[8,4,6,5,1,2,7,3]=>[4,2,1,1]
[1,5,6,3,7,8,2,4]=>[3,1,1,1,1,1]
[6,8,3,5,7,2,4,1]=>[4,1,1,1,1]
[1,5,2,4,3,8,7,6]=>[3,3,1,1]
[8,6,5,7,2,1,4,3]=>[5,2,1]
[1,6,3,8,4,5,7,2]=>[3,2,1,1,1]
[7,5,4,2,6,3,8,1]=>[5,2,1]
[2,3,8,4,7,5,6,1]=>[4,1,1,1,1]
[3,7,2,8,6,4,5,1]=>[4,2,1,1]
[6,3,7,5,8,2,4,1]=>[4,2,1,1]
[4,3,7,8,6,2,5,1]=>[4,2,1,1]
[3,8,1,7,5,2,4,6]=>[4,1,1,1,1]
[2,4,7,8,6,1,5,3]=>[4,1,1,1,1]
[2,4,8,5,1,7,3,6]=>[3,2,1,1,1]
[2,8,3,5,1,6,4,7]=>[3,2,1,1,1]
[8,2,4,6,3,7,5,1]=>[4,2,1,1]
[4,5,3,8,2,1,7,6]=>[4,2,1,1]
[4,8,3,2,5,1,6,7]=>[4,1,1,1,1]
[5,2,7,1,3,8,6,4]=>[3,3,1,1]
[1,4,6,2,7,5,3,8]=>[3,2,1,1,1]
[8,2,7,5,1,4,6,3]=>[5,1,1,1]
[1,7,4,6,8,3,5,2]=>[4,1,1,1,1]
[8,2,1,4,5,6,7,3]=>[3,2,1,1,1]
[7,3,1,2,5,6,4,8]=>[3,2,1,1,1]
[7,2,4,1,5,8,6,3]=>[3,3,1,1]
[7,8,2,1,5,4,6,3]=>[4,2,1,1]
[1,4,2,8,6,5,3,7]=>[4,2,1,1]
[1,4,8,5,2,6,3,7]=>[3,2,1,1,1]
[1,5,2,4,6,3,8,7]=>[3,2,1,1,1]
[1,8,5,3,2,6,4,7]=>[4,2,1,1]
[6,4,1,3,2,5,8,7]=>[4,2,1,1]
[5,2,3,7,8,1,6,4]=>[3,2,1,1,1]
[5,2,8,6,3,1,7,4]=>[4,2,2]
[6,2,3,5,1,8,7,4]=>[3,3,1,1]
[7,6,3,4,2,8,1,5]=>[5,1,1,1]
[6,2,4,5,7,8,1,3]=>[3,1,1,1,1,1]
[8,6,3,2,5,7,1,4]=>[5,1,1,1]
[6,2,5,3,7,1,8,4]=>[4,2,1,1]
[8,5,3,6,7,2,1,4]=>[5,1,1,1]
[4,5,7,8,6,2,1,3]=>[4,1,1,1,1]
[1,2,8,4,3,6,7,5]=>[3,2,1,1,1]
[1,8,3,2,4,6,7,5]=>[3,2,1,1,1]
[1,2,7,5,3,4,6,8]=>[3,1,1,1,1,1]
[1,2,7,4,5,3,8,6]=>[3,2,1,1,1]
[1,7,3,2,6,8,4,5]=>[3,2,1,1,1]
[8,2,7,1,4,3,5,6]=>[4,1,1,1,1]
[7,2,1,3,6,8,4,5]=>[3,2,1,1,1]
[6,2,1,7,8,3,4,5]=>[3,2,1,1,1]
[3,5,8,6,1,4,2,7]=>[4,1,1,1,1]
[1,8,4,2,7,6,3,5]=>[4,2,1,1]
[7,3,8,1,6,5,4,2]=>[5,2,1]
[7,3,8,2,6,5,4,1]=>[5,2,1]
[7,1,3,8,6,5,4,2]=>[5,2,1]
[8,1,3,7,6,5,4,2]=>[6,1,1]
[2,4,1,8,7,3,6,5]=>[4,2,1,1]
[7,3,8,6,1,5,4,2]=>[5,2,1]
[3,5,1,7,8,2,6,4]=>[3,2,1,1,1]
[5,4,7,8,2,1,6,3]=>[4,2,1,1]
[5,3,6,1,8,4,2,7]=>[3,3,1,1]
[6,3,8,7,1,5,4,2]=>[5,2,1]
[8,6,4,7,1,5,3,2]=>[5,2,1]
[3,4,6,2,1,8,5,7]=>[3,2,1,1,1]
[5,6,4,8,3,2,1,7]=>[5,1,1,1]
[5,7,4,8,2,1,6,3]=>[4,2,1,1]
[4,7,5,8,2,1,6,3]=>[4,2,1,1]
[5,7,4,2,6,3,8,1]=>[4,2,1,1]
[5,7,4,1,6,2,8,3]=>[3,2,2,1]
[8,5,6,1,7,3,2,4]=>[4,2,1,1]
[4,5,1,6,7,8,3,2]=>[3,2,1,1,1]
[4,5,2,6,1,3,8,7]=>[3,2,1,1,1]
[8,4,6,7,2,5,1,3]=>[4,1,1,1,1]
[3,4,6,7,2,5,8,1]=>[3,1,1,1,1,1]
[7,1,4,6,8,3,5,2]=>[4,1,1,1,1]
[6,7,1,2,4,8,5,3]=>[3,2,1,1,1]
[2,3,6,4,7,5,8,1]=>[3,2,1,1,1]
[7,8,1,3,4,5,6,2]=>[3,1,1,1,1,1]
[1,8,2,6,7,3,4,5]=>[3,1,1,1,1,1]
[4,7,3,2,8,1,5,6]=>[4,1,1,1,1]
[4,8,7,3,1,6,2,5]=>[4,2,1,1]
[4,7,8,3,1,6,2,5]=>[3,2,1,1,1]
[7,4,3,1,6,2,8,5]=>[4,2,2]
[7,4,3,1,8,6,2,5]=>[4,3,1]
[3,7,6,2,4,8,1,5]=>[4,1,1,1,1]
[4,3,7,2,8,6,1,5]=>[4,2,1,1]
[6,1,2,7,4,3,8,5]=>[3,2,2,1]
[5,1,2,6,3,8,7,4]=>[3,2,2,1]
[5,1,2,7,3,8,6,4]=>[3,2,2,1]
[6,1,2,7,3,5,8,4]=>[3,2,1,1,1]
[8,3,6,2,1,7,4,5]=>[4,2,1,1]
[7,5,3,2,1,8,6,4]=>[5,3]
[4,2,1,5,3,6,7,8]=>[3,2,1,1,1]
[6,2,5,4,1,8,7,3]=>[4,3,1]
[4,6,3,2,1,8,7,5]=>[4,3,1]
[6,5,3,2,1,8,7,4]=>[5,3]
[8,4,3,2,7,6,1,5]=>[5,2,1]
[1,5,8,4,7,6,3,2]=>[5,1,1,1]
[3,2,7,4,8,6,1,5]=>[3,2,2,1]
[7,4,3,2,8,6,1,5]=>[5,2,1]
[6,8,3,7,5,2,1,4]=>[5,1,1,1]
[5,7,8,4,3,2,1,6]=>[5,1,1,1]
[6,4,3,8,5,2,1,7]=>[5,2,1]
[8,2,5,4,7,6,1,3]=>[4,2,1,1]
[7,2,5,4,8,6,1,3]=>[4,2,1,1]
[4,5,3,2,8,6,1,7]=>[4,2,1,1]
[3,2,5,4,8,6,1,7]=>[3,2,2,1]
[3,2,8,6,5,4,1,7]=>[5,2,1]
[8,4,3,6,5,2,1,7]=>[5,2,1]
[8,4,3,7,5,2,1,6]=>[5,2,1]
[3,2,7,8,5,4,1,6]=>[4,2,1,1]
[6,8,7,4,3,2,1,5]=>[6,1,1]
[3,6,1,4,8,7,2,5]=>[3,2,1,1,1]
[5,8,1,3,7,2,6,4]=>[4,1,1,1,1]
[4,7,5,1,8,2,6,3]=>[3,3,1,1]
[6,3,2,1,8,7,4,5]=>[4,3,1]
[6,2,3,1,8,7,4,5]=>[3,3,1,1]
[3,4,7,1,8,5,6,2]=>[3,2,1,1,1]
[7,2,5,1,8,3,6,4]=>[3,3,1,1]
[7,2,1,5,8,4,6,3]=>[4,2,1,1]
[4,2,8,1,7,5,6,3]=>[4,2,1,1]
[8,3,6,4,1,7,5,2]=>[4,3,1]
[7,3,1,5,2,8,6,4]=>[3,3,2]
[7,1,6,4,2,8,5,3]=>[4,3,1]
[3,7,4,1,5,8,6,2]=>[3,3,1,1]
[5,8,6,1,2,7,4,3]=>[4,2,1,1]
[6,8,1,4,3,7,5,2]=>[4,2,1,1]
[6,7,1,4,3,8,5,2]=>[4,2,1,1]
[4,7,1,5,3,8,6,2]=>[4,2,1,1]
[6,8,1,2,4,7,5,3]=>[4,1,1,1,1]
[7,1,6,4,8,3,5,2]=>[5,1,1,1]
[8,6,4,1,3,7,5,2]=>[5,2,1]
[8,5,3,6,1,7,4,2]=>[4,3,1]
[7,2,1,4,5,8,6,3]=>[3,3,1,1]
[8,5,6,1,2,7,4,3]=>[4,2,1,1]
[8,6,2,5,4,7,3,1]=>[6,1,1]
[8,5,7,3,2,4,6,1]=>[5,1,1,1]
[8,5,2,1,4,3,6,7]=>[4,2,1,1]
[8,1,2,4,5,6,7,3]=>[3,1,1,1,1,1]
[6,1,4,3,2,7,8,5]=>[4,2,1,1]
[1,8,3,6,7,2,4,5]=>[3,1,1,1,1,1]
[1,2,8,3,7,4,6,5]=>[4,1,1,1,1]
[8,2,6,5,4,3,1,7]=>[6,1,1]
[8,2,7,6,4,5,3,1]=>[6,1,1]
[8,7,3,5,4,2,6,1]=>[6,1,1]
[4,6,7,2,1,8,3,5]=>[3,2,1,1,1]
[3,7,1,8,2,5,4,6]=>[3,2,1,1,1]
[4,5,8,6,1,3,7,2]=>[4,1,1,1,1]
[4,5,8,6,2,7,3,1]=>[4,2,1,1]
[4,6,7,1,5,3,8,2]=>[4,1,1,1,1]
[4,6,7,2,1,8,5,3]=>[3,3,1,1]
[4,2,5,6,7,8,3,1]=>[3,2,1,1,1]
[4,1,3,5,6,7,8,2]=>[3,1,1,1,1,1]
[3,7,8,4,5,1,6,2]=>[3,2,1,1,1]
[4,6,8,3,2,7,1,5]=>[4,1,1,1,1]
[4,6,8,2,3,7,1,5]=>[3,1,1,1,1,1]
[3,8,1,7,4,5,2,6]=>[4,1,1,1,1]
[4,5,8,3,7,1,2,6]=>[3,1,1,1,1,1]
[3,7,8,4,6,2,5,1]=>[4,1,1,1,1]
[3,6,1,5,7,8,2,4]=>[3,1,1,1,1,1]
[3,8,2,5,4,7,1,6]=>[4,1,1,1,1]
[3,8,6,2,5,1,7,4]=>[4,2,1,1]
[4,5,8,6,2,1,7,3]=>[4,2,1,1]
[4,5,8,6,1,2,7,3]=>[3,2,1,1,1]
[4,6,8,5,2,7,1,3]=>[4,1,1,1,1]
[3,7,8,5,2,6,1,4]=>[4,1,1,1,1]
[3,7,8,5,4,1,6,2]=>[4,2,1,1]
[4,6,8,5,3,1,7,2]=>[4,2,1,1]
[7,8,2,3,5,4,1,6]=>[4,1,1,1,1]
[5,1,3,7,6,4,8,2]=>[4,2,1,1]
[4,6,5,2,7,8,1,3]=>[4,1,1,1,1]
[1,6,5,2,3,4,8,7]=>[3,2,1,1,1]
[4,6,5,1,7,3,8,2]=>[4,2,1,1]
[5,7,3,1,2,4,8,6]=>[3,2,1,1,1]
[6,3,2,5,1,7,4,8]=>[4,2,1,1]
[6,1,2,4,8,5,3,7]=>[3,2,1,1,1]
[6,3,1,7,2,5,8,4]=>[3,3,1,1]
[3,7,2,8,5,1,4,6]=>[3,2,1,1,1]
[3,6,5,2,4,7,1,8]=>[4,1,1,1,1]
[3,6,5,8,1,7,2,4]=>[3,2,1,1,1]
[5,2,7,3,4,6,1,8]=>[3,2,1,1,1]
[1,3,5,8,6,4,7,2]=>[4,1,1,1,1]
[1,3,5,8,6,7,2,4]=>[3,1,1,1,1,1]
[6,1,7,4,8,5,3,2]=>[4,2,2]
[5,7,4,1,3,6,8,2]=>[4,1,1,1,1]
[7,8,1,4,6,5,3,2]=>[5,1,1,1]
[7,8,6,1,4,5,3,2]=>[5,1,1,1]
[6,2,7,3,8,5,4,1]=>[4,2,2]
[1,2,7,5,3,4,8,6]=>[3,2,1,1,1]
[7,2,8,3,6,4,5,1]=>[4,2,1,1]
[6,2,7,8,3,1,4,5]=>[3,2,1,1,1]
[1,7,8,2,5,3,4,6]=>[3,1,1,1,1,1]
[3,7,8,1,2,5,6,4]=>[3,1,1,1,1,1]
[1,2,8,7,3,4,6,5]=>[4,1,1,1,1]
[8,2,7,4,5,1,6,3]=>[4,2,1,1]
[3,8,1,5,7,2,6,4]=>[4,1,1,1,1]
[7,5,4,8,6,1,2,3]=>[4,2,1,1]
[7,1,8,6,4,5,2,3]=>[4,2,1,1]
[8,7,5,1,4,3,6,2]=>[6,1,1]
[1,5,7,8,3,4,2,6]=>[3,1,1,1,1,1]
[8,4,1,3,7,5,6,2]=>[4,2,1,1]
[4,8,1,3,7,5,6,2]=>[4,1,1,1,1]
[1,8,5,7,4,2,3,6]=>[4,1,1,1,1]
[4,5,1,3,8,6,7,2]=>[3,2,1,1,1]
[1,2,6,8,5,3,4,7]=>[3,1,1,1,1,1]
[5,6,8,7,3,1,2,4]=>[4,1,1,1,1]
[6,7,5,3,8,1,2,4]=>[4,1,1,1,1]
[6,8,5,7,3,1,2,4]=>[4,1,1,1,1]
[5,7,8,6,3,1,2,4]=>[4,1,1,1,1]
[5,1,4,2,6,8,7,3]=>[3,3,1,1]
[6,3,2,4,7,1,8,5]=>[4,2,1,1]
[1,5,6,8,4,2,3,7]=>[3,1,1,1,1,1]
[5,7,8,3,6,1,2,4]=>[3,1,1,1,1,1]
[1,5,8,6,2,4,3,7]=>[4,1,1,1,1]
[1,5,3,7,2,6,8,4]=>[3,2,1,1,1]
[5,1,8,6,2,4,3,7]=>[4,2,1,1]
[5,8,6,3,7,1,2,4]=>[4,1,1,1,1]
[1,5,2,4,8,6,7,3]=>[3,2,1,1,1]
[1,5,4,2,6,8,7,3]=>[3,3,1,1]
[5,7,6,3,8,1,2,4]=>[4,1,1,1,1]
[5,7,6,8,3,1,2,4]=>[4,1,1,1,1]
[6,8,7,5,3,1,2,4]=>[5,1,1,1]
[1,2,5,3,6,8,7,4]=>[3,2,1,1,1]
[6,8,7,2,1,5,3,4]=>[4,2,1,1]
[7,3,6,1,4,8,2,5]=>[4,1,1,1,1]
[7,8,1,6,5,3,4,2]=>[5,1,1,1]
[8,7,3,2,1,4,6,5]=>[5,2,1]
[8,3,5,1,7,4,2,6]=>[4,2,1,1]
[5,8,2,6,4,3,7,1]=>[5,1,1,1]
[2,8,6,3,4,1,7,5]=>[4,2,1,1]
[1,7,2,3,5,8,6,4]=>[3,2,1,1,1]
[4,6,2,3,5,1,7,8]=>[3,1,1,1,1,1]
[2,8,3,7,5,1,6,4]=>[4,2,1,1]
[6,4,8,7,2,1,5,3]=>[4,2,2]
[1,8,2,3,7,5,6,4]=>[4,1,1,1,1]
[2,8,4,3,6,7,1,5]=>[4,1,1,1,1]
[7,3,2,5,6,1,8,4]=>[4,2,1,1]
[1,6,7,8,2,4,3,5]=>[3,1,1,1,1,1]
[4,1,2,8,5,3,7,6]=>[3,2,2,1]
[3,8,4,2,5,1,7,6]=>[4,2,1,1]
[1,8,5,6,4,3,2,7]=>[5,1,1,1]
[2,8,3,5,6,4,1,7]=>[4,1,1,1,1]
[4,1,5,7,6,8,2,3]=>[3,2,1,1,1]
[7,6,8,3,2,5,1,4]=>[5,1,1,1]
[2,7,1,4,5,3,8,6]=>[3,2,1,1,1]
[1,5,2,7,4,3,6,8]=>[3,2,1,1,1]
[5,1,3,8,4,6,2,7]=>[3,2,1,1,1]
[6,5,8,7,1,3,2,4]=>[4,2,1,1]
[2,7,3,5,1,6,8,4]=>[3,2,1,1,1]
[5,7,6,8,2,1,4,3]=>[4,2,1,1]
[1,3,6,5,2,7,4,8]=>[3,2,1,1,1]
[1,2,6,5,3,4,7,8]=>[3,1,1,1,1,1]
[1,7,2,5,6,8,3,4]=>[3,1,1,1,1,1]
[1,7,2,4,8,3,5,6]=>[3,1,1,1,1,1]
[1,6,2,4,5,3,7,8]=>[3,1,1,1,1,1]
[1,3,2,8,4,5,7,6]=>[3,2,1,1,1]
[1,6,8,2,4,3,5,7]=>[3,1,1,1,1,1]
[1,6,7,2,5,3,4,8]=>[3,1,1,1,1,1]
[1,2,8,3,6,7,4,5]=>[3,1,1,1,1,1]
[1,7,2,5,3,4,8,6]=>[3,2,1,1,1]
[7,1,5,6,2,3,8,4]=>[3,2,1,1,1]
[8,2,1,4,6,7,3,5]=>[3,2,1,1,1]
[7,2,6,1,3,4,8,5]=>[3,2,1,1,1]
[4,1,3,7,2,5,8,6]=>[3,2,1,1,1]
[6,2,7,5,1,3,8,4]=>[3,2,2,1]
[1,7,5,6,2,3,8,4]=>[3,2,1,1,1]
[3,7,6,1,2,4,8,5]=>[3,2,1,1,1]
[8,6,1,3,5,7,2,4]=>[4,1,1,1,1]
[1,7,4,3,8,2,5,6]=>[4,1,1,1,1]
[6,1,5,3,4,8,2,7]=>[4,1,1,1,1]
[3,6,7,5,2,8,1,4]=>[4,1,1,1,1]
[7,8,4,1,5,6,2,3]=>[3,2,1,1,1]
[5,8,1,3,6,7,2,4]=>[3,1,1,1,1,1]
[2,8,4,3,7,1,5,6]=>[4,1,1,1,1]
[3,8,4,6,7,1,2,5]=>[3,1,1,1,1,1]
[6,3,8,4,7,1,2,5]=>[3,2,1,1,1]
[1,2,5,4,8,3,6,7]=>[3,1,1,1,1,1]
[7,1,3,8,2,4,5,6]=>[3,1,1,1,1,1]
[8,1,3,7,2,4,5,6]=>[3,1,1,1,1,1]
[3,5,4,7,8,1,2,6]=>[3,1,1,1,1,1]
[8,3,1,4,7,2,5,6]=>[3,2,1,1,1]
[1,6,4,7,8,2,3,5]=>[3,1,1,1,1,1]
[5,2,3,6,7,8,1,4]=>[3,1,1,1,1,1]
[6,2,7,3,8,5,1,4]=>[3,2,2,1]
[1,3,7,8,5,6,2,4]=>[3,1,1,1,1,1]
[8,2,6,7,5,1,3,4]=>[4,1,1,1,1]
[8,1,7,4,6,2,3,5]=>[4,1,1,1,1]
[2,5,8,4,7,1,3,6]=>[3,1,1,1,1,1]
[4,5,8,7,1,2,3,6]=>[3,1,1,1,1,1]
[4,1,8,5,7,2,3,6]=>[3,2,1,1,1]
[1,8,7,4,6,2,3,5]=>[4,1,1,1,1]
[2,6,5,4,1,8,3,7]=>[4,2,1,1]
[6,2,5,1,4,8,3,7]=>[4,1,1,1,1]
[6,5,4,1,3,8,2,7]=>[5,1,1,1]
[6,3,5,4,2,8,1,7]=>[5,1,1,1]
[1,3,8,7,4,2,6,5]=>[4,2,1,1]
[8,7,4,3,1,5,2,6]=>[5,2,1]
[8,2,5,1,4,6,7,3]=>[4,1,1,1,1]
[3,8,4,5,1,6,7,2]=>[3,2,1,1,1]
[8,5,4,1,3,6,7,2]=>[5,1,1,1]
[8,3,1,7,5,6,4,2]=>[5,2,1]
[8,4,7,6,5,3,1,2]=>[6,1,1]
[8,1,4,5,7,6,3,2]=>[5,1,1,1]
[2,4,1,8,5,7,6,3]=>[4,2,1,1]
[8,2,1,4,7,6,3,5]=>[4,2,1,1]
[8,3,1,7,4,2,6,5]=>[4,2,2]
[8,2,7,3,1,6,5,4]=>[5,2,1]
[1,8,4,2,3,7,6,5]=>[4,2,1,1]
[3,1,2,8,7,4,6,5]=>[4,2,1,1]
[8,5,1,2,4,3,7,6]=>[4,2,1,1]
[2,8,3,7,4,1,6,5]=>[4,2,1,1]
[8,4,5,7,6,2,3,1]=>[5,1,1,1]
[2,3,1,8,7,6,4,5]=>[4,2,1,1]
[4,2,8,7,3,1,5,6]=>[4,2,1,1]
[1,3,4,8,7,2,5,6]=>[3,1,1,1,1,1]
[8,1,3,4,6,7,2,5]=>[3,1,1,1,1,1]
[3,4,8,2,6,7,1,5]=>[3,1,1,1,1,1]
[3,6,8,2,5,1,7,4]=>[3,2,1,1,1]
[3,8,2,5,7,4,6,1]=>[4,1,1,1,1]
[8,4,2,1,7,5,6,3]=>[4,3,1]
[8,2,7,5,6,4,1,3]=>[5,1,1,1]
[6,2,8,5,4,1,7,3]=>[4,2,2]
[6,8,5,4,1,7,2,3]=>[4,2,1,1]
[2,8,1,5,7,6,3,4]=>[4,1,1,1,1]
[3,1,8,2,7,5,6,4]=>[4,2,1,1]
[8,5,7,1,6,4,2,3]=>[5,1,1,1]
[2,8,4,7,3,6,5,1]=>[5,1,1,1]
[8,4,7,2,1,6,5,3]=>[5,2,1]
[1,8,4,7,6,5,2,3]=>[5,1,1,1]
[3,5,8,1,7,4,6,2]=>[4,1,1,1,1]
[8,4,7,1,3,6,5,2]=>[5,1,1,1]
[2,3,4,7,6,8,1,5]=>[3,1,1,1,1,1]
[3,8,1,2,5,6,4,7]=>[3,1,1,1,1,1]
[8,5,2,1,4,6,7,3]=>[4,2,1,1]
[4,8,1,6,5,2,7,3]=>[4,2,1,1]
[4,2,6,3,8,5,7,1]=>[3,2,2,1]
[4,5,2,6,7,1,8,3]=>[3,2,1,1,1]
[8,3,5,4,2,7,1,6]=>[5,1,1,1]
[2,8,6,4,7,3,1,5]=>[5,1,1,1]
[3,1,8,6,5,2,7,4]=>[4,2,2]
[8,3,1,5,2,6,7,4]=>[3,2,2,1]
[3,8,2,4,1,5,7,6]=>[3,2,1,1,1]
[5,8,3,2,4,1,7,6]=>[4,2,1,1]
[6,5,3,2,4,8,1,7]=>[5,1,1,1]
[5,2,4,6,1,3,8,7]=>[3,2,1,1,1]
[7,2,3,4,6,8,1,5]=>[3,1,1,1,1,1]
[8,3,4,6,7,5,1,2]=>[4,1,1,1,1]
[6,8,3,4,7,5,2,1]=>[5,1,1,1]
[5,8,6,1,3,4,7,2]=>[4,1,1,1,1]
[4,8,1,5,7,6,3,2]=>[5,1,1,1]
[3,7,4,6,8,2,5,1]=>[4,1,1,1,1]
[4,7,1,6,8,3,2,5]=>[4,1,1,1,1]
[4,5,2,8,1,7,3,6]=>[3,2,1,1,1]
[3,7,5,2,8,6,1,4]=>[4,2,1,1]
[4,8,5,2,6,7,1,3]=>[4,1,1,1,1]
[5,4,8,6,1,2,7,3]=>[3,2,2,1]
[8,4,6,5,2,7,3,1]=>[5,2,1]
[8,1,6,4,7,5,2,3]=>[4,2,1,1]
[5,2,7,6,4,8,1,3]=>[4,2,1,1]
[8,6,2,3,5,1,7,4]=>[4,2,1,1]
[8,2,5,7,4,1,3,6]=>[4,1,1,1,1]
[7,2,4,5,6,8,1,3]=>[3,1,1,1,1,1]
[7,1,3,5,6,2,8,4]=>[3,2,1,1,1]
[7,1,5,8,4,6,3,2]=>[5,1,1,1]
[6,3,8,4,7,1,5,2]=>[4,2,1,1]
[7,1,4,3,2,8,5,6]=>[4,2,1,1]
[5,3,6,1,4,2,8,7]=>[3,2,2,1]
[5,7,2,1,4,3,8,6]=>[3,2,2,1]
[7,1,8,3,5,2,4,6]=>[3,2,1,1,1]
[7,2,4,8,1,5,6,3]=>[3,2,1,1,1]
[7,1,8,4,2,5,6,3]=>[3,2,2,1]
[6,4,2,5,8,1,7,3]=>[4,2,1,1]
[2,1,7,5,8,3,6,4]=>[3,2,2,1]
[7,3,8,5,6,2,1,4]=>[4,2,1,1]
[2,7,4,8,1,5,6,3]=>[3,2,1,1,1]
[7,4,8,3,1,5,6,2]=>[4,2,1,1]
[6,1,5,8,3,7,4,2]=>[4,2,1,1]
[2,6,3,5,8,7,4,1]=>[4,2,1,1]
[8,6,5,3,7,2,1,4]=>[6,1,1]
[4,8,5,3,7,2,1,6]=>[5,1,1,1]
[7,4,8,6,5,3,2,1]=>[6,2]
[7,4,8,5,6,3,1,2]=>[4,2,1,1]
[7,8,4,1,3,5,6,2]=>[4,1,1,1,1]
[7,8,3,4,1,5,6,2]=>[3,2,1,1,1]
[7,3,1,8,2,5,6,4]=>[3,3,1,1]
[7,2,3,8,1,5,6,4]=>[3,2,1,1,1]
[6,4,8,7,3,2,1,5]=>[5,2,1]
[2,7,4,8,6,3,1,5]=>[4,2,1,1]
[6,4,8,2,3,1,7,5]=>[4,2,1,1]
[7,2,1,8,3,5,6,4]=>[3,3,1,1]
[5,1,6,3,8,2,4,7]=>[3,2,1,1,1]
[3,6,5,1,4,8,7,2]=>[4,2,1,1]
[7,3,6,2,8,4,1,5]=>[4,2,1,1]
[6,5,1,8,4,7,2,3]=>[4,2,1,1]
[7,5,4,8,1,6,2,3]=>[4,2,1,1]
[4,3,5,8,7,1,2,6]=>[3,2,1,1,1]
[3,5,6,8,1,4,2,7]=>[3,1,1,1,1,1]
[4,3,5,8,2,1,6,7]=>[4,1,1,1,1]
[6,4,7,2,3,1,5,8]=>[4,1,1,1,1]
[6,8,1,5,4,2,7,3]=>[4,2,1,1]
[7,8,6,3,5,1,2,4]=>[4,1,1,1,1]
[6,1,8,4,7,2,3,5]=>[3,2,1,1,1]
[5,6,4,3,7,1,8,2]=>[4,2,1,1]
[6,5,3,7,2,4,8,1]=>[5,1,1,1]
[5,6,2,8,4,3,7,1]=>[4,2,1,1]
[4,1,2,6,8,3,7,5]=>[3,2,1,1,1]
[7,1,3,6,5,8,4,2]=>[5,1,1,1]
[5,7,4,3,6,8,2,1]=>[5,1,1,1]
[4,6,2,7,8,3,5,1]=>[3,2,1,1,1]
[5,1,2,4,6,7,8,3]=>[3,1,1,1,1,1]
[4,6,3,5,2,8,7,1]=>[4,2,1,1]
[5,6,3,4,8,2,7,1]=>[4,1,1,1,1]
[5,2,6,4,1,7,8,3]=>[3,2,2,1]
[5,8,4,6,3,2,7,1]=>[5,1,1,1]
[5,4,3,8,6,2,7,1]=>[5,2,1]
[5,7,8,2,4,3,6,1]=>[4,1,1,1,1]
[5,6,2,4,8,3,7,1]=>[4,1,1,1,1]
[6,4,7,8,2,3,5,1]=>[4,1,1,1,1]
[3,7,5,2,4,8,1,6]=>[4,1,1,1,1]
[4,7,5,2,3,8,6,1]=>[4,2,1,1]
[6,4,7,3,2,5,8,1]=>[5,1,1,1]
[5,7,3,2,8,4,6,1]=>[4,2,1,1]
[5,3,7,2,8,4,6,1]=>[4,2,1,1]
[4,3,7,2,5,8,6,1]=>[4,2,1,1]
[4,7,3,2,5,8,6,1]=>[4,2,1,1]
[4,7,3,2,6,8,5,1]=>[4,2,1,1]
[7,5,3,2,6,4,8,1]=>[5,2,1]
[8,5,2,6,7,3,4,1]=>[4,2,1,1]
[8,4,2,6,3,7,5,1]=>[4,2,2]
[7,4,6,2,3,8,5,1]=>[4,2,1,1]
[7,5,6,2,8,3,4,1]=>[4,2,1,1]
[5,7,6,2,8,3,4,1]=>[4,2,1,1]
[4,7,6,2,3,8,5,1]=>[4,2,1,1]
[7,6,3,2,5,8,1,4]=>[5,1,1,1]
[7,6,4,2,5,8,3,1]=>[5,2,1]
[6,3,8,5,4,7,2,1]=>[5,2,1]
[2,4,6,3,8,7,5,1]=>[4,2,1,1]
[2,4,6,1,8,7,3,5]=>[3,2,1,1,1]
[2,4,3,6,8,7,1,5]=>[3,2,1,1,1]
[2,4,6,3,8,7,1,5]=>[3,2,1,1,1]
[2,4,6,5,8,7,1,3]=>[3,2,1,1,1]
[2,4,6,8,5,7,3,1]=>[4,1,1,1,1]
[2,4,6,8,5,7,1,3]=>[3,1,1,1,1,1]
[2,4,6,8,3,7,1,5]=>[3,1,1,1,1,1]
[2,4,6,8,1,7,3,5]=>[3,1,1,1,1,1]
[2,4,6,5,1,8,7,3]=>[3,3,1,1]
[2,4,6,5,8,3,7,1]=>[4,1,1,1,1]
[2,4,6,5,8,1,7,3]=>[3,2,1,1,1]
[2,4,6,8,5,1,7,3]=>[3,2,1,1,1]
[2,4,6,8,7,3,5,1]=>[4,1,1,1,1]
[2,4,6,8,7,1,5,3]=>[4,1,1,1,1]
[2,4,6,8,7,1,3,5]=>[3,1,1,1,1,1]
[2,4,6,8,5,1,3,7]=>[3,1,1,1,1,1]
[2,4,6,5,1,8,3,7]=>[3,2,1,1,1]
[2,4,6,5,1,3,8,7]=>[3,2,1,1,1]
[2,4,6,5,3,8,1,7]=>[4,1,1,1,1]
[2,4,6,5,8,3,1,7]=>[4,1,1,1,1]
[2,4,6,8,5,3,1,7]=>[4,1,1,1,1]
[2,4,6,8,7,3,1,5]=>[4,1,1,1,1]
[2,4,6,8,7,5,1,3]=>[4,1,1,1,1]
[4,8,7,5,2,1,3,6]=>[5,1,1,1]
[6,1,4,7,5,8,2,3]=>[3,2,1,1,1]
[1,8,6,5,3,2,7,4]=>[5,2,1]
[1,6,3,5,8,2,4,7]=>[3,1,1,1,1,1]
[4,6,1,7,8,5,3,2]=>[4,2,1,1]
[6,1,2,7,8,4,5,3]=>[3,2,1,1,1]
[6,1,3,2,7,8,5,4]=>[3,3,1,1]
[5,6,3,1,7,4,8,2]=>[3,3,1,1]
[4,8,3,7,1,6,5,2]=>[5,1,1,1]
[8,7,2,6,5,1,4,3]=>[6,1,1]
[5,8,3,2,1,7,6,4]=>[4,3,1]
[5,4,3,8,1,7,6,2]=>[4,3,1]
[6,5,3,8,7,1,4,2]=>[4,3,1]
[4,3,8,2,7,6,5,1]=>[5,2,1]
[4,8,2,7,6,5,3,1]=>[6,1,1]
[7,8,2,6,5,4,1,3]=>[5,1,1,1]
[3,8,7,6,2,5,1,4]=>[5,1,1,1]
[4,8,3,7,2,1,6,5]=>[4,2,1,1]
[8,6,3,1,7,5,4,2]=>[5,3]
[8,6,3,7,1,5,4,2]=>[5,2,1]
[4,8,3,7,6,2,5,1]=>[5,1,1,1]
[5,8,2,7,6,4,1,3]=>[5,1,1,1]
[8,4,2,1,7,6,5,3]=>[5,3]
[1,6,4,2,5,3,7,8]=>[3,2,1,1,1]
[1,8,6,2,7,3,4,5]=>[3,2,1,1,1]
[1,6,3,2,4,5,7,8]=>[3,1,1,1,1,1]
[1,5,2,6,4,3,7,8]=>[3,2,1,1,1]
[1,5,2,4,6,3,7,8]=>[3,1,1,1,1,1]
[1,8,6,2,3,7,4,5]=>[3,2,1,1,1]
[1,5,2,8,6,3,4,7]=>[3,2,1,1,1]
[1,3,6,8,2,7,4,5]=>[3,1,1,1,1,1]
[1,4,3,8,2,5,6,7]=>[3,1,1,1,1,1]
[1,7,2,3,8,5,4,6]=>[3,2,1,1,1]
[1,3,8,4,2,5,6,7]=>[3,1,1,1,1,1]
[1,6,2,8,5,4,3,7]=>[4,2,1,1]
[1,7,2,3,8,6,4,5]=>[3,2,1,1,1]
[1,5,3,8,2,7,4,6]=>[3,2,1,1,1]
[1,4,8,2,5,6,3,7]=>[3,1,1,1,1,1]
[1,5,7,3,2,8,4,6]=>[3,2,1,1,1]
[1,2,7,3,6,8,4,5]=>[3,1,1,1,1,1]
[1,7,2,3,6,8,4,5]=>[3,1,1,1,1,1]
[1,4,8,3,2,5,6,7]=>[3,1,1,1,1,1]
[1,7,2,5,8,3,4,6]=>[3,1,1,1,1,1]
[6,2,3,5,8,1,7,4]=>[3,2,1,1,1]
[5,2,4,8,1,6,7,3]=>[3,2,1,1,1]
[2,6,4,5,7,3,1,8]=>[4,1,1,1,1]
[2,5,6,3,4,7,1,8]=>[3,1,1,1,1,1]
[1,3,7,5,6,8,4,2]=>[4,1,1,1,1]
[1,3,6,7,4,5,8,2]=>[3,1,1,1,1,1]
[1,5,6,3,4,2,7,8]=>[3,1,1,1,1,1]
[1,5,6,3,4,7,2,8]=>[3,1,1,1,1,1]
[1,5,3,6,4,2,7,8]=>[3,2,1,1,1]
[1,7,5,6,8,3,4,2]=>[4,1,1,1,1]
[1,7,5,6,3,8,4,2]=>[4,2,1,1]
[1,3,7,5,2,8,6,4]=>[3,3,1,1]
[1,3,7,2,5,8,6,4]=>[3,2,1,1,1]
[1,5,3,7,4,6,2,8]=>[3,2,1,1,1]
[1,5,3,7,6,4,2,8]=>[4,2,1,1]
[1,5,3,6,7,4,2,8]=>[3,2,1,1,1]
[1,5,6,3,7,4,2,8]=>[3,2,1,1,1]
[1,5,7,6,3,4,8,2]=>[4,1,1,1,1]
[1,5,7,3,6,4,8,2]=>[4,1,1,1,1]
[1,3,7,2,5,6,8,4]=>[3,1,1,1,1,1]
[1,3,7,5,6,2,8,4]=>[3,2,1,1,1]
[2,5,7,4,1,3,8,6]=>[3,2,1,1,1]
[6,7,3,1,8,5,2,4]=>[3,3,1,1]
[6,3,1,5,8,7,2,4]=>[3,3,1,1]
[8,3,5,1,7,6,2,4]=>[4,2,1,1]
[4,6,3,5,8,2,1,7]=>[4,1,1,1,1]
[2,3,6,4,1,8,7,5]=>[3,3,1,1]
[7,4,5,2,1,8,6,3]=>[4,3,1]
[4,7,5,2,1,8,6,3]=>[4,3,1]
[8,5,3,6,2,1,7,4]=>[5,2,1]
[4,5,7,3,1,2,8,6]=>[3,2,1,1,1]
[4,5,1,8,3,2,7,6]=>[3,2,2,1]
[5,7,4,6,3,2,1,8]=>[5,1,1,1]
[3,6,1,2,4,8,7,5]=>[3,2,1,1,1]
[2,5,3,8,4,1,7,6]=>[3,2,2,1]
[8,6,2,3,1,7,5,4]=>[4,3,1]
[7,5,2,3,1,8,6,4]=>[4,3,1]
[6,3,1,2,4,8,7,5]=>[3,3,1,1]
[4,7,5,2,3,6,1,8]=>[4,1,1,1,1]
[3,6,8,4,5,1,2,7]=>[3,1,1,1,1,1]
[5,2,3,7,6,4,1,8]=>[4,2,1,1]
[6,2,7,3,5,4,1,8]=>[4,2,1,1]
[7,2,6,5,3,4,1,8]=>[5,1,1,1]
[8,2,6,5,4,1,3,7]=>[5,1,1,1]
[6,2,8,4,5,1,3,7]=>[3,2,1,1,1]
[2,3,1,7,8,5,6,4]=>[3,2,1,1,1]
[7,2,8,5,1,4,3,6]=>[4,2,1,1]
[8,6,7,1,4,2,3,5]=>[4,1,1,1,1]
[6,8,7,1,4,3,2,5]=>[5,1,1,1]
[6,8,2,5,3,1,4,7]=>[4,1,1,1,1]
[3,7,8,5,1,4,2,6]=>[4,1,1,1,1]
[4,8,7,3,1,2,5,6]=>[4,1,1,1,1]
[4,8,6,2,3,1,5,7]=>[4,1,1,1,1]
[3,8,5,4,2,1,6,7]=>[5,1,1,1]
[4,5,3,8,2,1,6,7]=>[4,1,1,1,1]
[3,7,4,1,8,2,6,5]=>[3,3,1,1]
[3,8,4,1,7,6,2,5]=>[4,2,1,1]
[3,7,2,1,8,4,6,5]=>[3,3,1,1]
[8,7,1,6,5,2,3,4]=>[5,1,1,1]
[8,5,1,2,7,6,3,4]=>[4,2,1,1]
[3,8,2,1,7,6,4,5]=>[4,2,1,1]
[3,5,7,8,2,4,6,1]=>[3,1,1,1,1,1]
[7,8,2,5,4,3,6,1]=>[5,1,1,1]
[4,5,3,7,8,2,6,1]=>[4,1,1,1,1]
[1,5,4,7,3,6,2,8]=>[4,1,1,1,1]
[1,7,3,6,8,4,5,2]=>[4,1,1,1,1]
[4,6,8,2,7,3,5,1]=>[4,1,1,1,1]
[4,7,6,3,5,1,8,2]=>[4,2,1,1]
[7,8,3,6,1,5,4,2]=>[5,1,1,1]
[2,5,7,8,4,6,1,3]=>[3,1,1,1,1,1]
[3,7,5,6,2,1,4,8]=>[4,1,1,1,1]
[6,2,1,7,4,5,3,8]=>[3,3,1,1]
[1,2,6,4,7,5,3,8]=>[3,2,1,1,1]
[7,5,6,3,8,4,2,1]=>[5,2,1]
[8,5,4,2,1,6,7,3]=>[5,2,1]
[2,6,8,4,7,5,1,3]=>[4,1,1,1,1]
[6,7,5,1,4,8,3,2]=>[5,1,1,1]
[7,4,1,6,5,3,8,2]=>[5,2,1]
[5,8,2,7,3,6,4,1]=>[5,1,1,1]
[1,6,5,7,3,8,4,2]=>[4,2,1,1]
[1,5,6,8,4,2,7,3]=>[3,2,1,1,1]
[7,5,4,1,8,2,6,3]=>[4,3,1]
[6,4,1,8,2,7,5,3]=>[4,3,1]
[7,8,5,3,2,6,1,4]=>[5,1,1,1]
[8,2,5,1,7,6,4,3]=>[5,2,1]
[6,7,4,3,8,2,5,1]=>[5,1,1,1]
[3,4,2,7,8,6,1,5]=>[3,2,1,1,1]
[7,8,6,1,4,3,2,5]=>[5,1,1,1]
[2,4,7,8,6,1,3,5]=>[3,1,1,1,1,1]
[3,7,8,6,5,2,4,1]=>[5,1,1,1]
[4,5,2,7,8,6,3,1]=>[4,2,1,1]
[4,6,2,5,3,1,7,8]=>[4,1,1,1,1]
[4,1,5,6,3,2,7,8]=>[3,2,1,1,1]
[2,6,7,5,4,1,3,8]=>[4,1,1,1,1]
[4,1,6,7,5,3,2,8]=>[4,2,1,1]
[6,7,4,3,1,5,2,8]=>[4,2,1,1]
[1,7,5,6,4,3,2,8]=>[5,1,1,1]
[7,6,5,3,1,8,4,2]=>[5,3]
[7,8,6,4,3,1,5,2]=>[5,2,1]
[4,1,7,8,6,5,3,2]=>[5,2,1]
[4,5,7,3,8,6,1,2]=>[3,2,1,1,1]
[6,8,5,3,7,2,1,4]=>[5,1,1,1]
[4,7,1,5,8,2,6,3]=>[3,2,1,1,1]
[3,7,6,2,1,8,4,5]=>[4,2,1,1]
[2,7,5,8,3,6,4,1]=>[4,2,1,1]
[7,4,8,2,6,5,3,1]=>[5,2,1]
[7,5,4,8,2,6,3,1]=>[5,2,1]
[4,3,8,1,6,5,2,7]=>[4,2,1,1]
[2,3,6,5,7,8,1,4]=>[3,1,1,1,1,1]
[8,3,4,1,2,6,7,5]=>[3,2,1,1,1]
[7,3,4,8,5,2,1,6]=>[4,2,1,1]
[7,3,8,4,1,5,6,2]=>[3,2,2,1]
[7,2,4,5,1,8,3,6]=>[3,2,1,1,1]
[7,3,1,2,8,5,6,4]=>[3,3,1,1]
[4,8,2,3,5,7,6,1]=>[4,1,1,1,1]
[4,5,2,3,8,6,7,1]=>[3,2,1,1,1]
[6,7,4,8,5,3,2,1]=>[5,2,1]
[4,3,5,6,1,7,8,2]=>[3,2,1,1,1]
[3,5,2,6,4,7,8,1]=>[3,2,1,1,1]
[4,1,2,8,5,7,6,3]=>[4,2,1,1]
[3,1,5,6,4,7,8,2]=>[3,2,1,1,1]
[3,1,4,6,7,5,8,2]=>[3,2,1,1,1]
[2,6,4,5,8,1,3,7]=>[3,1,1,1,1,1]
[6,4,1,3,5,8,2,7]=>[4,1,1,1,1]
[3,4,1,7,2,6,8,5]=>[3,2,1,1,1]
[2,4,7,5,8,1,3,6]=>[3,1,1,1,1,1]
[3,7,6,2,1,5,8,4]=>[4,2,1,1]
[4,2,6,1,3,7,8,5]=>[3,2,1,1,1]
[8,5,4,2,7,6,3,1]=>[5,3]
[2,8,4,6,7,1,3,5]=>[3,1,1,1,1,1]
[5,8,2,1,4,6,7,3]=>[3,2,1,1,1]
[8,4,6,1,2,5,7,3]=>[4,1,1,1,1]
[3,7,8,4,2,6,5,1]=>[4,2,1,1]
[5,6,2,8,7,1,3,4]=>[3,2,1,1,1]
[7,1,3,8,4,5,6,2]=>[3,2,1,1,1]
[7,8,1,4,3,5,6,2]=>[4,1,1,1,1]
[3,6,7,2,8,1,5,4]=>[3,2,1,1,1]
[2,6,7,1,3,5,8,4]=>[3,1,1,1,1,1]
[3,6,7,1,8,2,5,4]=>[3,2,1,1,1]
[3,4,1,8,7,2,6,5]=>[4,2,1,1]
[3,1,5,7,2,8,6,4]=>[3,2,2,1]
[4,8,1,3,2,7,6,5]=>[4,2,1,1]
[4,1,8,3,2,7,6,5]=>[4,2,2]
[4,3,8,2,1,7,6,5]=>[4,3,1]
[3,2,4,8,7,1,6,5]=>[4,2,1,1]
[3,2,5,7,1,8,6,4]=>[3,3,1,1]
[4,2,8,3,1,7,6,5]=>[4,2,2]
[4,8,2,1,3,7,6,5]=>[4,2,1,1]
[4,2,8,1,3,7,6,5]=>[4,2,1,1]
[2,3,4,6,8,7,1,5]=>[3,1,1,1,1,1]
[5,6,4,7,1,2,8,3]=>[3,2,1,1,1]
[4,5,7,1,6,8,3,2]=>[4,1,1,1,1]
[3,2,7,6,8,1,4,5]=>[3,2,1,1,1]
[4,5,1,7,6,8,2,3]=>[3,2,1,1,1]
[6,7,2,8,3,1,4,5]=>[3,2,1,1,1]
[7,6,3,1,2,8,4,5]=>[4,2,1,1]
[6,2,7,8,4,1,3,5]=>[3,2,1,1,1]
[7,8,5,2,4,1,3,6]=>[4,1,1,1,1]
[7,6,2,3,1,8,4,5]=>[4,2,1,1]
[4,2,5,1,3,7,8,6]=>[3,2,1,1,1]
[3,5,1,4,2,7,8,6]=>[3,2,1,1,1]
[3,4,1,7,8,5,2,6]=>[3,2,1,1,1]
[4,1,3,7,8,5,2,6]=>[3,2,1,1,1]
[4,3,1,8,5,2,7,6]=>[3,3,2]
[3,1,8,5,4,2,7,6]=>[4,2,2]
[7,6,3,5,8,4,2,1]=>[6,1,1]
[4,5,1,3,2,7,8,6]=>[3,2,1,1,1]
[5,1,3,2,4,7,8,6]=>[3,2,1,1,1]
[8,3,5,6,1,7,2,4]=>[3,2,1,1,1]
[4,5,8,1,2,6,7,3]=>[3,1,1,1,1,1]
[5,3,6,7,8,2,1,4]=>[4,1,1,1,1]
[1,3,4,8,6,2,7,5]=>[3,2,1,1,1]
[7,2,4,1,3,8,5,6]=>[3,2,1,1,1]
[3,8,2,5,4,1,6,7]=>[4,1,1,1,1]
[8,4,5,2,6,1,7,3]=>[4,2,1,1]
[4,6,8,2,3,7,5,1]=>[4,1,1,1,1]
[2,7,3,4,1,5,6,8]=>[3,1,1,1,1,1]
[6,7,2,3,4,8,1,5]=>[3,1,1,1,1,1]
[3,5,2,4,6,7,8,1]=>[3,1,1,1,1,1]
[4,2,6,3,5,7,8,1]=>[3,2,1,1,1]
[1,4,8,5,6,2,7,3]=>[3,2,1,1,1]
[2,4,8,5,6,1,7,3]=>[3,2,1,1,1]
[6,3,5,8,4,7,1,2]=>[4,1,1,1,1]
[2,8,7,4,5,1,6,3]=>[4,2,1,1]
[1,3,8,5,2,6,7,4]=>[3,2,1,1,1]
[7,2,8,4,5,1,6,3]=>[3,2,2,1]
[6,2,3,5,1,7,8,4]=>[3,2,1,1,1]
[8,6,2,4,1,5,7,3]=>[4,2,1,1]
[1,6,4,3,2,7,8,5]=>[4,2,1,1]
[8,5,3,2,1,6,7,4]=>[5,2,1]
[1,7,5,2,3,6,8,4]=>[3,2,1,1,1]
[7,1,5,2,3,6,8,4]=>[3,2,1,1,1]
[8,1,2,5,3,6,7,4]=>[3,2,1,1,1]
[8,4,1,6,3,7,2,5]=>[4,2,1,1]
[6,7,5,3,8,2,1,4]=>[5,1,1,1]
[5,2,6,8,3,7,1,4]=>[3,2,1,1,1]
[4,2,5,8,6,7,1,3]=>[3,2,1,1,1]
[5,8,6,3,4,1,7,2]=>[4,2,1,1]
[3,7,2,4,1,8,6,5]=>[3,3,1,1]
[2,4,7,8,5,1,3,6]=>[3,1,1,1,1,1]
[2,5,3,8,4,1,6,7]=>[3,2,1,1,1]
[3,1,7,4,5,6,2,8]=>[3,2,1,1,1]
[2,4,8,3,5,7,1,6]=>[3,1,1,1,1,1]
[8,1,7,2,4,3,5,6]=>[4,1,1,1,1]
[1,3,8,2,4,7,5,6]=>[3,1,1,1,1,1]
[1,3,7,2,4,6,5,8]=>[3,1,1,1,1,1]
[1,7,3,2,4,6,5,8]=>[3,2,1,1,1]
[1,8,3,7,4,2,5,6]=>[4,1,1,1,1]
[8,7,3,1,4,2,5,6]=>[4,2,1,1]
[2,8,4,3,5,7,1,6]=>[4,1,1,1,1]
[3,2,8,7,4,1,5,6]=>[4,2,1,1]
[3,2,1,7,4,6,5,8]=>[3,3,1,1]
[3,2,6,5,1,7,8,4]=>[3,2,2,1]
[5,3,2,6,7,1,8,4]=>[4,2,1,1]
[3,2,8,6,7,4,1,5]=>[4,2,1,1]
[8,4,6,2,7,3,1,5]=>[4,2,1,1]
[4,3,8,6,7,2,1,5]=>[4,2,1,1]
[4,3,6,2,8,7,1,5]=>[4,2,1,1]
[3,8,4,7,6,5,1,2]=>[5,1,1,1]
[7,8,4,2,6,3,5,1]=>[4,2,1,1]
[3,2,7,8,6,4,5,1]=>[4,2,1,1]
[3,2,7,5,6,8,4,1]=>[4,2,1,1]
[5,7,8,6,3,2,4,1]=>[5,1,1,1]
[6,5,4,2,1,7,8,3]=>[5,2,1]
[5,4,2,1,7,6,3,8]=>[4,3,1]
[4,1,6,5,2,7,8,3]=>[3,2,2,1]
[5,4,1,6,7,2,8,3]=>[3,2,2,1]
[6,8,5,3,1,7,2,4]=>[4,2,1,1]
[5,2,6,3,8,7,1,4]=>[3,2,2,1]
[8,6,1,7,3,4,2,5]=>[4,2,1,1]
[1,8,3,6,7,4,2,5]=>[4,1,1,1,1]
[1,6,3,5,2,7,8,4]=>[3,2,1,1,1]
[1,5,7,3,2,6,4,8]=>[3,2,1,1,1]
[5,1,3,7,2,6,4,8]=>[3,2,1,1,1]
[8,1,6,7,2,4,3,5]=>[4,1,1,1,1]
[6,1,4,8,2,7,3,5]=>[3,2,1,1,1]
[6,2,4,8,3,7,1,5]=>[4,1,1,1,1]
[8,7,2,6,3,5,1,4]=>[5,1,1,1]
[8,1,7,6,5,2,3,4]=>[5,1,1,1]
[7,1,5,6,8,2,4,3]=>[4,1,1,1,1]
[6,7,1,5,2,4,8,3]=>[4,1,1,1,1]
[7,6,1,5,2,4,3,8]=>[5,1,1,1]
[7,1,6,3,5,4,2,8]=>[5,1,1,1]
[1,6,7,3,5,4,8,2]=>[4,1,1,1,1]
[1,7,3,5,6,8,4,2]=>[4,1,1,1,1]
[1,7,8,3,6,4,5,2]=>[4,1,1,1,1]
[1,8,7,6,4,5,2,3]=>[5,1,1,1]
[8,2,7,4,6,5,1,3]=>[5,1,1,1]
[2,8,5,7,6,4,1,3]=>[5,1,1,1]
[7,4,5,1,6,8,3,2]=>[4,2,1,1]
[4,1,7,5,6,8,3,2]=>[4,2,1,1]
[5,6,7,4,3,1,8,2]=>[4,2,1,1]
[6,7,8,5,3,1,4,2]=>[4,2,1,1]
[1,4,6,2,5,3,7,8]=>[3,1,1,1,1,1]
[1,6,3,2,5,4,7,8]=>[3,2,1,1,1]
[1,6,8,2,5,4,7,3]=>[4,1,1,1,1]
[1,5,4,2,6,3,7,8]=>[3,2,1,1,1]
[1,2,6,4,3,5,7,8]=>[3,1,1,1,1,1]
[1,6,8,2,7,5,4,3]=>[5,1,1,1]
[1,7,4,3,2,6,8,5]=>[4,2,1,1]
[1,5,4,7,2,6,8,3]=>[3,2,1,1,1]
[1,3,7,6,2,8,5,4]=>[4,2,1,1]
[1,7,6,2,8,4,3,5]=>[4,2,1,1]
[1,5,2,8,4,3,7,6]=>[3,2,2,1]
[1,2,8,4,3,6,5,7]=>[3,2,1,1,1]
[1,2,8,5,6,3,4,7]=>[3,1,1,1,1,1]
[1,7,3,5,2,8,6,4]=>[3,3,1,1]
[1,6,7,2,5,8,4,3]=>[4,1,1,1,1]
[1,5,8,3,2,7,4,6]=>[3,2,1,1,1]
[1,4,5,8,2,6,3,7]=>[3,1,1,1,1,1]
[1,7,6,4,8,2,5,3]=>[4,2,1,1]
[1,4,8,6,5,2,7,3]=>[4,2,1,1]
[1,3,8,2,6,5,4,7]=>[4,1,1,1,1]
[1,7,6,3,8,2,4,5]=>[4,1,1,1,1]
[1,5,2,7,6,4,8,3]=>[4,2,1,1]
[1,2,4,3,8,7,5,6]=>[3,2,1,1,1]
[1,4,3,8,7,2,5,6]=>[3,2,1,1,1]
[1,3,8,6,2,4,5,7]=>[3,1,1,1,1,1]
[1,3,8,5,4,2,6,7]=>[4,1,1,1,1]
[1,7,2,4,8,6,5,3]=>[4,2,1,1]
[1,6,5,3,2,8,7,4]=>[4,3,1]
[1,3,2,8,7,5,4,6]=>[4,2,1,1]
[1,2,8,6,5,4,3,7]=>[5,1,1,1]
[8,1,3,4,6,5,2,7]=>[4,1,1,1,1]
[8,3,1,4,6,5,2,7]=>[4,2,1,1]
[5,8,3,1,2,6,4,7]=>[3,2,1,1,1]
[4,8,1,7,5,2,3,6]=>[4,1,1,1,1]
[4,8,1,7,5,2,6,3]=>[4,2,1,1]
[8,5,1,4,2,6,3,7]=>[4,2,1,1]
[8,4,1,3,5,6,2,7]=>[4,1,1,1,1]
[8,5,3,2,1,6,4,7]=>[5,2,1]
[8,1,5,4,2,6,3,7]=>[4,2,1,1]
[8,5,2,4,1,6,3,7]=>[4,2,1,1]
[4,8,7,1,5,2,6,3]=>[4,2,1,1]
[4,8,7,1,5,2,3,6]=>[4,1,1,1,1]
[7,6,8,4,1,3,2,5]=>[5,1,1,1]
[7,6,8,4,1,3,5,2]=>[5,1,1,1]
[3,8,7,5,4,1,2,6]=>[5,1,1,1]
[4,8,2,7,5,1,3,6]=>[4,1,1,1,1]
[7,6,8,4,1,5,2,3]=>[4,2,1,1]
[8,7,6,1,5,2,3,4]=>[5,1,1,1]
[7,1,4,8,6,3,5,2]=>[4,2,1,1]
[8,1,6,5,3,4,7,2]=>[5,1,1,1]
[8,6,2,5,3,4,7,1]=>[5,1,1,1]
[8,6,5,1,3,4,7,2]=>[5,1,1,1]
[8,7,5,1,3,6,2,4]=>[5,1,1,1]
[8,7,1,5,3,6,2,4]=>[5,1,1,1]
[8,6,1,3,5,4,7,2]=>[5,1,1,1]
[7,1,4,8,3,6,5,2]=>[4,2,1,1]
[7,8,5,2,4,3,6,1]=>[5,1,1,1]
[7,3,8,2,5,4,6,1]=>[4,2,1,1]
[8,4,2,5,3,7,6,1]=>[4,2,2]
[4,8,1,5,3,7,6,2]=>[4,2,1,1]
[7,4,8,2,6,3,5,1]=>[4,2,1,1]
[7,4,8,2,6,3,1,5]=>[4,2,1,1]
[8,7,3,1,6,4,2,5]=>[5,2,1]
[8,7,3,1,6,4,5,2]=>[5,2,1]
[8,7,3,1,4,6,5,2]=>[5,2,1]
[8,4,3,2,7,5,6,1]=>[5,2,1]
[6,4,1,7,8,5,3,2]=>[4,3,1]
[7,6,3,4,1,8,5,2]=>[4,3,1]
[8,7,3,1,6,2,5,4]=>[5,2,1]
[7,8,6,4,2,5,1,3]=>[5,1,1,1]
[7,8,2,4,6,5,1,3]=>[4,1,1,1,1]
[8,1,7,3,5,6,2,4]=>[4,1,1,1,1]
[8,7,5,2,4,6,1,3]=>[5,1,1,1]
[8,1,7,5,4,6,2,3]=>[5,1,1,1]
[8,7,3,2,6,1,5,4]=>[5,2,1]
[5,3,1,7,6,4,2,8]=>[4,3,1]
[7,5,3,2,1,6,4,8]=>[5,2,1]
[7,6,5,3,1,4,2,8]=>[5,2,1]
[1,8,6,4,3,2,7,5]=>[5,2,1]
[1,8,7,6,4,2,5,3]=>[5,2,1]
[8,4,6,7,5,3,2,1]=>[6,1,1]
[1,4,8,6,7,5,3,2]=>[5,1,1,1]
[7,6,2,5,8,4,3,1]=>[6,1,1]
[1,7,3,6,8,5,4,2]=>[5,1,1,1]
[8,6,2,5,7,4,3,1]=>[6,1,1]
[7,1,3,6,8,5,4,2]=>[5,1,1,1]
[1,8,3,6,7,5,4,2]=>[5,1,1,1]
[8,1,7,6,4,5,3,2]=>[6,1,1]
[7,1,8,6,4,5,3,2]=>[5,2,1]
[1,6,2,7,4,5,3,8]=>[3,2,1,1,1]
[1,8,2,6,4,3,5,7]=>[4,1,1,1,1]
[1,7,2,6,4,3,5,8]=>[4,1,1,1,1]
[1,7,2,5,4,6,3,8]=>[4,1,1,1,1]
[6,5,7,2,8,3,4,1]=>[4,2,1,1]
[6,2,7,5,8,1,4,3]=>[4,2,1,1]
[6,7,2,5,8,1,4,3]=>[4,1,1,1,1]
[6,5,7,3,8,1,4,2]=>[4,2,1,1]
[6,3,7,4,8,2,5,1]=>[4,2,1,1]
[6,3,7,4,8,1,5,2]=>[3,2,2,1]
[8,7,6,4,2,5,3,1]=>[6,2]
[6,7,5,1,4,3,8,2]=>[5,1,1,1]
[7,8,5,1,4,3,6,2]=>[5,1,1,1]
[2,7,6,8,3,5,1,4]=>[4,1,1,1,1]
[7,2,1,5,3,8,6,4]=>[3,3,2]
[5,8,2,7,6,1,3,4]=>[4,1,1,1,1]
[5,1,8,7,3,4,2,6]=>[4,2,1,1]
[8,2,3,6,7,1,4,5]=>[3,1,1,1,1,1]
[4,2,3,1,5,8,6,7]=>[3,2,1,1,1]
[2,4,8,7,5,3,1,6]=>[5,1,1,1]
[2,6,8,7,5,3,4,1]=>[5,1,1,1]
[2,6,5,1,4,3,8,7]=>[4,2,1,1]
[6,5,1,2,4,3,8,7]=>[4,2,1,1]
[4,6,5,3,1,2,8,7]=>[4,2,1,1]
[4,8,7,5,3,1,2,6]=>[5,1,1,1]
[4,6,8,7,5,3,1,2]=>[5,1,1,1]
[6,8,7,5,3,1,4,2]=>[5,2,1]
[8,7,5,6,3,1,4,2]=>[5,2,1]
[8,7,3,4,6,5,1,2]=>[5,1,1,1]
[2,1,4,8,7,3,6,5]=>[4,2,1,1]
[4,8,7,3,1,2,6,5]=>[4,2,1,1]
[8,7,3,4,1,2,6,5]=>[4,2,1,1]
[8,7,3,1,6,5,2,4]=>[5,2,1]
[8,7,3,2,6,5,1,4]=>[5,2,1]
[2,8,7,3,4,6,5,1]=>[5,1,1,1]
[2,8,7,3,6,5,1,4]=>[5,1,1,1]
[2,8,7,1,6,5,3,4]=>[5,1,1,1]
[8,7,1,2,6,5,3,4]=>[5,1,1,1]
[8,7,1,2,4,3,6,5]=>[4,2,1,1]
[2,1,8,7,3,4,6,5]=>[4,2,1,1]
[8,7,5,1,2,4,3,6]=>[5,1,1,1]
[2,8,7,1,4,3,6,5]=>[4,2,1,1]
[2,8,7,3,4,1,6,5]=>[4,2,1,1]
[2,8,7,5,6,3,4,1]=>[5,1,1,1]
[2,4,8,7,3,1,6,5]=>[4,2,1,1]
[2,8,7,3,1,4,6,5]=>[4,2,1,1]
[2,4,3,1,8,7,5,6]=>[3,3,1,1]
[4,3,1,2,6,8,7,5]=>[3,3,1,1]
[2,8,7,5,6,3,1,4]=>[5,1,1,1]
[2,8,7,5,3,1,6,4]=>[5,2,1]
[2,8,7,5,3,6,4,1]=>[5,2,1]
[2,8,7,5,6,1,4,3]=>[5,1,1,1]
[2,6,8,7,5,1,4,3]=>[5,1,1,1]
[6,8,7,5,1,2,4,3]=>[5,1,1,1]
[8,7,5,6,1,2,4,3]=>[5,1,1,1]
[8,7,1,2,4,6,5,3]=>[5,1,1,1]
[2,4,8,7,3,6,5,1]=>[5,1,1,1]
[8,7,2,4,3,6,5,1]=>[5,2,1]
[4,8,7,1,2,6,5,3]=>[5,1,1,1]
[8,7,5,3,1,2,6,4]=>[5,2,1]
[8,7,5,3,6,4,1,2]=>[5,2,1]
[8,7,1,4,3,6,5,2]=>[5,2,1]
[8,7,3,4,1,6,5,2]=>[5,2,1]
[7,1,2,3,5,4,6,8]=>[3,1,1,1,1,1]
[7,1,2,6,4,5,3,8]=>[4,1,1,1,1]
[7,1,2,4,3,5,6,8]=>[3,1,1,1,1,1]
[4,7,3,6,5,1,2,8]=>[4,1,1,1,1]
[7,5,4,2,8,3,1,6]=>[5,2,1]
[8,3,6,1,5,2,4,7]=>[4,1,1,1,1]
[5,7,2,1,8,4,6,3]=>[3,3,1,1]
[7,2,8,6,4,3,1,5]=>[5,2,1]
[6,3,8,7,4,2,1,5]=>[5,2,1]
[7,6,3,2,8,4,1,5]=>[5,2,1]
[8,6,1,3,2,4,5,7]=>[4,1,1,1,1]
[5,8,3,7,4,2,1,6]=>[5,1,1,1]
[8,4,7,3,5,2,1,6]=>[5,1,1,1]
[5,4,8,1,3,2,6,7]=>[4,1,1,1,1]
[4,5,8,2,1,3,6,7]=>[3,1,1,1,1,1]
[8,1,3,5,2,4,6,7]=>[3,1,1,1,1,1]
[1,8,3,5,7,2,4,6]=>[3,1,1,1,1,1]
[8,6,2,1,3,7,5,4]=>[4,3,1]
[8,1,4,2,7,6,3,5]=>[4,2,1,1]
[1,5,7,3,6,8,2,4]=>[3,1,1,1,1,1]
[1,3,4,7,6,8,2,5]=>[3,1,1,1,1,1]
[1,2,4,7,8,5,3,6]=>[3,1,1,1,1,1]
[5,1,7,3,6,8,2,4]=>[3,2,1,1,1]
[5,8,6,1,7,3,2,4]=>[4,2,1,1]
[6,7,1,2,8,4,3,5]=>[3,2,1,1,1]
[1,3,2,8,6,5,4,7]=>[4,2,1,1]
[2,5,7,1,8,4,3,6]=>[3,2,1,1,1]
[3,5,7,1,6,8,2,4]=>[3,1,1,1,1,1]
[5,4,7,6,8,3,1,2]=>[4,2,1,1]
[8,4,6,7,5,2,1,3]=>[5,1,1,1]
[8,1,7,6,4,3,2,5]=>[6,1,1]
[1,5,8,4,3,7,6,2]=>[4,2,1,1]
[8,1,3,5,2,7,6,4]=>[4,2,1,1]
[8,1,4,5,6,3,7,2]=>[4,1,1,1,1]
[7,3,4,1,6,8,2,5]=>[3,2,1,1,1]
[7,2,1,6,3,4,8,5]=>[3,2,2,1]
[2,3,5,1,4,8,7,6]=>[3,2,1,1,1]
[2,7,1,3,8,4,6,5]=>[3,2,1,1,1]
[3,8,7,1,6,2,5,4]=>[5,1,1,1]
[8,3,7,2,4,1,5,6]=>[4,1,1,1,1]
[8,6,7,2,1,4,3,5]=>[4,2,1,1]
[8,3,7,5,1,2,6,4]=>[4,2,1,1]
[3,4,7,6,1,2,8,5]=>[3,2,1,1,1]
[4,5,8,7,6,1,3,2]=>[5,1,1,1]
[8,6,3,7,5,1,4,2]=>[5,2,1]
[8,7,3,5,6,1,4,2]=>[5,1,1,1]
[7,6,3,8,1,4,5,2]=>[4,2,1,1]
[8,5,2,7,6,1,3,4]=>[4,2,1,1]
[8,7,3,1,4,5,2,6]=>[4,2,1,1]
[8,4,2,5,1,6,7,3]=>[4,2,1,1]
[8,5,3,1,6,4,7,2]=>[4,3,1]
[8,7,3,1,4,5,6,2]=>[4,2,1,1]
[8,7,4,1,5,6,2,3]=>[4,2,1,1]
[8,6,4,1,7,5,2,3]=>[4,3,1]
[8,6,3,1,7,4,5,2]=>[4,3,1]
[8,5,3,1,6,7,4,2]=>[4,3,1]
[8,5,3,7,1,6,4,2]=>[5,2,1]
[7,6,3,8,1,4,2,5]=>[4,2,1,1]
[7,4,8,2,6,1,5,3]=>[4,2,1,1]
[6,4,7,3,1,5,2,8]=>[4,2,1,1]
[8,5,3,1,6,4,2,7]=>[4,3,1]
[8,7,4,1,5,2,3,6]=>[4,2,1,1]
[8,7,5,1,2,6,3,4]=>[4,2,1,1]
[8,6,4,1,2,7,5,3]=>[4,3,1]
[8,7,4,1,2,5,3,6]=>[4,2,1,1]
[8,7,5,1,2,3,6,4]=>[4,2,1,1]
[6,5,3,7,4,2,1,8]=>[5,2,1]
[1,6,3,8,4,2,5,7]=>[3,2,1,1,1]
[4,7,2,5,3,6,1,8]=>[4,1,1,1,1]
[1,8,3,4,5,2,6,7]=>[3,1,1,1,1,1]
[1,8,6,4,2,5,3,7]=>[4,2,1,1]
[8,2,6,4,1,5,7,3]=>[4,2,1,1]
[7,8,3,4,6,1,5,2]=>[4,1,1,1,1]
[4,8,7,5,3,1,6,2]=>[5,2,1]
[6,1,4,8,3,2,5,7]=>[4,1,1,1,1]
[4,1,8,5,3,2,6,7]=>[4,2,1,1]
[8,1,6,4,2,7,3,5]=>[4,2,1,1]
[3,1,7,4,2,5,8,6]=>[3,2,2,1]
[1,2,7,4,3,5,6,8]=>[3,1,1,1,1,1]
[6,1,8,5,2,4,3,7]=>[4,2,1,1]
[6,8,2,5,1,4,7,3]=>[4,1,1,1,1]
[4,5,2,1,6,8,7,3]=>[3,3,1,1]
[7,2,8,6,5,1,4,3]=>[5,2,1]
[7,4,8,6,1,5,3,2]=>[5,2,1]
[8,7,2,6,1,4,5,3]=>[5,1,1,1]
[1,7,8,6,2,4,3,5]=>[4,1,1,1,1]
[7,6,3,1,2,5,4,8]=>[4,2,1,1]
[8,5,3,1,2,4,7,6]=>[4,2,1,1]
[8,2,1,6,5,3,4,7]=>[4,2,1,1]
[3,8,1,5,6,2,4,7]=>[3,1,1,1,1,1]
[6,8,4,1,5,2,3,7]=>[3,2,1,1,1]
[3,2,8,1,6,4,5,7]=>[3,2,1,1,1]
[5,2,1,3,7,6,4,8]=>[3,3,1,1]
[5,4,1,2,8,3,7,6]=>[3,3,1,1]
[5,8,4,1,2,3,7,6]=>[3,2,1,1,1]
[7,1,2,5,3,4,6,8]=>[3,1,1,1,1,1]
[1,6,7,3,2,8,4,5]=>[3,2,1,1,1]
[1,8,6,3,2,7,4,5]=>[4,2,1,1]
[1,5,3,7,2,8,4,6]=>[3,2,1,1,1]
[1,4,6,2,8,5,3,7]=>[3,2,1,1,1]
[1,5,6,2,8,4,3,7]=>[3,2,1,1,1]
[2,4,6,3,1,7,5,8]=>[3,2,1,1,1]
[1,2,5,7,4,3,6,8]=>[3,1,1,1,1,1]
[1,2,5,7,4,6,8,3]=>[3,1,1,1,1,1]
[3,5,8,6,1,7,2,4]=>[3,2,1,1,1]
[2,3,6,8,1,7,4,5]=>[3,1,1,1,1,1]
[2,3,7,1,8,6,4,5]=>[3,2,1,1,1]
[2,6,1,7,8,5,3,4]=>[3,2,1,1,1]
[2,4,8,5,6,7,1,3]=>[3,1,1,1,1,1]
[1,4,8,5,6,7,3,2]=>[4,1,1,1,1]
[4,8,3,1,6,5,7,2]=>[4,2,1,1]
[1,6,8,5,4,2,7,3]=>[4,2,1,1]
[6,5,8,4,2,1,7,3]=>[5,2,1]
[1,7,8,6,5,4,2,3]=>[5,1,1,1]
[6,8,7,4,5,1,3,2]=>[5,1,1,1]
[6,1,3,5,4,2,8,7]=>[4,2,1,1]
[3,6,4,2,5,1,8,7]=>[4,2,1,1]
[2,1,5,8,6,4,7,3]=>[4,2,1,1]
[4,2,8,5,6,3,7,1]=>[4,2,1,1]
[5,7,2,3,4,6,8,1]=>[3,1,1,1,1,1]
[1,8,7,3,2,5,6,4]=>[4,2,1,1]
[5,7,1,2,3,8,6,4]=>[3,2,1,1,1]
[7,8,6,2,4,1,5,3]=>[4,2,1,1]
[7,2,8,4,6,1,5,3]=>[4,2,1,1]
[7,4,6,2,8,1,5,3]=>[4,2,1,1]
[7,1,5,8,2,3,6,4]=>[3,2,1,1,1]
[7,6,4,8,2,1,5,3]=>[5,2,1]
[6,1,8,4,2,3,5,7]=>[3,2,1,1,1]
[7,3,6,2,1,8,5,4]=>[4,3,1]
[1,8,6,4,2,5,7,3]=>[4,2,1,1]
[5,6,2,1,8,4,7,3]=>[3,3,1,1]
[2,8,1,6,5,7,3,4]=>[4,1,1,1,1]
[5,1,6,4,3,8,7,2]=>[4,2,2]
[5,4,6,8,1,3,7,2]=>[4,1,1,1,1]
[3,7,1,6,4,5,8,2]=>[4,1,1,1,1]
[3,5,2,1,4,6,7,8]=>[3,1,1,1,1,1]
[1,3,8,7,5,4,6,2]=>[5,1,1,1]
[6,7,3,4,8,5,1,2]=>[3,2,1,1,1]
[7,4,1,8,2,5,6,3]=>[3,3,1,1]
[3,1,7,2,5,6,8,4]=>[3,2,1,1,1]
[4,1,5,7,3,2,8,6]=>[3,2,2,1]
[6,4,1,7,2,8,5,3]=>[3,3,2]
[7,3,1,6,2,8,5,4]=>[4,2,2]
[4,8,2,5,3,1,6,7]=>[4,1,1,1,1]
[5,1,3,4,8,2,6,7]=>[3,1,1,1,1,1]
[6,1,4,5,7,8,2,3]=>[3,1,1,1,1,1]
[6,3,4,7,1,8,5,2]=>[3,3,1,1]
[7,1,3,4,5,6,8,2]=>[3,1,1,1,1,1]
[8,5,2,7,6,3,1,4]=>[5,2,1]
[1,8,3,5,6,2,7,4]=>[3,2,1,1,1]
[8,3,2,5,6,1,7,4]=>[4,2,1,1]
[4,2,5,1,6,8,7,3]=>[3,3,1,1]
[5,4,2,7,8,6,1,3]=>[4,2,1,1]
[6,8,7,2,1,3,4,5]=>[4,1,1,1,1]
[3,7,6,8,5,2,4,1]=>[5,1,1,1]
[1,7,8,5,2,6,3,4]=>[3,2,1,1,1]
[7,6,1,2,5,3,8,4]=>[4,2,1,1]
[7,6,2,4,8,1,5,3]=>[4,2,1,1]
[1,5,7,3,8,6,2,4]=>[3,2,1,1,1]
[6,7,5,1,8,2,3,4]=>[3,2,1,1,1]
[7,6,1,2,4,3,8,5]=>[4,2,1,1]
[6,7,2,1,5,3,8,4]=>[3,2,2,1]
[4,3,2,8,7,1,6,5]=>[4,3,1]
[4,8,3,2,7,1,6,5]=>[4,2,1,1]
[4,8,3,1,7,6,5,2]=>[5,2,1]
[5,3,8,7,1,6,4,2]=>[5,2,1]
[5,8,7,3,1,6,4,2]=>[5,2,1]
[5,3,8,2,1,7,6,4]=>[4,3,1]
[3,8,7,2,6,5,1,4]=>[5,1,1,1]
[7,4,1,8,6,5,3,2]=>[5,3]
[5,4,2,8,1,7,6,3]=>[4,3,1]
[5,8,4,2,1,7,6,3]=>[4,3,1]
[5,8,4,7,1,6,3,2]=>[5,1,1,1]
[5,4,8,3,1,7,6,2]=>[4,3,1]
[8,5,6,1,4,7,2,3]=>[4,1,1,1,1]
[6,7,4,1,2,5,8,3]=>[3,2,1,1,1]
[1,6,7,4,2,5,8,3]=>[3,2,1,1,1]
[3,6,7,5,8,1,2,4]=>[3,1,1,1,1,1]
[1,6,7,5,8,3,2,4]=>[4,1,1,1,1]
[3,8,6,5,7,4,1,2]=>[5,1,1,1]
[5,2,1,6,8,4,7,3]=>[3,3,1,1]
[6,5,8,7,4,2,3,1]=>[5,2,1]
[6,8,5,7,4,2,1,3]=>[5,1,1,1]
[3,6,7,5,8,2,1,4]=>[4,1,1,1,1]
[4,7,5,3,8,1,2,6]=>[4,1,1,1,1]
[4,7,5,3,6,1,2,8]=>[4,1,1,1,1]
[2,7,5,3,6,4,8,1]=>[4,2,1,1]
[4,7,5,3,8,1,6,2]=>[4,2,1,1]
[4,7,5,3,6,8,1,2]=>[4,1,1,1,1]
[2,7,5,6,3,8,4,1]=>[4,2,1,1]
[2,7,5,3,6,8,1,4]=>[4,1,1,1,1]
[8,7,5,3,1,4,6,2]=>[5,2,1]
[2,7,5,3,1,4,8,6]=>[4,2,1,1]
[2,7,5,3,4,8,6,1]=>[4,2,1,1]
[5,7,6,2,8,3,1,4]=>[4,2,1,1]
[5,1,6,3,2,4,8,7]=>[3,2,2,1]
[5,7,6,1,8,3,2,4]=>[4,2,1,1]
[3,8,7,2,1,5,4,6]=>[4,2,1,1]
[6,1,7,2,8,4,3,5]=>[3,2,2,1]
[4,8,5,6,7,3,1,2]=>[4,1,1,1,1]
[3,7,6,2,8,5,1,4]=>[4,2,1,1]
[6,1,7,3,8,5,2,4]=>[3,2,2,1]
[7,1,8,3,2,5,4,6]=>[3,2,2,1]
[4,8,5,6,7,2,1,3]=>[4,1,1,1,1]
[5,8,6,2,7,4,1,3]=>[4,2,1,1]
[2,4,6,7,8,5,1,3]=>[3,1,1,1,1,1]
[2,4,6,7,8,3,1,5]=>[3,1,1,1,1,1]
[4,7,6,2,8,5,1,3]=>[4,2,1,1]
[5,8,7,3,2,4,1,6]=>[5,1,1,1]
[4,6,5,8,7,3,1,2]=>[4,2,1,1]
[8,3,1,7,2,6,4,5]=>[4,2,1,1]
[4,5,1,2,8,7,3,6]=>[3,2,1,1,1]
[5,6,1,2,8,3,7,4]=>[3,2,1,1,1]
[5,8,7,1,6,2,4,3]=>[5,1,1,1]
[8,4,5,1,7,6,2,3]=>[4,2,1,1]
[6,3,1,4,8,2,7,5]=>[3,3,1,1]
[8,5,6,1,7,2,4,3]=>[4,2,1,1]
[7,5,6,1,3,8,4,2]=>[4,2,1,1]
[5,7,6,1,3,8,4,2]=>[4,2,1,1]
[6,7,1,4,2,8,5,3]=>[3,3,1,1]
[2,1,6,4,8,3,7,5]=>[3,2,2,1]
[1,5,7,8,4,2,3,6]=>[3,1,1,1,1,1]
[1,3,6,4,2,5,7,8]=>[3,1,1,1,1,1]
[1,4,5,7,8,3,6,2]=>[3,1,1,1,1,1]
[1,5,7,8,3,6,2,4]=>[3,1,1,1,1,1]
[1,5,7,8,2,4,3,6]=>[3,1,1,1,1,1]
[6,8,4,7,3,2,1,5]=>[5,1,1,1]
[6,8,5,4,2,7,1,3]=>[5,1,1,1]
[1,8,4,6,3,2,7,5]=>[4,2,1,1]
[6,4,8,5,3,2,1,7]=>[5,2,1]
[3,5,6,1,4,2,7,8]=>[3,1,1,1,1,1]
[1,6,3,8,4,2,7,5]=>[3,2,2,1]
[7,1,3,2,4,6,8,5]=>[3,2,1,1,1]
[2,6,5,7,8,3,1,4]=>[4,1,1,1,1]
[4,1,8,2,6,7,5,3]=>[4,2,1,1]
[3,6,7,8,2,1,4,5]=>[3,1,1,1,1,1]
[2,5,7,1,6,3,4,8]=>[3,1,1,1,1,1]
[4,2,8,3,6,5,1,7]=>[4,2,1,1]
[6,3,8,7,2,4,5,1]=>[4,2,1,1]
[7,6,1,8,2,4,5,3]=>[4,2,1,1]
[2,5,6,3,4,8,1,7]=>[3,1,1,1,1,1]
[5,2,4,7,8,6,1,3]=>[3,2,1,1,1]
[7,2,1,3,4,8,5,6]=>[3,2,1,1,1]
[2,4,5,7,1,8,6,3]=>[3,2,1,1,1]
[8,1,6,2,3,4,7,5]=>[3,2,1,1,1]
[6,1,4,2,5,7,8,3]=>[3,2,1,1,1]
[1,8,3,4,5,2,7,6]=>[3,2,1,1,1]
[1,8,3,6,4,7,2,5]=>[4,1,1,1,1]
[1,4,7,2,5,6,3,8]=>[3,1,1,1,1,1]
[7,3,5,8,2,6,1,4]=>[4,1,1,1,1]
[3,4,8,6,7,2,1,5]=>[4,1,1,1,1]
[3,4,8,2,5,1,7,6]=>[3,2,1,1,1]
[1,4,6,7,8,3,5,2]=>[3,1,1,1,1,1]
[4,1,5,3,6,8,7,2]=>[3,2,2,1]
[5,8,7,4,6,2,3,1]=>[5,1,1,1]
[1,6,8,3,5,2,7,4]=>[3,2,1,1,1]
[2,4,7,8,5,6,1,3]=>[3,1,1,1,1,1]
[4,1,7,8,5,6,3,2]=>[4,2,1,1]
[2,6,3,8,5,1,7,4]=>[3,2,2,1]
[4,1,5,8,6,7,3,2]=>[4,2,1,1]
[5,3,4,7,6,1,2,8]=>[3,2,1,1,1]
[2,8,5,4,1,3,7,6]=>[4,2,1,1]
[4,2,8,7,1,3,5,6]=>[3,2,1,1,1]
[5,4,6,3,1,7,2,8]=>[4,2,1,1]
[4,3,6,5,1,8,2,7]=>[3,2,2,1]
[1,5,6,8,7,3,2,4]=>[4,1,1,1,1]
[1,4,8,3,6,5,2,7]=>[4,1,1,1,1]
[1,3,8,6,4,7,2,5]=>[4,1,1,1,1]
[1,2,8,6,4,3,7,5]=>[4,2,1,1]
[6,5,1,8,7,3,2,4]=>[4,3,1]
[4,1,7,6,8,3,2,5]=>[4,2,1,1]
[1,8,4,7,6,2,3,5]=>[4,1,1,1,1]
[8,3,2,6,1,7,4,5]=>[4,2,1,1]
[1,6,3,7,4,5,2,8]=>[3,2,1,1,1]
[2,6,3,7,4,8,5,1]=>[3,2,2,1]
[4,6,1,7,8,2,5,3]=>[3,2,1,1,1]
[7,2,3,8,4,5,6,1]=>[3,2,1,1,1]
[5,2,6,7,8,3,4,1]=>[3,2,1,1,1]
[6,5,8,1,2,7,4,3]=>[4,2,1,1]
[6,5,1,8,7,2,4,3]=>[4,3,1]
[5,8,4,3,7,2,1,6]=>[5,1,1,1]
[6,1,2,8,7,3,4,5]=>[3,2,1,1,1]
[7,3,2,8,4,6,1,5]=>[4,2,1,1]
[4,5,1,7,6,2,8,3]=>[3,2,2,1]
[1,5,2,7,6,3,4,8]=>[3,2,1,1,1]
[7,2,6,8,3,5,4,1]=>[5,1,1,1]
[4,8,1,7,6,2,5,3]=>[5,1,1,1]
[7,2,8,6,5,3,4,1]=>[5,2,1]
[4,1,8,7,6,5,2,3]=>[5,2,1]
[6,5,1,8,7,4,3,2]=>[5,3]
[7,5,1,8,6,4,3,2]=>[5,3]
[8,5,1,7,6,4,3,2]=>[6,2]
[8,5,3,7,6,1,4,2]=>[5,2,1]
[3,8,7,6,1,5,4,2]=>[6,1,1]
[8,3,7,5,4,1,6,2]=>[5,2,1]
[4,5,3,1,8,7,2,6]=>[3,3,1,1]
[3,4,8,1,5,2,6,7]=>[3,1,1,1,1,1]
[8,6,5,7,1,3,2,4]=>[5,1,1,1]
[1,5,8,6,2,7,4,3]=>[4,2,1,1]
[3,1,8,5,7,2,6,4]=>[4,2,1,1]
[6,8,5,3,4,2,1,7]=>[5,1,1,1]
[8,5,2,6,4,3,1,7]=>[5,2,1]
[8,6,4,5,2,1,7,3]=>[5,2,1]
[8,5,2,6,1,4,7,3]=>[4,2,1,1]
[2,7,5,8,1,4,6,3]=>[4,1,1,1,1]
[3,2,6,7,1,8,5,4]=>[3,3,1,1]
[3,4,6,7,8,2,1,5]=>[3,1,1,1,1,1]
[3,2,6,7,8,4,1,5]=>[3,2,1,1,1]
[6,2,7,4,8,5,1,3]=>[3,2,2,1]
[6,7,1,3,8,5,4,2]=>[4,2,1,1]
[6,7,1,8,5,2,4,3]=>[4,2,1,1]
[1,2,6,7,8,5,3,4]=>[3,1,1,1,1,1]
[1,6,7,4,8,3,2,5]=>[4,1,1,1,1]
[1,4,6,7,8,3,2,5]=>[3,1,1,1,1,1]
[6,1,2,4,5,3,7,8]=>[3,1,1,1,1,1]
[8,1,7,3,2,6,4,5]=>[4,2,1,1]
[8,7,2,1,5,4,6,3]=>[5,2,1]
[2,7,4,8,6,5,3,1]=>[5,2,1]
[7,6,5,2,4,1,8,3]=>[5,2,1]
[7,6,4,3,1,5,8,2]=>[5,2,1]
[6,1,8,7,2,3,5,4]=>[4,2,1,1]
[8,6,1,2,7,3,4,5]=>[3,2,1,1,1]
[3,6,8,2,7,1,5,4]=>[4,1,1,1,1]
[2,8,6,1,4,5,7,3]=>[4,1,1,1,1]
[6,8,7,2,5,4,1,3]=>[5,1,1,1]
[3,2,6,4,8,7,5,1]=>[4,2,2]
[4,7,2,8,6,5,1,3]=>[4,2,1,1]
[4,7,1,8,6,5,3,2]=>[5,2,1]
[2,7,4,8,3,6,1,5]=>[4,1,1,1,1]
[4,7,3,8,6,1,5,2]=>[4,2,1,1]
[4,3,6,8,7,2,5,1]=>[4,2,1,1]
[4,3,8,2,5,7,6,1]=>[4,2,1,1]
[4,1,2,6,8,7,5,3]=>[4,2,1,1]
[3,1,6,4,8,7,2,5]=>[3,2,2,1]
[4,1,6,8,7,5,2,3]=>[4,2,1,1]
[3,8,1,4,5,7,2,6]=>[3,1,1,1,1,1]
[3,8,1,4,2,5,7,6]=>[3,2,1,1,1]
[4,1,8,3,5,2,7,6]=>[3,2,2,1]
[3,8,1,2,5,4,7,6]=>[3,2,1,1,1]
[4,2,3,6,8,7,1,5]=>[3,2,1,1,1]
[4,2,8,3,5,1,7,6]=>[3,2,2,1]
[4,2,8,3,5,7,6,1]=>[4,2,1,1]
[3,8,2,4,5,7,6,1]=>[4,1,1,1,1]
[3,8,2,5,1,4,7,6]=>[3,2,1,1,1]
[4,2,8,5,7,1,3,6]=>[3,2,1,1,1]
[3,8,1,5,2,4,7,6]=>[3,2,1,1,1]
[7,5,6,4,1,3,2,8]=>[5,1,1,1]
[7,8,6,4,1,3,2,5]=>[5,1,1,1]
[7,1,4,2,5,6,3,8]=>[3,2,1,1,1]
[7,3,2,1,4,6,5,8]=>[4,2,1,1]
[7,6,1,4,3,2,5,8]=>[5,1,1,1]
[7,4,1,3,5,6,2,8]=>[4,1,1,1,1]
[2,7,1,3,5,6,8,4]=>[3,1,1,1,1,1]
[3,6,2,1,5,8,7,4]=>[3,3,1,1]
[2,3,6,1,5,8,7,4]=>[3,2,1,1,1]
[3,4,7,1,5,6,8,2]=>[3,1,1,1,1,1]
[3,6,7,4,1,2,8,5]=>[3,2,1,1,1]
[4,3,2,7,1,6,8,5]=>[4,2,1,1]
[7,3,2,8,1,6,4,5]=>[4,2,1,1]
[7,4,8,1,5,6,3,2]=>[4,2,1,1]
[2,6,8,1,5,3,7,4]=>[3,2,1,1,1]
[6,8,2,1,5,3,7,4]=>[3,2,2,1]
[4,8,2,5,3,6,7,1]=>[4,1,1,1,1]
[4,5,8,2,3,6,7,1]=>[3,1,1,1,1,1]
[2,4,8,5,3,6,7,1]=>[4,1,1,1,1]
[5,3,2,6,4,8,7,1]=>[4,2,2]
[2,4,5,3,8,6,7,1]=>[3,2,1,1,1]
[4,3,5,2,8,6,7,1]=>[4,2,1,1]
[4,8,5,3,2,6,7,1]=>[5,1,1,1]
[3,5,4,2,8,6,7,1]=>[4,2,1,1]
[4,1,2,7,5,6,8,3]=>[3,2,1,1,1]
[5,6,7,4,2,8,3,1]=>[4,2,1,1]
[2,5,7,4,6,8,3,1]=>[4,1,1,1,1]
[7,5,2,4,3,8,6,1]=>[5,2,1]
[6,8,1,2,5,4,7,3]=>[4,1,1,1,1]
[6,4,1,8,5,2,7,3]=>[3,3,2]
[2,6,1,8,5,4,7,3]=>[4,2,1,1]
[7,1,2,8,5,6,4,3]=>[4,2,1,1]
[4,3,2,6,8,5,7,1]=>[4,2,1,1]
[3,7,6,4,8,5,2,1]=>[5,2,1]
[3,1,6,8,5,4,7,2]=>[4,2,1,1]
[2,3,5,8,4,6,7,1]=>[3,1,1,1,1,1]
[3,5,2,8,4,6,7,1]=>[3,2,1,1,1]
[3,4,5,8,2,6,7,1]=>[3,1,1,1,1,1]
[5,4,2,8,3,6,7,1]=>[4,2,1,1]
[5,3,4,8,2,6,7,1]=>[4,1,1,1,1]
[2,5,4,8,3,6,7,1]=>[4,1,1,1,1]
[6,3,2,5,8,4,7,1]=>[4,2,1,1]
[6,1,8,3,5,4,7,2]=>[4,2,1,1]
[5,4,8,3,2,6,7,1]=>[5,1,1,1]
[5,8,2,3,4,6,7,1]=>[3,1,1,1,1,1]
[6,2,1,7,8,5,4,3]=>[4,3,1]
[7,4,6,8,3,2,5,1]=>[5,1,1,1]
[3,4,5,2,7,1,6,8]=>[3,1,1,1,1,1]
[7,5,6,1,2,3,8,4]=>[3,2,1,1,1]
[1,5,7,6,3,2,8,4]=>[4,2,1,1]
[8,4,6,7,3,2,5,1]=>[5,1,1,1]
[8,4,6,2,3,1,5,7]=>[4,1,1,1,1]
[7,5,2,1,4,3,8,6]=>[4,2,2]
[3,1,7,8,5,4,2,6]=>[4,2,1,1]
[7,6,4,8,3,1,2,5]=>[5,1,1,1]
[7,4,8,5,6,1,2,3]=>[3,2,1,1,1]
[6,2,8,5,1,3,4,7]=>[3,2,1,1,1]
[3,2,7,8,6,1,4,5]=>[3,2,1,1,1]
[6,8,2,5,1,3,7,4]=>[3,2,1,1,1]
[6,7,4,2,1,5,3,8]=>[4,2,1,1]
[5,7,4,1,3,6,2,8]=>[4,1,1,1,1]
[4,2,7,5,1,8,3,6]=>[3,2,2,1]
[4,1,6,5,3,8,2,7]=>[4,2,1,1]
[1,5,4,6,3,8,2,7]=>[4,1,1,1,1]
[1,8,6,4,7,3,2,5]=>[5,1,1,1]
[4,7,1,8,6,3,5,2]=>[4,2,1,1]
[5,4,8,1,7,3,6,2]=>[4,2,1,1]
[4,3,8,6,2,1,7,5]=>[4,2,2]
[8,3,6,2,4,1,7,5]=>[4,2,1,1]
[7,8,3,2,4,6,5,1]=>[4,2,1,1]
[7,2,8,5,3,1,6,4]=>[4,2,2]
[2,5,4,8,7,3,6,1]=>[4,2,1,1]
[6,4,2,8,7,3,1,5]=>[4,3,1]
[3,6,8,1,7,4,2,5]=>[4,1,1,1,1]
[7,8,6,3,1,4,5,2]=>[4,2,1,1]
[3,8,6,1,7,5,2,4]=>[4,2,1,1]
[2,7,5,4,8,3,1,6]=>[5,1,1,1]
[6,8,7,5,2,1,3,4]=>[5,1,1,1]
[7,6,2,8,5,1,3,4]=>[4,2,1,1]
[1,5,7,6,2,8,4,3]=>[4,2,1,1]
[1,6,5,2,7,8,4,3]=>[4,2,1,1]
[4,7,8,5,6,2,3,1]=>[4,1,1,1,1]
[4,7,8,1,2,5,6,3]=>[3,1,1,1,1,1]
[8,6,4,1,2,5,7,3]=>[4,2,1,1]
[6,1,4,7,2,5,8,3]=>[3,2,1,1,1]
[5,6,3,2,7,4,1,8]=>[4,2,1,1]
[2,6,4,3,7,5,8,1]=>[4,2,1,1]
[7,2,3,6,1,8,4,5]=>[3,2,1,1,1]
[3,4,6,5,7,1,2,8]=>[3,1,1,1,1,1]
[7,6,2,3,5,4,8,1]=>[5,1,1,1]
[8,5,2,4,3,6,1,7]=>[5,1,1,1]
[8,5,7,2,4,1,6,3]=>[4,2,1,1]
[7,4,8,2,1,5,6,3]=>[4,2,1,1]
[2,3,6,7,8,5,1,4]=>[3,1,1,1,1,1]
[8,3,7,1,6,4,2,5]=>[5,1,1,1]
[8,2,1,7,6,5,3,4]=>[5,2,1]
[6,5,1,2,8,3,4,7]=>[3,2,1,1,1]
[5,6,8,1,3,7,2,4]=>[3,1,1,1,1,1]
[1,6,8,5,3,2,4,7]=>[4,1,1,1,1]
[5,8,1,6,7,4,2,3]=>[4,1,1,1,1]
[7,2,8,4,6,1,3,5]=>[3,2,1,1,1]
[6,2,7,4,3,8,1,5]=>[4,2,1,1]
[1,7,8,4,6,2,3,5]=>[3,1,1,1,1,1]
[7,1,8,4,6,2,3,5]=>[3,2,1,1,1]
[8,1,6,5,4,7,2,3]=>[5,1,1,1]
[4,1,6,8,7,3,2,5]=>[4,2,1,1]
[5,1,4,6,7,3,8,2]=>[4,1,1,1,1]
[7,1,3,4,6,2,8,5]=>[3,2,1,1,1]
[8,7,1,4,6,3,2,5]=>[5,1,1,1]
[6,5,2,8,4,7,1,3]=>[4,2,1,1]
[1,4,7,5,8,6,3,2]=>[4,2,1,1]
[6,1,8,3,4,7,2,5]=>[3,2,1,1,1]
[1,8,6,3,5,2,7,4]=>[4,2,1,1]
[4,7,1,6,8,3,5,2]=>[4,1,1,1,1]
[3,6,5,2,8,4,1,7]=>[4,2,1,1]
[8,2,5,6,3,1,7,4]=>[4,2,1,1]
[7,1,8,4,2,5,3,6]=>[3,2,2,1]
[1,4,8,7,5,2,6,3]=>[4,2,1,1]
[1,5,6,4,2,3,7,8]=>[3,1,1,1,1,1]
[5,8,7,4,2,1,3,6]=>[5,1,1,1]
[3,1,5,2,7,8,6,4]=>[3,2,2,1]
[1,8,7,3,2,5,4,6]=>[4,2,1,1]
[1,2,5,4,8,7,3,6]=>[3,2,1,1,1]
[1,2,4,8,6,3,5,7]=>[3,1,1,1,1,1]
[1,5,2,4,7,3,8,6]=>[3,2,1,1,1]
[8,6,3,5,7,4,1,2]=>[5,1,1,1]
[8,5,3,2,1,4,7,6]=>[5,2,1]
[1,2,7,6,8,4,3,5]=>[4,1,1,1,1]
[1,6,3,2,5,7,8,4]=>[3,2,1,1,1]
[1,7,3,4,2,6,8,5]=>[3,2,1,1,1]
[1,6,3,5,8,4,2,7]=>[4,1,1,1,1]
[1,5,6,3,2,8,4,7]=>[3,2,1,1,1]
[1,2,5,8,4,6,3,7]=>[3,1,1,1,1,1]
[1,5,3,2,7,8,4,6]=>[3,2,1,1,1]
[4,1,8,6,2,3,7,5]=>[3,2,2,1]
[7,5,8,6,2,3,4,1]=>[4,2,1,1]
[1,7,6,4,3,8,5,2]=>[5,2,1]
[1,8,5,7,6,3,2,4]=>[5,1,1,1]
[1,4,7,3,6,8,5,2]=>[4,1,1,1,1]
[1,6,3,5,7,8,4,2]=>[4,1,1,1,1]
[1,5,6,3,2,7,8,4]=>[3,2,1,1,1]
[1,2,7,6,8,4,5,3]=>[4,1,1,1,1]
[1,8,4,7,5,3,2,6]=>[5,1,1,1]
[6,8,5,2,1,7,4,3]=>[4,3,1]
[1,2,6,8,4,3,7,5]=>[3,2,1,1,1]
[5,3,7,2,6,4,1,8]=>[4,2,1,1]
[5,3,8,2,6,1,7,4]=>[4,2,1,1]
[7,6,2,5,3,4,1,8]=>[5,1,1,1]
[7,6,2,4,5,3,1,8]=>[5,1,1,1]
[7,6,2,4,3,5,1,8]=>[5,1,1,1]
[7,6,2,3,5,4,1,8]=>[5,1,1,1]
[8,4,2,7,1,6,3,5]=>[4,2,1,1]
[8,7,6,1,5,3,2,4]=>[6,1,1]
[8,7,6,1,4,3,5,2]=>[6,1,1]
[8,7,6,1,3,5,4,2]=>[6,1,1]
[8,7,6,1,5,4,2,3]=>[6,1,1]
[8,6,2,7,1,5,3,4]=>[4,2,1,1]
[5,3,7,2,8,1,6,4]=>[4,2,1,1]
[8,3,5,4,2,1,6,7]=>[5,1,1,1]
[7,8,4,3,1,5,2,6]=>[4,2,1,1]
[8,6,3,7,1,5,2,4]=>[4,2,1,1]
[8,7,6,1,2,5,3,4]=>[5,1,1,1]
[8,7,6,1,2,5,4,3]=>[6,1,1]
[8,7,6,1,4,2,5,3]=>[5,2,1]
[4,7,5,8,6,1,3,2]=>[4,2,1,1]
[6,5,7,3,8,4,1,2]=>[4,2,1,1]
[8,7,5,4,1,2,6,3]=>[5,2,1]
[8,6,7,1,5,3,2,4]=>[5,1,1,1]
[5,7,8,1,3,4,2,6]=>[3,1,1,1,1,1]
[5,7,8,3,4,6,1,2]=>[3,1,1,1,1,1]
[5,7,1,3,4,2,8,6]=>[3,2,1,1,1]
[7,3,5,6,4,8,1,2]=>[4,1,1,1,1]
[1,5,3,7,8,4,6,2]=>[3,2,1,1,1]
[1,5,7,3,8,2,6,4]=>[3,2,1,1,1]
[7,1,5,3,6,2,4,8]=>[4,1,1,1,1]
[1,3,7,5,8,6,2,4]=>[3,2,1,1,1]
[3,7,5,8,4,1,2,6]=>[4,1,1,1,1]
[7,5,6,8,1,3,4,2]=>[4,1,1,1,1]
[5,3,4,7,8,1,2,6]=>[3,1,1,1,1,1]
[5,3,7,6,8,1,2,4]=>[3,2,1,1,1]
[3,1,2,7,5,8,4,6]=>[3,2,1,1,1]
[3,1,2,5,7,8,6,4]=>[3,2,1,1,1]
[7,3,5,1,2,6,4,8]=>[3,2,1,1,1]
[3,7,1,2,8,5,6,4]=>[3,2,1,1,1]
[5,3,1,7,4,6,8,2]=>[3,3,1,1]
[7,4,8,3,5,6,1,2]=>[4,1,1,1,1]
[2,4,7,3,5,6,1,8]=>[3,1,1,1,1,1]
[5,7,6,4,2,3,1,8]=>[5,1,1,1]
[7,4,8,2,5,6,1,3]=>[4,1,1,1,1]
[5,8,2,4,6,1,3,7]=>[3,1,1,1,1,1]
[6,1,4,8,5,2,7,3]=>[3,2,2,1]
[3,4,5,8,1,6,7,2]=>[3,1,1,1,1,1]
[6,8,7,4,2,1,5,3]=>[5,2,1]
[5,6,8,4,7,3,1,2]=>[4,1,1,1,1]
[3,1,6,8,5,2,7,4]=>[3,2,2,1]
[2,3,8,1,5,6,4,7]=>[3,1,1,1,1,1]
[5,4,8,1,2,6,7,3]=>[3,2,1,1,1]
[5,1,8,2,4,6,7,3]=>[3,2,1,1,1]
[4,1,8,2,3,6,7,5]=>[3,2,1,1,1]
[5,2,3,8,1,7,4,6]=>[3,2,1,1,1]
[2,3,5,7,1,6,4,8]=>[3,1,1,1,1,1]
[1,5,3,8,2,4,6,7]=>[3,1,1,1,1,1]
[8,6,2,7,5,1,4,3]=>[5,2,1]
[5,7,6,1,3,2,8,4]=>[4,2,1,1]
[3,5,4,6,1,7,8,2]=>[3,2,1,1,1]
[8,1,5,4,6,3,7,2]=>[5,1,1,1]
[8,4,2,5,6,3,7,1]=>[4,2,1,1]
[5,4,7,2,8,6,1,3]=>[4,2,1,1]
[2,7,1,8,6,5,4,3]=>[5,2,1]
[3,7,6,1,8,5,4,2]=>[5,2,1]
[6,2,8,3,1,4,5,7]=>[3,2,1,1,1]
[2,7,8,3,1,4,5,6]=>[3,1,1,1,1,1]
[1,5,3,2,8,6,7,4]=>[3,3,1,1]
[1,8,5,3,2,6,7,4]=>[4,2,1,1]
[1,5,6,7,3,2,8,4]=>[3,2,1,1,1]
[1,7,5,2,3,4,8,6]=>[3,2,1,1,1]
[1,7,5,2,4,8,6,3]=>[4,2,1,1]
[1,6,7,8,3,2,4,5]=>[3,1,1,1,1,1]
[1,4,8,6,2,3,5,7]=>[3,1,1,1,1,1]
[1,2,8,6,3,4,5,7]=>[3,1,1,1,1,1]
[1,2,8,6,3,5,7,4]=>[4,1,1,1,1]
[1,2,7,8,4,3,5,6]=>[3,1,1,1,1,1]
[1,8,6,7,4,2,3,5]=>[4,1,1,1,1]
[1,6,7,8,4,2,3,5]=>[3,1,1,1,1,1]
[1,6,7,8,3,4,2,5]=>[3,1,1,1,1,1]
[1,7,4,2,3,8,5,6]=>[3,2,1,1,1]
[1,7,8,4,2,3,5,6]=>[3,1,1,1,1,1]
[1,7,3,5,6,2,8,4]=>[3,2,1,1,1]
[1,7,8,3,4,2,5,6]=>[3,1,1,1,1,1]
[1,2,3,7,8,5,4,6]=>[3,1,1,1,1,1]
[1,2,7,4,6,3,8,5]=>[3,2,1,1,1]
[1,7,8,4,5,2,3,6]=>[3,1,1,1,1,1]
[1,7,8,3,4,5,2,6]=>[3,1,1,1,1,1]
[1,2,8,4,5,6,3,7]=>[3,1,1,1,1,1]
[6,8,7,2,3,4,1,5]=>[4,1,1,1,1]
[3,8,7,5,2,6,1,4]=>[5,1,1,1]
[4,8,7,3,2,5,1,6]=>[5,1,1,1]
[5,3,8,1,6,7,4,2]=>[4,2,1,1]
[5,8,2,1,3,7,6,4]=>[4,2,1,1]
[5,1,8,3,6,7,4,2]=>[4,2,1,1]
[3,1,8,4,6,2,7,5]=>[3,2,2,1]
[8,4,1,6,5,2,3,7]=>[4,2,1,1]
[1,8,7,6,4,3,5,2]=>[6,1,1]
[6,1,8,7,5,3,4,2]=>[5,2,1]
[6,8,7,3,2,4,1,5]=>[5,1,1,1]
[2,3,7,5,6,8,4,1]=>[4,1,1,1,1]
[2,8,7,6,4,5,1,3]=>[5,1,1,1]
[4,8,7,6,3,1,5,2]=>[5,2,1]
[3,5,2,4,7,6,8,1]=>[3,2,1,1,1]
[5,3,2,6,4,7,8,1]=>[4,2,1,1]
[5,3,2,6,7,4,8,1]=>[4,2,1,1]
[5,3,2,7,6,4,8,1]=>[4,3,1]
[7,3,5,2,8,4,6,1]=>[4,2,1,1]
[3,5,2,7,4,6,8,1]=>[3,2,1,1,1]
[3,2,5,7,4,6,8,1]=>[3,2,1,1,1]
[3,2,7,5,4,8,6,1]=>[4,2,2]
[3,7,5,2,4,8,6,1]=>[4,2,1,1]
[2,3,7,5,4,8,6,1]=>[4,2,1,1]
[8,3,5,1,6,4,7,2]=>[4,2,1,1]
[8,4,5,6,1,3,7,2]=>[4,1,1,1,1]
[3,4,7,6,8,2,5,1]=>[4,1,1,1,1]
[5,2,8,4,1,3,6,7]=>[3,2,1,1,1]
[3,8,5,2,1,4,6,7]=>[4,1,1,1,1]
[7,6,4,1,8,2,5,3]=>[4,3,1]
[7,5,4,2,1,6,3,8]=>[5,2,1]
[8,1,6,7,3,4,2,5]=>[4,1,1,1,1]
[8,2,1,6,7,4,3,5]=>[4,2,1,1]
[5,2,8,6,3,7,1,4]=>[4,2,1,1]
[7,6,8,1,2,5,4,3]=>[5,1,1,1]
[2,1,3,4,8,5,7,6]=>[3,2,1,1,1]
[5,7,1,2,6,8,3,4]=>[3,1,1,1,1,1]
[1,5,2,3,6,8,7,4]=>[3,2,1,1,1]
[3,5,7,4,1,8,2,6]=>[3,2,1,1,1]
[8,6,4,7,5,1,2,3]=>[4,2,1,1]
[8,6,4,1,2,5,3,7]=>[4,2,1,1]
[2,8,4,3,1,6,5,7]=>[4,2,1,1]
[3,8,4,6,1,5,2,7]=>[4,1,1,1,1]
[8,3,5,6,1,4,7,2]=>[4,1,1,1,1]
[6,8,7,3,5,4,2,1]=>[6,1,1]
[3,1,2,8,5,7,4,6]=>[3,2,1,1,1]
[7,3,1,2,5,8,4,6]=>[3,2,1,1,1]
[8,3,5,7,2,1,4,6]=>[4,1,1,1,1]
[2,1,3,8,5,7,4,6]=>[3,2,1,1,1]
[7,3,1,2,8,4,5,6]=>[3,2,1,1,1]
[2,1,4,7,6,3,5,8]=>[3,2,1,1,1]
[7,2,4,5,3,8,1,6]=>[4,1,1,1,1]
[8,4,2,5,6,7,3,1]=>[4,2,1,1]
[5,4,1,6,3,7,8,2]=>[4,2,1,1]
[4,5,1,3,6,7,8,2]=>[3,1,1,1,1,1]
[5,1,7,6,3,4,8,2]=>[4,2,1,1]
[6,1,7,5,4,8,2,3]=>[4,2,1,1]
[3,7,2,1,6,8,4,5]=>[3,2,1,1,1]
[1,5,8,2,4,7,6,3]=>[4,1,1,1,1]
[5,8,1,6,4,7,3,2]=>[5,1,1,1]
[3,8,6,5,7,2,4,1]=>[5,1,1,1]
[6,8,1,4,7,3,5,2]=>[4,1,1,1,1]
[1,6,8,2,7,4,5,3]=>[4,1,1,1,1]
[5,7,2,1,8,4,3,6]=>[3,3,1,1]
[5,7,1,6,8,3,2,4]=>[4,1,1,1,1]
[5,6,2,1,8,3,4,7]=>[3,2,1,1,1]
[6,4,1,7,3,8,2,5]=>[4,2,1,1]
[8,2,5,6,7,1,4,3]=>[4,1,1,1,1]
[7,2,4,6,8,3,1,5]=>[4,1,1,1,1]
[6,2,4,7,8,1,3,5]=>[3,1,1,1,1,1]
[6,1,4,3,2,8,5,7]=>[4,2,1,1]
[2,7,4,8,6,1,5,3]=>[4,2,1,1]
[2,4,8,6,5,7,3,1]=>[5,1,1,1]
[3,7,8,6,4,2,5,1]=>[5,1,1,1]
[6,2,8,4,7,5,1,3]=>[4,2,1,1]
[4,5,7,3,6,8,1,2]=>[3,1,1,1,1,1]
[3,4,7,8,6,5,1,2]=>[4,1,1,1,1]
[1,4,7,2,6,8,5,3]=>[4,1,1,1,1]
[2,3,7,6,5,1,4,8]=>[4,1,1,1,1]
[3,2,7,6,4,1,5,8]=>[4,2,1,1]
[6,2,3,5,7,1,4,8]=>[3,1,1,1,1,1]
[7,8,1,2,5,6,4,3]=>[4,1,1,1,1]
[7,1,3,6,8,5,2,4]=>[4,1,1,1,1]
[4,2,8,5,1,6,3,7]=>[3,2,2,1]
[6,5,8,1,4,2,3,7]=>[4,1,1,1,1]
[3,8,2,4,5,1,6,7]=>[3,1,1,1,1,1]
[3,6,2,4,1,5,7,8]=>[3,1,1,1,1,1]
[2,3,8,4,1,6,5,7]=>[3,2,1,1,1]
[4,5,7,3,1,6,2,8]=>[3,2,1,1,1]
[2,3,1,4,8,5,7,6]=>[3,2,1,1,1]
[4,2,6,1,5,8,7,3]=>[3,3,1,1]
[7,5,1,8,4,3,6,2]=>[5,2,1]
[3,1,8,5,7,6,4,2]=>[5,2,1]
[5,1,8,7,4,6,3,2]=>[5,2,1]
[2,4,8,7,5,1,3,6]=>[4,1,1,1,1]
[3,5,7,6,1,8,4,2]=>[4,2,1,1]
[3,5,7,6,2,8,4,1]=>[4,2,1,1]
[1,5,3,2,8,7,6,4]=>[4,3,1]
[6,1,4,3,8,7,5,2]=>[4,3,1]
[6,3,1,8,7,4,2,5]=>[4,3,1]
[5,3,6,2,8,7,4,1]=>[4,3,1]
[6,3,5,2,1,8,7,4]=>[4,3,1]
[2,8,4,1,3,7,6,5]=>[4,2,1,1]
[3,8,1,4,7,6,5,2]=>[5,1,1,1]
[6,2,3,8,7,5,4,1]=>[5,2,1]
[4,1,3,5,8,7,6,2]=>[4,2,1,1]
[3,4,7,5,8,1,2,6]=>[3,1,1,1,1,1]
[2,7,8,3,4,1,5,6]=>[3,1,1,1,1,1]
[2,8,6,7,5,4,3,1]=>[6,1,1]
[7,2,6,8,1,4,3,5]=>[4,1,1,1,1]
[5,3,6,2,8,4,7,1]=>[4,2,1,1]
[8,1,6,3,7,4,5,2]=>[4,2,1,1]
[2,4,3,7,1,8,6,5]=>[3,3,1,1]
[2,6,5,7,3,8,4,1]=>[4,2,1,1]
[6,8,2,7,4,1,5,3]=>[4,2,1,1]
[6,1,7,8,5,3,2,4]=>[4,2,1,1]
[2,6,5,4,7,1,8,3]=>[4,2,1,1]
[5,8,3,4,6,1,7,2]=>[3,2,1,1,1]
[6,1,7,4,2,5,8,3]=>[3,2,2,1]
[6,8,7,1,5,4,2,3]=>[5,1,1,1]
[4,8,3,1,5,7,6,2]=>[4,2,1,1]
[5,3,8,2,7,1,6,4]=>[4,2,1,1]
[8,3,4,5,2,7,1,6]=>[4,1,1,1,1]
[7,1,5,2,6,3,4,8]=>[3,2,1,1,1]
[3,7,1,5,2,6,8,4]=>[3,2,1,1,1]
[6,7,1,8,3,4,5,2]=>[3,2,1,1,1]
[3,7,1,6,8,4,5,2]=>[4,1,1,1,1]
[3,8,5,2,6,7,1,4]=>[4,1,1,1,1]
[3,6,5,2,7,1,4,8]=>[4,1,1,1,1]
[6,8,3,4,7,1,5,2]=>[4,1,1,1,1]
[3,7,1,6,5,2,8,4]=>[4,2,1,1]
[8,3,5,2,7,1,6,4]=>[4,2,1,1]
[3,8,6,4,7,1,5,2]=>[4,2,1,1]
[3,7,1,4,8,6,5,2]=>[4,2,1,1]
[3,7,1,4,5,2,8,6]=>[3,2,1,1,1]
[2,3,7,6,5,8,1,4]=>[4,1,1,1,1]
[3,5,7,6,8,2,1,4]=>[4,1,1,1,1]
[4,2,5,3,7,6,1,8]=>[3,2,2,1]
[6,2,4,3,7,5,1,8]=>[4,2,1,1]
[1,3,6,4,7,5,2,8]=>[3,2,1,1,1]
[8,2,5,3,6,4,1,7]=>[4,2,1,1]
[7,2,5,3,6,4,1,8]=>[4,2,1,1]
[6,2,5,3,7,4,1,8]=>[4,2,1,1]
[4,2,6,3,7,5,1,8]=>[3,2,2,1]
[5,2,7,3,6,4,1,8]=>[4,2,1,1]
[7,3,6,2,5,4,1,8]=>[5,1,1,1]
[6,3,8,2,5,4,1,7]=>[4,2,1,1]
[7,3,1,4,6,5,2,8]=>[4,2,1,1]
[8,3,7,2,5,4,1,6]=>[5,1,1,1]
[5,2,8,3,6,4,1,7]=>[4,2,1,1]
[3,2,8,4,6,5,1,7]=>[4,2,1,1]
[1,4,7,3,6,5,2,8]=>[4,1,1,1,1]
[8,2,5,4,1,6,3,7]=>[4,2,1,1]
[8,2,6,4,1,5,3,7]=>[4,2,1,1]
[1,4,8,3,7,5,2,6]=>[4,1,1,1,1]
[6,2,1,4,8,5,3,7]=>[3,3,1,1]
[5,2,1,4,8,6,3,7]=>[3,3,1,1]
[3,2,1,5,8,6,4,7]=>[3,3,1,1]
[4,2,8,3,7,5,1,6]=>[4,2,1,1]
[5,2,8,3,7,4,1,6]=>[4,2,1,1]
[8,3,7,2,6,4,1,5]=>[5,1,1,1]
[7,3,1,4,8,5,2,6]=>[3,3,1,1]
[1,3,7,4,8,5,2,6]=>[3,2,1,1,1]
[8,2,6,3,7,4,1,5]=>[4,2,1,1]
[7,2,6,3,8,4,1,5]=>[4,2,1,1]
[5,2,7,3,8,4,1,6]=>[3,2,2,1]
[3,2,7,4,8,5,1,6]=>[3,2,2,1]
[5,2,6,3,8,4,1,7]=>[3,2,2,1]
[6,2,5,3,8,4,1,7]=>[4,2,1,1]
[7,2,5,3,8,4,1,6]=>[4,2,1,1]
[8,2,5,3,7,4,1,6]=>[4,2,1,1]
[1,3,6,4,8,5,2,7]=>[3,2,1,1,1]
[1,3,5,4,8,6,2,7]=>[3,2,1,1,1]
[8,2,4,3,7,5,1,6]=>[4,2,1,1]
[7,2,4,3,8,5,1,6]=>[4,2,1,1]
[6,2,4,3,8,5,1,7]=>[4,2,1,1]
[5,2,4,3,8,6,1,7]=>[4,2,1,1]
[4,2,5,3,8,6,1,7]=>[3,2,2,1]
[4,2,5,3,1,7,6,8]=>[3,2,2,1]
[6,2,4,3,1,7,5,8]=>[4,2,1,1]
[7,2,4,3,1,6,5,8]=>[4,2,1,1]
[8,5,1,3,6,4,2,7]=>[4,2,1,1]
[8,4,1,3,6,5,2,7]=>[4,2,1,1]
[1,5,2,4,7,6,3,8]=>[3,2,1,1,1]
[7,2,5,3,1,6,4,8]=>[4,2,1,1]
[6,2,5,3,1,7,4,8]=>[4,2,1,1]
[4,2,6,3,1,7,5,8]=>[3,2,2,1]
[3,2,6,4,1,7,5,8]=>[3,2,2,1]
[3,2,7,4,1,6,5,8]=>[3,2,2,1]
[4,2,7,3,1,6,5,8]=>[3,2,2,1]
[5,2,7,3,1,6,4,8]=>[3,2,2,1]
[6,2,7,3,1,5,4,8]=>[3,2,2,1]
[7,2,6,3,1,5,4,8]=>[4,2,1,1]
[1,5,2,4,8,6,3,7]=>[3,2,1,1,1]
[8,4,1,3,7,5,2,6]=>[4,2,1,1]
[6,2,1,5,3,7,4,8]=>[3,2,2,1]
[3,2,1,6,4,7,5,8]=>[3,2,2,1]
[3,2,8,5,1,6,4,7]=>[3,2,2,1]
[6,2,8,4,1,5,3,7]=>[3,2,2,1]
[8,3,7,4,1,5,2,6]=>[4,2,1,1]
[7,1,3,2,5,6,4,8]=>[3,2,1,1,1]
[6,3,5,2,4,8,1,7]=>[4,1,1,1,1]
[1,5,2,8,7,4,3,6]=>[4,2,1,1]
[5,7,2,8,1,4,3,6]=>[3,2,1,1,1]
[4,8,3,1,5,2,7,6]=>[3,2,2,1]
[7,1,5,3,2,6,8,4]=>[4,2,1,1]
[3,1,5,7,8,6,2,4]=>[3,2,1,1,1]
[8,6,2,3,1,5,7,4]=>[4,2,1,1]
[8,6,7,3,5,2,1,4]=>[5,1,1,1]
[1,4,2,7,3,6,8,5]=>[3,2,1,1,1]
[3,2,1,7,8,5,4,6]=>[3,3,1,1]
[7,3,4,2,1,5,8,6]=>[4,2,1,1]
[2,1,6,4,7,8,5,3]=>[3,2,2,1]
[1,6,3,2,4,7,8,5]=>[3,2,1,1,1]
[1,2,3,7,5,8,4,6]=>[3,1,1,1,1,1]
[1,8,5,3,2,4,7,6]=>[4,2,1,1]
[4,7,8,1,5,6,2,3]=>[3,1,1,1,1,1]
[3,6,7,1,8,4,2,5]=>[3,2,1,1,1]
[1,3,7,6,2,4,5,8]=>[3,1,1,1,1,1]
[2,7,3,8,4,5,6,1]=>[3,2,1,1,1]
[7,1,4,3,8,5,6,2]=>[4,2,1,1]
[5,6,2,7,8,3,4,1]=>[3,2,1,1,1]
[7,4,1,8,5,6,2,3]=>[3,3,1,1]
[7,2,5,8,1,6,3,4]=>[3,2,1,1,1]
[6,4,8,1,5,7,2,3]=>[3,2,1,1,1]
[6,2,1,4,7,5,8,3]=>[3,3,1,1]
[2,6,1,5,4,7,3,8]=>[4,1,1,1,1]
[2,3,6,8,4,1,7,5]=>[3,2,1,1,1]
[1,7,2,8,6,3,5,4]=>[4,2,1,1]
[8,4,2,3,7,1,6,5]=>[4,2,1,1]
[5,2,4,8,7,3,1,6]=>[4,2,1,1]
[3,2,4,6,7,8,1,5]=>[3,1,1,1,1,1]
[5,2,6,8,1,3,7,4]=>[3,2,1,1,1]
[4,8,1,6,3,7,5,2]=>[4,2,1,1]
[7,1,5,2,6,4,3,8]=>[4,2,1,1]
[8,3,5,2,6,1,4,7]=>[4,1,1,1,1]
[1,8,5,6,2,7,4,3]=>[4,2,1,1]
[4,2,7,6,1,8,5,3]=>[4,2,2]
[7,2,4,8,6,3,5,1]=>[4,2,1,1]
[7,3,2,1,8,5,4,6]=>[4,3,1]
[7,3,2,1,6,4,8,5]=>[4,2,2]
[3,6,5,2,1,8,4,7]=>[4,2,1,1]
[6,7,2,4,3,5,8,1]=>[4,1,1,1,1]
[4,5,3,7,2,1,6,8]=>[4,1,1,1,1]
[4,3,8,2,1,5,7,6]=>[4,2,1,1]
[4,3,2,8,1,6,7,5]=>[4,2,1,1]
[4,5,8,3,2,7,1,6]=>[4,1,1,1,1]
[6,8,5,2,7,3,4,1]=>[4,2,1,1]
[5,4,7,8,2,3,6,1]=>[4,1,1,1,1]
[4,3,8,2,1,6,7,5]=>[4,2,1,1]
[3,5,7,4,6,2,8,1]=>[4,1,1,1,1]
[5,3,7,6,2,4,8,1]=>[4,2,1,1]
[4,6,7,2,5,3,8,1]=>[4,1,1,1,1]
[6,4,7,8,3,1,5,2]=>[4,2,1,1]
[8,4,7,3,1,5,6,2]=>[4,2,1,1]
[5,8,1,7,6,4,2,3]=>[5,1,1,1]
[5,6,7,1,8,3,4,2]=>[3,2,1,1,1]
[7,1,8,6,2,5,4,3]=>[5,2,1]
[1,5,8,2,6,4,7,3]=>[4,1,1,1,1]
[1,5,7,4,6,8,3,2]=>[4,1,1,1,1]
[1,4,7,5,6,8,3,2]=>[4,1,1,1,1]
[5,6,7,4,8,1,3,2]=>[4,1,1,1,1]
[8,1,2,6,4,5,7,3]=>[4,1,1,1,1]
[4,8,1,7,2,5,6,3]=>[4,1,1,1,1]
[2,6,7,1,5,4,8,3]=>[4,1,1,1,1]
[3,2,7,6,5,8,1,4]=>[4,2,1,1]
[1,7,3,4,5,8,2,6]=>[3,1,1,1,1,1]
[7,1,8,4,5,6,3,2]=>[4,2,1,1]
[1,2,7,4,5,8,3,6]=>[3,1,1,1,1,1]
[6,7,3,2,5,8,1,4]=>[4,1,1,1,1]
[6,1,8,4,5,3,7,2]=>[4,2,1,1]
[4,6,2,5,1,8,7,3]=>[3,3,1,1]
[5,1,4,6,2,8,7,3]=>[3,3,1,1]
[7,3,5,2,1,6,8,4]=>[4,2,1,1]
[8,5,1,2,6,3,7,4]=>[3,2,2,1]
[1,5,8,7,4,6,3,2]=>[5,1,1,1]
[5,7,2,1,3,6,8,4]=>[3,2,1,1,1]
[3,7,2,6,8,1,5,4]=>[4,1,1,1,1]
[7,4,8,6,5,1,3,2]=>[5,2,1]
[2,7,6,8,5,1,4,3]=>[5,1,1,1]
[1,6,4,5,7,3,8,2]=>[4,1,1,1,1]
[1,5,4,7,8,6,2,3]=>[3,2,1,1,1]
[7,3,1,6,8,2,5,4]=>[4,2,1,1]
[7,1,6,8,5,2,4,3]=>[5,1,1,1]
[3,5,8,7,6,4,1,2]=>[5,1,1,1]
[1,5,7,8,6,2,4,3]=>[4,1,1,1,1]
[3,6,2,1,4,7,8,5]=>[3,2,1,1,1]
[6,8,2,7,5,4,3,1]=>[6,1,1]
[5,8,1,7,6,4,3,2]=>[6,1,1]
[8,6,3,2,1,5,4,7]=>[5,2,1]
[8,5,3,2,4,1,7,6]=>[5,2,1]
[7,5,2,4,3,6,8,1]=>[5,1,1,1]
[8,5,1,4,6,3,2,7]=>[5,1,1,1]
[8,5,1,6,3,4,2,7]=>[4,2,1,1]
[8,4,3,6,1,5,2,7]=>[4,2,1,1]
[8,4,3,5,2,1,7,6]=>[5,2,1]
[6,4,3,2,8,7,1,5]=>[5,2,1]
[8,5,1,4,3,7,2,6]=>[5,1,1,1]
[8,5,4,2,1,3,7,6]=>[5,2,1]
[4,7,3,6,1,8,5,2]=>[4,2,1,1]
[7,6,2,4,1,5,8,3]=>[4,2,1,1]
[8,1,6,3,7,4,2,5]=>[4,2,1,1]
[5,3,8,2,6,7,1,4]=>[4,1,1,1,1]
[8,2,5,1,7,6,3,4]=>[4,2,1,1]
[8,2,4,6,3,7,1,5]=>[4,1,1,1,1]
[7,2,6,4,3,5,8,1]=>[5,1,1,1]
[7,3,6,2,4,5,8,1]=>[4,1,1,1,1]
[8,3,7,2,1,4,6,5]=>[4,2,1,1]
[7,6,4,1,3,2,8,5]=>[5,2,1]
[7,3,8,2,1,5,6,4]=>[4,2,1,1]
[6,2,5,7,4,3,8,1]=>[5,1,1,1]
[6,2,5,4,8,7,1,3]=>[4,2,1,1]
[7,2,4,8,5,1,6,3]=>[3,2,2,1]
[4,2,7,6,8,5,1,3]=>[4,2,1,1]
[7,1,6,2,8,5,4,3]=>[5,2,1]
[7,1,6,3,8,5,2,4]=>[4,2,1,1]
[7,2,6,8,1,3,5,4]=>[4,1,1,1,1]
[7,2,8,5,1,3,6,4]=>[3,2,2,1]
[7,1,8,5,3,2,6,4]=>[4,2,2]
[7,1,8,2,5,6,4,3]=>[4,2,1,1]
[6,1,5,8,7,2,4,3]=>[4,2,1,1]
[6,1,5,7,4,8,3,2]=>[5,1,1,1]
[6,1,5,7,8,3,4,2]=>[4,1,1,1,1]
[4,6,7,3,1,8,5,2]=>[3,3,1,1]
[4,2,6,3,1,8,7,5]=>[3,3,2]
[6,1,4,2,5,8,7,3]=>[3,3,1,1]
[1,5,3,8,4,6,2,7]=>[3,2,1,1,1]
[7,2,3,5,8,4,1,6]=>[4,1,1,1,1]
[7,6,4,2,8,5,1,3]=>[5,2,1]
[1,7,6,4,8,5,3,2]=>[5,2,1]
[8,7,4,2,1,5,6,3]=>[5,2,1]
[8,2,3,5,1,4,6,7]=>[3,1,1,1,1,1]
[8,7,4,1,3,2,6,5]=>[5,2,1]
[7,1,4,8,3,6,2,5]=>[4,1,1,1,1]
[4,1,8,5,7,6,2,3]=>[4,2,1,1]
[3,7,5,8,4,2,1,6]=>[5,1,1,1]
[6,1,5,8,3,4,2,7]=>[4,1,1,1,1]
[6,7,5,1,3,2,4,8]=>[4,1,1,1,1]
[5,2,6,1,7,3,4,8]=>[3,2,1,1,1]
[4,2,6,8,3,7,1,5]=>[3,2,1,1,1]
[6,8,5,1,4,2,3,7]=>[4,1,1,1,1]
[7,8,4,5,1,3,6,2]=>[4,1,1,1,1]
[1,7,8,5,3,4,6,2]=>[4,1,1,1,1]
[1,5,8,3,6,4,7,2]=>[4,1,1,1,1]
[6,3,8,1,4,2,7,5]=>[3,2,2,1]
[4,8,1,5,6,3,7,2]=>[4,1,1,1,1]
[1,8,2,6,5,3,7,4]=>[4,2,1,1]
[3,8,1,7,2,6,5,4]=>[5,1,1,1]
[7,3,8,1,2,6,5,4]=>[4,2,1,1]
[8,1,4,2,3,5,7,6]=>[3,2,1,1,1]
[8,1,2,4,6,5,7,3]=>[4,1,1,1,1]
[5,1,8,3,7,4,6,2]=>[4,2,1,1]
[8,3,7,1,5,4,6,2]=>[5,1,1,1]
[8,4,7,1,5,3,6,2]=>[5,1,1,1]
[7,2,5,3,4,6,1,8]=>[4,1,1,1,1]
[7,6,4,2,5,3,1,8]=>[5,2,1]
[5,8,4,3,6,2,7,1]=>[5,1,1,1]
[1,7,2,6,3,4,8,5]=>[3,2,1,1,1]
[7,5,1,6,3,2,4,8]=>[4,2,1,1]
[7,1,2,6,3,4,5,8]=>[3,1,1,1,1,1]
[7,2,5,1,6,3,4,8]=>[3,2,1,1,1]
[7,3,1,4,6,2,5,8]=>[3,2,1,1,1]
[7,1,6,5,4,2,3,8]=>[5,1,1,1]
[5,8,4,3,1,7,2,6]=>[4,2,1,1]
[3,6,8,5,2,4,7,1]=>[4,1,1,1,1]
[5,7,8,4,3,2,6,1]=>[5,1,1,1]
[1,3,8,4,7,2,6,5]=>[4,1,1,1,1]
[3,2,1,4,5,8,6,7]=>[3,2,1,1,1]
[6,7,1,3,2,8,5,4]=>[3,3,1,1]
[1,5,3,2,6,8,4,7]=>[3,2,1,1,1]
[3,7,6,5,8,2,4,1]=>[5,1,1,1]
[5,7,4,2,8,6,1,3]=>[4,2,1,1]
[5,4,3,7,8,2,6,1]=>[5,1,1,1]
[3,8,5,7,6,2,4,1]=>[5,1,1,1]
[1,3,6,8,7,2,5,4]=>[4,1,1,1,1]
[5,8,7,1,4,2,3,6]=>[4,1,1,1,1]
[2,6,3,7,1,4,5,8]=>[3,1,1,1,1,1]
[7,6,8,4,3,1,5,2]=>[5,2,1]
[1,7,6,5,3,2,4,8]=>[5,1,1,1]
[2,7,6,5,4,1,3,8]=>[5,1,1,1]
[6,2,3,5,8,4,1,7]=>[4,1,1,1,1]
[4,7,6,1,5,8,3,2]=>[5,1,1,1]
[6,8,7,1,5,4,3,2]=>[6,1,1]
[7,2,6,1,5,8,3,4]=>[4,1,1,1,1]
[4,7,3,6,8,2,1,5]=>[4,1,1,1,1]
[5,4,7,3,8,2,1,6]=>[5,1,1,1]
[8,7,2,4,6,3,5,1]=>[5,1,1,1]
[1,7,2,8,5,4,3,6]=>[4,2,1,1]
[5,4,8,3,6,2,1,7]=>[5,1,1,1]
[6,8,2,5,7,1,4,3]=>[4,1,1,1,1]
[3,8,6,2,7,5,1,4]=>[4,2,1,1]
[5,8,4,2,7,3,6,1]=>[4,2,1,1]
[8,2,7,3,4,5,1,6]=>[4,1,1,1,1]
[8,1,5,2,4,6,3,7]=>[4,1,1,1,1]
[8,6,1,3,4,5,7,2]=>[4,1,1,1,1]
[8,5,1,2,4,6,7,3]=>[4,1,1,1,1]
[2,6,8,7,3,4,5,1]=>[4,1,1,1,1]
[1,7,8,5,6,4,2,3]=>[4,1,1,1,1]
[8,3,1,2,4,6,7,5]=>[3,2,1,1,1]
[3,1,7,5,8,2,4,6]=>[3,2,1,1,1]
[8,1,3,2,4,6,5,7]=>[3,2,1,1,1]
[8,1,5,6,4,2,3,7]=>[4,1,1,1,1]
[8,1,6,5,4,3,2,7]=>[6,1,1]
[2,6,8,1,5,4,3,7]=>[4,1,1,1,1]
[5,2,1,7,6,3,8,4]=>[3,3,2]
[3,5,8,2,1,4,7,6]=>[3,2,1,1,1]
[4,2,8,5,3,7,6,1]=>[4,2,2]
[4,2,7,5,3,8,6,1]=>[4,2,2]
[6,4,5,1,8,3,2,7]=>[4,2,1,1]
[5,4,7,8,3,1,2,6]=>[4,1,1,1,1]
[4,5,8,1,3,7,2,6]=>[3,1,1,1,1,1]
[1,5,3,6,8,7,2,4]=>[3,2,1,1,1]
[7,6,2,8,1,4,3,5]=>[4,2,1,1]
[4,7,2,6,8,3,5,1]=>[4,1,1,1,1]
[6,3,2,8,7,4,5,1]=>[4,3,1]
[7,4,3,8,5,6,2,1]=>[5,2,1]
[3,1,5,8,7,6,2,4]=>[4,2,1,1]
[8,2,1,6,5,7,3,4]=>[4,2,1,1]
[3,1,8,6,5,7,2,4]=>[4,2,1,1]
[1,2,7,6,4,5,8,3]=>[4,1,1,1,1]
[7,2,6,5,1,8,3,4]=>[4,2,1,1]
[4,2,8,5,6,3,1,7]=>[4,2,1,1]
[4,7,3,2,5,1,6,8]=>[4,1,1,1,1]
[4,2,5,3,8,7,1,6]=>[3,2,2,1]
[7,2,5,3,8,4,6,1]=>[4,2,1,1]
[8,7,3,2,5,4,6,1]=>[5,2,1]
[7,5,6,1,8,3,2,4]=>[4,2,1,1]
[4,5,6,2,7,3,1,8]=>[3,2,1,1,1]
[5,3,4,7,1,6,2,8]=>[3,2,1,1,1]
[3,5,1,4,6,8,2,7]=>[3,1,1,1,1,1]
[8,5,7,4,2,1,3,6]=>[5,1,1,1]
[2,3,7,4,1,8,6,5]=>[3,3,1,1]
[2,4,5,1,8,6,3,7]=>[3,2,1,1,1]
[2,4,1,6,7,5,3,8]=>[3,2,1,1,1]
[6,3,7,1,5,2,4,8]=>[3,2,1,1,1]
[4,1,3,7,8,2,6,5]=>[3,2,1,1,1]
[7,1,4,8,6,5,2,3]=>[4,2,1,1]
[8,3,4,2,1,7,5,6]=>[4,2,1,1]
[1,4,5,3,8,6,7,2]=>[3,2,1,1,1]
[4,6,2,7,5,8,1,3]=>[3,2,1,1,1]
[7,3,2,5,1,8,4,6]=>[4,2,1,1]
[7,8,1,4,2,3,5,6]=>[3,1,1,1,1,1]
[6,5,2,4,8,7,1,3]=>[4,2,1,1]
[8,5,2,4,1,3,7,6]=>[4,2,1,1]
[5,1,2,4,3,6,8,7]=>[3,2,1,1,1]
[5,2,1,4,3,7,6,8]=>[3,2,2,1]
[8,6,2,7,5,3,1,4]=>[5,2,1]
[6,2,1,5,8,3,4,7]=>[3,2,1,1,1]
[2,3,8,7,1,5,4,6]=>[4,1,1,1,1]
[4,3,8,1,5,2,6,7]=>[3,2,1,1,1]
[4,1,3,6,7,2,8,5]=>[3,2,1,1,1]
[7,1,4,5,8,2,6,3]=>[3,2,1,1,1]
[6,1,3,2,4,5,8,7]=>[3,2,1,1,1]
[7,4,8,6,5,1,2,3]=>[4,2,1,1]
[3,7,8,6,5,1,2,4]=>[4,1,1,1,1]
[8,4,5,7,2,6,3,1]=>[5,1,1,1]
[4,5,8,2,7,3,1,6]=>[4,1,1,1,1]
[6,5,8,2,7,3,1,4]=>[4,2,1,1]
[6,4,8,2,7,3,1,5]=>[4,2,1,1]
[7,8,1,3,6,4,2,5]=>[4,1,1,1,1]
[4,3,8,2,7,5,1,6]=>[4,2,1,1]
[4,5,7,8,3,2,1,6]=>[4,1,1,1,1]
[5,7,3,4,2,6,8,1]=>[4,1,1,1,1]
[5,7,4,2,3,6,8,1]=>[4,1,1,1,1]
[5,4,7,3,2,8,1,6]=>[5,1,1,1]
[6,8,3,2,4,5,1,7]=>[4,1,1,1,1]
[5,8,3,4,6,1,2,7]=>[3,1,1,1,1,1]
[6,4,3,8,5,1,2,7]=>[4,2,1,1]
[6,4,8,2,3,5,1,7]=>[4,1,1,1,1]
[5,4,6,8,2,3,1,7]=>[4,1,1,1,1]
[5,6,8,4,1,2,3,7]=>[3,1,1,1,1,1]
[6,4,8,5,1,2,3,7]=>[3,2,1,1,1]
[7,4,8,3,1,2,5,6]=>[4,1,1,1,1]
[5,7,8,2,3,1,4,6]=>[3,1,1,1,1,1]
[5,4,7,8,2,1,3,6]=>[4,1,1,1,1]
[5,8,6,3,1,2,4,7]=>[4,1,1,1,1]
[6,8,5,2,1,3,4,7]=>[4,1,1,1,1]
[5,6,1,3,2,4,8,7]=>[3,2,1,1,1]
[8,1,5,4,6,2,7,3]=>[4,2,1,1]
[4,3,8,1,2,5,7,6]=>[3,2,1,1,1]
[5,3,7,2,1,8,6,4]=>[4,3,1]
[7,4,3,2,5,1,8,6]=>[5,2,1]
[5,4,8,3,7,2,1,6]=>[5,1,1,1]
[3,6,8,5,2,1,7,4]=>[4,2,1,1]
[6,1,5,4,7,2,8,3]=>[4,2,1,1]
[5,4,8,3,2,7,1,6]=>[5,1,1,1]
[5,4,3,7,8,2,1,6]=>[5,1,1,1]
[1,4,8,6,3,2,7,5]=>[4,2,1,1]
[4,1,8,6,2,5,7,3]=>[4,2,1,1]
[6,7,2,5,3,8,4,1]=>[4,2,1,1]
[6,3,4,8,1,2,7,5]=>[3,2,1,1,1]
[6,2,8,1,7,4,5,3]=>[4,2,1,1]
[2,6,3,1,5,8,7,4]=>[3,3,1,1]
[7,1,3,2,6,5,8,4]=>[4,2,1,1]
[1,3,5,8,4,7,2,6]=>[3,1,1,1,1,1]
[2,3,8,7,5,1,6,4]=>[4,2,1,1]
[4,1,3,5,6,2,8,7]=>[3,2,1,1,1]
[6,4,8,7,3,5,2,1]=>[5,2,1]
[8,2,3,5,6,1,4,7]=>[3,1,1,1,1,1]
[3,8,2,7,6,4,1,5]=>[5,1,1,1]
[4,3,8,6,2,7,1,5]=>[4,2,1,1]
[8,3,4,5,1,6,7,2]=>[3,2,1,1,1]
[7,8,1,3,5,4,6,2]=>[4,1,1,1,1]
[7,8,1,3,5,2,4,6]=>[3,1,1,1,1,1]
[3,5,7,6,4,8,1,2]=>[4,1,1,1,1]
[1,3,7,8,5,4,6,2]=>[4,1,1,1,1]
[1,3,2,7,8,5,4,6]=>[3,2,1,1,1]
[1,5,7,6,8,3,4,2]=>[4,1,1,1,1]
[3,5,7,4,6,8,1,2]=>[3,1,1,1,1,1]
[6,5,8,4,3,7,1,2]=>[5,1,1,1]
[6,7,3,1,5,2,4,8]=>[3,2,1,1,1]
[2,1,7,4,3,8,5,6]=>[3,2,2,1]
[7,2,3,8,5,4,1,6]=>[4,2,1,1]
[4,1,5,7,6,3,8,2]=>[4,2,1,1]
[1,4,8,2,3,6,5,7]=>[3,1,1,1,1,1]
[1,4,6,7,3,5,2,8]=>[3,1,1,1,1,1]
[1,4,8,2,6,7,5,3]=>[4,1,1,1,1]
[1,7,3,2,4,5,6,8]=>[3,1,1,1,1,1]
[1,7,3,2,4,5,8,6]=>[3,2,1,1,1]
[1,6,4,3,2,5,7,8]=>[4,1,1,1,1]
[4,2,6,5,3,1,7,8]=>[4,2,1,1]
[5,2,1,6,8,7,4,3]=>[4,3,1]
[1,3,5,8,6,2,7,4]=>[3,2,1,1,1]
[2,3,8,4,1,7,6,5]=>[4,2,1,1]
[3,7,8,5,4,2,6,1]=>[5,1,1,1]
[1,3,8,5,7,4,2,6]=>[4,1,1,1,1]
[1,2,3,7,5,4,6,8]=>[3,1,1,1,1,1]
[1,4,2,8,6,3,5,7]=>[3,2,1,1,1]
[2,8,6,3,5,7,4,1]=>[5,1,1,1]
[6,1,8,2,5,3,4,7]=>[3,2,1,1,1]
[3,8,6,4,2,7,1,5]=>[5,1,1,1]
[1,5,4,2,3,6,8,7]=>[3,2,1,1,1]
[6,1,5,2,3,4,8,7]=>[3,2,1,1,1]
[6,5,2,1,7,3,4,8]=>[4,2,1,1]
[3,1,2,4,8,6,7,5]=>[3,2,1,1,1]
[3,1,2,5,8,7,4,6]=>[3,2,1,1,1]
[6,5,2,1,8,4,7,3]=>[4,3,1]
[3,7,5,2,8,1,4,6]=>[4,1,1,1,1]
[5,1,4,7,3,2,8,6]=>[4,2,1,1]
[4,1,5,8,6,2,3,7]=>[3,2,1,1,1]
[5,4,8,6,3,7,1,2]=>[4,2,1,1]
[6,5,2,3,1,8,7,4]=>[4,3,1]
[6,4,7,5,3,8,1,2]=>[4,2,1,1]
[5,7,4,8,3,1,6,2]=>[4,2,1,1]
[3,1,4,7,5,2,8,6]=>[3,2,2,1]
[2,5,3,6,1,8,4,7]=>[3,2,1,1,1]
[2,5,6,8,3,1,7,4]=>[3,2,1,1,1]
[7,1,4,5,3,6,2,8]=>[4,1,1,1,1]
[1,7,2,4,5,3,6,8]=>[3,1,1,1,1,1]
[1,7,4,5,3,2,6,8]=>[4,1,1,1,1]
[1,6,4,7,3,5,2,8]=>[4,1,1,1,1]
[3,5,6,4,8,2,1,7]=>[4,1,1,1,1]
[1,6,4,7,5,2,3,8]=>[3,2,1,1,1]
[1,5,2,6,7,4,3,8]=>[3,2,1,1,1]
[8,5,6,1,4,3,7,2]=>[5,1,1,1]
[2,5,4,7,8,3,1,6]=>[4,1,1,1,1]
[6,4,5,8,2,3,1,7]=>[4,1,1,1,1]
[8,6,1,3,2,5,7,4]=>[4,2,1,1]
[7,5,8,1,4,6,3,2]=>[5,1,1,1]
[4,2,6,7,8,1,5,3]=>[3,2,1,1,1]
[3,4,6,7,8,1,5,2]=>[3,1,1,1,1,1]
[4,7,3,8,5,1,6,2]=>[3,2,2,1]
[4,3,2,7,5,8,1,6]=>[4,2,1,1]
[4,8,5,3,2,6,1,7]=>[5,1,1,1]
[2,8,4,5,3,6,1,7]=>[4,1,1,1,1]
[8,1,5,3,2,4,7,6]=>[4,2,1,1]
[7,8,4,1,3,6,5,2]=>[4,2,1,1]
[8,6,1,3,2,7,4,5]=>[4,2,1,1]
[6,2,3,7,8,1,5,4]=>[3,2,1,1,1]
[6,3,7,8,1,5,4,2]=>[4,2,1,1]
[2,6,3,7,8,1,5,4]=>[3,2,1,1,1]
[7,5,8,1,6,4,2,3]=>[4,2,1,1]
[8,1,4,3,7,5,6,2]=>[4,2,1,1]
[1,4,8,5,3,2,6,7]=>[4,1,1,1,1]
[8,2,7,6,4,1,5,3]=>[5,2,1]
[2,7,4,3,8,5,1,6]=>[4,2,1,1]
[6,8,2,7,3,1,5,4]=>[4,2,1,1]
[8,2,6,3,4,1,7,5]=>[4,2,1,1]
[6,1,2,8,5,3,7,4]=>[3,2,2,1]
[4,1,5,8,3,6,7,2]=>[3,2,1,1,1]
[7,5,2,8,1,6,3,4]=>[4,2,1,1]
[3,4,7,2,1,5,8,6]=>[3,2,1,1,1]
[4,8,2,7,1,3,6,5]=>[4,1,1,1,1]
[8,2,1,7,4,6,3,5]=>[4,2,1,1]
[4,2,5,8,3,6,7,1]=>[3,2,1,1,1]
[5,1,6,8,3,2,7,4]=>[3,2,2,1]
[4,1,5,6,8,2,7,3]=>[3,2,1,1,1]
[5,7,8,2,4,1,3,6]=>[3,1,1,1,1,1]
[4,5,2,8,7,3,1,6]=>[4,2,1,1]
[4,8,5,3,1,6,7,2]=>[4,2,1,1]
[6,2,3,1,7,8,5,4]=>[3,3,1,1]
[5,2,3,6,8,4,7,1]=>[3,2,1,1,1]
[6,2,1,7,8,4,3,5]=>[3,3,1,1]
[5,2,1,3,8,4,7,6]=>[3,3,1,1]
[5,2,7,8,4,1,6,3]=>[3,2,2,1]
[6,2,7,8,3,5,4,1]=>[4,2,1,1]
[5,2,8,6,4,1,7,3]=>[4,2,2]
[5,1,2,8,4,3,7,6]=>[3,2,2,1]
[6,7,8,3,2,5,4,1]=>[4,2,1,1]
[5,7,2,6,4,8,1,3]=>[4,1,1,1,1]
[6,2,3,4,7,8,5,1]=>[3,2,1,1,1]
[7,2,1,8,4,3,5,6]=>[3,3,1,1]
[6,2,1,3,7,5,8,4]=>[3,3,1,1]
[6,8,7,3,4,5,1,2]=>[4,1,1,1,1]
[6,2,3,7,8,1,4,5]=>[3,1,1,1,1,1]
[7,4,3,2,5,8,1,6]=>[5,1,1,1]
[7,2,4,3,5,8,1,6]=>[4,1,1,1,1]
[1,7,6,4,2,3,5,8]=>[4,1,1,1,1]
[1,3,2,5,8,6,4,7]=>[3,2,1,1,1]
[6,1,4,7,2,8,5,3]=>[3,3,1,1]
[1,7,5,8,4,2,3,6]=>[4,1,1,1,1]
[1,6,7,2,4,8,5,3]=>[3,2,1,1,1]
[5,7,2,4,3,6,8,1]=>[4,1,1,1,1]
[5,7,3,4,6,2,8,1]=>[4,1,1,1,1]
[2,8,3,6,1,7,4,5]=>[3,2,1,1,1]
[4,3,1,8,5,2,6,7]=>[3,3,1,1]
[1,8,4,5,6,2,7,3]=>[3,2,1,1,1]
[7,3,8,2,1,4,5,6]=>[4,1,1,1,1]
[8,2,5,3,1,7,4,6]=>[4,2,1,1]
[6,3,5,8,1,7,4,2]=>[4,2,1,1]
[3,5,4,8,6,1,7,2]=>[3,2,2,1]
[7,5,2,3,8,4,6,1]=>[4,2,1,1]
[2,7,5,1,4,8,3,6]=>[4,1,1,1,1]
[5,7,6,1,2,8,3,4]=>[3,2,1,1,1]
[7,4,6,5,1,8,2,3]=>[4,2,1,1]
[7,1,3,2,6,8,4,5]=>[3,2,1,1,1]
[4,3,5,2,8,1,6,7]=>[4,1,1,1,1]
[1,7,3,8,2,4,6,5]=>[3,2,1,1,1]
[2,7,4,8,5,3,1,6]=>[4,2,1,1]
[6,1,3,8,4,2,7,5]=>[3,2,2,1]
[5,4,1,8,6,2,7,3]=>[3,3,2]
[5,4,6,8,1,3,2,7]=>[4,1,1,1,1]
[3,6,1,5,8,4,7,2]=>[4,1,1,1,1]
[6,4,8,3,5,7,2,1]=>[5,1,1,1]
[3,5,8,2,4,1,7,6]=>[3,2,1,1,1]
[7,2,8,4,1,3,6,5]=>[3,2,2,1]
[5,8,1,2,4,3,6,7]=>[3,1,1,1,1,1]
[8,4,3,5,7,2,6,1]=>[5,1,1,1]
[4,1,5,2,3,8,7,6]=>[3,2,2,1]
[6,3,5,8,2,4,7,1]=>[4,1,1,1,1]
[2,8,7,1,4,6,3,5]=>[4,1,1,1,1]
[1,8,5,3,7,4,2,6]=>[4,2,1,1]
[7,5,6,2,8,4,3,1]=>[5,2,1]
[5,7,6,2,8,1,4,3]=>[4,2,1,1]
[6,3,8,1,2,5,4,7]=>[3,2,1,1,1]
[7,6,4,8,5,3,2,1]=>[6,2]
[1,5,7,2,4,3,6,8]=>[3,1,1,1,1,1]
[1,6,5,3,2,4,7,8]=>[4,1,1,1,1]
[1,7,2,4,6,5,3,8]=>[4,1,1,1,1]
[1,4,7,2,6,5,3,8]=>[4,1,1,1,1]
[1,2,6,8,7,4,3,5]=>[4,1,1,1,1]
[1,2,7,4,3,5,8,6]=>[3,2,1,1,1]
[1,6,2,8,7,4,3,5]=>[4,2,1,1]
[1,7,4,2,3,5,8,6]=>[3,2,1,1,1]
[1,8,5,2,3,6,4,7]=>[3,2,1,1,1]
[1,7,4,8,5,2,3,6]=>[3,2,1,1,1]
[1,4,7,5,2,8,6,3]=>[3,3,1,1]
[1,6,3,7,4,2,8,5]=>[3,2,2,1]
[1,8,5,2,7,4,3,6]=>[4,2,1,1]
[1,4,8,7,5,3,2,6]=>[5,1,1,1]
[1,2,5,8,6,3,7,4]=>[3,2,1,1,1]
[1,2,4,7,5,8,6,3]=>[3,2,1,1,1]
[1,5,8,7,6,2,4,3]=>[5,1,1,1]
[1,3,5,8,7,6,2,4]=>[4,1,1,1,1]
[1,5,2,4,3,6,8,7]=>[3,2,1,1,1]
[1,6,8,7,5,3,2,4]=>[5,1,1,1]
[1,2,5,7,4,3,8,6]=>[3,2,1,1,1]
[1,5,3,2,6,8,7,4]=>[3,3,1,1]
[1,4,2,6,8,7,5,3]=>[4,2,1,1]
[1,5,8,6,3,2,7,4]=>[4,2,1,1]
[1,8,5,2,6,3,4,7]=>[3,2,1,1,1]
[1,7,4,6,3,2,8,5]=>[4,2,1,1]
[1,6,3,2,8,5,4,7]=>[3,3,1,1]
[1,3,8,6,4,2,5,7]=>[4,1,1,1,1]
[1,5,7,4,2,3,8,6]=>[3,2,1,1,1]
[6,3,7,5,4,2,8,1]=>[5,2,1]
[7,5,2,6,3,4,8,1]=>[4,2,1,1]
[3,8,2,7,5,4,1,6]=>[5,1,1,1]
[5,4,8,6,7,1,2,3]=>[3,2,1,1,1]
[2,7,3,6,8,5,4,1]=>[5,1,1,1]
[3,7,2,8,1,6,4,5]=>[3,2,1,1,1]
[8,5,2,4,6,7,3,1]=>[5,1,1,1]
[2,5,8,7,1,4,3,6]=>[4,1,1,1,1]
[3,4,6,5,8,2,7,1]=>[4,1,1,1,1]
[5,2,4,1,6,7,8,3]=>[3,2,1,1,1]
[4,2,7,1,6,8,3,5]=>[3,2,1,1,1]
[5,2,8,6,4,7,1,3]=>[4,2,1,1]
[6,1,3,4,7,2,8,5]=>[3,2,1,1,1]
[8,4,7,2,5,3,1,6]=>[5,1,1,1]
[8,3,4,5,2,1,7,6]=>[4,2,1,1]
[8,6,1,4,7,3,5,2]=>[5,1,1,1]
[5,3,6,7,2,8,4,1]=>[4,2,1,1]
[5,3,6,7,2,4,8,1]=>[4,1,1,1,1]
[8,6,4,2,7,1,5,3]=>[5,2,1]
[8,6,1,4,7,5,2,3]=>[4,2,1,1]
[1,5,8,2,6,7,4,3]=>[4,1,1,1,1]
[7,1,3,6,5,2,8,4]=>[4,2,1,1]
[8,2,1,4,5,7,6,3]=>[4,2,1,1]
[1,4,7,5,2,3,8,6]=>[3,2,1,1,1]
[6,1,7,5,4,2,8,3]=>[4,2,2]
[2,7,3,6,5,1,8,4]=>[4,2,1,1]
[8,6,5,1,3,7,4,2]=>[5,2,1]
[5,7,6,2,4,8,1,3]=>[4,1,1,1,1]
[3,7,5,6,4,8,1,2]=>[4,1,1,1,1]
[7,6,8,1,3,5,4,2]=>[5,1,1,1]
[2,8,4,6,1,7,5,3]=>[4,2,1,1]
[2,8,6,4,7,3,5,1]=>[5,1,1,1]
[8,7,1,4,6,5,3,2]=>[6,1,1]
[3,5,8,6,7,1,4,2]=>[4,1,1,1,1]
[1,2,4,6,8,5,3,7]=>[3,1,1,1,1,1]
[3,1,5,8,6,2,4,7]=>[3,2,1,1,1]
[2,5,4,6,8,1,3,7]=>[3,1,1,1,1,1]
[6,5,2,4,7,8,1,3]=>[4,1,1,1,1]
[7,2,5,8,6,4,1,3]=>[4,2,1,1]
[5,2,8,3,4,7,6,1]=>[4,2,1,1]
[2,4,3,8,7,1,6,5]=>[4,2,1,1]
[1,5,8,7,4,2,6,3]=>[4,2,1,1]
[6,8,7,5,4,3,1,2]=>[6,1,1]
[5,3,4,8,6,2,7,1]=>[4,2,1,1]
[3,4,5,8,6,2,7,1]=>[4,1,1,1,1]
[5,4,2,3,6,1,8,7]=>[4,2,1,1]
[5,1,7,4,3,6,8,2]=>[4,2,1,1]
[4,3,7,6,8,2,1,5]=>[4,2,1,1]
[8,1,4,7,2,3,5,6]=>[3,1,1,1,1,1]
[6,1,8,5,2,7,3,4]=>[3,2,2,1]
[8,7,2,6,3,1,4,5]=>[5,1,1,1]
[8,7,1,6,4,5,2,3]=>[5,1,1,1]
[5,4,1,3,7,2,8,6]=>[4,2,1,1]
[3,1,8,7,5,2,4,6]=>[4,2,1,1]
[6,5,8,7,2,4,3,1]=>[5,2,1]
[4,3,6,5,8,2,1,7]=>[4,2,1,1]
[7,6,3,2,8,5,4,1]=>[5,3]
[3,2,6,8,7,1,4,5]=>[3,2,1,1,1]
[4,3,7,1,8,5,2,6]=>[3,3,1,1]
[3,2,8,5,6,7,1,4]=>[3,2,1,1,1]
[8,3,2,1,4,7,5,6]=>[4,2,1,1]
[4,7,3,1,8,5,2,6]=>[3,3,1,1]
[3,7,8,2,5,6,1,4]=>[3,1,1,1,1,1]
[7,5,1,4,2,3,6,8]=>[4,1,1,1,1]
[7,8,6,1,2,4,5,3]=>[4,1,1,1,1]
[1,5,3,4,7,8,6,2]=>[3,2,1,1,1]
[5,1,2,4,7,8,6,3]=>[3,2,1,1,1]
[5,1,7,8,6,2,3,4]=>[3,2,1,1,1]
[8,5,1,6,7,2,3,4]=>[3,2,1,1,1]
[7,5,1,2,4,6,8,3]=>[4,1,1,1,1]
[6,1,5,2,7,3,4,8]=>[3,2,1,1,1]
[7,1,2,6,4,5,8,3]=>[4,1,1,1,1]
[1,7,3,6,4,5,8,2]=>[4,1,1,1,1]
[1,8,3,6,4,5,7,2]=>[4,1,1,1,1]
[8,1,6,2,7,3,4,5]=>[3,2,1,1,1]
[7,1,6,2,5,3,4,8]=>[4,1,1,1,1]
[8,1,6,2,5,3,4,7]=>[4,1,1,1,1]
[8,1,7,2,5,3,4,6]=>[4,1,1,1,1]
[8,1,2,7,4,5,6,3]=>[4,1,1,1,1]
[1,8,3,7,4,5,6,2]=>[4,1,1,1,1]
[8,1,6,7,5,2,3,4]=>[4,1,1,1,1]
[7,3,1,2,6,4,5,8]=>[3,2,1,1,1]
[3,1,2,8,5,6,7,4]=>[3,2,1,1,1]
[6,3,1,2,7,4,5,8]=>[3,2,1,1,1]
[6,1,7,4,2,3,5,8]=>[3,2,1,1,1]
[1,7,3,4,6,8,5,2]=>[4,1,1,1,1]
[1,7,3,8,4,5,6,2]=>[3,2,1,1,1]
[7,1,8,2,5,3,4,6]=>[3,2,1,1,1]
[6,1,7,2,5,3,4,8]=>[3,2,1,1,1]
[5,1,7,2,6,3,4,8]=>[3,2,1,1,1]
[5,1,8,2,6,3,4,7]=>[3,2,1,1,1]
[1,6,3,7,4,5,8,2]=>[3,2,1,1,1]
[2,4,7,3,5,1,6,8]=>[3,1,1,1,1,1]
[2,4,8,6,3,5,1,7]=>[4,1,1,1,1]
[2,3,7,5,4,1,6,8]=>[4,1,1,1,1]
[3,4,6,2,1,5,8,7]=>[3,2,1,1,1]
[3,4,7,2,1,6,5,8]=>[3,2,1,1,1]
[2,6,8,3,5,1,4,7]=>[3,1,1,1,1,1]
[2,3,6,1,5,8,4,7]=>[3,1,1,1,1,1]
[2,3,7,1,6,5,8,4]=>[4,1,1,1,1]
[2,4,7,1,3,6,8,5]=>[3,1,1,1,1,1]
[5,4,7,8,1,3,2,6]=>[4,1,1,1,1]
[2,5,7,1,4,6,3,8]=>[3,1,1,1,1,1]
[2,4,7,1,6,3,5,8]=>[3,1,1,1,1,1]
[2,3,7,1,6,5,4,8]=>[4,1,1,1,1]
[2,5,7,1,4,3,6,8]=>[3,1,1,1,1,1]
[2,5,7,3,1,4,6,8]=>[3,1,1,1,1,1]
[3,4,7,2,1,6,8,5]=>[3,2,1,1,1]
[4,6,3,7,1,5,2,8]=>[3,2,1,1,1]
[5,7,3,2,8,1,4,6]=>[4,1,1,1,1]
[2,6,5,7,1,8,4,3]=>[4,2,1,1]
[3,6,8,5,4,1,7,2]=>[4,2,1,1]
[5,4,7,8,1,3,6,2]=>[4,1,1,1,1]
[2,5,7,1,4,6,8,3]=>[3,1,1,1,1,1]
[2,4,7,1,6,3,8,5]=>[3,2,1,1,1]
[2,4,7,1,6,8,3,5]=>[3,1,1,1,1,1]
[2,4,8,3,1,7,6,5]=>[4,2,1,1]
[8,6,5,1,2,4,3,7]=>[5,1,1,1]
[7,6,1,4,2,3,5,8]=>[4,1,1,1,1]
[6,5,1,4,8,3,2,7]=>[5,1,1,1]
[8,7,1,4,3,2,5,6]=>[5,1,1,1]
[8,7,5,1,4,2,3,6]=>[5,1,1,1]
[8,4,1,2,5,3,6,7]=>[3,2,1,1,1]
[8,6,1,4,2,5,3,7]=>[4,2,1,1]
[8,7,1,4,3,2,6,5]=>[5,2,1]
[8,7,6,3,1,5,4,2]=>[6,2]
[2,8,3,7,4,5,6,1]=>[4,1,1,1,1]
[8,7,5,2,4,3,6,1]=>[6,1,1]
[4,2,5,7,3,1,6,8]=>[3,2,1,1,1]
[8,2,4,5,3,1,6,7]=>[4,1,1,1,1]
[8,4,5,1,3,2,6,7]=>[4,1,1,1,1]
[4,3,7,5,2,1,6,8]=>[4,2,1,1]
[1,6,7,4,3,2,5,8]=>[4,1,1,1,1]
[1,4,5,7,3,2,6,8]=>[3,1,1,1,1,1]
[3,5,1,4,7,2,6,8]=>[3,1,1,1,1,1]
[2,5,1,4,7,8,3,6]=>[3,1,1,1,1,1]
[4,3,7,1,5,2,6,8]=>[3,2,1,1,1]
[3,5,1,6,4,2,7,8]=>[3,2,1,1,1]
[6,4,3,1,7,2,5,8]=>[4,2,1,1]
[6,2,7,4,3,1,5,8]=>[4,2,1,1]
[2,6,4,1,7,3,5,8]=>[3,2,1,1,1]
[6,3,2,7,4,5,1,8]=>[4,2,1,1]
[7,2,4,1,3,6,8,5]=>[3,2,1,1,1]
[6,3,2,5,7,1,4,8]=>[4,1,1,1,1]
[3,2,6,5,7,1,4,8]=>[3,2,1,1,1]
[1,7,3,2,5,6,4,8]=>[3,2,1,1,1]
[2,1,7,3,5,6,8,4]=>[3,2,1,1,1]
[2,1,6,3,5,7,8,4]=>[3,2,1,1,1]
[1,6,3,2,5,7,4,8]=>[3,2,1,1,1]
[1,4,6,5,2,7,3,8]=>[3,2,1,1,1]
[5,6,2,1,4,3,7,8]=>[3,2,1,1,1]
[2,5,1,6,4,3,7,8]=>[3,2,1,1,1]
[2,5,4,1,6,3,7,8]=>[3,2,1,1,1]
[4,6,1,5,2,7,3,8]=>[3,2,1,1,1]
[1,6,5,3,7,2,4,8]=>[4,1,1,1,1]
[1,2,5,4,7,3,6,8]=>[3,1,1,1,1,1]
[1,2,5,3,4,8,7,6]=>[3,2,1,1,1]
[5,2,7,6,1,8,4,3]=>[4,2,2]
[5,8,2,6,1,7,4,3]=>[4,2,1,1]
[1,5,8,3,6,2,7,4]=>[3,2,1,1,1]
[6,8,7,1,4,5,2,3]=>[4,1,1,1,1]
[1,2,6,4,7,3,8,5]=>[3,2,1,1,1]
[1,2,7,8,3,5,6,4]=>[3,1,1,1,1,1]
[4,8,7,6,2,1,5,3]=>[5,2,1]
[2,7,4,5,8,1,6,3]=>[3,2,1,1,1]
[5,8,6,2,3,4,1,7]=>[4,1,1,1,1]
[4,5,8,6,2,1,3,7]=>[4,1,1,1,1]
[6,4,7,5,8,2,1,3]=>[4,2,1,1]
[6,3,7,4,2,5,8,1]=>[4,2,1,1]
[6,2,1,5,8,4,3,7]=>[4,2,1,1]
[7,5,6,2,4,3,8,1]=>[5,1,1,1]
[4,6,2,5,7,3,8,1]=>[4,1,1,1,1]
[8,1,7,4,5,6,2,3]=>[4,1,1,1,1]
[2,1,7,8,4,5,6,3]=>[3,2,1,1,1]
[8,2,1,4,3,7,6,5]=>[4,2,2]
[7,6,5,3,1,2,8,4]=>[5,2,1]
[5,4,1,6,2,8,3,7]=>[3,2,2,1]
[3,1,8,6,7,2,4,5]=>[3,2,1,1,1]
[4,2,5,1,8,6,7,3]=>[3,3,1,1]
[4,5,3,7,1,6,8,2]=>[3,2,1,1,1]
[2,8,6,3,5,4,7,1]=>[5,1,1,1]
[3,5,2,8,6,4,7,1]=>[4,2,1,1]
[7,3,5,1,6,4,8,2]=>[4,2,1,1]
[5,1,4,7,2,6,8,3]=>[3,2,1,1,1]
[1,8,2,5,6,4,7,3]=>[4,1,1,1,1]
[2,7,1,4,8,5,6,3]=>[3,2,1,1,1]
[2,8,4,6,1,3,7,5]=>[3,2,1,1,1]
[8,4,6,2,5,3,7,1]=>[5,1,1,1]
[8,3,7,6,2,1,5,4]=>[5,2,1]
[8,5,2,7,6,1,4,3]=>[5,2,1]
[5,8,2,7,6,1,4,3]=>[5,1,1,1]
[8,3,7,6,2,5,1,4]=>[5,1,1,1]
[7,3,8,6,5,1,4,2]=>[5,2,1]
[2,6,3,7,5,4,8,1]=>[4,2,1,1]
[5,4,7,1,3,8,6,2]=>[4,2,1,1]
[2,8,5,1,4,7,3,6]=>[4,1,1,1,1]
[8,1,4,2,5,7,3,6]=>[3,2,1,1,1]
[7,2,6,5,8,4,3,1]=>[6,1,1]
[3,4,8,5,6,2,7,1]=>[4,1,1,1,1]
[5,8,2,3,4,6,1,7]=>[3,1,1,1,1,1]
[6,1,3,4,2,5,7,8]=>[3,1,1,1,1,1]
[1,5,6,3,2,4,7,8]=>[3,1,1,1,1,1]
[6,3,5,2,4,1,7,8]=>[4,1,1,1,1]
[7,8,3,5,2,4,6,1]=>[4,1,1,1,1]
[2,4,5,7,3,6,1,8]=>[3,1,1,1,1,1]
[2,5,3,1,6,4,7,8]=>[3,2,1,1,1]
[6,5,1,3,4,2,7,8]=>[4,1,1,1,1]
[5,7,4,3,2,6,1,8]=>[5,1,1,1]
[6,8,7,4,3,5,1,2]=>[5,1,1,1]
[2,6,7,8,4,3,5,1]=>[4,1,1,1,1]
[1,7,8,4,5,3,6,2]=>[4,1,1,1,1]
[7,1,8,5,3,4,6,2]=>[4,2,1,1]
[5,7,4,2,1,6,3,8]=>[4,2,1,1]
[5,1,4,7,3,6,2,8]=>[4,1,1,1,1]
[7,4,8,6,3,5,2,1]=>[5,2,1]
[4,7,6,3,5,2,1,8]=>[5,1,1,1]
[1,6,5,8,7,4,2,3]=>[4,2,1,1]
[6,1,3,8,7,5,2,4]=>[4,2,1,1]
[7,6,2,1,8,3,5,4]=>[4,3,1]
[7,1,3,6,8,2,5,4]=>[4,1,1,1,1]
[1,7,5,6,8,2,4,3]=>[4,1,1,1,1]
[3,6,7,5,8,2,4,1]=>[4,1,1,1,1]
[1,7,4,5,2,8,6,3]=>[3,3,1,1]
[7,5,4,2,1,8,6,3]=>[5,3]
[3,6,7,4,2,8,5,1]=>[4,2,1,1]
[4,6,3,2,7,8,5,1]=>[4,2,1,1]
[7,6,1,3,4,2,5,8]=>[4,1,1,1,1]
[7,8,2,6,4,5,3,1]=>[5,1,1,1]
[7,2,5,4,6,1,3,8]=>[4,1,1,1,1]
[7,1,2,4,5,6,3,8]=>[3,1,1,1,1,1]
[7,3,2,1,5,6,4,8]=>[4,2,1,1]
[3,6,2,1,7,5,4,8]=>[3,3,1,1]
[2,6,7,3,1,5,4,8]=>[3,2,1,1,1]
[2,1,6,4,7,5,3,8]=>[3,2,2,1]
[7,2,8,5,6,4,3,1]=>[5,2,1]
[7,6,8,5,4,1,3,2]=>[6,1,1]
[7,1,8,4,6,5,3,2]=>[5,2,1]
[7,8,6,3,1,5,4,2]=>[5,2,1]
[7,6,1,4,5,3,2,8]=>[5,1,1,1]
[7,1,5,6,4,3,2,8]=>[5,1,1,1]
[4,1,3,8,6,2,7,5]=>[3,2,2,1]
[5,6,3,2,8,1,7,4]=>[4,2,1,1]
[8,2,6,3,1,5,7,4]=>[4,2,1,1]
[8,2,5,6,7,4,3,1]=>[5,1,1,1]
[8,2,5,3,4,7,6,1]=>[4,2,1,1]
[7,5,3,2,4,1,8,6]=>[5,2,1]
[7,1,2,3,6,8,4,5]=>[3,1,1,1,1,1]
[6,7,2,8,3,4,5,1]=>[3,2,1,1,1]
[3,1,8,4,6,5,7,2]=>[4,2,1,1]
[6,1,2,3,8,4,7,5]=>[3,2,1,1,1]
[8,1,6,7,4,2,3,5]=>[4,1,1,1,1]
[8,1,6,4,5,2,3,7]=>[4,1,1,1,1]
[8,6,4,7,2,3,5,1]=>[5,1,1,1]
[8,6,4,1,2,3,7,5]=>[4,2,1,1]
[8,6,1,4,2,5,7,3]=>[4,2,1,1]
[8,6,7,4,2,5,1,3]=>[5,1,1,1]
[8,6,4,2,5,3,7,1]=>[5,2,1]
[8,6,4,2,5,3,1,7]=>[5,2,1]
[8,6,4,2,7,3,1,5]=>[5,2,1]
[8,6,4,1,5,7,2,3]=>[4,2,1,1]
[8,6,4,2,1,5,7,3]=>[5,2,1]
[8,6,4,2,1,7,3,5]=>[5,2,1]
[8,6,1,4,7,2,5,3]=>[4,2,1,1]
[8,6,4,1,5,2,3,7]=>[4,2,1,1]
[8,6,7,1,4,5,2,3]=>[4,1,1,1,1]
[8,6,4,5,2,7,3,1]=>[5,2,1]
[8,6,7,4,2,1,5,3]=>[5,2,1]
[8,6,4,7,2,1,5,3]=>[5,2,1]
[8,6,4,2,5,7,3,1]=>[5,2,1]
[8,6,4,2,5,1,7,3]=>[5,2,1]
[8,6,4,2,5,7,1,3]=>[5,1,1,1]
[3,4,7,5,8,2,6,1]=>[4,1,1,1,1]
[8,7,1,4,6,5,2,3]=>[5,1,1,1]
[8,3,7,6,4,5,1,2]=>[5,1,1,1]
[5,3,8,6,4,1,7,2]=>[4,2,2]
[7,4,5,1,2,8,6,3]=>[3,3,1,1]
[6,4,7,1,8,5,2,3]=>[3,3,1,1]
[5,7,4,2,3,8,6,1]=>[4,2,1,1]
[3,8,2,5,1,7,4,6]=>[3,2,1,1,1]
[5,8,4,2,3,7,1,6]=>[4,1,1,1,1]
[4,8,5,2,1,7,3,6]=>[4,2,1,1]
[8,5,7,6,1,2,4,3]=>[5,1,1,1]
[6,8,7,5,2,4,1,3]=>[5,1,1,1]
[5,7,6,8,4,1,3,2]=>[5,1,1,1]
[7,3,1,6,8,5,4,2]=>[5,2,1]
[5,3,1,7,4,8,6,2]=>[3,3,2]
[7,3,1,8,6,4,5,2]=>[4,3,1]
[8,6,4,1,7,3,2,5]=>[5,2,1]
[4,6,8,3,7,1,2,5]=>[3,1,1,1,1,1]
[3,5,2,8,4,7,1,6]=>[3,2,1,1,1]
[6,4,8,3,7,2,1,5]=>[5,1,1,1]
[3,6,2,8,7,4,1,5]=>[4,2,1,1]
[6,8,4,2,7,3,1,5]=>[4,2,1,1]
[3,4,7,8,5,1,2,6]=>[3,1,1,1,1,1]
[4,7,3,2,5,6,8,1]=>[4,1,1,1,1]
[3,2,7,6,4,5,8,1]=>[4,2,1,1]
[1,7,3,6,8,4,2,5]=>[4,1,1,1,1]
[2,3,6,5,1,8,7,4]=>[3,3,1,1]
[8,3,1,2,6,4,7,5]=>[3,2,2,1]
[1,7,8,2,4,3,5,6]=>[3,1,1,1,1,1]
[3,6,4,7,1,2,8,5]=>[3,2,1,1,1]
[5,7,4,8,1,3,2,6]=>[4,1,1,1,1]
[4,3,7,8,1,5,2,6]=>[3,2,1,1,1]
[8,5,4,2,6,1,7,3]=>[5,2,1]
[3,2,6,8,7,4,1,5]=>[4,2,1,1]
[2,3,7,5,1,8,6,4]=>[3,3,1,1]
[6,3,1,2,8,7,4,5]=>[3,3,1,1]
[5,2,1,3,8,7,6,4]=>[4,3,1]
[7,2,1,5,3,8,4,6]=>[3,2,2,1]
[1,5,8,2,4,3,6,7]=>[3,1,1,1,1,1]
[4,3,6,8,1,5,2,7]=>[3,2,1,1,1]
[5,4,6,8,3,1,7,2]=>[4,2,1,1]
[3,6,8,4,5,1,7,2]=>[3,2,1,1,1]
[8,6,1,7,2,4,3,5]=>[4,2,1,1]
[7,3,1,2,8,6,4,5]=>[3,3,1,1]
[2,3,7,6,1,8,5,4]=>[4,2,1,1]
[3,2,7,8,6,4,1,5]=>[4,2,1,1]
[6,2,8,3,1,4,7,5]=>[3,2,2,1]
[3,1,2,8,7,4,5,6]=>[3,2,1,1,1]
[2,1,3,8,7,4,6,5]=>[4,2,1,1]
[2,1,3,8,7,4,5,6]=>[3,2,1,1,1]
[1,6,8,3,2,4,7,5]=>[3,2,1,1,1]
[8,5,1,7,2,4,3,6]=>[4,2,1,1]
[8,4,1,7,3,2,5,6]=>[4,2,1,1]
[8,3,1,6,2,7,5,4]=>[4,2,2]
[1,3,2,8,7,6,4,5]=>[4,2,1,1]
[2,1,3,8,7,6,4,5]=>[4,2,1,1]
[1,6,3,7,2,5,4,8]=>[3,2,1,1,1]
[1,7,2,4,6,3,5,8]=>[3,1,1,1,1,1]
[5,7,2,8,4,1,3,6]=>[3,2,1,1,1]
[5,6,2,8,4,1,3,7]=>[3,2,1,1,1]
[2,4,8,3,1,6,7,5]=>[3,2,1,1,1]
[3,5,8,4,2,1,6,7]=>[4,1,1,1,1]
[2,5,8,3,1,4,6,7]=>[3,1,1,1,1,1]
[2,8,1,3,5,7,4,6]=>[3,1,1,1,1,1]
[5,4,7,8,3,2,6,1]=>[5,1,1,1]
[3,6,8,2,5,1,4,7]=>[3,1,1,1,1,1]
[3,6,8,7,2,5,4,1]=>[5,1,1,1]
[3,4,6,5,8,2,1,7]=>[4,1,1,1,1]
[2,4,6,7,8,3,5,1]=>[3,1,1,1,1,1]
[1,4,2,5,7,6,3,8]=>[3,2,1,1,1]
[1,4,2,6,8,5,3,7]=>[3,2,1,1,1]
[1,2,6,8,3,5,4,7]=>[3,1,1,1,1,1]
[1,6,8,3,5,4,2,7]=>[4,1,1,1,1]
[1,5,3,2,4,6,8,7]=>[3,2,1,1,1]
[1,5,8,7,6,3,2,4]=>[5,1,1,1]
[1,5,7,6,3,2,4,8]=>[4,1,1,1,1]
[1,6,3,2,4,7,5,8]=>[3,2,1,1,1]
[1,6,3,2,4,8,7,5]=>[3,3,1,1]
[1,2,7,6,4,3,5,8]=>[4,1,1,1,1]
[1,8,7,5,2,4,6,3]=>[5,1,1,1]
[1,7,5,2,4,6,3,8]=>[4,1,1,1,1]
[1,7,4,2,5,3,6,8]=>[3,2,1,1,1]
[1,8,4,7,5,2,6,3]=>[4,2,1,1]
[1,7,5,2,3,6,4,8]=>[3,2,1,1,1]
[1,7,5,2,6,3,4,8]=>[3,2,1,1,1]
[1,6,3,7,4,2,5,8]=>[3,2,1,1,1]
[1,6,3,2,7,5,4,8]=>[3,3,1,1]
[1,4,7,5,2,6,3,8]=>[3,2,1,1,1]
[1,3,6,4,8,7,5,2]=>[4,2,1,1]
[1,3,7,6,4,2,5,8]=>[4,1,1,1,1]
[1,3,2,4,8,5,7,6]=>[3,2,1,1,1]
[1,3,8,7,5,2,4,6]=>[4,1,1,1,1]
[1,4,6,3,2,7,5,8]=>[3,2,1,1,1]
[1,4,6,3,2,8,7,5]=>[3,3,1,1]
[1,5,7,6,4,2,3,8]=>[4,1,1,1,1]
[1,6,3,2,8,4,7,5]=>[3,3,1,1]
[1,6,3,5,2,7,4,8]=>[3,2,1,1,1]
[1,6,3,5,2,8,7,4]=>[3,3,1,1]
[1,8,3,7,5,2,4,6]=>[4,1,1,1,1]
[6,4,7,1,5,3,8,2]=>[4,2,1,1]
[5,3,8,2,6,4,7,1]=>[4,2,1,1]
[4,3,8,2,6,5,7,1]=>[4,2,1,1]
[2,6,1,8,3,4,7,5]=>[3,2,1,1,1]
[5,7,1,4,8,2,3,6]=>[3,1,1,1,1,1]
[6,5,7,1,4,3,8,2]=>[5,1,1,1]
[4,8,3,5,7,6,1,2]=>[4,1,1,1,1]
[5,7,6,1,2,4,8,3]=>[4,1,1,1,1]
[4,8,3,5,7,6,2,1]=>[5,1,1,1]
[1,3,4,2,8,5,7,6]=>[3,2,1,1,1]
[5,7,6,2,4,8,3,1]=>[5,1,1,1]
[6,7,5,2,3,8,4,1]=>[4,2,1,1]
[6,7,5,3,8,4,2,1]=>[5,2,1]
[3,2,1,4,8,5,7,6]=>[3,3,1,1]
[7,3,1,4,2,6,5,8]=>[3,2,2,1]
[5,4,1,8,2,6,3,7]=>[3,3,1,1]
[5,3,1,8,2,6,4,7]=>[3,3,1,1]
[4,7,1,5,2,6,3,8]=>[3,2,1,1,1]
[6,5,1,4,2,7,3,8]=>[4,2,1,1]
[1,8,7,3,4,5,2,6]=>[4,1,1,1,1]
[1,8,7,4,5,2,3,6]=>[4,1,1,1,1]
[1,2,6,8,7,3,4,5]=>[3,1,1,1,1,1]
[1,3,7,8,4,5,6,2]=>[3,1,1,1,1,1]
[8,4,2,3,1,6,5,7]=>[4,2,1,1]
[6,4,5,2,8,1,7,3]=>[4,2,1,1]
[4,8,6,2,3,1,7,5]=>[4,2,1,1]
[6,4,2,1,8,5,3,7]=>[4,3,1]
[4,2,6,1,5,8,3,7]=>[3,2,1,1,1]
[6,4,2,3,5,8,1,7]=>[4,1,1,1,1]
[2,8,6,4,5,1,7,3]=>[4,2,1,1]
[8,2,4,6,7,1,5,3]=>[4,1,1,1,1]
[2,6,3,1,7,4,8,5]=>[3,2,2,1]
[6,5,1,8,3,2,7,4]=>[4,2,2]
[1,4,3,7,2,8,6,5]=>[3,3,1,1]
[1,8,7,4,5,3,2,6]=>[5,1,1,1]
[3,2,6,7,8,4,5,1]=>[3,2,1,1,1]
[1,7,4,6,3,8,2,5]=>[4,1,1,1,1]
[5,6,4,1,3,8,2,7]=>[4,1,1,1,1]
[4,5,3,1,8,7,6,2]=>[4,3,1]
[6,3,4,2,7,8,5,1]=>[4,2,1,1]
[8,7,4,5,1,6,3,2]=>[5,2,1]
[6,2,7,8,1,3,5,4]=>[3,2,1,1,1]
[5,1,8,4,3,7,2,6]=>[4,2,1,1]
[7,2,8,1,4,5,6,3]=>[3,2,1,1,1]
[1,4,8,2,5,6,7,3]=>[3,1,1,1,1,1]
[8,1,6,7,2,5,4,3]=>[5,1,1,1]
[7,5,2,3,6,8,4,1]=>[4,2,1,1]
[8,1,4,6,5,3,2,7]=>[5,1,1,1]
[8,1,4,7,6,5,2,3]=>[5,1,1,1]
[8,1,2,7,6,5,4,3]=>[6,1,1]
[4,5,8,1,6,7,2,3]=>[3,1,1,1,1,1]
[3,7,2,5,8,4,6,1]=>[4,1,1,1,1]
[6,7,8,4,1,5,2,3]=>[3,2,1,1,1]
[6,2,8,3,5,1,4,7]=>[3,2,1,1,1]
[6,2,7,4,5,3,1,8]=>[4,2,1,1]
[6,8,2,5,3,4,1,7]=>[4,1,1,1,1]
[6,8,7,5,4,1,2,3]=>[5,1,1,1]
[7,4,5,6,1,8,2,3]=>[3,2,1,1,1]
[6,3,5,2,8,1,7,4]=>[4,2,1,1]
[6,1,8,7,4,5,2,3]=>[4,2,1,1]
[4,8,7,1,6,3,2,5]=>[5,1,1,1]
[4,8,2,7,5,3,6,1]=>[5,1,1,1]
[1,3,2,6,8,7,4,5]=>[3,2,1,1,1]
[1,3,8,2,5,4,6,7]=>[3,1,1,1,1,1]
[1,6,2,5,8,7,3,4]=>[3,2,1,1,1]
[1,6,8,7,2,3,5,4]=>[4,1,1,1,1]
[1,6,8,7,2,5,3,4]=>[4,1,1,1,1]
[1,5,2,4,8,3,6,7]=>[3,1,1,1,1,1]
[1,2,4,5,8,6,3,7]=>[3,1,1,1,1,1]
[1,2,8,3,5,4,7,6]=>[3,2,1,1,1]
[1,3,8,2,5,4,7,6]=>[3,2,1,1,1]
[1,6,7,5,2,4,8,3]=>[4,1,1,1,1]
[1,5,6,4,7,2,3,8]=>[3,1,1,1,1,1]
[1,7,4,2,5,8,3,6]=>[3,2,1,1,1]
[1,6,4,3,7,5,2,8]=>[4,2,1,1]
[1,6,5,4,7,2,3,8]=>[4,1,1,1,1]
[1,7,3,2,6,4,8,5]=>[3,2,2,1]
[1,5,8,2,3,6,7,4]=>[3,1,1,1,1,1]
[1,3,2,6,8,5,4,7]=>[3,2,1,1,1]
[1,6,3,2,7,4,5,8]=>[3,2,1,1,1]
[1,7,8,5,4,2,3,6]=>[4,1,1,1,1]
[1,8,4,2,3,6,5,7]=>[3,2,1,1,1]
[1,4,2,7,5,3,8,6]=>[3,2,2,1]
[1,5,7,6,2,4,3,8]=>[4,1,1,1,1]
[1,8,4,7,3,2,6,5]=>[4,2,1,1]
[1,3,8,4,2,6,5,7]=>[3,2,1,1,1]
[1,7,4,2,6,5,8,3]=>[4,2,1,1]
[1,6,5,8,3,7,4,2]=>[4,2,1,1]
[1,7,4,8,3,2,5,6]=>[4,1,1,1,1]
[1,4,8,3,2,7,5,6]=>[3,2,1,1,1]
[1,8,3,6,4,5,2,7]=>[4,1,1,1,1]
[1,6,4,7,3,2,8,5]=>[4,2,1,1]
[8,2,3,7,4,5,6,1]=>[4,1,1,1,1]
[8,5,7,2,3,6,4,1]=>[5,1,1,1]
[7,5,2,1,6,8,3,4]=>[4,2,1,1]
[7,6,1,5,4,8,2,3]=>[5,1,1,1]
[7,6,3,2,1,8,4,5]=>[5,2,1]
[2,8,7,3,4,6,1,5]=>[4,1,1,1,1]
[6,5,1,3,7,2,8,4]=>[4,2,1,1]
[8,1,7,3,4,5,2,6]=>[4,1,1,1,1]
[7,1,8,3,4,5,2,6]=>[3,2,1,1,1]
[6,8,7,3,4,2,1,5]=>[5,1,1,1]
[3,8,7,1,2,4,5,6]=>[3,1,1,1,1,1]
[1,8,5,3,4,6,2,7]=>[4,1,1,1,1]
[7,1,6,5,4,3,8,2]=>[6,1,1]
[7,1,3,6,4,5,8,2]=>[4,1,1,1,1]
[7,1,5,3,6,4,8,2]=>[4,2,1,1]
[6,1,5,3,7,8,2,4]=>[4,1,1,1,1]
[5,8,7,1,2,6,3,4]=>[4,1,1,1,1]
[6,8,2,3,4,7,1,5]=>[3,1,1,1,1,1]
[5,1,7,3,8,6,2,4]=>[3,2,2,1]
[6,1,3,2,4,7,8,5]=>[3,2,1,1,1]
[6,2,1,3,4,7,8,5]=>[3,2,1,1,1]
[3,2,5,8,7,4,1,6]=>[4,2,1,1]
[4,2,5,8,7,3,1,6]=>[4,2,1,1]
[8,3,4,1,6,5,2,7]=>[4,2,1,1]
[3,4,8,5,7,2,1,6]=>[4,1,1,1,1]
[3,6,4,8,5,7,2,1]=>[4,2,1,1]
[5,8,4,7,3,6,2,1]=>[5,1,1,1]
[4,2,8,7,3,1,6,5]=>[4,2,2]
[6,5,8,2,1,7,4,3]=>[4,3,1]
[6,1,4,3,8,7,2,5]=>[4,2,1,1]
[5,1,3,2,6,8,7,4]=>[3,3,1,1]
[6,1,3,8,7,2,4,5]=>[3,2,1,1,1]
[1,2,8,4,5,7,3,6]=>[3,1,1,1,1,1]
[4,2,1,8,7,6,3,5]=>[4,3,1]
[3,2,5,8,7,1,4,6]=>[3,2,1,1,1]
[5,6,3,8,7,2,1,4]=>[4,2,1,1]
[2,5,8,4,7,1,6,3]=>[4,1,1,1,1]
[1,6,2,4,8,5,7,3]=>[3,2,1,1,1]
[3,1,6,5,8,7,2,4]=>[3,2,2,1]
[4,8,5,3,6,7,1,2]=>[4,1,1,1,1]
[1,8,5,3,4,7,6,2]=>[4,2,1,1]
[2,7,1,3,6,4,5,8]=>[3,1,1,1,1,1]
[8,1,7,3,5,4,6,2]=>[5,1,1,1]
[3,2,4,8,5,7,1,6]=>[3,2,1,1,1]
[8,1,2,4,7,5,6,3]=>[4,1,1,1,1]
[6,4,5,8,3,1,7,2]=>[4,2,1,1]
[8,6,2,1,5,7,3,4]=>[4,2,1,1]
[4,6,2,8,5,3,7,1]=>[4,2,1,1]
[8,7,2,4,1,5,3,6]=>[4,2,1,1]
[7,5,3,4,8,6,2,1]=>[5,2,1]
[2,8,3,1,4,6,7,5]=>[3,2,1,1,1]
[4,3,6,5,1,2,7,8]=>[3,2,1,1,1]
[5,8,3,7,6,4,2,1]=>[6,1,1]
[1,3,8,7,6,5,2,4]=>[5,1,1,1]
[4,8,7,2,6,3,1,5]=>[5,1,1,1]
[1,8,7,2,6,3,5,4]=>[5,1,1,1]
[8,7,2,1,4,3,5,6]=>[4,2,1,1]
[2,8,7,1,6,3,4,5]=>[4,1,1,1,1]
[4,2,8,7,6,5,1,3]=>[5,2,1]
[1,2,5,7,4,8,6,3]=>[3,2,1,1,1]
[6,2,1,8,7,5,3,4]=>[4,3,1]
[6,3,8,7,4,5,2,1]=>[5,2,1]
[2,8,3,4,1,5,6,7]=>[3,1,1,1,1,1]
[1,3,7,5,4,8,6,2]=>[4,2,1,1]
[4,5,6,3,1,8,2,7]=>[3,2,1,1,1]
[5,2,1,4,3,6,8,7]=>[3,2,2,1]
[1,5,6,3,8,4,2,7]=>[3,2,1,1,1]
[2,6,5,3,8,4,1,7]=>[4,2,1,1]
[5,7,3,8,4,2,6,1]=>[4,2,1,1]
[5,3,6,2,8,4,1,7]=>[4,2,1,1]
[2,3,6,5,4,8,1,7]=>[4,1,1,1,1]
[3,7,5,4,8,2,6,1]=>[5,1,1,1]
[5,3,7,1,2,8,4,6]=>[3,2,1,1,1]
[6,3,8,7,2,5,4,1]=>[5,2,1]
[2,8,7,6,1,5,3,4]=>[5,1,1,1]
[6,8,4,1,7,5,2,3]=>[4,2,1,1]
[8,1,4,6,7,5,2,3]=>[4,1,1,1,1]
[2,6,8,1,4,7,5,3]=>[4,1,1,1,1]
[6,4,8,1,2,7,5,3]=>[4,2,1,1]
[8,1,4,6,7,2,5,3]=>[4,1,1,1,1]
[8,2,1,6,7,4,5,3]=>[4,2,1,1]
[4,2,8,1,6,7,5,3]=>[4,2,1,1]
[8,1,2,6,4,7,5,3]=>[4,2,1,1]
[8,4,1,6,2,7,5,3]=>[4,2,2]
[4,8,1,2,6,7,5,3]=>[4,1,1,1,1]
[4,8,2,1,6,7,5,3]=>[4,2,1,1]
[8,1,6,2,4,7,5,3]=>[4,2,1,1]
[8,2,4,6,1,7,5,3]=>[4,2,1,1]
[5,4,7,6,3,1,2,8]=>[4,2,1,1]
[3,6,4,8,1,5,2,7]=>[3,2,1,1,1]
[3,6,8,4,1,5,2,7]=>[3,2,1,1,1]
[8,7,1,4,2,3,5,6]=>[4,1,1,1,1]
[3,8,6,4,1,5,2,7]=>[4,2,1,1]
[8,2,6,5,7,1,3,4]=>[4,1,1,1,1]
[4,6,1,3,2,8,7,5]=>[3,3,1,1]
[7,1,4,8,2,3,6,5]=>[3,2,1,1,1]
[4,5,3,6,7,1,8,2]=>[3,2,1,1,1]
[1,4,7,8,3,5,2,6]=>[3,1,1,1,1,1]
[4,6,1,3,5,2,8,7]=>[3,2,1,1,1]
[2,5,1,4,8,3,7,6]=>[3,2,1,1,1]
[6,1,2,5,4,8,7,3]=>[4,2,1,1]
[8,4,1,7,3,5,6,2]=>[4,2,1,1]
[8,4,1,2,5,7,3,6]=>[3,2,1,1,1]
[2,4,5,6,8,3,1,7]=>[3,1,1,1,1,1]
[3,4,5,8,6,2,1,7]=>[4,1,1,1,1]
[4,5,1,8,6,3,7,2]=>[4,2,1,1]
[8,3,7,2,1,6,5,4]=>[5,2,1]
[8,4,7,6,2,5,1,3]=>[5,1,1,1]
[8,4,7,3,6,2,1,5]=>[5,1,1,1]
[3,8,7,5,6,4,1,2]=>[5,1,1,1]
[3,8,7,5,6,2,1,4]=>[5,1,1,1]
[3,8,7,5,6,2,4,1]=>[5,1,1,1]
[2,8,7,5,6,4,1,3]=>[5,1,1,1]
[1,5,6,3,8,2,7,4]=>[3,2,1,1,1]
[2,6,3,8,4,7,1,5]=>[3,2,1,1,1]
[2,6,3,5,7,8,1,4]=>[3,1,1,1,1,1]
[1,5,6,3,7,2,8,4]=>[3,2,1,1,1]
[1,7,5,3,6,2,8,4]=>[4,2,1,1]
[1,5,7,3,4,2,8,6]=>[3,2,1,1,1]
[1,5,8,3,4,2,7,6]=>[3,2,1,1,1]
[1,4,5,3,7,2,8,6]=>[3,2,1,1,1]
[1,4,5,3,8,2,7,6]=>[3,2,1,1,1]
[6,5,1,4,2,7,8,3]=>[4,2,1,1]
[6,5,1,4,2,8,7,3]=>[4,3,1]
[1,7,5,4,2,8,6,3]=>[4,3,1]
[5,1,6,8,3,7,2,4]=>[3,2,1,1,1]
[3,8,5,2,1,4,7,6]=>[4,2,1,1]
[3,5,4,8,2,6,7,1]=>[4,1,1,1,1]
[5,4,7,1,8,6,3,2]=>[4,3,1]
[1,4,8,2,6,5,3,7]=>[4,1,1,1,1]
[8,5,1,3,6,2,4,7]=>[4,1,1,1,1]
[5,2,8,1,7,4,3,6]=>[4,2,1,1]
[1,4,8,2,6,7,3,5]=>[3,1,1,1,1,1]
[1,2,5,6,8,7,3,4]=>[3,1,1,1,1,1]
[1,5,6,8,2,7,4,3]=>[4,1,1,1,1]
[2,6,7,3,4,1,8,5]=>[3,2,1,1,1]
[1,6,5,7,8,2,4,3]=>[4,1,1,1,1]
[1,5,6,7,2,8,4,3]=>[3,2,1,1,1]
[3,7,6,1,8,2,4,5]=>[3,2,1,1,1]
[1,3,7,2,6,4,8,5]=>[3,2,1,1,1]
[1,5,8,6,7,3,4,2]=>[4,1,1,1,1]
[1,6,5,8,7,2,4,3]=>[4,2,1,1]
[1,5,7,6,2,8,3,4]=>[3,2,1,1,1]
[1,2,5,8,6,7,4,3]=>[4,1,1,1,1]
[1,2,6,5,7,3,8,4]=>[3,2,1,1,1]
[1,7,5,8,6,4,2,3]=>[4,2,1,1]
[3,6,5,8,1,2,7,4]=>[3,2,1,1,1]
[5,4,7,8,1,6,3,2]=>[4,2,1,1]
[2,5,6,8,1,3,7,4]=>[3,1,1,1,1,1]
[5,3,6,8,1,2,7,4]=>[3,2,1,1,1]
[4,6,5,8,3,2,7,1]=>[5,1,1,1]
[4,5,6,8,2,3,7,1]=>[3,1,1,1,1,1]
[2,5,8,7,1,6,4,3]=>[5,1,1,1]
[4,7,5,8,3,6,2,1]=>[5,1,1,1]
[7,3,6,8,5,2,1,4]=>[5,1,1,1]
[8,3,6,7,5,2,4,1]=>[5,1,1,1]
[8,4,5,7,3,6,2,1]=>[5,1,1,1]
[2,4,7,8,5,6,3,1]=>[4,1,1,1,1]
[3,6,8,7,5,2,4,1]=>[5,1,1,1]
[6,4,7,8,5,1,3,2]=>[4,2,1,1]
[7,8,4,6,5,3,1,2]=>[5,1,1,1]
[6,8,4,7,5,1,3,2]=>[5,1,1,1]
[7,6,1,2,3,5,4,8]=>[4,1,1,1,1]
[2,8,7,5,1,6,3,4]=>[4,2,1,1]
[8,7,6,4,2,1,5,3]=>[6,2]
[3,8,7,5,2,6,4,1]=>[5,2,1]
[3,8,7,5,1,2,6,4]=>[4,2,1,1]
[5,8,3,7,1,4,6,2]=>[4,1,1,1,1]
[3,8,7,4,2,6,5,1]=>[5,2,1]
[5,8,3,2,4,7,6,1]=>[4,2,1,1]
[5,3,8,2,4,6,1,7]=>[4,1,1,1,1]
[4,5,8,3,2,6,1,7]=>[4,1,1,1,1]
[5,8,2,1,4,6,3,7]=>[3,2,1,1,1]
[4,1,5,8,3,6,2,7]=>[3,2,1,1,1]
[4,5,8,3,6,1,2,7]=>[3,1,1,1,1,1]
[3,2,7,1,8,5,4,6]=>[3,3,1,1]
[4,7,8,5,2,3,1,6]=>[4,1,1,1,1]
[6,2,7,8,1,5,3,4]=>[3,2,1,1,1]
[2,7,1,3,8,5,4,6]=>[3,2,1,1,1]
[2,6,7,8,4,1,3,5]=>[3,1,1,1,1,1]
[2,6,7,8,4,3,1,5]=>[4,1,1,1,1]
[7,1,2,6,3,8,4,5]=>[3,2,1,1,1]
[8,1,2,6,5,3,7,4]=>[4,2,1,1]
[7,4,1,8,2,5,3,6]=>[3,3,1,1]
[7,2,1,8,3,6,4,5]=>[3,3,1,1]
[7,4,8,3,1,2,6,5]=>[4,2,1,1]
[8,4,5,3,1,6,7,2]=>[4,2,1,1]
[8,2,1,7,4,3,5,6]=>[4,2,1,1]
[7,2,6,8,4,1,3,5]=>[4,1,1,1,1]
[7,2,5,1,6,8,3,4]=>[3,2,1,1,1]
[6,2,1,7,4,8,3,5]=>[3,3,1,1]
[1,7,4,3,2,5,6,8]=>[4,1,1,1,1]
[1,7,4,3,6,2,5,8]=>[4,1,1,1,1]
[3,7,5,8,2,4,6,1]=>[4,1,1,1,1]
[5,2,1,6,3,4,8,7]=>[3,2,2,1]
[5,1,3,4,6,2,8,7]=>[3,2,1,1,1]
[3,8,4,5,7,2,6,1]=>[4,1,1,1,1]
[3,8,4,7,5,6,2,1]=>[5,1,1,1]
[4,2,8,6,3,7,5,1]=>[4,2,2]
[4,1,7,6,3,8,5,2]=>[4,2,2]
[7,4,1,8,5,3,6,2]=>[4,3,1]
[3,5,6,8,4,7,1,2]=>[3,1,1,1,1,1]
[5,4,1,8,6,7,2,3]=>[3,3,1,1]
[6,2,8,4,5,3,7,1]=>[4,2,1,1]
[4,5,2,1,8,7,3,6]=>[3,3,1,1]
[4,7,3,8,2,6,5,1]=>[4,2,1,1]
[4,7,3,1,8,6,2,5]=>[3,3,1,1]
[6,2,1,3,7,4,8,5]=>[3,2,2,1]
[6,3,7,1,2,5,8,4]=>[3,2,1,1,1]
[5,1,4,7,8,2,6,3]=>[3,2,1,1,1]
[7,2,5,8,1,3,6,4]=>[3,2,1,1,1]
[8,3,6,7,2,4,5,1]=>[4,1,1,1,1]
[3,8,7,5,2,1,6,4]=>[5,2,1]
[3,8,5,6,2,7,4,1]=>[4,2,1,1]
[3,6,5,8,4,2,7,1]=>[5,1,1,1]
[6,8,3,2,5,7,4,1]=>[4,2,1,1]
[4,1,5,6,8,7,3,2]=>[4,2,1,1]
[8,4,2,3,6,7,5,1]=>[4,2,1,1]
[6,1,2,4,5,7,8,3]=>[3,1,1,1,1,1]
[4,5,1,3,7,6,8,2]=>[3,2,1,1,1]
[3,5,4,8,6,2,7,1]=>[4,2,1,1]
[3,6,2,4,5,8,7,1]=>[3,2,1,1,1]
[8,1,3,7,4,5,6,2]=>[4,1,1,1,1]
[8,1,5,3,6,4,7,2]=>[4,2,1,1]
[2,6,4,8,3,1,5,7]=>[4,1,1,1,1]
[2,6,4,1,5,8,7,3]=>[3,3,1,1]
[3,6,4,5,2,8,1,7]=>[4,1,1,1,1]
[8,1,5,4,7,3,6,2]=>[5,1,1,1]
[7,6,5,4,1,8,2,3]=>[5,2,1]
[3,6,4,1,5,7,2,8]=>[3,2,1,1,1]
[8,1,5,4,7,6,3,2]=>[5,2,1]
[2,5,1,4,6,7,3,8]=>[3,1,1,1,1,1]
[3,6,4,1,5,7,8,2]=>[3,2,1,1,1]
[7,6,5,2,8,4,1,3]=>[5,2,1]
[3,1,6,5,2,8,7,4]=>[3,3,2]
[1,7,2,4,3,5,8,6]=>[3,2,1,1,1]
[3,8,1,7,4,2,6,5]=>[4,2,1,1]
[8,1,7,4,3,5,6,2]=>[5,1,1,1]
[6,8,2,4,5,3,7,1]=>[4,1,1,1,1]
[4,8,5,3,6,1,7,2]=>[4,2,1,1]
[2,8,3,1,4,7,5,6]=>[3,2,1,1,1]
[8,6,3,2,7,4,1,5]=>[5,2,1]
[2,7,3,1,8,4,5,6]=>[3,2,1,1,1]
[1,2,8,3,5,6,4,7]=>[3,1,1,1,1,1]
[2,8,1,3,5,4,6,7]=>[3,1,1,1,1,1]
[1,5,2,8,6,4,3,7]=>[4,2,1,1]
[7,4,8,6,3,1,2,5]=>[4,2,1,1]
[3,6,8,4,1,2,5,7]=>[3,1,1,1,1,1]
[4,7,8,5,2,1,3,6]=>[4,1,1,1,1]
[6,1,5,2,8,7,3,4]=>[3,3,1,1]
[8,1,3,5,7,4,2,6]=>[4,1,1,1,1]
[3,1,8,5,4,7,2,6]=>[4,2,1,1]
[3,1,6,4,8,5,2,7]=>[3,2,2,1]
[5,1,3,4,2,6,8,7]=>[3,2,1,1,1]
[3,2,6,4,1,5,7,8]=>[3,2,1,1,1]
[5,4,2,1,8,3,6,7]=>[4,2,1,1]
[4,2,5,1,8,7,3,6]=>[3,3,1,1]
[6,8,2,7,1,4,3,5]=>[4,1,1,1,1]
[1,8,4,7,3,2,5,6]=>[4,1,1,1,1]
[8,6,3,1,5,7,2,4]=>[4,2,1,1]
[5,8,3,1,4,7,6,2]=>[4,2,1,1]
[1,2,5,4,7,8,3,6]=>[3,1,1,1,1,1]
[1,8,3,2,6,4,7,5]=>[3,2,2,1]
[4,7,1,2,5,3,6,8]=>[3,1,1,1,1,1]
[6,8,4,1,3,7,2,5]=>[4,1,1,1,1]
[3,2,6,1,7,8,5,4]=>[3,3,1,1]
[7,6,4,1,8,3,5,2]=>[5,2,1]
[5,4,1,6,7,3,2,8]=>[4,2,1,1]
[7,4,1,6,5,8,2,3]=>[4,2,1,1]
[8,5,4,1,6,7,3,2]=>[5,2,1]
[5,2,1,6,4,7,8,3]=>[3,3,1,1]
[1,6,2,3,5,7,8,4]=>[3,1,1,1,1,1]
[1,3,4,8,5,2,6,7]=>[3,1,1,1,1,1]
[8,2,4,6,1,7,3,5]=>[3,2,1,1,1]
[1,5,7,2,3,6,8,4]=>[3,1,1,1,1,1]
[7,3,1,4,2,5,8,6]=>[3,2,2,1]
[3,2,5,7,8,4,1,6]=>[3,2,1,1,1]
[4,3,5,1,6,2,7,8]=>[3,2,1,1,1]
[8,6,3,5,4,1,2,7]=>[5,1,1,1]
[8,3,2,6,1,5,4,7]=>[4,2,1,1]
[8,5,1,7,4,6,2,3]=>[4,2,1,1]
[4,8,1,7,6,3,5,2]=>[5,1,1,1]
[8,5,1,7,4,3,6,2]=>[5,2,1]
[8,5,7,6,2,1,3,4]=>[5,1,1,1]
[5,4,8,3,1,7,2,6]=>[4,2,1,1]
[5,1,4,8,3,2,7,6]=>[4,2,1,1]
[4,8,1,7,6,5,2,3]=>[5,1,1,1]
[4,3,8,7,2,6,1,5]=>[4,2,1,1]
[3,8,7,2,6,4,1,5]=>[5,1,1,1]
[8,2,5,7,4,3,6,1]=>[5,1,1,1]
[3,8,7,4,6,1,2,5]=>[4,1,1,1,1]
[8,7,6,3,5,4,1,2]=>[6,1,1]
[2,8,4,7,6,1,5,3]=>[5,1,1,1]
[2,5,4,8,3,1,7,6]=>[4,2,1,1]
[5,4,8,2,1,3,7,6]=>[4,2,1,1]
[3,8,7,2,6,1,5,4]=>[5,1,1,1]
[1,8,4,7,6,3,5,2]=>[5,1,1,1]
[1,8,3,7,6,5,2,4]=>[5,1,1,1]
[1,4,3,8,7,2,6,5]=>[4,2,1,1]
[7,1,5,4,6,2,3,8]=>[4,1,1,1,1]
[7,4,1,3,6,2,5,8]=>[4,1,1,1,1]
[5,4,3,1,7,6,2,8]=>[4,3,1]
[4,1,3,7,5,6,2,8]=>[3,2,1,1,1]
[2,6,8,3,1,7,4,5]=>[3,2,1,1,1]
[2,5,4,8,1,7,3,6]=>[3,2,1,1,1]
[7,2,6,5,8,3,4,1]=>[5,1,1,1]
[5,6,3,1,4,2,7,8]=>[3,2,1,1,1]
[2,6,5,3,4,8,7,1]=>[4,2,1,1]
[2,6,1,5,3,4,7,8]=>[3,1,1,1,1,1]
[3,4,7,8,5,1,6,2]=>[3,2,1,1,1]
[5,3,6,4,8,7,2,1]=>[4,2,2]
[1,5,4,8,6,2,7,3]=>[3,2,2,1]
[4,5,2,7,6,3,8,1]=>[4,2,1,1]
[7,6,2,5,3,8,4,1]=>[5,2,1]
[8,4,6,1,3,7,2,5]=>[4,1,1,1,1]
[4,8,5,1,2,3,6,7]=>[3,1,1,1,1,1]
[8,6,2,4,5,1,3,7]=>[4,1,1,1,1]
[4,5,1,3,8,6,2,7]=>[3,2,1,1,1]
[2,1,6,7,4,8,3,5]=>[3,2,1,1,1]
[7,8,3,1,6,2,5,4]=>[4,2,1,1]
[7,5,2,8,1,4,6,3]=>[4,2,1,1]
[6,7,8,2,5,4,3,1]=>[5,1,1,1]
[7,8,1,6,2,5,4,3]=>[5,1,1,1]
[5,1,6,8,3,4,7,2]=>[3,2,1,1,1]
[7,1,6,8,5,4,3,2]=>[6,1,1]
[5,6,8,1,2,3,7,4]=>[3,1,1,1,1,1]
[4,8,1,2,7,6,5,3]=>[5,1,1,1]
[4,6,1,2,8,5,7,3]=>[3,2,1,1,1]
[6,4,7,3,5,2,1,8]=>[5,1,1,1]
[5,7,8,4,2,1,3,6]=>[4,1,1,1,1]
[6,4,8,3,5,2,1,7]=>[5,1,1,1]
[3,1,6,2,5,7,8,4]=>[3,2,1,1,1]
[1,6,4,5,2,7,3,8]=>[3,2,1,1,1]
[1,4,7,3,2,5,6,8]=>[3,1,1,1,1,1]
[6,2,1,4,5,3,7,8]=>[3,2,1,1,1]
[1,2,4,6,8,3,7,5]=>[3,1,1,1,1,1]
[1,3,5,8,2,6,7,4]=>[3,1,1,1,1,1]
[6,1,3,7,2,8,5,4]=>[3,3,1,1]
[6,4,5,8,3,7,1,2]=>[4,1,1,1,1]
[8,1,4,3,6,7,2,5]=>[4,1,1,1,1]
[2,6,8,4,3,1,7,5]=>[4,2,1,1]
[8,1,5,2,6,4,3,7]=>[4,2,1,1]
[1,6,7,4,2,8,3,5]=>[3,2,1,1,1]
[1,7,8,4,3,6,2,5]=>[4,1,1,1,1]
[1,5,8,7,4,3,2,6]=>[5,1,1,1]
[1,4,7,2,3,6,8,5]=>[3,1,1,1,1,1]
[3,1,2,6,7,8,5,4]=>[3,2,1,1,1]
[3,8,1,6,4,2,7,5]=>[4,2,1,1]
[1,6,3,4,7,8,2,5]=>[3,1,1,1,1,1]
[3,1,5,7,6,2,8,4]=>[3,2,2,1]
[6,3,1,4,2,7,8,5]=>[3,2,2,1]
[2,4,3,7,6,1,8,5]=>[3,2,2,1]
[3,1,7,6,5,2,8,4]=>[4,2,2]
[1,4,7,6,8,3,2,5]=>[4,1,1,1,1]
[7,2,1,5,6,3,8,4]=>[3,2,2,1]
[4,3,1,8,6,2,7,5]=>[3,3,2]
[3,1,5,2,8,7,6,4]=>[4,2,2]
[1,2,8,4,3,7,6,5]=>[4,2,1,1]
[2,6,1,8,7,4,3,5]=>[4,2,1,1]
[7,5,1,8,3,2,6,4]=>[4,2,2]
[4,7,6,3,1,8,2,5]=>[4,2,1,1]
[5,3,1,8,6,2,4,7]=>[3,3,1,1]
[5,1,8,6,3,2,4,7]=>[4,2,1,1]
[1,5,4,2,8,6,3,7]=>[3,3,1,1]
[1,4,2,8,5,3,7,6]=>[3,2,2,1]
[8,3,1,6,4,2,5,7]=>[4,2,1,1]
[1,7,4,8,3,5,2,6]=>[4,1,1,1,1]
[7,3,2,4,8,5,1,6]=>[4,2,1,1]
[5,7,8,1,4,2,6,3]=>[3,2,1,1,1]
[2,6,3,8,1,7,5,4]=>[4,2,1,1]
[2,5,1,8,6,3,7,4]=>[3,2,2,1]
[2,8,6,4,1,7,3,5]=>[4,2,1,1]
[1,8,4,2,7,5,3,6]=>[4,2,1,1]
[6,5,1,7,2,8,4,3]=>[4,2,2]
[2,8,1,7,5,3,6,4]=>[4,2,1,1]
[1,2,8,7,6,4,3,5]=>[5,1,1,1]
[4,1,7,8,6,3,5,2]=>[4,2,1,1]
[1,6,5,7,8,4,2,3]=>[4,1,1,1,1]
[4,1,8,7,6,3,5,2]=>[5,2,1]
[4,8,2,6,3,5,1,7]=>[4,1,1,1,1]
[4,1,8,5,3,6,2,7]=>[4,2,1,1]
[3,1,5,8,2,7,4,6]=>[3,2,1,1,1]
[6,1,8,4,5,3,2,7]=>[4,2,1,1]
[6,3,8,4,5,1,7,2]=>[3,2,2,1]
[2,6,1,8,5,7,4,3]=>[4,2,1,1]
[6,3,8,4,5,2,1,7]=>[4,2,1,1]
[6,5,8,7,2,3,4,1]=>[4,2,1,1]
[6,3,8,4,5,2,7,1]=>[4,2,1,1]
[2,1,6,8,5,3,7,4]=>[3,2,2,1]
[6,5,8,7,4,1,2,3]=>[4,2,1,1]
[6,5,8,7,4,2,1,3]=>[5,2,1]
[6,5,8,7,2,4,1,3]=>[4,2,1,1]
[6,2,8,4,5,7,1,3]=>[3,2,1,1,1]
[6,1,8,4,5,7,3,2]=>[4,2,1,1]
[3,6,2,4,8,5,7,1]=>[3,2,1,1,1]
[2,7,5,4,3,8,6,1]=>[5,2,1]
[3,5,1,8,4,7,6,2]=>[4,2,1,1]
[3,6,1,8,5,4,7,2]=>[4,2,1,1]
[2,4,8,3,7,6,5,1]=>[5,1,1,1]
[3,6,8,2,5,7,4,1]=>[4,1,1,1,1]
[2,6,8,5,4,3,7,1]=>[5,1,1,1]
[3,6,8,2,5,4,7,1]=>[4,1,1,1,1]
[4,6,8,3,2,5,7,1]=>[4,1,1,1,1]
[4,6,2,8,3,5,7,1]=>[3,2,1,1,1]
[3,6,1,8,5,7,4,2]=>[4,2,1,1]
[5,2,6,8,4,1,7,3]=>[3,2,2,1]
[3,5,8,2,7,4,6,1]=>[4,1,1,1,1]
[2,6,8,5,7,4,3,1]=>[5,1,1,1]
[2,4,8,7,6,3,5,1]=>[5,1,1,1]
[7,5,1,6,3,2,8,4]=>[4,2,2]
[2,7,6,3,4,1,8,5]=>[4,2,1,1]
[5,7,6,3,1,2,8,4]=>[4,2,1,1]
[4,8,2,1,7,5,6,3]=>[4,2,1,1]
[6,3,8,5,7,2,4,1]=>[4,2,1,1]
[1,5,4,8,6,2,3,7]=>[3,2,1,1,1]
[8,2,1,7,5,3,6,4]=>[4,2,2]
[8,2,1,6,7,3,5,4]=>[4,2,1,1]
[6,2,8,1,7,5,3,4]=>[4,2,1,1]
[3,5,1,8,7,6,2,4]=>[4,2,1,1]
[4,7,3,5,6,1,2,8]=>[3,1,1,1,1,1]
[4,7,8,3,5,6,1,2]=>[3,1,1,1,1,1]
[3,2,5,6,8,4,7,1]=>[3,2,1,1,1]
[8,4,5,2,6,3,7,1]=>[4,2,1,1]
[2,5,6,4,8,3,7,1]=>[4,1,1,1,1]
[4,2,5,7,3,8,1,6]=>[3,2,1,1,1]
[4,7,3,1,6,8,2,5]=>[3,2,1,1,1]
[4,2,7,6,8,1,3,5]=>[3,2,1,1,1]
[1,7,4,6,8,3,2,5]=>[4,1,1,1,1]
[4,7,2,5,6,3,1,8]=>[4,1,1,1,1]
[5,4,1,3,7,8,2,6]=>[4,1,1,1,1]
[6,1,5,8,3,7,2,4]=>[4,1,1,1,1]
[4,1,3,5,7,8,2,6]=>[3,1,1,1,1,1]
[6,1,5,8,4,3,2,7]=>[5,1,1,1]
[7,2,1,6,8,3,5,4]=>[4,2,1,1]
[5,6,4,1,8,3,2,7]=>[4,2,1,1]
[1,2,6,7,4,3,5,8]=>[3,1,1,1,1,1]
[5,8,6,3,4,1,2,7]=>[4,1,1,1,1]
[6,2,3,1,8,5,4,7]=>[3,3,1,1]
[5,1,2,6,4,8,3,7]=>[3,2,1,1,1]
[8,6,2,3,7,5,1,4]=>[4,2,1,1]
[4,5,2,8,6,1,3,7]=>[3,2,1,1,1]
[3,4,8,2,5,6,1,7]=>[3,1,1,1,1,1]
[2,8,3,6,7,4,5,1]=>[4,1,1,1,1]
[6,8,2,7,5,3,1,4]=>[5,1,1,1]
[6,3,2,5,8,4,1,7]=>[4,2,1,1]
[5,6,7,2,8,4,1,3]=>[3,2,1,1,1]
[5,8,3,6,4,1,7,2]=>[4,2,1,1]
[4,3,8,5,2,7,1,6]=>[4,2,1,1]
[2,8,4,5,1,6,3,7]=>[3,2,1,1,1]
[2,5,8,1,3,4,7,6]=>[3,1,1,1,1,1]
[3,5,1,8,7,4,2,6]=>[4,2,1,1]
[4,6,1,3,8,2,7,5]=>[3,2,1,1,1]
[8,6,1,2,3,5,7,4]=>[4,1,1,1,1]
[5,1,7,8,3,2,4,6]=>[3,2,1,1,1]
[3,1,7,6,2,8,5,4]=>[4,2,2]
[5,3,6,7,4,2,8,1]=>[4,2,1,1]
[5,4,2,8,6,7,3,1]=>[4,3,1]
[6,1,4,2,8,7,3,5]=>[3,3,1,1]
[3,7,2,6,8,4,5,1]=>[4,1,1,1,1]
[4,6,5,2,7,8,3,1]=>[4,2,1,1]
[5,4,6,2,7,8,3,1]=>[4,2,1,1]
[5,1,8,6,4,2,7,3]=>[4,2,2]
[6,2,1,8,5,7,4,3]=>[4,3,1]
[5,4,6,2,3,1,8,7]=>[4,2,1,1]
[6,5,7,8,1,3,4,2]=>[4,1,1,1,1]
[2,1,7,6,8,4,5,3]=>[4,2,1,1]
[6,4,7,2,8,3,1,5]=>[4,2,1,1]
[6,3,2,7,8,4,5,1]=>[4,2,1,1]
[4,7,3,1,5,2,8,6]=>[3,2,2,1]
[2,1,4,7,5,3,8,6]=>[3,2,2,1]
[4,7,6,3,1,5,8,2]=>[4,2,1,1]
[2,7,3,1,8,5,4,6]=>[3,3,1,1]
[2,8,3,1,7,4,5,6]=>[3,2,1,1,1]
[1,5,6,8,3,2,4,7]=>[3,1,1,1,1,1]
[1,8,2,7,3,5,6,4]=>[4,1,1,1,1]
[1,7,4,8,6,5,3,2]=>[5,2,1]
[1,6,3,5,7,4,8,2]=>[4,1,1,1,1]
[1,5,4,7,2,8,3,6]=>[3,2,1,1,1]
[3,8,5,2,6,1,7,4]=>[4,2,1,1]
[3,7,4,8,5,2,6,1]=>[4,2,1,1]
[8,1,2,6,5,3,4,7]=>[4,1,1,1,1]
[3,7,4,2,5,6,1,8]=>[4,1,1,1,1]
[6,8,7,1,3,4,2,5]=>[4,1,1,1,1]
[3,4,2,8,6,7,5,1]=>[4,2,1,1]
[3,7,8,6,1,4,2,5]=>[4,1,1,1,1]
[3,6,1,5,2,7,8,4]=>[3,2,1,1,1]
[8,1,2,6,3,5,7,4]=>[4,1,1,1,1]
[6,2,8,4,7,1,3,5]=>[3,2,1,1,1]
[3,7,8,4,2,5,6,1]=>[4,1,1,1,1]
[3,4,2,8,5,1,6,7]=>[3,2,1,1,1]
[6,8,2,7,5,4,1,3]=>[5,1,1,1]
[1,8,4,3,7,6,2,5]=>[4,2,1,1]
[4,3,8,7,1,2,6,5]=>[4,2,1,1]
[1,8,4,5,7,6,2,3]=>[4,1,1,1,1]
[4,3,8,5,7,1,6,2]=>[4,2,1,1]
[6,3,4,8,7,2,1,5]=>[4,2,1,1]
[5,3,8,4,7,1,6,2]=>[4,2,1,1]
[5,2,8,7,1,4,6,3]=>[4,2,1,1]
[3,2,8,7,1,6,4,5]=>[4,2,1,1]
[2,7,8,3,1,6,4,5]=>[3,2,1,1,1]
[2,7,8,5,1,4,6,3]=>[4,1,1,1,1]
[3,5,8,7,4,1,6,2]=>[4,2,1,1]
[7,4,6,8,3,5,1,2]=>[4,1,1,1,1]
[2,7,8,1,3,6,4,5]=>[3,1,1,1,1,1]
[2,7,8,1,5,4,6,3]=>[4,1,1,1,1]
[2,7,8,1,4,5,6,3]=>[3,1,1,1,1,1]
[3,6,7,8,2,4,1,5]=>[3,1,1,1,1,1]
[4,5,7,8,6,3,1,2]=>[4,1,1,1,1]
[5,4,6,8,7,3,1,2]=>[4,2,1,1]
[4,5,8,6,7,1,3,2]=>[4,1,1,1,1]
[5,7,6,8,2,1,3,4]=>[4,1,1,1,1]
[3,7,6,8,2,4,1,5]=>[4,1,1,1,1]
[5,4,7,8,6,3,1,2]=>[4,2,1,1]
[4,5,7,8,2,6,1,3]=>[3,1,1,1,1,1]
[4,5,6,8,7,3,1,2]=>[4,1,1,1,1]
[6,1,5,3,8,4,7,2]=>[4,2,1,1]
[1,8,6,2,5,4,7,3]=>[5,1,1,1]
[3,8,4,1,7,5,2,6]=>[4,2,1,1]
[6,2,7,4,8,3,1,5]=>[4,2,1,1]
[2,8,5,1,4,3,7,6]=>[4,2,1,1]
[6,8,2,7,5,1,4,3]=>[5,1,1,1]
[8,3,4,5,6,1,7,2]=>[3,2,1,1,1]
[5,3,6,4,7,2,1,8]=>[4,2,1,1]
[4,2,6,5,7,3,1,8]=>[4,2,1,1]
[5,4,6,2,7,3,1,8]=>[4,2,1,1]
[3,2,6,5,8,4,1,7]=>[4,2,1,1]
[3,2,6,5,8,7,1,4]=>[3,2,2,1]
[4,2,6,5,8,7,1,3]=>[3,2,2,1]
[5,2,6,4,8,7,1,3]=>[3,2,2,1]
[5,4,7,6,8,2,1,3]=>[4,2,1,1]
[6,4,7,5,8,3,1,2]=>[4,2,1,1]
[4,2,7,5,8,6,1,3]=>[3,2,2,1]
[3,2,7,5,8,4,1,6]=>[4,2,1,1]
[4,3,7,2,8,5,1,6]=>[4,2,1,1]
[4,3,6,2,8,5,1,7]=>[4,2,1,1]
[4,3,7,6,8,5,1,2]=>[4,2,1,1]
[5,3,7,6,8,2,1,4]=>[4,2,1,1]
[5,3,7,2,8,6,1,4]=>[4,2,1,1]
[3,2,6,4,8,7,1,5]=>[3,2,2,1]
[4,2,7,3,8,6,1,5]=>[3,2,2,1]
[5,2,7,6,8,3,1,4]=>[4,2,1,1]
[3,2,7,6,8,4,1,5]=>[4,2,1,1]
[3,2,7,6,8,5,1,4]=>[4,2,1,1]
[6,2,7,5,8,4,1,3]=>[4,2,1,1]
[4,8,1,7,3,2,5,6]=>[4,1,1,1,1]
[3,7,4,8,2,1,5,6]=>[4,1,1,1,1]
[3,7,8,2,5,4,6,1]=>[4,1,1,1,1]
[4,7,5,8,3,2,6,1]=>[5,1,1,1]
[6,7,1,3,2,5,8,4]=>[3,2,1,1,1]
[8,7,6,4,1,5,3,2]=>[6,2]
[3,8,5,2,6,4,7,1]=>[4,2,1,1]
[7,2,5,3,4,8,1,6]=>[4,1,1,1,1]
[4,2,5,3,7,8,6,1]=>[3,2,2,1]
[5,3,6,2,4,1,8,7]=>[4,2,1,1]
[7,8,6,2,3,5,4,1]=>[5,1,1,1]
[5,8,2,6,3,7,4,1]=>[4,2,1,1]
[4,8,2,3,7,5,6,1]=>[4,1,1,1,1]
[7,5,6,2,3,8,4,1]=>[4,2,1,1]
[2,7,5,6,4,3,8,1]=>[5,1,1,1]
[2,8,4,3,7,5,6,1]=>[4,2,1,1]
[3,8,5,7,6,4,2,1]=>[6,1,1]
[7,8,6,3,5,4,2,1]=>[6,1,1]
[2,7,6,3,8,5,4,1]=>[5,2,1]
[7,4,2,5,6,3,8,1]=>[4,2,1,1]
[6,2,7,5,3,8,4,1]=>[4,2,2]
[2,4,8,3,7,5,6,1]=>[4,1,1,1,1]
[4,8,3,7,5,6,2,1]=>[5,1,1,1]
[6,2,5,8,3,7,4,1]=>[4,2,1,1]
[4,7,3,8,2,5,6,1]=>[4,1,1,1,1]
[8,2,5,6,3,7,4,1]=>[4,2,1,1]
[4,5,3,7,1,2,6,8]=>[3,1,1,1,1,1]
[8,5,6,4,1,3,2,7]=>[5,1,1,1]
[6,7,2,8,4,3,1,5]=>[4,2,1,1]
[6,7,3,2,8,4,1,5]=>[4,2,1,1]
[4,7,8,3,1,5,2,6]=>[3,2,1,1,1]
[4,5,8,1,3,2,6,7]=>[3,1,1,1,1,1]
[4,7,8,1,6,3,2,5]=>[4,1,1,1,1]
[4,7,1,3,8,6,5,2]=>[4,2,1,1]
[2,6,7,4,3,8,1,5]=>[4,1,1,1,1]
[3,7,6,4,5,8,1,2]=>[4,1,1,1,1]
[5,7,2,8,3,4,6,1]=>[3,2,1,1,1]
[3,7,2,8,5,6,4,1]=>[4,2,1,1]
[3,1,5,8,6,4,7,2]=>[4,2,1,1]
[2,3,8,6,4,7,5,1]=>[4,2,1,1]
[3,6,2,8,7,4,5,1]=>[4,2,1,1]
[2,5,6,1,8,7,3,4]=>[3,2,1,1,1]
[3,6,2,8,4,7,5,1]=>[4,2,1,1]
[2,3,8,5,7,4,6,1]=>[4,1,1,1,1]
[8,5,6,3,1,4,2,7]=>[4,2,1,1]
[8,3,5,1,6,4,2,7]=>[4,2,1,1]
[5,7,8,3,4,6,2,1]=>[4,1,1,1,1]
[3,5,1,8,6,4,2,7]=>[4,2,1,1]
[7,5,3,8,6,4,2,1]=>[5,3]
[5,1,3,8,6,4,2,7]=>[4,2,1,1]
[1,5,8,3,6,4,2,7]=>[4,1,1,1,1]
[7,5,8,3,6,4,2,1]=>[5,2,1]
[1,5,8,6,3,4,2,7]=>[4,1,1,1,1]
[3,7,5,8,2,6,4,1]=>[4,2,1,1]
[5,7,8,1,4,6,2,3]=>[3,1,1,1,1,1]
[1,3,7,8,4,2,6,5]=>[3,2,1,1,1]
[6,1,2,5,3,4,7,8]=>[3,1,1,1,1,1]
[5,1,4,6,7,3,2,8]=>[4,1,1,1,1]
[1,4,6,5,7,2,3,8]=>[3,1,1,1,1,1]
[6,7,3,5,4,1,2,8]=>[4,1,1,1,1]
[4,2,5,1,3,7,6,8]=>[3,2,1,1,1]
[1,3,2,6,8,4,7,5]=>[3,2,1,1,1]
[8,2,5,4,1,6,7,3]=>[4,2,1,1]
[8,1,7,5,4,2,6,3]=>[5,2,1]
[1,2,6,4,7,3,5,8]=>[3,1,1,1,1,1]
[1,6,4,3,7,2,5,8]=>[4,1,1,1,1]
[5,7,8,3,2,6,1,4]=>[4,1,1,1,1]
[8,4,5,1,3,7,6,2]=>[4,2,1,1]
[8,6,4,3,7,1,5,2]=>[5,2,1]
[7,5,6,8,1,3,2,4]=>[4,1,1,1,1]
[7,3,1,8,6,5,2,4]=>[4,3,1]
[2,7,3,1,4,8,6,5]=>[3,3,1,1]
[3,1,6,5,7,8,4,2]=>[4,2,1,1]
[4,3,1,5,8,7,6,2]=>[4,3,1]
[4,7,1,3,2,5,6,8]=>[3,1,1,1,1,1]
[4,1,6,7,3,2,8,5]=>[3,2,2,1]
[1,7,2,5,6,8,4,3]=>[4,1,1,1,1]
[4,7,6,8,3,1,5,2]=>[4,2,1,1]
[5,4,8,6,1,7,3,2]=>[4,2,2]
[3,5,4,7,1,8,6,2]=>[3,3,1,1]
[7,1,5,4,2,3,6,8]=>[4,1,1,1,1]
[7,1,3,6,4,5,2,8]=>[4,1,1,1,1]
[6,1,3,8,4,5,2,7]=>[3,2,1,1,1]
[5,8,6,3,1,2,7,4]=>[4,2,1,1]
[5,8,2,7,1,3,6,4]=>[4,1,1,1,1]
[2,6,5,4,1,3,7,8]=>[4,1,1,1,1]
[4,1,5,7,6,3,2,8]=>[4,2,1,1]
[6,3,4,2,1,8,7,5]=>[4,3,1]
[4,5,1,7,6,3,2,8]=>[4,2,1,1]
[5,4,2,1,8,7,3,6]=>[4,3,1]
[6,2,1,5,4,3,8,7]=>[4,2,2]
[1,4,2,6,7,8,5,3]=>[3,2,1,1,1]
[1,4,2,5,6,8,7,3]=>[3,2,1,1,1]
[2,5,3,6,7,8,4,1]=>[3,2,1,1,1]
[1,8,6,2,4,3,5,7]=>[4,1,1,1,1]
[2,3,4,7,5,8,6,1]=>[3,2,1,1,1]
[6,5,2,8,7,4,3,1]=>[5,3]
[7,8,5,4,2,1,6,3]=>[5,2,1]
[7,5,2,8,6,4,3,1]=>[5,3]
[7,8,3,2,6,5,4,1]=>[5,2,1]
[8,2,6,3,7,5,1,4]=>[4,2,1,1]
[8,6,7,2,5,3,1,4]=>[5,1,1,1]
[1,6,2,7,8,4,5,3]=>[3,2,1,1,1]
[8,6,2,7,5,4,1,3]=>[5,2,1]
[1,6,8,2,7,5,3,4]=>[4,1,1,1,1]
[7,6,3,2,8,1,5,4]=>[5,2,1]
[5,1,7,4,3,8,6,2]=>[4,2,2]
[8,6,3,7,2,4,1,5]=>[5,1,1,1]
[1,7,8,6,4,2,3,5]=>[4,1,1,1,1]
[7,2,8,6,4,1,3,5]=>[4,2,1,1]
[1,5,3,7,4,2,6,8]=>[3,2,1,1,1]
[1,7,6,3,4,2,5,8]=>[4,1,1,1,1]
[1,2,7,4,3,8,6,5]=>[3,3,1,1]
[1,5,4,2,3,8,7,6]=>[3,3,1,1]
[1,5,3,2,4,6,7,8]=>[3,1,1,1,1,1]
[1,5,4,2,3,7,8,6]=>[3,2,1,1,1]
[1,2,7,6,3,5,8,4]=>[4,1,1,1,1]
[8,1,3,2,6,5,7,4]=>[4,2,1,1]
[3,2,7,5,6,1,8,4]=>[3,2,2,1]
[7,5,6,1,3,2,8,4]=>[4,2,1,1]
[7,4,5,1,6,3,8,2]=>[4,2,1,1]
[7,5,6,1,4,3,8,2]=>[5,1,1,1]
[8,1,4,3,5,2,7,6]=>[4,2,1,1]
[8,3,6,5,4,1,2,7]=>[5,1,1,1]
[1,7,5,8,4,6,3,2]=>[5,1,1,1]
[6,5,7,1,2,8,3,4]=>[3,2,1,1,1]
[7,1,4,2,3,8,6,5]=>[3,3,1,1]
[3,7,5,6,8,1,2,4]=>[3,1,1,1,1,1]
[8,1,2,5,3,7,6,4]=>[4,2,1,1]
[8,6,5,2,4,1,7,3]=>[5,2,1]
[3,6,5,2,4,1,7,8]=>[4,1,1,1,1]
[6,8,5,2,4,3,1,7]=>[5,1,1,1]
[3,4,2,8,6,7,1,5]=>[3,2,1,1,1]
[4,6,7,2,5,1,8,3]=>[3,2,1,1,1]
[3,6,2,5,1,7,8,4]=>[3,2,1,1,1]
[3,4,2,7,8,1,5,6]=>[3,1,1,1,1,1]
[3,8,5,2,4,7,1,6]=>[4,1,1,1,1]
[7,1,4,2,5,8,6,3]=>[3,3,1,1]
[7,8,5,1,2,4,3,6]=>[4,1,1,1,1]
[5,8,1,4,3,6,7,2]=>[4,1,1,1,1]
[7,2,3,8,6,4,1,5]=>[4,2,1,1]
[5,2,3,8,7,4,1,6]=>[4,2,1,1]
[5,7,6,3,1,2,4,8]=>[4,1,1,1,1]
[4,6,2,7,8,1,3,5]=>[3,1,1,1,1,1]
[6,2,3,7,1,4,5,8]=>[3,1,1,1,1,1]
[4,6,7,8,2,1,3,5]=>[3,1,1,1,1,1]
[8,6,3,2,1,7,5,4]=>[5,3]
[5,3,4,1,7,8,2,6]=>[3,2,1,1,1]
[6,1,3,4,2,5,8,7]=>[3,2,1,1,1]
[5,1,3,6,2,4,8,7]=>[3,2,1,1,1]
[1,5,7,6,8,2,4,3]=>[4,1,1,1,1]
[5,7,1,3,8,4,2,6]=>[3,2,1,1,1]
[2,6,1,4,3,7,8,5]=>[3,2,1,1,1]
[1,6,2,4,3,5,8,7]=>[3,2,1,1,1]
[5,3,7,6,1,8,4,2]=>[4,2,2]
[1,5,6,3,7,8,4,2]=>[3,2,1,1,1]
[1,5,7,6,3,8,4,2]=>[4,2,1,1]
[7,3,5,6,1,8,4,2]=>[4,2,1,1]
[7,3,6,1,5,8,4,2]=>[5,1,1,1]
[1,6,3,7,8,5,4,2]=>[4,2,1,1]
[1,7,8,6,3,5,4,2]=>[5,1,1,1]
[3,7,5,6,1,8,4,2]=>[4,2,1,1]
[5,6,2,8,4,7,3,1]=>[4,2,1,1]
[5,7,6,3,4,8,1,2]=>[4,1,1,1,1]
[3,7,5,4,6,1,2,8]=>[4,1,1,1,1]
[5,3,4,7,6,8,1,2]=>[3,2,1,1,1]
[5,3,7,4,6,1,2,8]=>[3,2,1,1,1]
[7,3,5,4,6,1,2,8]=>[4,1,1,1,1]
[7,8,3,5,4,1,2,6]=>[4,1,1,1,1]
[7,3,5,4,1,2,6,8]=>[4,1,1,1,1]
[5,7,6,3,4,1,2,8]=>[4,1,1,1,1]
[3,5,4,1,2,7,6,8]=>[3,2,1,1,1]
[5,7,6,1,3,2,4,8]=>[4,1,1,1,1]
[5,3,4,1,2,7,6,8]=>[3,2,1,1,1]
[7,8,3,1,2,5,4,6]=>[3,2,1,1,1]
[7,8,5,1,3,2,4,6]=>[4,1,1,1,1]
[7,5,6,1,3,2,4,8]=>[4,1,1,1,1]
[7,5,1,3,8,6,2,4]=>[4,2,1,1]
[3,1,5,4,7,2,6,8]=>[3,2,1,1,1]
[5,7,6,1,3,8,2,4]=>[4,1,1,1,1]
[5,7,6,3,8,1,4,2]=>[4,2,1,1]
[5,1,3,7,6,2,4,8]=>[3,2,1,1,1]
[1,6,3,7,2,4,5,8]=>[3,1,1,1,1,1]
[5,3,2,4,8,1,7,6]=>[4,2,1,1]
[6,8,5,3,2,7,1,4]=>[5,1,1,1]
[8,3,7,2,6,5,1,4]=>[5,1,1,1]
[4,6,2,7,1,3,8,5]=>[3,2,1,1,1]
[3,4,6,5,1,8,7,2]=>[3,3,1,1]
[8,7,1,5,3,2,6,4]=>[5,2,1]
[3,5,1,4,7,2,8,6]=>[3,2,1,1,1]
[5,1,4,8,7,3,2,6]=>[4,2,1,1]
[6,1,3,4,2,7,8,5]=>[3,2,1,1,1]
[6,5,2,3,7,8,1,4]=>[4,1,1,1,1]
[1,5,3,8,4,2,7,6]=>[3,2,2,1]
[5,4,2,1,8,3,7,6]=>[4,3,1]
[3,1,7,4,2,6,8,5]=>[3,2,2,1]
[7,4,8,2,3,5,1,6]=>[4,1,1,1,1]
[8,4,1,3,2,6,7,5]=>[4,2,1,1]
[8,1,7,3,2,5,6,4]=>[4,2,1,1]
[8,6,5,2,7,3,1,4]=>[5,2,1]
[3,1,6,8,4,2,7,5]=>[3,2,2,1]
[1,5,2,8,3,6,7,4]=>[3,2,1,1,1]
[5,6,2,3,7,4,1,8]=>[3,2,1,1,1]
[6,2,4,7,3,5,1,8]=>[4,1,1,1,1]
[1,4,8,5,3,6,7,2]=>[4,1,1,1,1]
[2,5,6,3,1,8,4,7]=>[3,2,1,1,1]
[4,5,1,2,7,8,6,3]=>[3,2,1,1,1]
[4,8,5,1,2,6,7,3]=>[3,2,1,1,1]
[4,6,7,5,1,2,8,3]=>[3,2,1,1,1]
[7,2,8,1,4,5,3,6]=>[3,2,1,1,1]
[6,1,4,7,3,8,2,5]=>[4,1,1,1,1]
[7,1,6,3,4,8,2,5]=>[4,1,1,1,1]
[2,8,4,6,3,1,5,7]=>[4,1,1,1,1]
[8,2,6,3,5,1,4,7]=>[4,1,1,1,1]
[3,7,4,1,5,8,2,6]=>[3,2,1,1,1]
[3,8,4,1,7,2,5,6]=>[3,2,1,1,1]
[6,7,5,1,3,8,2,4]=>[4,1,1,1,1]
[8,5,1,3,6,7,2,4]=>[4,1,1,1,1]
[7,8,6,2,4,1,3,5]=>[4,1,1,1,1]
[8,2,4,1,3,6,7,5]=>[3,2,1,1,1]
[8,1,3,6,2,5,7,4]=>[4,1,1,1,1]
[1,5,6,3,8,4,7,2]=>[3,2,1,1,1]
[5,6,1,3,7,2,8,4]=>[3,2,1,1,1]
[5,6,1,8,2,3,7,4]=>[3,2,1,1,1]
[5,6,1,2,8,4,7,3]=>[3,2,1,1,1]
[3,7,8,1,6,4,2,5]=>[4,1,1,1,1]
[1,7,8,6,3,4,2,5]=>[4,1,1,1,1]
[1,7,3,8,6,4,2,5]=>[4,2,1,1]
[5,7,1,8,6,4,2,3]=>[4,2,1,1]
[7,8,1,5,6,4,2,3]=>[4,1,1,1,1]
[7,1,8,5,6,4,2,3]=>[4,2,1,1]
[7,1,5,8,6,4,2,3]=>[4,2,1,1]
[8,1,3,5,6,4,2,7]=>[4,1,1,1,1]
[1,3,8,5,6,4,2,7]=>[4,1,1,1,1]
[1,3,5,8,6,4,2,7]=>[4,1,1,1,1]
[1,5,7,8,6,4,2,3]=>[4,1,1,1,1]
[1,8,2,6,5,3,4,7]=>[4,1,1,1,1]
[8,6,1,5,2,3,4,7]=>[4,1,1,1,1]
[8,5,1,6,2,3,4,7]=>[3,2,1,1,1]
[7,6,1,2,3,8,4,5]=>[3,2,1,1,1]
[2,7,8,4,1,3,5,6]=>[3,1,1,1,1,1]
[6,8,1,2,3,7,4,5]=>[3,1,1,1,1,1]
[8,1,3,5,6,7,2,4]=>[3,1,1,1,1,1]
[8,1,2,5,3,4,7,6]=>[3,2,1,1,1]
[5,2,7,3,4,8,1,6]=>[3,2,1,1,1]
[8,6,4,7,3,5,2,1]=>[6,1,1]
[4,2,1,6,5,7,8,3]=>[3,3,1,1]
[2,7,5,4,1,3,6,8]=>[4,1,1,1,1]
[2,7,4,6,5,1,8,3]=>[4,2,1,1]
[6,8,7,5,2,1,4,3]=>[5,2,1]
[2,8,6,3,5,1,4,7]=>[4,1,1,1,1]
[1,2,8,6,4,5,3,7]=>[4,1,1,1,1]
[1,5,8,7,6,3,4,2]=>[5,1,1,1]
[1,6,4,8,5,7,3,2]=>[4,2,1,1]
[1,6,8,5,2,7,3,4]=>[3,2,1,1,1]
[1,6,8,5,4,2,3,7]=>[4,1,1,1,1]
[3,1,6,4,2,5,8,7]=>[3,2,2,1]
[5,4,2,3,6,8,1,7]=>[4,1,1,1,1]
[8,2,6,3,5,7,1,4]=>[4,1,1,1,1]
[3,1,7,8,6,2,5,4]=>[4,2,1,1]
[2,8,1,6,5,3,7,4]=>[4,2,1,1]
[2,1,5,7,6,3,8,4]=>[3,2,2,1]
[4,3,5,1,7,8,6,2]=>[3,3,1,1]
[1,8,5,2,3,4,7,6]=>[3,2,1,1,1]
[1,5,8,2,3,4,7,6]=>[3,1,1,1,1,1]
[1,2,7,8,4,5,6,3]=>[3,1,1,1,1,1]
[4,3,8,7,6,2,5,1]=>[5,2,1]
[5,4,8,2,7,6,3,1]=>[5,2,1]
[2,3,6,1,7,5,8,4]=>[3,2,1,1,1]
[4,6,5,2,1,7,8,3]=>[4,2,1,1]
[4,6,1,7,5,8,3,2]=>[4,2,1,1]
[4,1,5,7,6,8,3,2]=>[4,2,1,1]
[3,5,6,2,1,4,7,8]=>[3,1,1,1,1,1]
[4,3,6,5,1,7,8,2]=>[3,2,2,1]
[4,6,5,3,1,7,8,2]=>[4,2,1,1]
[5,8,1,4,2,3,6,7]=>[3,1,1,1,1,1]
[4,5,8,2,3,1,6,7]=>[3,1,1,1,1,1]
[3,5,4,8,1,7,2,6]=>[3,2,1,1,1]
[5,3,6,8,1,4,7,2]=>[3,2,1,1,1]
[3,5,1,8,6,4,7,2]=>[4,2,1,1]
[4,7,2,8,3,1,6,5]=>[3,2,2,1]
[1,2,5,6,8,3,7,4]=>[3,1,1,1,1,1]
[5,3,8,4,6,2,7,1]=>[4,2,1,1]
[7,4,8,1,5,2,6,3]=>[3,2,2,1]
[8,3,2,1,6,5,7,4]=>[4,3,1]
[4,1,5,6,8,7,2,3]=>[3,2,1,1,1]
[1,2,5,6,8,4,7,3]=>[3,1,1,1,1,1]
[1,5,6,8,4,7,2,3]=>[3,1,1,1,1,1]
[5,6,8,1,2,4,7,3]=>[3,1,1,1,1,1]
[6,8,1,4,5,7,2,3]=>[3,1,1,1,1,1]
[4,3,5,1,8,6,7,2]=>[3,3,1,1]
[1,3,5,6,8,4,7,2]=>[3,1,1,1,1,1]
[5,6,8,2,3,4,7,1]=>[3,1,1,1,1,1]
[6,5,1,2,4,8,7,3]=>[4,2,1,1]
[5,8,7,2,1,3,6,4]=>[4,2,1,1]
[5,1,7,2,8,6,3,4]=>[3,2,2,1]
[6,1,5,3,4,8,7,2]=>[4,2,1,1]
[5,8,6,3,2,1,4,7]=>[5,1,1,1]
[8,7,1,6,3,5,4,2]=>[6,1,1]
[3,2,1,7,8,6,4,5]=>[3,3,1,1]
[8,6,7,1,2,5,3,4]=>[4,1,1,1,1]
[1,5,6,4,2,8,7,3]=>[3,3,1,1]
[7,5,1,4,8,2,3,6]=>[4,1,1,1,1]
[3,2,8,1,7,5,6,4]=>[4,2,1,1]
[8,4,3,1,7,5,6,2]=>[4,3,1]
[6,1,7,8,4,2,3,5]=>[3,2,1,1,1]
[7,4,3,1,8,5,2,6]=>[4,3,1]
[7,8,1,6,3,4,5,2]=>[4,1,1,1,1]
[6,8,1,7,3,4,2,5]=>[4,1,1,1,1]
[4,6,5,3,8,2,7,1]=>[5,1,1,1]
[4,5,6,3,8,1,7,2]=>[3,2,1,1,1]
[7,8,3,5,2,1,6,4]=>[4,2,1,1]
[6,3,7,5,2,4,1,8]=>[4,2,1,1]
[6,2,4,5,7,3,1,8]=>[4,1,1,1,1]
[7,8,1,5,6,4,3,2]=>[5,1,1,1]
[6,3,7,5,1,4,2,8]=>[4,2,1,1]
[1,3,8,2,4,6,7,5]=>[3,1,1,1,1,1]
[6,1,7,3,4,2,5,8]=>[3,2,1,1,1]
[3,1,7,2,5,8,6,4]=>[3,2,2,1]
[2,8,7,6,3,5,1,4]=>[5,1,1,1]
[2,8,7,1,5,6,4,3]=>[5,1,1,1]
[3,5,6,2,8,1,7,4]=>[3,2,1,1,1]
[5,3,1,8,6,2,7,4]=>[3,3,2]
[3,1,4,6,8,2,7,5]=>[3,2,1,1,1]
[4,1,5,7,3,8,2,6]=>[3,2,1,1,1]
[6,2,5,8,4,7,3,1]=>[5,1,1,1]
[7,2,8,5,4,3,6,1]=>[5,2,1]
[7,1,6,8,2,5,3,4]=>[4,1,1,1,1]
[2,6,5,7,8,4,1,3]=>[4,1,1,1,1]
[3,6,5,7,4,1,8,2]=>[4,2,1,1]
[1,6,5,7,4,2,3,8]=>[4,1,1,1,1]
[3,4,7,5,2,1,8,6]=>[4,2,1,1]
[3,6,7,5,8,4,1,2]=>[4,1,1,1,1]
[3,4,7,2,5,6,8,1]=>[3,1,1,1,1,1]
[2,5,3,7,8,6,4,1]=>[4,2,1,1]
[7,2,8,4,5,6,3,1]=>[4,2,1,1]
[6,2,3,8,5,4,7,1]=>[4,2,1,1]
[6,8,7,3,2,4,5,1]=>[5,1,1,1]
[3,8,6,1,4,5,7,2]=>[4,1,1,1,1]
[7,5,8,6,4,1,3,2]=>[5,2,1]
[2,7,6,3,8,5,1,4]=>[4,2,1,1]
[2,3,1,8,4,6,5,7]=>[3,2,1,1,1]
[2,3,1,8,4,6,7,5]=>[3,2,1,1,1]
[4,2,3,5,1,8,6,7]=>[3,2,1,1,1]
[5,8,7,2,6,4,1,3]=>[5,1,1,1]
[6,8,5,1,7,4,3,2]=>[5,2,1]
[6,8,5,2,7,4,1,3]=>[4,2,1,1]
[7,3,8,6,5,2,1,4]=>[5,2,1]
[7,5,8,1,6,4,3,2]=>[5,2,1]
[7,5,8,2,6,4,1,3]=>[4,2,1,1]
[6,3,2,8,1,7,5,4]=>[4,3,1]
[2,6,8,7,1,3,5,4]=>[4,1,1,1,1]
[5,3,8,7,6,2,1,4]=>[5,2,1]
[3,7,6,1,4,5,2,8]=>[4,1,1,1,1]
[4,1,6,2,7,5,3,8]=>[3,2,2,1]
[7,6,2,5,3,1,4,8]=>[5,1,1,1]
[4,3,1,7,6,2,5,8]=>[3,3,1,1]
[4,5,3,1,2,8,6,7]=>[3,2,1,1,1]
[2,4,5,3,1,8,6,7]=>[3,2,1,1,1]
[5,7,6,2,3,1,4,8]=>[4,1,1,1,1]
[4,1,3,7,5,2,6,8]=>[3,2,1,1,1]
[4,1,6,3,2,7,5,8]=>[3,2,2,1]
[7,5,4,1,3,2,6,8]=>[5,1,1,1]
[2,4,8,5,6,3,1,7]=>[4,1,1,1,1]
[2,5,7,4,1,3,6,8]=>[3,1,1,1,1,1]
[5,7,4,1,3,2,6,8]=>[4,1,1,1,1]
[2,6,8,4,5,3,1,7]=>[4,1,1,1,1]
[5,2,3,7,4,1,6,8]=>[3,2,1,1,1]
[4,5,1,6,3,2,7,8]=>[3,2,1,1,1]
[5,1,6,3,2,4,7,8]=>[3,2,1,1,1]
[4,2,5,1,6,3,7,8]=>[3,2,1,1,1]
[5,1,6,2,4,3,7,8]=>[3,2,1,1,1]
[5,3,4,8,7,6,2,1]=>[5,2,1]
[8,3,1,6,7,5,4,2]=>[5,2,1]
[8,4,6,5,7,2,3,1]=>[5,1,1,1]
[1,8,2,6,7,4,5,3]=>[4,1,1,1,1]
[8,5,7,2,4,3,6,1]=>[5,1,1,1]
[8,5,3,6,4,7,2,1]=>[5,2,1]
[8,2,5,3,6,7,4,1]=>[4,2,1,1]
[1,2,8,3,4,7,6,5]=>[4,1,1,1,1]
[6,8,5,2,7,1,3,4]=>[4,1,1,1,1]
[7,6,4,5,2,1,8,3]=>[5,2,1]
[8,2,4,7,6,3,1,5]=>[5,1,1,1]
[7,3,8,5,4,2,1,6]=>[5,2,1]
[6,3,4,7,2,8,5,1]=>[4,2,1,1]
[8,1,7,3,6,4,2,5]=>[5,1,1,1]
[7,1,8,5,3,4,2,6]=>[4,2,1,1]
[6,8,4,3,1,5,2,7]=>[4,2,1,1]
[1,4,5,8,3,2,6,7]=>[3,1,1,1,1,1]
[1,5,2,4,7,8,6,3]=>[3,2,1,1,1]
[5,2,7,4,3,8,6,1]=>[4,2,2]
[2,7,3,4,8,5,6,1]=>[3,2,1,1,1]
[2,7,6,8,3,5,4,1]=>[5,1,1,1]
[2,7,4,5,3,8,6,1]=>[4,2,1,1]
[6,2,3,7,4,5,8,1]=>[3,2,1,1,1]
[1,6,3,2,7,5,8,4]=>[3,3,1,1]
[7,3,5,2,6,8,1,4]=>[4,1,1,1,1]
[6,4,2,7,1,5,8,3]=>[4,2,1,1]
[2,5,3,6,4,7,8,1]=>[3,2,1,1,1]
[4,2,5,3,6,7,8,1]=>[3,2,1,1,1]
[1,6,5,2,4,7,3,8]=>[4,1,1,1,1]
[1,8,7,2,4,6,3,5]=>[4,1,1,1,1]
[1,8,7,2,5,4,3,6]=>[5,1,1,1]
[1,5,4,2,7,3,6,8]=>[3,2,1,1,1]
[1,5,4,2,8,7,3,6]=>[3,3,1,1]
[1,6,8,3,5,2,4,7]=>[3,1,1,1,1,1]
[1,7,6,2,3,5,8,4]=>[4,1,1,1,1]
[1,2,8,3,6,5,4,7]=>[4,1,1,1,1]
[1,3,8,6,5,2,4,7]=>[4,1,1,1,1]
[1,4,7,3,2,8,6,5]=>[3,3,1,1]
[1,8,6,5,2,4,7,3]=>[5,1,1,1]
[1,6,8,4,3,2,5,7]=>[4,1,1,1,1]
[1,7,5,3,2,6,4,8]=>[4,2,1,1]
[1,2,6,5,3,8,4,7]=>[3,2,1,1,1]
[1,7,3,2,8,4,6,5]=>[3,3,1,1]
[1,6,5,2,8,4,7,3]=>[4,2,1,1]
[1,8,3,7,2,4,6,5]=>[4,1,1,1,1]
[5,4,2,8,7,6,1,3]=>[4,3,1]
[8,6,3,2,5,7,4,1]=>[5,2,1]
[7,3,2,1,6,5,8,4]=>[4,3,1]
[7,3,2,6,1,5,8,4]=>[4,2,1,1]
[6,8,5,2,7,1,4,3]=>[4,2,1,1]
[6,8,2,5,1,7,4,3]=>[4,2,1,1]
[6,8,5,7,2,1,4,3]=>[4,2,1,1]
[6,5,8,2,7,4,1,3]=>[4,2,1,1]
[6,2,1,7,5,8,4,3]=>[4,3,1]
[1,6,4,8,5,3,7,2]=>[4,2,1,1]
[1,6,5,3,4,7,8,2]=>[4,1,1,1,1]
[4,2,6,7,8,1,3,5]=>[3,1,1,1,1,1]
[4,6,5,1,3,7,8,2]=>[4,1,1,1,1]
[5,1,7,2,6,4,8,3]=>[4,2,1,1]
[4,1,7,6,5,8,2,3]=>[4,2,1,1]
[5,2,1,7,6,4,8,3]=>[4,3,1]
[4,2,3,6,7,8,1,5]=>[3,1,1,1,1,1]
[4,7,2,1,6,5,8,3]=>[4,2,1,1]
[2,7,6,4,1,5,8,3]=>[4,2,1,1]
[2,4,3,6,7,8,1,5]=>[3,1,1,1,1,1]
[6,8,5,2,7,3,1,4]=>[4,2,1,1]
[7,5,2,4,1,8,3,6]=>[4,2,1,1]
[6,5,1,3,7,8,2,4]=>[4,1,1,1,1]
[7,2,1,4,3,5,8,6]=>[3,2,2,1]
[6,1,2,4,3,7,8,5]=>[3,2,1,1,1]
[8,1,5,4,2,3,6,7]=>[4,1,1,1,1]
[7,1,2,4,6,3,8,5]=>[3,2,1,1,1]
[7,1,2,6,5,3,8,4]=>[4,2,1,1]
[7,5,6,1,2,4,8,3]=>[4,1,1,1,1]
[7,1,4,5,2,3,6,8]=>[3,1,1,1,1,1]
[6,1,4,8,7,2,3,5]=>[3,2,1,1,1]
[6,1,8,5,7,2,3,4]=>[3,2,1,1,1]
[1,6,7,5,8,3,4,2]=>[4,1,1,1,1]
[6,1,7,5,8,2,3,4]=>[3,2,1,1,1]
[6,1,4,7,8,2,3,5]=>[3,1,1,1,1,1]
[8,1,2,3,7,5,4,6]=>[4,1,1,1,1]
[5,8,6,1,2,4,7,3]=>[4,1,1,1,1]
[1,6,8,7,5,3,4,2]=>[5,1,1,1]
[6,1,8,7,5,2,3,4]=>[4,2,1,1]
[8,3,1,2,4,6,5,7]=>[3,2,1,1,1]
[8,3,1,2,4,5,7,6]=>[3,2,1,1,1]
[6,3,1,2,4,7,5,8]=>[3,2,1,1,1]
[6,7,1,4,2,3,5,8]=>[3,1,1,1,1,1]
[6,1,7,4,8,2,3,5]=>[3,2,1,1,1]
[6,7,8,5,1,2,4,3]=>[4,1,1,1,1]
[4,3,8,5,6,2,7,1]=>[4,2,1,1]
[4,3,8,6,7,2,5,1]=>[4,2,1,1]
[7,6,8,1,5,3,4,2]=>[5,1,1,1]
[7,4,6,1,5,3,8,2]=>[5,1,1,1]
[6,3,8,1,7,2,5,4]=>[4,2,1,1]
[6,1,5,4,8,2,7,3]=>[4,2,1,1]
[6,2,5,4,7,1,8,3]=>[4,2,1,1]
[8,3,6,7,5,1,2,4]=>[4,1,1,1,1]
[2,7,1,8,5,6,4,3]=>[4,2,1,1]
[4,6,8,2,3,5,1,7]=>[3,1,1,1,1,1]
[6,8,2,1,3,5,4,7]=>[3,2,1,1,1]
[3,5,1,6,4,8,2,7]=>[3,2,1,1,1]
[3,5,8,6,2,1,4,7]=>[4,1,1,1,1]
[2,4,8,5,6,1,3,7]=>[3,1,1,1,1,1]
[4,8,2,5,6,1,3,7]=>[3,1,1,1,1,1]
[5,3,8,4,2,7,6,1]=>[4,2,2]
[2,8,5,3,1,4,7,6]=>[4,2,1,1]
[1,7,8,4,6,3,2,5]=>[4,1,1,1,1]
[8,7,2,4,6,3,1,5]=>[5,1,1,1]
[8,7,3,2,1,6,4,5]=>[5,2,1]
[7,8,3,4,6,5,2,1]=>[5,1,1,1]
[8,7,3,6,5,2,4,1]=>[6,1,1]
[3,1,2,8,6,5,7,4]=>[4,2,1,1]
[3,8,2,7,5,4,6,1]=>[5,1,1,1]
[8,7,1,4,5,3,6,2]=>[5,1,1,1]
[2,8,7,4,6,3,5,1]=>[5,1,1,1]
[2,8,7,4,6,3,1,5]=>[5,1,1,1]
[8,3,4,1,2,5,7,6]=>[3,2,1,1,1]
[8,4,1,3,2,5,7,6]=>[4,2,1,1]
[7,3,8,6,2,1,4,5]=>[4,2,1,1]
[7,2,8,4,6,5,1,3]=>[4,2,1,1]
[5,8,6,4,7,2,3,1]=>[5,1,1,1]
[4,7,2,6,5,8,3,1]=>[5,1,1,1]
[3,6,8,5,7,4,2,1]=>[5,1,1,1]
[6,7,5,2,4,8,3,1]=>[5,1,1,1]
[8,1,2,7,5,6,3,4]=>[4,1,1,1,1]
[8,2,7,3,4,6,1,5]=>[4,1,1,1,1]
[6,7,5,4,8,1,3,2]=>[5,1,1,1]
[8,3,5,6,4,7,2,1]=>[5,1,1,1]
[8,5,6,2,4,3,7,1]=>[5,1,1,1]
[6,5,8,1,3,4,2,7]=>[4,1,1,1,1]
[6,8,4,5,1,3,2,7]=>[4,1,1,1,1]
[6,4,8,7,5,3,2,1]=>[6,2]
[6,7,1,4,3,2,8,5]=>[4,2,1,1]
[7,2,5,1,4,8,3,6]=>[4,1,1,1,1]
[5,8,1,3,4,2,7,6]=>[3,2,1,1,1]
[1,5,6,3,2,8,7,4]=>[3,3,1,1]
[1,3,7,6,8,4,2,5]=>[4,1,1,1,1]
[1,6,7,3,2,8,5,4]=>[3,3,1,1]
[3,2,7,6,8,4,5,1]=>[4,2,1,1]
[1,3,8,5,2,7,6,4]=>[4,2,1,1]
[6,4,1,5,2,8,7,3]=>[3,3,2]
[7,6,5,3,1,8,2,4]=>[5,2,1]
[2,5,1,4,7,3,6,8]=>[3,1,1,1,1,1]
[3,1,6,5,7,2,4,8]=>[3,2,1,1,1]
[2,6,1,5,7,4,8,3]=>[4,1,1,1,1]
[2,5,7,1,6,3,8,4]=>[3,2,1,1,1]
[2,6,1,5,7,4,3,8]=>[4,1,1,1,1]
[3,1,6,5,2,4,7,8]=>[3,2,1,1,1]
[3,6,5,1,4,2,7,8]=>[4,1,1,1,1]
[3,6,5,1,7,2,4,8]=>[3,2,1,1,1]
[3,6,5,2,1,4,7,8]=>[4,1,1,1,1]
[5,4,3,6,1,7,2,8]=>[4,2,1,1]
[4,5,2,7,6,1,3,8]=>[3,2,1,1,1]
[4,6,5,3,1,2,7,8]=>[4,1,1,1,1]
[5,4,1,6,3,7,2,8]=>[4,2,1,1]
[5,4,2,6,3,7,8,1]=>[4,2,1,1]
[3,6,5,7,1,4,2,8]=>[4,1,1,1,1]
[3,6,5,1,4,7,2,8]=>[4,1,1,1,1]
[4,3,6,5,7,1,2,8]=>[3,2,1,1,1]
[4,2,6,5,1,3,7,8]=>[3,2,1,1,1]
[4,1,6,5,3,7,8,2]=>[4,2,1,1]
[4,2,5,7,6,1,3,8]=>[3,2,1,1,1]
[3,4,7,6,1,2,5,8]=>[3,1,1,1,1,1]
[4,2,5,7,6,3,8,1]=>[4,2,1,1]
[4,1,6,5,2,7,3,8]=>[3,2,2,1]
[3,6,5,7,2,1,4,8]=>[4,1,1,1,1]
[3,5,7,6,2,4,1,8]=>[4,1,1,1,1]
[5,4,2,6,3,7,1,8]=>[4,2,1,1]
[4,6,5,2,7,3,1,8]=>[4,2,1,1]
[4,6,5,2,1,7,3,8]=>[4,2,1,1]
[3,5,8,2,1,4,6,7]=>[3,1,1,1,1,1]
[3,5,8,2,4,6,7,1]=>[3,1,1,1,1,1]
[5,3,8,2,1,4,6,7]=>[4,1,1,1,1]
[5,3,1,8,2,4,6,7]=>[3,2,1,1,1]
[5,1,3,8,2,4,6,7]=>[3,1,1,1,1,1]
[1,5,8,4,2,3,6,7]=>[3,1,1,1,1,1]
[5,8,2,1,4,3,6,7]=>[3,2,1,1,1]
[5,8,2,4,1,6,7,3]=>[3,2,1,1,1]
[5,8,2,4,6,3,1,7]=>[4,1,1,1,1]
[5,8,2,4,3,6,1,7]=>[4,1,1,1,1]
[5,8,1,4,6,2,3,7]=>[3,1,1,1,1,1]
[1,5,8,4,6,7,2,3]=>[3,1,1,1,1,1]
[5,1,8,4,6,7,2,3]=>[3,2,1,1,1]
[5,8,2,4,6,3,7,1]=>[4,1,1,1,1]
[3,8,4,6,7,2,1,5]=>[4,1,1,1,1]
[3,8,4,6,7,2,5,1]=>[4,1,1,1,1]
[8,4,3,6,7,2,5,1]=>[5,1,1,1]
[8,4,3,6,7,2,1,5]=>[5,1,1,1]
[8,6,2,4,5,3,7,1]=>[5,1,1,1]
[1,8,6,4,5,7,2,3]=>[4,1,1,1,1]
[8,6,2,4,5,3,1,7]=>[5,1,1,1]
[1,8,6,4,2,3,5,7]=>[4,1,1,1,1]
[3,8,1,6,2,4,5,7]=>[3,1,1,1,1,1]
[3,8,6,2,1,4,5,7]=>[4,1,1,1,1]
[3,8,6,2,4,1,5,7]=>[4,1,1,1,1]
[3,8,6,2,4,5,7,1]=>[4,1,1,1,1]
[8,3,6,2,4,5,1,7]=>[4,1,1,1,1]
[8,1,3,6,2,4,5,7]=>[3,1,1,1,1,1]
[8,3,6,7,2,1,4,5]=>[4,1,1,1,1]
[3,8,6,7,2,1,4,5]=>[4,1,1,1,1]
[8,2,6,4,5,1,7,3]=>[4,2,1,1]
[1,8,4,6,7,5,2,3]=>[4,1,1,1,1]
[8,4,6,2,3,7,5,1]=>[4,2,1,1]
[8,4,7,2,1,3,6,5]=>[4,2,1,1]
[2,7,1,6,3,5,8,4]=>[4,1,1,1,1]
[8,2,1,4,7,3,6,5]=>[4,2,1,1]
[1,6,2,5,8,4,7,3]=>[4,1,1,1,1]
[3,2,1,7,4,5,8,6]=>[3,2,2,1]
[2,6,8,5,1,7,4,3]=>[4,2,1,1]
[2,1,5,8,7,3,6,4]=>[4,2,1,1]
[3,2,1,6,7,4,8,5]=>[3,2,2,1]
[4,3,1,7,8,5,2,6]=>[3,3,1,1]
[5,6,8,2,4,3,7,1]=>[4,1,1,1,1]
[2,8,5,3,6,4,7,1]=>[4,2,1,1]
[1,2,8,6,4,7,3,5]=>[4,1,1,1,1]
[5,3,2,7,8,6,4,1]=>[4,3,1]
[4,2,7,8,3,5,6,1]=>[3,2,1,1,1]
[2,8,3,7,1,4,6,5]=>[4,1,1,1,1]
[2,8,7,1,5,3,6,4]=>[4,2,1,1]
[7,3,5,6,4,2,8,1]=>[5,1,1,1]
[3,8,4,2,7,6,5,1]=>[5,2,1]
[4,8,3,2,7,5,6,1]=>[4,2,1,1]
[3,2,4,8,7,5,6,1]=>[4,2,1,1]
[2,6,8,1,5,3,4,7]=>[3,1,1,1,1,1]
[3,2,5,6,8,1,4,7]=>[3,1,1,1,1,1]
[3,8,1,6,4,5,2,7]=>[4,1,1,1,1]
[8,1,3,6,5,4,2,7]=>[5,1,1,1]
[7,4,3,6,2,1,8,5]=>[5,2,1]
[1,2,4,8,6,3,7,5]=>[3,2,1,1,1]
[7,2,1,5,3,4,8,6]=>[3,2,2,1]
[5,7,2,3,1,4,8,6]=>[3,2,1,1,1]
[7,1,5,2,4,6,8,3]=>[4,1,1,1,1]
[8,4,2,7,3,5,6,1]=>[4,2,1,1]
[1,8,6,4,7,5,3,2]=>[5,2,1]
[7,4,1,5,8,6,3,2]=>[4,3,1]
[4,5,8,7,3,1,2,6]=>[4,1,1,1,1]
[1,3,8,7,6,4,2,5]=>[5,1,1,1]
[2,8,5,1,7,4,6,3]=>[4,2,1,1]
[1,8,6,4,7,5,2,3]=>[4,2,1,1]
[2,7,4,6,3,8,5,1]=>[4,2,1,1]
[1,2,8,6,4,7,5,3]=>[4,2,1,1]
[4,1,8,6,3,7,5,2]=>[4,2,2]
[8,4,3,1,6,2,5,7]=>[4,2,1,1]
[7,5,4,3,8,1,6,2]=>[5,2,1]
[5,3,1,6,2,8,7,4]=>[3,3,2]
[3,5,4,1,7,8,2,6]=>[3,2,1,1,1]
[6,4,2,1,5,7,3,8]=>[4,2,1,1]
[3,1,5,8,7,2,4,6]=>[3,2,1,1,1]
[3,2,5,7,8,4,6,1]=>[3,2,1,1,1]
[5,3,7,4,2,6,8,1]=>[4,2,1,1]
[5,3,7,4,2,6,1,8]=>[4,2,1,1]
[5,3,8,4,2,1,6,7]=>[4,2,1,1]
[5,2,8,4,3,1,6,7]=>[4,2,1,1]
[5,1,8,4,3,2,6,7]=>[4,2,1,1]
[5,2,7,4,3,6,1,8]=>[4,2,1,1]
[5,2,7,4,3,6,8,1]=>[4,2,1,1]
[5,3,7,4,1,6,8,2]=>[3,2,2,1]
[3,1,5,7,8,4,6,2]=>[3,2,1,1,1]
[3,1,5,7,8,4,2,6]=>[3,2,1,1,1]
[5,2,7,4,1,3,8,6]=>[3,2,2,1]
[6,2,3,7,4,8,5,1]=>[3,2,2,1]
[6,2,3,7,4,8,1,5]=>[3,2,1,1,1]
[6,2,3,7,4,5,1,8]=>[3,2,1,1,1]
[6,1,3,7,4,5,8,2]=>[3,2,1,1,1]
[1,2,8,6,4,3,5,7]=>[4,1,1,1,1]
[6,1,3,7,4,5,2,8]=>[3,2,1,1,1]
[1,8,6,3,5,4,2,7]=>[5,1,1,1]
[2,6,1,8,5,3,4,7]=>[3,2,1,1,1]
[4,5,7,8,1,6,3,2]=>[4,1,1,1,1]
[2,5,7,8,4,6,3,1]=>[4,1,1,1,1]
[1,8,2,7,5,3,4,6]=>[4,1,1,1,1]
[2,5,4,1,8,6,7,3]=>[3,3,1,1]
[7,3,5,1,4,8,6,2]=>[4,2,1,1]
[7,1,3,2,4,5,6,8]=>[3,1,1,1,1,1]
[3,8,7,1,4,2,5,6]=>[4,1,1,1,1]
[5,1,7,8,2,4,3,6]=>[3,2,1,1,1]
[8,5,4,6,1,7,3,2]=>[5,2,1]
[5,3,2,1,4,6,8,7]=>[4,2,1,1]
[5,3,2,4,8,1,6,7]=>[4,1,1,1,1]
[5,3,2,4,7,1,8,6]=>[4,2,1,1]
[8,4,5,3,7,1,2,6]=>[4,1,1,1,1]
[4,8,1,7,3,5,6,2]=>[4,1,1,1,1]
[5,3,2,4,6,8,1,7]=>[4,1,1,1,1]
[2,7,6,3,1,4,8,5]=>[4,2,1,1]
[3,7,4,5,6,8,2,1]=>[4,1,1,1,1]
[8,7,1,4,2,5,3,6]=>[4,2,1,1]
[4,6,8,3,7,1,5,2]=>[4,1,1,1,1]
[4,7,3,5,8,1,6,2]=>[3,2,1,1,1]
[8,4,3,5,7,1,6,2]=>[4,2,1,1]
[1,7,6,4,2,5,3,8]=>[4,2,1,1]
[7,6,4,2,8,3,1,5]=>[5,2,1]
[8,5,2,4,3,7,1,6]=>[5,1,1,1]
[8,5,1,4,3,7,6,2]=>[5,2,1]
[7,5,4,1,3,6,8,2]=>[5,1,1,1]
[3,6,7,2,5,1,8,4]=>[3,2,1,1,1]
[2,6,5,7,1,4,8,3]=>[4,1,1,1,1]
[3,5,1,7,8,4,6,2]=>[3,2,1,1,1]
[1,5,2,4,6,8,7,3]=>[3,2,1,1,1]
[8,1,2,4,7,6,5,3]=>[5,1,1,1]
[3,4,1,8,6,7,5,2]=>[4,2,1,1]
[4,3,8,5,1,7,6,2]=>[4,2,2]
[6,1,3,2,8,5,7,4]=>[3,3,1,1]
[8,5,3,2,4,7,1,6]=>[5,1,1,1]
[6,7,4,2,5,8,3,1]=>[4,2,1,1]
[8,5,4,2,6,3,1,7]=>[5,2,1]
[8,5,2,1,6,4,3,7]=>[4,3,1]
[8,4,6,5,1,3,2,7]=>[5,1,1,1]
[1,3,8,4,7,5,2,6]=>[4,1,1,1,1]
[5,3,7,1,4,6,8,2]=>[3,2,1,1,1]
[5,7,2,6,1,4,8,3]=>[4,1,1,1,1]
[3,8,5,7,6,1,2,4]=>[4,1,1,1,1]
[8,4,7,5,2,1,3,6]=>[5,1,1,1]
[3,8,6,4,7,2,1,5]=>[5,1,1,1]
[5,2,7,4,6,8,3,1]=>[4,2,1,1]
[4,8,6,3,7,2,1,5]=>[5,1,1,1]
[2,8,3,1,7,6,4,5]=>[4,2,1,1]
[2,5,6,4,8,1,7,3]=>[3,2,1,1,1]
[5,7,2,1,6,8,3,4]=>[3,2,1,1,1]
[4,7,8,5,1,6,2,3]=>[3,2,1,1,1]
[4,5,2,1,6,7,8,3]=>[3,2,1,1,1]
[4,5,6,3,1,7,8,2]=>[3,2,1,1,1]
[3,5,6,7,4,1,8,2]=>[3,2,1,1,1]
[3,5,1,4,2,8,7,6]=>[3,3,1,1]
[3,5,1,4,2,6,8,7]=>[3,2,1,1,1]
[3,5,1,4,2,6,7,8]=>[3,1,1,1,1,1]
[1,3,8,4,6,2,5,7]=>[3,1,1,1,1,1]
[1,8,4,2,3,7,5,6]=>[3,2,1,1,1]
[1,4,8,3,2,7,6,5]=>[4,2,1,1]
[1,3,7,6,5,2,4,8]=>[4,1,1,1,1]
[1,2,8,6,7,5,4,3]=>[5,1,1,1]
[1,7,5,4,3,2,6,8]=>[5,1,1,1]
[3,8,5,7,4,6,2,1]=>[5,1,1,1]
[7,6,3,2,5,1,8,4]=>[5,2,1]
[4,2,5,7,8,6,3,1]=>[4,2,1,1]
[6,7,2,4,5,1,8,3]=>[3,2,1,1,1]
[5,2,7,8,3,6,1,4]=>[3,2,1,1,1]
[2,4,7,8,1,3,6,5]=>[3,1,1,1,1,1]
[8,5,1,2,3,7,4,6]=>[3,2,1,1,1]
[5,2,8,3,1,4,7,6]=>[3,2,2,1]
[8,7,2,5,1,4,3,6]=>[5,1,1,1]
[8,4,1,3,2,7,6,5]=>[4,3,1]
[8,3,5,1,2,4,7,6]=>[3,2,1,1,1]
[8,7,4,5,1,2,6,3]=>[4,2,1,1]
[3,8,6,2,7,1,5,4]=>[4,2,1,1]
[3,4,8,2,1,7,6,5]=>[4,2,1,1]
[3,8,4,2,1,7,6,5]=>[4,3,1]
[8,4,1,7,5,2,6,3]=>[4,2,2]
[8,4,2,7,5,3,1,6]=>[5,2,1]
[8,5,7,6,4,3,1,2]=>[6,1,1]
[1,4,6,8,2,5,7,3]=>[3,1,1,1,1,1]
[7,3,8,2,4,6,1,5]=>[4,1,1,1,1]
[1,5,2,6,8,3,7,4]=>[3,2,1,1,1]
[4,5,3,1,8,2,6,7]=>[3,2,1,1,1]
[7,2,8,4,1,3,5,6]=>[3,2,1,1,1]
[6,1,7,3,2,8,4,5]=>[3,2,2,1]
[6,2,1,7,3,8,4,5]=>[3,2,2,1]
[5,8,2,1,3,4,6,7]=>[3,1,1,1,1,1]
[4,2,5,1,8,3,6,7]=>[3,2,1,1,1]
[7,4,2,8,3,1,5,6]=>[4,2,1,1]
[7,4,2,8,3,5,1,6]=>[4,2,1,1]
[6,7,8,5,2,1,4,3]=>[4,2,1,1]
[1,6,2,7,8,4,3,5]=>[3,2,1,1,1]
[7,3,4,1,8,6,2,5]=>[3,3,1,1]
[4,7,6,3,5,8,2,1]=>[5,1,1,1]
[3,7,6,5,2,4,8,1]=>[5,1,1,1]
[1,4,7,8,6,2,5,3]=>[4,1,1,1,1]
[1,6,7,8,3,2,5,4]=>[3,2,1,1,1]
[1,3,2,7,8,4,6,5]=>[3,2,1,1,1]
[6,8,2,3,5,7,4,1]=>[4,1,1,1,1]
[5,7,1,4,6,2,8,3]=>[3,2,1,1,1]
[6,3,1,4,7,8,2,5]=>[3,2,1,1,1]
[4,5,7,1,8,6,2,3]=>[3,2,1,1,1]
[4,3,8,6,5,2,7,1]=>[5,2,1]
[2,3,8,6,5,1,7,4]=>[4,2,1,1]
[5,4,7,3,1,2,6,8]=>[4,1,1,1,1]
[7,6,2,1,5,4,3,8]=>[5,2,1]
[3,1,2,6,5,7,8,4]=>[3,2,1,1,1]
[7,3,2,6,1,4,8,5]=>[4,2,1,1]
[3,2,5,6,8,4,1,7]=>[3,2,1,1,1]
[7,2,6,8,5,4,3,1]=>[6,1,1]
[3,7,5,6,2,4,1,8]=>[4,1,1,1,1]
[4,2,5,1,3,6,8,7]=>[3,2,1,1,1]
[5,3,4,2,7,1,8,6]=>[4,2,1,1]
[5,6,8,2,1,3,4,7]=>[3,1,1,1,1,1]
[6,5,2,1,3,8,4,7]=>[4,2,1,1]
[2,4,3,5,6,8,1,7]=>[3,1,1,1,1,1]
[6,3,2,4,8,5,1,7]=>[4,2,1,1]
[6,3,1,2,7,8,4,5]=>[3,2,1,1,1]
[8,4,7,1,2,5,3,6]=>[4,1,1,1,1]
[7,4,6,1,8,5,2,3]=>[4,2,1,1]
[8,5,6,7,2,1,4,3]=>[4,2,1,1]
[2,5,6,3,8,4,7,1]=>[3,2,1,1,1]
[6,8,4,2,3,1,7,5]=>[4,2,1,1]
[1,7,6,2,8,3,5,4]=>[4,2,1,1]
[7,1,5,6,3,2,8,4]=>[4,2,1,1]
[4,1,3,8,5,2,7,6]=>[3,2,2,1]
[1,8,5,4,7,2,3,6]=>[4,1,1,1,1]
[8,2,5,6,4,3,1,7]=>[5,1,1,1]
[2,4,3,8,6,5,1,7]=>[4,2,1,1]
[3,1,4,5,8,6,2,7]=>[3,2,1,1,1]
[1,8,3,2,5,4,6,7]=>[3,2,1,1,1]
[5,1,7,3,2,8,4,6]=>[3,2,2,1]
[5,7,8,1,3,2,4,6]=>[3,1,1,1,1,1]
[8,2,4,1,6,7,3,5]=>[3,2,1,1,1]
[8,7,3,6,2,4,1,5]=>[5,1,1,1]
[1,7,4,8,3,6,2,5]=>[4,1,1,1,1]
[7,8,6,1,3,5,4,2]=>[5,1,1,1]
[1,7,5,8,4,3,2,6]=>[5,1,1,1]
[6,3,1,2,7,8,5,4]=>[3,3,1,1]
[8,2,7,5,3,4,1,6]=>[5,1,1,1]
[6,3,1,2,8,7,5,4]=>[4,3,1]
[8,4,7,2,6,3,1,5]=>[5,1,1,1]
[7,6,3,4,2,1,8,5]=>[5,2,1]
[8,4,6,2,3,7,1,5]=>[4,1,1,1,1]
[3,4,5,8,1,7,2,6]=>[3,1,1,1,1,1]
[6,3,4,2,7,8,1,5]=>[4,1,1,1,1]
[5,6,3,7,8,2,1,4]=>[4,1,1,1,1]
[8,6,3,4,7,2,1,5]=>[5,1,1,1]
[4,3,8,6,7,5,1,2]=>[4,2,1,1]
[4,5,6,2,7,8,3,1]=>[3,2,1,1,1]
[4,5,6,2,7,1,8,3]=>[3,2,1,1,1]
[4,5,6,2,1,7,8,3]=>[3,2,1,1,1]
[4,5,6,2,1,7,3,8]=>[3,2,1,1,1]
[6,8,7,2,3,1,4,5]=>[4,1,1,1,1]
[4,5,1,6,7,3,2,8]=>[3,2,1,1,1]
[2,5,1,8,3,7,4,6]=>[3,2,1,1,1]
[5,7,2,1,3,8,4,6]=>[3,2,1,1,1]
[3,7,5,4,1,6,8,2]=>[4,2,1,1]
[7,1,5,4,2,6,3,8]=>[4,2,1,1]
[8,5,6,3,7,2,1,4]=>[5,1,1,1]
[2,7,4,5,6,8,1,3]=>[3,1,1,1,1,1]
[2,3,4,6,8,1,7,5]=>[3,1,1,1,1,1]
[2,3,5,8,1,6,7,4]=>[3,1,1,1,1,1]
[2,4,7,5,6,8,1,3]=>[3,1,1,1,1,1]
[7,3,4,6,2,8,1,5]=>[4,1,1,1,1]
[4,7,6,5,2,8,3,1]=>[5,2,1]
[2,5,4,8,6,7,3,1]=>[4,2,1,1]
[7,5,4,1,6,8,2,3]=>[4,2,1,1]
[8,5,2,1,7,6,3,4]=>[4,3,1]
[2,7,3,6,4,1,8,5]=>[4,2,1,1]
[7,2,1,8,5,6,4,3]=>[4,3,1]
[3,6,5,1,4,8,2,7]=>[4,1,1,1,1]
[6,3,5,4,8,1,2,7]=>[4,1,1,1,1]
[2,5,1,4,6,3,8,7]=>[3,2,1,1,1]
[3,1,5,6,4,2,8,7]=>[3,2,2,1]
[8,5,6,4,3,1,7,2]=>[5,2,1]
[8,3,5,6,7,1,2,4]=>[3,1,1,1,1,1]
[2,1,4,7,3,6,8,5]=>[3,2,1,1,1]
[5,3,7,6,4,8,2,1]=>[5,2,1]
[3,7,6,4,2,8,1,5]=>[5,1,1,1]
[8,6,1,4,3,7,2,5]=>[5,1,1,1]
[8,4,7,5,1,6,3,2]=>[5,2,1]
[2,1,5,3,7,8,6,4]=>[3,2,2,1]
[5,1,4,7,6,8,2,3]=>[3,2,1,1,1]
[8,4,1,3,7,6,5,2]=>[5,2,1]
[8,3,4,1,6,7,5,2]=>[4,2,1,1]
[8,1,4,2,6,5,7,3]=>[4,2,1,1]
[8,6,4,3,7,2,1,5]=>[6,1,1]
[5,8,1,4,3,2,6,7]=>[4,1,1,1,1]
[5,6,4,3,8,2,7,1]=>[5,1,1,1]
[1,6,4,3,8,2,7,5]=>[4,2,1,1]
[6,7,4,1,3,2,5,8]=>[4,1,1,1,1]
[7,8,1,4,3,2,5,6]=>[4,1,1,1,1]
[7,1,8,4,5,3,6,2]=>[4,2,1,1]
[4,3,1,8,6,5,7,2]=>[4,3,1]
[4,3,2,7,5,1,8,6]=>[4,2,2]
[5,2,3,7,4,1,8,6]=>[3,2,2,1]
[2,1,7,4,3,6,8,5]=>[3,2,2,1]
[7,1,2,4,5,6,8,3]=>[3,1,1,1,1,1]
[2,8,7,1,4,5,6,3]=>[4,1,1,1,1]
[8,7,1,3,4,5,6,2]=>[4,1,1,1,1]
[5,8,3,1,4,6,7,2]=>[3,2,1,1,1]
[1,7,2,5,4,6,8,3]=>[4,1,1,1,1]
[2,5,3,8,1,6,7,4]=>[3,2,1,1,1]
[1,6,4,2,5,7,8,3]=>[3,2,1,1,1]
[6,5,3,4,1,7,8,2]=>[4,2,1,1]
[5,6,3,4,1,7,8,2]=>[3,2,1,1,1]
[2,5,3,1,4,7,8,6]=>[3,2,1,1,1]
[6,8,2,3,1,5,7,4]=>[3,2,1,1,1]
[4,3,1,5,2,7,8,6]=>[3,2,2,1]
[5,2,3,1,4,7,8,6]=>[3,2,1,1,1]
[7,2,1,3,5,6,8,4]=>[3,2,1,1,1]
[5,2,4,7,8,6,3,1]=>[4,2,1,1]
[5,4,8,7,2,3,1,6]=>[4,2,1,1]
[8,1,4,5,3,6,2,7]=>[4,1,1,1,1]
[8,3,5,1,4,6,2,7]=>[4,1,1,1,1]
[5,8,2,1,7,4,3,6]=>[4,2,1,1]
[6,5,7,2,1,8,4,3]=>[4,3,1]
[1,5,4,7,3,8,6,2]=>[4,2,1,1]
[7,4,1,3,8,5,6,2]=>[4,2,1,1]
[3,6,8,4,1,7,2,5]=>[3,2,1,1,1]
[2,1,8,4,7,6,3,5]=>[4,2,1,1]
[2,7,5,6,8,4,3,1]=>[5,1,1,1]
[3,5,2,4,7,8,6,1]=>[3,2,1,1,1]
[7,5,6,3,8,2,1,4]=>[5,1,1,1]
[1,6,2,7,4,5,8,3]=>[3,2,1,1,1]
[7,4,2,6,1,5,8,3]=>[4,2,1,1]
[8,4,1,6,2,5,7,3]=>[4,2,1,1]
[7,3,4,5,1,6,8,2]=>[3,2,1,1,1]
[8,4,2,7,6,1,5,3]=>[5,2,1]
[8,4,7,1,2,6,5,3]=>[5,1,1,1]
[8,4,7,6,1,2,5,3]=>[5,1,1,1]
[8,7,6,2,1,5,3,4]=>[5,2,1]
[5,7,8,1,6,2,4,3]=>[4,1,1,1,1]
[6,8,4,7,5,2,1,3]=>[5,1,1,1]
[6,8,2,7,1,5,4,3]=>[5,1,1,1]
[6,8,7,4,2,5,1,3]=>[5,1,1,1]
[6,8,4,5,7,2,1,3]=>[4,1,1,1,1]
[6,8,4,2,5,1,3,7]=>[4,1,1,1,1]
[2,5,3,7,6,4,8,1]=>[4,2,1,1]
[3,1,5,7,6,4,2,8]=>[4,2,1,1]
[3,1,6,5,4,7,2,8]=>[4,2,1,1]
[2,5,6,8,3,4,7,1]=>[3,1,1,1,1,1]
[4,1,3,6,5,2,7,8]=>[3,2,1,1,1]
[3,6,2,4,5,7,1,8]=>[3,1,1,1,1,1]
[3,6,2,5,4,7,1,8]=>[4,1,1,1,1]
[3,5,1,7,6,4,2,8]=>[4,2,1,1]
[3,6,1,4,5,7,2,8]=>[3,1,1,1,1,1]
[4,3,1,6,5,2,7,8]=>[3,3,1,1]
[4,1,2,6,5,3,7,8]=>[3,2,1,1,1]
[4,6,1,3,5,2,7,8]=>[3,1,1,1,1,1]
[3,6,4,2,5,7,1,8]=>[4,1,1,1,1]
[4,2,6,3,5,1,7,8]=>[3,2,1,1,1]
[3,4,7,6,5,1,2,8]=>[4,1,1,1,1]
[4,5,2,7,1,3,6,8]=>[3,1,1,1,1,1]
[4,6,1,2,5,3,7,8]=>[3,1,1,1,1,1]
[5,8,4,7,1,3,6,2]=>[4,1,1,1,1]
[6,4,7,1,3,5,2,8]=>[4,1,1,1,1]
[6,8,1,3,5,7,4,2]=>[4,1,1,1,1]
[5,8,3,2,7,4,6,1]=>[4,2,1,1]
[6,8,3,1,5,4,7,2]=>[4,2,1,1]
[6,8,1,2,5,3,7,4]=>[3,2,1,1,1]
[5,2,8,3,4,6,7,1]=>[3,2,1,1,1]
[5,2,7,1,6,4,8,3]=>[4,2,1,1]
[4,5,2,6,1,3,7,8]=>[3,1,1,1,1,1]
[4,3,5,8,6,1,7,2]=>[3,2,2,1]
[5,1,3,6,7,4,2,8]=>[3,2,1,1,1]
[4,2,8,3,6,7,5,1]=>[4,2,1,1]
[3,1,7,8,5,6,2,4]=>[3,2,1,1,1]
[6,2,1,7,5,3,4,8]=>[3,3,1,1]
[3,7,1,8,5,2,4,6]=>[3,2,1,1,1]
[4,2,8,6,7,1,3,5]=>[3,2,1,1,1]
[6,1,2,4,7,3,5,8]=>[3,1,1,1,1,1]
[5,3,1,6,4,7,2,8]=>[3,3,1,1]
[1,2,4,5,8,7,3,6]=>[3,1,1,1,1,1]
[1,3,4,7,5,8,6,2]=>[3,2,1,1,1]
[1,5,2,3,7,8,6,4]=>[3,2,1,1,1]
[4,2,8,1,6,5,7,3]=>[4,2,1,1]
[5,6,1,4,8,3,2,7]=>[4,1,1,1,1]
[3,6,4,1,7,2,8,5]=>[3,2,2,1]
[5,2,6,3,7,8,4,1]=>[3,2,2,1]
[2,4,1,3,7,8,6,5]=>[3,2,1,1,1]
[2,6,1,5,7,8,4,3]=>[4,1,1,1,1]
[5,1,6,4,7,8,2,3]=>[3,2,1,1,1]
[8,4,6,3,7,5,1,2]=>[4,2,1,1]
[4,7,6,8,2,3,5,1]=>[4,1,1,1,1]
[5,7,4,8,1,2,6,3]=>[3,2,1,1,1]
[3,6,7,5,8,1,4,2]=>[4,1,1,1,1]
[3,7,5,6,8,2,4,1]=>[4,1,1,1,1]
[2,7,1,6,8,4,5,3]=>[4,1,1,1,1]
[1,5,4,7,2,6,3,8]=>[3,2,1,1,1]
[2,4,5,8,3,1,7,6]=>[3,2,1,1,1]
[1,4,7,5,8,3,6,2]=>[4,1,1,1,1]
[2,6,8,7,3,5,1,4]=>[4,1,1,1,1]
[4,7,8,6,2,5,1,3]=>[4,1,1,1,1]
[4,8,7,3,5,6,2,1]=>[5,1,1,1]
[1,7,6,3,5,4,2,8]=>[5,1,1,1]
[4,3,8,1,6,5,7,2]=>[4,2,1,1]
[1,3,6,2,5,8,7,4]=>[3,2,1,1,1]
[5,8,7,1,4,6,3,2]=>[5,1,1,1]
[5,7,1,4,3,2,6,8]=>[4,1,1,1,1]
[7,8,5,3,2,1,6,4]=>[5,2,1]
[1,2,6,7,8,4,5,3]=>[3,1,1,1,1,1]
[6,1,4,8,2,7,5,3]=>[4,2,1,1]
[5,2,3,7,1,8,4,6]=>[3,2,1,1,1]
[7,2,3,1,8,4,6,5]=>[3,3,1,1]
[7,3,4,5,1,8,6,2]=>[3,3,1,1]
[1,5,6,7,4,8,2,3]=>[3,1,1,1,1,1]
[6,3,2,5,7,4,8,1]=>[4,2,1,1]
[5,7,3,8,1,2,4,6]=>[3,1,1,1,1,1]
[4,5,2,7,6,3,1,8]=>[4,2,1,1]
[4,5,2,1,7,6,3,8]=>[3,3,1,1]
[2,6,7,8,3,1,4,5]=>[3,1,1,1,1,1]
[6,3,2,5,1,7,8,4]=>[4,2,1,1]
[4,6,3,7,8,2,1,5]=>[4,1,1,1,1]
[5,6,7,1,8,4,2,3]=>[3,2,1,1,1]
[1,7,8,4,6,5,2,3]=>[4,1,1,1,1]
[1,7,3,2,8,6,5,4]=>[4,3,1]
[3,7,1,2,8,6,5,4]=>[4,2,1,1]
[2,7,8,1,6,5,3,4]=>[4,1,1,1,1]
[8,1,5,7,3,4,6,2]=>[4,1,1,1,1]
[2,8,4,7,6,3,1,5]=>[5,1,1,1]
[1,8,2,4,7,6,3,5]=>[4,1,1,1,1]
[4,5,8,7,1,6,2,3]=>[4,1,1,1,1]
[1,8,2,4,6,7,5,3]=>[4,1,1,1,1]
[3,4,2,8,1,7,6,5]=>[4,2,1,1]
[2,4,5,8,1,7,6,3]=>[4,1,1,1,1]
[3,1,8,2,6,7,5,4]=>[4,2,1,1]
[2,6,8,1,4,3,7,5]=>[3,2,1,1,1]
[4,1,8,2,6,7,3,5]=>[3,2,1,1,1]
[1,6,5,2,8,7,3,4]=>[3,3,1,1]
[2,6,1,5,8,7,3,4]=>[3,2,1,1,1]
[8,1,7,3,5,2,4,6]=>[4,1,1,1,1]
[8,1,3,2,7,6,4,5]=>[4,2,1,1]
[7,3,4,8,6,2,5,1]=>[4,2,1,1]
[7,5,8,1,6,2,3,4]=>[3,2,1,1,1]
[6,8,4,5,3,1,7,2]=>[4,2,1,1]
[6,7,5,3,2,8,4,1]=>[5,2,1]
[6,2,5,3,8,1,4,7]=>[4,1,1,1,1]
[7,6,1,3,5,2,4,8]=>[4,1,1,1,1]
[6,2,4,5,3,8,1,7]=>[4,1,1,1,1]
[6,1,5,4,7,2,3,8]=>[4,1,1,1,1]
[6,8,5,4,7,1,3,2]=>[5,1,1,1]
[1,6,8,4,2,5,7,3]=>[3,2,1,1,1]
[7,5,8,1,3,4,2,6]=>[4,1,1,1,1]
[1,4,2,8,3,5,7,6]=>[3,2,1,1,1]
[1,3,5,4,8,7,2,6]=>[3,2,1,1,1]
[1,6,2,4,8,3,7,5]=>[3,2,1,1,1]
[1,7,8,5,4,2,6,3]=>[4,2,1,1]
[1,5,2,8,6,4,7,3]=>[4,2,1,1]
[1,6,5,2,7,4,8,3]=>[4,2,1,1]
[5,1,6,7,4,2,8,3]=>[3,2,2,1]
[1,5,4,2,8,6,7,3]=>[3,3,1,1]
[1,7,5,4,6,2,8,3]=>[4,2,1,1]
[5,8,4,1,6,2,7,3]=>[3,2,2,1]
[4,8,1,3,7,6,2,5]=>[4,1,1,1,1]
[4,5,3,1,2,8,7,6]=>[3,3,1,1]
[6,4,2,3,1,8,7,5]=>[4,3,1]
[6,5,2,1,3,8,7,4]=>[4,3,1]
[7,6,1,8,2,5,3,4]=>[4,2,1,1]
[8,4,2,3,7,6,1,5]=>[4,2,1,1]
[5,7,8,1,2,4,3,6]=>[3,1,1,1,1,1]
[1,7,6,8,3,5,4,2]=>[5,1,1,1]
[5,7,6,4,2,1,3,8]=>[5,1,1,1]
[6,5,7,4,1,3,2,8]=>[5,1,1,1]
[4,6,1,8,3,5,2,7]=>[3,2,1,1,1]
[7,1,6,8,2,5,4,3]=>[5,1,1,1]
[4,7,1,8,3,2,5,6]=>[3,2,1,1,1]
[4,8,3,6,1,5,2,7]=>[4,1,1,1,1]
[1,7,8,6,4,5,3,2]=>[5,1,1,1]
[3,2,8,6,4,5,1,7]=>[4,2,1,1]
[8,4,3,6,2,5,1,7]=>[5,1,1,1]
[1,6,8,7,4,3,5,2]=>[5,1,1,1]
[3,1,2,6,8,7,5,4]=>[4,2,1,1]
[5,7,4,2,1,8,6,3]=>[4,3,1]
[8,6,5,7,2,4,3,1]=>[6,1,1]
[7,4,6,1,8,5,3,2]=>[5,2,1]
[7,4,6,3,8,1,5,2]=>[4,2,1,1]
[7,4,8,1,6,3,2,5]=>[4,2,1,1]
[7,4,8,3,6,2,1,5]=>[5,1,1,1]
[6,4,8,2,3,5,7,1]=>[4,1,1,1,1]
[4,6,8,2,5,7,1,3]=>[3,1,1,1,1,1]
[6,4,8,2,5,7,1,3]=>[4,1,1,1,1]
[6,2,4,5,8,3,7,1]=>[4,1,1,1,1]
[6,8,2,4,7,3,5,1]=>[4,1,1,1,1]
[8,4,6,2,7,1,3,5]=>[4,1,1,1,1]
[6,8,4,2,7,1,3,5]=>[4,1,1,1,1]
[6,8,2,4,1,7,3,5]=>[3,2,1,1,1]
[7,5,1,6,2,4,8,3]=>[4,2,1,1]
[4,2,5,7,1,6,8,3]=>[3,2,1,1,1]
[2,4,8,5,6,7,3,1]=>[4,1,1,1,1]
[4,5,2,3,8,7,1,6]=>[3,2,1,1,1]
[2,5,4,7,6,1,3,8]=>[3,2,1,1,1]
[5,2,3,7,6,1,4,8]=>[3,2,1,1,1]
[4,2,3,7,6,1,5,8]=>[3,2,1,1,1]
[4,2,7,3,5,1,6,8]=>[3,2,1,1,1]
[5,6,2,3,8,4,7,1]=>[3,2,1,1,1]
[5,6,2,3,1,7,8,4]=>[3,2,1,1,1]
[5,7,2,3,4,1,6,8]=>[3,1,1,1,1,1]
[6,2,7,3,5,1,4,8]=>[3,2,1,1,1]
[7,2,6,3,5,1,4,8]=>[4,1,1,1,1]
[6,5,2,3,1,7,8,4]=>[4,2,1,1]
[6,5,2,3,8,4,7,1]=>[4,2,1,1]
[7,5,2,1,4,6,8,3]=>[4,2,1,1]
[8,5,2,3,1,6,4,7]=>[4,2,1,1]
[8,6,2,3,1,5,4,7]=>[4,2,1,1]
[8,2,6,3,1,7,4,5]=>[4,2,1,1]
[1,6,3,4,2,7,5,8]=>[3,2,1,1,1]
[8,5,2,7,3,4,6,1]=>[4,2,1,1]
[1,7,2,4,5,6,8,3]=>[3,1,1,1,1,1]
[1,8,3,2,5,6,4,7]=>[3,2,1,1,1]
[7,2,8,1,4,6,3,5]=>[3,2,1,1,1]
[2,7,8,1,5,6,3,4]=>[3,1,1,1,1,1]
[6,8,2,3,1,5,4,7]=>[3,2,1,1,1]
[5,8,2,3,1,6,4,7]=>[3,2,1,1,1]
[5,7,2,1,4,6,8,3]=>[3,2,1,1,1]
[4,2,7,1,5,6,8,3]=>[3,2,1,1,1]
[4,2,3,8,1,7,5,6]=>[3,2,1,1,1]
[4,2,1,5,3,7,6,8]=>[3,2,2,1]
[5,1,3,8,4,6,7,2]=>[3,2,1,1,1]
[5,1,3,2,6,7,8,4]=>[3,2,1,1,1]
[5,1,3,4,2,7,6,8]=>[3,2,1,1,1]
[6,1,3,4,2,7,5,8]=>[3,2,1,1,1]
[7,2,1,3,5,8,4,6]=>[3,2,1,1,1]
[6,8,7,2,3,4,5,1]=>[4,1,1,1,1]
[3,7,2,8,1,4,5,6]=>[3,1,1,1,1,1]
[5,2,3,7,4,6,1,8]=>[3,2,1,1,1]
[2,5,3,7,4,6,1,8]=>[3,2,1,1,1]
[2,6,7,3,4,5,1,8]=>[3,1,1,1,1,1]
[6,2,7,3,4,5,1,8]=>[3,2,1,1,1]
[3,8,4,5,2,1,6,7]=>[4,1,1,1,1]
[2,7,6,3,4,5,1,8]=>[4,1,1,1,1]
[2,8,7,5,1,3,4,6]=>[4,1,1,1,1]
[4,5,7,2,8,3,6,1]=>[3,2,1,1,1]
[5,2,1,3,6,7,8,4]=>[3,2,1,1,1]
[1,6,5,7,2,8,3,4]=>[3,2,1,1,1]
[7,5,2,6,1,8,4,3]=>[4,3,1]
[6,1,5,2,7,8,4,3]=>[4,2,1,1]
[1,6,5,7,2,8,4,3]=>[4,2,1,1]
[1,5,4,6,2,8,7,3]=>[3,3,1,1]
[1,5,4,6,2,8,3,7]=>[3,2,1,1,1]
[1,5,6,4,8,2,3,7]=>[3,1,1,1,1,1]
[6,2,1,5,8,4,7,3]=>[4,2,1,1]
[7,5,6,8,4,1,3,2]=>[5,1,1,1]
[8,3,7,5,1,4,2,6]=>[5,1,1,1]
[8,1,5,7,3,6,2,4]=>[4,1,1,1,1]
[8,3,2,6,4,5,1,7]=>[4,2,1,1]
[8,5,3,7,4,1,2,6]=>[4,2,1,1]
[8,5,6,2,7,1,3,4]=>[4,1,1,1,1]
[8,4,7,2,6,5,1,3]=>[5,1,1,1]
[8,5,7,3,2,6,1,4]=>[5,1,1,1]
[8,1,2,3,6,4,7,5]=>[3,2,1,1,1]
[7,6,2,3,5,8,1,4]=>[4,1,1,1,1]
[4,5,3,7,8,1,6,2]=>[3,2,1,1,1]
[3,4,2,8,1,6,7,5]=>[3,2,1,1,1]
[8,3,4,1,5,7,6,2]=>[4,2,1,1]
[4,3,7,5,1,6,2,8]=>[3,2,2,1]
[5,2,6,1,4,3,7,8]=>[3,2,1,1,1]
[5,3,7,4,2,8,6,1]=>[4,2,2]
[7,2,5,8,6,1,4,3]=>[4,2,1,1]
[5,3,1,4,6,7,8,2]=>[3,2,1,1,1]
[4,6,2,1,3,7,8,5]=>[3,2,1,1,1]
[2,5,4,1,3,6,7,8]=>[3,1,1,1,1,1]
[6,5,2,7,4,1,3,8]=>[4,2,1,1]
[3,1,6,7,8,4,5,2]=>[3,2,1,1,1]
[7,4,5,6,2,1,8,3]=>[4,2,1,1]
[3,7,5,6,2,1,8,4]=>[4,2,1,1]
[1,7,6,3,8,4,5,2]=>[4,2,1,1]
[6,4,1,2,7,8,3,5]=>[3,2,1,1,1]
[6,4,1,3,5,2,7,8]=>[4,1,1,1,1]
[5,1,8,3,4,6,2,7]=>[3,2,1,1,1]
[4,5,8,2,3,7,1,6]=>[3,1,1,1,1,1]
[7,3,4,8,2,5,1,6]=>[4,1,1,1,1]
[4,7,2,5,1,6,8,3]=>[3,2,1,1,1]
[8,7,2,1,5,3,6,4]=>[4,2,2]
[7,2,8,1,5,6,4,3]=>[4,2,1,1]
[5,6,4,2,1,8,3,7]=>[4,2,1,1]
[5,7,3,6,4,1,2,8]=>[4,1,1,1,1]
[2,4,3,5,8,1,6,7]=>[3,1,1,1,1,1]
[2,6,5,3,8,1,4,7]=>[4,1,1,1,1]
[6,1,2,4,3,5,7,8]=>[3,1,1,1,1,1]
[6,5,8,2,7,3,4,1]=>[4,2,1,1]
[1,7,6,8,4,3,2,5]=>[5,1,1,1]
[1,7,6,5,3,8,2,4]=>[5,1,1,1]
[6,1,2,4,3,5,8,7]=>[3,2,1,1,1]
[4,6,1,3,7,8,5,2]=>[3,2,1,1,1]
[1,5,6,3,8,7,2,4]=>[3,2,1,1,1]
[5,3,2,6,8,7,1,4]=>[4,2,1,1]
[6,3,5,2,7,1,4,8]=>[4,1,1,1,1]
[8,5,2,6,7,1,4,3]=>[4,2,1,1]
[5,3,8,7,1,4,2,6]=>[4,2,1,1]
[6,4,5,3,1,8,7,2]=>[4,3,1]
[8,5,1,2,3,6,7,4]=>[3,2,1,1,1]
[2,8,6,1,5,4,7,3]=>[5,1,1,1]
[8,3,2,6,1,5,7,4]=>[4,2,1,1]
[3,8,6,4,7,1,2,5]=>[4,1,1,1,1]
[1,8,7,5,4,3,2,6]=>[6,1,1]
[8,6,4,7,1,3,2,5]=>[5,1,1,1]
[3,1,4,7,6,2,5,8]=>[3,2,1,1,1]
[5,3,4,1,6,2,7,8]=>[3,2,1,1,1]
[2,7,1,4,6,3,5,8]=>[3,1,1,1,1,1]
[7,3,1,6,5,2,4,8]=>[4,2,1,1]
[7,1,5,2,4,6,3,8]=>[4,1,1,1,1]
[6,1,4,5,2,7,3,8]=>[3,2,1,1,1]
[6,1,5,8,2,7,4,3]=>[4,2,1,1]
[7,1,2,3,6,4,5,8]=>[3,1,1,1,1,1]
[6,1,3,8,7,4,5,2]=>[4,2,1,1]
[2,8,4,6,5,1,7,3]=>[4,2,1,1]
[7,4,1,3,6,5,2,8]=>[4,2,1,1]
[5,7,2,8,1,3,6,4]=>[3,2,1,1,1]
[6,5,1,4,7,3,2,8]=>[5,1,1,1]
[2,7,8,4,1,3,6,5]=>[3,2,1,1,1]
[2,4,6,5,7,8,1,3]=>[3,1,1,1,1,1]
[2,4,6,7,5,8,1,3]=>[3,1,1,1,1,1]
[2,4,6,3,7,8,1,5]=>[3,1,1,1,1,1]
[2,4,5,6,8,7,1,3]=>[3,1,1,1,1,1]
[2,4,5,6,8,3,7,1]=>[3,1,1,1,1,1]
[2,4,5,6,3,8,1,7]=>[3,1,1,1,1,1]
[2,3,4,6,8,5,1,7]=>[3,1,1,1,1,1]
[5,2,8,3,4,1,6,7]=>[3,2,1,1,1]
[3,6,4,1,2,7,8,5]=>[3,2,1,1,1]
[4,1,7,3,8,6,2,5]=>[3,2,2,1]
[8,4,1,2,5,3,7,6]=>[3,2,2,1]
[1,5,2,7,6,8,4,3]=>[4,2,1,1]
[4,7,6,8,3,1,2,5]=>[4,1,1,1,1]
[4,8,2,7,6,5,1,3]=>[5,1,1,1]
[7,4,2,8,6,5,1,3]=>[4,3,1]
[8,6,5,2,7,1,4,3]=>[5,2,1]
[6,5,8,2,7,1,4,3]=>[4,2,1,1]
[7,5,8,2,1,6,4,3]=>[4,3,1]
[3,2,1,6,5,8,4,7]=>[3,3,1,1]
[2,6,4,8,5,7,3,1]=>[4,2,1,1]
[6,3,1,4,5,8,2,7]=>[3,2,1,1,1]
[3,4,8,5,2,1,7,6]=>[4,2,1,1]
[4,8,7,1,3,2,6,5]=>[4,2,1,1]
[5,8,7,4,6,1,3,2]=>[5,1,1,1]
[3,4,1,8,7,6,2,5]=>[4,2,1,1]
[1,3,5,6,8,7,2,4]=>[3,1,1,1,1,1]
[2,8,7,5,4,1,6,3]=>[5,2,1]
[8,1,5,7,4,2,6,3]=>[4,2,1,1]
[5,8,7,3,4,1,6,2]=>[4,2,1,1]
[4,6,1,3,2,8,5,7]=>[3,2,1,1,1]
[2,6,5,8,3,1,4,7]=>[4,1,1,1,1]
[6,7,8,2,4,5,3,1]=>[4,1,1,1,1]
[3,2,8,4,5,7,1,6]=>[3,2,1,1,1]
[6,1,8,2,4,5,3,7]=>[3,2,1,1,1]
[8,3,6,4,2,7,1,5]=>[5,1,1,1]
[1,3,8,4,7,6,2,5]=>[4,1,1,1,1]
[8,3,7,5,4,1,2,6]=>[5,1,1,1]
[2,6,4,7,8,5,1,3]=>[3,2,1,1,1]
[5,4,3,7,6,1,8,2]=>[4,2,2]
[8,6,3,7,1,4,2,5]=>[4,2,1,1]
[3,1,2,8,7,6,4,5]=>[4,2,1,1]
[8,5,4,1,2,3,7,6]=>[4,2,1,1]
[8,3,2,1,6,4,7,5]=>[4,2,2]
[2,3,8,4,1,7,5,6]=>[3,2,1,1,1]
[4,6,1,3,2,7,8,5]=>[3,2,1,1,1]
[6,7,2,5,8,4,1,3]=>[4,1,1,1,1]
[4,1,7,8,2,5,6,3]=>[3,2,1,1,1]
[3,4,6,7,1,5,8,2]=>[3,1,1,1,1,1]
[3,4,5,7,8,1,6,2]=>[3,1,1,1,1,1]
[1,8,7,4,3,5,2,6]=>[5,1,1,1]
[2,4,5,8,1,3,7,6]=>[3,1,1,1,1,1]
[2,7,8,6,5,3,1,4]=>[5,1,1,1]
[6,3,1,5,8,4,2,7]=>[4,2,1,1]
[2,8,3,5,6,1,4,7]=>[3,1,1,1,1,1]
[1,3,6,4,2,7,5,8]=>[3,2,1,1,1]
[2,3,7,5,8,1,4,6]=>[3,1,1,1,1,1]
[3,2,8,5,6,1,4,7]=>[3,2,1,1,1]
[7,2,5,8,1,4,6,3]=>[4,1,1,1,1]
[4,7,5,8,1,2,6,3]=>[3,2,1,1,1]
[4,7,5,8,1,2,3,6]=>[3,1,1,1,1,1]
[3,4,7,5,2,8,1,6]=>[4,1,1,1,1]
[4,3,2,5,7,8,1,6]=>[4,1,1,1,1]
[2,4,7,5,8,3,1,6]=>[4,1,1,1,1]
[2,5,4,7,3,8,1,6]=>[4,1,1,1,1]
[3,7,8,4,2,1,6,5]=>[4,2,1,1]
[8,5,4,7,6,3,1,2]=>[5,2,1]
[1,5,4,8,7,6,2,3]=>[4,2,1,1]
[3,2,4,5,8,1,6,7]=>[3,1,1,1,1,1]
[3,6,8,4,2,7,1,5]=>[4,1,1,1,1]
[1,4,7,6,3,8,2,5]=>[4,1,1,1,1]
[3,6,5,1,7,2,8,4]=>[3,2,2,1]
[7,4,1,6,2,8,5,3]=>[4,2,2]
[1,3,6,8,2,4,7,5]=>[3,1,1,1,1,1]
[1,6,7,4,3,8,2,5]=>[4,1,1,1,1]
[8,5,4,1,6,2,7,3]=>[4,2,2]
[4,7,2,8,5,1,6,3]=>[3,2,2,1]
[7,8,6,2,1,5,4,3]=>[5,2,1]
[8,6,2,7,3,5,1,4]=>[4,2,1,1]
[2,1,3,8,7,5,6,4]=>[4,2,1,1]
[8,1,7,3,6,5,2,4]=>[5,1,1,1]
[1,6,4,7,3,8,5,2]=>[4,2,1,1]
[4,8,1,6,3,7,2,5]=>[4,1,1,1,1]
[8,5,4,1,6,3,7,2]=>[5,2,1]
[1,7,6,2,4,8,5,3]=>[4,2,1,1]
[5,7,3,2,4,8,6,1]=>[4,2,1,1]
[2,8,4,6,3,5,1,7]=>[4,1,1,1,1]
[3,8,1,4,6,5,2,7]=>[4,1,1,1,1]
[2,7,5,4,1,8,3,6]=>[4,2,1,1]
[4,6,1,8,5,3,2,7]=>[4,2,1,1]
[3,8,5,2,1,6,4,7]=>[4,2,1,1]
[5,1,4,8,2,6,3,7]=>[3,2,1,1,1]
[4,5,8,1,3,7,6,2]=>[4,1,1,1,1]
[8,6,7,1,4,3,2,5]=>[5,1,1,1]
[1,4,7,8,6,3,5,2]=>[4,1,1,1,1]
[8,5,2,6,3,4,7,1]=>[4,2,1,1]
[8,3,6,1,2,7,4,5]=>[3,2,1,1,1]
[3,8,6,1,2,5,7,4]=>[4,1,1,1,1]
[3,7,6,2,1,8,5,4]=>[4,3,1]
[4,3,7,6,1,8,5,2]=>[4,2,2]
[8,6,3,2,7,1,5,4]=>[5,2,1]
[6,8,1,5,4,7,2,3]=>[4,1,1,1,1]
[6,7,2,5,4,8,1,3]=>[4,1,1,1,1]
[7,6,2,4,8,5,1,3]=>[4,2,1,1]
[4,6,8,7,3,1,2,5]=>[4,1,1,1,1]
[4,7,5,2,6,3,8,1]=>[4,2,1,1]
[3,5,6,2,8,1,4,7]=>[3,1,1,1,1,1]
[5,1,2,4,3,7,6,8]=>[3,2,1,1,1]
[6,1,8,2,4,3,5,7]=>[3,2,1,1,1]
[1,6,8,2,5,3,4,7]=>[3,1,1,1,1,1]
[8,7,6,2,4,5,1,3]=>[5,1,1,1]
[5,4,8,7,1,2,6,3]=>[4,2,1,1]
[2,5,6,4,3,8,1,7]=>[4,1,1,1,1]
[8,7,3,5,1,4,6,2]=>[5,1,1,1]
[8,6,3,5,2,1,4,7]=>[5,1,1,1]
[8,7,3,5,2,4,6,1]=>[5,1,1,1]
[4,6,3,8,5,2,7,1]=>[4,2,1,1]
[8,7,1,4,5,6,2,3]=>[4,1,1,1,1]
[4,1,3,8,5,6,2,7]=>[3,2,1,1,1]
[5,2,8,3,1,6,7,4]=>[3,2,2,1]
[1,7,8,6,3,2,5,4]=>[4,2,1,1]
[3,7,2,4,5,6,1,8]=>[3,1,1,1,1,1]
[3,2,8,1,5,7,4,6]=>[3,2,1,1,1]
[3,4,6,7,2,1,5,8]=>[3,1,1,1,1,1]
[2,6,7,1,4,3,8,5]=>[3,2,1,1,1]
[3,2,7,4,8,5,6,1]=>[3,2,2,1]
[5,8,2,7,4,6,3,1]=>[5,1,1,1]
[4,5,2,8,3,7,1,6]=>[3,2,1,1,1]
[7,8,5,1,6,4,3,2]=>[5,2,1]
[8,7,5,1,6,4,3,2]=>[6,2]
[4,5,8,3,1,2,7,6]=>[3,2,1,1,1]
[4,6,8,3,2,1,7,5]=>[4,2,1,1]
[4,6,8,3,5,1,2,7]=>[3,1,1,1,1,1]
[1,4,6,3,7,5,2,8]=>[3,2,1,1,1]
[4,5,2,6,8,7,3,1]=>[4,2,1,1]
[1,3,8,7,4,5,6,2]=>[4,1,1,1,1]
[7,3,1,8,4,5,6,2]=>[3,3,1,1]
[6,2,4,3,7,5,8,1]=>[4,2,1,1]
[6,4,2,5,1,7,8,3]=>[4,2,1,1]
[3,8,2,1,5,7,6,4]=>[4,2,1,1]
[1,3,2,8,7,4,6,5]=>[4,2,1,1]
[7,5,2,8,3,1,6,4]=>[4,2,2]
[5,4,2,7,3,8,6,1]=>[4,2,2]
[4,6,3,7,8,1,2,5]=>[3,1,1,1,1,1]
[8,3,5,4,7,1,2,6]=>[4,1,1,1,1]
[6,2,5,4,1,7,8,3]=>[4,2,1,1]
[4,1,5,6,3,8,7,2]=>[3,2,2,1]
[8,5,1,6,3,2,4,7]=>[4,2,1,1]
[6,8,7,4,3,2,5,1]=>[6,1,1]
[2,8,5,1,3,7,6,4]=>[4,2,1,1]
[5,6,4,1,8,2,7,3]=>[3,3,1,1]
[6,4,5,1,3,8,7,2]=>[4,2,1,1]
[6,1,3,5,4,8,2,7]=>[4,1,1,1,1]
[1,3,8,7,2,5,6,4]=>[4,1,1,1,1]
[2,5,4,1,8,3,7,6]=>[3,3,1,1]
[5,1,4,8,3,7,6,2]=>[4,2,1,1]
[8,4,1,2,7,6,5,3]=>[5,2,1]
[4,8,3,2,7,6,5,1]=>[5,2,1]
[1,8,7,3,4,6,5,2]=>[5,1,1,1]
[5,3,1,2,4,6,8,7]=>[3,2,1,1,1]
[8,5,7,3,1,2,4,6]=>[4,1,1,1,1]
[3,1,2,8,7,5,4,6]=>[4,2,1,1]
[1,4,3,8,5,7,2,6]=>[3,2,1,1,1]
[6,7,1,5,2,8,4,3]=>[4,2,1,1]
[1,5,3,7,6,4,8,2]=>[4,2,1,1]
[4,8,1,3,6,2,7,5]=>[3,2,1,1,1]
[2,7,3,4,8,6,5,1]=>[4,2,1,1]
[1,8,2,4,7,3,6,5]=>[4,1,1,1,1]
[2,7,1,6,5,8,3,4]=>[4,1,1,1,1]
[6,2,3,8,1,5,7,4]=>[3,2,1,1,1]
[2,5,7,4,8,3,6,1]=>[4,1,1,1,1]
[8,5,6,2,4,7,1,3]=>[4,1,1,1,1]
[4,8,5,6,7,1,3,2]=>[4,1,1,1,1]
[8,1,5,7,3,6,4,2]=>[5,1,1,1]
[2,7,6,4,3,8,5,1]=>[5,2,1]
[3,8,6,2,7,5,4,1]=>[5,2,1]
[4,8,1,6,2,5,3,7]=>[4,1,1,1,1]
[1,8,4,2,5,7,3,6]=>[3,2,1,1,1]
[5,8,3,1,2,4,6,7]=>[3,1,1,1,1,1]
[1,4,8,5,2,3,6,7]=>[3,1,1,1,1,1]
[1,4,8,5,2,3,7,6]=>[3,2,1,1,1]
[1,5,8,7,2,4,3,6]=>[4,1,1,1,1]
[1,5,4,2,8,3,7,6]=>[3,3,1,1]
[1,2,8,7,3,5,4,6]=>[4,1,1,1,1]
[8,7,1,3,2,5,4,6]=>[4,2,1,1]
[6,7,4,2,8,1,3,5]=>[4,1,1,1,1]
[4,1,6,8,7,2,3,5]=>[3,2,1,1,1]
[4,7,5,6,2,8,3,1]=>[4,2,1,1]
[8,4,3,6,7,5,2,1]=>[5,2,1]
[6,7,5,2,8,4,3,1]=>[5,2,1]
[6,8,4,3,2,7,5,1]=>[5,2,1]
[6,1,7,3,5,8,2,4]=>[3,2,1,1,1]
[1,3,7,6,4,8,2,5]=>[4,1,1,1,1]
[2,6,4,8,7,3,1,5]=>[4,2,1,1]
[2,1,8,7,3,5,4,6]=>[4,2,1,1]
[6,1,5,8,7,4,3,2]=>[5,2,1]
[6,1,8,5,7,4,3,2]=>[5,2,1]
[8,5,1,4,7,6,3,2]=>[5,2,1]
[8,1,3,7,2,4,6,5]=>[4,1,1,1,1]
[2,6,7,3,5,8,4,1]=>[4,1,1,1,1]
[2,6,7,3,5,8,1,4]=>[3,1,1,1,1,1]
[5,3,1,6,4,8,2,7]=>[3,3,1,1]
[2,5,6,7,1,4,8,3]=>[3,1,1,1,1,1]
[4,7,5,3,2,8,1,6]=>[5,1,1,1]
[4,7,5,2,8,6,1,3]=>[4,2,1,1]
[5,8,1,2,7,4,3,6]=>[4,1,1,1,1]
[4,6,3,7,8,1,5,2]=>[3,2,1,1,1]
[6,3,1,8,4,5,2,7]=>[3,3,1,1]
[2,1,4,7,5,8,6,3]=>[3,2,2,1]
[7,6,2,4,8,3,1,5]=>[5,1,1,1]
[6,5,8,1,4,3,7,2]=>[5,1,1,1]
[8,1,4,2,7,5,6,3]=>[4,2,1,1]
[8,6,3,5,2,1,7,4]=>[5,2,1]
[6,8,3,1,2,5,4,7]=>[3,2,1,1,1]
[5,8,6,4,7,1,2,3]=>[4,1,1,1,1]
[2,5,1,8,7,3,4,6]=>[3,2,1,1,1]
[7,2,4,3,8,6,1,5]=>[4,2,1,1]
[6,8,4,3,5,1,7,2]=>[4,2,1,1]
[1,4,7,3,6,8,2,5]=>[3,1,1,1,1,1]
[3,7,1,4,6,8,2,5]=>[3,1,1,1,1,1]
[2,4,7,3,6,8,1,5]=>[3,1,1,1,1,1]
[8,5,7,6,1,3,2,4]=>[5,1,1,1]
[2,7,5,6,1,8,4,3]=>[4,2,1,1]
[1,2,6,7,4,5,8,3]=>[3,1,1,1,1,1]
[6,5,2,8,7,1,4,3]=>[4,3,1]
[7,2,3,6,8,1,4,5]=>[3,1,1,1,1,1]
[2,6,1,3,8,5,4,7]=>[3,2,1,1,1]
[6,4,1,8,3,2,5,7]=>[4,2,1,1]
[5,8,1,4,2,7,3,6]=>[3,2,1,1,1]
[6,4,8,2,1,7,3,5]=>[4,2,1,1]
[2,3,1,8,7,5,6,4]=>[4,2,1,1]
[1,5,6,7,2,4,3,8]=>[3,1,1,1,1,1]
[2,8,6,4,1,5,3,7]=>[4,2,1,1]
[1,5,7,3,6,2,4,8]=>[3,1,1,1,1,1]
[6,7,4,5,1,3,8,2]=>[4,1,1,1,1]
[1,6,5,3,8,2,4,7]=>[4,1,1,1,1]
[5,6,1,2,4,8,3,7]=>[3,1,1,1,1,1]
[8,7,4,5,1,3,2,6]=>[5,1,1,1]
[8,5,1,2,7,4,3,6]=>[4,2,1,1]
[4,1,8,7,2,5,3,6]=>[4,2,1,1]
[3,2,4,6,1,8,7,5]=>[3,3,1,1]
[3,6,7,4,1,2,5,8]=>[3,1,1,1,1,1]
[1,4,7,5,8,2,3,6]=>[3,1,1,1,1,1]
[1,6,8,4,7,3,2,5]=>[4,1,1,1,1]
[3,6,7,5,4,8,1,2]=>[4,1,1,1,1]
[4,5,7,2,6,3,8,1]=>[4,1,1,1,1]
[2,1,5,7,4,6,8,3]=>[3,2,1,1,1]
[2,3,5,7,8,1,6,4]=>[3,1,1,1,1,1]
[1,5,7,4,2,3,6,8]=>[3,1,1,1,1,1]
[2,4,7,5,3,6,8,1]=>[4,1,1,1,1]
[8,1,7,2,4,6,3,5]=>[4,1,1,1,1]
[1,2,4,7,8,6,3,5]=>[3,1,1,1,1,1]
[1,3,6,2,5,8,4,7]=>[3,1,1,1,1,1]
[1,5,3,6,8,2,4,7]=>[3,1,1,1,1,1]
[4,8,1,2,6,3,7,5]=>[3,2,1,1,1]
[5,8,1,2,6,3,7,4]=>[3,2,1,1,1]
[1,6,2,3,7,5,8,4]=>[3,2,1,1,1]
[4,1,2,6,5,7,8,3]=>[3,2,1,1,1]
[1,8,4,2,7,3,6,5]=>[4,2,1,1]
[1,7,5,2,3,8,6,4]=>[3,3,1,1]
[8,1,4,7,3,5,2,6]=>[4,1,1,1,1]
[8,4,3,6,1,7,2,5]=>[4,2,1,1]
[2,6,1,8,3,7,4,5]=>[3,2,1,1,1]
[8,4,2,1,3,7,5,6]=>[4,2,1,1]
[2,5,1,7,6,8,3,4]=>[3,2,1,1,1]
[5,3,1,8,2,4,7,6]=>[3,3,1,1]
[1,2,6,3,7,5,8,4]=>[3,2,1,1,1]
[5,1,8,3,2,4,7,6]=>[3,2,2,1]
[3,1,5,4,6,7,8,2]=>[3,2,1,1,1]
[2,8,5,7,3,1,4,6]=>[4,1,1,1,1]
[2,6,8,7,3,1,4,5]=>[4,1,1,1,1]
[7,4,2,1,3,8,5,6]=>[4,2,1,1]
[7,2,1,3,8,5,4,6]=>[3,3,1,1]
[2,1,7,3,8,6,4,5]=>[3,2,2,1]
[1,7,5,3,2,4,8,6]=>[4,2,1,1]
[1,4,2,7,6,5,8,3]=>[4,2,1,1]
[3,4,1,6,5,7,8,2]=>[3,2,1,1,1]
[2,8,7,3,4,1,5,6]=>[4,1,1,1,1]
[5,7,6,2,3,8,1,4]=>[4,1,1,1,1]
[4,5,7,6,2,8,1,3]=>[4,1,1,1,1]
[3,1,8,7,5,2,6,4]=>[4,2,2]
[4,5,6,8,7,2,1,3]=>[4,1,1,1,1]
[2,8,3,1,5,4,7,6]=>[3,2,2,1]
[3,8,4,1,5,2,7,6]=>[3,2,2,1]
[5,1,7,8,3,2,6,4]=>[3,2,2,1]
[4,8,3,1,6,2,7,5]=>[3,2,2,1]
[2,8,3,1,6,4,7,5]=>[3,2,2,1]
[6,2,7,1,5,8,4,3]=>[4,2,1,1]
[4,8,5,1,3,2,6,7]=>[4,1,1,1,1]
[5,4,3,1,2,7,6,8]=>[4,2,1,1]
[4,1,6,5,2,3,7,8]=>[3,2,1,1,1]
[7,1,5,2,3,6,4,8]=>[3,2,1,1,1]
[4,1,6,3,7,2,5,8]=>[3,2,1,1,1]
[4,6,1,2,8,3,7,5]=>[3,2,1,1,1]
[4,1,3,6,7,2,5,8]=>[3,1,1,1,1,1]
[2,6,5,1,3,4,7,8]=>[3,1,1,1,1,1]
[2,6,7,4,3,1,5,8]=>[4,1,1,1,1]
[2,6,3,1,7,4,5,8]=>[3,2,1,1,1]
[6,5,3,7,2,4,1,8]=>[5,1,1,1]
[2,3,6,7,1,5,4,8]=>[3,1,1,1,1,1]
[2,7,5,8,1,3,6,4]=>[3,2,1,1,1]
[5,1,6,7,3,2,4,8]=>[3,2,1,1,1]
[5,6,1,4,7,2,3,8]=>[3,1,1,1,1,1]
[1,2,5,7,8,6,3,4]=>[3,1,1,1,1,1]
[1,2,6,7,4,5,3,8]=>[3,1,1,1,1,1]
[1,2,7,8,4,6,3,5]=>[3,1,1,1,1,1]
[8,6,5,2,1,7,4,3]=>[5,3]
[4,3,8,6,7,1,5,2]=>[4,2,1,1]
[7,3,2,8,6,1,5,4]=>[4,3,1]
[7,5,8,2,6,1,4,3]=>[4,2,1,1]
[7,4,1,2,6,5,8,3]=>[4,2,1,1]
[5,2,7,4,6,1,8,3]=>[3,2,2,1]
[5,4,8,6,3,2,1,7]=>[5,2,1]
[8,4,6,7,3,1,5,2]=>[4,2,1,1]
[4,6,8,5,1,2,7,3]=>[3,2,1,1,1]
[4,1,3,6,8,5,2,7]=>[3,2,1,1,1]
[6,3,5,7,1,2,8,4]=>[3,2,1,1,1]
[1,8,5,3,2,4,6,7]=>[4,1,1,1,1]
[1,6,7,3,4,2,5,8]=>[3,1,1,1,1,1]
[1,6,8,3,4,2,5,7]=>[3,1,1,1,1,1]
[1,8,7,5,3,4,2,6]=>[5,1,1,1]
[1,7,8,5,3,4,2,6]=>[4,1,1,1,1]
[1,7,6,8,4,2,3,5]=>[4,1,1,1,1]
[1,7,8,6,4,3,2,5]=>[5,1,1,1]
[5,1,7,8,4,2,3,6]=>[3,2,1,1,1]
[3,8,2,1,6,7,5,4]=>[4,2,1,1]
[2,8,3,1,7,5,6,4]=>[4,2,1,1]
[8,5,6,2,1,4,7,3]=>[4,2,1,1]
[2,7,4,1,5,8,3,6]=>[3,2,1,1,1]
[2,1,6,4,7,8,3,5]=>[3,2,1,1,1]
[5,7,8,3,4,2,1,6]=>[4,1,1,1,1]
[4,7,5,3,8,2,6,1]=>[5,1,1,1]
[2,6,4,7,8,5,3,1]=>[4,2,1,1]
[7,8,4,5,6,1,3,2]=>[4,1,1,1,1]
[2,5,1,8,4,6,7,3]=>[3,2,1,1,1]
[5,2,8,4,6,7,1,3]=>[3,2,1,1,1]
[6,5,8,3,4,2,1,7]=>[5,1,1,1]
[1,3,5,8,4,6,7,2]=>[3,1,1,1,1,1]
[8,2,7,6,3,4,5,1]=>[5,1,1,1]
[6,8,7,3,2,1,4,5]=>[5,1,1,1]
[3,4,8,2,7,1,5,6]=>[3,1,1,1,1,1]
[7,2,6,1,4,8,3,5]=>[4,1,1,1,1]
[7,8,1,2,4,6,3,5]=>[3,1,1,1,1,1]
[7,2,8,3,4,5,1,6]=>[3,2,1,1,1]
[6,1,8,3,4,2,5,7]=>[3,2,1,1,1]
[7,5,1,2,4,3,8,6]=>[4,2,1,1]
[7,6,8,1,4,2,3,5]=>[4,1,1,1,1]
[2,4,3,7,8,5,6,1]=>[3,2,1,1,1]
[2,1,7,6,3,4,5,8]=>[3,2,1,1,1]
[6,3,5,2,1,8,4,7]=>[4,2,1,1]
[6,1,5,3,8,2,4,7]=>[4,1,1,1,1]
[2,3,6,8,5,1,7,4]=>[3,2,1,1,1]
[3,2,4,8,6,1,7,5]=>[3,2,2,1]
[2,1,3,8,4,5,7,6]=>[3,2,1,1,1]
[3,1,2,8,5,4,7,6]=>[3,2,2,1]
[2,1,3,7,8,4,6,5]=>[3,2,1,1,1]
[2,1,3,8,4,7,6,5]=>[4,2,1,1]
[3,1,2,8,4,5,7,6]=>[3,2,1,1,1]
[1,2,8,7,5,4,6,3]=>[5,1,1,1]
[4,6,7,2,3,8,1,5]=>[3,1,1,1,1,1]
[3,2,6,5,7,8,1,4]=>[3,2,1,1,1]
[3,2,7,5,6,8,1,4]=>[3,2,1,1,1]
[2,1,8,7,4,6,5,3]=>[5,2,1]
[6,1,5,8,4,7,3,2]=>[5,1,1,1]
[1,4,6,8,5,7,2,3]=>[3,1,1,1,1,1]
[2,4,7,1,8,3,6,5]=>[3,2,1,1,1]
[6,1,5,4,2,3,8,7]=>[4,2,1,1]
[6,4,5,1,2,8,3,7]=>[3,2,1,1,1]
[8,4,1,5,7,6,3,2]=>[5,2,1]
[8,1,6,3,5,2,4,7]=>[4,1,1,1,1]
[4,6,2,5,3,8,1,7]=>[4,1,1,1,1]
[4,6,5,2,1,8,3,7]=>[4,2,1,1]
[5,8,4,3,6,7,2,1]=>[5,1,1,1]
[6,8,2,1,5,3,4,7]=>[3,2,1,1,1]
[2,5,3,8,6,7,4,1]=>[4,2,1,1]
[3,2,6,5,1,8,4,7]=>[3,2,2,1]
[7,4,5,8,1,6,2,3]=>[3,2,1,1,1]
[4,5,8,1,6,7,3,2]=>[4,1,1,1,1]
[5,1,8,4,6,7,3,2]=>[4,2,1,1]
[6,5,3,8,1,7,2,4]=>[4,2,1,1]
[8,3,7,1,6,2,4,5]=>[4,1,1,1,1]
[8,1,4,6,5,7,2,3]=>[4,1,1,1,1]
[8,1,7,5,6,4,2,3]=>[5,1,1,1]
[8,6,1,5,3,7,2,4]=>[5,1,1,1]
[7,2,3,6,8,1,5,4]=>[4,1,1,1,1]
[2,6,3,7,8,1,4,5]=>[3,1,1,1,1,1]
[6,3,8,7,2,1,5,4]=>[4,2,2]
[7,2,5,6,3,4,8,1]=>[4,1,1,1,1]
[7,2,8,6,3,1,5,4]=>[4,2,2]
[7,2,4,5,8,6,3,1]=>[4,2,1,1]
[6,3,8,4,7,2,5,1]=>[4,2,1,1]
[7,2,3,6,8,5,4,1]=>[5,1,1,1]
[7,2,8,5,4,1,3,6]=>[4,2,1,1]
[7,4,5,2,8,1,6,3]=>[4,2,1,1]
[7,5,4,2,8,1,6,3]=>[5,2,1]
[7,6,3,2,8,4,5,1]=>[5,2,1]
[7,2,3,6,8,4,5,1]=>[4,1,1,1,1]
[7,2,5,4,8,3,6,1]=>[5,1,1,1]
[7,2,8,3,6,1,4,5]=>[3,2,1,1,1]
[7,4,5,2,8,3,6,1]=>[4,2,1,1]
[3,1,6,7,4,5,2,8]=>[3,2,1,1,1]
[3,1,5,4,7,6,2,8]=>[3,2,2,1]
[7,3,6,8,2,4,5,1]=>[4,1,1,1,1]
[5,1,3,2,4,6,8,7]=>[3,2,1,1,1]
[8,4,2,5,1,7,3,6]=>[4,2,1,1]
[6,4,2,5,7,3,8,1]=>[4,2,1,1]
[5,7,8,4,2,3,6,1]=>[4,1,1,1,1]
[6,4,5,2,8,3,7,1]=>[4,2,1,1]
[6,5,2,4,3,8,7,1]=>[5,2,1]
[6,5,3,4,1,8,2,7]=>[4,2,1,1]
[6,4,5,3,8,1,2,7]=>[4,1,1,1,1]
[5,6,4,8,3,1,2,7]=>[4,1,1,1,1]
[7,2,4,6,3,8,5,1]=>[4,2,1,1]
[2,8,3,7,6,1,5,4]=>[5,1,1,1]
[5,4,2,6,8,7,3,1]=>[4,3,1]
[3,7,2,5,8,6,4,1]=>[4,2,1,1]
[4,6,5,3,8,1,7,2]=>[4,2,1,1]
[2,4,8,7,6,1,5,3]=>[5,1,1,1]
[3,2,8,7,4,6,5,1]=>[5,2,1]
[8,2,6,5,1,4,3,7]=>[5,1,1,1]
[4,8,5,2,7,6,3,1]=>[5,2,1]
[2,8,6,5,7,1,3,4]=>[4,1,1,1,1]
[3,8,4,7,2,1,6,5]=>[4,2,1,1]
[4,8,5,1,7,6,3,2]=>[5,2,1]
[5,8,1,7,6,2,3,4]=>[4,1,1,1,1]
[3,4,6,2,5,7,1,8]=>[3,1,1,1,1,1]
[1,7,5,2,6,8,3,4]=>[3,2,1,1,1]
[5,1,7,2,4,6,3,8]=>[3,2,1,1,1]
[6,8,2,1,3,4,7,5]=>[3,2,1,1,1]
[5,2,1,7,6,4,3,8]=>[4,3,1]
[7,4,8,3,6,5,1,2]=>[4,2,1,1]
[6,4,8,5,1,7,2,3]=>[3,2,2,1]
[5,2,8,1,3,6,7,4]=>[3,2,1,1,1]
[6,3,2,7,4,5,8,1]=>[4,2,1,1]
[7,4,3,8,5,6,1,2]=>[4,2,1,1]
[6,2,1,8,7,4,5,3]=>[4,3,1]
[6,2,1,8,7,3,5,4]=>[4,3,1]
[5,2,1,7,6,3,4,8]=>[3,3,1,1]
[4,2,6,8,5,7,1,3]=>[3,2,1,1,1]
[8,6,4,3,2,7,5,1]=>[6,2]
[1,3,4,7,8,2,6,5]=>[3,1,1,1,1,1]
[1,5,4,3,8,7,2,6]=>[4,2,1,1]
[1,2,5,8,4,3,6,7]=>[3,1,1,1,1,1]
[1,5,8,2,6,4,3,7]=>[4,1,1,1,1]
[3,5,6,2,4,7,8,1]=>[3,1,1,1,1,1]
[3,5,6,7,2,4,8,1]=>[3,1,1,1,1,1]
[3,5,7,6,8,2,4,1]=>[4,1,1,1,1]
[3,5,7,2,6,8,4,1]=>[4,1,1,1,1]
[3,5,2,7,6,8,4,1]=>[4,2,1,1]
[3,5,7,4,2,6,8,1]=>[4,1,1,1,1]
[3,5,4,7,2,6,8,1]=>[4,1,1,1,1]
[3,4,5,7,2,6,8,1]=>[3,1,1,1,1,1]
[3,4,5,7,2,8,6,1]=>[3,2,1,1,1]
[3,5,4,7,8,2,6,1]=>[4,1,1,1,1]
[3,5,4,7,2,8,6,1]=>[4,2,1,1]
[3,2,5,7,4,8,6,1]=>[3,2,2,1]
[3,5,7,4,2,8,6,1]=>[4,2,1,1]
[3,5,7,8,4,2,6,1]=>[4,1,1,1,1]
[2,3,5,7,8,4,6,1]=>[3,1,1,1,1,1]
[3,5,2,7,8,6,4,1]=>[4,2,1,1]
[3,5,7,8,2,6,4,1]=>[4,1,1,1,1]
[3,5,7,8,6,2,4,1]=>[4,1,1,1,1]
[4,2,5,6,7,3,8,1]=>[3,2,1,1,1]
[8,6,1,4,3,5,2,7]=>[5,1,1,1]
[6,1,8,4,3,5,2,7]=>[4,2,1,1]
[5,1,6,4,8,2,3,7]=>[3,2,1,1,1]
[8,1,4,2,5,3,6,7]=>[3,2,1,1,1]
[2,8,4,1,5,3,6,7]=>[3,2,1,1,1]
[8,4,1,3,5,2,6,7]=>[4,1,1,1,1]
[4,1,8,3,5,2,6,7]=>[3,2,1,1,1]
[8,3,1,2,5,4,6,7]=>[3,2,1,1,1]
[3,1,8,2,5,4,6,7]=>[3,2,1,1,1]
[4,2,5,1,8,7,6,3]=>[4,3,1]
[5,2,4,8,1,7,6,3]=>[4,2,1,1]
[7,3,2,4,6,8,1,5]=>[4,1,1,1,1]
[1,4,8,6,7,2,5,3]=>[4,1,1,1,1]
[1,4,5,7,3,8,2,6]=>[3,1,1,1,1,1]
[4,6,8,1,2,5,3,7]=>[3,1,1,1,1,1]
[3,5,6,8,2,1,4,7]=>[3,1,1,1,1,1]
[8,2,5,4,1,3,7,6]=>[4,2,1,1]
[2,4,5,8,6,3,1,7]=>[4,1,1,1,1]
[5,4,8,2,3,1,7,6]=>[4,2,1,1]
[4,7,5,8,2,3,1,6]=>[4,1,1,1,1]
[4,6,7,5,1,8,3,2]=>[4,2,1,1]
[1,7,3,6,5,8,2,4]=>[4,1,1,1,1]
[8,3,4,2,6,7,1,5]=>[4,1,1,1,1]
[7,5,3,8,6,2,1,4]=>[5,2,1]
[7,3,1,8,2,6,5,4]=>[4,3,1]
[4,6,7,5,2,8,3,1]=>[4,2,1,1]
[5,8,7,2,4,3,1,6]=>[5,1,1,1]
[5,1,2,8,6,7,3,4]=>[3,2,1,1,1]
[2,5,7,8,6,1,4,3]=>[4,1,1,1,1]
[7,2,6,8,4,5,1,3]=>[4,1,1,1,1]
[5,1,7,6,8,2,3,4]=>[3,2,1,1,1]
[1,7,6,2,4,3,8,5]=>[4,2,1,1]
[7,1,6,2,4,5,3,8]=>[4,1,1,1,1]
[5,7,1,6,2,3,4,8]=>[3,1,1,1,1,1]
[6,2,5,8,3,4,1,7]=>[4,1,1,1,1]
[1,5,3,4,8,2,6,7]=>[3,1,1,1,1,1]
[2,1,3,6,5,8,4,7]=>[3,2,1,1,1]
[2,8,6,5,7,4,3,1]=>[6,1,1]
[2,8,6,5,7,4,1,3]=>[5,1,1,1]
[6,5,2,7,4,3,1,8]=>[5,2,1]
[6,5,2,8,4,3,7,1]=>[5,2,1]
[7,5,8,3,4,2,1,6]=>[5,1,1,1]
[7,6,8,5,2,4,1,3]=>[5,1,1,1]
[5,3,7,2,4,1,8,6]=>[4,2,1,1]
[5,1,2,8,6,3,7,4]=>[3,2,2,1]
[6,1,5,7,2,4,3,8]=>[4,1,1,1,1]
[4,1,8,2,6,5,7,3]=>[4,2,1,1]
[6,1,4,7,8,5,3,2]=>[4,2,1,1]
[6,1,5,7,8,4,2,3]=>[4,1,1,1,1]
[4,6,1,5,7,2,8,3]=>[3,2,1,1,1]
[2,5,8,4,6,3,7,1]=>[4,1,1,1,1]
[4,3,7,1,2,6,8,5]=>[3,2,1,1,1]
[8,1,6,5,2,7,4,3]=>[5,2,1]
[6,8,1,5,2,7,4,3]=>[4,2,1,1]
[4,5,8,2,3,7,6,1]=>[4,1,1,1,1]
[5,6,2,7,4,8,3,1]=>[4,2,1,1]
[1,7,3,2,4,8,6,5]=>[3,3,1,1]
[4,3,1,8,2,6,7,5]=>[3,3,1,1]
[4,8,1,3,2,5,7,6]=>[3,2,1,1,1]
[1,7,5,3,8,6,2,4]=>[4,2,1,1]
[2,5,3,8,1,4,7,6]=>[3,2,1,1,1]
[4,2,5,8,1,3,7,6]=>[3,2,1,1,1]
[8,1,2,4,3,5,7,6]=>[3,2,1,1,1]
[2,4,3,8,1,5,7,6]=>[3,2,1,1,1]
[3,1,7,4,8,6,5,2]=>[4,2,2]
[6,4,5,3,2,8,7,1]=>[5,2,1]
[2,7,3,8,5,1,6,4]=>[3,2,2,1]
[8,7,3,2,5,6,4,1]=>[5,2,1]
[3,1,8,2,6,5,4,7]=>[4,2,1,1]
[7,6,2,8,1,4,5,3]=>[4,2,1,1]
[2,3,8,4,1,5,7,6]=>[3,2,1,1,1]
[8,4,2,3,1,5,7,6]=>[4,2,1,1]
[8,2,3,4,1,5,7,6]=>[3,2,1,1,1]
[7,1,6,2,4,8,3,5]=>[4,1,1,1,1]
[2,7,8,1,4,3,6,5]=>[3,2,1,1,1]
[6,5,8,1,3,2,4,7]=>[4,1,1,1,1]
[2,1,8,5,3,4,6,7]=>[3,2,1,1,1]
[8,4,1,3,2,5,6,7]=>[4,1,1,1,1]
[8,6,1,2,3,5,4,7]=>[4,1,1,1,1]
[7,8,1,5,2,4,6,3]=>[4,1,1,1,1]
[2,8,6,3,1,5,4,7]=>[4,2,1,1]
[5,7,2,8,4,1,6,3]=>[3,2,2,1]
[2,5,6,3,8,1,4,7]=>[3,1,1,1,1,1]
[7,4,5,6,8,1,3,2]=>[4,1,1,1,1]
[7,6,8,1,4,5,3,2]=>[5,1,1,1]
[7,5,1,8,4,6,3,2]=>[5,2,1]
[1,7,8,5,6,4,3,2]=>[5,1,1,1]
[7,3,6,2,5,4,8,1]=>[5,1,1,1]
[1,6,2,3,5,8,4,7]=>[3,1,1,1,1,1]
[1,8,5,6,4,3,7,2]=>[5,1,1,1]
[2,6,8,4,5,1,7,3]=>[3,2,1,1,1]
[5,3,2,1,7,8,4,6]=>[4,2,1,1]
[8,4,1,3,6,7,2,5]=>[4,1,1,1,1]
[1,6,5,3,8,4,7,2]=>[4,2,1,1]
[7,6,2,3,5,1,4,8]=>[4,1,1,1,1]
[6,2,5,3,4,8,1,7]=>[4,1,1,1,1]
[6,2,5,3,4,8,7,1]=>[4,2,1,1]
[2,6,5,3,4,8,1,7]=>[4,1,1,1,1]
[5,3,4,8,1,7,2,6]=>[3,2,1,1,1]
[5,1,3,4,8,7,2,6]=>[3,2,1,1,1]
[1,5,3,4,8,7,2,6]=>[3,2,1,1,1]
[5,1,3,8,4,7,6,2]=>[4,2,1,1]
[5,3,8,1,4,7,6,2]=>[4,2,1,1]
[4,3,5,8,1,7,6,2]=>[4,2,1,1]
[3,6,5,4,8,1,2,7]=>[4,1,1,1,1]
[3,6,5,4,8,2,7,1]=>[5,1,1,1]
[3,5,2,4,8,7,6,1]=>[4,2,1,1]
[2,5,3,6,8,4,1,7]=>[3,2,1,1,1]
[4,6,2,5,1,7,8,3]=>[3,2,1,1,1]
[2,3,1,7,4,8,6,5]=>[3,2,2,1]
[2,3,8,7,6,4,1,5]=>[5,1,1,1]
[7,5,2,3,1,6,4,8]=>[4,2,1,1]
[1,8,3,6,4,2,7,5]=>[4,2,1,1]
[2,1,7,4,8,5,3,6]=>[3,2,2,1]
[8,1,7,3,2,5,4,6]=>[4,2,1,1]
[7,8,5,2,6,4,3,1]=>[5,2,1]
[4,2,8,1,3,6,7,5]=>[3,2,1,1,1]
[8,1,2,5,7,4,6,3]=>[4,1,1,1,1]
[7,4,6,3,1,2,5,8]=>[4,1,1,1,1]
[8,2,5,3,6,1,4,7]=>[4,1,1,1,1]
[3,7,5,1,4,6,2,8]=>[4,1,1,1,1]
[6,8,7,4,1,5,2,3]=>[4,2,1,1]
[8,6,4,7,5,1,3,2]=>[5,2,1]
[6,1,2,4,7,8,3,5]=>[3,1,1,1,1,1]
[2,4,6,5,7,1,8,3]=>[3,2,1,1,1]
[4,2,6,7,8,5,3,1]=>[4,2,1,1]
[6,2,4,7,8,5,3,1]=>[4,2,1,1]
[3,5,2,1,7,8,6,4]=>[3,3,1,1]
[4,2,7,8,6,5,1,3]=>[4,2,1,1]
[1,2,7,8,6,4,5,3]=>[4,1,1,1,1]
[4,8,1,2,6,5,3,7]=>[4,1,1,1,1]
[6,4,8,1,2,3,7,5]=>[3,2,1,1,1]
[7,4,1,3,6,8,5,2]=>[4,2,1,1]
[5,2,7,1,4,6,3,8]=>[3,2,1,1,1]
[6,3,8,5,7,1,4,2]=>[4,2,1,1]
[2,4,3,8,5,7,1,6]=>[3,2,1,1,1]
[2,8,3,1,4,6,5,7]=>[3,2,1,1,1]
[4,5,7,6,1,3,8,2]=>[4,1,1,1,1]
[3,7,1,6,5,8,2,4]=>[4,1,1,1,1]
[7,4,3,6,8,2,1,5]=>[5,1,1,1]
[3,8,5,4,7,6,1,2]=>[4,2,1,1]
[1,4,6,8,7,3,5,2]=>[4,1,1,1,1]
[4,6,5,1,3,8,7,2]=>[4,2,1,1]
[5,4,6,2,1,8,7,3]=>[4,3,1]
[3,2,8,5,1,4,6,7]=>[3,2,1,1,1]
[3,5,4,1,2,8,6,7]=>[3,2,1,1,1]
[5,3,8,1,4,2,6,7]=>[3,2,1,1,1]
[5,3,8,1,4,2,7,6]=>[3,2,2,1]
[1,4,7,5,8,6,2,3]=>[3,2,1,1,1]
[8,5,7,6,3,4,1,2]=>[5,1,1,1]
[7,5,2,6,1,4,8,3]=>[4,2,1,1]
[2,4,5,1,8,3,7,6]=>[3,2,1,1,1]
[7,2,8,5,3,4,1,6]=>[4,2,1,1]
[6,4,5,3,1,7,8,2]=>[4,2,1,1]
[7,3,5,6,4,1,8,2]=>[4,2,1,1]
[2,5,6,3,4,1,8,7]=>[3,2,1,1,1]
[4,6,2,1,5,8,3,7]=>[3,2,1,1,1]
[4,6,7,2,3,8,5,1]=>[3,2,1,1,1]
[4,5,3,7,8,1,2,6]=>[3,1,1,1,1,1]
[2,3,5,8,1,6,4,7]=>[3,1,1,1,1,1]
[1,7,4,5,8,3,6,2]=>[4,1,1,1,1]
[2,8,5,6,3,1,4,7]=>[4,1,1,1,1]
[4,8,2,6,1,5,7,3]=>[4,1,1,1,1]
[2,3,7,8,1,5,4,6]=>[3,1,1,1,1,1]
[5,2,6,7,8,3,1,4]=>[3,2,1,1,1]
[5,6,2,7,8,3,1,4]=>[3,2,1,1,1]
[2,3,7,5,8,4,6,1]=>[4,1,1,1,1]
[3,7,8,5,1,4,6,2]=>[4,1,1,1,1]
[2,5,6,7,1,8,4,3]=>[3,2,1,1,1]
[8,5,3,6,4,2,1,7]=>[5,2,1]
[6,4,7,8,1,2,5,3]=>[3,2,1,1,1]
[7,5,8,1,2,3,6,4]=>[3,2,1,1,1]
[1,2,8,7,4,6,5,3]=>[5,1,1,1]
[5,1,4,8,7,3,6,2]=>[4,2,1,1]
[4,3,1,8,7,5,6,2]=>[4,3,1]
[4,3,2,7,6,1,5,8]=>[4,2,1,1]
[7,2,6,5,3,1,4,8]=>[5,1,1,1]
[1,3,7,6,2,4,8,5]=>[3,2,1,1,1]
[1,3,8,2,7,4,6,5]=>[4,1,1,1,1]
[8,2,7,1,6,4,3,5]=>[5,1,1,1]
[4,3,2,8,1,7,5,6]=>[4,2,1,1]
[7,5,4,1,6,3,8,2]=>[5,2,1]
[1,6,5,3,2,4,8,7]=>[4,2,1,1]
[1,7,3,5,2,4,8,6]=>[3,2,1,1,1]
[4,3,7,2,5,1,6,8]=>[4,1,1,1,1]
[5,1,4,3,2,6,8,7]=>[4,2,1,1]
[7,2,1,3,5,4,6,8]=>[3,2,1,1,1]
[8,3,7,5,4,2,6,1]=>[6,1,1]
[1,6,8,7,5,2,3,4]=>[4,1,1,1,1]
[4,3,6,1,8,5,2,7]=>[3,3,1,1]
[1,3,6,2,5,4,8,7]=>[3,2,1,1,1]
[1,4,8,7,3,6,2,5]=>[4,1,1,1,1]
[4,5,7,6,3,1,8,2]=>[4,2,1,1]
[4,6,7,5,1,3,8,2]=>[4,1,1,1,1]
[3,6,5,1,4,7,8,2]=>[4,1,1,1,1]
[4,6,7,3,1,5,8,2]=>[3,2,1,1,1]
[6,2,4,7,5,3,1,8]=>[4,2,1,1]
[6,2,5,1,8,7,3,4]=>[3,3,1,1]
[3,2,6,1,5,8,7,4]=>[3,3,1,1]
[4,2,3,6,7,5,1,8]=>[3,2,1,1,1]
[6,2,3,5,7,4,1,8]=>[4,1,1,1,1]
[1,6,3,8,4,7,2,5]=>[3,2,1,1,1]
[8,1,5,2,4,7,3,6]=>[4,1,1,1,1]
[7,5,8,1,4,2,3,6]=>[4,1,1,1,1]
[1,3,4,8,5,6,2,7]=>[3,1,1,1,1,1]
[3,2,7,1,8,6,5,4]=>[4,3,1]
[1,3,8,5,6,7,2,4]=>[3,1,1,1,1,1]
[6,2,4,1,5,7,8,3]=>[3,2,1,1,1]
[5,8,4,1,3,6,7,2]=>[4,1,1,1,1]
[6,7,2,3,8,1,4,5]=>[3,1,1,1,1,1]
[3,2,7,4,8,1,5,6]=>[3,2,1,1,1]
[5,2,8,1,7,4,6,3]=>[4,2,1,1]
[2,5,4,7,3,1,8,6]=>[4,2,1,1]
[4,6,3,1,2,5,7,8]=>[3,1,1,1,1,1]
[7,4,6,8,3,1,2,5]=>[4,1,1,1,1]
[8,5,4,7,3,1,2,6]=>[5,1,1,1]
[7,3,2,1,5,4,8,6]=>[4,2,2]
[2,5,6,4,8,1,3,7]=>[3,1,1,1,1,1]
[5,4,1,6,2,3,7,8]=>[3,2,1,1,1]
[1,3,6,5,2,4,7,8]=>[3,1,1,1,1,1]
[5,4,1,2,7,6,3,8]=>[3,3,1,1]
[5,8,7,3,1,2,4,6]=>[4,1,1,1,1]
[2,7,8,1,4,5,3,6]=>[3,1,1,1,1,1]
[4,1,2,8,7,3,6,5]=>[4,2,1,1]
[6,1,2,4,3,8,7,5]=>[3,3,1,1]
[3,7,8,1,2,4,6,5]=>[3,1,1,1,1,1]
[7,3,4,1,2,6,8,5]=>[3,2,1,1,1]
[8,4,3,1,2,6,5,7]=>[4,2,1,1]
[3,8,2,7,4,5,1,6]=>[4,1,1,1,1]
[8,6,2,3,5,4,1,7]=>[5,1,1,1]
[8,2,6,1,3,5,4,7]=>[4,1,1,1,1]
[8,4,3,7,2,5,6,1]=>[5,1,1,1]
[8,3,1,7,4,5,2,6]=>[4,2,1,1]
[8,2,4,5,1,7,3,6]=>[3,2,1,1,1]
[6,8,2,4,5,1,7,3]=>[3,2,1,1,1]
[4,3,8,1,7,5,6,2]=>[4,2,1,1]
[8,4,3,7,1,5,6,2]=>[4,2,1,1]
[8,3,4,7,2,6,5,1]=>[5,1,1,1]
[8,1,3,7,6,4,5,2]=>[5,1,1,1]
[8,3,7,1,4,5,6,2]=>[4,1,1,1,1]
[8,7,3,6,1,2,5,4]=>[5,1,1,1]
[8,3,7,6,2,4,5,1]=>[5,1,1,1]
[8,7,2,3,6,1,5,4]=>[5,1,1,1]
[8,2,7,1,3,4,6,5]=>[4,1,1,1,1]
[5,1,8,4,2,3,7,6]=>[3,2,2,1]
[8,2,4,7,3,1,6,5]=>[4,2,1,1]
[8,2,7,6,3,1,4,5]=>[5,1,1,1]
[6,8,1,4,7,3,2,5]=>[4,1,1,1,1]
[8,5,7,2,6,3,1,4]=>[5,1,1,1]
[5,8,2,7,3,1,6,4]=>[4,2,1,1]
[8,1,2,6,7,5,4,3]=>[5,1,1,1]
[8,4,1,7,5,6,2,3]=>[4,2,1,1]
[8,2,4,7,6,5,1,3]=>[5,1,1,1]
[8,2,7,6,4,5,1,3]=>[5,1,1,1]
[8,4,7,2,3,6,5,1]=>[5,1,1,1]
[8,2,4,7,3,6,5,1]=>[5,1,1,1]
[8,1,7,6,4,5,2,3]=>[5,1,1,1]
[8,1,2,7,6,4,5,3]=>[5,1,1,1]
[8,1,4,7,3,6,5,2]=>[5,1,1,1]
[2,8,1,5,3,7,6,4]=>[4,2,1,1]
[1,8,2,4,7,5,6,3]=>[4,1,1,1,1]
[2,3,8,4,7,1,6,5]=>[4,1,1,1,1]
[1,8,2,3,5,6,4,7]=>[3,1,1,1,1,1]
[1,4,7,6,2,3,5,8]=>[3,1,1,1,1,1]
[1,7,6,2,3,8,4,5]=>[3,2,1,1,1]
[1,8,2,3,7,6,4,5]=>[4,1,1,1,1]
[1,7,3,8,6,2,5,4]=>[4,2,1,1]
[5,8,2,3,7,4,1,6]=>[4,1,1,1,1]
[1,3,5,6,4,8,2,7]=>[3,1,1,1,1,1]
[3,1,7,8,5,2,4,6]=>[3,2,1,1,1]
[4,6,1,8,2,7,5,3]=>[4,2,1,1]
[6,3,5,2,8,4,7,1]=>[4,2,1,1]
[1,6,3,5,2,8,4,7]=>[3,2,1,1,1]
[5,4,8,6,3,7,2,1]=>[5,2,1]
[6,4,5,8,1,3,7,2]=>[4,1,1,1,1]
[6,3,5,1,8,4,7,2]=>[4,2,1,1]
[2,6,3,1,5,8,4,7]=>[3,2,1,1,1]
[2,5,4,8,6,3,1,7]=>[4,2,1,1]
[2,5,4,8,6,3,7,1]=>[4,2,1,1]
[1,2,5,4,8,6,3,7]=>[3,2,1,1,1]
[6,4,5,8,2,1,7,3]=>[4,2,1,1]
[5,3,4,1,2,6,8,7]=>[3,2,1,1,1]
[1,4,3,5,2,8,6,7]=>[3,2,1,1,1]
[1,3,5,4,8,2,6,7]=>[3,1,1,1,1,1]
[3,5,4,8,2,6,1,7]=>[4,1,1,1,1]
[3,6,4,5,1,2,8,7]=>[3,2,1,1,1]
[4,3,5,1,8,6,2,7]=>[3,3,1,1]
[3,5,4,8,1,6,2,7]=>[3,2,1,1,1]
[3,4,8,5,6,1,2,7]=>[3,1,1,1,1,1]
[3,4,8,5,6,2,1,7]=>[4,1,1,1,1]
[3,5,4,8,1,6,7,2]=>[3,2,1,1,1]
[2,4,3,1,5,8,6,7]=>[3,2,1,1,1]
[1,7,6,2,5,4,8,3]=>[5,1,1,1]
[5,6,1,7,4,3,8,2]=>[4,2,1,1]
[3,1,5,6,4,2,7,8]=>[3,2,1,1,1]
[8,3,4,1,6,5,7,2]=>[4,2,1,1]
[8,1,6,4,3,5,2,7]=>[5,1,1,1]
[1,3,7,8,2,6,4,5]=>[3,1,1,1,1,1]
[2,1,6,5,3,8,7,4]=>[3,3,2]
[3,7,5,6,4,2,1,8]=>[5,1,1,1]
[6,1,4,3,7,5,8,2]=>[4,2,1,1]
[3,8,6,4,5,2,7,1]=>[5,1,1,1]
[4,5,8,6,2,3,7,1]=>[4,1,1,1,1]
[4,6,8,5,3,7,2,1]=>[5,1,1,1]
[4,5,7,2,8,6,3,1]=>[4,2,1,1]
[3,7,4,5,1,6,8,2]=>[3,2,1,1,1]
[4,6,8,1,2,5,7,3]=>[3,1,1,1,1,1]
[4,6,8,5,1,3,7,2]=>[4,1,1,1,1]
[3,7,4,5,2,8,6,1]=>[4,2,1,1]
[3,7,8,4,6,1,5,2]=>[4,1,1,1,1]
[4,5,7,2,1,6,8,3]=>[3,2,1,1,1]
[4,5,1,6,8,3,7,2]=>[3,2,1,1,1]
[8,3,5,4,6,1,2,7]=>[4,1,1,1,1]
[1,7,4,5,2,6,8,3]=>[3,2,1,1,1]
[1,4,2,6,5,3,8,7]=>[3,2,2,1]
[3,1,5,8,4,6,2,7]=>[3,2,1,1,1]
[8,2,6,3,4,1,5,7]=>[4,1,1,1,1]
[4,6,5,8,2,1,3,7]=>[4,1,1,1,1]
[1,4,8,3,5,6,2,7]=>[3,1,1,1,1,1]
[1,8,7,4,2,3,6,5]=>[4,2,1,1]
[7,4,6,2,1,3,8,5]=>[4,2,1,1]
[5,4,8,7,6,2,3,1]=>[5,2,1]
[5,2,3,8,7,1,6,4]=>[4,2,1,1]
[7,5,2,4,1,3,8,6]=>[4,2,1,1]
[7,2,6,8,5,1,3,4]=>[4,1,1,1,1]
[8,2,3,4,1,6,7,5]=>[3,2,1,1,1]
[7,4,3,8,1,6,5,2]=>[4,3,1]
[6,5,1,4,3,8,7,2]=>[5,2,1]
[4,7,6,2,5,8,1,3]=>[4,1,1,1,1]
[6,3,2,4,5,8,1,7]=>[4,1,1,1,1]
[2,6,4,5,8,3,1,7]=>[4,1,1,1,1]
[7,3,5,2,8,1,4,6]=>[4,1,1,1,1]
[1,5,8,7,4,2,3,6]=>[4,1,1,1,1]
[1,7,2,4,5,8,6,3]=>[3,2,1,1,1]
[1,4,6,8,7,2,5,3]=>[4,1,1,1,1]
[1,6,2,7,5,3,4,8]=>[3,2,1,1,1]
[1,3,7,2,6,4,5,8]=>[3,1,1,1,1,1]
[1,7,3,2,8,5,6,4]=>[3,3,1,1]
[1,6,5,2,4,8,3,7]=>[4,1,1,1,1]
[1,7,3,8,4,2,5,6]=>[3,2,1,1,1]
[1,6,2,4,7,5,8,3]=>[3,2,1,1,1]
[1,6,2,7,4,3,8,5]=>[3,2,2,1]
[1,5,8,2,3,6,4,7]=>[3,1,1,1,1,1]
[2,5,3,6,7,1,4,8]=>[3,1,1,1,1,1]
[6,4,1,5,7,2,3,8]=>[3,2,1,1,1]
[6,4,1,5,7,3,8,2]=>[4,2,1,1]
[1,2,7,3,8,5,6,4]=>[3,2,1,1,1]
[7,4,1,6,3,8,2,5]=>[4,2,1,1]
[1,5,7,4,3,8,6,2]=>[4,2,1,1]
[2,7,3,1,4,5,8,6]=>[3,2,1,1,1]
[6,5,8,3,2,7,1,4]=>[5,1,1,1]
[8,4,3,1,7,6,5,2]=>[5,3]
[1,2,6,8,7,4,5,3]=>[4,1,1,1,1]
[3,4,5,6,8,2,7,1]=>[3,1,1,1,1,1]
[7,2,1,4,5,6,3,8]=>[3,2,1,1,1]
[1,5,6,7,3,4,2,8]=>[3,1,1,1,1,1]
[4,6,8,5,2,1,7,3]=>[4,2,1,1]
[1,6,7,8,2,4,5,3]=>[3,1,1,1,1,1]
[4,7,8,2,1,3,5,6]=>[3,1,1,1,1,1]
[5,7,8,3,2,4,6,1]=>[4,1,1,1,1]
[5,7,8,2,3,1,6,4]=>[3,2,1,1,1]
[4,5,2,7,8,6,1,3]=>[3,2,1,1,1]
[1,3,5,8,7,2,6,4]=>[4,1,1,1,1]
[6,4,1,8,5,7,3,2]=>[4,3,1]
[4,1,3,8,7,5,2,6]=>[4,2,1,1]
[8,5,1,6,7,2,4,3]=>[4,2,1,1]
[3,6,7,2,1,5,8,4]=>[3,2,1,1,1]
[2,5,6,1,3,8,7,4]=>[3,2,1,1,1]
[7,2,5,6,1,3,8,4]=>[3,2,1,1,1]
[6,4,1,2,5,8,3,7]=>[3,2,1,1,1]
[4,6,3,5,7,1,8,2]=>[3,2,1,1,1]
[4,7,3,5,2,6,8,1]=>[4,1,1,1,1]
[6,8,4,1,5,7,3,2]=>[4,2,1,1]
[8,1,6,2,3,7,5,4]=>[4,2,1,1]
[2,8,3,6,4,1,7,5]=>[4,2,1,1]
[6,5,3,4,8,2,1,7]=>[5,1,1,1]
[5,4,8,7,3,6,2,1]=>[5,2,1]
[5,2,7,6,8,3,4,1]=>[4,2,1,1]
[8,4,5,2,7,3,6,1]=>[4,2,1,1]
[6,3,7,4,5,2,8,1]=>[4,2,1,1]
[7,3,4,2,8,5,6,1]=>[4,2,1,1]
[4,3,6,5,8,2,7,1]=>[4,2,1,1]
[8,2,7,4,5,3,6,1]=>[5,1,1,1]
[7,2,8,4,5,3,6,1]=>[4,2,1,1]
[6,3,8,2,7,4,5,1]=>[4,2,1,1]
[3,2,8,4,7,5,6,1]=>[4,2,1,1]
[8,3,6,2,7,4,5,1]=>[4,2,1,1]
[1,7,8,4,3,6,5,2]=>[4,2,1,1]
[1,7,8,3,6,5,4,2]=>[5,1,1,1]
[6,4,5,8,7,2,1,3]=>[4,2,1,1]
[5,8,1,7,2,4,3,6]=>[4,1,1,1,1]
[2,5,7,3,8,1,4,6]=>[3,1,1,1,1,1]
[8,3,5,2,1,6,7,4]=>[4,2,1,1]
[2,6,4,7,1,8,5,3]=>[3,3,1,1]
[1,6,5,7,3,8,2,4]=>[4,1,1,1,1]
[1,8,5,3,7,6,2,4]=>[4,2,1,1]
[6,4,2,3,8,7,5,1]=>[4,3,1]
[6,1,4,2,7,8,3,5]=>[3,2,1,1,1]
[6,5,1,3,7,8,4,2]=>[4,2,1,1]
[5,1,3,2,7,8,6,4]=>[3,3,1,1]
[6,7,4,2,3,8,5,1]=>[4,2,1,1]
[5,8,7,3,2,4,6,1]=>[5,1,1,1]
[5,7,1,4,6,8,2,3]=>[3,1,1,1,1,1]
[2,4,1,7,5,6,3,8]=>[3,2,1,1,1]
[1,4,3,7,6,2,8,5]=>[3,2,2,1]
[1,6,2,5,7,3,8,4]=>[3,2,1,1,1]
[1,4,3,8,2,5,7,6]=>[3,2,1,1,1]
[1,5,7,3,6,4,2,8]=>[4,1,1,1,1]
[1,6,7,2,4,8,3,5]=>[3,1,1,1,1,1]
[3,7,2,8,4,1,5,6]=>[3,2,1,1,1]
[5,3,4,1,7,8,6,2]=>[3,3,1,1]
[4,7,6,5,8,2,3,1]=>[5,1,1,1]
[4,1,8,3,2,6,5,7]=>[3,2,2,1]
[1,2,6,8,4,3,5,7]=>[3,1,1,1,1,1]
[7,2,6,3,1,8,4,5]=>[4,2,1,1]
[5,8,4,1,3,7,2,6]=>[4,1,1,1,1]
[3,4,2,1,6,8,5,7]=>[3,2,1,1,1]
[8,1,3,5,6,4,7,2]=>[4,1,1,1,1]
[3,4,7,1,5,6,2,8]=>[3,1,1,1,1,1]
[4,8,2,6,5,3,7,1]=>[5,1,1,1]
[4,8,7,2,5,6,1,3]=>[4,1,1,1,1]
[5,8,6,4,7,3,2,1]=>[6,1,1]
[8,5,2,3,1,6,7,4]=>[4,2,1,1]
[2,8,6,3,5,1,7,4]=>[4,2,1,1]
[8,3,2,6,4,1,7,5]=>[4,2,2]
[8,4,1,5,3,6,7,2]=>[4,2,1,1]
[8,3,5,1,4,6,7,2]=>[4,1,1,1,1]
[8,5,1,3,4,6,7,2]=>[4,1,1,1,1]
[3,8,6,2,5,4,7,1]=>[5,1,1,1]
[3,8,4,6,5,2,7,1]=>[5,1,1,1]
[8,1,7,4,2,5,3,6]=>[4,2,1,1]
[8,3,2,5,1,4,7,6]=>[4,2,1,1]
[8,4,5,1,2,6,7,3]=>[3,2,1,1,1]
[8,1,5,3,2,6,7,4]=>[4,2,1,1]
[8,1,5,2,4,6,7,3]=>[4,1,1,1,1]
[5,2,6,4,1,3,8,7]=>[3,2,2,1]
[7,1,3,5,2,8,6,4]=>[3,3,1,1]
[8,6,4,7,1,3,5,2]=>[5,1,1,1]
[6,8,4,3,2,1,7,5]=>[5,2,1]
[2,1,8,5,4,3,7,6]=>[4,2,2]
[6,2,8,5,4,1,3,7]=>[4,2,1,1]
[6,4,8,5,3,2,7,1]=>[5,2,1]
[8,5,4,6,2,7,1,3]=>[5,1,1,1]
[6,8,5,4,7,2,3,1]=>[5,1,1,1]
[2,5,7,3,4,8,1,6]=>[3,1,1,1,1,1]
[5,2,4,7,8,1,3,6]=>[3,1,1,1,1,1]
[4,8,5,6,1,2,7,3]=>[3,2,1,1,1]
[2,5,6,8,7,1,4,3]=>[4,1,1,1,1]
[1,7,8,5,4,6,2,3]=>[4,1,1,1,1]
[4,6,8,1,5,2,7,3]=>[3,2,1,1,1]
[8,2,3,6,4,1,7,5]=>[4,2,1,1]
[2,3,7,5,8,6,1,4]=>[3,2,1,1,1]
[1,3,6,4,8,2,7,5]=>[3,2,1,1,1]
[1,7,6,2,8,5,3,4]=>[4,2,1,1]
[1,5,8,6,4,7,2,3]=>[4,1,1,1,1]
[5,6,2,8,1,7,3,4]=>[3,2,1,1,1]
[6,8,4,5,1,3,7,2]=>[4,1,1,1,1]
[5,2,3,8,1,4,6,7]=>[3,1,1,1,1,1]
[1,6,8,3,2,4,5,7]=>[3,1,1,1,1,1]
[8,6,5,2,4,3,7,1]=>[6,1,1]
[6,2,5,3,7,4,8,1]=>[4,2,1,1]
[8,5,4,2,6,3,7,1]=>[5,2,1]
[8,5,3,2,6,4,7,1]=>[5,2,1]
[7,4,6,5,8,2,3,1]=>[5,1,1,1]
[7,3,6,5,8,2,4,1]=>[5,1,1,1]
[7,3,6,4,8,2,5,1]=>[5,1,1,1]
[7,3,5,4,8,2,6,1]=>[5,1,1,1]
[7,3,6,8,4,5,1,2]=>[4,1,1,1,1]
[1,6,5,7,4,2,8,3]=>[4,2,1,1]
[1,2,7,4,8,5,6,3]=>[3,2,1,1,1]
[2,6,7,4,8,5,1,3]=>[3,2,1,1,1]
[2,5,8,6,4,3,7,1]=>[5,1,1,1]
[6,4,2,5,7,1,8,3]=>[4,2,1,1]
[2,7,5,4,6,8,1,3]=>[4,1,1,1,1]
[8,1,4,7,3,5,6,2]=>[4,1,1,1,1]
[8,3,7,2,4,5,6,1]=>[4,1,1,1,1]
[8,1,4,5,7,3,6,2]=>[4,1,1,1,1]
[5,6,3,4,2,8,7,1]=>[4,2,1,1]
[2,5,7,4,6,8,1,3]=>[3,1,1,1,1,1]
[2,5,6,4,1,3,8,7]=>[3,2,1,1,1]
[4,6,1,3,5,7,2,8]=>[3,1,1,1,1,1]
[3,2,7,5,8,1,6,4]=>[3,2,2,1]
[4,3,6,8,5,2,1,7]=>[4,2,1,1]
[4,5,3,2,1,8,6,7]=>[4,2,1,1]
[3,6,5,8,1,7,4,2]=>[4,2,1,1]
[4,1,6,8,5,2,3,7]=>[3,2,1,1,1]
[4,5,2,8,6,7,1,3]=>[3,2,1,1,1]
[4,5,2,8,6,7,3,1]=>[4,2,1,1]
[3,5,8,6,2,4,7,1]=>[4,1,1,1,1]
[2,5,1,6,4,8,3,7]=>[3,2,1,1,1]
[3,2,4,5,8,6,1,7]=>[3,2,1,1,1]
[4,5,2,1,3,8,6,7]=>[3,2,1,1,1]
[4,2,3,6,8,5,1,7]=>[3,2,1,1,1]
[4,5,1,3,2,8,6,7]=>[3,2,1,1,1]
[3,4,5,8,6,1,7,2]=>[3,2,1,1,1]
[3,4,5,8,6,1,2,7]=>[3,1,1,1,1,1]
[6,4,1,3,7,8,2,5]=>[4,1,1,1,1]
[6,3,1,2,5,4,8,7]=>[3,2,2,1]
[7,3,1,2,5,4,8,6]=>[3,2,2,1]
[1,5,8,2,4,3,7,6]=>[3,2,1,1,1]
[4,3,7,8,2,6,5,1]=>[4,2,1,1]
[3,8,5,1,2,6,7,4]=>[3,2,1,1,1]
[2,4,7,8,3,6,5,1]=>[4,1,1,1,1]
[5,4,7,8,3,6,1,2]=>[4,1,1,1,1]
[6,8,1,3,2,5,7,4]=>[3,2,1,1,1]
[1,4,8,5,7,2,3,6]=>[3,1,1,1,1,1]
[1,8,7,3,2,4,5,6]=>[4,1,1,1,1]
[8,6,2,7,3,4,1,5]=>[4,2,1,1]
[8,6,2,7,3,4,5,1]=>[4,2,1,1]
[5,6,3,2,8,7,1,4]=>[4,2,1,1]
[5,1,6,7,8,3,2,4]=>[3,2,1,1,1]
[1,5,6,3,7,2,4,8]=>[3,1,1,1,1,1]
[1,5,6,7,4,2,3,8]=>[3,1,1,1,1,1]
[5,1,6,7,3,4,2,8]=>[3,2,1,1,1]
[8,6,1,7,3,4,5,2]=>[4,2,1,1]
[6,8,5,1,7,4,2,3]=>[4,2,1,1]
[8,4,2,3,5,7,6,1]=>[4,2,1,1]
[4,8,5,2,3,1,6,7]=>[4,1,1,1,1]
[5,4,8,3,1,2,6,7]=>[4,1,1,1,1]
[8,4,7,3,2,5,6,1]=>[5,1,1,1]
[6,8,5,1,7,3,4,2]=>[4,2,1,1]
[6,2,7,3,8,1,4,5]=>[3,2,1,1,1]
[8,4,2,6,7,1,5,3]=>[4,2,1,1]
[1,7,8,3,6,5,2,4]=>[4,1,1,1,1]
[4,6,7,5,1,8,2,3]=>[3,2,1,1,1]
[3,5,2,6,8,7,4,1]=>[4,2,1,1]
[7,3,6,8,4,1,2,5]=>[4,1,1,1,1]
[6,4,2,3,7,5,8,1]=>[4,2,1,1]
[6,3,7,5,1,2,8,4]=>[3,2,2,1]
[7,2,5,4,8,6,3,1]=>[5,2,1]
[6,2,3,8,7,4,5,1]=>[4,2,1,1]
[7,1,2,8,4,6,5,3]=>[4,2,1,1]
[3,5,8,1,2,7,6,4]=>[4,1,1,1,1]
[1,4,3,6,8,5,2,7]=>[3,2,1,1,1]
[7,6,2,8,5,3,4,1]=>[5,2,1]
[6,8,3,5,4,7,2,1]=>[5,1,1,1]
[8,2,7,6,4,1,3,5]=>[5,1,1,1]
[8,3,7,5,1,6,2,4]=>[4,2,1,1]
[8,5,7,1,4,2,6,3]=>[4,2,1,1]
[4,7,1,5,6,3,2,8]=>[4,1,1,1,1]
[4,5,7,1,6,3,8,2]=>[4,1,1,1,1]
[4,6,5,7,2,3,8,1]=>[4,1,1,1,1]
[3,6,7,2,5,8,4,1]=>[4,1,1,1,1]
[5,3,6,7,4,8,1,2]=>[3,2,1,1,1]
[4,2,7,8,3,6,5,1]=>[4,2,1,1]
[4,2,7,8,5,6,1,3]=>[3,2,1,1,1]
[5,4,3,7,8,1,6,2]=>[4,2,1,1]
[3,5,7,8,4,2,1,6]=>[4,1,1,1,1]
[4,6,7,3,2,8,1,5]=>[4,1,1,1,1]
[4,6,5,3,7,8,1,2]=>[4,1,1,1,1]
[5,6,2,4,7,8,3,1]=>[4,1,1,1,1]
[5,6,3,2,8,4,7,1]=>[4,2,1,1]
[5,6,2,8,3,4,7,1]=>[3,2,1,1,1]
[3,7,4,8,1,6,5,2]=>[4,2,1,1]
[5,2,4,8,6,7,3,1]=>[4,2,1,1]
[5,2,6,4,8,7,3,1]=>[4,2,2]
[2,4,7,8,6,5,1,3]=>[4,1,1,1,1]
[5,2,6,7,8,1,4,3]=>[3,2,1,1,1]
[4,8,2,7,5,3,1,6]=>[5,1,1,1]
[1,2,4,6,5,8,3,7]=>[3,1,1,1,1,1]
[5,4,2,3,1,7,8,6]=>[4,2,1,1]
[5,8,6,1,7,2,3,4]=>[3,2,1,1,1]
[5,1,4,3,8,2,6,7]=>[4,1,1,1,1]
[8,4,7,5,6,2,1,3]=>[5,1,1,1]
[3,8,6,7,5,2,4,1]=>[5,1,1,1]
[8,2,5,4,7,3,6,1]=>[5,1,1,1]
[4,2,8,7,3,6,5,1]=>[5,2,1]
[3,7,8,6,1,4,5,2]=>[4,1,1,1,1]
[4,6,7,8,2,1,5,3]=>[3,2,1,1,1]
[4,7,6,3,8,1,5,2]=>[4,2,1,1]
[3,8,1,4,6,2,5,7]=>[3,1,1,1,1,1]
[2,4,5,3,8,7,1,6]=>[3,2,1,1,1]
[4,7,5,6,2,8,1,3]=>[4,1,1,1,1]
[8,7,5,1,6,3,2,4]=>[5,2,1]
[7,8,6,2,3,5,1,4]=>[4,1,1,1,1]
[2,8,4,6,7,3,5,1]=>[4,1,1,1,1]
[4,1,6,7,8,2,5,3]=>[3,2,1,1,1]
[8,6,3,4,1,2,7,5]=>[4,2,1,1]
[2,5,8,4,6,1,3,7]=>[3,1,1,1,1,1]
[4,7,8,6,5,1,3,2]=>[5,1,1,1]
[8,4,6,7,3,5,2,1]=>[5,1,1,1]
[6,8,4,7,3,5,2,1]=>[5,1,1,1]
[7,4,5,8,3,6,2,1]=>[5,1,1,1]
[8,4,7,3,5,6,2,1]=>[5,1,1,1]
[3,6,4,2,8,1,7,5]=>[4,2,1,1]
[8,4,6,2,1,7,3,5]=>[4,2,1,1]
[3,8,6,2,1,7,4,5]=>[4,2,1,1]
[3,1,8,2,4,6,5,7]=>[3,2,1,1,1]
[8,1,7,6,2,5,4,3]=>[6,1,1]
[8,5,4,3,7,6,1,2]=>[5,2,1]
[4,8,1,3,6,7,5,2]=>[4,1,1,1,1]
[3,5,8,6,1,7,4,2]=>[4,2,1,1]
[8,1,4,7,5,2,6,3]=>[4,2,1,1]
[1,4,8,6,7,3,5,2]=>[4,1,1,1,1]
[4,1,6,7,8,5,3,2]=>[4,2,1,1]
[3,7,8,6,4,1,5,2]=>[4,2,1,1]
[4,6,1,5,7,2,3,8]=>[3,1,1,1,1,1]
[4,8,5,3,2,7,1,6]=>[5,1,1,1]
[5,4,8,1,3,7,2,6]=>[4,1,1,1,1]
[8,4,5,3,1,7,2,6]=>[4,2,1,1]
[7,4,5,3,1,8,6,2]=>[4,3,1]
[5,6,8,7,2,4,3,1]=>[5,1,1,1]
[5,7,8,6,4,2,3,1]=>[5,1,1,1]
[6,8,7,5,1,3,2,4]=>[5,1,1,1]
[3,8,2,6,7,5,1,4]=>[4,1,1,1,1]
[4,7,6,3,8,2,5,1]=>[5,1,1,1]
[6,7,4,1,8,2,5,3]=>[3,3,1,1]
[5,7,6,8,3,2,4,1]=>[5,1,1,1]
[7,6,4,2,8,1,5,3]=>[5,2,1]
[6,3,4,8,7,1,2,5]=>[3,2,1,1,1]
[2,7,4,8,1,6,3,5]=>[3,2,1,1,1]
[5,3,1,6,7,8,2,4]=>[3,2,1,1,1]
[3,4,7,8,6,1,2,5]=>[3,1,1,1,1,1]
[2,1,4,7,8,6,3,5]=>[3,2,1,1,1]
[2,4,5,8,1,6,3,7]=>[3,1,1,1,1,1]
[3,4,6,8,2,5,7,1]=>[3,1,1,1,1,1]
[1,8,5,6,4,2,3,7]=>[4,1,1,1,1]
[1,8,7,6,2,4,5,3]=>[5,1,1,1]
[6,4,8,5,7,3,1,2]=>[4,2,1,1]
[1,6,4,7,2,5,8,3]=>[3,2,1,1,1]
[2,7,5,1,8,6,3,4]=>[3,3,1,1]
[4,7,1,6,5,3,8,2]=>[5,1,1,1]
[1,7,5,6,4,8,2,3]=>[4,1,1,1,1]
[8,3,1,4,6,2,7,5]=>[3,2,2,1]
[7,2,6,4,5,8,1,3]=>[4,1,1,1,1]
[7,2,5,4,6,8,1,3]=>[4,1,1,1,1]
[2,7,1,5,3,8,6,4]=>[3,3,1,1]
[3,5,7,2,8,4,1,6]=>[3,2,1,1,1]
[2,4,3,8,5,1,7,6]=>[3,2,2,1]
[7,3,2,1,4,8,6,5]=>[4,3,1]
[2,8,3,4,1,7,6,5]=>[4,2,1,1]
[4,7,6,8,2,5,3,1]=>[5,1,1,1]
[2,6,7,1,4,5,8,3]=>[3,1,1,1,1,1]
[8,7,2,6,1,5,3,4]=>[5,1,1,1]
[7,1,3,8,2,6,4,5]=>[3,2,1,1,1]
[6,2,5,3,4,7,1,8]=>[4,1,1,1,1]
[2,7,3,4,1,5,8,6]=>[3,2,1,1,1]
[2,5,8,1,6,7,3,4]=>[3,1,1,1,1,1]
[6,2,8,3,4,5,1,7]=>[3,2,1,1,1]
[7,3,4,6,8,2,1,5]=>[4,1,1,1,1]
[5,1,3,7,2,8,4,6]=>[3,2,1,1,1]
[5,2,4,6,1,7,8,3]=>[3,2,1,1,1]
[3,8,4,6,1,5,7,2]=>[4,1,1,1,1]
[8,7,3,2,5,1,6,4]=>[5,2,1]
[3,6,4,1,2,5,8,7]=>[3,2,1,1,1]
[5,2,7,1,4,3,6,8]=>[3,2,1,1,1]
[6,3,1,4,2,5,8,7]=>[3,2,2,1]
[5,2,3,1,4,6,8,7]=>[3,2,1,1,1]
[4,2,7,1,3,5,8,6]=>[3,2,1,1,1]
[3,5,4,1,6,2,8,7]=>[3,2,2,1]
[4,5,7,2,8,3,1,6]=>[3,2,1,1,1]
[3,5,1,7,6,2,8,4]=>[3,2,2,1]
[8,3,6,2,7,5,4,1]=>[5,2,1]
[8,4,2,6,5,3,7,1]=>[5,2,1]
[5,4,2,7,1,8,6,3]=>[4,3,1]
[4,1,7,6,5,3,2,8]=>[5,2,1]
[2,3,6,7,1,8,5,4]=>[3,2,1,1,1]
[3,6,1,2,7,8,5,4]=>[3,2,1,1,1]
[4,5,1,8,7,6,3,2]=>[5,2,1]
[8,4,5,2,7,6,3,1]=>[5,2,1]
[4,1,3,6,7,5,2,8]=>[3,2,1,1,1]
[3,1,4,5,7,6,2,8]=>[3,2,1,1,1]
[4,5,1,3,6,8,7,2]=>[3,2,1,1,1]
[3,8,5,1,2,4,6,7]=>[3,1,1,1,1,1]
[8,5,1,2,4,3,6,7]=>[4,1,1,1,1]
[5,8,4,1,2,3,6,7]=>[3,1,1,1,1,1]
[3,5,8,1,4,2,7,6]=>[3,2,1,1,1]
[2,8,5,7,1,4,3,6]=>[4,1,1,1,1]
[4,8,7,5,1,2,3,6]=>[4,1,1,1,1]
[8,1,2,4,6,3,7,5]=>[3,2,1,1,1]
[7,6,1,4,2,3,8,5]=>[4,2,1,1]
[6,1,2,7,8,4,3,5]=>[3,2,1,1,1]
[7,8,1,2,5,3,4,6]=>[3,1,1,1,1,1]
[1,8,4,7,5,2,3,6]=>[4,1,1,1,1]
[8,4,7,2,1,6,3,5]=>[4,2,1,1]
[4,5,8,2,1,6,7,3]=>[3,2,1,1,1]
[4,8,1,5,3,6,7,2]=>[4,1,1,1,1]
[5,1,4,6,3,7,8,2]=>[4,1,1,1,1]
[7,1,5,3,6,8,2,4]=>[4,1,1,1,1]
[8,1,5,3,6,7,2,4]=>[4,1,1,1,1]
[3,6,5,2,4,7,8,1]=>[4,1,1,1,1]
[1,7,5,4,6,8,2,3]=>[4,1,1,1,1]
[4,7,8,2,5,6,1,3]=>[3,1,1,1,1,1]
[2,8,5,4,6,7,1,3]=>[4,1,1,1,1]
[4,5,2,6,1,8,3,7]=>[3,2,1,1,1]
[5,1,8,6,7,3,4,2]=>[4,2,1,1]
[6,8,3,2,4,1,5,7]=>[4,1,1,1,1]
[5,4,8,2,1,3,6,7]=>[4,1,1,1,1]
[1,4,8,3,2,6,5,7]=>[3,2,1,1,1]
[1,3,8,4,2,7,5,6]=>[3,2,1,1,1]
[7,2,8,3,1,4,5,6]=>[3,2,1,1,1]
[8,1,3,2,7,5,4,6]=>[4,2,1,1]
[7,6,1,8,2,5,4,3]=>[5,2,1]
[8,4,1,6,7,3,5,2]=>[4,2,1,1]
[5,8,4,2,1,6,3,7]=>[4,2,1,1]
[7,6,4,1,2,5,3,8]=>[4,2,1,1]
[5,4,2,8,1,6,3,7]=>[4,2,1,1]
[8,7,2,6,4,5,3,1]=>[6,1,1]
[7,2,8,4,3,6,1,5]=>[4,2,1,1]
[1,7,5,4,8,6,2,3]=>[4,2,1,1]
[4,8,6,3,5,2,1,7]=>[5,1,1,1]
[5,8,6,3,2,7,1,4]=>[5,1,1,1]
[5,7,6,3,2,4,8,1]=>[5,1,1,1]
[5,7,3,2,8,6,4,1]=>[4,3,1]
[4,5,1,6,8,2,7,3]=>[3,2,1,1,1]
[1,6,3,7,2,4,8,5]=>[3,2,1,1,1]
[4,3,1,6,7,2,5,8]=>[3,2,1,1,1]
[6,3,1,5,7,2,4,8]=>[3,2,1,1,1]
[5,2,1,4,8,6,7,3]=>[3,3,1,1]
[4,5,2,1,3,7,6,8]=>[3,2,1,1,1]
[8,2,7,4,1,6,5,3]=>[5,2,1]
[3,2,8,4,1,6,5,7]=>[3,2,2,1]
[3,7,6,4,1,5,8,2]=>[4,2,1,1]
[7,1,8,4,2,3,6,5]=>[3,2,2,1]
[2,7,6,4,5,1,8,3]=>[4,2,1,1]
[4,6,8,1,7,3,5,2]=>[4,1,1,1,1]
[3,6,8,1,5,7,4,2]=>[4,1,1,1,1]
[2,8,3,1,6,7,4,5]=>[3,2,1,1,1]
[4,5,6,8,2,1,7,3]=>[3,2,1,1,1]
[4,5,6,8,1,3,7,2]=>[3,1,1,1,1,1]
[4,5,8,3,2,1,7,6]=>[4,2,1,1]
[4,5,1,3,2,6,7,8]=>[3,1,1,1,1,1]
[4,7,3,2,1,6,5,8]=>[4,2,1,1]
[4,7,8,3,5,1,6,2]=>[3,2,1,1,1]
[4,7,1,3,5,6,2,8]=>[3,1,1,1,1,1]
[4,8,3,2,1,6,7,5]=>[4,2,1,1]
[5,2,8,1,4,6,7,3]=>[3,2,1,1,1]
[5,6,3,7,8,1,4,2]=>[3,2,1,1,1]
[5,7,1,4,3,6,2,8]=>[4,1,1,1,1]
[6,2,3,7,1,5,4,8]=>[3,2,1,1,1]
[6,2,8,1,5,4,7,3]=>[4,2,1,1]
[6,1,3,4,5,2,7,8]=>[3,1,1,1,1,1]
[7,1,3,4,5,6,2,8]=>[3,1,1,1,1,1]
[7,2,5,1,3,6,4,8]=>[3,2,1,1,1]
[6,5,2,7,8,4,3,1]=>[5,2,1]
[7,5,3,6,4,2,1,8]=>[5,2,1]
[1,3,6,7,5,2,4,8]=>[3,1,1,1,1,1]
[1,5,2,6,8,7,3,4]=>[3,2,1,1,1]
[5,3,4,7,2,1,6,8]=>[4,1,1,1,1]
[4,2,3,7,6,1,8,5]=>[3,2,2,1]
[4,2,6,3,1,5,7,8]=>[3,2,1,1,1]
[4,6,3,2,5,8,7,1]=>[4,2,1,1]
[5,8,4,3,2,6,1,7]=>[5,1,1,1]
[6,1,5,7,3,8,2,4]=>[4,1,1,1,1]
[1,2,7,8,6,4,3,5]=>[4,1,1,1,1]
[3,5,1,7,8,6,2,4]=>[3,2,1,1,1]
[5,2,4,1,7,6,8,3]=>[3,3,1,1]
[5,4,3,8,1,7,2,6]=>[4,2,1,1]
[7,3,1,5,6,8,4,2]=>[4,2,1,1]
[4,1,8,2,5,6,3,7]=>[3,2,1,1,1]
[5,7,8,1,6,2,3,4]=>[3,1,1,1,1,1]
[1,6,4,2,7,3,8,5]=>[3,2,2,1]
[1,4,2,5,8,6,3,7]=>[3,2,1,1,1]
[4,8,2,1,5,7,3,6]=>[3,2,1,1,1]
[6,2,8,7,3,4,5,1]=>[4,2,1,1]
[7,3,4,8,5,6,2,1]=>[4,2,1,1]
[7,3,6,8,4,5,2,1]=>[5,1,1,1]
[5,6,2,8,3,1,7,4]=>[3,2,2,1]
[1,4,7,5,6,2,8,3]=>[3,2,1,1,1]
[1,7,4,8,3,5,6,2]=>[4,1,1,1,1]
[5,3,1,4,8,6,2,7]=>[3,3,1,1]
[5,2,4,8,3,1,6,7]=>[4,1,1,1,1]
[7,4,5,1,8,6,2,3]=>[3,3,1,1]
[8,1,5,7,6,3,2,4]=>[5,1,1,1]
[1,8,6,7,5,3,2,4]=>[5,1,1,1]
[7,4,8,3,1,6,5,2]=>[4,3,1]
[8,1,5,3,7,6,2,4]=>[4,2,1,1]
[6,4,8,7,3,5,1,2]=>[4,2,1,1]
[6,1,4,2,3,5,7,8]=>[3,1,1,1,1,1]
[7,1,4,3,8,6,5,2]=>[4,3,1]
[6,1,5,7,2,8,3,4]=>[3,2,1,1,1]
[1,8,2,6,7,4,3,5]=>[4,1,1,1,1]
[7,2,4,1,8,5,3,6]=>[3,3,1,1]
[4,7,2,6,1,8,3,5]=>[3,2,1,1,1]
[8,7,3,5,2,1,6,4]=>[5,2,1]
[7,5,3,2,1,6,8,4]=>[5,2,1]
[6,8,1,3,4,2,5,7]=>[3,1,1,1,1,1]
[3,6,1,4,7,8,2,5]=>[3,1,1,1,1,1]
[2,5,7,1,3,6,4,8]=>[3,1,1,1,1,1]
[1,4,7,2,5,3,6,8]=>[3,1,1,1,1,1]
[4,5,3,1,2,6,8,7]=>[3,2,1,1,1]
[4,5,1,3,8,2,6,7]=>[3,1,1,1,1,1]
[4,1,5,3,2,7,6,8]=>[3,2,2,1]
[7,3,5,1,4,2,6,8]=>[4,1,1,1,1]
[6,2,1,7,4,3,8,5]=>[3,3,2]
[2,4,3,6,7,1,5,8]=>[3,1,1,1,1,1]
[7,3,5,2,1,6,4,8]=>[4,2,1,1]
[4,6,5,2,1,3,7,8]=>[4,1,1,1,1]
[2,5,6,1,4,3,7,8]=>[3,1,1,1,1,1]
[6,1,5,3,7,2,4,8]=>[4,1,1,1,1]
[3,6,5,4,1,7,2,8]=>[4,2,1,1]
[6,8,7,5,4,2,1,3]=>[6,1,1]
[1,6,8,7,3,2,4,5]=>[4,1,1,1,1]
[8,7,5,4,6,1,3,2]=>[6,1,1]
[1,7,8,2,4,6,3,5]=>[3,1,1,1,1,1]
[7,5,4,8,1,3,6,2]=>[5,1,1,1]
[5,6,1,8,4,3,7,2]=>[4,2,1,1]
[1,8,2,6,7,5,4,3]=>[5,1,1,1]
[2,7,5,1,6,8,3,4]=>[3,2,1,1,1]
[3,8,6,1,2,4,5,7]=>[3,1,1,1,1,1]
[1,8,5,3,2,7,4,6]=>[4,2,1,1]
[1,8,4,7,2,3,5,6]=>[3,1,1,1,1,1]
[3,2,8,1,7,5,4,6]=>[4,2,1,1]
[7,1,5,6,2,3,4,8]=>[3,1,1,1,1,1]
[6,5,1,7,2,3,4,8]=>[3,2,1,1,1]
[1,6,8,2,7,3,4,5]=>[3,1,1,1,1,1]
[1,6,8,7,3,4,2,5]=>[4,1,1,1,1]
[4,1,3,6,7,8,5,2]=>[3,2,1,1,1]
[7,4,1,5,6,8,3,2]=>[4,2,1,1]
[4,1,2,6,7,8,5,3]=>[3,2,1,1,1]
[6,3,7,1,8,2,4,5]=>[3,2,1,1,1]
[3,7,8,1,5,2,6,4]=>[3,2,1,1,1]
[1,5,4,7,8,3,6,2]=>[4,1,1,1,1]
[5,1,4,7,8,3,6,2]=>[4,1,1,1,1]
[4,8,1,5,6,2,3,7]=>[3,1,1,1,1,1]
[5,6,4,1,7,3,8,2]=>[4,2,1,1]
[4,3,7,8,2,5,1,6]=>[4,1,1,1,1]
[3,7,8,5,4,2,1,6]=>[5,1,1,1]
[1,7,4,5,6,8,3,2]=>[4,1,1,1,1]
[7,2,4,5,6,8,3,1]=>[4,1,1,1,1]
[2,7,4,5,6,8,3,1]=>[4,1,1,1,1]
[2,4,7,8,3,1,6,5]=>[3,2,1,1,1]
[5,4,3,6,8,1,7,2]=>[4,2,1,1]
[3,7,4,5,8,1,6,2]=>[3,2,1,1,1]
[1,4,3,5,6,8,2,7]=>[3,1,1,1,1,1]
[1,4,6,5,8,2,7,3]=>[3,2,1,1,1]
[4,6,1,7,3,2,8,5]=>[3,2,2,1]
[1,7,3,6,4,2,8,5]=>[4,2,1,1]
[4,7,3,5,1,2,8,6]=>[3,2,1,1,1]
[1,6,4,2,3,5,8,7]=>[3,2,1,1,1]
[4,8,3,5,2,1,6,7]=>[4,1,1,1,1]
[1,6,8,4,7,5,3,2]=>[5,1,1,1]
[8,7,3,1,5,2,6,4]=>[4,2,2]
[4,7,1,6,8,2,3,5]=>[3,1,1,1,1,1]
[4,6,5,8,2,3,7,1]=>[4,1,1,1,1]
[7,1,8,2,4,5,3,6]=>[3,2,1,1,1]
[5,7,8,2,3,4,1,6]=>[3,1,1,1,1,1]
[5,2,3,8,7,1,4,6]=>[3,2,1,1,1]
[2,7,6,4,8,3,1,5]=>[5,1,1,1]
[2,6,3,7,5,8,4,1]=>[4,2,1,1]
[7,5,1,2,3,8,4,6]=>[3,2,1,1,1]
[8,6,2,1,3,7,4,5]=>[4,2,1,1]
[4,2,3,6,8,5,7,1]=>[3,2,1,1,1]
[4,7,3,2,6,5,1,8]=>[4,2,1,1]
[4,3,7,8,2,1,6,5]=>[4,2,1,1]
[6,3,5,8,4,1,2,7]=>[4,1,1,1,1]
[4,5,3,6,8,1,2,7]=>[3,1,1,1,1,1]
[3,7,6,4,1,5,2,8]=>[4,2,1,1]
[5,2,8,4,7,1,3,6]=>[3,2,1,1,1]
[7,3,1,2,8,6,5,4]=>[4,3,1]
[8,7,1,3,2,4,5,6]=>[4,1,1,1,1]
[4,1,3,6,5,7,2,8]=>[3,2,1,1,1]
[4,1,3,5,7,2,8,6]=>[3,2,1,1,1]
[5,1,8,2,4,6,3,7]=>[3,2,1,1,1]
[6,8,2,1,4,5,3,7]=>[3,2,1,1,1]
[4,2,7,3,6,8,5,1]=>[4,2,1,1]
[3,1,5,8,6,7,2,4]=>[3,2,1,1,1]
[6,8,2,1,4,5,7,3]=>[3,2,1,1,1]
[1,5,4,8,7,3,2,6]=>[4,2,1,1]
[4,3,1,2,6,5,7,8]=>[3,2,1,1,1]
[7,1,4,5,8,3,6,2]=>[4,1,1,1,1]
[7,5,8,1,2,4,6,3]=>[4,1,1,1,1]
[6,1,5,2,8,7,4,3]=>[4,3,1]
[8,4,6,3,1,2,7,5]=>[4,2,1,1]
[3,8,6,4,1,5,7,2]=>[4,2,1,1]
[8,7,1,4,5,2,3,6]=>[4,1,1,1,1]
[3,8,6,4,5,1,7,2]=>[4,2,1,1]
[3,7,6,4,5,1,2,8]=>[4,1,1,1,1]
[7,4,6,3,1,2,8,5]=>[4,2,1,1]
[4,6,2,5,7,8,1,3]=>[3,1,1,1,1,1]
[4,6,3,5,7,1,2,8]=>[3,1,1,1,1,1]
[4,7,3,5,8,6,1,2]=>[3,2,1,1,1]
[4,8,3,5,7,1,6,2]=>[4,1,1,1,1]
[4,8,3,5,6,1,2,7]=>[3,1,1,1,1,1]
[4,7,2,5,6,8,1,3]=>[3,1,1,1,1,1]
[4,8,2,5,6,7,1,3]=>[3,1,1,1,1,1]
[1,4,7,2,6,5,8,3]=>[4,1,1,1,1]
[1,5,7,2,6,4,8,3]=>[4,1,1,1,1]
[7,2,4,6,1,8,3,5]=>[3,2,1,1,1]
[1,2,7,8,3,5,4,6]=>[3,1,1,1,1,1]
[1,7,6,2,8,5,4,3]=>[5,2,1]
[1,2,7,8,3,4,6,5]=>[3,1,1,1,1,1]
[1,7,6,8,3,4,2,5]=>[4,1,1,1,1]
[3,4,1,7,8,6,5,2]=>[4,2,1,1]
[2,4,8,6,5,7,1,3]=>[4,1,1,1,1]
[5,1,3,4,8,2,7,6]=>[3,2,1,1,1]
[8,7,3,6,1,4,2,5]=>[5,1,1,1]
[6,5,1,8,3,4,7,2]=>[4,2,1,1]
[8,2,1,5,6,4,7,3]=>[4,2,1,1]
[7,5,6,1,3,4,8,2]=>[4,1,1,1,1]
[5,7,2,4,6,1,8,3]=>[3,2,1,1,1]
[2,1,5,6,3,8,7,4]=>[3,2,2,1]
[3,2,7,5,8,6,4,1]=>[4,2,2]
[2,4,5,3,8,1,7,6]=>[3,2,1,1,1]
[7,2,5,4,3,8,6,1]=>[5,2,1]
[8,5,3,1,2,6,7,4]=>[4,2,1,1]
[7,2,5,1,3,6,8,4]=>[3,2,1,1,1]
[8,4,7,3,1,2,6,5]=>[4,2,1,1]
[1,8,7,3,5,2,6,4]=>[4,2,1,1]
[2,4,8,3,6,5,7,1]=>[4,1,1,1,1]
[3,1,8,2,6,5,7,4]=>[4,2,1,1]
[4,6,7,8,5,2,1,3]=>[4,1,1,1,1]
[4,7,2,1,8,6,5,3]=>[4,3,1]
[5,6,2,8,4,1,7,3]=>[3,2,2,1]
[5,7,2,4,8,6,1,3]=>[3,2,1,1,1]
[6,7,2,4,8,5,1,3]=>[3,2,1,1,1]
[6,7,3,2,8,5,1,4]=>[4,2,1,1]
[7,2,3,1,8,6,5,4]=>[4,3,1]
[7,2,8,3,5,6,1,4]=>[3,2,1,1,1]
[7,2,3,8,4,6,1,5]=>[3,2,1,1,1]
[1,7,3,4,8,5,2,6]=>[3,2,1,1,1]
[1,7,3,8,5,4,2,6]=>[4,2,1,1]
[7,2,8,4,5,3,1,6]=>[4,2,1,1]
[2,8,6,4,3,1,7,5]=>[5,2,1]
[1,7,3,4,8,2,5,6]=>[3,1,1,1,1,1]
[1,5,8,3,4,6,2,7]=>[3,1,1,1,1,1]
[1,3,8,4,2,5,7,6]=>[3,2,1,1,1]
[1,4,7,6,2,3,8,5]=>[3,2,1,1,1]
[1,8,4,6,7,2,3,5]=>[3,1,1,1,1,1]
[1,4,2,3,7,8,6,5]=>[3,2,1,1,1]
[5,7,1,6,4,8,3,2]=>[5,1,1,1]
[7,4,5,8,1,3,6,2]=>[4,1,1,1,1]
[1,4,3,6,2,5,8,7]=>[3,2,1,1,1]
[1,4,6,3,2,5,8,7]=>[3,2,1,1,1]
[1,3,6,5,8,2,4,7]=>[3,1,1,1,1,1]
[1,4,6,3,2,8,5,7]=>[3,2,1,1,1]
[6,8,4,1,5,7,2,3]=>[3,2,1,1,1]
[5,2,6,7,4,1,8,3]=>[3,2,2,1]
[8,5,6,4,1,7,3,2]=>[5,2,1]
[7,8,3,1,6,4,5,2]=>[4,2,1,1]
[5,8,2,6,3,1,7,4]=>[4,2,1,1]
[4,5,8,1,6,3,7,2]=>[4,1,1,1,1]
[8,1,4,6,2,5,7,3]=>[4,1,1,1,1]
[4,5,8,1,6,2,7,3]=>[3,2,1,1,1]
[5,2,6,8,1,4,3,7]=>[3,2,1,1,1]
[6,7,3,8,2,1,4,5]=>[4,1,1,1,1]
[2,7,3,5,4,1,8,6]=>[4,2,1,1]
[2,6,3,7,4,1,8,5]=>[3,2,2,1]
[2,1,4,8,5,3,7,6]=>[3,2,2,1]
[2,7,3,8,4,1,6,5]=>[3,2,2,1]
[2,6,3,1,5,4,8,7]=>[3,2,2,1]
[1,5,8,3,4,7,2,6]=>[3,1,1,1,1,1]
[5,3,8,1,4,6,2,7]=>[3,2,1,1,1]
[4,5,8,1,3,6,2,7]=>[3,1,1,1,1,1]
[7,4,6,5,2,8,3,1]=>[5,2,1]
[4,1,3,8,5,7,6,2]=>[4,2,1,1]
[4,1,3,7,2,8,6,5]=>[3,3,1,1]
[4,6,3,1,7,2,8,5]=>[3,2,2,1]
[7,2,6,3,1,8,5,4]=>[4,3,1]
[4,8,7,2,5,3,1,6]=>[5,1,1,1]
[1,6,3,2,8,7,4,5]=>[3,3,1,1]
[2,8,1,7,5,4,6,3]=>[5,1,1,1]
[6,8,3,1,5,7,2,4]=>[3,2,1,1,1]
[8,7,3,1,2,5,6,4]=>[4,2,1,1]
[5,4,3,6,1,7,8,2]=>[4,2,1,1]
[3,2,7,8,5,6,1,4]=>[3,2,1,1,1]
[4,8,3,2,1,7,5,6]=>[4,2,1,1]
[5,1,2,6,4,7,8,3]=>[3,2,1,1,1]
[1,8,4,5,6,3,2,7]=>[4,1,1,1,1]
[8,5,1,7,4,6,3,2]=>[5,2,1]
[3,4,8,1,6,7,2,5]=>[3,1,1,1,1,1]
[3,6,7,8,4,1,5,2]=>[3,2,1,1,1]
[2,3,7,8,4,6,1,5]=>[3,1,1,1,1,1]
[1,3,7,8,4,6,2,5]=>[3,1,1,1,1,1]
[3,1,7,8,4,6,2,5]=>[3,2,1,1,1]
[4,3,8,1,6,7,2,5]=>[3,2,1,1,1]
[4,8,7,3,6,1,2,5]=>[4,1,1,1,1]
[5,8,4,3,7,1,2,6]=>[4,1,1,1,1]
[4,1,8,3,7,5,2,6]=>[4,2,1,1]
[2,4,8,3,6,7,1,5]=>[3,1,1,1,1,1]
[1,6,5,8,7,3,2,4]=>[4,2,1,1]
[5,6,4,8,7,2,1,3]=>[4,2,1,1]
[7,2,6,8,3,5,1,4]=>[4,1,1,1,1]
[7,2,8,6,5,3,1,4]=>[5,2,1]
[4,8,3,7,6,1,2,5]=>[4,1,1,1,1]
[2,8,4,7,1,3,6,5]=>[4,1,1,1,1]
[6,8,3,4,5,2,1,7]=>[4,1,1,1,1]
[3,7,1,4,5,6,2,8]=>[3,1,1,1,1,1]
[3,6,1,4,5,2,7,8]=>[3,1,1,1,1,1]
[3,8,2,4,5,1,7,6]=>[3,2,1,1,1]
[3,7,2,1,5,6,4,8]=>[3,2,1,1,1]
[3,6,8,1,5,4,7,2]=>[4,1,1,1,1]
[1,7,4,6,3,5,2,8]=>[4,1,1,1,1]
[1,3,6,5,7,2,4,8]=>[3,1,1,1,1,1]
[1,7,2,5,6,4,3,8]=>[4,1,1,1,1]
[1,6,8,5,4,3,7,2]=>[5,1,1,1]
[2,5,7,8,4,3,1,6]=>[4,1,1,1,1]
[6,8,5,3,2,4,1,7]=>[5,1,1,1]
[1,6,8,5,3,2,7,4]=>[4,2,1,1]
[4,6,1,8,7,5,3,2]=>[5,2,1]
[1,3,7,6,8,5,2,4]=>[4,1,1,1,1]
[4,1,7,8,6,5,2,3]=>[4,2,1,1]
[5,4,3,7,6,1,2,8]=>[4,2,1,1]
[4,7,6,1,2,3,8,5]=>[3,2,1,1,1]
[4,5,2,6,7,8,1,3]=>[3,1,1,1,1,1]
[1,7,6,2,3,8,5,4]=>[4,2,1,1]
[7,2,3,8,6,4,5,1]=>[4,2,1,1]
[1,5,4,3,8,6,2,7]=>[4,2,1,1]
[1,3,7,5,8,4,6,2]=>[4,1,1,1,1]
[7,8,1,5,3,4,6,2]=>[4,1,1,1,1]
[7,3,5,4,1,6,2,8]=>[4,2,1,1]
[3,5,7,1,6,4,2,8]=>[4,1,1,1,1]
[3,7,5,6,1,4,2,8]=>[4,1,1,1,1]
[1,7,5,6,3,4,8,2]=>[4,1,1,1,1]
[5,3,1,2,7,8,4,6]=>[3,2,1,1,1]
[5,1,3,7,8,2,6,4]=>[3,2,1,1,1]
[5,8,1,2,7,6,4,3]=>[5,1,1,1]
[1,6,7,4,5,3,2,8]=>[4,1,1,1,1]
[1,4,2,6,7,5,3,8]=>[3,2,1,1,1]
[1,8,2,4,6,5,3,7]=>[4,1,1,1,1]
[1,4,8,7,2,3,6,5]=>[4,1,1,1,1]
[4,1,3,6,5,8,2,7]=>[3,2,1,1,1]
[4,3,7,1,5,8,2,6]=>[3,2,1,1,1]
[1,8,6,5,2,7,4,3]=>[5,2,1]
[7,2,6,4,1,8,5,3]=>[4,3,1]
[6,4,1,8,3,7,5,2]=>[4,3,1]
[4,5,8,7,3,6,2,1]=>[5,1,1,1]
[3,5,4,1,7,8,6,2]=>[3,3,1,1]
[6,8,7,2,1,5,4,3]=>[5,2,1]
[8,1,6,3,7,5,4,2]=>[5,2,1]
[8,5,1,3,7,6,4,2]=>[5,2,1]
[8,3,6,5,4,2,1,7]=>[6,1,1]
[6,1,3,5,7,2,8,4]=>[3,2,1,1,1]
[1,6,7,5,8,4,2,3]=>[4,1,1,1,1]
[7,4,1,6,5,2,8,3]=>[4,2,2]
[7,4,2,8,6,5,3,1]=>[5,3]
[6,8,4,7,3,2,5,1]=>[5,1,1,1]
[5,8,7,3,2,1,6,4]=>[5,2,1]
[5,8,7,2,6,4,3,1]=>[6,1,1]
[6,8,7,3,5,1,4,2]=>[5,1,1,1]
[7,2,5,6,8,3,4,1]=>[4,1,1,1,1]
[1,6,5,7,8,3,2,4]=>[4,1,1,1,1]
[8,6,7,2,3,5,4,1]=>[5,1,1,1]
[5,4,8,6,7,3,1,2]=>[4,2,1,1]
[4,2,7,3,1,6,8,5]=>[3,2,2,1]
[7,3,6,4,2,1,8,5]=>[5,2,1]
[4,8,5,2,7,3,1,6]=>[4,2,1,1]
[6,4,3,1,8,5,2,7]=>[4,3,1]
[7,4,3,1,5,8,6,2]=>[4,3,1]
[7,4,8,6,5,3,1,2]=>[5,2,1]
[4,8,5,2,6,7,3,1]=>[4,2,1,1]
[7,3,2,1,8,5,6,4]=>[4,3,1]
[5,1,3,8,2,7,4,6]=>[3,2,1,1,1]
[8,1,6,3,2,4,7,5]=>[4,2,1,1]
[6,8,4,3,5,1,2,7]=>[4,1,1,1,1]
[8,7,3,5,4,1,2,6]=>[5,1,1,1]
[6,3,8,5,7,2,1,4]=>[4,2,1,1]
[8,7,3,6,4,1,2,5]=>[5,1,1,1]
[5,2,7,4,6,1,3,8]=>[3,2,1,1,1]
[8,7,2,3,5,1,4,6]=>[4,1,1,1,1]
[7,6,3,4,1,8,2,5]=>[4,2,1,1]
[6,3,5,2,8,1,4,7]=>[4,1,1,1,1]
[6,4,5,3,1,7,2,8]=>[4,2,1,1]
[8,7,2,4,3,1,5,6]=>[5,1,1,1]
[7,6,2,3,1,4,8,5]=>[4,2,1,1]
[4,7,6,2,3,1,5,8]=>[4,1,1,1,1]
[4,7,6,1,3,2,8,5]=>[4,2,1,1]
[7,6,3,1,8,5,2,4]=>[4,3,1]
[1,6,4,7,8,5,3,2]=>[4,2,1,1]
[7,2,5,8,6,1,3,4]=>[3,2,1,1,1]
[4,1,3,6,2,5,8,7]=>[3,2,1,1,1]
[7,1,4,6,3,2,5,8]=>[4,1,1,1,1]
[7,4,5,8,6,2,3,1]=>[4,2,1,1]
[6,7,2,3,8,4,1,5]=>[3,2,1,1,1]
[1,5,2,6,8,7,4,3]=>[4,2,1,1]
[3,1,6,7,5,2,8,4]=>[3,2,2,1]
[8,6,2,4,5,1,7,3]=>[4,2,1,1]
[8,6,7,5,2,1,4,3]=>[5,2,1]
[4,1,6,2,3,8,7,5]=>[3,2,2,1]
[4,1,7,6,5,2,8,3]=>[4,2,2]
[8,4,1,5,6,2,7,3]=>[3,2,2,1]
[8,4,5,3,6,1,7,2]=>[4,2,1,1]
[2,8,4,7,3,5,6,1]=>[4,1,1,1,1]
[1,5,4,8,3,2,6,7]=>[4,1,1,1,1]
[1,5,7,6,3,8,2,4]=>[4,1,1,1,1]
[2,6,3,1,7,8,4,5]=>[3,2,1,1,1]
[2,1,7,8,3,5,4,6]=>[3,2,1,1,1]
[1,5,8,6,7,4,2,3]=>[4,1,1,1,1]
[8,7,1,3,5,2,6,4]=>[4,2,1,1]
[3,7,8,2,5,4,1,6]=>[4,1,1,1,1]
[4,7,6,5,8,1,3,2]=>[5,1,1,1]
[4,7,8,6,2,1,5,3]=>[4,2,1,1]
[4,8,6,3,2,1,7,5]=>[5,2,1]
[5,1,4,7,6,8,3,2]=>[4,2,1,1]
[5,6,4,7,1,8,3,2]=>[4,2,1,1]
[5,3,7,4,6,1,8,2]=>[3,2,2,1]
[4,1,5,7,8,6,3,2]=>[4,2,1,1]
[3,6,7,1,5,4,8,2]=>[4,1,1,1,1]
[3,6,4,7,5,8,2,1]=>[4,2,1,1]
[8,1,7,3,2,4,5,6]=>[4,1,1,1,1]
[6,4,7,1,5,2,8,3]=>[3,2,2,1]
[4,8,1,3,5,2,7,6]=>[3,2,1,1,1]
[1,6,5,2,8,7,4,3]=>[4,3,1]
[4,1,7,2,5,8,3,6]=>[3,2,1,1,1]
[3,2,5,8,6,1,7,4]=>[3,2,2,1]
[4,5,1,7,2,8,6,3]=>[3,2,2,1]
[2,8,5,3,6,7,4,1]=>[4,2,1,1]
[8,3,5,2,6,7,4,1]=>[4,2,1,1]
[2,8,6,3,4,7,5,1]=>[4,2,1,1]
[6,4,7,2,5,3,1,8]=>[4,2,1,1]
[7,1,4,3,6,8,2,5]=>[4,1,1,1,1]
[4,8,7,3,5,1,6,2]=>[4,2,1,1]
[5,3,8,7,1,6,2,4]=>[4,2,1,1]
[5,2,6,7,4,3,1,8]=>[4,2,1,1]
[8,5,1,6,4,3,2,7]=>[5,2,1]
[8,6,3,5,2,7,1,4]=>[5,1,1,1]
[8,4,6,2,1,5,7,3]=>[4,2,1,1]
[8,5,2,1,6,4,7,3]=>[4,3,1]
[1,7,2,8,5,4,6,3]=>[4,2,1,1]
[6,7,1,4,8,5,3,2]=>[4,2,1,1]
[7,3,2,8,5,1,4,6]=>[4,2,1,1]
[4,1,7,3,2,8,5,6]=>[3,2,2,1]
[8,3,5,2,4,7,1,6]=>[4,1,1,1,1]
[4,3,7,8,6,1,5,2]=>[4,2,1,1]
[1,2,6,3,7,8,5,4]=>[3,2,1,1,1]
[6,1,3,7,8,5,4,2]=>[4,2,1,1]
[2,6,4,7,5,3,1,8]=>[4,2,1,1]
[5,6,3,7,2,8,4,1]=>[4,2,1,1]
[4,5,1,8,6,2,7,3]=>[3,2,2,1]
[5,6,1,8,7,2,3,4]=>[3,2,1,1,1]
[4,5,1,6,8,7,3,2]=>[4,2,1,1]
[3,8,6,1,5,2,4,7]=>[4,1,1,1,1]
[3,2,8,1,5,6,4,7]=>[3,2,1,1,1]
[5,8,7,3,2,1,4,6]=>[5,1,1,1]
[3,4,7,6,8,2,1,5]=>[4,1,1,1,1]
[2,8,1,3,7,5,6,4]=>[4,1,1,1,1]
[1,8,7,2,5,6,4,3]=>[5,1,1,1]
[3,4,7,1,5,8,2,6]=>[3,1,1,1,1,1]
[4,2,7,1,5,8,3,6]=>[3,2,1,1,1]
[2,4,6,3,5,1,7,8]=>[3,1,1,1,1,1]
[4,1,6,2,5,8,3,7]=>[3,2,1,1,1]
[1,8,2,5,7,3,4,6]=>[3,1,1,1,1,1]
[1,4,6,3,8,5,2,7]=>[3,2,1,1,1]
[4,5,6,3,1,7,2,8]=>[3,2,1,1,1]
[3,4,6,2,5,1,7,8]=>[3,1,1,1,1,1]
[1,4,7,5,2,3,6,8]=>[3,1,1,1,1,1]
[1,4,6,5,8,2,3,7]=>[3,1,1,1,1,1]
[1,4,8,3,7,6,2,5]=>[4,1,1,1,1]
[1,4,5,3,7,2,6,8]=>[3,1,1,1,1,1]
[2,5,7,6,8,3,4,1]=>[4,1,1,1,1]
[3,1,6,7,2,8,5,4]=>[3,2,2,1]
[1,5,3,6,8,4,7,2]=>[3,2,1,1,1]
[6,5,1,3,8,4,7,2]=>[4,2,1,1]
[1,7,4,8,5,3,2,6]=>[4,2,1,1]
[7,3,1,6,8,4,5,2]=>[4,2,1,1]
[8,5,1,4,6,7,3,2]=>[5,1,1,1]
[3,4,7,5,6,8,2,1]=>[4,1,1,1,1]
[3,4,7,8,5,2,6,1]=>[4,1,1,1,1]
[4,8,1,7,5,6,3,2]=>[5,1,1,1]
[1,8,7,5,2,6,3,4]=>[4,2,1,1]
[1,7,6,3,4,5,8,2]=>[4,1,1,1,1]
[1,8,7,4,5,6,2,3]=>[4,1,1,1,1]
[1,8,7,3,6,4,2,5]=>[5,1,1,1]
[1,4,7,5,8,2,6,3]=>[3,2,1,1,1]
[1,4,7,2,3,6,5,8]=>[3,1,1,1,1,1]
[1,7,2,5,6,3,4,8]=>[3,1,1,1,1,1]
[1,2,6,5,8,3,4,7]=>[3,1,1,1,1,1]
[1,5,8,2,6,3,4,7]=>[3,1,1,1,1,1]
[6,8,3,2,7,5,1,4]=>[4,2,1,1]
[4,1,5,7,2,6,3,8]=>[3,2,1,1,1]
[5,7,2,1,3,6,4,8]=>[3,2,1,1,1]
[3,5,6,7,2,4,1,8]=>[3,1,1,1,1,1]
[6,4,7,5,2,3,1,8]=>[4,2,1,1]
[1,5,6,4,8,3,2,7]=>[4,1,1,1,1]
[2,1,5,6,4,8,3,7]=>[3,2,1,1,1]
[5,1,4,7,8,6,2,3]=>[3,2,1,1,1]
[1,6,7,2,8,5,4,3]=>[4,2,1,1]
[5,3,2,1,7,8,6,4]=>[4,3,1]
[7,4,3,8,6,1,5,2]=>[4,3,1]
[4,3,7,1,5,8,6,2]=>[3,3,1,1]
[8,2,4,5,3,1,7,6]=>[4,2,1,1]
[1,4,3,2,7,5,8,6]=>[3,2,2,1]
[4,8,7,2,6,1,3,5]=>[4,1,1,1,1]
[4,5,8,2,1,7,3,6]=>[3,2,1,1,1]
[6,8,4,1,7,3,2,5]=>[4,2,1,1]
[6,4,1,3,2,5,7,8]=>[4,1,1,1,1]
[4,1,7,8,3,2,5,6]=>[3,2,1,1,1]
[5,4,7,1,3,6,2,8]=>[4,1,1,1,1]
[7,6,2,8,4,5,3,1]=>[5,2,1]
[5,8,2,1,3,6,4,7]=>[3,2,1,1,1]
[8,5,1,7,3,4,6,2]=>[4,2,1,1]
[5,7,6,3,4,1,8,2]=>[4,2,1,1]
[7,1,2,6,4,3,5,8]=>[4,1,1,1,1]
[7,1,2,6,5,3,4,8]=>[4,1,1,1,1]
[4,7,8,6,2,3,5,1]=>[4,1,1,1,1]
[7,1,2,4,8,6,5,3]=>[4,2,1,1]
[2,7,5,6,4,8,1,3]=>[4,1,1,1,1]
[2,8,3,6,5,7,1,4]=>[4,1,1,1,1]
[7,4,3,1,6,5,2,8]=>[4,3,1]
[3,5,1,2,6,8,7,4]=>[3,2,1,1,1]
[3,1,2,4,8,7,5,6]=>[3,2,1,1,1]
[5,4,1,2,3,7,8,6]=>[3,2,1,1,1]
[1,6,7,2,5,8,3,4]=>[3,1,1,1,1,1]
[7,8,5,6,2,4,3,1]=>[5,1,1,1]
[5,3,8,6,2,4,1,7]=>[4,2,1,1]
[2,7,4,6,3,8,1,5]=>[4,1,1,1,1]
[5,4,7,8,6,2,1,3]=>[4,2,1,1]
[2,7,4,8,3,1,5,6]=>[4,1,1,1,1]
[8,2,1,3,7,4,6,5]=>[4,2,1,1]
[6,5,8,2,3,4,7,1]=>[4,1,1,1,1]
[7,8,2,3,6,4,5,1]=>[4,1,1,1,1]
[8,1,2,7,5,3,4,6]=>[4,1,1,1,1]
[4,2,8,1,3,7,5,6]=>[3,2,1,1,1]
[7,5,1,8,2,3,4,6]=>[3,2,1,1,1]
[8,2,4,1,3,7,5,6]=>[3,2,1,1,1]
[8,1,6,2,3,7,4,5]=>[3,2,1,1,1]
[7,1,8,2,3,6,4,5]=>[3,2,1,1,1]
[4,2,6,7,5,1,8,3]=>[3,2,2,1]
[4,7,2,5,3,8,1,6]=>[4,1,1,1,1]
[3,5,7,4,2,8,1,6]=>[4,1,1,1,1]
[2,4,7,6,3,8,1,5]=>[4,1,1,1,1]
[4,6,8,5,1,2,3,7]=>[3,1,1,1,1,1]
[4,6,5,7,1,2,3,8]=>[3,1,1,1,1,1]
[4,6,5,7,1,3,8,2]=>[4,1,1,1,1]
[3,4,7,6,1,8,2,5]=>[3,2,1,1,1]
[8,5,2,1,6,3,4,7]=>[4,2,1,1]
[7,1,8,5,3,2,4,6]=>[4,2,1,1]
[8,6,1,3,2,7,5,4]=>[4,3,1]
[8,1,7,5,2,4,6,3]=>[5,1,1,1]
[8,2,7,5,4,1,6,3]=>[5,2,1]
[8,6,1,2,7,3,5,4]=>[4,2,1,1]
[4,2,8,5,7,1,6,3]=>[4,2,1,1]
[6,8,7,4,5,3,2,1]=>[6,1,1]
[5,2,6,7,4,8,3,1]=>[4,2,1,1]
[6,5,8,1,7,3,2,4]=>[4,2,1,1]
[6,4,8,1,5,2,3,7]=>[3,2,1,1,1]
[7,2,4,1,6,3,5,8]=>[3,2,1,1,1]
[2,6,1,5,3,4,8,7]=>[3,2,1,1,1]
[3,8,7,5,4,2,6,1]=>[6,1,1]
[5,7,8,2,3,6,4,1]=>[4,1,1,1,1]
[2,8,7,3,1,4,5,6]=>[4,1,1,1,1]
[5,6,1,2,4,7,8,3]=>[3,1,1,1,1,1]
[3,8,6,7,5,4,2,1]=>[6,1,1]
[7,8,5,1,4,6,2,3]=>[4,1,1,1,1]
[8,2,7,5,4,6,1,3]=>[5,1,1,1]
[8,4,7,6,3,1,2,5]=>[5,1,1,1]
[4,6,7,1,3,2,8,5]=>[3,2,1,1,1]
[6,4,7,5,3,2,8,1]=>[5,2,1]
[8,4,6,3,1,5,7,2]=>[4,2,1,1]
[7,3,1,4,5,6,8,2]=>[3,2,1,1,1]
[6,7,3,4,2,1,8,5]=>[4,2,1,1]
[6,4,8,3,1,5,7,2]=>[4,2,1,1]
[7,4,2,3,5,1,8,6]=>[4,2,1,1]
[3,1,6,5,2,4,8,7]=>[3,2,2,1]
[2,5,3,8,6,4,1,7]=>[4,2,1,1]
[5,8,4,1,3,2,7,6]=>[4,2,1,1]
[5,3,4,7,6,1,8,2]=>[3,2,2,1]
[4,5,2,1,6,3,8,7]=>[3,2,2,1]
[4,5,2,1,6,7,3,8]=>[3,2,1,1,1]
[5,3,8,6,2,4,7,1]=>[4,2,1,1]
[2,5,1,6,4,3,8,7]=>[3,2,2,1]
[3,6,2,8,5,7,1,4]=>[3,2,1,1,1]
[4,6,8,1,5,7,2,3]=>[3,1,1,1,1,1]
[4,1,2,5,7,6,3,8]=>[3,2,1,1,1]
[4,6,5,8,1,7,3,2]=>[4,2,1,1]
[2,1,3,6,4,8,7,5]=>[3,2,2,1]
[4,8,1,2,7,5,6,3]=>[4,1,1,1,1]
[1,6,4,3,8,7,5,2]=>[4,3,1]
[4,5,1,6,8,7,2,3]=>[3,2,1,1,1]
[2,5,1,8,6,4,7,3]=>[4,2,1,1]
[3,8,7,2,6,1,4,5]=>[4,1,1,1,1]
[8,4,5,1,6,7,2,3]=>[3,2,1,1,1]
[8,4,7,3,1,5,2,6]=>[4,2,1,1]
[2,5,1,8,3,6,4,7]=>[3,2,1,1,1]
[5,8,4,7,3,2,1,6]=>[5,1,1,1]
[5,6,8,4,2,7,1,3]=>[4,1,1,1,1]
[4,3,8,6,1,2,5,7]=>[3,2,1,1,1]
[4,8,6,5,7,1,3,2]=>[5,1,1,1]
[7,2,3,5,6,8,4,1]=>[4,1,1,1,1]
[5,8,1,3,4,7,2,6]=>[3,1,1,1,1,1]
[8,7,5,6,4,1,3,2]=>[6,1,1]
[7,2,4,5,3,1,6,8]=>[4,1,1,1,1]
[7,6,3,1,4,5,8,2]=>[4,2,1,1]
[5,4,1,7,8,6,2,3]=>[3,3,1,1]
[5,3,4,7,8,1,6,2]=>[3,2,1,1,1]
[4,3,7,6,5,1,8,2]=>[4,2,2]
[5,1,4,8,2,3,7,6]=>[3,2,1,1,1]
[3,2,8,5,4,1,6,7]=>[4,2,1,1]
[1,2,8,3,4,6,5,7]=>[3,1,1,1,1,1]
[8,1,2,7,3,5,4,6]=>[4,1,1,1,1]
[5,7,1,2,6,3,4,8]=>[3,1,1,1,1,1]
[1,2,7,5,6,3,4,8]=>[3,1,1,1,1,1]
[5,1,4,7,2,3,6,8]=>[3,1,1,1,1,1]
[4,8,1,2,3,6,5,7]=>[3,1,1,1,1,1]
[6,2,3,8,7,1,4,5]=>[3,2,1,1,1]
[8,2,3,6,4,7,5,1]=>[4,2,1,1]
[7,2,3,6,4,8,1,5]=>[4,1,1,1,1]
[5,4,1,6,2,7,8,3]=>[3,2,2,1]
[7,1,3,5,4,2,8,6]=>[4,2,1,1]
[7,6,8,2,4,5,3,1]=>[5,1,1,1]
[4,2,8,6,5,1,3,7]=>[4,2,1,1]
[3,8,5,4,7,1,2,6]=>[4,1,1,1,1]
[1,4,8,3,6,2,7,5]=>[3,2,1,1,1]
[6,3,2,4,8,7,1,5]=>[4,2,1,1]
[8,3,2,7,4,1,5,6]=>[4,2,1,1]
[7,3,2,6,5,8,1,4]=>[4,2,1,1]
[3,6,2,5,7,4,8,1]=>[4,1,1,1,1]
[2,7,1,5,8,6,4,3]=>[4,2,1,1]
[7,2,4,1,6,8,5,3]=>[4,2,1,1]
[6,4,7,2,3,8,5,1]=>[4,2,1,1]
[6,1,8,5,7,4,2,3]=>[4,2,1,1]
[7,1,4,3,6,5,8,2]=>[4,2,1,1]
[7,1,5,6,3,4,8,2]=>[4,1,1,1,1]
[6,1,8,5,4,7,3,2]=>[5,2,1]
[7,6,1,5,4,2,8,3]=>[5,2,1]
[5,1,6,8,7,2,4,3]=>[4,2,1,1]
[4,6,7,5,3,1,8,2]=>[4,2,1,1]
[5,3,2,6,8,7,4,1]=>[4,3,1]
[5,4,6,2,8,7,3,1]=>[4,3,1]
[4,5,8,6,7,2,3,1]=>[4,1,1,1,1]
[4,5,7,6,1,2,8,3]=>[3,2,1,1,1]
[4,6,5,7,2,1,8,3]=>[4,2,1,1]
[7,4,8,6,3,5,1,2]=>[4,2,1,1]
[7,2,4,3,6,1,8,5]=>[4,2,1,1]
[2,3,4,7,8,6,1,5]=>[3,1,1,1,1,1]
[6,3,7,1,4,2,8,5]=>[3,2,2,1]
[4,6,3,5,1,8,2,7]=>[3,2,1,1,1]
[8,5,7,6,2,3,4,1]=>[5,1,1,1]
[3,4,6,7,8,2,5,1]=>[3,1,1,1,1,1]
[2,5,6,7,3,8,1,4]=>[3,1,1,1,1,1]
[5,8,4,6,2,1,7,3]=>[4,2,1,1]
[1,6,8,3,4,2,7,5]=>[3,2,1,1,1]
[4,1,7,6,2,8,3,5]=>[3,2,2,1]
[4,1,8,2,7,5,3,6]=>[4,2,1,1]
[4,1,7,2,8,5,3,6]=>[3,2,2,1]
[2,5,6,3,7,4,8,1]=>[3,2,1,1,1]
[2,6,5,3,8,4,7,1]=>[4,2,1,1]
[2,6,5,3,7,4,8,1]=>[4,2,1,1]
[7,1,6,3,5,4,8,2]=>[5,1,1,1]
[5,7,3,2,8,4,1,6]=>[4,2,1,1]
[2,8,6,1,7,5,3,4]=>[4,2,1,1]
[8,1,5,2,7,4,3,6]=>[4,2,1,1]
[7,1,4,2,8,5,3,6]=>[3,3,1,1]
[2,6,8,1,7,5,3,4]=>[4,1,1,1,1]
[1,4,6,5,3,8,2,7]=>[4,1,1,1,1]
[2,4,5,8,7,1,3,6]=>[3,1,1,1,1,1]
[3,1,6,8,7,5,4,2]=>[5,2,1]
[3,1,8,7,5,6,4,2]=>[5,2,1]
[5,1,8,7,6,3,4,2]=>[5,2,1]
[8,2,7,5,3,6,4,1]=>[5,2,1]
[8,7,2,3,1,5,6,4]=>[4,2,1,1]
[2,8,5,7,6,1,3,4]=>[4,1,1,1,1]
[1,8,7,2,6,4,5,3]=>[5,1,1,1]
[8,7,2,1,6,4,5,3]=>[5,2,1]
[1,8,4,7,6,2,5,3]=>[5,1,1,1]
[8,7,1,6,4,3,5,2]=>[6,1,1]
[8,4,1,7,3,6,5,2]=>[5,2,1]
[8,3,6,2,1,5,4,7]=>[4,2,1,1]
[4,5,1,8,7,3,6,2]=>[4,2,1,1]
[3,8,5,2,6,7,4,1]=>[4,2,1,1]
[3,6,4,7,5,2,1,8]=>[4,2,1,1]
[5,7,4,1,2,6,8,3]=>[3,2,1,1,1]
[2,8,6,7,5,3,1,4]=>[5,1,1,1]
[7,4,5,2,6,3,1,8]=>[4,2,1,1]
[8,6,3,4,5,1,7,2]=>[4,2,1,1]
[8,6,3,5,4,1,7,2]=>[5,2,1]
[8,7,4,5,1,3,6,2]=>[5,1,1,1]
[8,6,2,5,3,1,4,7]=>[5,1,1,1]
[8,4,7,3,1,2,5,6]=>[4,1,1,1,1]
[8,7,3,5,1,6,4,2]=>[5,2,1]
[4,8,3,2,6,1,7,5]=>[4,2,1,1]
[4,3,7,6,1,5,2,8]=>[4,2,1,1]
[7,5,4,3,6,1,8,2]=>[5,2,1]
[4,6,8,5,3,1,2,7]=>[4,1,1,1,1]
[5,6,8,4,3,7,2,1]=>[5,1,1,1]
[7,5,8,4,2,1,6,3]=>[5,2,1]
[1,4,8,7,6,2,5,3]=>[5,1,1,1]
[7,2,4,1,5,3,8,6]=>[3,2,2,1]
[8,5,3,4,1,7,2,6]=>[4,2,1,1]
[2,8,5,4,3,6,1,7]=>[5,1,1,1]
[8,6,5,3,1,2,7,4]=>[5,2,1]
[7,4,6,5,3,2,8,1]=>[6,1,1]
[5,6,7,2,3,8,4,1]=>[3,2,1,1,1]
[8,4,2,6,5,7,3,1]=>[5,2,1]
[1,7,4,2,8,5,6,3]=>[3,3,1,1]
[3,2,1,7,4,6,8,5]=>[3,3,1,1]
[6,2,5,7,1,4,3,8]=>[4,1,1,1,1]
[4,8,5,3,1,2,6,7]=>[4,1,1,1,1]
[8,5,2,4,6,1,3,7]=>[4,1,1,1,1]
[1,5,3,4,7,2,6,8]=>[3,1,1,1,1,1]
[8,4,6,1,5,7,3,2]=>[5,1,1,1]
[6,4,7,2,1,3,8,5]=>[4,2,1,1]
[6,7,3,1,2,4,8,5]=>[3,2,1,1,1]
[3,1,8,7,6,2,5,4]=>[5,2,1]
[1,3,8,6,7,2,5,4]=>[4,1,1,1,1]
[5,2,3,6,1,8,4,7]=>[3,2,1,1,1]
[3,2,6,4,7,1,5,8]=>[3,2,1,1,1]
[3,6,2,5,7,8,4,1]=>[4,1,1,1,1]
[2,7,4,6,8,3,5,1]=>[4,1,1,1,1]
[3,7,6,8,1,5,4,2]=>[5,1,1,1]
[1,5,7,6,8,4,2,3]=>[4,1,1,1,1]
[2,7,4,6,8,5,3,1]=>[5,1,1,1]
[3,7,6,8,5,1,4,2]=>[5,1,1,1]
[7,1,3,8,6,2,4,5]=>[3,2,1,1,1]
[2,7,1,8,6,5,3,4]=>[4,2,1,1]
[5,3,4,7,6,2,1,8]=>[4,2,1,1]
[4,1,8,5,7,2,6,3]=>[4,2,1,1]
[4,1,8,2,7,5,6,3]=>[4,2,1,1]
[7,6,8,2,4,3,5,1]=>[5,1,1,1]
[7,4,5,3,8,1,6,2]=>[4,2,1,1]
[7,3,6,1,4,2,8,5]=>[4,2,1,1]
[8,7,2,6,4,5,1,3]=>[5,1,1,1]
[7,3,2,5,1,6,8,4]=>[4,2,1,1]
[3,5,1,7,6,4,8,2]=>[4,2,1,1]
[8,7,4,2,1,6,5,3]=>[5,3]
[5,4,7,6,2,1,8,3]=>[4,2,2]
[3,5,2,8,7,1,6,4]=>[4,2,1,1]
[3,7,6,5,4,1,8,2]=>[5,2,1]
[4,6,5,3,1,8,7,2]=>[4,3,1]
[4,5,2,6,7,3,8,1]=>[3,2,1,1,1]
[8,6,7,4,3,1,5,2]=>[5,2,1]
[4,7,1,8,5,3,2,6]=>[4,2,1,1]
[8,6,7,1,4,3,5,2]=>[5,1,1,1]
[8,6,7,2,1,3,5,4]=>[4,2,1,1]
[8,5,6,1,7,4,2,3]=>[4,2,1,1]
[6,4,1,2,5,7,8,3]=>[3,2,1,1,1]
[6,1,5,4,2,7,3,8]=>[4,2,1,1]
[6,4,2,3,1,7,5,8]=>[4,2,1,1]
[3,4,6,1,8,2,7,5]=>[3,2,1,1,1]
[5,3,1,4,7,6,2,8]=>[3,3,1,1]
[6,4,5,2,7,1,3,8]=>[4,1,1,1,1]
[7,4,3,5,1,6,2,8]=>[4,2,1,1]
[7,5,3,6,2,1,4,8]=>[5,1,1,1]
[6,4,3,7,1,8,2,5]=>[4,2,1,1]
[3,1,2,7,6,4,5,8]=>[3,2,1,1,1]
[5,1,2,7,6,3,4,8]=>[3,2,1,1,1]
[5,6,1,7,2,4,3,8]=>[3,2,1,1,1]
[3,5,6,8,1,2,7,4]=>[3,1,1,1,1,1]
[2,6,5,7,1,3,4,8]=>[3,1,1,1,1,1]
[2,3,7,1,5,6,4,8]=>[3,1,1,1,1,1]
[2,6,5,3,4,1,7,8]=>[4,1,1,1,1]
[2,6,1,3,5,4,7,8]=>[3,1,1,1,1,1]
[4,6,1,5,2,8,7,3]=>[3,3,1,1]
[6,1,5,4,2,7,8,3]=>[4,2,1,1]
[4,6,1,5,2,7,8,3]=>[3,2,1,1,1]
[2,8,6,5,1,3,7,4]=>[4,2,1,1]
[5,1,8,6,2,7,4,3]=>[4,2,2]
[3,6,8,2,7,5,1,4]=>[4,1,1,1,1]
[5,6,4,1,7,2,8,3]=>[3,2,2,1]
[3,8,6,1,5,7,4,2]=>[5,1,1,1]
[8,1,6,3,4,2,5,7]=>[4,1,1,1,1]
[7,4,2,3,1,6,8,5]=>[4,2,1,1]
[1,6,4,5,7,3,2,8]=>[4,1,1,1,1]
[1,6,4,5,7,2,8,3]=>[3,2,1,1,1]
[1,7,5,6,4,8,3,2]=>[5,1,1,1]
[1,5,6,7,3,2,4,8]=>[3,1,1,1,1,1]
[8,2,4,3,1,7,5,6]=>[4,2,1,1]
[8,2,1,4,3,7,5,6]=>[3,2,2,1]
[7,6,8,2,1,5,3,4]=>[4,2,1,1]
[8,6,2,5,1,3,7,4]=>[4,2,1,1]
[5,7,2,6,4,1,8,3]=>[4,2,1,1]
[4,5,6,1,3,8,2,7]=>[3,1,1,1,1,1]
[6,3,5,7,4,2,8,1]=>[5,1,1,1]
[7,6,4,8,5,3,1,2]=>[5,2,1]
[8,2,1,6,4,7,3,5]=>[4,2,1,1]
[1,3,8,6,5,2,7,4]=>[4,2,1,1]
[2,7,3,8,5,6,4,1]=>[4,2,1,1]
[1,2,8,5,7,4,6,3]=>[4,1,1,1,1]
[1,6,8,5,4,7,2,3]=>[4,1,1,1,1]
[5,7,1,8,3,2,6,4]=>[3,2,2,1]
[2,1,3,8,6,4,7,5]=>[3,2,2,1]
[8,2,5,4,3,7,1,6]=>[5,1,1,1]
[5,8,4,3,7,6,2,1]=>[5,2,1]
[8,1,5,3,4,7,2,6]=>[4,1,1,1,1]
[6,1,8,7,4,5,3,2]=>[5,2,1]
[1,5,8,6,4,3,7,2]=>[5,1,1,1]
[5,8,6,4,2,1,7,3]=>[5,2,1]
[2,6,1,8,4,7,5,3]=>[4,2,1,1]
[5,3,8,6,1,2,7,4]=>[3,2,2,1]
[5,8,1,4,6,2,7,3]=>[3,2,1,1,1]
[3,7,6,2,1,4,8,5]=>[4,2,1,1]
[4,6,2,3,7,1,8,5]=>[3,2,1,1,1]
[6,8,7,5,1,3,4,2]=>[5,1,1,1]
[6,4,3,2,7,8,5,1]=>[5,2,1]
[2,7,6,1,5,3,8,4]=>[4,2,1,1]
[7,8,6,4,2,5,3,1]=>[5,2,1]
[6,4,5,8,7,1,3,2]=>[4,2,1,1]
[6,4,1,7,8,3,2,5]=>[4,2,1,1]
[5,4,7,2,1,3,8,6]=>[4,2,1,1]
[2,6,4,5,7,1,8,3]=>[3,2,1,1,1]
[3,7,4,6,1,5,8,2]=>[4,1,1,1,1]
[3,4,6,5,2,8,1,7]=>[4,1,1,1,1]
[4,6,7,5,8,2,1,3]=>[4,1,1,1,1]
[2,5,7,6,4,1,8,3]=>[4,2,1,1]
[5,1,4,6,2,7,8,3]=>[3,2,1,1,1]
[1,2,5,3,7,8,6,4]=>[3,2,1,1,1]
[4,8,3,5,1,2,7,6]=>[3,2,1,1,1]
[6,1,3,7,2,8,4,5]=>[3,2,1,1,1]
[3,8,5,4,1,7,2,6]=>[4,2,1,1]
[3,1,5,8,2,6,7,4]=>[3,2,1,1,1]
[2,8,5,3,1,7,4,6]=>[4,2,1,1]
[6,5,2,3,7,1,8,4]=>[4,2,1,1]
[7,2,1,6,4,8,3,5]=>[4,2,1,1]
[2,1,3,7,5,8,4,6]=>[3,2,1,1,1]
[6,2,4,5,7,1,8,3]=>[3,2,1,1,1]
[2,3,8,7,1,4,6,5]=>[4,1,1,1,1]
[4,2,7,5,6,8,1,3]=>[3,2,1,1,1]
[6,8,2,5,4,7,3,1]=>[5,1,1,1]
[2,7,6,3,8,4,5,1]=>[4,2,1,1]
[4,6,8,2,3,1,7,5]=>[3,2,1,1,1]
[4,7,2,3,5,1,8,6]=>[3,2,1,1,1]
[6,4,2,1,3,7,5,8]=>[4,2,1,1]
[5,3,2,7,6,1,8,4]=>[4,2,2]
[5,6,4,2,8,7,1,3]=>[4,2,1,1]
[5,7,4,2,6,1,8,3]=>[4,2,1,1]
[5,4,7,1,6,2,8,3]=>[3,2,2,1]
[4,5,8,7,6,2,1,3]=>[5,1,1,1]
[6,4,7,1,2,3,8,5]=>[3,2,1,1,1]
[1,8,7,2,3,4,6,5]=>[4,1,1,1,1]
[1,8,3,7,6,2,5,4]=>[5,1,1,1]
[1,3,8,2,5,6,4,7]=>[3,1,1,1,1,1]
[1,3,2,7,4,6,8,5]=>[3,2,1,1,1]
[1,3,8,4,6,2,7,5]=>[3,2,1,1,1]
[8,2,3,6,7,4,5,1]=>[4,1,1,1,1]
[5,6,4,2,1,7,3,8]=>[4,2,1,1]
[2,5,7,6,3,8,4,1]=>[4,2,1,1]
[6,4,7,1,2,5,3,8]=>[3,2,1,1,1]
[1,2,7,5,8,6,3,4]=>[3,2,1,1,1]
[7,4,5,1,6,8,2,3]=>[3,2,1,1,1]
[1,7,8,4,2,6,3,5]=>[3,2,1,1,1]
[6,3,2,5,7,4,1,8]=>[4,2,1,1]
[6,2,1,5,3,7,8,4]=>[3,2,2,1]
[6,2,5,1,3,8,7,4]=>[3,3,1,1]
[6,2,8,5,1,3,7,4]=>[3,2,2,1]
[4,1,7,8,3,6,5,2]=>[4,2,1,1]
[6,4,2,1,7,3,5,8]=>[4,2,1,1]
[5,8,4,2,1,3,6,7]=>[4,1,1,1,1]
[1,7,5,8,4,3,6,2]=>[5,1,1,1]
[5,8,1,6,4,7,2,3]=>[4,1,1,1,1]
[2,4,7,5,1,8,6,3]=>[3,3,1,1]
[2,3,7,1,8,5,6,4]=>[3,2,1,1,1]
[6,5,1,2,7,4,8,3]=>[4,2,1,1]
[3,6,5,7,8,2,4,1]=>[4,1,1,1,1]
[3,6,5,1,8,7,4,2]=>[4,3,1]
[7,8,1,2,5,4,3,6]=>[4,1,1,1,1]
[2,8,4,3,5,1,7,6]=>[4,2,1,1]
[5,2,4,7,6,8,1,3]=>[3,2,1,1,1]
[3,1,5,7,4,8,6,2]=>[3,2,2,1]
[4,1,7,6,8,2,5,3]=>[4,2,1,1]
[7,2,6,4,1,5,3,8]=>[4,2,1,1]
[1,2,6,5,8,3,7,4]=>[3,2,1,1,1]
[7,3,5,6,1,4,2,8]=>[4,1,1,1,1]
[5,8,3,1,6,7,4,2]=>[4,2,1,1]
[4,5,8,1,7,3,6,2]=>[4,1,1,1,1]
[4,7,1,6,8,5,2,3]=>[4,1,1,1,1]
[5,8,7,1,6,4,2,3]=>[5,1,1,1]
[1,7,3,8,2,5,4,6]=>[3,2,1,1,1]
[8,4,1,3,6,7,5,2]=>[4,2,1,1]
[5,3,1,8,6,7,4,2]=>[4,3,1]
[6,2,7,1,4,3,5,8]=>[3,2,1,1,1]
[8,3,2,6,5,1,7,4]=>[4,2,2]
[7,3,2,6,5,1,4,8]=>[4,2,1,1]
[2,6,8,4,7,1,3,5]=>[3,1,1,1,1,1]
[7,8,6,3,2,5,4,1]=>[5,2,1]
[5,2,8,6,3,1,4,7]=>[4,2,1,1]
[1,6,4,8,2,3,5,7]=>[3,1,1,1,1,1]
[2,8,5,6,4,1,7,3]=>[4,2,1,1]
[1,4,7,3,5,8,6,2]=>[3,2,1,1,1]
[3,7,8,2,5,1,6,4]=>[3,2,1,1,1]
[8,6,1,4,3,2,7,5]=>[5,2,1]
[7,3,8,2,4,1,5,6]=>[4,1,1,1,1]
[6,3,7,8,1,2,5,4]=>[3,2,1,1,1]
[7,6,1,5,2,3,8,4]=>[4,2,1,1]
[5,1,8,6,7,2,3,4]=>[3,2,1,1,1]
[5,7,1,6,8,2,3,4]=>[3,1,1,1,1,1]
[6,8,4,2,1,7,3,5]=>[4,2,1,1]
[6,3,2,8,1,7,4,5]=>[4,2,1,1]
[6,4,1,3,7,8,5,2]=>[4,2,1,1]
[6,8,5,4,3,7,1,2]=>[5,1,1,1]
[5,7,4,8,3,1,2,6]=>[4,1,1,1,1]
[6,1,2,4,8,3,7,5]=>[3,2,1,1,1]
[2,5,6,8,1,4,7,3]=>[3,1,1,1,1,1]
[7,4,1,6,5,2,3,8]=>[4,2,1,1]
[4,1,6,5,2,3,8,7]=>[3,2,2,1]
[4,5,1,7,8,6,2,3]=>[3,2,1,1,1]
[8,5,7,3,4,6,2,1]=>[5,1,1,1]
[6,8,7,4,3,5,2,1]=>[6,1,1]
[6,8,7,5,3,4,2,1]=>[6,1,1]
[5,8,6,2,4,7,3,1]=>[5,1,1,1]
[4,8,6,2,5,7,3,1]=>[5,1,1,1]
[1,6,4,7,5,3,2,8]=>[4,2,1,1]
[1,6,5,3,2,7,4,8]=>[4,2,1,1]
[1,6,8,7,4,5,3,2]=>[5,1,1,1]
[1,4,7,5,3,2,6,8]=>[4,1,1,1,1]
[1,7,5,4,3,2,8,6]=>[5,2,1]
[1,4,7,5,3,2,8,6]=>[4,2,1,1]
[1,7,4,6,8,5,3,2]=>[5,1,1,1]
[6,8,7,2,3,5,4,1]=>[5,1,1,1]
[5,7,6,1,8,2,4,3]=>[4,2,1,1]
[4,8,6,5,7,2,3,1]=>[5,1,1,1]
[2,7,8,5,1,4,3,6]=>[4,1,1,1,1]
[8,5,6,2,4,7,3,1]=>[5,1,1,1]
[3,5,8,4,2,6,1,7]=>[4,1,1,1,1]
[8,1,3,6,4,5,2,7]=>[4,1,1,1,1]
[4,3,1,6,2,5,8,7]=>[3,2,2,1]
[7,5,2,1,8,4,3,6]=>[4,3,1]
[5,3,1,4,7,8,2,6]=>[3,2,1,1,1]
[7,1,2,4,8,3,5,6]=>[3,1,1,1,1,1]
[8,6,1,3,5,7,4,2]=>[5,1,1,1]
[7,1,5,8,2,3,4,6]=>[3,1,1,1,1,1]
[3,6,8,5,1,4,2,7]=>[4,1,1,1,1]
[5,2,4,1,6,8,3,7]=>[3,2,1,1,1]
[2,5,3,4,6,8,1,7]=>[3,1,1,1,1,1]
[4,7,1,2,5,6,3,8]=>[3,1,1,1,1,1]
[6,7,3,1,8,2,4,5]=>[3,2,1,1,1]
[7,3,1,4,6,2,8,5]=>[3,2,2,1]
[7,4,1,2,5,6,3,8]=>[3,2,1,1,1]
[5,4,1,3,6,8,7,2]=>[4,2,1,1]
[5,7,4,8,1,6,3,2]=>[4,2,1,1]
[4,3,1,2,5,7,6,8]=>[3,2,1,1,1]
[1,2,4,7,8,5,6,3]=>[3,1,1,1,1,1]
[5,3,1,8,4,2,6,7]=>[3,3,1,1]
[4,5,3,6,8,7,1,2]=>[3,2,1,1,1]
[2,1,6,5,8,7,3,4]=>[3,2,2,1]
[6,1,5,4,7,3,8,2]=>[5,1,1,1]
[5,3,2,8,7,1,6,4]=>[4,3,1]
[8,6,7,4,1,3,5,2]=>[5,1,1,1]
[4,1,3,6,5,2,8,7]=>[3,2,2,1]
[4,6,3,2,5,1,8,7]=>[4,2,1,1]
[4,8,3,2,6,5,7,1]=>[4,2,1,1]
[4,8,3,6,5,2,7,1]=>[5,1,1,1]
[8,1,6,2,5,4,7,3]=>[5,1,1,1]
[2,4,3,8,6,1,7,5]=>[3,2,2,1]
[2,6,3,8,5,4,7,1]=>[4,2,1,1]
[6,1,3,2,5,8,7,4]=>[3,3,1,1]
[6,8,4,2,5,3,7,1]=>[4,2,1,1]
[6,8,4,3,5,2,7,1]=>[5,1,1,1]
[8,1,4,6,5,3,7,2]=>[5,1,1,1]
[3,5,4,6,1,2,8,7]=>[3,2,1,1,1]
[7,3,5,6,1,8,2,4]=>[3,2,1,1,1]
[5,7,6,3,4,2,8,1]=>[5,1,1,1]
[4,6,7,2,3,5,8,1]=>[3,1,1,1,1,1]
[6,5,4,8,7,2,3,1]=>[5,2,1]
[5,7,4,3,6,2,1,8]=>[5,1,1,1]
[1,8,5,6,2,3,7,4]=>[3,2,1,1,1]
[7,2,4,6,8,1,5,3]=>[4,1,1,1,1]
[6,2,5,4,7,8,1,3]=>[4,1,1,1,1]
[3,8,2,6,1,7,4,5]=>[3,2,1,1,1]
[8,5,6,1,3,2,7,4]=>[4,2,1,1]
[5,3,7,8,2,6,1,4]=>[4,1,1,1,1]
[4,5,8,3,6,1,7,2]=>[3,2,1,1,1]
[4,5,8,7,2,3,1,6]=>[4,1,1,1,1]
[5,7,1,3,6,2,4,8]=>[3,1,1,1,1,1]
[4,7,5,2,3,6,8,1]=>[4,1,1,1,1]
[3,6,4,1,2,5,7,8]=>[3,1,1,1,1,1]
[4,7,1,3,2,5,8,6]=>[3,2,1,1,1]
[4,7,1,3,2,6,8,5]=>[3,2,1,1,1]
[5,7,1,3,6,2,8,4]=>[3,2,1,1,1]
[6,8,2,5,7,3,1,4]=>[4,1,1,1,1]
[4,8,5,2,3,6,1,7]=>[4,1,1,1,1]
[5,8,6,3,4,7,2,1]=>[5,1,1,1]
[3,7,5,4,2,8,1,6]=>[5,1,1,1]
[4,6,5,1,7,8,2,3]=>[3,2,1,1,1]
[4,7,1,3,2,8,5,6]=>[3,2,1,1,1]
[3,6,5,1,8,2,4,7]=>[3,2,1,1,1]
[5,8,7,3,4,2,6,1]=>[5,1,1,1]
[8,5,2,3,7,4,6,1]=>[4,2,1,1]
[6,3,1,5,4,8,2,7]=>[4,2,1,1]
[4,7,6,3,5,2,8,1]=>[5,1,1,1]
[1,7,5,3,4,8,6,2]=>[4,2,1,1]
[5,8,2,3,4,7,6,1]=>[4,1,1,1,1]
[8,7,3,2,6,4,5,1]=>[5,2,1]
[8,3,1,4,7,5,2,6]=>[4,2,1,1]
[5,3,1,6,4,8,7,2]=>[3,3,2]
[3,4,8,5,7,2,6,1]=>[4,1,1,1,1]
[8,5,1,2,7,6,4,3]=>[5,2,1]
[8,2,6,3,1,5,4,7]=>[4,2,1,1]
[3,7,8,5,6,2,4,1]=>[4,1,1,1,1]
[7,4,3,6,2,5,8,1]=>[5,1,1,1]
[4,3,8,7,1,6,2,5]=>[4,2,1,1]
[1,5,3,8,4,7,2,6]=>[3,2,1,1,1]
[8,2,3,1,6,5,7,4]=>[4,2,1,1]
[8,4,2,7,1,3,6,5]=>[4,2,1,1]
[8,4,2,3,1,6,7,5]=>[4,2,1,1]
[4,7,2,3,6,5,8,1]=>[4,1,1,1,1]
[3,8,2,6,4,7,1,5]=>[4,1,1,1,1]
[1,7,5,8,6,2,4,3]=>[4,2,1,1]
[6,5,1,7,4,8,3,2]=>[5,2,1]
[7,6,3,5,1,4,8,2]=>[5,1,1,1]
[6,5,4,1,7,2,3,8]=>[4,2,1,1]
[8,3,6,1,7,4,5,2]=>[4,2,1,1]
[7,1,2,6,4,8,3,5]=>[4,1,1,1,1]
[3,5,1,8,6,2,4,7]=>[3,2,1,1,1]
[1,8,7,5,4,6,2,3]=>[5,1,1,1]
[8,1,6,7,4,5,3,2]=>[5,1,1,1]
[8,1,6,4,7,5,3,2]=>[5,2,1]
[6,4,8,1,5,3,7,2]=>[4,2,1,1]
[1,6,4,3,5,8,2,7]=>[4,1,1,1,1]
[5,1,4,3,7,8,6,2]=>[4,2,1,1]
[5,7,1,8,6,3,2,4]=>[4,2,1,1]
[5,7,6,3,4,2,1,8]=>[5,1,1,1]
[4,3,6,1,2,7,8,5]=>[3,2,1,1,1]
[5,8,3,6,7,2,4,1]=>[4,1,1,1,1]
[8,1,6,2,5,7,4,3]=>[5,1,1,1]
[2,7,1,5,3,6,8,4]=>[3,2,1,1,1]
[6,8,7,3,4,2,5,1]=>[5,1,1,1]
[1,8,6,2,4,7,5,3]=>[4,2,1,1]
[5,7,3,6,4,2,1,8]=>[5,1,1,1]
[5,7,3,6,4,1,8,2]=>[4,2,1,1]
[3,7,5,6,4,1,8,2]=>[4,2,1,1]
[2,8,5,7,3,4,6,1]=>[4,1,1,1,1]
[2,1,3,8,5,4,6,7]=>[3,2,1,1,1]
[5,3,6,8,2,4,1,7]=>[4,1,1,1,1]
[1,7,8,6,3,2,4,5]=>[4,1,1,1,1]
[7,1,2,5,3,8,4,6]=>[3,2,1,1,1]
[3,7,4,2,5,1,8,6]=>[4,2,1,1]
[1,8,3,4,5,7,2,6]=>[3,1,1,1,1,1]
[2,6,7,5,3,8,1,4]=>[4,1,1,1,1]
[4,5,2,6,8,7,1,3]=>[3,2,1,1,1]
[4,5,2,6,8,3,1,7]=>[3,2,1,1,1]
[7,5,8,2,4,3,6,1]=>[5,1,1,1]
[6,5,8,2,3,4,1,7]=>[4,1,1,1,1]
[8,1,5,3,4,6,2,7]=>[4,1,1,1,1]
[5,8,7,2,4,3,6,1]=>[5,1,1,1]
[1,7,2,4,8,5,6,3]=>[3,2,1,1,1]
[5,8,2,3,7,4,6,1]=>[4,1,1,1,1]
[7,8,2,3,5,4,6,1]=>[4,1,1,1,1]
[8,4,1,3,2,6,5,7]=>[4,2,1,1]
[8,7,2,3,5,4,6,1]=>[5,1,1,1]
[1,7,6,8,4,5,3,2]=>[5,1,1,1]
[2,7,3,1,8,5,6,4]=>[3,3,1,1]
[3,8,5,2,1,6,7,4]=>[4,2,1,1]
[2,8,6,1,5,7,4,3]=>[5,1,1,1]
[8,3,5,1,7,6,4,2]=>[5,2,1]
[8,3,5,4,7,1,6,2]=>[4,2,1,1]
[6,4,1,5,7,8,2,3]=>[3,2,1,1,1]
[4,8,7,1,2,5,3,6]=>[4,1,1,1,1]
[8,7,2,6,1,4,3,5]=>[5,1,1,1]
[6,1,7,3,8,2,4,5]=>[3,2,1,1,1]
[7,1,8,6,4,2,3,5]=>[4,2,1,1]
[4,1,3,5,8,2,6,7]=>[3,1,1,1,1,1]
[1,8,5,7,4,6,3,2]=>[5,1,1,1]
[1,4,7,6,8,3,5,2]=>[4,1,1,1,1]
[1,7,2,8,6,5,3,4]=>[4,2,1,1]
[5,7,1,6,4,2,3,8]=>[4,1,1,1,1]
[4,8,2,7,5,1,6,3]=>[4,2,1,1]
[2,8,4,6,7,1,5,3]=>[4,1,1,1,1]
[3,8,5,1,4,2,6,7]=>[4,1,1,1,1]
[1,7,6,2,5,3,8,4]=>[4,2,1,1]
[1,7,5,2,4,3,8,6]=>[4,2,1,1]
[2,8,5,1,4,3,6,7]=>[4,1,1,1,1]
[3,1,2,5,7,6,8,4]=>[3,2,1,1,1]
[5,1,7,3,2,6,8,4]=>[3,2,2,1]
[4,7,2,3,5,1,6,8]=>[3,1,1,1,1,1]
[4,8,2,3,7,5,1,6]=>[4,1,1,1,1]
[8,7,2,4,3,5,6,1]=>[5,1,1,1]
[8,6,2,4,3,5,1,7]=>[5,1,1,1]
[8,1,2,4,7,3,5,6]=>[3,1,1,1,1,1]
[7,6,2,8,4,5,1,3]=>[4,2,1,1]
[6,8,1,5,7,3,2,4]=>[4,1,1,1,1]
[4,1,7,5,6,8,2,3]=>[3,2,1,1,1]
[3,7,6,2,1,4,5,8]=>[4,1,1,1,1]
[1,6,8,7,2,5,4,3]=>[5,1,1,1]
[1,4,8,7,6,3,5,2]=>[5,1,1,1]
[3,1,8,4,5,2,7,6]=>[3,2,2,1]
[2,3,7,6,1,8,4,5]=>[3,2,1,1,1]
[4,8,5,2,1,3,7,6]=>[4,2,1,1]
[5,8,4,2,1,3,7,6]=>[4,2,1,1]
[4,6,7,5,2,3,1,8]=>[4,1,1,1,1]
[6,2,5,3,1,8,7,4]=>[4,3,1]
[6,2,5,3,8,7,1,4]=>[4,2,1,1]
[6,4,5,3,8,7,1,2]=>[4,2,1,1]
[1,6,4,5,8,7,3,2]=>[4,2,1,1]
[8,4,7,5,2,3,1,6]=>[5,1,1,1]
[8,2,7,4,5,3,1,6]=>[5,1,1,1]
[8,2,4,7,5,3,1,6]=>[5,1,1,1]
[8,2,6,7,5,3,1,4]=>[5,1,1,1]
[8,4,6,7,5,3,1,2]=>[5,1,1,1]
[6,4,5,8,7,3,1,2]=>[4,2,1,1]
[6,2,8,7,5,3,1,4]=>[5,2,1]
[4,6,5,3,8,7,1,2]=>[4,2,1,1]
[6,7,2,4,5,3,1,8]=>[4,1,1,1,1]
[6,8,7,4,5,3,1,2]=>[5,1,1,1]
[2,8,4,7,5,3,1,6]=>[5,1,1,1]
[5,8,7,4,6,3,1,2]=>[5,1,1,1]
[6,5,8,4,7,2,1,3]=>[5,1,1,1]
[4,8,6,2,5,7,1,3]=>[4,1,1,1,1]
[8,1,6,2,5,7,3,4]=>[4,1,1,1,1]
[6,8,1,2,4,7,3,5]=>[3,1,1,1,1,1]
[8,1,5,3,2,7,4,6]=>[4,2,1,1]
[8,3,7,6,2,5,4,1]=>[6,1,1]
[4,6,1,3,5,8,2,7]=>[3,1,1,1,1,1]
[4,5,1,3,8,7,2,6]=>[3,2,1,1,1]
[6,2,7,1,8,3,4,5]=>[3,2,1,1,1]
[6,4,5,8,1,7,2,3]=>[3,2,1,1,1]
[6,2,8,5,1,4,7,3]=>[4,2,1,1]
[2,4,7,6,1,8,3,5]=>[3,2,1,1,1]
[7,4,5,8,6,3,2,1]=>[5,2,1]
[7,4,1,3,6,8,2,5]=>[4,1,1,1,1]
[6,8,1,2,7,3,4,5]=>[3,1,1,1,1,1]
[1,6,2,8,7,3,4,5]=>[3,2,1,1,1]
[1,6,8,5,7,4,3,2]=>[5,1,1,1]
[3,8,1,2,4,7,6,5]=>[4,1,1,1,1]
[1,4,5,7,3,6,8,2]=>[3,1,1,1,1,1]
[2,3,8,1,4,6,5,7]=>[3,1,1,1,1,1]
[3,6,2,4,7,5,8,1]=>[3,2,1,1,1]
[3,1,8,4,6,2,5,7]=>[3,2,1,1,1]
[4,2,7,3,5,8,1,6]=>[3,2,1,1,1]
[3,1,8,4,5,6,2,7]=>[3,2,1,1,1]
[4,2,7,8,6,3,1,5]=>[4,2,1,1]
[7,1,4,2,8,6,3,5]=>[3,3,1,1]
[2,3,7,4,8,1,6,5]=>[3,2,1,1,1]
[1,6,3,5,8,7,4,2]=>[4,2,1,1]
[8,4,6,3,5,1,7,2]=>[4,2,1,1]
[7,3,2,6,8,4,5,1]=>[4,2,1,1]
[2,4,5,7,1,6,8,3]=>[3,1,1,1,1,1]
[8,4,2,6,7,3,5,1]=>[4,2,1,1]
[4,1,5,7,8,6,2,3]=>[3,2,1,1,1]
[6,1,4,8,2,3,7,5]=>[3,2,1,1,1]
[7,6,2,3,5,8,4,1]=>[5,1,1,1]
[2,8,5,7,6,3,4,1]=>[5,1,1,1]
[2,5,7,8,6,4,1,3]=>[4,1,1,1,1]
[7,4,1,6,2,5,8,3]=>[4,2,1,1]
[1,7,5,4,6,2,3,8]=>[4,1,1,1,1]
[6,2,7,5,3,1,4,8]=>[4,2,1,1]
[6,1,7,4,8,5,2,3]=>[3,2,2,1]
[8,2,4,6,3,1,7,5]=>[4,2,1,1]
[5,6,2,4,8,7,3,1]=>[4,2,1,1]
[8,5,6,2,3,7,4,1]=>[4,2,1,1]
[7,8,1,4,5,6,2,3]=>[3,1,1,1,1,1]
[7,4,8,3,5,6,2,1]=>[5,1,1,1]
[2,6,1,4,7,5,8,3]=>[3,2,1,1,1]
[3,1,5,7,2,6,8,4]=>[3,2,1,1,1]
[3,1,7,5,2,6,8,4]=>[3,2,2,1]
[3,2,7,5,1,6,8,4]=>[3,2,2,1]
[5,2,7,3,1,6,8,4]=>[3,2,2,1]
[6,7,2,1,3,4,8,5]=>[3,2,1,1,1]
[4,6,3,1,2,7,8,5]=>[3,2,1,1,1]
[2,3,5,6,8,4,7,1]=>[3,1,1,1,1,1]
[2,4,5,8,3,6,7,1]=>[3,1,1,1,1,1]
[4,5,8,7,6,3,1,2]=>[5,1,1,1]
[8,7,4,6,5,3,1,2]=>[6,1,1]
[8,1,4,3,6,2,5,7]=>[4,1,1,1,1]
[1,6,3,7,8,4,2,5]=>[3,2,1,1,1]
[5,3,8,4,6,7,2,1]=>[4,2,1,1]
[4,3,5,8,6,7,2,1]=>[4,2,1,1]
[3,2,7,8,5,6,4,1]=>[4,2,1,1]
[4,7,3,8,5,6,2,1]=>[4,2,1,1]
[7,1,4,8,5,6,3,2]=>[4,2,1,1]
[4,3,8,7,2,5,6,1]=>[4,2,1,1]
[1,7,3,8,6,4,5,2]=>[4,2,1,1]
[7,4,2,8,5,6,3,1]=>[4,3,1]
[3,4,8,2,6,7,5,1]=>[4,1,1,1,1]
[1,6,3,8,7,4,5,2]=>[4,2,1,1]
[1,4,5,8,7,6,2,3]=>[4,1,1,1,1]
[5,2,1,3,8,4,6,7]=>[3,2,1,1,1]
[1,4,3,5,8,2,6,7]=>[3,1,1,1,1,1]
[2,1,3,8,6,4,5,7]=>[3,2,1,1,1]
[1,3,6,4,5,8,2,7]=>[3,1,1,1,1,1]
[6,1,4,3,5,8,2,7]=>[4,1,1,1,1]
[6,5,1,3,8,2,4,7]=>[4,1,1,1,1]
[1,4,3,8,6,2,5,7]=>[3,2,1,1,1]
[4,1,3,8,6,2,5,7]=>[3,2,1,1,1]
[7,1,5,4,6,3,8,2]=>[5,1,1,1]
[6,4,7,8,3,5,1,2]=>[4,1,1,1,1]
[3,5,6,7,1,8,4,2]=>[3,2,1,1,1]
[2,7,8,3,6,1,5,4]=>[4,1,1,1,1]
[1,7,8,3,6,2,5,4]=>[4,1,1,1,1]
[7,4,3,5,8,1,6,2]=>[4,2,1,1]
[7,3,6,4,1,8,5,2]=>[4,3,1]
[7,8,4,3,6,1,5,2]=>[4,2,1,1]
[7,1,6,4,3,8,5,2]=>[5,2,1]
[8,7,3,4,1,5,2,6]=>[4,2,1,1]
[7,2,6,4,3,8,5,1]=>[5,2,1]
[1,7,5,4,3,8,2,6]=>[5,1,1,1]
[4,5,8,1,7,3,2,6]=>[4,1,1,1,1]
[4,6,7,1,3,8,2,5]=>[3,1,1,1,1,1]
[2,6,3,1,4,7,8,5]=>[3,2,1,1,1]
[2,7,3,4,1,8,5,6]=>[3,2,1,1,1]
[8,6,4,5,1,3,7,2]=>[5,1,1,1]
[7,4,8,5,3,6,1,2]=>[4,2,1,1]
[8,4,6,5,1,3,7,2]=>[5,1,1,1]
[4,5,3,8,7,1,2,6]=>[3,2,1,1,1]
[8,5,4,7,6,1,2,3]=>[4,2,1,1]
[2,3,7,8,1,4,6,5]=>[3,1,1,1,1,1]
[8,2,3,5,4,1,7,6]=>[4,2,1,1]
[7,1,3,8,2,4,6,5]=>[3,2,1,1,1]
[7,2,3,6,4,1,8,5]=>[4,2,1,1]
[6,5,2,4,1,8,3,7]=>[4,2,1,1]
[5,7,2,4,1,3,8,6]=>[3,2,1,1,1]
[6,2,5,4,1,8,3,7]=>[4,2,1,1]
[4,2,6,3,5,8,1,7]=>[3,2,1,1,1]
[7,4,2,6,8,5,3,1]=>[5,2,1]
[8,5,2,4,6,3,1,7]=>[5,1,1,1]
[7,4,1,2,8,5,6,3]=>[3,3,1,1]
[6,4,1,8,5,2,3,7]=>[3,3,1,1]
[8,4,1,6,3,5,2,7]=>[4,2,1,1]
[7,3,4,1,6,8,5,2]=>[4,2,1,1]
[8,6,2,3,5,7,4,1]=>[5,1,1,1]
[8,6,2,5,7,3,4,1]=>[5,1,1,1]
[6,3,4,8,5,1,2,7]=>[3,2,1,1,1]
[8,5,1,2,7,4,6,3]=>[4,2,1,1]
[7,2,6,8,3,4,5,1]=>[4,1,1,1,1]
[1,6,7,5,4,8,2,3]=>[4,1,1,1,1]
[1,8,5,4,2,6,3,7]=>[4,2,1,1]
[5,7,3,6,2,1,4,8]=>[4,1,1,1,1]
[5,8,6,1,2,4,3,7]=>[4,1,1,1,1]
[4,1,5,7,3,6,8,2]=>[3,2,1,1,1]
[1,4,5,7,6,8,2,3]=>[3,1,1,1,1,1]
[5,7,2,1,6,8,4,3]=>[4,2,1,1]
[2,6,3,1,7,8,5,4]=>[3,3,1,1]
[6,2,5,7,4,1,8,3]=>[4,2,1,1]
[3,6,1,8,7,4,5,2]=>[4,2,1,1]
[4,7,1,3,5,6,8,2]=>[3,1,1,1,1,1]
[4,3,5,7,8,2,6,1]=>[4,1,1,1,1]
[5,3,2,7,6,4,1,8]=>[4,3,1]
[5,3,7,4,6,2,1,8]=>[4,2,1,1]
[5,7,3,2,1,8,6,4]=>[4,3,1]
[5,7,6,3,2,1,8,4]=>[5,2,1]
[3,2,7,5,4,1,8,6]=>[4,2,2]
[1,7,3,5,4,2,6,8]=>[4,1,1,1,1]
[5,3,7,4,1,8,6,2]=>[3,3,2]
[7,3,5,4,1,6,8,2]=>[4,2,1,1]
[7,5,1,6,8,3,2,4]=>[4,2,1,1]
[5,3,1,7,6,8,2,4]=>[3,3,1,1]
[7,1,5,3,2,4,8,6]=>[4,2,1,1]
[7,1,5,2,4,3,6,8]=>[4,1,1,1,1]
[6,8,7,3,2,1,5,4]=>[5,2,1]
[3,6,8,7,2,4,1,5]=>[4,1,1,1,1]
[5,7,3,6,2,1,8,4]=>[4,2,1,1]
[3,6,5,2,4,8,1,7]=>[4,1,1,1,1]
[1,8,3,6,2,4,7,5]=>[3,2,1,1,1]
[1,8,7,5,6,4,2,3]=>[5,1,1,1]
[6,8,2,1,5,4,3,7]=>[4,2,1,1]
[6,3,2,1,5,8,4,7]=>[4,2,1,1]
[4,3,5,6,2,8,1,7]=>[4,1,1,1,1]
[6,3,5,2,7,8,4,1]=>[4,2,1,1]
[4,5,3,1,6,8,2,7]=>[3,2,1,1,1]
[3,4,6,7,5,1,8,2]=>[3,2,1,1,1]
[7,4,1,2,5,6,8,3]=>[3,2,1,1,1]
[4,8,2,6,7,1,5,3]=>[4,1,1,1,1]
[6,5,8,3,7,1,4,2]=>[4,2,1,1]
[1,5,2,4,7,6,8,3]=>[3,2,1,1,1]
[2,5,4,7,1,8,3,6]=>[3,2,1,1,1]
[1,5,4,7,3,8,2,6]=>[4,1,1,1,1]
[1,2,6,7,3,5,4,8]=>[3,1,1,1,1,1]
[8,1,2,4,6,3,5,7]=>[3,1,1,1,1,1]
[3,7,8,4,5,6,1,2]=>[3,1,1,1,1,1]
[1,3,8,6,7,4,5,2]=>[4,1,1,1,1]
[2,6,5,3,7,1,8,4]=>[4,2,1,1]
[5,7,1,3,6,4,8,2]=>[4,1,1,1,1]
[8,2,5,4,1,7,3,6]=>[4,2,1,1]
[8,1,7,6,4,2,3,5]=>[5,1,1,1]
[5,7,3,4,2,8,6,1]=>[4,2,1,1]
[5,8,3,4,2,7,6,1]=>[4,2,1,1]
[7,6,4,2,3,8,5,1]=>[5,2,1]
[3,5,6,8,2,4,7,1]=>[3,1,1,1,1,1]
[4,8,7,3,2,5,6,1]=>[5,1,1,1]
[3,7,4,2,6,8,5,1]=>[4,2,1,1]
[6,4,8,7,3,2,5,1]=>[5,2,1]
[5,6,2,8,7,4,3,1]=>[5,2,1]
[3,7,5,6,4,2,8,1]=>[5,1,1,1]
[5,2,3,8,6,1,4,7]=>[3,2,1,1,1]
[1,4,3,8,5,6,2,7]=>[3,2,1,1,1]
[7,8,2,6,4,3,5,1]=>[5,1,1,1]
[4,5,8,7,2,3,6,1]=>[4,1,1,1,1]
[7,8,6,1,4,2,5,3]=>[4,2,1,1]
[8,3,6,5,2,7,1,4]=>[5,1,1,1]
[5,1,3,6,4,2,7,8]=>[3,2,1,1,1]
[6,1,2,4,7,5,3,8]=>[3,2,1,1,1]
[8,3,1,4,6,7,2,5]=>[3,2,1,1,1]
[7,8,5,1,2,6,3,4]=>[3,2,1,1,1]
[6,4,5,1,8,7,3,2]=>[4,3,1]
[8,6,2,1,7,3,5,4]=>[4,3,1]
[7,8,6,1,4,3,5,2]=>[5,1,1,1]
[4,3,6,2,5,7,1,8]=>[4,1,1,1,1]
[1,6,5,7,3,4,8,2]=>[4,1,1,1,1]
[8,2,6,5,1,7,4,3]=>[5,2,1]
[7,6,4,1,2,5,8,3]=>[4,2,1,1]
[2,6,5,4,8,7,1,3]=>[4,2,1,1]
[5,6,7,1,3,2,4,8]=>[3,1,1,1,1,1]
[7,1,8,4,3,2,6,5]=>[4,2,2]
[1,8,5,2,7,6,4,3]=>[5,2,1]
[1,7,6,8,2,5,4,3]=>[5,1,1,1]
[1,7,8,6,2,5,4,3]=>[5,1,1,1]
[4,6,5,7,1,8,2,3]=>[3,2,1,1,1]
[7,5,3,6,8,4,2,1]=>[5,2,1]
[7,2,5,6,4,8,3,1]=>[5,1,1,1]
[7,4,6,2,8,5,3,1]=>[5,2,1]
[1,6,3,4,2,5,8,7]=>[3,2,1,1,1]
[1,5,7,6,2,3,8,4]=>[3,2,1,1,1]
[1,4,3,7,6,2,5,8]=>[3,2,1,1,1]
[1,3,7,4,6,8,5,2]=>[4,1,1,1,1]
[3,7,4,6,8,1,5,2]=>[4,1,1,1,1]
[4,8,3,1,7,6,2,5]=>[4,2,1,1]
[5,6,1,4,3,8,7,2]=>[4,2,1,1]
[5,8,6,4,3,1,7,2]=>[5,2,1]
[4,1,3,7,8,6,5,2]=>[4,2,1,1]
[9,1,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[8,1,2,3,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[7,1,2,3,4,5,9,6,8]=>[2,2,1,1,1,1,1]
[9,1,2,3,4,5,8,6,7]=>[3,1,1,1,1,1,1]
[7,1,2,3,4,5,8,9,6]=>[2,2,1,1,1,1,1]
[6,1,2,3,4,9,5,7,8]=>[2,2,1,1,1,1,1]
[6,1,2,3,4,8,5,9,7]=>[2,2,2,1,1,1]
[9,1,2,3,4,7,5,6,8]=>[3,1,1,1,1,1,1]
[9,1,2,3,4,8,5,6,7]=>[3,1,1,1,1,1,1]
[8,1,2,3,4,7,5,9,6]=>[3,2,1,1,1,1]
[6,1,2,3,4,7,9,5,8]=>[2,2,1,1,1,1,1]
[6,1,2,3,4,9,8,5,7]=>[3,2,1,1,1,1]
[9,1,2,3,4,7,8,5,6]=>[3,1,1,1,1,1,1]
[6,1,2,3,4,7,8,9,5]=>[2,2,1,1,1,1,1]
[5,1,2,3,8,4,6,9,7]=>[2,2,2,1,1,1]
[8,1,2,3,9,4,5,6,7]=>[2,2,1,1,1,1,1]
[5,1,2,3,9,8,4,6,7]=>[3,2,1,1,1,1]
[9,1,2,3,6,8,4,5,7]=>[3,1,1,1,1,1,1]
[5,1,2,3,6,9,8,4,7]=>[3,2,1,1,1,1]
[5,1,2,3,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[4,1,2,8,3,5,6,9,7]=>[2,2,2,1,1,1]
[4,1,2,9,3,5,8,6,7]=>[3,2,1,1,1,1]
[4,1,2,9,3,8,5,6,7]=>[3,2,1,1,1,1]
[9,1,2,8,3,4,5,6,7]=>[3,1,1,1,1,1,1]
[7,1,2,8,3,4,5,9,6]=>[2,2,2,1,1,1]
[4,1,2,5,9,3,6,7,8]=>[2,2,1,1,1,1,1]
[4,1,2,8,9,3,5,6,7]=>[2,2,1,1,1,1,1]
[8,1,2,5,9,3,4,6,7]=>[3,1,1,1,1,1,1]
[8,1,2,9,6,3,4,5,7]=>[3,2,1,1,1,1]
[4,1,2,5,9,8,3,6,7]=>[3,2,1,1,1,1]
[9,1,2,8,6,7,3,4,5]=>[4,1,1,1,1,1]
[4,1,2,5,6,7,9,3,8]=>[2,2,1,1,1,1,1]
[4,1,2,9,6,7,8,3,5]=>[3,2,1,1,1,1]
[9,1,2,5,6,7,8,3,4]=>[3,1,1,1,1,1,1]
[4,1,2,5,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[3,1,9,2,4,5,6,7,8]=>[2,2,1,1,1,1,1]
[3,1,8,2,4,5,6,9,7]=>[2,2,2,1,1,1]
[3,1,9,2,4,5,8,6,7]=>[3,2,1,1,1,1]
[3,1,5,2,7,4,9,6,8]=>[2,2,2,2,1]
[8,1,4,2,3,5,6,9,7]=>[3,2,1,1,1,1]
[9,1,4,2,3,5,8,6,7]=>[3,2,1,1,1,1]
[6,1,4,2,3,7,8,9,5]=>[3,2,1,1,1,1]
[9,1,8,2,3,4,5,6,7]=>[3,1,1,1,1,1,1]
[8,1,7,2,3,4,5,9,6]=>[3,2,1,1,1,1]
[3,1,4,9,2,5,6,7,8]=>[2,2,1,1,1,1,1]
[3,1,4,9,2,5,8,6,7]=>[3,2,1,1,1,1]
[3,1,9,8,2,4,5,6,7]=>[3,2,1,1,1,1]
[9,1,4,5,2,3,6,7,8]=>[3,1,1,1,1,1,1]
[7,1,4,5,2,3,8,9,6]=>[3,2,1,1,1,1]
[7,1,4,9,2,3,5,6,8]=>[3,1,1,1,1,1,1]
[9,1,4,8,2,3,5,6,7]=>[3,1,1,1,1,1,1]
[9,1,6,5,2,3,4,7,8]=>[4,1,1,1,1,1]
[7,1,9,6,2,3,4,5,8]=>[3,2,1,1,1,1]
[9,1,8,6,2,3,4,5,7]=>[4,1,1,1,1,1]
[7,1,8,9,2,3,4,5,6]=>[2,2,1,1,1,1,1]
[3,1,4,8,9,2,5,6,7]=>[2,2,1,1,1,1,1]
[3,1,8,9,7,2,4,5,6]=>[3,2,1,1,1,1]
[8,1,4,5,6,2,3,9,7]=>[3,2,1,1,1,1]
[8,1,4,9,7,2,3,5,6]=>[3,2,1,1,1,1]
[8,1,9,5,6,2,3,4,7]=>[3,2,1,1,1,1]
[8,1,9,7,6,2,3,4,5]=>[4,2,1,1,1]
[7,1,4,5,6,2,8,9,3]=>[3,2,1,1,1,1]
[3,1,4,5,6,9,2,7,8]=>[2,2,1,1,1,1,1]
[3,1,4,5,6,8,2,9,7]=>[2,2,2,1,1,1]
[3,1,4,9,8,7,2,5,6]=>[4,2,1,1,1]
[3,1,9,8,6,7,2,4,5]=>[4,2,1,1,1]
[9,1,4,5,6,7,2,3,8]=>[3,1,1,1,1,1,1]
[9,1,4,8,6,7,2,3,5]=>[4,1,1,1,1,1]
[9,1,8,5,6,7,2,3,4]=>[4,1,1,1,1,1]
[8,1,4,5,6,7,2,9,3]=>[3,2,1,1,1,1]
[3,1,4,5,6,7,9,2,8]=>[2,2,1,1,1,1,1]
[3,1,4,9,6,7,8,2,5]=>[3,2,1,1,1,1]
[3,1,9,5,6,7,8,2,4]=>[3,2,1,1,1,1]
[9,1,4,5,6,7,8,2,3]=>[3,1,1,1,1,1,1]
[3,1,4,5,6,7,8,9,2]=>[2,2,1,1,1,1,1]
[2,9,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[2,8,1,3,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[2,7,1,3,4,5,9,6,8]=>[2,2,1,1,1,1,1]
[2,9,1,3,4,5,8,6,7]=>[3,1,1,1,1,1,1]
[2,7,1,3,4,5,8,9,6]=>[2,2,1,1,1,1,1]
[2,6,1,3,4,9,5,7,8]=>[2,2,1,1,1,1,1]
[2,9,1,3,4,8,5,6,7]=>[3,1,1,1,1,1,1]
[2,8,1,3,9,4,5,6,7]=>[2,2,1,1,1,1,1]
[2,9,1,3,8,7,4,5,6]=>[4,1,1,1,1,1]
[2,9,1,3,6,7,8,4,5]=>[3,1,1,1,1,1,1]
[2,5,1,3,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[2,4,1,6,3,8,5,9,7]=>[2,2,2,2,1]
[2,9,1,8,3,4,5,6,7]=>[3,1,1,1,1,1,1]
[2,7,1,6,3,4,8,9,5]=>[3,2,1,1,1,1]
[2,6,1,5,3,7,8,9,4]=>[3,2,1,1,1,1]
[2,4,1,5,9,3,6,7,8]=>[2,2,1,1,1,1,1]
[2,4,1,8,9,3,5,6,7]=>[2,2,1,1,1,1,1]
[2,8,1,9,7,3,4,5,6]=>[3,2,1,1,1,1]
[2,9,1,8,6,7,3,4,5]=>[4,1,1,1,1,1]
[2,4,1,5,6,7,9,3,8]=>[2,2,1,1,1,1,1]
[2,4,1,5,6,9,8,3,7]=>[3,2,1,1,1,1]
[2,9,1,5,6,7,8,3,4]=>[3,1,1,1,1,1,1]
[2,4,1,5,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[9,3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[8,3,1,2,4,5,6,9,7]=>[3,2,1,1,1,1]
[9,3,1,2,4,5,8,6,7]=>[3,2,1,1,1,1]
[6,3,1,2,4,7,8,9,5]=>[3,2,1,1,1,1]
[9,3,1,2,6,7,8,4,5]=>[3,2,1,1,1,1]
[5,3,1,2,6,7,8,9,4]=>[3,2,1,1,1,1]
[9,4,1,2,3,5,6,7,8]=>[3,1,1,1,1,1,1]
[7,4,1,2,3,5,8,9,6]=>[3,2,1,1,1,1]
[6,4,1,2,3,7,8,9,5]=>[3,2,1,1,1,1]
[5,9,1,2,3,4,6,7,8]=>[2,1,1,1,1,1,1,1]
[5,8,1,2,3,4,6,9,7]=>[2,2,1,1,1,1,1]
[5,7,1,2,3,4,8,9,6]=>[2,2,1,1,1,1,1]
[9,6,1,2,3,4,5,7,8]=>[3,1,1,1,1,1,1]
[8,6,1,2,3,4,5,9,7]=>[3,2,1,1,1,1]
[9,7,1,2,3,4,5,6,8]=>[3,1,1,1,1,1,1]
[8,9,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1]
[8,7,1,2,3,4,5,9,6]=>[3,2,1,1,1,1]
[7,6,1,2,3,4,9,5,8]=>[3,2,1,1,1,1]
[9,6,1,2,3,4,8,5,7]=>[3,2,1,1,1,1]
[9,7,1,2,3,4,8,5,6]=>[3,2,1,1,1,1]
[7,6,1,2,3,4,8,9,5]=>[3,2,1,1,1,1]
[5,6,1,2,3,9,4,7,8]=>[2,2,1,1,1,1,1]
[5,9,1,2,3,8,4,6,7]=>[3,1,1,1,1,1,1]
[9,6,1,2,3,7,4,5,8]=>[3,2,1,1,1,1]
[9,8,1,2,3,7,4,5,6]=>[4,1,1,1,1,1]
[8,6,1,2,3,7,4,9,5]=>[3,2,2,1,1]
[5,6,1,2,3,7,9,4,8]=>[2,2,1,1,1,1,1]
[9,6,1,2,3,7,8,4,5]=>[3,2,1,1,1,1]
[5,6,1,2,3,7,8,9,4]=>[2,2,1,1,1,1,1]
[5,4,1,2,9,3,6,7,8]=>[3,2,1,1,1,1]
[8,4,1,2,9,3,5,6,7]=>[3,2,1,1,1,1]
[5,9,1,2,6,3,4,7,8]=>[3,1,1,1,1,1,1]
[9,7,1,2,6,3,8,4,5]=>[4,2,1,1,1]
[5,4,1,2,6,9,3,7,8]=>[3,2,1,1,1,1]
[9,8,1,2,6,7,3,4,5]=>[4,1,1,1,1,1]
[5,4,1,2,6,7,9,3,8]=>[3,2,1,1,1,1]
[5,4,1,2,6,7,8,9,3]=>[3,2,1,1,1,1]
[4,3,1,9,2,5,6,7,8]=>[3,2,1,1,1,1]
[9,3,1,8,2,4,5,6,7]=>[3,2,1,1,1,1]
[9,4,1,5,2,3,6,7,8]=>[3,2,1,1,1,1]
[9,4,1,8,2,3,5,6,7]=>[3,2,1,1,1,1]
[6,9,1,5,2,3,4,7,8]=>[3,1,1,1,1,1,1]
[9,7,1,6,2,3,4,5,8]=>[4,1,1,1,1,1]
[8,7,1,9,2,3,4,5,6]=>[3,2,1,1,1,1]
[8,7,1,6,2,3,4,9,5]=>[4,2,1,1,1]
[9,8,1,6,2,7,3,4,5]=>[4,2,1,1,1]
[4,3,1,5,9,2,6,7,8]=>[3,2,1,1,1,1]
[9,8,1,7,6,2,3,4,5]=>[5,1,1,1,1]
[4,3,1,5,6,8,2,9,7]=>[3,2,2,1,1]
[4,3,1,5,9,8,2,6,7]=>[3,3,1,1,1]
[4,3,1,5,8,7,2,9,6]=>[3,3,2,1]
[8,9,1,5,6,7,2,3,4]=>[3,1,1,1,1,1,1]
[4,3,1,5,6,7,9,2,8]=>[3,2,1,1,1,1]
[4,3,1,5,6,9,8,2,7]=>[3,3,1,1,1]
[9,3,1,5,6,7,8,2,4]=>[3,2,1,1,1,1]
[9,4,1,5,6,7,8,2,3]=>[3,2,1,1,1,1]
[4,3,1,5,6,7,8,9,2]=>[3,2,1,1,1,1]
[2,3,9,1,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[2,3,8,1,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[2,3,9,1,4,5,8,6,7]=>[3,1,1,1,1,1,1]
[2,3,9,1,4,7,8,5,6]=>[3,1,1,1,1,1,1]
[2,3,9,1,8,7,4,5,6]=>[4,1,1,1,1,1]
[2,3,8,1,6,7,4,9,5]=>[3,2,1,1,1,1]
[2,3,5,1,6,7,9,4,8]=>[2,2,1,1,1,1,1]
[2,3,9,1,6,7,8,4,5]=>[3,1,1,1,1,1,1]
[2,3,5,1,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[2,9,4,1,3,5,6,7,8]=>[3,1,1,1,1,1,1]
[2,6,4,1,3,7,8,9,5]=>[3,2,1,1,1,1]
[2,9,5,1,3,4,6,7,8]=>[3,1,1,1,1,1,1]
[2,6,9,1,3,4,5,7,8]=>[2,1,1,1,1,1,1,1]
[2,9,7,1,3,4,5,6,8]=>[3,1,1,1,1,1,1]
[2,9,8,1,3,4,5,6,7]=>[3,1,1,1,1,1,1]
[2,6,7,1,3,4,8,9,5]=>[2,2,1,1,1,1,1]
[2,9,4,1,6,3,5,7,8]=>[3,2,1,1,1,1]
[2,8,4,1,9,3,5,6,7]=>[3,2,1,1,1,1]
[2,9,4,1,6,3,8,5,7]=>[3,2,2,1,1]
[2,9,8,1,7,3,4,5,6]=>[4,1,1,1,1,1]
[2,9,5,1,6,7,8,3,4]=>[3,2,1,1,1,1]
[9,3,4,1,2,5,6,7,8]=>[3,1,1,1,1,1,1]
[6,3,4,1,2,7,8,9,5]=>[3,2,1,1,1,1]
[9,3,7,1,2,4,5,6,8]=>[3,1,1,1,1,1,1]
[9,3,8,1,2,4,5,6,7]=>[3,1,1,1,1,1,1]
[9,5,4,1,2,3,6,7,8]=>[4,1,1,1,1,1]
[8,5,4,1,2,3,6,9,7]=>[4,2,1,1,1]
[6,9,4,1,2,3,5,7,8]=>[3,1,1,1,1,1,1]
[6,8,4,1,2,3,5,9,7]=>[3,2,1,1,1,1]
[9,7,4,1,2,3,5,6,8]=>[4,1,1,1,1,1]
[9,8,4,1,2,3,5,6,7]=>[4,1,1,1,1,1]
[6,9,5,1,2,3,4,7,8]=>[3,1,1,1,1,1,1]
[6,8,5,1,2,3,4,9,7]=>[3,2,1,1,1,1]
[8,7,5,1,2,3,4,9,6]=>[4,2,1,1,1]
[6,7,9,1,2,3,4,5,8]=>[2,1,1,1,1,1,1,1]
[6,9,8,1,2,3,4,5,7]=>[3,1,1,1,1,1,1]
[9,7,8,1,2,3,4,5,6]=>[3,1,1,1,1,1,1]
[6,7,8,1,2,3,4,9,5]=>[2,2,1,1,1,1,1]
[6,5,4,1,2,8,3,9,7]=>[4,2,2,1]
[7,8,9,1,6,2,3,4,5]=>[3,1,1,1,1,1,1]
[7,8,5,1,6,2,3,9,4]=>[3,2,2,1,1]
[5,3,4,1,6,8,2,9,7]=>[3,2,2,1,1]
[9,3,4,1,8,7,2,5,6]=>[4,2,1,1,1]
[8,3,4,1,6,7,2,9,5]=>[3,2,2,1,1]
[8,5,4,1,6,7,2,9,3]=>[4,2,2,1]
[5,3,4,1,9,7,8,2,6]=>[3,3,1,1,1]
[9,3,5,1,6,7,8,2,4]=>[3,2,1,1,1,1]
[9,5,4,1,6,7,8,2,3]=>[4,2,1,1,1]
[5,3,4,1,6,7,8,9,2]=>[3,2,1,1,1,1]
[2,3,4,9,1,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,9,1,5,8,6,7]=>[3,1,1,1,1,1,1]
[2,3,4,9,1,7,8,5,6]=>[3,1,1,1,1,1,1]
[2,3,4,6,1,7,8,9,5]=>[2,2,1,1,1,1,1]
[2,3,9,5,1,4,6,7,8]=>[3,1,1,1,1,1,1]
[2,3,9,6,1,4,5,7,8]=>[3,1,1,1,1,1,1]
[2,3,7,9,1,4,5,6,8]=>[2,1,1,1,1,1,1,1]
[2,3,9,8,1,4,5,6,7]=>[3,1,1,1,1,1,1]
[2,3,9,5,1,7,4,6,8]=>[3,2,1,1,1,1]
[2,3,9,6,1,7,8,4,5]=>[3,2,1,1,1,1]
[2,9,4,5,1,3,6,7,8]=>[3,1,1,1,1,1,1]
[2,7,4,5,1,3,8,9,6]=>[3,2,1,1,1,1]
[2,9,8,6,1,3,4,5,7]=>[4,1,1,1,1,1]
[2,7,8,9,1,3,4,5,6]=>[2,1,1,1,1,1,1,1]
[2,8,9,6,1,7,3,4,5]=>[3,2,1,1,1,1]
[2,9,6,5,1,7,8,3,4]=>[4,2,1,1,1]
[7,3,4,5,1,2,8,9,6]=>[3,2,1,1,1,1]
[9,3,4,8,1,2,5,6,7]=>[3,1,1,1,1,1,1]
[7,3,4,8,1,2,5,9,6]=>[3,2,1,1,1,1]
[7,3,8,9,1,2,4,5,6]=>[3,1,1,1,1,1,1]
[9,8,4,5,1,2,3,6,7]=>[4,1,1,1,1,1]
[7,8,4,6,1,2,3,9,5]=>[3,2,1,1,1,1]
[9,8,6,5,1,2,3,4,7]=>[5,1,1,1,1]
[7,8,9,6,1,2,3,4,5]=>[3,1,1,1,1,1,1]
[7,8,6,5,1,2,3,9,4]=>[4,2,1,1,1]
[8,3,9,6,1,7,2,4,5]=>[3,2,2,1,1]
[8,3,6,5,1,7,2,9,4]=>[4,2,2,1]
[8,6,4,5,1,7,2,9,3]=>[4,2,2,1]
[6,3,4,5,1,7,9,2,8]=>[3,2,1,1,1,1]
[6,3,4,5,1,9,8,2,7]=>[3,3,1,1,1]
[9,3,4,6,1,7,8,2,5]=>[3,2,1,1,1,1]
[6,3,4,5,1,7,8,9,2]=>[3,2,1,1,1,1]
[2,3,4,5,9,1,6,7,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,8,1,6,9,7]=>[2,2,1,1,1,1,1]
[2,3,4,5,9,1,8,6,7]=>[3,1,1,1,1,1,1]
[2,3,4,5,7,1,8,9,6]=>[2,2,1,1,1,1,1]
[2,3,4,9,6,1,5,7,8]=>[3,1,1,1,1,1,1]
[2,3,4,9,7,1,5,6,8]=>[3,1,1,1,1,1,1]
[2,3,4,9,6,1,8,5,7]=>[3,2,1,1,1,1]
[2,3,4,9,7,1,8,5,6]=>[3,2,1,1,1,1]
[2,3,9,5,6,1,4,7,8]=>[3,1,1,1,1,1,1]
[2,3,8,5,6,1,4,9,7]=>[3,2,1,1,1,1]
[2,3,9,5,6,1,8,4,7]=>[3,2,1,1,1,1]
[2,8,4,5,6,1,3,9,7]=>[3,2,1,1,1,1]
[2,8,9,5,7,1,3,4,6]=>[3,1,1,1,1,1,1]
[2,8,9,7,6,1,3,4,5]=>[4,1,1,1,1,1]
[2,9,7,5,6,1,8,3,4]=>[4,2,1,1,1]
[8,3,4,5,6,1,2,9,7]=>[3,2,1,1,1,1]
[8,3,4,7,6,1,2,9,5]=>[4,2,1,1,1]
[8,3,9,7,6,1,2,4,5]=>[4,2,1,1,1]
[8,3,7,5,6,1,2,9,4]=>[4,2,1,1,1]
[9,7,4,5,6,1,2,3,8]=>[4,1,1,1,1,1]
[8,9,4,5,6,1,2,3,7]=>[3,1,1,1,1,1,1]
[8,9,7,5,6,1,2,3,4]=>[4,1,1,1,1,1]
[8,7,4,5,6,1,2,9,3]=>[4,2,1,1,1]
[7,3,4,5,6,1,9,2,8]=>[3,2,1,1,1,1]
[9,3,4,5,6,1,8,2,7]=>[3,2,1,1,1,1]
[9,3,7,5,6,1,8,2,4]=>[4,2,1,1,1]
[7,3,4,5,6,1,8,9,2]=>[3,2,1,1,1,1]
[2,3,4,5,6,9,1,7,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,8,1,9,7]=>[2,2,1,1,1,1,1]
[2,3,4,5,9,7,1,6,8]=>[3,1,1,1,1,1,1]
[2,3,4,5,9,8,1,6,7]=>[3,1,1,1,1,1,1]
[2,3,4,9,6,7,1,5,8]=>[3,1,1,1,1,1,1]
[2,3,9,5,6,7,1,4,8]=>[3,1,1,1,1,1,1]
[2,3,9,5,6,8,1,4,7]=>[3,1,1,1,1,1,1]
[2,9,4,5,6,7,1,3,8]=>[3,1,1,1,1,1,1]
[2,9,4,5,6,8,1,3,7]=>[3,1,1,1,1,1,1]
[2,9,4,5,8,7,1,3,6]=>[4,1,1,1,1,1]
[2,9,4,8,6,7,1,3,5]=>[4,1,1,1,1,1]
[2,9,8,5,6,7,1,3,4]=>[4,1,1,1,1,1]
[2,8,4,5,6,7,1,9,3]=>[3,2,1,1,1,1]
[9,3,4,5,6,7,1,2,8]=>[3,1,1,1,1,1,1]
[9,3,4,5,6,8,1,2,7]=>[3,1,1,1,1,1,1]
[9,8,4,5,6,7,1,2,3]=>[4,1,1,1,1,1]
[8,3,4,5,6,7,1,9,2]=>[3,2,1,1,1,1]
[2,3,4,5,6,7,9,1,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,9,8,1,7]=>[3,1,1,1,1,1,1]
[2,3,4,5,9,7,8,1,6]=>[3,1,1,1,1,1,1]
[2,3,4,9,6,7,8,1,5]=>[3,1,1,1,1,1,1]
[2,3,9,5,6,7,8,1,4]=>[3,1,1,1,1,1,1]
[2,9,4,5,6,7,8,1,3]=>[3,1,1,1,1,1,1]
[9,3,4,5,6,7,8,1,2]=>[3,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,1]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,1,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,8,9,1,7]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,7,8,9,1,6]=>[2,1,1,1,1,1,1,1]
[2,3,4,6,7,8,9,1,5]=>[2,1,1,1,1,1,1,1]
[2,3,5,6,7,8,9,1,4]=>[2,1,1,1,1,1,1,1]
[2,4,5,6,7,8,9,1,3]=>[2,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,1,2]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,1,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,1,9,7,8]=>[2,2,1,1,1,1,1]
[2,3,4,5,1,8,9,6,7]=>[2,2,1,1,1,1,1]
[2,3,4,1,7,8,9,5,6]=>[2,2,1,1,1,1,1]
[2,3,1,6,7,8,9,4,5]=>[2,2,1,1,1,1,1]
[2,1,5,6,7,8,9,3,4]=>[2,2,1,1,1,1,1]
[1,4,5,6,7,8,9,2,3]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,9,8]=>[2,1,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,8,2,3,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[7,1,2,3,4,5,6,9,8]=>[2,2,1,1,1,1,1]
[2,1,9,3,4,5,6,7,8]=>[2,2,1,1,1,1,1]
[2,8,1,3,4,5,6,7,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,9,7]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,9,6]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,9,5]=>[2,1,1,1,1,1,1,1]
[1,2,3,5,6,7,8,9,4]=>[2,1,1,1,1,1,1,1]
[1,2,4,5,6,7,8,9,3]=>[2,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,2]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,9,8,7]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,8,7,9,6]=>[3,1,1,1,1,1,1]
[1,2,3,4,7,6,8,9,5]=>[3,1,1,1,1,1,1]
[1,2,3,6,5,7,8,9,4]=>[3,1,1,1,1,1,1]
[1,2,5,4,6,7,8,9,3]=>[3,1,1,1,1,1,1]
[1,4,3,5,6,7,8,9,2]=>[3,1,1,1,1,1,1]
[3,2,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[9,8,7,6,5,4,3,2,1]=>[9]
[8,9,7,6,5,4,3,2,1]=>[8,1]
[8,7,9,6,5,4,3,2,1]=>[8,1]
[8,7,6,9,5,4,3,2,1]=>[8,1]
[8,7,6,5,9,4,3,2,1]=>[8,1]
[8,7,6,5,4,9,3,2,1]=>[8,1]
[8,7,6,5,4,3,9,2,1]=>[8,1]
[8,7,6,5,4,3,2,9,1]=>[8,1]
[8,7,6,5,4,3,2,1,9]=>[8,1]
[7,8,9,6,5,4,3,2,1]=>[7,1,1]
[8,6,7,9,5,4,3,2,1]=>[7,1,1]
[8,7,5,6,9,4,3,2,1]=>[7,1,1]
[8,7,6,4,5,9,3,2,1]=>[7,1,1]
[8,7,6,5,3,4,9,2,1]=>[7,1,1]
[8,7,6,5,4,2,3,9,1]=>[7,1,1]
[8,7,6,5,4,3,1,2,9]=>[7,1,1]
[1,9,8,7,6,5,4,3,2]=>[8,1]
[8,7,6,4,5,3,2,1,9]=>[7,1,1]
[1,9,8,7,5,6,4,3,2]=>[7,1,1]
[8,7,5,4,6,3,2,1,9]=>[7,1,1]
[8,7,4,6,5,3,2,1,9]=>[7,1,1]
[1,9,8,6,5,7,4,3,2]=>[7,1,1]
[1,9,8,5,7,6,4,3,2]=>[7,1,1]
[9,2,1,3,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[9,2,3,1,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[4,2,3,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[3,4,2,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,6,9,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,8,6,9,7]=>[2,2,1,1,1,1,1]
[1,2,3,4,7,5,8,9,6]=>[2,2,1,1,1,1,1]
[1,2,3,6,4,7,8,9,5]=>[2,2,1,1,1,1,1]
[1,2,5,3,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[1,4,2,5,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[9,8,1,2,3,4,5,6,7]=>[3,1,1,1,1,1,1]
[7,8,9,1,2,3,4,5,6]=>[2,1,1,1,1,1,1,1]
[9,8,7,1,2,3,4,5,6]=>[4,1,1,1,1,1]
[6,7,8,9,1,2,3,4,5]=>[2,1,1,1,1,1,1,1]
[9,6,7,8,1,2,3,4,5]=>[3,1,1,1,1,1,1]
[8,9,6,7,1,2,3,4,5]=>[3,1,1,1,1,1,1]
[9,8,6,7,1,2,3,4,5]=>[4,1,1,1,1,1]
[9,8,7,6,1,2,3,4,5]=>[5,1,1,1,1]
[9,5,6,7,8,1,2,3,4]=>[3,1,1,1,1,1,1]
[8,9,5,6,7,1,2,3,4]=>[3,1,1,1,1,1,1]
[9,8,5,6,7,1,2,3,4]=>[4,1,1,1,1,1]
[9,7,8,5,6,1,2,3,4]=>[4,1,1,1,1,1]
[9,8,7,5,6,1,2,3,4]=>[5,1,1,1,1]
[9,8,7,6,5,1,2,3,4]=>[6,1,1,1]
[7,8,9,4,5,6,1,2,3]=>[3,1,1,1,1,1,1]
[9,7,8,4,5,6,1,2,3]=>[4,1,1,1,1,1]
[9,8,7,4,5,6,1,2,3]=>[5,1,1,1,1]
[8,9,6,7,4,5,1,2,3]=>[4,1,1,1,1,1]
[9,8,6,7,4,5,1,2,3]=>[5,1,1,1,1]
[9,8,7,6,4,5,1,2,3]=>[6,1,1,1]
[9,8,7,6,5,4,1,2,3]=>[7,1,1]
[9,7,8,5,6,3,4,1,2]=>[5,1,1,1,1]
[9,8,7,5,6,3,4,1,2]=>[6,1,1,1]
[9,8,7,6,5,3,4,1,2]=>[7,1,1]
[9,8,7,6,5,4,3,1,2]=>[8,1]
[7,8,6,5,4,3,2,1,9]=>[7,1,1]
[7,6,8,5,4,3,2,1,9]=>[7,1,1]
[8,1,2,3,4,5,6,7,9]=>[2,1,1,1,1,1,1,1]
[1,9,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[7,8,1,2,3,4,5,6,9]=>[2,1,1,1,1,1,1,1]
[1,8,9,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1]
[7,1,8,2,3,4,5,6,9]=>[2,2,1,1,1,1,1]
[6,8,1,2,3,4,5,7,9]=>[2,1,1,1,1,1,1,1]
[1,8,2,9,3,4,5,6,7]=>[2,2,1,1,1,1,1]
[1,7,9,2,3,4,5,6,8]=>[2,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,9]=>[2,2,2,2,1]
[2,4,1,3,6,5,8,7,9]=>[2,2,2,1,1,1]
[2,4,1,6,3,5,8,7,9]=>[2,2,2,1,1,1]
[2,4,1,6,3,8,5,7,9]=>[2,2,2,1,1,1]
[2,4,1,6,3,7,5,9,8]=>[2,2,2,2,1]
[2,4,1,5,3,7,6,9,8]=>[2,2,2,2,1]
[2,3,1,5,4,7,6,9,8]=>[2,2,2,2,1]
[1,3,2,5,4,7,6,9,8]=>[2,2,2,2,1]
[2,4,6,1,3,5,8,7,9]=>[2,2,1,1,1,1,1]
[2,4,1,6,8,3,5,7,9]=>[2,2,1,1,1,1,1]
[2,4,1,6,3,8,9,5,7]=>[2,2,2,1,1,1]
[2,4,1,6,3,7,5,8,9]=>[2,2,2,1,1,1]
[2,4,1,5,3,8,6,9,7]=>[2,2,2,2,1]
[2,3,1,6,4,7,5,9,8]=>[2,2,2,2,1]
[1,4,2,5,3,7,6,9,8]=>[2,2,2,2,1]
[7,1,2,3,4,5,6,8,9]=>[2,1,1,1,1,1,1,1]
[3,4,1,2,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[3,2,1,4,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[4,5,6,1,2,3,7,8,9]=>[2,1,1,1,1,1,1,1]
[4,2,5,1,3,6,7,8,9]=>[3,1,1,1,1,1,1]
[4,3,2,1,5,6,7,8,9]=>[4,1,1,1,1,1]
[5,6,7,8,1,2,3,4,9]=>[2,1,1,1,1,1,1,1]
[5,2,6,7,1,3,4,8,9]=>[3,1,1,1,1,1,1]
[5,6,3,4,1,2,7,8,9]=>[3,1,1,1,1,1,1]
[5,3,2,6,1,4,7,8,9]=>[4,1,1,1,1,1]
[5,4,3,2,1,6,7,8,9]=>[5,1,1,1,1]
[6,2,7,8,9,1,3,4,5]=>[3,1,1,1,1,1,1]
[6,7,3,4,8,1,2,5,9]=>[3,1,1,1,1,1,1]
[6,3,2,7,8,1,4,5,9]=>[4,1,1,1,1,1]
[6,4,7,2,5,1,3,8,9]=>[4,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9]=>[5,1,1,1,1]
[6,5,4,3,2,1,7,8,9]=>[6,1,1,1]
[7,4,8,2,5,9,1,3,6]=>[4,1,1,1,1,1]
[7,4,3,2,8,9,1,5,6]=>[5,1,1,1,1]
[7,8,5,6,3,4,1,2,9]=>[4,1,1,1,1,1]
[7,5,3,8,2,6,1,4,9]=>[5,1,1,1,1]
[7,5,4,3,2,8,1,6,9]=>[6,1,1,1]
[7,6,5,4,3,2,1,8,9]=>[7,1,1]
[8,6,9,4,7,2,5,1,3]=>[5,1,1,1,1]
[8,6,4,3,9,2,7,1,5]=>[6,1,1,1]
[8,6,5,4,3,2,9,1,7]=>[7,1,1]
[2,3,1,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,1,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,1,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,1,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,4,3,1,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[2,3,4,5,6,8,7,1,9]=>[3,1,1,1,1,1,1]
[2,3,4,5,6,7,9,8,1]=>[3,1,1,1,1,1,1]
[3,4,1,5,6,7,8,9,2]=>[2,2,1,1,1,1,1]
[3,4,5,1,6,7,8,9,2]=>[2,2,1,1,1,1,1]
[3,4,5,6,1,7,8,9,2]=>[2,2,1,1,1,1,1]
[3,4,5,6,7,1,8,9,2]=>[2,2,1,1,1,1,1]
[3,4,5,6,7,8,1,9,2]=>[2,2,1,1,1,1,1]
[3,1,2,5,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[3,4,1,2,6,7,8,9,5]=>[2,2,1,1,1,1,1]
[3,4,5,1,2,7,8,9,6]=>[2,2,1,1,1,1,1]
[3,4,5,6,1,2,8,9,7]=>[2,2,1,1,1,1,1]
[3,4,5,6,7,1,2,9,8]=>[2,2,1,1,1,1,1]
[3,4,5,6,7,8,1,2,9]=>[2,1,1,1,1,1,1,1]
[8,7,6,5,4,3,1,9,2]=>[7,2]
[7,9,6,5,4,3,2,1,8]=>[7,1,1]
[7,9,6,5,4,3,2,8,1]=>[7,1,1]
[8,9,6,5,4,3,2,1,7]=>[7,1,1]
[8,7,6,5,4,3,9,1,2]=>[7,1,1]
[9,7,6,5,4,3,1,8,2]=>[7,2]
[7,9,8,6,5,4,3,2,1]=>[8,1]
[6,9,8,7,5,4,3,2,1]=>[8,1]
[5,9,8,7,6,4,3,2,1]=>[8,1]
[4,9,8,7,6,5,3,2,1]=>[8,1]
[3,9,8,7,6,5,4,2,1]=>[8,1]
[2,9,8,7,6,5,4,3,1]=>[8,1]
[1,9,8,7,6,5,4,2,3]=>[7,1,1]
[1,2,3,4,5,9,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,9,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,9,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,9,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,9,7,6,8]=>[3,1,1,1,1,1,1]
[1,2,3,4,9,6,5,7,8]=>[3,1,1,1,1,1,1]
[1,2,3,9,5,4,6,7,8]=>[3,1,1,1,1,1,1]
[1,2,9,4,3,5,6,7,8]=>[3,1,1,1,1,1,1]
[1,9,3,2,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[6,7,8,9,5,4,3,2,1]=>[6,1,1,1]
[5,6,7,8,9,4,3,2,1]=>[5,1,1,1,1]
[4,5,6,7,8,9,3,2,1]=>[4,1,1,1,1,1]
[3,2,5,4,7,6,9,8,1]=>[3,2,2,2]
[3,4,5,6,7,8,9,2,1]=>[3,1,1,1,1,1,1]
[3,1,2,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,4,1,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,5,1,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,6,1,5,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,7,1,6,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,8,1,7,9]=>[2,1,1,1,1,1,1,1]
[7,6,5,4,3,2,9,1,8]=>[7,1,1]
[6,5,4,3,9,2,8,1,7]=>[6,1,1,1]
[6,5,4,3,2,8,1,7,9]=>[6,1,1,1]
[5,4,9,3,8,2,7,1,6]=>[5,1,1,1,1]
[5,4,3,8,2,7,1,6,9]=>[5,1,1,1,1]
[5,4,3,2,7,9,1,6,8]=>[5,1,1,1,1]
[5,4,3,2,7,1,6,8,9]=>[5,1,1,1,1]
[4,8,3,7,2,6,1,5,9]=>[4,1,1,1,1,1]
[4,3,7,2,6,9,1,5,8]=>[4,1,1,1,1,1]
[4,3,7,2,6,1,5,8,9]=>[4,1,1,1,1,1]
[4,3,2,6,8,1,5,7,9]=>[4,1,1,1,1,1]
[4,3,2,6,1,5,7,8,9]=>[4,1,1,1,1,1]
[3,6,9,2,5,8,1,4,7]=>[3,1,1,1,1,1,1]
[3,6,2,5,8,1,4,7,9]=>[3,1,1,1,1,1,1]
[3,6,2,5,1,4,7,8,9]=>[3,1,1,1,1,1,1]
[3,2,5,7,9,1,4,6,8]=>[3,1,1,1,1,1,1]
[3,2,5,7,1,4,6,8,9]=>[3,1,1,1,1,1,1]
[3,2,5,1,4,6,7,8,9]=>[3,1,1,1,1,1,1]
[2,4,6,8,1,3,5,7,9]=>[2,1,1,1,1,1,1,1]
[2,4,6,1,3,5,7,8,9]=>[2,1,1,1,1,1,1,1]
[8,7,6,4,3,2,1,9,5]=>[7,2]
[8,6,5,4,3,2,1,9,7]=>[7,2]
[7,6,5,4,3,2,1,9,8]=>[7,2]
[9,6,5,4,3,2,1,8,7]=>[7,2]
[2,9,8,7,6,5,4,1,3]=>[7,1,1]
[2,4,5,6,7,8,1,3,9]=>[2,1,1,1,1,1,1,1]
[1,4,5,6,7,8,2,9,3]=>[2,2,1,1,1,1,1]
[9,7,8,5,6,3,1,4,2]=>[5,2,1,1]
[9,7,8,5,3,6,1,4,2]=>[5,2,1,1]
[9,7,5,8,3,6,1,4,2]=>[5,2,1,1]
[7,9,5,8,3,6,1,4,2]=>[5,1,1,1,1]
[8,9,5,7,3,6,1,4,2]=>[5,1,1,1,1]
[8,9,6,7,3,5,1,4,2]=>[5,1,1,1,1]
[8,9,6,7,4,5,1,3,2]=>[5,1,1,1,1]
[8,9,6,7,4,5,2,3,1]=>[5,1,1,1,1]
[9,7,8,5,3,1,6,4,2]=>[5,3,1]
[9,7,5,3,8,6,1,4,2]=>[5,3,1]
[7,5,9,8,3,6,1,4,2]=>[5,2,1,1]
[9,8,5,7,3,6,1,4,2]=>[6,1,1,1]
[7,9,6,8,3,5,1,4,2]=>[5,1,1,1,1]
[8,9,5,7,4,6,1,3,2]=>[5,1,1,1,1]
[8,9,6,7,3,5,2,4,1]=>[5,1,1,1,1]
[6,5,4,3,2,1,9,8,7]=>[6,3]
[5,4,3,2,1,9,8,7,6]=>[5,4]
[3,2,1,5,4,7,6,9,8]=>[3,2,2,2]
[2,1,4,3,5,6,7,8,9]=>[2,2,1,1,1,1,1]
[3,1,4,2,6,5,8,7,9]=>[2,2,2,2,1]
[3,1,5,2,6,4,8,7,9]=>[2,2,2,2,1]
[3,1,5,2,7,4,8,6,9]=>[2,2,2,2,1]
[3,1,5,2,7,4,6,9,8]=>[2,2,2,2,1]
[3,1,5,2,4,7,6,9,8]=>[2,2,2,2,1]
[3,1,2,5,4,7,6,9,8]=>[2,2,2,2,1]
[4,1,5,2,6,3,8,7,9]=>[2,2,2,2,1]
[3,1,6,2,7,4,8,5,9]=>[2,2,2,2,1]
[3,1,5,2,8,4,9,6,7]=>[2,2,2,2,1]
[3,1,5,2,7,4,6,8,9]=>[2,2,2,1,1,1]
[3,1,5,2,4,7,9,6,8]=>[2,2,2,1,1,1]
[3,1,2,5,7,4,6,9,8]=>[2,2,2,1,1,1]
[1,3,5,2,4,7,6,9,8]=>[2,2,2,1,1,1]
[4,5,6,7,8,9,1,2,3]=>[2,1,1,1,1,1,1,1]
[4,5,6,7,8,9,2,3,1]=>[3,1,1,1,1,1,1]
[5,6,7,8,9,1,2,3,4]=>[2,1,1,1,1,1,1,1]
[5,6,7,8,9,2,3,4,1]=>[3,1,1,1,1,1,1]
[5,6,7,8,9,3,4,1,2]=>[3,1,1,1,1,1,1]
[5,6,7,8,9,3,4,2,1]=>[4,1,1,1,1,1]
[6,7,8,9,2,3,4,5,1]=>[3,1,1,1,1,1,1]
[6,7,8,9,3,4,5,1,2]=>[3,1,1,1,1,1,1]
[6,7,8,9,3,4,5,2,1]=>[4,1,1,1,1,1]
[6,7,8,9,4,5,2,3,1]=>[4,1,1,1,1,1]
[6,7,8,9,4,5,3,2,1]=>[5,1,1,1,1]
[7,8,9,4,5,6,2,3,1]=>[4,1,1,1,1,1]
[7,8,9,4,5,6,3,2,1]=>[5,1,1,1,1]
[7,8,9,5,6,3,4,1,2]=>[4,1,1,1,1,1]
[7,8,9,5,6,3,4,2,1]=>[5,1,1,1,1]
[7,8,9,5,6,4,3,2,1]=>[6,1,1,1]
[8,9,6,7,4,5,3,2,1]=>[6,1,1,1]
[8,9,6,7,5,4,3,2,1]=>[7,1,1]
[9,8,7,6,5,4,2,1,3]=>[8,1]
[9,8,7,6,4,3,2,1,5]=>[8,1]
[9,8,6,5,4,3,2,1,7]=>[8,1]
[9,7,6,5,4,3,2,1,8]=>[8,1]
[9,8,7,6,5,4,1,3,2]=>[8,1]
[9,8,7,6,5,2,4,1,3]=>[7,1,1]
[9,8,7,3,6,2,5,1,4]=>[6,1,1,1]
[9,8,7,6,3,5,1,2,4]=>[6,1,1,1]
[9,4,8,3,7,2,6,1,5]=>[5,1,1,1,1]
[9,8,4,7,3,6,1,2,5]=>[5,1,1,1,1]
[9,8,7,2,4,6,1,3,5]=>[5,1,1,1,1]
[9,8,7,4,6,1,2,3,5]=>[5,1,1,1,1]
[5,9,4,8,3,7,1,2,6]=>[4,1,1,1,1,1]
[9,5,8,2,4,7,1,3,6]=>[4,1,1,1,1,1]
[9,5,8,4,7,1,2,3,6]=>[4,1,1,1,1,1]
[9,8,3,5,7,1,2,4,6]=>[4,1,1,1,1,1]
[9,8,5,7,1,2,3,4,6]=>[4,1,1,1,1,1]
[6,9,3,5,8,1,2,4,7]=>[3,1,1,1,1,1,1]
[6,9,5,8,1,2,3,4,7]=>[3,1,1,1,1,1,1]
[9,2,4,6,8,1,3,5,7]=>[3,1,1,1,1,1,1]
[9,4,6,8,1,2,3,5,7]=>[3,1,1,1,1,1,1]
[9,6,8,1,2,3,4,5,7]=>[3,1,1,1,1,1,1]
[3,5,7,9,1,2,4,6,8]=>[2,1,1,1,1,1,1,1]
[5,7,9,1,2,3,4,6,8]=>[2,1,1,1,1,1,1,1]
[7,9,1,2,3,4,5,6,8]=>[2,1,1,1,1,1,1,1]
[7,6,5,4,3,2,9,8,1]=>[7,2]
[9,6,5,4,3,2,8,1,7]=>[7,1,1]
[9,7,5,4,3,2,1,8,6]=>[7,2]
[7,6,5,4,3,9,2,8,1]=>[7,1,1]
[8,6,5,4,3,2,9,7,1]=>[7,2]
[7,6,5,8,4,3,2,1,9]=>[7,1,1]
[7,6,5,4,9,3,2,1,8]=>[7,1,1]
[7,6,5,4,3,8,2,1,9]=>[7,1,1]
[7,6,5,4,3,2,8,1,9]=>[7,1,1]
[6,9,8,5,4,3,2,1,7]=>[7,1,1]
[7,5,8,9,4,3,2,1,6]=>[6,1,1,1]
[7,6,4,8,9,3,2,1,5]=>[6,1,1,1]
[7,6,5,3,9,8,2,1,4]=>[6,2,1]
[7,6,5,4,2,8,9,1,3]=>[6,1,1,1]
[7,6,5,4,3,1,8,9,2]=>[6,2,1]
[6,5,8,7,4,3,2,1,9]=>[6,2,1]
[7,5,4,8,6,3,2,1,9]=>[6,2,1]
[5,9,8,7,4,3,2,1,6]=>[7,1,1]
[7,6,4,3,9,5,2,1,8]=>[6,2,1]
[7,4,8,9,6,3,2,1,5]=>[5,2,1,1]
[7,6,5,3,2,8,4,1,9]=>[6,2,1]
[7,6,3,8,9,5,2,1,4]=>[5,2,1,1]
[7,6,5,4,2,1,8,3,9]=>[6,2,1]
[7,6,5,2,9,8,4,1,3]=>[5,3,1]
[7,6,5,4,1,8,9,3,2]=>[6,2,1]
[2,3,4,5,6,8,9,7,1]=>[3,1,1,1,1,1,1]
[8,1,9,7,6,5,4,3,2]=>[7,2]
[8,9,1,7,6,5,4,3,2]=>[7,1,1]
[8,1,2,3,4,5,9,6,7]=>[2,2,1,1,1,1,1]
[8,1,2,3,4,9,5,6,7]=>[2,2,1,1,1,1,1]
[8,1,2,9,3,4,5,6,7]=>[2,2,1,1,1,1,1]
[8,1,9,2,3,4,5,6,7]=>[2,2,1,1,1,1,1]
[4,1,2,3,8,9,5,6,7]=>[2,2,1,1,1,1,1]
[2,1,8,9,3,4,5,6,7]=>[2,2,1,1,1,1,1]
[9,6,7,5,4,3,2,1,8]=>[7,1,1]
[8,2,1,7,6,5,4,3,9]=>[6,2,1]
[3,2,8,7,6,5,4,1,9]=>[6,2,1]
[8,3,1,7,6,5,4,9,2]=>[6,2,1]
[8,2,9,1,6,5,4,3,7]=>[5,2,1,1]
[4,2,8,7,6,5,9,1,3]=>[5,2,1,1]
[3,9,2,7,6,5,4,1,8]=>[6,1,1,1]
[8,4,1,7,6,5,9,3,2]=>[6,2,1]
[8,3,2,1,6,5,4,7,9]=>[4,3,1,1]
[8,2,9,7,1,5,4,3,6]=>[5,2,1,1]
[5,2,8,7,6,9,4,1,3]=>[5,2,1,1]
[4,3,2,7,6,5,8,1,9]=>[4,3,1,1]
[3,9,8,2,6,5,4,1,7]=>[6,1,1,1]
[8,7,6,5,4,2,1,3,9]=>[7,1,1]
[1,9,8,7,6,5,3,2,4]=>[7,1,1]
[2,1,9,8,7,6,5,4,3]=>[7,2]
[1,2,9,8,7,6,5,4,3]=>[7,1,1]
[3,2,1,9,8,7,6,5,4]=>[6,3]
[1,2,3,9,8,7,6,5,4]=>[6,1,1,1]
[4,3,2,1,9,8,7,6,5]=>[5,4]
[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1]
[1,2,3,4,5,9,8,7,6]=>[4,1,1,1,1,1]
[1,2,3,5,4,7,6,9,8]=>[2,2,2,1,1,1]
[1,2,3,4,5,7,6,9,8]=>[2,2,1,1,1,1,1]
[9,1,8,7,6,5,4,3,2]=>[8,1]
[7,1,9,8,6,5,4,3,2]=>[7,2]
[6,1,9,8,7,5,4,3,2]=>[7,2]
[5,1,9,8,7,6,4,3,2]=>[7,2]
[4,1,9,8,7,6,5,3,2]=>[7,2]
[3,1,9,8,7,6,5,4,2]=>[7,2]
[9,8,1,7,6,5,4,3,2]=>[8,1]
[8,7,9,1,6,5,4,3,2]=>[7,1,1]
[7,6,9,8,1,5,4,3,2]=>[6,2,1]
[6,5,9,8,7,1,4,3,2]=>[6,2,1]
[5,4,9,8,7,6,1,3,2]=>[6,2,1]
[4,3,9,8,7,6,5,1,2]=>[6,2,1]
[3,2,9,8,7,6,5,4,1]=>[7,2]
[9,1,2,3,4,5,6,8,7]=>[3,1,1,1,1,1,1]
[9,1,2,3,4,5,7,8,6]=>[3,1,1,1,1,1,1]
[2,3,4,5,6,9,7,8,1]=>[3,1,1,1,1,1,1]
[9,2,1,8,7,6,5,4,3]=>[7,2]
[7,9,6,8,5,4,3,2,1]=>[7,1,1]
[6,9,8,5,7,4,3,2,1]=>[7,1,1]
[5,9,8,7,4,6,3,2,1]=>[7,1,1]
[4,9,8,7,6,3,5,2,1]=>[7,1,1]
[3,9,8,7,6,5,2,4,1]=>[7,1,1]
[1,3,4,5,6,7,9,2,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,1,9,8]=>[2,2,1,1,1,1,1]
[2,1,4,5,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[3,1,4,5,6,7,8,2,9]=>[2,2,1,1,1,1,1]
[1,2,3,4,5,7,9,6,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,6,9,5,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,5,9,4,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,2,4,9,3,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,3,9,2,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[2,9,8,7,1,6,5,4,3]=>[7,1,1]
[1,6,7,8,9,2,3,4,5]=>[2,1,1,1,1,1,1,1]
[6,7,8,1,2,3,4,5,9]=>[2,1,1,1,1,1,1,1]
[1,7,8,9,2,3,4,5,6]=>[2,1,1,1,1,1,1,1]
[5,6,7,1,8,2,3,4,9]=>[2,2,1,1,1,1,1]
[4,6,7,8,1,2,3,5,9]=>[2,1,1,1,1,1,1,1]
[1,6,7,8,2,9,3,4,5]=>[2,2,1,1,1,1,1]
[1,5,7,8,9,2,3,4,6]=>[2,1,1,1,1,1,1,1]
[9,2,3,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[8,2,3,4,5,6,7,1,9]=>[3,1,1,1,1,1,1]
[7,2,3,4,5,6,1,8,9]=>[3,1,1,1,1,1,1]
[1,2,4,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,2,4,6,8,9,7,5,3]=>[4,1,1,1,1,1]
[1,2,4,5,3,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,4,1,3,6,8,5,7,9]=>[2,2,1,1,1,1,1]
[8,2,1,3,4,5,6,7,9]=>[3,1,1,1,1,1,1]
[3,2,4,5,6,7,8,1,9]=>[3,1,1,1,1,1,1]
[8,3,1,2,4,5,6,7,9]=>[3,1,1,1,1,1,1]
[8,2,3,1,4,5,6,7,9]=>[3,1,1,1,1,1,1]
[1,9,3,4,5,6,7,8,2]=>[3,1,1,1,1,1,1]
[1,9,8,4,5,6,7,3,2]=>[5,1,1,1,1]
[1,7,2,3,4,5,6,9,8]=>[2,2,1,1,1,1,1]
[1,3,4,5,6,7,9,8,2]=>[3,1,1,1,1,1,1]
[7,3,4,5,6,8,1,2,9]=>[3,1,1,1,1,1,1]
[2,3,4,5,7,6,8,1,9]=>[3,1,1,1,1,1,1]
[1,8,4,5,6,7,9,2,3]=>[3,1,1,1,1,1,1]
[1,3,4,5,6,8,7,9,2]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,9,7,8,6]=>[3,1,1,1,1,1,1]
[1,2,3,4,9,6,7,8,5]=>[3,1,1,1,1,1,1]
[1,2,3,9,5,6,7,8,4]=>[3,1,1,1,1,1,1]
[1,2,9,4,5,6,7,8,3]=>[3,1,1,1,1,1,1]
[1,2,3,4,9,7,6,8,5]=>[4,1,1,1,1,1]
[1,2,3,9,6,5,7,8,4]=>[4,1,1,1,1,1]
[1,2,9,5,4,6,7,8,3]=>[4,1,1,1,1,1]
[1,9,4,3,5,6,7,8,2]=>[4,1,1,1,1,1]
[9,3,2,4,5,6,7,8,1]=>[4,1,1,1,1,1]
[3,5,6,7,8,9,4,2,1]=>[4,1,1,1,1,1]
[1,2,3,5,7,4,6,9,8]=>[2,2,1,1,1,1,1]
[1,2,3,6,4,7,5,9,8]=>[2,2,2,1,1,1]
[1,2,3,4,6,8,5,7,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,7,5,8,6,9]=>[2,2,1,1,1,1,1]
[1,2,5,7,3,4,6,9,8]=>[2,2,1,1,1,1,1]
[1,2,4,5,7,3,6,9,8]=>[2,2,1,1,1,1,1]
[1,2,6,3,4,7,5,9,8]=>[2,2,2,1,1,1]
[1,2,5,6,3,7,4,9,8]=>[2,2,2,1,1,1]
[2,3,1,9,4,5,6,7,8]=>[2,2,1,1,1,1,1]
[4,9,1,2,3,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[3,9,1,2,4,5,6,7,8]=>[2,1,1,1,1,1,1,1]
[1,8,2,3,4,5,6,7,9]=>[2,1,1,1,1,1,1,1]
[9,8,7,5,6,4,3,2,1]=>[8,1]
[2,1,9,8,6,7,5,4,3]=>[6,2,1]
[9,8,7,5,4,6,3,2,1]=>[8,1]
[9,8,7,4,6,5,3,2,1]=>[8,1]
[2,1,9,8,6,5,7,4,3]=>[6,2,1]
[2,1,9,8,5,7,6,4,3]=>[6,2,1]
[1,8,7,6,5,4,3,2,9]=>[7,1,1]
[2,1,8,7,6,5,4,3,9]=>[6,2,1]
[4,5,6,7,8,1,2,9,3]=>[2,2,1,1,1,1,1]
[4,5,6,7,1,2,8,9,3]=>[2,2,1,1,1,1,1]
[4,5,6,1,2,7,8,9,3]=>[2,2,1,1,1,1,1]
[4,5,1,2,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[7,8,1,2,3,4,5,9,6]=>[2,2,1,1,1,1,1]
[2,8,9,1,3,4,5,6,7]=>[2,1,1,1,1,1,1,1]
[7,1,8,2,9,3,4,5,6]=>[2,2,2,1,1,1]
[6,1,7,2,8,3,9,4,5]=>[2,2,2,2,1]
[5,1,6,2,7,3,8,4,9]=>[2,2,2,2,1]
[7,1,8,2,3,9,4,5,6]=>[2,2,2,1,1,1]
[6,1,7,2,8,3,4,9,5]=>[2,2,2,2,1]
[5,1,6,2,7,3,9,4,8]=>[2,2,2,2,1]
[4,1,5,2,7,3,8,6,9]=>[2,2,2,2,1]
[2,1,3,4,5,6,8,9,7]=>[2,2,1,1,1,1,1]
[2,1,3,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]
[2,3,1,4,5,6,8,9,7]=>[2,2,1,1,1,1,1]
[1,3,2,4,5,6,8,9,7]=>[2,2,1,1,1,1,1]
[2,3,1,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]
[1,3,2,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]
[6,7,1,2,3,4,8,9,5]=>[2,2,1,1,1,1,1]
[9,7,6,5,4,3,1,2,8]=>[7,1,1]
[2,4,3,5,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,9,2,1,3]=>[3,1,1,1,1,1,1]
[5,6,7,8,9,2,1,3,4]=>[3,1,1,1,1,1,1]
[8,6,4,3,2,1,9,7,5]=>[6,3]
[7,5,3,1,8,6,4,2,9]=>[4,4,1]
[7,4,1,8,5,2,9,6,3]=>[3,3,3]
[5,3,1,6,4,2,7,8,9]=>[3,3,1,1,1]
[4,1,5,2,6,3,7,8,9]=>[2,2,2,1,1,1]
[3,1,4,2,5,6,7,8,9]=>[2,2,1,1,1,1,1]
[1,7,2,3,4,5,6,8,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,7,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,7,6,8,9]=>[2,1,1,1,1,1,1,1]
[9,2,3,4,5,6,7,1,8]=>[3,1,1,1,1,1,1]
[8,2,3,4,5,6,9,1,7]=>[3,1,1,1,1,1,1]
[8,2,3,9,5,6,7,1,4]=>[3,2,1,1,1,1]
[8,2,9,4,5,6,7,1,3]=>[3,2,1,1,1,1]
[8,9,3,4,5,6,7,1,2]=>[3,1,1,1,1,1,1]
[4,2,3,1,9,8,7,6,5]=>[5,3,1]
[3,2,1,9,8,6,7,5,4]=>[5,3,1]
[1,3,2,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,4,2,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[8,2,3,4,5,6,7,9,1]=>[3,1,1,1,1,1,1]
[7,2,3,4,5,6,9,8,1]=>[3,2,1,1,1,1]
[6,2,3,4,5,9,7,8,1]=>[3,2,1,1,1,1]
[5,2,3,4,9,6,7,8,1]=>[3,2,1,1,1,1]
[4,2,3,9,5,6,7,8,1]=>[3,2,1,1,1,1]
[3,2,9,4,5,6,7,8,1]=>[3,2,1,1,1,1]
[2,9,3,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[6,2,3,4,5,1,8,9,7]=>[3,2,1,1,1,1]
[5,2,3,4,1,7,9,8,6]=>[3,3,1,1,1]
[4,2,3,1,6,9,7,8,5]=>[3,3,1,1,1]
[3,2,1,5,9,6,7,8,4]=>[3,3,1,1,1]
[2,1,4,9,5,6,7,8,3]=>[3,2,1,1,1,1]
[1,3,9,4,5,6,7,8,2]=>[3,1,1,1,1,1,1]
[2,3,5,6,4,7,8,1,9]=>[3,1,1,1,1,1,1]
[1,3,4,6,7,5,8,9,2]=>[3,1,1,1,1,1,1]
[2,3,6,5,7,4,8,1,9]=>[4,1,1,1,1,1]
[2,3,5,6,7,1,8,4,9]=>[2,2,1,1,1,1,1]
[1,3,4,7,6,8,5,9,2]=>[4,1,1,1,1,1]
[1,3,4,6,7,8,2,9,5]=>[2,2,1,1,1,1,1]
[2,3,4,5,6,1,8,7,9]=>[2,2,1,1,1,1,1]
[2,3,4,5,1,7,6,8,9]=>[2,2,1,1,1,1,1]
[2,3,4,1,6,5,7,8,9]=>[2,2,1,1,1,1,1]
[2,3,1,5,4,6,7,8,9]=>[2,2,1,1,1,1,1]
[1,8,6,4,2,9,7,5,3]=>[4,4,1]
[8,6,4,2,1,7,5,3,9]=>[5,3,1]
[8,7,5,3,1,6,4,2,9]=>[5,3,1]
[1,9,7,5,3,2,8,6,4]=>[5,3,1]
[1,9,8,6,4,2,7,5,3]=>[5,3,1]
[6,3,5,1,2,4,7,8,9]=>[3,1,1,1,1,1,1]
[8,6,5,4,3,2,1,7,9]=>[7,1,1]
[9,4,3,2,5,6,7,8,1]=>[5,1,1,1,1]
[8,1,2,3,4,5,7,6,9]=>[3,1,1,1,1,1,1]
[1,9,2,3,4,5,6,8,7]=>[3,1,1,1,1,1,1]
[8,1,2,3,4,7,6,5,9]=>[4,1,1,1,1,1]
[8,1,2,3,4,6,5,7,9]=>[3,1,1,1,1,1,1]
[1,9,2,3,4,5,8,7,6]=>[4,1,1,1,1,1]
[1,9,2,3,4,5,7,6,8]=>[3,1,1,1,1,1,1]
[1,3,4,5,6,7,8,2,9]=>[2,1,1,1,1,1,1,1]
[2,1,4,5,6,7,9,3,8]=>[2,2,1,1,1,1,1]
[2,1,4,5,6,7,8,3,9]=>[2,2,1,1,1,1,1]
[1,3,9,8,7,6,5,4,2]=>[7,1,1]
[9,3,4,2,5,6,7,8,1]=>[4,1,1,1,1,1]
[1,2,3,4,5,7,9,8,6]=>[3,1,1,1,1,1,1]
[1,2,3,4,6,7,9,8,5]=>[3,1,1,1,1,1,1]
[1,2,3,4,6,8,9,7,5]=>[3,1,1,1,1,1,1]
[1,2,3,4,6,9,8,7,5]=>[4,1,1,1,1,1]
[1,2,3,5,6,7,9,8,4]=>[3,1,1,1,1,1,1]
[1,2,3,5,6,8,9,7,4]=>[3,1,1,1,1,1,1]
[1,2,3,5,6,9,8,7,4]=>[4,1,1,1,1,1]
[1,2,3,5,7,9,8,6,4]=>[4,1,1,1,1,1]
[1,2,3,5,9,8,7,6,4]=>[5,1,1,1,1]
[1,2,4,5,7,8,9,6,3]=>[3,1,1,1,1,1,1]
[1,2,4,5,7,9,8,6,3]=>[4,1,1,1,1,1]
[1,2,4,5,9,8,7,6,3]=>[5,1,1,1,1]
[1,2,4,6,9,8,7,5,3]=>[5,1,1,1,1]
[1,2,4,9,8,7,6,5,3]=>[6,1,1,1]
[1,3,5,7,9,8,6,4,2]=>[5,1,1,1,1]
[1,3,5,9,8,7,6,4,2]=>[6,1,1,1]
[6,5,1,2,3,7,8,9,4]=>[3,2,1,1,1,1]
[4,1,3,2,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[6,1,2,4,5,3,7,8,9]=>[3,1,1,1,1,1,1]
[5,4,1,2,3,6,7,8,9]=>[3,1,1,1,1,1,1]
[8,1,2,3,5,6,7,4,9]=>[3,1,1,1,1,1,1]
[4,1,6,3,5,2,7,8,9]=>[3,2,1,1,1,1]
[8,1,7,3,2,6,4,5,9]=>[4,2,1,1,1]
[5,7,1,6,2,4,3,8,9]=>[4,1,1,1,1,1]
[7,3,4,6,1,2,5,8,9]=>[3,1,1,1,1,1,1]
[6,1,2,9,4,5,7,8,3]=>[3,2,1,1,1,1]
[4,1,6,3,8,5,7,2,9]=>[3,2,2,1,1]
[6,8,5,1,7,2,3,4,9]=>[3,2,1,1,1,1]
[8,3,4,5,7,1,2,6,9]=>[3,1,1,1,1,1,1]
[5,7,1,9,2,8,4,6,3]=>[4,2,1,1,1]
[7,9,4,6,1,8,2,3,5]=>[3,2,1,1,1,1]
[3,4,1,6,2,5,8,7,9]=>[2,2,2,1,1,1]
[3,4,1,2,6,5,8,7,9]=>[2,2,2,1,1,1]
[3,5,1,6,2,4,8,7,9]=>[2,2,2,1,1,1]
[2,5,1,6,3,4,8,7,9]=>[2,2,2,1,1,1]
[3,5,1,2,6,4,8,7,9]=>[2,2,2,1,1,1]
[2,5,1,3,6,4,8,7,9]=>[2,2,2,1,1,1]
[8,6,4,2,1,3,5,7,9]=>[5,1,1,1,1]
[8,6,2,1,4,3,5,7,9]=>[4,2,1,1,1]
[8,4,2,1,6,3,5,7,9]=>[4,2,1,1,1]
[6,4,2,1,8,3,5,7,9]=>[4,2,1,1,1]
[8,6,4,2,9,1,3,5,7]=>[5,1,1,1,1]
[9,6,4,2,7,1,3,5,8]=>[5,1,1,1,1]
[9,7,4,2,5,1,3,6,8]=>[5,1,1,1,1]
[9,7,5,2,3,1,4,6,8]=>[5,1,1,1,1]
[9,7,5,3,1,2,4,6,8]=>[5,1,1,1,1]
[8,2,1,4,3,6,5,7,9]=>[3,2,2,1,1]
[4,2,1,6,3,5,8,7,9]=>[3,2,2,1,1]
[6,4,2,1,8,3,5,9,7]=>[4,2,2,1]
[6,4,2,7,1,3,5,8,9]=>[4,1,1,1,1,1]
[8,9,4,2,5,1,3,6,7]=>[4,1,1,1,1,1]
[9,6,7,2,3,1,4,5,8]=>[4,1,1,1,1,1]
[9,7,4,5,1,2,3,6,8]=>[4,1,1,1,1,1]
[1,2,9,3,4,5,6,8,7]=>[3,1,1,1,1,1,1]
[1,2,3,8,4,5,9,6,7]=>[2,2,1,1,1,1,1]
[1,2,3,4,9,5,6,8,7]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,9,6,8,7]=>[3,1,1,1,1,1,1]
[7,1,2,3,4,8,5,9,6]=>[2,2,2,1,1,1]
[6,9,1,2,3,4,8,5,7]=>[3,1,1,1,1,1,1]
[5,1,9,2,3,4,8,6,7]=>[3,2,1,1,1,1]
[4,1,2,3,5,8,6,9,7]=>[2,2,2,1,1,1]
[3,1,2,4,9,5,8,6,7]=>[3,2,1,1,1,1]
[2,1,3,4,5,9,6,8,7]=>[3,2,1,1,1,1]
[1,7,2,3,4,5,9,8,6]=>[3,2,1,1,1,1]
[1,6,2,3,4,5,9,8,7]=>[3,2,1,1,1,1]
[6,1,2,3,7,4,8,9,5]=>[2,2,2,1,1,1]
[1,2,3,8,5,4,6,9,7]=>[3,2,1,1,1,1]
[5,9,1,2,6,3,4,8,7]=>[3,2,1,1,1,1]
[1,4,2,3,5,6,9,8,7]=>[3,2,1,1,1,1]
[4,1,9,5,2,3,6,8,7]=>[3,2,2,1,1]
[1,3,2,4,5,6,9,8,7]=>[3,2,1,1,1,1]
[3,4,1,2,5,6,8,9,7]=>[2,2,1,1,1,1,1]
[2,3,1,4,9,5,6,8,7]=>[3,2,1,1,1,1]
[8,1,2,3,4,6,9,5,7]=>[3,1,1,1,1,1,1]
[8,1,2,4,6,9,3,5,7]=>[3,1,1,1,1,1,1]
[6,1,2,3,4,5,9,8,7]=>[3,2,1,1,1,1]
[5,1,2,3,4,8,6,9,7]=>[2,2,2,1,1,1]
[4,1,2,3,9,6,8,5,7]=>[3,2,1,1,1,1]
[3,1,2,8,4,6,9,5,7]=>[3,2,1,1,1,1]
[2,1,9,4,6,8,3,5,7]=>[3,2,1,1,1,1]
[1,8,2,4,6,9,3,5,7]=>[3,1,1,1,1,1,1]
[4,3,5,6,7,8,9,1,2]=>[3,1,1,1,1,1,1]
[6,7,8,5,4,3,2,1,9]=>[6,1,1,1]
[6,5,7,8,4,3,2,1,9]=>[6,1,1,1]
[6,5,4,7,8,3,2,1,9]=>[6,1,1,1]
[6,5,4,3,7,8,2,1,9]=>[6,1,1,1]
[6,5,4,3,2,7,8,1,9]=>[6,1,1,1]
[7,8,9,5,4,3,2,1,6]=>[6,1,1,1]
[6,7,8,9,4,3,2,1,5]=>[5,1,1,1,1]
[6,5,7,8,9,3,2,1,4]=>[5,1,1,1,1]
[6,5,4,7,8,9,2,1,3]=>[5,1,1,1,1]
[6,5,4,3,7,8,9,1,2]=>[5,1,1,1,1]
[6,5,4,3,2,7,8,9,1]=>[6,1,1,1]
[8,7,6,5,3,2,1,4,9]=>[7,1,1]
[8,7,6,4,3,2,1,5,9]=>[7,1,1]
[8,7,5,4,3,2,1,6,9]=>[7,1,1]
[8,7,6,5,4,1,2,3,9]=>[6,1,1,1]
[8,7,6,5,2,3,1,4,9]=>[6,1,1,1]
[8,7,6,3,4,2,1,5,9]=>[6,1,1,1]
[8,7,4,5,3,2,1,6,9]=>[6,1,1,1]
[8,5,6,4,3,2,1,7,9]=>[6,1,1,1]
[6,7,5,4,3,2,1,8,9]=>[6,1,1,1]
[6,8,7,9,5,4,3,2,1]=>[7,1,1]
[5,8,7,6,9,4,3,2,1]=>[7,1,1]
[4,8,7,6,5,9,3,2,1]=>[7,1,1]
[3,8,7,6,5,4,9,2,1]=>[7,1,1]
[2,8,7,6,5,4,3,9,1]=>[7,1,1]
[1,9,2,4,5,6,7,8,3]=>[3,1,1,1,1,1,1]
[9,1,3,4,5,6,7,8,2]=>[3,1,1,1,1,1,1]
[1,8,3,4,5,6,9,2,7]=>[3,1,1,1,1,1,1]
[8,2,3,4,5,1,9,7,6]=>[3,3,1,1,1]
[8,1,9,4,5,6,7,3,2]=>[4,2,1,1,1]
[7,9,3,4,5,6,1,8,2]=>[3,2,1,1,1,1]
[1,2,8,4,5,6,9,3,7]=>[3,1,1,1,1,1,1]
[7,8,3,4,5,2,9,1,6]=>[4,1,1,1,1,1]
[8,2,3,4,1,6,9,7,5]=>[3,3,1,1,1]
[8,1,3,9,5,6,7,4,2]=>[4,2,1,1,1]
[7,8,9,4,5,6,3,1,2]=>[4,1,1,1,1,1]
[6,9,3,4,5,1,7,8,2]=>[3,2,1,1,1,1]
[4,1,5,6,7,8,9,2,3]=>[2,2,1,1,1,1,1]
[2,3,4,5,8,9,1,6,7]=>[2,1,1,1,1,1,1,1]
[9,8,7,6,5,4,2,3,1]=>[8,1]
[2,3,9,8,7,6,5,4,1]=>[7,1,1]
[9,1,3,2,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[9,8,7,1,6,5,4,3,2]=>[8,1]
[9,8,7,6,1,5,4,3,2]=>[8,1]
[9,8,7,6,5,1,4,3,2]=>[8,1]
[3,5,2,4,7,6,9,8,1]=>[3,2,2,1,1]
[2,4,3,6,5,8,7,1,9]=>[3,2,2,1,1]
[3,5,1,2,4,7,6,9,8]=>[2,2,2,1,1,1]
[3,4,5,6,7,8,2,9,1]=>[3,1,1,1,1,1,1]
[8,7,6,4,5,3,2,9,1]=>[7,1,1]
[2,9,8,7,5,6,4,3,1]=>[7,1,1]
[8,6,9,7,5,4,3,2,1]=>[7,2]
[5,6,4,7,3,8,2,9,1]=>[5,1,1,1,1]
[5,6,4,7,3,9,2,8,1]=>[5,1,1,1,1]
[5,4,6,3,7,2,8,1,9]=>[5,1,1,1,1]
[1,8,3,4,5,6,7,9,2]=>[3,1,1,1,1,1,1]
[7,2,3,4,5,6,1,9,8]=>[3,2,1,1,1,1]
[2,1,9,4,5,6,7,8,3]=>[3,2,1,1,1,1]
[2,8,3,4,5,6,7,1,9]=>[3,1,1,1,1,1,1]
[2,9,1,8,7,6,5,4,3]=>[7,1,1]
[2,9,8,1,7,6,5,4,3]=>[7,1,1]
[6,1,2,3,4,5,7,8,9]=>[2,1,1,1,1,1,1,1]
[5,1,2,3,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[4,1,2,3,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[9,8,2,3,4,5,6,7,1]=>[4,1,1,1,1,1]
[8,9,2,3,4,5,6,7,1]=>[3,1,1,1,1,1,1]
[9,8,7,6,4,5,3,2,1]=>[8,1]
[5,6,7,8,9,1,4,3,2]=>[4,1,1,1,1,1]
[1,8,9,3,4,5,6,7,2]=>[3,1,1,1,1,1,1]
[3,4,5,6,1,8,9,2,7]=>[2,2,1,1,1,1,1]
[3,4,5,6,8,1,9,2,7]=>[2,2,1,1,1,1,1]
[3,4,5,6,8,9,1,2,7]=>[2,1,1,1,1,1,1,1]
[2,4,5,1,6,7,8,9,3]=>[2,2,1,1,1,1,1]
[2,3,4,1,6,7,8,9,5]=>[2,2,1,1,1,1,1]
[3,4,5,6,1,2,9,7,8]=>[2,2,1,1,1,1,1]
[3,4,5,6,8,1,2,7,9]=>[2,1,1,1,1,1,1,1]
[3,4,5,1,6,7,8,2,9]=>[2,2,1,1,1,1,1]
[5,6,1,7,8,9,2,3,4]=>[2,2,1,1,1,1,1]
[1,3,5,2,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[2,1,4,3,6,7,8,9,5]=>[2,2,2,1,1,1]
[2,3,1,5,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[9,7,8,5,4,3,2,1,6]=>[7,1,1]
[1,2,3,4,6,5,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,5,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,8,2,3,4,5,9,6,7]=>[2,2,1,1,1,1,1]
[1,3,4,5,6,8,9,2,7]=>[2,1,1,1,1,1,1,1]
[4,5,2,3,6,7,8,9,1]=>[3,1,1,1,1,1,1]
[4,3,2,5,6,7,8,9,1]=>[4,1,1,1,1,1]
[5,6,7,2,3,4,8,9,1]=>[3,1,1,1,1,1,1]
[5,3,6,2,4,7,8,9,1]=>[4,1,1,1,1,1]
[5,4,3,2,6,7,8,9,1]=>[5,1,1,1,1]
[6,3,7,8,2,4,5,9,1]=>[4,1,1,1,1,1]
[6,7,4,5,2,3,8,9,1]=>[4,1,1,1,1,1]
[6,4,3,7,2,5,8,9,1]=>[5,1,1,1,1]
[7,8,4,5,9,2,3,6,1]=>[4,1,1,1,1,1]
[7,4,3,8,9,2,5,6,1]=>[5,1,1,1,1]
[7,5,8,3,6,2,4,9,1]=>[5,1,1,1,1]
[7,5,4,3,8,2,6,9,1]=>[6,1,1,1]
[7,6,5,4,3,2,8,9,1]=>[7,1,1]
[8,6,4,9,3,7,2,5,1]=>[6,1,1,1]
[8,6,5,4,3,9,2,7,1]=>[7,1,1]
[2,4,1,5,3,6,7,8,9]=>[2,2,1,1,1,1,1]
[8,9,2,3,4,5,1,6,7]=>[3,1,1,1,1,1,1]
[6,5,7,8,9,1,2,3,4]=>[3,1,1,1,1,1,1]
[7,1,2,3,4,5,8,6,9]=>[2,2,1,1,1,1,1]
[6,1,2,3,4,7,5,8,9]=>[2,2,1,1,1,1,1]
[5,1,2,3,6,4,7,8,9]=>[2,2,1,1,1,1,1]
[4,1,2,5,3,6,7,8,9]=>[2,2,1,1,1,1,1]
[8,1,2,3,4,5,9,7,6]=>[3,2,1,1,1,1]
[8,1,2,3,4,9,6,7,5]=>[3,2,1,1,1,1]
[9,1,2,3,8,5,6,7,4]=>[4,1,1,1,1,1]
[9,1,2,3,4,6,7,8,5]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,8,9,6,7]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,7,9,5,8,6]=>[3,1,1,1,1,1,1]
[1,2,3,6,9,4,7,8,5]=>[3,1,1,1,1,1,1]
[1,2,5,9,3,6,7,8,4]=>[3,1,1,1,1,1,1]
[1,4,9,2,5,6,7,8,3]=>[3,1,1,1,1,1,1]
[3,9,1,4,5,6,7,8,2]=>[3,1,1,1,1,1,1]
[2,8,1,9,3,4,5,6,7]=>[2,2,1,1,1,1,1]
[1,4,2,3,6,5,8,7,9]=>[2,2,2,1,1,1]
[1,3,4,2,6,5,8,7,9]=>[2,2,2,1,1,1]
[2,3,1,4,6,5,8,7,9]=>[2,2,2,1,1,1]
[4,6,1,2,3,5,8,7,9]=>[2,2,1,1,1,1,1]
[3,4,5,1,6,2,8,7,9]=>[2,2,2,1,1,1]
[3,1,2,4,6,5,8,7,9]=>[2,2,2,1,1,1]
[2,1,3,4,5,6,9,7,8]=>[2,2,1,1,1,1,1]
[1,2,3,4,5,7,8,6,9]=>[2,1,1,1,1,1,1,1]
[7,1,9,3,4,5,6,2,8]=>[3,2,1,1,1,1]
[7,2,1,9,4,5,6,3,8]=>[3,3,1,1,1]
[6,9,7,3,4,5,1,2,8]=>[4,1,1,1,1,1]
[3,8,1,2,9,5,6,7,4]=>[3,2,1,1,1,1]
[8,7,9,1,2,3,4,5,6]=>[3,1,1,1,1,1,1]
[7,2,3,1,9,5,6,4,8]=>[3,3,1,1,1]
[6,1,2,7,4,5,9,3,8]=>[3,2,1,1,1,1]
[5,9,6,3,4,1,7,2,8]=>[4,2,1,1,1]
[3,8,1,4,2,9,6,7,5]=>[3,3,1,1,1]
[9,7,2,3,8,5,6,1,4]=>[4,2,1,1,1]
[7,6,8,9,1,2,3,4,5]=>[3,1,1,1,1,1,1]
[5,4,6,7,8,9,1,2,3]=>[3,1,1,1,1,1,1]
[1,4,3,2,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[2,3,4,5,6,9,8,7,1]=>[4,1,1,1,1,1]
[2,3,4,5,8,7,9,6,1]=>[4,1,1,1,1,1]
[2,3,6,5,7,8,9,4,1]=>[4,1,1,1,1,1]
[3,4,5,6,7,1,2,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,5,1,4,7,6,9,8]=>[2,2,2,1,1,1]
[3,4,1,5,2,7,6,9,8]=>[2,2,2,2,1]
[4,1,2,5,3,7,6,9,8]=>[2,2,2,2,1]
[4,2,6,8,1,3,5,7,9]=>[3,1,1,1,1,1,1]
[4,6,2,8,1,3,5,7,9]=>[3,1,1,1,1,1,1]
[4,6,8,2,1,3,5,7,9]=>[3,1,1,1,1,1,1]
[4,6,8,2,9,1,3,5,7]=>[3,1,1,1,1,1,1]
[4,6,2,7,9,1,3,5,8]=>[3,1,1,1,1,1,1]
[4,2,5,7,9,1,3,6,8]=>[3,1,1,1,1,1,1]
[2,3,5,7,9,1,4,6,8]=>[2,1,1,1,1,1,1,1]
[6,4,2,8,1,3,5,7,9]=>[4,1,1,1,1,1]
[8,4,6,2,1,3,5,7,9]=>[4,1,1,1,1,1]
[4,6,8,9,2,1,3,5,7]=>[3,1,1,1,1,1,1]
[4,6,2,7,1,3,5,8,9]=>[3,1,1,1,1,1,1]
[4,8,2,5,9,1,3,6,7]=>[3,1,1,1,1,1,1]
[6,2,3,7,9,1,4,5,8]=>[3,1,1,1,1,1,1]
[1,4,5,7,9,2,3,6,8]=>[2,1,1,1,1,1,1,1]
[8,6,4,9,7,5,3,2,1]=>[6,3]
[8,6,4,2,9,7,5,3,1]=>[5,4]
[6,2,7,3,8,4,9,5,1]=>[3,2,2,2]
[4,5,6,7,8,2,9,3,1]=>[3,2,1,1,1,1]
[4,5,6,7,1,8,2,9,3]=>[2,2,2,1,1,1]
[2,3,4,5,9,6,7,8,1]=>[3,1,1,1,1,1,1]
[2,3,4,9,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[2,3,9,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[2,3,4,5,9,7,6,8,1]=>[4,1,1,1,1,1]
[2,3,4,9,6,5,7,8,1]=>[4,1,1,1,1,1]
[2,3,9,5,4,6,7,8,1]=>[4,1,1,1,1,1]
[2,9,4,3,5,6,7,8,1]=>[4,1,1,1,1,1]
[2,3,4,5,9,7,8,6,1]=>[4,1,1,1,1,1]
[2,1,8,3,4,5,6,7,9]=>[2,2,1,1,1,1,1]
[1,9,6,2,3,4,5,8,7]=>[3,2,1,1,1,1]
[9,8,7,4,5,6,3,2,1]=>[7,1,1]
[1,5,6,7,8,9,2,3,4]=>[2,1,1,1,1,1,1,1]
[1,7,2,8,9,3,4,5,6]=>[2,2,1,1,1,1,1]
[1,6,2,7,8,9,3,4,5]=>[2,2,1,1,1,1,1]
[1,5,2,6,7,8,9,3,4]=>[2,2,1,1,1,1,1]
[3,4,2,1,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[4,3,1,2,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[4,5,2,1,3,6,7,8,9]=>[3,1,1,1,1,1,1]
[3,4,2,5,1,6,7,8,9]=>[3,1,1,1,1,1,1]
[5,3,1,2,4,6,7,8,9]=>[3,1,1,1,1,1,1]
[4,3,5,1,2,6,7,8,9]=>[3,1,1,1,1,1,1]
[5,4,3,1,2,6,7,8,9]=>[4,1,1,1,1,1]
[6,5,4,3,1,2,7,8,9]=>[5,1,1,1,1]
[8,5,4,3,9,1,2,6,7]=>[5,1,1,1,1]
[6,2,3,4,5,1,9,7,8]=>[3,2,1,1,1,1]
[2,3,4,5,9,7,1,8,6]=>[3,2,1,1,1,1]
[2,3,4,9,6,7,1,8,5]=>[3,2,1,1,1,1]
[2,3,9,5,6,1,7,8,4]=>[3,2,1,1,1,1]
[2,3,9,5,1,7,4,8,6]=>[3,2,2,1,1]
[2,1,3,4,5,6,8,7,9]=>[2,2,1,1,1,1,1]
[2,3,4,5,6,8,7,9,1]=>[3,1,1,1,1,1,1]
[8,6,5,4,3,2,7,9,1]=>[7,1,1]
[8,9,5,4,3,2,1,6,7]=>[6,1,1,1]
[7,6,5,4,3,8,9,1,2]=>[6,1,1,1]
[9,6,5,4,3,2,7,1,8]=>[7,1,1]
[9,2,3,4,5,6,1,7,8]=>[3,1,1,1,1,1,1]
[3,1,5,6,7,8,9,2,4]=>[2,2,1,1,1,1,1]
[2,1,3,5,6,7,8,9,4]=>[2,2,1,1,1,1,1]
[3,4,5,7,8,9,1,2,6]=>[2,1,1,1,1,1,1,1]
[3,5,6,7,8,9,1,2,4]=>[2,1,1,1,1,1,1,1]
[3,4,5,6,9,1,2,7,8]=>[2,1,1,1,1,1,1,1]
[3,4,5,6,1,2,7,8,9]=>[2,1,1,1,1,1,1,1]
[5,1,6,7,8,9,2,3,4]=>[2,2,1,1,1,1,1]
[1,2,4,3,5,7,8,9,6]=>[2,2,1,1,1,1,1]
[3,1,2,4,5,6,7,9,8]=>[2,2,1,1,1,1,1]
[9,8,7,1,5,6,4,3,2]=>[7,1,1]
[9,1,7,8,6,5,4,3,2]=>[7,1,1]
[3,2,4,1,6,5,8,7,9]=>[3,2,2,1,1]
[4,2,5,1,6,3,8,7,9]=>[3,2,2,1,1]
[4,2,6,1,7,3,8,5,9]=>[3,2,2,1,1]
[4,2,6,1,8,3,9,5,7]=>[3,2,2,1,1]
[4,2,6,1,7,3,5,9,8]=>[3,2,2,1,1]
[4,2,5,1,3,7,6,9,8]=>[3,2,2,1,1]
[3,2,5,4,6,1,8,7,9]=>[3,2,2,1,1]
[4,2,5,1,7,6,8,3,9]=>[3,3,1,1,1]
[4,2,6,1,7,3,9,8,5]=>[3,3,2,1]
[4,2,6,1,7,3,5,8,9]=>[3,2,1,1,1,1]
[4,2,5,1,3,8,9,6,7]=>[3,2,1,1,1,1]
[3,2,1,6,7,4,5,9,8]=>[3,2,2,1,1]
[1,4,5,2,3,7,6,9,8]=>[2,2,2,1,1,1]
[2,3,4,8,6,7,9,5,1]=>[4,1,1,1,1,1]
[2,3,8,5,6,7,9,1,4]=>[3,1,1,1,1,1,1]
[2,8,4,5,6,7,9,3,1]=>[4,1,1,1,1,1]
[8,3,4,5,6,7,9,2,1]=>[4,1,1,1,1,1]
[2,3,4,5,7,9,1,8,6]=>[3,1,1,1,1,1,1]
[2,3,4,6,7,1,9,5,8]=>[2,2,1,1,1,1,1]
[2,3,5,6,1,7,9,4,8]=>[2,2,1,1,1,1,1]
[2,4,5,1,6,7,9,8,3]=>[3,2,1,1,1,1]
[3,4,1,5,6,7,9,2,8]=>[2,2,1,1,1,1,1]
[3,2,4,5,6,7,9,1,8]=>[3,1,1,1,1,1,1]
[2,3,4,7,6,9,8,5,1]=>[4,2,1,1,1]
[2,3,4,6,9,1,7,8,5]=>[3,1,1,1,1,1,1]
[2,5,4,6,8,7,9,1,3]=>[3,2,1,1,1,1]
[2,3,5,7,1,6,9,4,8]=>[3,1,1,1,1,1,1]
[4,3,5,8,6,7,9,2,1]=>[4,2,1,1,1]
[2,4,6,1,5,7,9,3,8]=>[3,1,1,1,1,1,1]
[2,4,8,5,6,7,9,1,3]=>[3,1,1,1,1,1,1]
[3,5,1,4,6,7,9,8,2]=>[3,2,1,1,1,1]
[4,2,3,5,6,7,9,1,8]=>[3,1,1,1,1,1,1]
[1,4,2,6,3,7,5,9,8]=>[2,2,2,2,1]
[1,3,2,6,4,7,5,9,8]=>[2,2,2,2,1]
[2,1,6,3,7,4,8,5,9]=>[2,2,2,2,1]
[7,9,6,8,4,5,2,3,1]=>[5,1,1,1,1]
[7,9,5,8,4,6,2,3,1]=>[5,1,1,1,1]
[7,9,5,8,3,6,2,4,1]=>[5,1,1,1,1]
[7,9,5,8,3,6,4,1,2]=>[5,1,1,1,1]
[7,9,5,8,6,3,4,1,2]=>[5,1,1,1,1]
[7,9,8,5,6,3,4,1,2]=>[5,1,1,1,1]
[6,9,5,8,4,7,2,3,1]=>[5,1,1,1,1]
[7,9,4,8,3,6,2,5,1]=>[5,1,1,1,1]
[7,9,5,8,2,6,1,4,3]=>[5,1,1,1,1]
[7,9,5,8,3,6,4,2,1]=>[6,1,1,1]
[7,9,5,8,6,3,1,4,2]=>[5,2,1,1]
[7,9,8,5,3,6,4,1,2]=>[5,2,1,1]
[9,7,5,8,6,3,4,1,2]=>[5,2,1,1]
[6,5,4,3,2,7,1,8,9]=>[6,1,1,1]
[5,4,3,2,6,1,7,8,9]=>[5,1,1,1,1]
[4,3,2,5,1,6,7,8,9]=>[4,1,1,1,1,1]
[3,2,4,1,5,6,7,8,9]=>[3,1,1,1,1,1,1]
[1,3,5,2,7,4,6,9,8]=>[2,2,2,1,1,1]
[1,2,4,3,6,5,8,7,9]=>[2,2,2,1,1,1]
[1,3,5,7,2,4,6,9,8]=>[2,2,1,1,1,1,1]
[1,3,5,7,2,9,4,6,8]=>[2,2,1,1,1,1,1]
[5,6,2,1,3,7,4,8,9]=>[3,2,1,1,1,1]
[3,2,5,1,6,4,7,8,9]=>[3,2,1,1,1,1]
[6,7,2,1,8,3,4,9,5]=>[3,2,2,1,1]
[3,6,4,1,7,2,8,5,9]=>[3,2,2,1,1]
[3,6,7,2,1,4,8,5,9]=>[3,2,1,1,1,1]
[4,2,6,1,7,5,3,8,9]=>[3,3,1,1,1]
[4,3,2,6,1,7,5,8,9]=>[4,2,1,1,1]
[4,7,2,5,1,8,3,9,6]=>[3,2,2,1,1]
[4,3,7,8,2,1,5,9,6]=>[4,2,1,1,1]
[3,5,2,7,1,8,6,4,9]=>[3,3,1,1,1]
[5,4,3,2,7,1,8,6,9]=>[5,2,1,1]
[6,4,2,8,1,9,7,5,3]=>[4,4,1]
[4,3,6,2,8,1,9,7,5]=>[4,3,1,1]
[6,5,4,3,2,8,1,9,7]=>[6,2,1]
[3,1,2,9,4,5,6,7,8]=>[2,2,1,1,1,1,1]
[4,1,2,3,9,5,6,7,8]=>[2,2,1,1,1,1,1]
[5,1,2,3,4,9,6,7,8]=>[2,2,1,1,1,1,1]
[6,1,2,3,4,5,9,7,8]=>[2,2,1,1,1,1,1]
[3,4,1,2,9,5,6,7,8]=>[2,2,1,1,1,1,1]
[4,5,1,2,3,9,6,7,8]=>[2,2,1,1,1,1,1]
[5,6,1,2,3,4,9,7,8]=>[2,2,1,1,1,1,1]
[6,7,1,2,3,4,5,9,8]=>[2,2,1,1,1,1,1]
[9,7,5,3,1,8,6,4,2]=>[5,4]
[9,6,3,8,5,2,7,4,1]=>[5,2,2]
[8,5,2,9,6,3,7,4,1]=>[4,3,2]
[9,5,1,6,2,7,3,8,4]=>[3,2,2,2]
[9,5,1,8,4,7,3,6,2]=>[5,2,1,1]
[8,4,7,3,6,2,9,5,1]=>[5,2,1,1]
[7,3,8,4,6,2,9,5,1]=>[4,2,2,1]
[9,4,7,2,5,8,3,6,1]=>[5,1,1,1,1]
[9,4,6,1,8,3,5,7,2]=>[4,2,1,1,1]
[8,3,5,7,2,9,4,6,1]=>[4,2,1,1,1]
[7,2,8,3,9,4,5,6,1]=>[3,2,2,1,1]
[8,3,7,2,9,4,5,6,1]=>[4,2,1,1,1]
[5,8,3,7,2,9,4,6,1]=>[4,2,1,1,1]
[4,5,6,9,3,8,2,7,1]=>[4,1,1,1,1,1]
[4,5,6,8,2,9,3,7,1]=>[3,2,1,1,1,1]
[9,3,6,5,4,7,1,8,2]=>[5,2,1,1]
[8,2,9,3,6,5,4,7,1]=>[5,2,1,1]
[6,5,4,8,2,9,3,7,1]=>[5,2,1,1]
[5,6,4,8,2,9,3,7,1]=>[4,2,1,1,1]
[9,2,7,4,5,6,3,8,1]=>[5,1,1,1,1]
[7,4,5,6,3,9,2,8,1]=>[5,1,1,1,1]
[5,7,4,6,3,9,2,8,1]=>[5,1,1,1,1]
[4,2,5,6,7,8,9,1,3]=>[3,1,1,1,1,1,1]
[5,6,7,9,1,2,3,4,8]=>[2,1,1,1,1,1,1,1]
[4,5,6,7,9,1,2,3,8]=>[2,1,1,1,1,1,1,1]
[1,6,5,7,4,8,3,9,2]=>[5,1,1,1,1]
[5,4,6,3,8,2,7,1,9]=>[5,1,1,1,1]
[3,4,5,6,7,8,2,1,9]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,1,2,3,9]=>[2,1,1,1,1,1,1,1]
[4,3,1,2,6,5,8,7,9]=>[3,2,2,1,1]
[6,5,3,1,2,4,8,7,9]=>[4,2,1,1,1]
[8,7,5,3,1,2,4,6,9]=>[5,1,1,1,1]
[7,5,3,1,2,4,6,9,8]=>[4,2,1,1,1]
[5,3,1,2,4,7,6,9,8]=>[3,2,2,1,1]
[4,1,2,6,5,3,8,7,9]=>[3,2,2,1,1]
[6,3,1,2,4,8,7,5,9]=>[3,3,1,1,1]
[8,5,3,1,2,4,6,9,7]=>[4,2,1,1,1]
[7,5,3,1,2,4,6,8,9]=>[4,1,1,1,1,1]
[5,3,1,2,4,9,7,6,8]=>[3,3,1,1,1]
[3,1,2,7,5,4,6,9,8]=>[3,2,2,1,1]
[1,5,3,2,4,7,6,9,8]=>[3,2,2,1,1]
[2,9,8,7,6,5,1,4,3]=>[7,1,1]
[1,7,6,5,4,3,2,9,8]=>[6,2,1]
[1,4,5,6,7,8,9,3,2]=>[3,1,1,1,1,1,1]
[9,7,8,6,5,4,3,2,1]=>[8,1]
[3,2,5,6,7,8,9,1,4]=>[3,1,1,1,1,1,1]
[4,2,5,6,7,8,9,3,1]=>[3,2,1,1,1,1]
[1,3,4,5,6,7,2,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,7,8,9,1,5,6]=>[2,1,1,1,1,1,1,1]
[2,3,6,7,8,9,1,4,5]=>[2,1,1,1,1,1,1,1]
[2,5,6,7,8,9,1,3,4]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,1,9,6,7,8]=>[2,2,1,1,1,1,1]
[2,3,4,1,8,9,5,6,7]=>[2,2,1,1,1,1,1]
[2,3,1,7,8,9,4,5,6]=>[2,2,1,1,1,1,1]
[2,1,6,7,8,9,3,4,5]=>[2,2,1,1,1,1,1]
[4,1,2,3,6,5,8,7,9]=>[2,2,2,1,1,1]
[4,1,6,2,3,5,8,7,9]=>[2,2,2,1,1,1]
[2,3,1,9,8,7,6,5,4]=>[6,2,1]
[3,4,5,6,1,7,2,9,8]=>[2,2,2,1,1,1]
[1,4,5,9,6,7,2,8,3]=>[3,2,1,1,1,1]
[2,4,5,9,6,1,7,3,8]=>[3,2,1,1,1,1]
[3,4,5,7,6,1,9,2,8]=>[3,2,1,1,1,1]
[3,5,6,9,7,1,8,2,4]=>[3,2,1,1,1,1]
[1,4,8,5,6,2,7,9,3]=>[3,2,1,1,1,1]
[2,5,9,6,7,3,1,4,8]=>[4,1,1,1,1,1]
[4,1,5,2,7,6,3,9,8]=>[3,2,2,2]
[3,4,1,6,9,5,7,2,8]=>[3,2,1,1,1,1]
[6,7,9,8,1,3,4,2,5]=>[4,1,1,1,1,1]
[9,1,5,2,8,6,3,7,4]=>[4,2,2,1]
[1,7,4,5,2,6,8,9,3]=>[3,2,1,1,1,1]
[9,2,3,4,5,6,1,8,7]=>[3,2,1,1,1,1]
[9,2,3,4,5,1,7,8,6]=>[3,2,1,1,1,1]
[9,2,3,4,1,6,7,8,5]=>[3,2,1,1,1,1]
[9,2,3,1,5,6,7,8,4]=>[3,2,1,1,1,1]
[9,2,1,4,5,6,7,8,3]=>[3,2,1,1,1,1]
[5,2,3,4,1,9,6,8,7]=>[3,3,1,1,1]
[4,2,3,1,9,5,7,8,6]=>[3,3,1,1,1]
[3,2,1,9,4,6,7,8,5]=>[3,3,1,1,1]
[2,1,9,3,5,6,7,8,4]=>[3,2,1,1,1,1]
[6,8,9,1,2,3,4,5,7]=>[2,1,1,1,1,1,1,1]
[5,8,9,1,2,3,4,6,7]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,1,7,6,9,8]=>[2,2,2,1,1,1]
[2,3,4,1,6,5,8,7,9]=>[2,2,2,1,1,1]
[2,3,4,5,1,8,6,9,7]=>[2,2,2,1,1,1]
[2,3,4,1,7,5,8,6,9]=>[2,2,2,1,1,1]
[3,4,5,6,7,9,1,8,2]=>[3,1,1,1,1,1,1]
[3,4,5,6,7,9,2,8,1]=>[3,1,1,1,1,1,1]
[3,4,5,6,7,1,9,8,2]=>[3,2,1,1,1,1]
[5,3,4,2,1,9,8,7,6]=>[4,4,1]
[6,5,3,4,2,1,9,8,7]=>[5,3,1]
[7,6,4,5,3,2,1,9,8]=>[6,2,1]
[3,4,5,1,2,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,4,1,5,3,6,8,7,9]=>[2,2,2,1,1,1]
[2,4,1,7,3,8,5,6,9]=>[2,2,2,1,1,1]
[8,5,9,3,6,1,2,4,7]=>[4,1,1,1,1,1]
[9,7,1,5,8,3,6,2,4]=>[5,1,1,1,1]
[9,7,5,4,1,3,8,2,6]=>[6,1,1,1]
[9,6,5,4,3,2,1,7,8]=>[7,1,1]
[9,1,2,3,4,5,8,7,6]=>[4,1,1,1,1,1]
[9,1,2,3,4,8,6,7,5]=>[4,1,1,1,1,1]
[9,1,2,8,4,5,6,7,3]=>[4,1,1,1,1,1]
[9,1,8,3,4,5,6,7,2]=>[4,1,1,1,1,1]
[9,1,2,3,4,7,8,6,5]=>[4,1,1,1,1,1]
[9,1,2,3,6,8,5,7,4]=>[4,1,1,1,1,1]
[9,1,2,5,8,4,6,7,3]=>[4,1,1,1,1,1]
[9,1,4,8,3,5,6,7,2]=>[4,1,1,1,1,1]
[9,3,8,2,4,5,6,7,1]=>[4,1,1,1,1,1]
[3,9,2,1,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[3,4,5,6,8,9,1,7,2]=>[3,1,1,1,1,1,1]
[3,4,6,7,8,9,1,5,2]=>[3,1,1,1,1,1,1]
[3,5,6,7,8,9,1,4,2]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,9,1,3,2]=>[3,1,1,1,1,1,1]
[5,4,2,3,6,7,8,9,1]=>[4,1,1,1,1,1]
[6,5,4,2,3,7,8,9,1]=>[5,1,1,1,1]
[7,6,5,4,2,3,8,9,1]=>[6,1,1,1]
[4,6,7,8,9,1,2,3,5]=>[2,1,1,1,1,1,1,1]
[5,7,8,9,1,2,3,4,6]=>[2,1,1,1,1,1,1,1]
[7,5,1,3,2,6,4,8,9]=>[4,2,1,1,1]
[9,6,1,3,4,2,7,8,5]=>[4,2,1,1,1]
[8,3,6,1,4,2,7,5,9]=>[4,2,1,1,1]
[9,8,1,7,2,3,4,5,6]=>[4,1,1,1,1,1]
[9,3,4,7,1,5,2,8,6]=>[4,2,1,1,1]
[8,7,5,4,6,3,2,9,1]=>[7,1,1]
[8,7,4,6,5,3,2,9,1]=>[7,1,1]
[2,3,4,5,6,1,9,8,7]=>[3,2,1,1,1,1]
[2,3,4,5,1,9,8,7,6]=>[4,2,1,1,1]
[8,9,7,6,5,4,3,1,2]=>[7,1,1]
[8,6,7,5,4,3,2,1,9]=>[7,1,1]
[8,7,9,6,5,4,3,1,2]=>[7,1,1]
[9,7,8,6,5,4,3,1,2]=>[7,1,1]
[3,2,1,5,6,7,8,9,4]=>[3,2,1,1,1,1]
[3,2,6,1,4,7,8,9,5]=>[3,2,1,1,1,1]
[4,3,2,1,6,7,8,9,5]=>[4,2,1,1,1]
[3,2,7,8,1,4,5,9,6]=>[3,2,1,1,1,1]
[4,7,2,5,1,3,8,9,6]=>[3,2,1,1,1,1]
[4,3,2,7,1,5,8,9,6]=>[4,2,1,1,1]
[5,4,3,2,1,7,8,9,6]=>[5,2,1,1]
[4,3,2,8,9,1,5,6,7]=>[4,1,1,1,1,1]
[8,5,6,3,4,1,2,9,7]=>[4,2,1,1,1]
[5,3,8,2,6,1,4,9,7]=>[4,2,1,1,1]
[5,4,3,2,8,1,6,9,7]=>[5,2,1,1]
[6,5,4,3,2,1,8,9,7]=>[6,2,1]
[6,9,4,7,2,5,1,3,8]=>[4,1,1,1,1,1]
[6,4,3,9,2,7,1,5,8]=>[5,1,1,1,1]
[6,5,4,3,2,9,1,7,8]=>[6,1,1,1]
[2,3,4,9,6,7,8,5,1]=>[4,1,1,1,1,1]
[2,3,9,5,6,7,8,4,1]=>[4,1,1,1,1,1]
[2,9,4,5,6,7,8,3,1]=>[4,1,1,1,1,1]
[9,3,4,5,6,7,8,2,1]=>[4,1,1,1,1,1]
[2,3,4,1,9,7,8,6,5]=>[4,2,1,1,1]
[2,3,1,9,6,7,8,5,4]=>[4,2,1,1,1]
[2,1,9,5,6,7,8,4,3]=>[4,2,1,1,1]
[1,9,4,5,6,7,8,3,2]=>[4,1,1,1,1,1]
[5,6,4,7,3,9,1,8,2]=>[4,2,1,1,1]
[5,6,4,9,1,8,2,7,3]=>[4,2,1,1,1]
[5,9,1,8,2,7,3,6,4]=>[5,1,1,1,1]
[9,1,8,2,7,3,6,4,5]=>[5,1,1,1,1]
[5,4,9,1,8,2,7,3,6]=>[4,2,1,1,1]
[5,4,6,3,9,1,8,2,7]=>[4,2,1,1,1]
[5,4,6,3,7,2,9,1,8]=>[5,1,1,1,1]
[5,6,4,8,2,9,1,7,3]=>[4,2,1,1,1]
[5,7,3,9,1,8,2,6,4]=>[4,2,1,1,1]
[6,4,9,1,8,2,7,3,5]=>[4,2,1,1,1]
[4,5,9,1,8,2,7,3,6]=>[4,1,1,1,1,1]
[6,4,5,3,9,1,8,2,7]=>[4,2,1,1,1]
[5,4,7,3,6,2,9,1,8]=>[5,1,1,1,1]
[9,8,3,4,5,6,7,1,2]=>[4,1,1,1,1,1]
[9,8,2,3,4,5,6,1,7]=>[4,1,1,1,1,1]
[9,4,5,6,7,8,2,1,3]=>[4,1,1,1,1,1]
[9,3,4,5,6,7,2,1,8]=>[4,1,1,1,1,1]
[7,2,9,8,3,4,5,6,1]=>[4,2,1,1,1]
[9,8,2,3,4,5,1,6,7]=>[4,1,1,1,1,1]
[9,5,6,7,8,2,1,3,4]=>[4,1,1,1,1,1]
[8,3,9,4,5,6,7,2,1]=>[4,2,1,1,1]
[9,3,4,5,6,2,1,7,8]=>[4,1,1,1,1,1]
[1,6,2,7,3,8,4,9,5]=>[2,2,2,2,1]
[6,7,1,9,2,3,4,5,8]=>[2,2,1,1,1,1,1]
[6,1,8,9,2,3,4,5,7]=>[2,2,1,1,1,1,1]
[3,4,5,2,1,6,7,8,9]=>[3,1,1,1,1,1,1]
[3,4,5,8,9,1,2,6,7]=>[2,1,1,1,1,1,1,1]
[3,4,7,8,9,1,2,5,6]=>[2,1,1,1,1,1,1,1]
[3,6,7,8,9,1,2,4,5]=>[2,1,1,1,1,1,1,1]
[3,4,5,6,1,7,2,8,9]=>[2,2,1,1,1,1,1]
[3,4,5,1,6,2,7,8,9]=>[2,2,1,1,1,1,1]
[3,4,1,5,9,2,6,7,8]=>[2,2,1,1,1,1,1]
[1,3,7,8,9,2,4,5,6]=>[2,1,1,1,1,1,1,1]
[2,6,7,8,9,1,3,4,5]=>[2,1,1,1,1,1,1,1]
[4,3,5,2,6,1,7,8,9]=>[4,1,1,1,1,1]
[4,5,3,6,2,7,1,8,9]=>[4,1,1,1,1,1]
[1,3,5,7,2,8,4,9,6]=>[2,2,2,1,1,1]
[1,3,5,6,2,7,4,9,8]=>[2,2,2,1,1,1]
[1,3,4,5,2,7,6,9,8]=>[2,2,2,1,1,1]
[3,5,7,1,2,4,6,9,8]=>[2,2,1,1,1,1,1]
[3,5,7,8,1,9,2,4,6]=>[2,2,1,1,1,1,1]
[3,5,6,7,1,8,2,9,4]=>[2,2,2,1,1,1]
[7,1,2,3,4,9,6,8,5]=>[3,2,1,1,1,1]
[7,1,2,3,4,8,6,9,5]=>[3,2,1,1,1,1]
[8,1,2,3,9,5,6,7,4]=>[3,2,1,1,1,1]
[7,1,2,3,9,5,6,8,4]=>[3,2,1,1,1,1]
[7,1,2,3,8,5,6,9,4]=>[3,2,1,1,1,1]
[6,1,2,3,8,5,9,7,4]=>[3,2,2,1,1]
[6,1,2,3,7,5,8,9,4]=>[3,2,1,1,1,1]
[6,1,2,8,4,5,9,7,3]=>[3,2,2,1,1]
[6,1,2,7,4,5,8,9,3]=>[3,2,1,1,1,1]
[5,1,2,7,4,9,6,8,3]=>[3,2,2,1,1]
[5,1,2,7,4,8,6,9,3]=>[3,2,2,1,1]
[5,1,2,6,4,7,8,9,3]=>[3,2,1,1,1,1]
[4,1,6,3,8,5,9,7,2]=>[3,2,2,2]
[4,1,6,3,7,5,8,9,2]=>[3,2,2,1,1]
[4,1,5,3,6,7,8,9,2]=>[3,2,1,1,1,1]
[1,9,8,7,6,4,3,2,5]=>[7,1,1]
[1,9,8,7,5,4,3,2,6]=>[7,1,1]
[1,9,8,6,5,4,3,2,7]=>[7,1,1]
[1,9,7,6,5,4,3,2,8]=>[7,1,1]
[1,9,8,7,6,5,2,3,4]=>[6,1,1,1]
[1,9,8,7,6,3,4,2,5]=>[6,1,1,1]
[1,9,8,7,4,5,3,2,6]=>[6,1,1,1]
[1,9,8,5,6,4,3,2,7]=>[6,1,1,1]
[1,9,6,7,5,4,3,2,8]=>[6,1,1,1]
[1,7,8,6,5,4,3,2,9]=>[6,1,1,1]
[8,9,2,3,4,5,6,1,7]=>[3,1,1,1,1,1,1]
[7,8,9,2,3,4,5,1,6]=>[3,1,1,1,1,1,1]
[6,7,8,9,2,3,4,1,5]=>[3,1,1,1,1,1,1]
[5,6,7,8,9,2,3,1,4]=>[3,1,1,1,1,1,1]
[7,8,9,2,3,4,1,5,6]=>[3,1,1,1,1,1,1]
[6,7,8,9,2,3,1,4,5]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,1,9,2,3]=>[2,2,1,1,1,1,1]
[7,9,3,4,5,6,2,1,8]=>[4,1,1,1,1,1]
[3,9,2,1,5,6,7,8,4]=>[3,2,1,1,1,1]
[3,8,1,4,5,6,7,2,9]=>[3,1,1,1,1,1,1]
[6,9,3,4,5,2,7,1,8]=>[4,1,1,1,1,1]
[3,9,2,4,1,6,7,8,5]=>[3,2,1,1,1,1]
[3,8,9,1,5,6,7,4,2]=>[4,1,1,1,1,1]
[3,7,1,4,5,6,2,8,9]=>[3,1,1,1,1,1,1]
[2,8,7,6,5,4,3,1,9]=>[7,1,1]
[2,1,4,9,8,7,6,5,3]=>[6,2,1]
[2,9,8,7,6,1,5,4,3]=>[7,1,1]
[4,9,8,7,6,5,2,1,3]=>[7,1,1]
[5,9,8,7,6,2,1,4,3]=>[6,2,1]
[6,9,8,7,2,1,5,4,3]=>[6,2,1]
[7,9,8,2,1,6,5,4,3]=>[6,2,1]
[8,9,2,1,7,6,5,4,3]=>[6,2,1]
[7,8,1,9,2,3,4,5,6]=>[2,2,1,1,1,1,1]
[6,7,8,1,9,2,3,4,5]=>[2,2,1,1,1,1,1]
[5,6,7,8,1,9,2,3,4]=>[2,2,1,1,1,1,1]
[9,1,2,3,4,5,7,6,8]=>[3,1,1,1,1,1,1]
[2,1,3,4,5,9,6,7,8]=>[2,2,1,1,1,1,1]
[7,2,6,5,4,3,1,9,8]=>[6,2,1]
[3,2,1,9,5,8,7,6,4]=>[5,3,1]
[6,3,5,4,2,1,9,8,7]=>[5,3,1]
[4,3,2,1,9,7,8,6,5]=>[4,4,1]
[9,1,2,3,4,8,6,5,7]=>[4,1,1,1,1,1]
[9,1,2,3,8,5,6,4,7]=>[4,1,1,1,1,1]
[8,1,2,9,4,5,6,3,7]=>[3,2,1,1,1,1]
[9,1,8,3,4,5,6,2,7]=>[4,1,1,1,1,1]
[7,1,2,3,4,9,5,8,6]=>[3,2,1,1,1,1]
[6,1,2,3,8,4,5,9,7]=>[2,2,2,1,1,1]
[5,1,2,8,3,4,6,9,7]=>[2,2,2,1,1,1]
[4,1,9,2,3,5,6,8,7]=>[3,2,1,1,1,1]
[3,8,1,2,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[8,2,1,3,4,5,6,9,7]=>[3,2,1,1,1,1]
[9,1,2,3,8,5,4,7,6]=>[4,2,1,1,1]
[6,1,2,3,9,4,7,8,5]=>[3,2,1,1,1,1]
[5,1,2,8,3,6,4,9,7]=>[3,2,2,1,1]
[9,8,2,1,4,5,6,7,3]=>[4,2,1,1,1]
[4,1,8,2,5,3,6,9,7]=>[3,2,2,1,1]
[3,9,1,4,2,5,6,8,7]=>[3,2,1,1,1,1]
[8,2,3,1,4,5,6,9,7]=>[3,2,1,1,1,1]
[2,3,4,5,7,8,1,9,6]=>[2,2,1,1,1,1,1]
[1,3,4,5,2,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,7,9,1,6,8]=>[2,1,1,1,1,1,1,1]
[2,3,4,5,1,6,7,9,8]=>[2,2,1,1,1,1,1]
[4,5,6,1,7,8,9,2,3]=>[2,2,1,1,1,1,1]
[2,1,4,5,3,6,7,8,9]=>[2,2,1,1,1,1,1]
[1,3,2,5,4,6,7,8,9]=>[2,2,1,1,1,1,1]
[2,3,4,5,9,8,6,7,1]=>[4,1,1,1,1,1]
[2,3,4,9,7,5,8,6,1]=>[4,2,1,1,1]
[2,3,9,6,4,7,8,5,1]=>[4,2,1,1,1]
[2,9,5,3,6,7,8,4,1]=>[4,2,1,1,1]
[9,4,2,5,6,7,8,3,1]=>[4,2,1,1,1]
[4,1,6,2,8,3,5,7,9]=>[2,2,2,1,1,1]
[4,1,6,2,8,3,9,5,7]=>[2,2,2,2,1]
[4,1,6,2,7,3,8,5,9]=>[2,2,2,2,1]
[8,7,9,1,4,5,6,2,3]=>[4,1,1,1,1,1]
[7,6,9,1,4,5,2,8,3]=>[4,2,1,1,1]
[3,9,2,4,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[1,3,5,2,4,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[4,1,2,3,5,6,8,7,9]=>[2,2,1,1,1,1,1]
[1,2,4,7,3,5,6,8,9]=>[2,1,1,1,1,1,1,1]
[5,1,2,3,4,7,6,8,9]=>[2,2,1,1,1,1,1]
[5,6,4,3,2,1,7,8,9]=>[5,1,1,1,1]
[4,5,3,2,1,6,7,8,9]=>[4,1,1,1,1,1]
[6,7,4,3,2,1,5,8,9]=>[5,1,1,1,1]
[5,6,4,3,2,7,1,8,9]=>[5,1,1,1,1]
[7,5,4,3,1,2,6,8,9]=>[5,1,1,1,1]
[6,5,4,3,7,1,2,8,9]=>[5,1,1,1,1]
[7,6,4,3,5,2,1,9,8]=>[6,2,1]
[7,6,3,5,4,2,1,9,8]=>[6,2,1]
[9,8,6,1,2,3,4,5,7]=>[4,1,1,1,1,1]
[9,8,7,5,1,2,3,4,6]=>[5,1,1,1,1]
[9,8,7,6,4,1,2,3,5]=>[6,1,1,1]
[9,8,7,6,5,3,1,2,4]=>[7,1,1]
[9,8,4,7,6,5,3,2,1]=>[8,1]
[9,8,3,7,6,5,4,2,1]=>[8,1]
[9,3,8,7,6,5,4,2,1]=>[8,1]
[9,2,8,7,6,5,4,3,1]=>[8,1]
[9,8,4,6,5,7,3,2,1]=>[7,1,1]
[9,8,3,6,5,4,7,2,1]=>[7,1,1]
[9,3,7,6,5,4,8,2,1]=>[7,1,1]
[9,2,7,6,5,4,3,8,1]=>[7,1,1]
[4,2,1,3,6,5,8,7,9]=>[3,2,2,1,1]
[6,2,1,4,3,5,8,7,9]=>[3,2,2,1,1]
[9,2,3,4,1,5,6,7,8]=>[3,1,1,1,1,1,1]
[9,8,4,5,7,6,3,2,1]=>[7,1,1]
[9,8,5,4,6,7,3,2,1]=>[7,1,1]
[9,8,4,5,3,7,6,2,1]=>[6,2,1]
[9,8,3,5,7,6,4,2,1]=>[7,1,1]
[9,8,5,4,6,3,7,2,1]=>[7,1,1]
[9,8,4,3,6,7,5,2,1]=>[6,2,1]
[7,8,9,1,3,4,5,6,2]=>[3,1,1,1,1,1,1]
[1,3,4,2,5,6,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,2,4,5,6,3,7,8,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,5,6,7,8,4,9]=>[2,1,1,1,1,1,1,1]
[2,1,5,3,6,7,4,8,9]=>[2,2,2,1,1,1]
[1,3,5,6,4,2,7,8,9]=>[3,1,1,1,1,1,1]
[3,5,2,1,6,4,7,8,9]=>[3,2,1,1,1,1]
[2,1,3,6,4,7,8,9,5]=>[2,2,2,1,1,1]
[1,3,4,6,7,2,8,5,9]=>[2,2,1,1,1,1,1]
[3,2,6,1,4,7,8,5,9]=>[3,2,1,1,1,1]
[2,4,6,1,7,5,3,8,9]=>[3,2,1,1,1,1]
[4,6,3,2,1,7,5,8,9]=>[4,2,1,1,1]
[2,4,1,7,5,8,3,9,6]=>[3,2,2,1,1]
[4,3,7,2,1,5,8,9,6]=>[4,2,1,1,1]
[1,3,5,7,8,6,4,2,9]=>[4,1,1,1,1,1]
[3,5,7,2,1,8,6,4,9]=>[3,3,1,1,1]
[5,7,4,3,2,1,8,6,9]=>[5,2,1,1]
[2,4,6,8,1,9,7,5,3]=>[4,2,1,1,1]
[4,6,8,3,2,1,9,7,5]=>[4,3,1,1]
[6,8,5,4,3,2,1,9,7]=>[6,2,1]
[4,5,6,3,7,2,8,1,9]=>[4,1,1,1,1,1]
[1,5,6,7,4,8,3,9,2]=>[4,1,1,1,1,1]
[3,5,6,7,8,9,2,4,1]=>[3,1,1,1,1,1,1]
[2,4,6,7,8,9,1,3,5]=>[2,1,1,1,1,1,1,1]
[2,5,6,7,8,9,3,1,4]=>[3,1,1,1,1,1,1]
[5,4,6,3,8,1,7,2,9]=>[4,2,1,1,1]
[1,6,5,7,4,9,2,8,3]=>[4,2,1,1,1]
[5,4,8,1,7,2,6,3,9]=>[4,2,1,1,1]
[5,4,8,1,6,3,7,2,9]=>[4,2,1,1,1]
[1,6,5,9,2,8,3,7,4]=>[4,2,1,1,1]
[1,6,5,9,2,7,4,8,3]=>[4,2,1,1,1]
[2,5,6,7,8,1,9,3,4]=>[2,2,1,1,1,1,1]
[4,5,6,7,1,2,8,3,9]=>[2,2,1,1,1,1,1]
[1,3,6,7,8,9,2,4,5]=>[2,1,1,1,1,1,1,1]
[3,5,6,7,8,1,2,9,4]=>[2,2,1,1,1,1,1]
[2,3,4,5,7,6,8,9,1]=>[3,1,1,1,1,1,1]
[2,3,4,5,8,7,6,9,1]=>[4,1,1,1,1,1]
[1,2,3,4,7,9,5,6,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,6,7,9,5,8]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,8,5,6,9,7]=>[2,2,1,1,1,1,1]
[1,2,3,4,7,8,5,9,6]=>[2,2,1,1,1,1,1]
[2,3,4,5,8,6,7,9,1]=>[3,1,1,1,1,1,1]
[2,3,4,5,9,6,8,7,1]=>[4,1,1,1,1,1]
[9,3,4,5,2,6,7,8,1]=>[4,1,1,1,1,1]
[7,8,2,3,4,5,1,6,9]=>[3,1,1,1,1,1,1]
[1,8,9,3,4,5,6,2,7]=>[3,1,1,1,1,1,1]
[2,1,3,4,5,8,6,7,9]=>[2,2,1,1,1,1,1]
[9,2,3,4,5,1,6,7,8]=>[3,1,1,1,1,1,1]
[7,2,3,4,5,6,9,1,8]=>[3,1,1,1,1,1,1]
[6,2,3,4,5,9,1,7,8]=>[3,1,1,1,1,1,1]
[5,2,3,4,9,1,6,7,8]=>[3,1,1,1,1,1,1]
[4,2,3,9,1,5,6,7,8]=>[3,1,1,1,1,1,1]
[3,2,9,1,4,5,6,7,8]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,1,3,9,2]=>[3,1,1,1,1,1,1]
[4,5,3,6,7,8,9,1,2]=>[3,1,1,1,1,1,1]
[5,3,4,6,7,8,9,1,2]=>[3,1,1,1,1,1,1]
[9,5,4,3,2,1,6,7,8]=>[6,1,1,1]
[1,2,3,7,4,8,5,9,6]=>[2,2,2,1,1,1]
[1,2,3,4,7,5,9,8,6]=>[3,2,1,1,1,1]
[1,2,6,3,7,4,9,8,5]=>[3,2,2,1,1]
[1,2,3,8,6,4,9,7,5]=>[3,3,1,1,1]
[1,2,3,6,4,9,8,7,5]=>[4,2,1,1,1]
[5,1,6,2,7,3,9,8,4]=>[3,2,2,2]
[1,5,2,8,6,3,9,7,4]=>[3,3,2,1]
[1,5,2,6,3,9,8,7,4]=>[4,2,2,1]
[1,2,7,5,3,9,8,6,4]=>[4,3,1,1]
[1,2,5,3,9,8,7,6,4]=>[5,2,1,1]
[4,1,7,5,2,9,8,6,3]=>[4,3,2]
[4,1,5,2,9,8,7,6,3]=>[5,2,2]
[1,6,4,2,9,8,7,5,3]=>[5,3,1]
[1,4,2,9,8,7,6,5,3]=>[6,2,1]
[7,5,3,1,9,8,6,4,2]=>[5,4]
[5,3,1,9,8,7,6,4,2]=>[6,3]
[1,2,3,4,5,8,9,7,6]=>[3,1,1,1,1,1,1]
[1,2,3,4,8,9,6,7,5]=>[3,1,1,1,1,1,1]
[1,2,3,8,9,5,6,7,4]=>[3,1,1,1,1,1,1]
[1,2,8,9,4,5,6,7,3]=>[3,1,1,1,1,1,1]
[9,4,2,3,5,6,7,8,1]=>[4,1,1,1,1,1]
[1,4,2,5,6,7,9,8,3]=>[3,2,1,1,1,1]
[2,1,4,5,6,9,7,3,8]=>[3,2,1,1,1,1]
[3,1,5,2,9,6,7,8,4]=>[3,2,2,1,1]
[4,5,1,6,8,7,9,2,3]=>[3,2,1,1,1,1]
[2,3,1,5,9,6,7,4,8]=>[3,2,1,1,1,1]
[1,2,4,5,7,9,6,3,8]=>[3,1,1,1,1,1,1]
[3,4,6,5,7,1,2,9,8]=>[3,2,1,1,1,1]
[3,1,9,4,2,6,7,8,5]=>[3,2,2,1,1]
[1,2,5,3,9,6,8,7,4]=>[4,2,1,1,1]
[4,5,1,7,6,8,2,9,3]=>[3,2,2,1,1]
[4,8,7,6,5,3,2,1,9]=>[7,1,1]
[5,8,7,4,6,3,2,1,9]=>[6,1,1,1]
[8,4,7,6,5,3,2,1,9]=>[7,1,1]
[6,9,8,5,7,4,1,3,2]=>[6,1,1,1]
[9,8,7,5,1,6,4,3,2]=>[7,2]
[1,2,8,3,4,5,6,9,7]=>[2,2,1,1,1,1,1]
[1,9,5,2,3,8,4,6,7]=>[3,2,1,1,1,1]
[1,8,2,9,4,3,5,6,7]=>[3,2,1,1,1,1]
[1,3,2,4,9,8,5,6,7]=>[3,2,1,1,1,1]
[2,1,3,4,5,9,8,6,7]=>[3,2,1,1,1,1]
[9,1,7,2,3,4,5,8,6]=>[3,2,1,1,1,1]
[1,8,5,2,3,4,6,9,7]=>[3,2,1,1,1,1]
[9,8,1,2,3,5,6,4,7]=>[4,1,1,1,1,1]
[1,4,2,3,9,5,6,8,7]=>[3,2,1,1,1,1]
[4,9,8,1,2,5,3,6,7]=>[4,1,1,1,1,1]
[1,3,2,4,5,9,6,8,7]=>[3,2,1,1,1,1]
[1,8,3,9,4,2,5,6,7]=>[3,2,1,1,1,1]
[2,3,1,4,9,8,5,6,7]=>[3,2,1,1,1,1]
[8,7,6,5,4,1,9,3,2]=>[7,2]
[8,7,6,5,2,9,1,3,4]=>[6,1,1,1]
[8,7,6,3,9,2,1,4,5]=>[6,1,1,1]
[8,7,4,9,3,2,1,6,5]=>[6,2,1]
[8,5,9,4,3,2,1,6,7]=>[6,1,1,1]
[6,9,5,4,3,2,1,7,8]=>[6,1,1,1]
[8,7,6,5,2,1,4,3,9]=>[6,2,1]
[8,7,6,3,2,5,1,4,9]=>[6,1,1,1]
[8,7,6,5,1,9,4,3,2]=>[7,2]
[8,7,4,3,6,2,1,9,5]=>[6,2,1]
[8,7,6,2,9,5,1,3,4]=>[5,2,1,1]
[8,5,4,7,3,2,1,6,9]=>[6,1,1,1]
[8,7,3,9,6,2,1,4,5]=>[5,2,1,1]
[6,5,8,4,3,2,1,7,9]=>[6,1,1,1]
[8,4,9,7,3,2,1,6,5]=>[5,2,2]
[5,9,8,4,3,2,1,6,7]=>[6,1,1,1]
[8,7,5,6,4,3,2,1,9]=>[7,1,1]
[8,6,5,7,4,3,2,1,9]=>[7,1,1]
[9,8,7,6,4,3,2,5,1]=>[8,1]
[9,8,7,6,4,3,5,2,1]=>[8,1]
[8,5,6,7,4,3,2,1,9]=>[6,1,1,1]
[6,7,5,8,4,3,2,1,9]=>[6,1,1,1]
[8,9,7,6,4,3,2,1,5]=>[7,1,1]
[7,6,5,3,2,1,4,8,9]=>[6,1,1,1]
[9,8,7,6,4,3,5,1,2]=>[7,1,1]
[9,8,7,6,4,5,2,3,1]=>[7,1,1]
[9,8,7,6,5,3,4,2,1]=>[8,1]
[7,1,8,2,3,4,5,9,6]=>[2,2,2,1,1,1]
[6,8,1,2,3,4,5,9,7]=>[2,2,1,1,1,1,1]
[9,6,7,4,5,2,3,1,8]=>[5,1,1,1,1]
[9,8,6,5,4,3,7,2,1]=>[8,1]
[2,3,6,4,5,1,7,8,9]=>[3,1,1,1,1,1,1]
[2,3,4,8,5,6,7,1,9]=>[3,1,1,1,1,1,1]
[3,5,4,7,2,6,1,8,9]=>[4,1,1,1,1,1]
[2,6,4,1,5,3,7,8,9]=>[3,2,1,1,1,1]
[4,5,2,6,3,1,7,8,9]=>[3,2,1,1,1,1]
[3,6,4,5,9,2,7,8,1]=>[4,1,1,1,1,1]
[2,5,4,7,8,6,3,1,9]=>[4,2,1,1,1]
[4,6,2,5,8,3,7,1,9]=>[4,1,1,1,1,1]
[3,5,7,6,1,4,2,8,9]=>[4,1,1,1,1,1]
[5,6,2,3,7,4,1,8,9]=>[3,2,1,1,1,1]
[5,7,2,3,6,9,4,8,1]=>[4,1,1,1,1,1]
[2,8,4,1,6,3,7,5,9]=>[3,2,2,1,1]
[4,6,7,8,3,1,5,2,9]=>[3,2,1,1,1,1]
[6,7,2,3,4,8,5,1,9]=>[3,2,1,1,1,1]
[3,5,9,7,1,8,2,6,4]=>[4,2,1,1,1]
[5,7,8,3,9,4,1,6,2]=>[3,2,2,1,1]
[7,8,2,3,4,5,9,6,1]=>[3,2,1,1,1,1]
[9,7,6,5,4,3,2,8,1]=>[8,1]
[3,1,4,6,2,5,8,7,9]=>[2,2,2,1,1,1]
[1,3,2,5,7,4,6,9,8]=>[2,2,2,1,1,1]
[1,9,8,5,6,7,4,3,2]=>[6,1,1,1]
[1,9,8,5,4,6,7,3,2]=>[6,1,1,1]
[1,9,5,4,6,7,8,3,2]=>[5,1,1,1,1]
[1,2,3,4,7,5,6,9,8]=>[2,2,1,1,1,1,1]
[9,8,7,6,5,3,1,4,2]=>[7,2]
[9,8,7,6,4,1,5,3,2]=>[7,2]
[9,8,6,1,7,5,4,3,2]=>[7,2]
[9,7,1,8,6,5,4,3,2]=>[7,2]
[1,2,7,4,5,6,8,9,3]=>[3,1,1,1,1,1,1]
[1,2,3,4,7,8,5,6,9]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,6,5,8,7,9]=>[2,2,1,1,1,1,1]
[1,2,3,4,8,9,5,6,7]=>[2,1,1,1,1,1,1,1]
[2,1,7,8,9,3,4,5,6]=>[2,2,1,1,1,1,1]
[9,7,5,3,8,6,4,2,1]=>[6,3]
[8,6,9,7,4,3,2,1,5]=>[6,2,1]
[8,6,3,2,1,4,9,7,5]=>[5,3,1]
[8,6,4,9,7,5,2,1,3]=>[5,3,1]
[9,7,5,3,8,6,4,1,2]=>[5,3,1]
[9,6,7,8,5,4,3,2,1]=>[7,1,1]
[8,5,6,9,7,4,3,2,1]=>[6,2,1]
[8,6,3,2,1,9,7,4,5]=>[5,3,1]
[9,7,8,4,3,2,1,5,6]=>[6,1,1,1]
[8,6,3,4,9,7,5,2,1]=>[5,3,1]
[8,6,9,7,3,2,1,4,5]=>[5,2,1,1]
[9,7,5,2,3,8,6,4,1]=>[5,3,1]
[8,6,2,1,3,4,9,7,5]=>[4,3,1,1]
[8,6,4,9,7,5,1,2,3]=>[4,3,1,1]
[2,5,1,6,3,7,4,8,9]=>[2,2,2,1,1,1]
[2,6,1,7,3,8,4,9,5]=>[2,2,2,2,1]
[3,4,6,1,7,2,8,5,9]=>[2,2,2,1,1,1]
[3,2,6,1,7,4,8,5,9]=>[3,2,2,1,1]
[4,2,5,6,1,7,3,8,9]=>[3,2,1,1,1,1]
[3,4,2,6,1,7,5,8,9]=>[3,2,1,1,1,1]
[4,2,5,7,1,8,3,9,6]=>[3,2,2,1,1]
[3,4,2,7,1,8,5,9,6]=>[3,2,2,1,1]
[5,3,6,4,7,1,8,2,9]=>[3,2,2,1,1]
[3,5,2,6,7,1,8,4,9]=>[3,2,1,1,1,1]
[4,3,5,2,7,1,8,6,9]=>[4,2,1,1,1]
[4,6,2,7,5,8,1,9,3]=>[3,2,2,1,1]
[4,3,6,2,7,8,1,9,5]=>[4,2,1,1,1]
[4,5,3,6,2,8,1,9,7]=>[4,2,1,1,1]
[6,1,7,8,9,2,3,4,5]=>[2,2,1,1,1,1,1]
[4,5,6,7,1,9,2,3,8]=>[2,2,1,1,1,1,1]
[3,5,6,7,9,1,2,4,8]=>[2,1,1,1,1,1,1,1]
[5,1,6,7,8,2,9,3,4]=>[2,2,2,1,1,1]
[4,1,6,7,8,9,2,3,5]=>[2,2,1,1,1,1,1]
[5,6,7,8,9,1,3,4,2]=>[3,1,1,1,1,1,1]
[6,7,8,9,1,3,4,5,2]=>[3,1,1,1,1,1,1]
[6,7,8,9,1,4,5,2,3]=>[3,1,1,1,1,1,1]
[6,7,8,9,1,4,5,3,2]=>[4,1,1,1,1,1]
[6,7,8,9,1,5,4,3,2]=>[5,1,1,1,1]
[7,8,9,1,4,5,6,2,3]=>[3,1,1,1,1,1,1]
[7,8,9,1,4,5,6,3,2]=>[4,1,1,1,1,1]
[7,8,9,1,5,6,3,4,2]=>[4,1,1,1,1,1]
[7,8,9,1,5,6,4,3,2]=>[5,1,1,1,1]
[7,8,9,1,6,5,4,3,2]=>[6,1,1,1]
[8,9,1,5,6,7,3,4,2]=>[4,1,1,1,1,1]
[8,9,1,5,6,7,4,3,2]=>[5,1,1,1,1]
[8,9,1,6,7,4,5,2,3]=>[4,1,1,1,1,1]
[8,9,1,6,7,4,5,3,2]=>[5,1,1,1,1]
[8,9,1,6,7,5,4,3,2]=>[6,1,1,1]
[9,1,7,8,5,6,3,4,2]=>[5,1,1,1,1]
[9,1,7,8,5,6,4,3,2]=>[6,1,1,1]
[2,3,4,5,7,9,6,8,1]=>[3,1,1,1,1,1,1]
[2,3,4,6,9,5,7,8,1]=>[3,1,1,1,1,1,1]
[2,3,5,9,4,6,7,8,1]=>[3,1,1,1,1,1,1]
[2,4,9,3,5,6,7,8,1]=>[3,1,1,1,1,1,1]
[5,9,8,7,6,4,3,1,2]=>[7,1,1]
[5,4,8,7,6,3,2,1,9]=>[6,2,1]
[6,5,9,8,7,4,3,1,2]=>[6,2,1]
[9,5,8,7,6,4,3,1,2]=>[7,1,1]
[2,3,4,5,6,1,8,9,7]=>[2,2,1,1,1,1,1]
[2,3,4,5,1,7,8,9,6]=>[2,2,1,1,1,1,1]
[2,9,3,4,5,6,1,7,8]=>[3,1,1,1,1,1,1]
[2,8,3,4,5,1,6,9,7]=>[3,2,1,1,1,1]
[2,7,3,4,1,5,8,9,6]=>[3,2,1,1,1,1]
[2,6,3,1,4,7,8,9,5]=>[3,2,1,1,1,1]
[4,2,5,3,7,6,9,8,1]=>[3,2,2,2]
[4,2,6,3,7,5,9,8,1]=>[3,2,2,2]
[4,2,6,3,8,5,9,7,1]=>[3,2,2,2]
[4,2,6,3,8,5,1,7,9]=>[3,2,2,1,1]
[4,2,6,3,8,5,7,1,9]=>[3,2,2,1,1]
[4,2,6,3,5,8,7,1,9]=>[3,2,2,1,1]
[4,2,3,6,5,8,7,1,9]=>[3,2,2,1,1]
[5,2,6,3,7,4,9,8,1]=>[3,2,2,2]
[4,2,7,3,8,5,9,6,1]=>[3,2,2,2]
[4,2,6,3,9,5,1,7,8]=>[3,2,2,1,1]
[4,2,6,3,8,5,7,9,1]=>[3,2,2,1,1]
[4,2,6,3,5,8,1,7,9]=>[3,2,1,1,1,1]
[4,2,3,6,8,5,7,1,9]=>[3,2,1,1,1,1]
[2,4,6,3,5,8,7,1,9]=>[3,2,1,1,1,1]
[3,4,5,6,9,2,1,8,7]=>[3,2,1,1,1,1]
[3,4,5,8,2,9,1,7,6]=>[3,2,1,1,1,1]
[3,4,7,2,8,9,1,5,6]=>[3,1,1,1,1,1,1]
[3,6,2,7,8,9,1,5,4]=>[3,2,1,1,1,1]
[5,2,6,7,8,9,1,4,3]=>[3,2,1,1,1,1]
[3,4,5,6,9,1,7,8,2]=>[3,1,1,1,1,1,1]
[3,4,5,8,9,6,1,7,2]=>[3,2,1,1,1,1]
[3,4,7,8,5,9,1,2,6]=>[3,1,1,1,1,1,1]
[3,4,5,9,2,6,1,8,7]=>[3,2,1,1,1,1]
[3,6,7,4,8,9,1,5,2]=>[3,2,1,1,1,1]
[3,4,8,2,5,9,1,7,6]=>[3,2,1,1,1,1]
[5,6,3,7,8,9,1,4,2]=>[3,2,1,1,1,1]
[3,7,2,4,8,9,1,5,6]=>[3,1,1,1,1,1,1]
[6,2,3,7,8,9,1,5,4]=>[3,2,1,1,1,1]
[8,9,7,6,5,4,1,3,2]=>[7,1,1]
[8,7,9,6,5,4,1,3,2]=>[7,1,1]
[9,7,8,6,5,4,1,3,2]=>[7,1,1]
[1,3,2,4,5,6,9,7,8]=>[2,2,1,1,1,1,1]
[2,3,1,4,5,6,9,7,8]=>[2,2,1,1,1,1,1]
[4,3,9,5,6,7,8,2,1]=>[4,2,1,1,1]
[3,2,8,5,6,7,1,9,4]=>[3,2,2,1,1]
[7,8,4,5,6,1,3,9,2]=>[4,1,1,1,1,1]
[3,4,1,9,6,7,8,2,5]=>[3,2,1,1,1,1]
[4,8,9,5,6,7,2,1,3]=>[4,1,1,1,1,1]
[4,2,3,8,6,7,1,9,5]=>[3,2,2,1,1]
[6,8,4,5,1,3,7,9,2]=>[4,1,1,1,1,1]
[3,5,1,4,9,7,8,2,6]=>[3,2,1,1,1,1]
[8,3,4,9,6,7,2,5,1]=>[4,2,1,1,1]
[4,7,9,5,6,2,1,8,3]=>[4,2,1,1,1]
[8,1,2,5,3,4,6,7,9]=>[3,1,1,1,1,1,1]
[1,9,2,3,6,4,5,7,8]=>[3,1,1,1,1,1,1]
[8,1,2,6,4,3,5,7,9]=>[4,1,1,1,1,1]
[8,1,2,6,3,5,4,7,9]=>[4,1,1,1,1,1]
[1,9,2,3,7,5,4,6,8]=>[4,1,1,1,1,1]
[1,9,2,3,7,4,6,5,8]=>[4,1,1,1,1,1]
[5,6,7,8,9,3,2,1,4]=>[4,1,1,1,1,1]
[6,7,8,9,3,4,1,2,5]=>[3,1,1,1,1,1,1]
[6,7,8,9,3,4,2,1,5]=>[4,1,1,1,1,1]
[7,8,9,3,4,5,1,2,6]=>[3,1,1,1,1,1,1]
[7,8,9,3,4,5,2,1,6]=>[4,1,1,1,1,1]
[7,8,9,4,5,2,3,1,6]=>[4,1,1,1,1,1]
[7,8,9,4,5,3,2,1,6]=>[5,1,1,1,1]
[8,9,4,5,6,2,3,1,7]=>[4,1,1,1,1,1]
[8,9,4,5,6,3,2,1,7]=>[5,1,1,1,1]
[8,9,5,6,3,4,1,2,7]=>[4,1,1,1,1,1]
[8,9,5,6,3,4,2,1,7]=>[5,1,1,1,1]
[8,9,5,6,4,3,2,1,7]=>[6,1,1,1]
[9,6,7,4,5,3,2,1,8]=>[6,1,1,1]
[4,2,6,1,3,5,8,7,9]=>[3,2,1,1,1,1]
[4,2,6,1,8,3,5,7,9]=>[3,2,1,1,1,1]
[4,2,8,1,3,6,5,7,9]=>[3,2,1,1,1,1]
[4,2,6,1,9,3,5,8,7]=>[3,3,1,1,1]
[9,1,2,8,4,3,5,6,7]=>[4,1,1,1,1,1]
[8,1,9,3,2,4,6,5,7]=>[3,2,2,1,1]
[9,8,2,1,3,5,6,4,7]=>[4,2,1,1,1]
[8,1,9,2,4,5,6,3,7]=>[3,2,1,1,1,1]
[1,4,3,6,5,8,7,9,2]=>[3,2,2,1,1]
[1,4,2,6,5,8,7,9,3]=>[3,2,2,1,1]
[1,5,2,6,4,8,7,9,3]=>[3,2,2,1,1]
[1,5,2,7,4,8,6,9,3]=>[3,2,2,1,1]
[1,5,2,7,4,9,6,8,3]=>[3,2,2,1,1]
[1,5,2,7,4,6,9,8,3]=>[3,2,2,1,1]
[1,5,2,4,7,6,9,8,3]=>[3,2,2,1,1]
[1,2,5,4,7,6,9,8,3]=>[3,2,2,1,1]
[1,5,2,6,3,8,7,9,4]=>[3,2,2,1,1]
[1,6,2,7,4,8,5,9,3]=>[3,2,2,1,1]
[1,5,2,8,4,9,6,7,3]=>[3,2,2,1,1]
[1,5,2,7,4,6,8,9,3]=>[3,2,1,1,1,1]
[1,5,2,4,7,9,6,8,3]=>[3,2,1,1,1,1]
[1,2,5,7,4,6,9,8,3]=>[3,2,1,1,1,1]
[3,4,5,6,8,9,7,1,2]=>[3,1,1,1,1,1,1]
[3,4,5,7,8,9,6,1,2]=>[3,1,1,1,1,1,1]
[3,5,6,7,8,9,4,1,2]=>[3,1,1,1,1,1,1]
[4,5,6,7,8,9,3,1,2]=>[3,1,1,1,1,1,1]
[3,4,5,8,1,9,7,6,2]=>[4,2,1,1,1]
[3,4,7,1,8,9,6,5,2]=>[4,2,1,1,1]
[3,6,1,7,8,9,4,5,2]=>[3,2,1,1,1,1]
[5,1,6,7,8,9,4,3,2]=>[4,2,1,1,1]
[1,5,6,7,8,9,3,2,4]=>[3,1,1,1,1,1,1]
[3,4,5,8,9,6,7,1,2]=>[3,1,1,1,1,1,1]
[3,4,7,8,5,9,6,1,2]=>[3,2,1,1,1,1]
[3,4,5,9,1,6,7,8,2]=>[3,1,1,1,1,1,1]
[3,4,8,1,5,9,7,6,2]=>[4,2,1,1,1]
[5,6,3,7,8,9,4,1,2]=>[3,2,1,1,1,1]
[3,7,1,4,8,9,6,5,2]=>[4,2,1,1,1]
[5,2,6,7,8,9,3,1,4]=>[3,2,1,1,1,1]
[6,1,3,7,8,9,4,5,2]=>[3,2,1,1,1,1]
[1,2,6,7,8,9,4,3,5]=>[3,1,1,1,1,1,1]
[9,3,4,5,6,8,7,2,1]=>[5,1,1,1,1]
[9,4,3,5,6,7,8,2,1]=>[5,1,1,1,1]
[9,8,3,4,5,7,6,2,1]=>[6,1,1,1]
[9,8,4,3,5,6,7,2,1]=>[6,1,1,1]
[9,3,4,5,6,2,8,7,1]=>[4,2,1,1,1]
[9,2,4,5,6,8,7,3,1]=>[5,1,1,1,1]
[9,4,3,5,6,7,2,8,1]=>[5,1,1,1,1]
[9,3,2,5,6,7,8,4,1]=>[4,2,1,1,1]
[4,6,3,5,7,2,8,1,9]=>[4,1,1,1,1,1]
[5,6,3,4,7,2,8,1,9]=>[4,1,1,1,1,1]
[1,5,7,4,6,8,3,9,2]=>[4,1,1,1,1,1]
[1,6,7,4,5,8,3,9,2]=>[4,1,1,1,1,1]
[1,2,3,4,8,5,9,6,7]=>[2,2,1,1,1,1,1]
[1,2,3,7,4,5,8,6,9]=>[2,2,1,1,1,1,1]
[1,2,3,4,8,6,5,7,9]=>[3,1,1,1,1,1,1]
[1,2,3,4,9,7,5,6,8]=>[3,1,1,1,1,1,1]
[2,1,4,9,3,5,6,7,8]=>[2,2,1,1,1,1,1]
[3,7,1,2,4,5,6,9,8]=>[2,2,1,1,1,1,1]
[3,1,2,6,9,4,5,7,8]=>[2,2,1,1,1,1,1]
[4,6,1,2,3,5,9,7,8]=>[2,2,1,1,1,1,1]
[9,7,6,5,4,3,8,2,1]=>[8,1]
[9,8,6,5,4,7,3,2,1]=>[8,1]
[5,4,3,2,1,9,7,8,6]=>[5,3,1]
[2,1,4,3,6,5,8,7,10,9]=>[2,2,2,2,2]
[3,4,1,2,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[4,3,2,1,6,5,8,7,10,9]=>[4,2,2,2]
[6,3,2,5,4,1,8,7,10,9]=>[4,2,2,2]
[8,3,2,5,4,7,6,1,10,9]=>[4,2,2,2]
[10,3,2,5,4,7,6,9,8,1]=>[4,2,2,2]
[4,5,6,1,2,3,8,7,10,9]=>[2,2,2,1,1,1,1]
[3,5,1,6,2,4,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,5,6,3,4,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,6,5,4,3,8,7,10,9]=>[4,2,2,2]
[6,5,4,3,2,1,8,7,10,9]=>[6,2,2]
[8,5,4,3,2,7,6,1,10,9]=>[6,2,2]
[10,5,4,3,2,7,6,9,8,1]=>[6,2,2]
[2,1,8,5,4,7,6,3,10,9]=>[4,2,2,2]
[8,7,4,3,6,5,2,1,10,9]=>[6,2,2]
[10,7,4,3,6,5,2,9,8,1]=>[6,2,2]
[2,1,10,5,4,7,6,9,8,3]=>[4,2,2,2]
[10,9,4,3,6,5,8,7,2,1]=>[6,2,2]
[8,9,5,6,3,4,10,1,2,7]=>[4,1,1,1,1,1,1]
[5,6,7,8,1,2,3,4,10,9]=>[2,2,1,1,1,1,1,1]
[4,6,7,1,8,2,3,5,10,9]=>[2,2,2,1,1,1,1]
[3,6,1,7,8,2,4,5,10,9]=>[2,2,2,1,1,1,1]
[2,1,6,7,8,3,4,5,10,9]=>[2,2,2,1,1,1,1]
[2,1,5,7,3,8,4,6,10,9]=>[2,2,2,2,1,1]
[3,5,1,7,2,8,4,6,10,9]=>[2,2,2,2,1,1]
[4,5,7,1,2,8,3,6,10,9]=>[2,2,2,1,1,1,1]
[3,4,1,2,7,8,5,6,10,9]=>[2,2,2,1,1,1,1]
[2,1,4,3,7,8,5,6,10,9]=>[2,2,2,2,1,1]
[2,1,4,3,8,7,6,5,10,9]=>[4,2,2,2]
[4,3,2,1,8,7,6,5,10,9]=>[4,4,2]
[8,3,2,7,6,5,4,1,10,9]=>[6,2,2]
[10,3,2,7,6,5,4,9,8,1]=>[6,2,2]
[2,1,8,7,6,5,4,3,10,9]=>[6,2,2]
[8,7,6,5,4,3,2,1,10,9]=>[8,2]
[9,7,6,5,4,3,2,10,1,8]=>[8,1,1]
[10,7,6,5,4,3,2,9,8,1]=>[8,2]
[2,1,10,7,6,5,4,9,8,3]=>[6,2,2]
[10,9,6,5,4,3,8,7,2,1]=>[8,2]
[2,1,4,3,10,7,6,9,8,5]=>[4,2,2,2]
[4,3,2,1,10,7,6,9,8,5]=>[4,4,2]
[10,3,2,9,6,5,8,7,4,1]=>[6,2,2]
[2,1,10,9,6,5,8,7,4,3]=>[6,2,2]
[10,9,8,5,4,7,6,3,2,1]=>[8,2]
[10,8,9,6,7,4,5,2,3,1]=>[6,1,1,1,1]
[2,1,7,8,9,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[3,7,1,8,9,10,2,4,5,6]=>[2,2,1,1,1,1,1,1]
[4,7,8,1,9,10,2,3,5,6]=>[2,2,1,1,1,1,1,1]
[5,7,8,9,1,10,2,3,4,6]=>[2,2,1,1,1,1,1,1]
[6,7,8,9,10,1,2,3,4,5]=>[2,1,1,1,1,1,1,1,1]
[5,6,8,9,1,2,10,3,4,7]=>[2,2,1,1,1,1,1,1]
[4,6,8,1,9,2,10,3,5,7]=>[2,2,2,1,1,1,1]
[3,6,1,8,9,2,10,4,5,7]=>[2,2,2,1,1,1,1]
[2,1,6,8,9,3,10,4,5,7]=>[2,2,2,1,1,1,1]
[2,1,5,8,3,9,10,4,6,7]=>[2,2,2,1,1,1,1]
[3,5,1,8,2,9,10,4,6,7]=>[2,2,2,1,1,1,1]
[4,5,8,1,2,9,10,3,6,7]=>[2,2,1,1,1,1,1,1]
[7,3,2,8,9,10,1,4,5,6]=>[4,1,1,1,1,1,1]
[3,4,1,2,8,9,10,5,6,7]=>[2,2,1,1,1,1,1,1]
[2,1,4,3,8,9,10,5,6,7]=>[2,2,2,1,1,1,1]
[2,1,4,3,7,9,5,10,6,8]=>[2,2,2,2,1,1]
[3,4,1,2,7,9,5,10,6,8]=>[2,2,2,1,1,1,1]
[4,5,7,1,2,9,3,10,6,8]=>[2,2,2,1,1,1,1]
[3,5,1,7,2,9,4,10,6,8]=>[2,2,2,2,1,1]
[2,1,5,7,3,9,4,10,6,8]=>[2,2,2,2,1,1]
[2,1,6,7,9,3,4,10,5,8]=>[2,2,2,1,1,1,1]
[3,6,1,7,9,2,4,10,5,8]=>[2,2,2,1,1,1,1]
[4,6,7,1,9,2,3,10,5,8]=>[2,2,2,1,1,1,1]
[5,6,7,9,1,2,3,10,4,8]=>[2,2,1,1,1,1,1,1]
[8,5,4,3,2,9,10,1,6,7]=>[6,1,1,1,1]
[2,1,5,6,3,4,9,10,7,8]=>[2,2,2,1,1,1,1]
[3,5,1,6,2,4,9,10,7,8]=>[2,2,2,1,1,1,1]
[4,5,6,1,2,3,9,10,7,8]=>[2,2,1,1,1,1,1,1]
[3,4,1,2,6,5,9,10,7,8]=>[2,2,2,1,1,1,1]
[2,1,4,3,6,5,9,10,7,8]=>[2,2,2,2,1,1]
[2,1,4,3,6,5,10,9,8,7]=>[4,2,2,2]
[4,3,2,1,6,5,10,9,8,7]=>[4,4,2]
[6,3,2,5,4,1,10,9,8,7]=>[4,4,2]
[10,3,2,5,4,9,8,7,6,1]=>[6,2,2]
[2,1,6,5,4,3,10,9,8,7]=>[4,4,2]
[6,5,4,3,2,1,10,9,8,7]=>[6,4]
[10,5,4,3,2,9,8,7,6,1]=>[6,4]
[2,1,10,5,4,9,8,7,6,3]=>[6,2,2]
[10,9,4,3,8,7,6,5,2,1]=>[8,2]
[9,7,5,10,3,8,2,6,1,4]=>[6,1,1,1,1]
[2,1,4,3,10,9,8,7,6,5]=>[6,2,2]
[4,3,2,1,10,9,8,7,6,5]=>[6,4]
[10,3,2,9,8,7,6,5,4,1]=>[8,2]
[2,1,10,9,8,7,6,5,4,3]=>[8,2]
[9,10,8,7,6,5,4,3,1,2]=>[8,1,1]
[10,9,8,7,6,5,4,3,2,1]=>[10]
[3,4,2,1,6,5,8,7,10,9]=>[3,2,2,2,1]
[3,5,2,6,4,1,8,7,10,9]=>[3,2,2,2,1]
[3,5,2,7,4,8,6,1,10,9]=>[3,2,2,2,1]
[3,5,2,7,4,9,6,10,8,1]=>[3,2,2,2,1]
[2,1,5,6,4,3,8,7,10,9]=>[3,2,2,2,1]
[4,5,6,3,2,1,8,7,10,9]=>[4,2,2,1,1]
[4,5,7,3,2,8,6,1,10,9]=>[4,2,2,1,1]
[4,5,7,3,2,9,6,10,8,1]=>[4,2,2,1,1]
[2,1,5,7,4,8,6,3,10,9]=>[3,2,2,2,1]
[4,6,7,3,8,5,2,1,10,9]=>[4,2,2,1,1]
[4,6,7,3,9,5,2,10,8,1]=>[4,2,2,1,1]
[2,1,5,7,4,9,6,10,8,3]=>[3,2,2,2,1]
[4,6,8,3,9,5,10,7,2,1]=>[4,2,2,1,1]
[2,1,4,3,7,8,6,5,10,9]=>[3,2,2,2,1]
[3,4,2,1,7,8,6,5,10,9]=>[3,3,2,1,1]
[3,6,2,7,8,5,4,1,10,9]=>[4,2,2,1,1]
[3,6,2,7,9,5,4,10,8,1]=>[4,2,2,1,1]
[2,1,6,7,8,5,4,3,10,9]=>[4,2,2,1,1]
[5,6,7,8,4,3,2,1,10,9]=>[5,2,1,1,1]
[5,6,7,9,4,3,2,10,8,1]=>[5,2,1,1,1]
[2,1,6,7,9,5,4,10,8,3]=>[4,2,2,1,1]
[5,6,8,9,4,3,10,7,2,1]=>[5,2,1,1,1]
[2,1,4,3,7,9,6,10,8,5]=>[3,2,2,2,1]
[3,4,2,1,7,9,6,10,8,5]=>[3,3,2,1,1]
[3,6,2,8,9,5,10,7,4,1]=>[4,2,2,1,1]
[2,1,6,8,9,5,10,7,4,3]=>[4,2,2,1,1]
[5,7,8,9,4,10,6,3,2,1]=>[5,2,1,1,1]
[6,7,8,9,10,4,5,3,2,1]=>[5,1,1,1,1,1]
[6,7,8,9,10,1,4,5,3,2]=>[4,1,1,1,1,1,1]
[6,7,8,9,10,1,4,5,2,3]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,10,4,5,2,3,1]=>[4,1,1,1,1,1,1]
[6,7,8,9,10,4,3,2,1,5]=>[5,1,1,1,1,1]
[6,7,8,9,10,3,4,5,2,1]=>[4,1,1,1,1,1,1]
[6,7,8,9,10,3,4,5,1,2]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,10,1,3,4,5,2]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,10,3,4,1,2,5]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,10,3,4,2,1,5]=>[4,1,1,1,1,1,1]
[6,7,8,9,10,2,3,4,1,5]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,10,2,3,4,5,1]=>[3,1,1,1,1,1,1,1]
[2,1,4,3,6,5,9,10,8,7]=>[3,2,2,2,1]
[3,4,2,1,6,5,9,10,8,7]=>[3,3,2,1,1]
[3,5,2,6,4,1,9,10,8,7]=>[3,3,2,1,1]
[3,5,2,8,4,9,10,7,6,1]=>[4,2,2,1,1]
[2,1,5,6,4,3,9,10,8,7]=>[3,3,2,1,1]
[4,5,6,3,2,1,9,10,8,7]=>[4,3,1,1,1]
[4,5,8,3,2,9,10,7,6,1]=>[4,3,1,1,1]
[2,1,5,8,4,9,10,7,6,3]=>[4,2,2,1,1]
[4,7,8,3,9,10,6,5,2,1]=>[5,2,1,1,1]
[2,1,4,3,8,9,10,7,6,5]=>[4,2,2,1,1]
[3,4,2,1,8,9,10,7,6,5]=>[4,3,1,1,1]
[3,7,2,8,9,10,6,5,4,1]=>[5,2,1,1,1]
[2,1,7,8,9,10,6,5,4,3]=>[5,2,1,1,1]
[6,7,8,9,10,1,5,4,3,2]=>[5,1,1,1,1,1]
[6,7,8,9,10,5,4,3,2,1]=>[6,1,1,1,1]
[2,3,4,5,6,7,8,9,10,1]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,1,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,10,1,9]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,9,10,1,8]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,8,9,10,1,7]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,7,8,9,10,1,6]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,6,7,8,9,10,1,5]=>[2,1,1,1,1,1,1,1,1]
[2,3,5,6,7,8,9,10,1,4]=>[2,1,1,1,1,1,1,1,1]
[2,4,5,6,7,8,9,10,1,3]=>[2,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,10,1,2]=>[2,1,1,1,1,1,1,1,1]
[10,8,9,5,6,7,1,2,3,4]=>[4,1,1,1,1,1,1]
[10,8,9,4,5,6,1,2,3,7]=>[4,1,1,1,1,1,1]
[10,7,8,5,6,9,1,2,3,4]=>[4,1,1,1,1,1,1]
[10,7,8,4,5,9,1,2,3,6]=>[4,1,1,1,1,1,1]
[10,6,7,4,5,8,1,2,3,9]=>[4,1,1,1,1,1,1]
[10,7,8,3,4,9,1,2,5,6]=>[4,1,1,1,1,1,1]
[10,6,7,3,4,8,1,2,5,9]=>[4,1,1,1,1,1,1]
[9,8,10,5,6,7,1,2,3,4]=>[4,1,1,1,1,1,1]
[9,8,10,4,5,6,1,2,3,7]=>[4,1,1,1,1,1,1]
[9,7,10,5,6,8,1,2,3,4]=>[4,1,1,1,1,1,1]
[9,7,10,4,5,8,1,2,3,6]=>[4,1,1,1,1,1,1]
[9,6,10,4,5,7,1,2,3,8]=>[4,1,1,1,1,1,1]
[9,7,10,3,4,8,1,2,5,6]=>[4,1,1,1,1,1,1]
[9,6,10,3,4,7,1,2,5,8]=>[4,1,1,1,1,1,1]
[8,7,9,5,6,10,1,2,3,4]=>[4,1,1,1,1,1,1]
[8,7,9,4,5,10,1,2,3,6]=>[4,1,1,1,1,1,1]
[8,6,9,4,5,10,1,2,3,7]=>[4,1,1,1,1,1,1]
[7,6,8,4,5,9,1,2,3,10]=>[4,1,1,1,1,1,1]
[8,7,9,3,4,10,1,2,5,6]=>[4,1,1,1,1,1,1]
[8,6,9,3,4,10,1,2,5,7]=>[4,1,1,1,1,1,1]
[7,6,8,3,4,9,1,2,5,10]=>[4,1,1,1,1,1,1]
[9,6,10,5,7,8,1,2,3,4]=>[4,1,1,1,1,1,1]
[9,6,10,4,7,8,1,2,3,5]=>[4,1,1,1,1,1,1]
[9,5,10,4,6,7,1,2,3,8]=>[4,1,1,1,1,1,1]
[9,6,10,3,7,8,1,2,4,5]=>[4,1,1,1,1,1,1]
[9,5,10,3,6,7,1,2,4,8]=>[4,1,1,1,1,1,1]
[8,6,9,5,7,10,1,2,3,4]=>[4,1,1,1,1,1,1]
[8,6,9,4,7,10,1,2,3,5]=>[4,1,1,1,1,1,1]
[8,5,9,4,6,10,1,2,3,7]=>[4,1,1,1,1,1,1]
[7,5,8,4,6,9,1,2,3,10]=>[4,1,1,1,1,1,1]
[8,6,9,3,7,10,1,2,4,5]=>[4,1,1,1,1,1,1]
[8,5,9,3,6,10,1,2,4,7]=>[4,1,1,1,1,1,1]
[7,5,8,3,6,9,1,2,4,10]=>[4,1,1,1,1,1,1]
[8,4,9,3,5,10,1,2,6,7]=>[4,1,1,1,1,1,1]
[7,4,8,3,5,9,1,2,6,10]=>[4,1,1,1,1,1,1]
[9,6,10,2,7,8,1,3,4,5]=>[4,1,1,1,1,1,1]
[9,5,10,2,6,7,1,3,4,8]=>[4,1,1,1,1,1,1]
[8,6,9,2,7,10,1,3,4,5]=>[4,1,1,1,1,1,1]
[8,5,9,2,6,10,1,3,4,7]=>[4,1,1,1,1,1,1]
[7,5,8,2,6,9,1,3,4,10]=>[4,1,1,1,1,1,1]
[8,4,9,2,5,10,1,3,6,7]=>[4,1,1,1,1,1,1]
[7,4,8,2,5,9,1,3,6,10]=>[4,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,10,9]=>[2,1,1,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[9,1,2,3,4,5,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[2,10,1,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,9,10,8]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,9,10,7]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,9,10,6]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,9,10,5]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,5,6,7,8,9,10,4]=>[2,1,1,1,1,1,1,1,1]
[1,2,4,5,6,7,8,9,10,3]=>[2,1,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,10,2]=>[2,1,1,1,1,1,1,1,1]
[9,10,8,7,6,5,4,3,2,1]=>[9,1]
[9,8,10,7,6,5,4,3,2,1]=>[9,1]
[9,8,7,10,6,5,4,3,2,1]=>[9,1]
[9,8,7,6,10,5,4,3,2,1]=>[9,1]
[9,8,7,6,5,10,4,3,2,1]=>[9,1]
[9,8,7,6,5,4,10,3,2,1]=>[9,1]
[9,8,7,6,5,4,3,10,2,1]=>[9,1]
[9,8,7,6,5,4,3,2,10,1]=>[9,1]
[9,8,7,6,5,4,3,2,1,10]=>[9,1]
[10,1,2,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[10,1,2,3,4,5,6,9,7,8]=>[3,1,1,1,1,1,1,1]
[10,1,2,3,4,5,9,6,7,8]=>[3,1,1,1,1,1,1,1]
[9,1,2,3,4,10,5,6,7,8]=>[2,2,1,1,1,1,1,1]
[10,1,2,3,9,4,5,6,7,8]=>[3,1,1,1,1,1,1,1]
[10,1,2,9,3,4,5,6,7,8]=>[3,1,1,1,1,1,1,1]
[9,1,10,2,3,4,5,6,7,8]=>[2,2,1,1,1,1,1,1]
[10,9,1,2,3,4,5,6,7,8]=>[3,1,1,1,1,1,1,1]
[8,1,2,3,4,5,6,9,10,7]=>[2,2,1,1,1,1,1,1]
[7,1,2,3,4,5,10,9,6,8]=>[3,2,1,1,1,1,1]
[6,1,2,3,4,10,9,5,7,8]=>[3,2,1,1,1,1,1]
[5,1,2,3,9,10,4,6,7,8]=>[2,2,1,1,1,1,1,1]
[4,1,2,10,9,3,5,6,7,8]=>[3,2,1,1,1,1,1]
[3,1,10,9,2,4,5,6,7,8]=>[3,2,1,1,1,1,1]
[2,9,10,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1,1]
[1,10,9,8,7,6,5,4,3,2]=>[9,1]
[9,8,7,5,6,4,3,2,1,10]=>[8,1,1]
[1,10,9,8,6,7,5,4,3,2]=>[8,1,1]
[10,2,1,3,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[3,2,4,5,6,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[2,4,6,8,10,1,3,5,7,9]=>[2,1,1,1,1,1,1,1,1]
[2,4,6,9,10,1,3,5,7,8]=>[2,1,1,1,1,1,1,1,1]
[2,4,7,8,10,1,3,5,6,9]=>[2,1,1,1,1,1,1,1,1]
[2,4,7,9,10,1,3,5,6,8]=>[2,1,1,1,1,1,1,1,1]
[2,4,8,9,10,1,3,5,6,7]=>[2,1,1,1,1,1,1,1,1]
[2,5,6,8,10,1,3,4,7,9]=>[2,1,1,1,1,1,1,1,1]
[2,5,6,9,10,1,3,4,7,8]=>[2,1,1,1,1,1,1,1,1]
[2,5,7,8,10,1,3,4,6,9]=>[2,1,1,1,1,1,1,1,1]
[2,5,7,9,10,1,3,4,6,8]=>[2,1,1,1,1,1,1,1,1]
[2,5,8,9,10,1,3,4,6,7]=>[2,1,1,1,1,1,1,1,1]
[2,6,7,8,10,1,3,4,5,9]=>[2,1,1,1,1,1,1,1,1]
[2,6,7,9,10,1,3,4,5,8]=>[2,1,1,1,1,1,1,1,1]
[2,6,8,9,10,1,3,4,5,7]=>[2,1,1,1,1,1,1,1,1]
[2,7,8,9,10,1,3,4,5,6]=>[2,1,1,1,1,1,1,1,1]
[3,4,6,8,10,1,2,5,7,9]=>[2,1,1,1,1,1,1,1,1]
[3,4,6,9,10,1,2,5,7,8]=>[2,1,1,1,1,1,1,1,1]
[3,4,7,8,10,1,2,5,6,9]=>[2,1,1,1,1,1,1,1,1]
[3,4,7,9,10,1,2,5,6,8]=>[2,1,1,1,1,1,1,1,1]
[3,4,8,9,10,1,2,5,6,7]=>[2,1,1,1,1,1,1,1,1]
[3,5,6,8,10,1,2,4,7,9]=>[2,1,1,1,1,1,1,1,1]
[3,5,6,9,10,1,2,4,7,8]=>[2,1,1,1,1,1,1,1,1]
[3,5,7,8,10,1,2,4,6,9]=>[2,1,1,1,1,1,1,1,1]
[3,5,7,9,10,1,2,4,6,8]=>[2,1,1,1,1,1,1,1,1]
[3,5,8,9,10,1,2,4,6,7]=>[2,1,1,1,1,1,1,1,1]
[3,6,7,8,10,1,2,4,5,9]=>[2,1,1,1,1,1,1,1,1]
[3,6,7,9,10,1,2,4,5,8]=>[2,1,1,1,1,1,1,1,1]
[3,6,8,9,10,1,2,4,5,7]=>[2,1,1,1,1,1,1,1,1]
[3,7,8,9,10,1,2,4,5,6]=>[2,1,1,1,1,1,1,1,1]
[4,5,6,8,10,1,2,3,7,9]=>[2,1,1,1,1,1,1,1,1]
[4,5,6,9,10,1,2,3,7,8]=>[2,1,1,1,1,1,1,1,1]
[4,5,7,8,10,1,2,3,6,9]=>[2,1,1,1,1,1,1,1,1]
[4,5,7,9,10,1,2,3,6,8]=>[2,1,1,1,1,1,1,1,1]
[4,5,8,9,10,1,2,3,6,7]=>[2,1,1,1,1,1,1,1,1]
[4,6,7,8,10,1,2,3,5,9]=>[2,1,1,1,1,1,1,1,1]
[4,6,7,9,10,1,2,3,5,8]=>[2,1,1,1,1,1,1,1,1]
[4,6,8,9,10,1,2,3,5,7]=>[2,1,1,1,1,1,1,1,1]
[4,7,8,9,10,1,2,3,5,6]=>[2,1,1,1,1,1,1,1,1]
[5,6,7,8,10,1,2,3,4,9]=>[2,1,1,1,1,1,1,1,1]
[5,6,7,9,10,1,2,3,4,8]=>[2,1,1,1,1,1,1,1,1]
[5,6,8,9,10,1,2,3,4,7]=>[2,1,1,1,1,1,1,1,1]
[5,7,8,9,10,1,2,3,4,6]=>[2,1,1,1,1,1,1,1,1]
[3,1,4,5,6,7,8,9,10,2]=>[2,2,1,1,1,1,1,1]
[10,3,4,5,6,7,8,1,2,9]=>[3,1,1,1,1,1,1,1]
[10,1,4,5,6,7,8,9,2,3]=>[3,1,1,1,1,1,1,1]
[2,10,4,5,6,7,8,1,3,9]=>[3,1,1,1,1,1,1,1]
[8,3,4,5,6,7,1,10,2,9]=>[3,2,1,1,1,1,1]
[3,1,10,5,6,7,8,9,2,4]=>[3,2,1,1,1,1,1]
[9,1,4,5,6,7,8,2,10,3]=>[3,2,1,1,1,1,1]
[9,10,1,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1,1]
[8,9,10,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1]
[10,8,9,1,2,3,4,5,6,7]=>[3,1,1,1,1,1,1,1]
[10,9,8,1,2,3,4,5,6,7]=>[4,1,1,1,1,1,1]
[7,8,9,10,1,2,3,4,5,6]=>[2,1,1,1,1,1,1,1,1]
[10,7,8,9,1,2,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[9,10,7,8,1,2,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[10,9,7,8,1,2,3,4,5,6]=>[4,1,1,1,1,1,1]
[10,9,8,7,1,2,3,4,5,6]=>[5,1,1,1,1,1]
[10,6,7,8,9,1,2,3,4,5]=>[3,1,1,1,1,1,1,1]
[9,10,6,7,8,1,2,3,4,5]=>[3,1,1,1,1,1,1,1]
[10,9,6,7,8,1,2,3,4,5]=>[4,1,1,1,1,1,1]
[10,8,9,6,7,1,2,3,4,5]=>[4,1,1,1,1,1,1]
[10,9,8,6,7,1,2,3,4,5]=>[5,1,1,1,1,1]
[10,9,8,7,6,1,2,3,4,5]=>[6,1,1,1,1]
[9,10,5,6,7,8,1,2,3,4]=>[3,1,1,1,1,1,1,1]
[10,9,5,6,7,8,1,2,3,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,7,1,2,3,4]=>[3,1,1,1,1,1,1,1]
[10,9,8,5,6,7,1,2,3,4]=>[5,1,1,1,1,1]
[9,10,7,8,5,6,1,2,3,4]=>[4,1,1,1,1,1,1]
[10,9,7,8,5,6,1,2,3,4]=>[5,1,1,1,1,1]
[10,9,8,7,5,6,1,2,3,4]=>[6,1,1,1,1]
[10,9,8,7,6,5,1,2,3,4]=>[7,1,1,1]
[10,7,8,9,4,5,6,1,2,3]=>[4,1,1,1,1,1,1]
[9,10,7,8,4,5,6,1,2,3]=>[4,1,1,1,1,1,1]
[10,9,7,8,4,5,6,1,2,3]=>[5,1,1,1,1,1]
[10,9,8,7,4,5,6,1,2,3]=>[6,1,1,1,1]
[10,8,9,6,7,4,5,1,2,3]=>[5,1,1,1,1,1]
[10,9,8,6,7,4,5,1,2,3]=>[6,1,1,1,1]
[10,9,8,7,6,4,5,1,2,3]=>[7,1,1,1]
[10,9,8,7,6,5,4,1,2,3]=>[8,1,1]
[9,10,7,8,5,6,3,4,1,2]=>[5,1,1,1,1,1]
[10,9,7,8,5,6,3,4,1,2]=>[6,1,1,1,1]
[10,9,8,7,5,6,3,4,1,2]=>[7,1,1,1]
[10,9,8,7,6,5,3,4,1,2]=>[8,1,1]
[10,9,8,7,6,5,4,3,1,2]=>[9,1]
[8,9,7,6,5,4,3,2,1,10]=>[8,1,1]
[9,1,2,3,4,5,6,7,8,10]=>[2,1,1,1,1,1,1,1,1]
[1,10,2,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[8,9,1,2,3,4,5,6,7,10]=>[2,1,1,1,1,1,1,1,1]
[1,9,10,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[2,4,1,6,3,5,8,7,10,9]=>[2,2,2,2,1,1]
[2,4,1,6,3,8,5,7,10,9]=>[2,2,2,2,1,1]
[2,4,1,6,3,8,5,10,7,9]=>[2,2,2,2,1,1]
[2,4,1,6,3,8,5,9,7,10]=>[2,2,2,2,1,1]
[2,4,1,6,3,7,5,9,8,10]=>[2,2,2,2,1,1]
[2,4,1,5,3,7,6,9,8,10]=>[2,2,2,2,1,1]
[2,3,1,5,4,7,6,9,8,10]=>[2,2,2,2,1,1]
[1,3,2,5,4,7,6,9,8,10]=>[2,2,2,2,1,1]
[3,4,1,2,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[3,2,1,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[4,5,6,1,2,3,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[4,2,5,1,3,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[4,3,2,1,5,6,7,8,9,10]=>[4,1,1,1,1,1,1]
[5,6,7,8,1,2,3,4,9,10]=>[2,1,1,1,1,1,1,1,1]
[5,2,6,7,1,3,4,8,9,10]=>[3,1,1,1,1,1,1,1]
[5,6,3,4,1,2,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[5,3,2,6,1,4,7,8,9,10]=>[4,1,1,1,1,1,1]
[5,4,3,2,1,6,7,8,9,10]=>[5,1,1,1,1,1]
[6,2,7,8,9,1,3,4,5,10]=>[3,1,1,1,1,1,1,1]
[6,7,3,4,8,1,2,5,9,10]=>[3,1,1,1,1,1,1,1]
[6,3,2,7,8,1,4,5,9,10]=>[4,1,1,1,1,1,1]
[6,4,7,2,5,1,3,8,9,10]=>[4,1,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9,10]=>[5,1,1,1,1,1]
[6,5,4,3,2,1,7,8,9,10]=>[6,1,1,1,1]
[7,8,3,4,9,10,1,2,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,4,5,6,1,2,3,10]=>[3,1,1,1,1,1,1,1]
[7,4,3,2,8,9,1,5,6,10]=>[5,1,1,1,1,1]
[7,8,5,6,3,4,1,2,9,10]=>[4,1,1,1,1,1,1]
[7,5,3,8,2,6,1,4,9,10]=>[5,1,1,1,1,1]
[7,5,4,3,2,8,1,6,9,10]=>[6,1,1,1,1]
[7,6,5,4,3,2,1,8,9,10]=>[7,1,1,1]
[8,5,9,10,2,6,7,1,3,4]=>[4,1,1,1,1,1,1]
[8,5,3,9,2,6,10,1,4,7]=>[5,1,1,1,1,1]
[8,6,9,4,7,2,5,1,3,10]=>[5,1,1,1,1,1]
[8,6,4,3,9,2,7,1,5,10]=>[6,1,1,1,1]
[8,6,5,4,3,2,9,1,7,10]=>[7,1,1,1]
[8,7,6,5,4,3,2,1,9,10]=>[8,1,1]
[9,7,5,4,3,10,2,8,1,6]=>[7,1,1,1]
[2,3,1,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,1,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,1,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,1,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,1,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,1,9,10]=>[2,1,1,1,1,1,1,1,1]
[3,4,1,5,6,7,8,9,10,2]=>[2,2,1,1,1,1,1,1]
[3,4,5,1,6,7,8,9,10,2]=>[2,2,1,1,1,1,1,1]
[3,4,5,6,1,7,8,9,10,2]=>[2,2,1,1,1,1,1,1]
[3,4,5,6,7,1,8,9,10,2]=>[2,2,1,1,1,1,1,1]
[3,4,5,6,7,8,1,9,10,2]=>[2,2,1,1,1,1,1,1]
[3,4,5,6,7,8,9,1,10,2]=>[2,2,1,1,1,1,1,1]
[9,8,7,6,5,4,3,1,10,2]=>[8,2]
[8,10,7,6,5,4,3,2,1,9]=>[8,1,1]
[1,8,7,6,5,4,3,10,9,2]=>[7,2,1]
[8,10,9,7,6,5,4,3,2,1]=>[9,1]
[7,10,9,8,6,5,4,3,2,1]=>[9,1]
[6,10,9,8,7,5,4,3,2,1]=>[9,1]
[5,10,9,8,7,6,4,3,2,1]=>[9,1]
[4,10,9,8,7,6,5,3,2,1]=>[9,1]
[3,10,9,8,7,6,5,4,2,1]=>[9,1]
[2,10,9,8,7,6,5,4,3,1]=>[9,1]
[1,2,3,4,5,6,7,10,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,10,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,10,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,10,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,10,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,2,10,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[8,9,10,7,6,5,4,3,2,1]=>[8,1,1]
[7,8,9,10,6,5,4,3,2,1]=>[7,1,1,1]
[5,4,3,2,1,10,9,8,7,6]=>[5,5]
[5,6,7,8,9,10,4,3,2,1]=>[5,1,1,1,1,1]
[4,7,3,9,6,2,10,8,5,1]=>[4,3,2,1]
[4,5,6,7,8,9,10,3,2,1]=>[4,1,1,1,1,1,1]
[3,4,5,6,7,8,9,10,2,1]=>[3,1,1,1,1,1,1,1]
[7,8,10,9,5,6,3,4,1,2]=>[5,1,1,1,1,1]
[9,10,5,6,8,7,3,4,1,2]=>[5,1,1,1,1,1]
[5,8,10,6,9,7,3,4,1,2]=>[5,1,1,1,1,1]
[5,6,7,10,9,8,3,4,1,2]=>[5,1,1,1,1,1]
[9,10,7,8,3,4,6,5,1,2]=>[5,1,1,1,1,1]
[7,8,10,9,3,4,6,5,1,2]=>[5,1,1,1,1,1]
[9,10,3,6,8,4,7,5,1,2]=>[5,1,1,1,1,1]
[3,8,10,6,9,4,7,5,1,2]=>[5,1,1,1,1,1]
[3,6,7,10,9,4,8,5,1,2]=>[5,1,1,1,1,1]
[9,10,3,4,5,8,7,6,1,2]=>[5,1,1,1,1,1]
[3,8,10,4,5,9,7,6,1,2]=>[5,1,1,1,1,1]
[3,4,7,10,5,9,8,6,1,2]=>[5,1,1,1,1,1]
[3,4,5,6,10,9,8,7,1,2]=>[5,1,1,1,1,1]
[9,10,7,8,5,6,1,2,4,3]=>[5,1,1,1,1,1]
[7,8,10,9,5,6,1,2,4,3]=>[5,1,1,1,1,1]
[9,10,5,6,8,7,1,2,4,3]=>[5,1,1,1,1,1]
[5,8,10,6,9,7,1,2,4,3]=>[5,1,1,1,1,1]
[5,6,7,10,9,8,1,2,4,3]=>[5,1,1,1,1,1]
[9,10,7,8,1,4,6,2,5,3]=>[5,1,1,1,1,1]
[7,8,10,9,1,4,6,2,5,3]=>[5,1,1,1,1,1]
[9,10,1,6,8,4,7,2,5,3]=>[5,1,1,1,1,1]
[1,8,10,6,9,4,7,2,5,3]=>[5,1,1,1,1,1]
[1,6,7,10,9,4,8,2,5,3]=>[5,1,1,1,1,1]
[9,10,1,4,5,8,7,2,6,3]=>[5,1,1,1,1,1]
[1,8,10,4,5,9,7,2,6,3]=>[5,1,1,1,1,1]
[1,4,7,10,5,9,8,2,6,3]=>[5,1,1,1,1,1]
[1,4,5,6,10,9,8,2,7,3]=>[5,1,1,1,1,1]
[9,10,7,8,1,2,3,6,5,4]=>[5,1,1,1,1,1]
[7,8,10,9,1,2,3,6,5,4]=>[5,1,1,1,1,1]
[9,10,1,6,8,2,3,7,5,4]=>[5,1,1,1,1,1]
[1,8,10,6,9,2,3,7,5,4]=>[5,1,1,1,1,1]
[1,6,7,10,9,2,3,8,5,4]=>[5,1,1,1,1,1]
[9,10,1,2,5,8,3,7,6,4]=>[5,1,1,1,1,1]
[1,8,10,2,5,9,3,7,6,4]=>[5,1,1,1,1,1]
[1,2,7,10,5,9,3,8,6,4]=>[5,1,1,1,1,1]
[1,2,5,6,10,9,3,8,7,4]=>[5,1,1,1,1,1]
[9,10,1,2,3,4,8,7,6,5]=>[5,1,1,1,1,1]
[1,8,10,2,3,4,9,7,6,5]=>[5,1,1,1,1,1]
[1,2,7,10,3,4,9,8,6,5]=>[5,1,1,1,1,1]
[1,2,3,6,10,4,9,8,7,5]=>[5,1,1,1,1,1]
[1,2,3,4,5,10,9,8,7,6]=>[5,1,1,1,1,1]
[4,3,2,1,7,6,5,9,8,10]=>[4,3,2,1]
[4,3,1,2,6,5,8,7,10,9]=>[3,2,2,2,1]
[8,7,6,5,4,3,2,10,1,9]=>[8,1,1]
[7,6,5,4,3,10,2,9,1,8]=>[7,1,1,1]
[7,6,5,4,3,2,9,1,8,10]=>[7,1,1,1]
[6,5,4,10,3,9,2,8,1,7]=>[6,1,1,1,1]
[6,5,4,3,9,2,8,1,7,10]=>[6,1,1,1,1]
[6,5,4,3,2,8,10,1,7,9]=>[6,1,1,1,1]
[6,5,4,3,2,8,1,7,9,10]=>[6,1,1,1,1]
[5,10,4,9,3,8,2,7,1,6]=>[5,1,1,1,1,1]
[5,4,9,3,8,2,7,1,6,10]=>[5,1,1,1,1,1]
[5,4,3,8,2,7,10,1,6,9]=>[5,1,1,1,1,1]
[5,4,3,8,2,7,1,6,9,10]=>[5,1,1,1,1,1]
[5,4,3,2,7,9,1,6,8,10]=>[5,1,1,1,1,1]
[5,4,3,2,7,1,6,8,9,10]=>[5,1,1,1,1,1]
[4,8,3,7,2,6,10,1,5,9]=>[4,1,1,1,1,1,1]
[4,8,3,7,2,6,1,5,9,10]=>[4,1,1,1,1,1,1]
[4,3,7,10,2,6,9,1,5,8]=>[4,1,1,1,1,1,1]
[4,3,7,2,6,9,1,5,8,10]=>[4,1,1,1,1,1,1]
[4,3,7,2,6,1,5,8,9,10]=>[4,1,1,1,1,1,1]
[4,3,2,6,8,10,1,5,7,9]=>[4,1,1,1,1,1,1]
[4,3,2,6,8,1,5,7,9,10]=>[4,1,1,1,1,1,1]
[4,3,2,6,1,5,7,8,9,10]=>[4,1,1,1,1,1,1]
[3,6,9,2,5,8,1,4,7,10]=>[3,1,1,1,1,1,1,1]
[3,6,2,5,8,10,1,4,7,9]=>[3,1,1,1,1,1,1,1]
[3,6,2,5,8,1,4,7,9,10]=>[3,1,1,1,1,1,1,1]
[3,6,2,5,1,4,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[3,2,5,7,9,1,4,6,8,10]=>[3,1,1,1,1,1,1,1]
[3,2,5,7,1,4,6,8,9,10]=>[3,1,1,1,1,1,1,1]
[3,2,5,1,4,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[2,4,6,8,1,3,5,7,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,4,6,1,3,5,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,4,1,3,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[9,8,7,6,4,3,2,1,10,5]=>[8,2]
[9,7,6,5,4,3,2,1,10,8]=>[8,2]
[7,8,9,10,4,5,6,2,3,1]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,6,10,2,3,1]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,2,3,6,1]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,10,2,3,6,1]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,2,3,6,10,1]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,10,2,3,6,1]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,2,3,6,10,1]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,6,2,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,6,10,2,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,2,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,10,2,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,2,6,10,1,3]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,10,2,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,2,6,10,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,2,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,10,2,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,2,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,5,2,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,10,2,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,2,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,4,5,9,2,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,2,5,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,4,10,2,5,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,4,2,5,6,10,1,3]=>[4,1,1,1,1,1,1]
[7,8,4,9,10,2,5,6,1,3]=>[4,1,1,1,1,1,1]
[7,8,4,9,2,5,6,10,1,3]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,2,5,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,10,2,5,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,2,5,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,4,2,5,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,8,4,9,10,2,5,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,4,9,2,5,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,4,9,2,5,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,8,4,2,5,9,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,8,4,2,5,9,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,4,8,9,10,2,5,6,1,3]=>[4,1,1,1,1,1,1]
[7,4,8,9,2,5,6,10,1,3]=>[4,1,1,1,1,1,1]
[7,4,8,9,10,2,5,1,3,6]=>[4,1,1,1,1,1,1]
[7,4,8,9,2,5,10,1,3,6]=>[4,1,1,1,1,1,1]
[7,4,8,9,2,5,1,3,6,10]=>[4,1,1,1,1,1,1]
[7,4,8,2,5,9,10,1,3,6]=>[4,1,1,1,1,1,1]
[8,10,7,9,5,6,3,4,1,2]=>[5,1,1,1,1,1]
[9,10,6,8,5,7,3,4,1,2]=>[5,1,1,1,1,1]
[8,10,6,9,5,7,3,4,1,2]=>[5,1,1,1,1,1]
[7,10,6,9,5,8,3,4,1,2]=>[5,1,1,1,1,1]
[9,10,7,8,4,6,3,5,1,2]=>[5,1,1,1,1,1]
[8,10,7,9,4,6,3,5,1,2]=>[5,1,1,1,1,1]
[9,10,6,8,4,7,3,5,1,2]=>[5,1,1,1,1,1]
[8,10,6,9,4,7,3,5,1,2]=>[5,1,1,1,1,1]
[7,10,6,9,4,8,3,5,1,2]=>[5,1,1,1,1,1]
[9,10,5,8,4,7,3,6,1,2]=>[5,1,1,1,1,1]
[8,10,5,9,4,7,3,6,1,2]=>[5,1,1,1,1,1]
[7,10,5,9,4,8,3,6,1,2]=>[5,1,1,1,1,1]
[6,10,5,9,4,8,3,7,1,2]=>[5,1,1,1,1,1]
[9,10,7,8,5,6,2,4,1,3]=>[5,1,1,1,1,1]
[8,10,7,9,5,6,2,4,1,3]=>[5,1,1,1,1,1]
[9,10,6,8,5,7,2,4,1,3]=>[5,1,1,1,1,1]
[8,10,6,9,5,7,2,4,1,3]=>[5,1,1,1,1,1]
[7,10,6,9,5,8,2,4,1,3]=>[5,1,1,1,1,1]
[9,10,7,8,4,6,2,5,1,3]=>[5,1,1,1,1,1]
[8,10,7,9,4,6,2,5,1,3]=>[5,1,1,1,1,1]
[9,10,6,8,4,7,2,5,1,3]=>[5,1,1,1,1,1]
[8,10,6,9,4,7,2,5,1,3]=>[5,1,1,1,1,1]
[7,10,6,9,4,8,2,5,1,3]=>[5,1,1,1,1,1]
[9,10,5,8,4,7,2,6,1,3]=>[5,1,1,1,1,1]
[8,10,5,9,4,7,2,6,1,3]=>[5,1,1,1,1,1]
[7,10,5,9,4,8,2,6,1,3]=>[5,1,1,1,1,1]
[6,10,5,9,4,8,2,7,1,3]=>[5,1,1,1,1,1]
[9,10,7,8,3,6,2,5,1,4]=>[5,1,1,1,1,1]
[8,10,7,9,3,6,2,5,1,4]=>[5,1,1,1,1,1]
[9,10,6,8,3,7,2,5,1,4]=>[5,1,1,1,1,1]
[8,10,6,9,3,7,2,5,1,4]=>[5,1,1,1,1,1]
[7,10,6,9,3,8,2,5,1,4]=>[5,1,1,1,1,1]
[9,10,5,8,3,7,2,6,1,4]=>[5,1,1,1,1,1]
[8,10,5,9,3,7,2,6,1,4]=>[5,1,1,1,1,1]
[7,10,5,9,3,8,2,6,1,4]=>[5,1,1,1,1,1]
[6,10,5,9,3,8,2,7,1,4]=>[5,1,1,1,1,1]
[9,10,4,8,3,7,2,6,1,5]=>[5,1,1,1,1,1]
[8,10,4,9,3,7,2,6,1,5]=>[5,1,1,1,1,1]
[7,10,4,9,3,8,2,6,1,5]=>[5,1,1,1,1,1]
[6,10,4,9,3,8,2,7,1,5]=>[5,1,1,1,1,1]
[3,4,5,6,7,8,9,1,2,10]=>[2,1,1,1,1,1,1,1,1]
[1,4,5,6,7,8,9,10,2,3]=>[2,1,1,1,1,1,1,1,1]
[9,10,7,8,5,6,3,1,4,2]=>[5,2,1,1,1]
[9,10,7,8,5,3,6,1,4,2]=>[5,2,1,1,1]
[9,10,7,5,8,3,6,1,4,2]=>[5,2,1,1,1]
[9,7,10,5,8,3,6,1,4,2]=>[5,2,1,1,1]
[10,7,9,5,8,3,6,1,4,2]=>[6,1,1,1,1]
[10,8,9,5,7,3,6,1,4,2]=>[6,1,1,1,1]
[10,8,9,6,7,3,5,1,4,2]=>[6,1,1,1,1]
[10,8,9,6,7,4,5,1,3,2]=>[6,1,1,1,1]
[7,6,5,4,3,2,1,10,9,8]=>[7,3]
[3,2,1,5,4,7,6,9,8,10]=>[3,2,2,2,1]
[3,1,4,2,6,5,8,7,10,9]=>[2,2,2,2,2]
[3,1,5,2,6,4,8,7,10,9]=>[2,2,2,2,2]
[3,1,5,2,7,4,8,6,10,9]=>[2,2,2,2,2]
[3,1,5,2,7,4,9,6,10,8]=>[2,2,2,2,2]
[3,1,5,2,7,4,9,6,8,10]=>[2,2,2,2,1,1]
[3,1,5,2,7,4,6,9,8,10]=>[2,2,2,2,1,1]
[3,1,5,2,4,7,6,9,8,10]=>[2,2,2,2,1,1]
[3,1,2,5,4,7,6,9,8,10]=>[2,2,2,2,1,1]
[4,5,6,7,8,9,10,1,2,3]=>[2,1,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,2,3,1]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,1,2,3,4]=>[2,1,1,1,1,1,1,1,1]
[5,6,7,8,9,10,2,3,4,1]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,3,4,1,2]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,3,4,2,1]=>[4,1,1,1,1,1,1]
[7,8,9,10,3,4,5,6,1,2]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,3,4,5,6,2,1]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,6,1,2,3]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,4,5,6,3,2,1]=>[5,1,1,1,1,1]
[7,8,9,10,5,6,3,4,1,2]=>[4,1,1,1,1,1,1]
[7,8,9,10,5,6,3,4,2,1]=>[5,1,1,1,1,1]
[7,8,9,10,5,6,4,3,2,1]=>[6,1,1,1,1]
[8,9,10,5,6,7,2,3,4,1]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,7,3,4,1,2]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,7,3,4,2,1]=>[5,1,1,1,1,1]
[8,9,10,5,6,7,4,3,2,1]=>[6,1,1,1,1]
[8,9,10,6,7,4,5,2,3,1]=>[5,1,1,1,1,1]
[8,9,10,6,7,4,5,3,2,1]=>[6,1,1,1,1]
[8,9,10,6,7,5,4,3,2,1]=>[7,1,1,1]
[9,10,7,8,5,6,3,4,2,1]=>[6,1,1,1,1]
[9,10,7,8,5,6,4,3,2,1]=>[7,1,1,1]
[9,10,7,8,6,5,4,3,2,1]=>[8,1,1]
[9,7,5,3,1,10,8,6,4,2]=>[5,5]
[6,1,7,2,8,3,9,4,10,5]=>[2,2,2,2,2]
[6,1,7,2,8,3,9,10,4,5]=>[2,2,2,2,1,1]
[6,1,7,2,8,9,3,4,10,5]=>[2,2,2,2,1,1]
[6,1,7,2,8,9,3,10,4,5]=>[2,2,2,2,1,1]
[6,1,7,2,8,9,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,2,3,9,4,10,5]=>[2,2,2,2,1,1]
[6,1,7,8,2,3,9,10,4,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,2,9,3,4,10,5]=>[2,2,2,2,1,1]
[6,1,7,8,2,9,3,10,4,5]=>[2,2,2,2,1,1]
[6,1,7,8,2,9,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,9,2,3,4,10,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,9,2,3,10,4,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,9,2,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,1,7,8,9,10,2,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,1,2,8,3,9,4,10,5]=>[2,2,2,2,1,1]
[6,7,1,2,8,3,9,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,2,8,9,3,4,10,5]=>[2,2,2,1,1,1,1]
[6,7,1,2,8,9,3,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,2,8,9,10,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,1,8,2,3,9,4,10,5]=>[2,2,2,2,1,1]
[6,7,1,8,2,3,9,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,8,2,9,3,4,10,5]=>[2,2,2,2,1,1]
[6,7,1,8,2,9,3,10,4,5]=>[2,2,2,2,1,1]
[6,7,1,8,2,9,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,8,9,2,3,4,10,5]=>[2,2,2,1,1,1,1]
[6,7,1,8,9,2,3,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,8,9,2,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,7,1,8,9,10,2,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,1,2,3,9,4,10,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,2,3,9,10,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,1,2,9,3,4,10,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,2,9,3,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,2,9,10,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,1,9,2,3,4,10,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,9,2,3,10,4,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,9,2,10,3,4,5]=>[2,2,2,1,1,1,1]
[6,7,8,1,9,10,2,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,9,1,2,3,4,10,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,9,1,2,3,10,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,9,1,2,10,3,4,5]=>[2,2,1,1,1,1,1,1]
[6,7,8,9,1,10,2,3,4,5]=>[2,2,1,1,1,1,1,1]
[10,9,8,7,6,5,4,2,1,3]=>[9,1]
[10,9,8,7,6,4,3,2,1,5]=>[9,1]
[10,9,8,6,5,4,3,2,1,7]=>[9,1]
[10,8,7,6,5,4,3,2,1,9]=>[9,1]
[10,3,1,2,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,4,1,2,3,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[5,10,1,2,3,4,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[10,6,1,2,3,4,5,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,7,1,2,3,4,5,6,8,9]=>[3,1,1,1,1,1,1,1]
[8,10,1,2,3,4,5,6,7,9]=>[2,1,1,1,1,1,1,1,1]
[2,3,10,1,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[4,3,1,10,2,5,6,7,8,9]=>[3,2,1,1,1,1,1]
[5,4,1,2,10,3,6,7,8,9]=>[3,2,1,1,1,1,1]
[5,6,1,2,3,10,4,7,8,9]=>[2,2,1,1,1,1,1,1]
[7,6,1,2,3,4,10,5,8,9]=>[3,2,1,1,1,1,1]
[8,7,1,2,3,4,5,10,6,9]=>[3,2,1,1,1,1,1]
[8,9,1,2,3,4,5,6,10,7]=>[2,2,1,1,1,1,1,1]
[10,9,8,7,6,5,2,4,1,3]=>[8,1,1]
[10,9,8,7,3,6,2,5,1,4]=>[7,1,1,1]
[10,9,8,7,6,3,5,1,2,4]=>[7,1,1,1]
[10,9,4,8,3,7,2,6,1,5]=>[6,1,1,1,1]
[10,9,8,4,7,3,6,1,2,5]=>[6,1,1,1,1]
[10,9,8,7,2,4,6,1,3,5]=>[6,1,1,1,1]
[10,9,8,7,4,6,1,2,3,5]=>[6,1,1,1,1]
[10,5,9,4,8,3,7,1,2,6]=>[5,1,1,1,1,1]
[10,9,5,8,2,4,7,1,3,6]=>[5,1,1,1,1,1]
[10,9,5,8,4,7,1,2,3,6]=>[5,1,1,1,1,1]
[10,9,8,3,5,7,1,2,4,6]=>[5,1,1,1,1,1]
[10,9,8,5,7,1,2,3,4,6]=>[5,1,1,1,1,1]
[6,10,5,9,2,4,8,1,3,7]=>[4,1,1,1,1,1,1]
[6,10,5,9,4,8,1,2,3,7]=>[4,1,1,1,1,1,1]
[10,3,6,9,2,5,8,1,4,7]=>[4,1,1,1,1,1,1]
[10,6,9,3,5,8,1,2,4,7]=>[4,1,1,1,1,1,1]
[10,6,9,5,8,1,2,3,4,7]=>[4,1,1,1,1,1,1]
[10,9,2,4,6,8,1,3,5,7]=>[4,1,1,1,1,1,1]
[10,9,4,6,8,1,2,3,5,7]=>[4,1,1,1,1,1,1]
[10,9,6,8,1,2,3,4,5,7]=>[4,1,1,1,1,1,1]
[4,7,10,3,6,9,1,2,5,8]=>[3,1,1,1,1,1,1,1]
[7,10,2,4,6,9,1,3,5,8]=>[3,1,1,1,1,1,1,1]
[7,10,4,6,9,1,2,3,5,8]=>[3,1,1,1,1,1,1,1]
[7,10,6,9,1,2,3,4,5,8]=>[3,1,1,1,1,1,1,1]
[10,3,5,7,9,1,2,4,6,8]=>[3,1,1,1,1,1,1,1]
[10,5,7,9,1,2,3,4,6,8]=>[3,1,1,1,1,1,1,1]
[10,7,9,1,2,3,4,5,6,8]=>[3,1,1,1,1,1,1,1]
[4,6,8,10,1,2,3,5,7,9]=>[2,1,1,1,1,1,1,1,1]
[6,8,10,1,2,3,4,5,7,9]=>[2,1,1,1,1,1,1,1,1]
[10,7,6,5,4,3,2,1,9,8]=>[8,2]
[8,7,6,5,4,3,2,10,9,1]=>[8,2]
[9,10,5,6,7,8,3,4,1,2]=>[4,1,1,1,1,1,1]
[5,8,9,6,7,10,3,4,1,2]=>[4,1,1,1,1,1,1]
[9,10,7,8,3,4,5,6,1,2]=>[4,1,1,1,1,1,1]
[9,10,3,6,7,4,5,8,1,2]=>[4,1,1,1,1,1,1]
[3,8,9,6,7,4,5,10,1,2]=>[4,1,1,1,1,1,1]
[3,6,7,8,9,4,5,10,1,2]=>[3,1,1,1,1,1,1,1]
[9,10,3,4,5,6,7,8,1,2]=>[3,1,1,1,1,1,1,1]
[3,8,9,4,5,6,7,10,1,2]=>[3,1,1,1,1,1,1,1]
[3,4,7,8,5,6,9,10,1,2]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,5,6,1,2,3,4]=>[3,1,1,1,1,1,1,1]
[5,8,9,6,7,10,1,2,3,4]=>[3,1,1,1,1,1,1,1]
[9,10,7,8,1,4,5,2,3,6]=>[4,1,1,1,1,1,1]
[7,8,9,10,1,4,5,2,3,6]=>[3,1,1,1,1,1,1,1]
[9,10,1,6,7,4,5,2,3,8]=>[4,1,1,1,1,1,1]
[1,8,9,6,7,4,5,2,3,10]=>[4,1,1,1,1,1,1]
[1,6,7,8,9,4,5,2,3,10]=>[3,1,1,1,1,1,1,1]
[9,10,1,4,5,6,7,2,3,8]=>[3,1,1,1,1,1,1,1]
[1,8,9,4,5,6,7,2,3,10]=>[3,1,1,1,1,1,1,1]
[1,4,7,8,5,6,9,2,3,10]=>[3,1,1,1,1,1,1,1]
[1,4,5,6,7,8,9,2,3,10]=>[2,1,1,1,1,1,1,1,1]
[9,10,1,6,7,2,3,4,5,8]=>[3,1,1,1,1,1,1,1]
[1,8,9,6,7,2,3,4,5,10]=>[3,1,1,1,1,1,1,1]
[1,6,7,8,9,2,3,4,5,10]=>[2,1,1,1,1,1,1,1,1]
[9,10,1,2,5,6,3,4,7,8]=>[3,1,1,1,1,1,1,1]
[1,8,9,2,5,6,3,4,7,10]=>[3,1,1,1,1,1,1,1]
[1,2,7,8,5,6,3,4,9,10]=>[3,1,1,1,1,1,1,1]
[1,2,5,6,7,8,3,4,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,8,9,2,3,4,5,6,7,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,7,8,3,4,5,6,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,6,7,4,5,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[9,8,7,6,4,5,3,2,1,10]=>[8,1,1]
[8,7,9,6,5,4,3,2,1,10]=>[8,1,1]
[8,7,6,9,5,4,3,2,1,10]=>[8,1,1]
[8,7,6,5,10,4,3,2,1,9]=>[8,1,1]
[8,7,6,5,4,9,3,2,1,10]=>[8,1,1]
[8,7,6,5,4,3,9,2,1,10]=>[8,1,1]
[7,10,9,6,5,4,3,2,1,8]=>[8,1,1]
[8,6,9,10,5,4,3,2,1,7]=>[7,1,1,1]
[8,7,5,9,10,4,3,2,1,6]=>[7,1,1,1]
[8,7,6,4,10,9,3,2,1,5]=>[7,2,1]
[8,7,6,5,3,9,10,2,1,4]=>[7,1,1,1]
[8,7,6,5,4,2,9,10,1,3]=>[7,1,1,1]
[8,7,6,5,4,3,1,10,9,2]=>[7,3]
[2,3,4,5,6,7,10,1,8,9]=>[2,1,1,1,1,1,1,1,1]
[2,10,9,8,7,6,5,4,1,3]=>[8,1,1]
[9,1,10,8,7,6,5,4,3,2]=>[8,2]
[9,1,2,3,4,5,6,10,7,8]=>[2,2,1,1,1,1,1,1]
[9,2,1,8,7,6,5,4,3,10]=>[7,2,1]
[3,2,9,8,7,6,5,4,1,10]=>[7,2,1]
[9,3,1,8,7,6,5,4,10,2]=>[7,2,1]
[9,2,10,1,7,6,5,4,3,8]=>[6,2,1,1]
[4,2,9,8,7,6,5,10,1,3]=>[6,2,1,1]
[3,10,2,8,7,6,5,4,1,9]=>[7,1,1,1]
[9,8,7,6,5,4,3,1,2,10]=>[8,1,1]
[1,10,9,8,7,6,5,4,2,3]=>[8,1,1]
[1,2,10,9,8,7,6,5,4,3]=>[8,1,1]
[3,2,1,10,9,8,7,6,5,4]=>[7,3]
[1,2,3,10,9,8,7,6,5,4]=>[7,1,1,1]
[1,2,3,4,10,9,8,7,6,5]=>[6,1,1,1,1]
[1,2,3,4,5,6,10,9,8,7]=>[4,1,1,1,1,1,1]
[1,2,3,4,5,6,7,10,9,8]=>[3,1,1,1,1,1,1,1]
[10,1,9,8,7,6,5,4,3,2]=>[9,1]
[8,1,10,9,7,6,5,4,3,2]=>[8,2]
[7,1,10,9,8,6,5,4,3,2]=>[8,2]
[6,1,10,9,8,7,5,4,3,2]=>[8,2]
[5,1,10,9,8,7,6,4,3,2]=>[8,2]
[4,1,10,9,8,7,6,5,3,2]=>[8,2]
[3,1,10,9,8,7,6,5,4,2]=>[8,2]
[10,1,2,3,4,5,6,7,9,8]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,10,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,6,5,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[9,7,10,5,8,3,6,2,4,1]=>[6,1,1,1,1]
[2,10,9,8,7,1,6,5,4,3]=>[8,1,1]
[2,10,1,9,8,7,6,5,4,3]=>[8,1,1]
[10,2,1,4,3,6,5,8,7,9]=>[3,2,2,2,1]
[10,2,1,4,3,6,5,7,9,8]=>[3,2,2,2,1]
[10,2,1,4,3,5,7,8,6,9]=>[3,2,2,1,1,1]
[10,2,1,4,3,5,7,6,9,8]=>[3,2,2,2,1]
[10,2,1,4,3,5,6,8,9,7]=>[3,2,2,1,1,1]
[10,2,1,3,5,6,4,8,7,9]=>[3,2,2,1,1,1]
[10,2,1,3,5,6,4,7,9,8]=>[3,2,2,1,1,1]
[10,2,1,3,5,4,7,8,6,9]=>[3,2,2,1,1,1]
[10,2,1,3,5,4,7,6,9,8]=>[3,2,2,2,1]
[10,2,1,3,5,4,6,8,9,7]=>[3,2,2,1,1,1]
[10,2,1,3,4,6,7,8,5,9]=>[3,2,1,1,1,1,1]
[10,2,1,3,4,6,7,5,9,8]=>[3,2,2,1,1,1]
[10,2,1,3,4,6,5,8,9,7]=>[3,2,2,1,1,1]
[10,2,1,3,4,5,7,8,9,6]=>[3,2,1,1,1,1,1]
[10,1,3,4,2,6,5,8,7,9]=>[3,2,2,1,1,1]
[10,1,3,4,2,6,5,7,9,8]=>[3,2,2,1,1,1]
[10,1,3,4,2,5,7,8,6,9]=>[3,2,1,1,1,1,1]
[10,1,3,4,2,5,7,6,9,8]=>[3,2,2,1,1,1]
[10,1,3,4,2,5,6,8,9,7]=>[3,2,1,1,1,1,1]
[10,1,3,2,5,6,4,8,7,9]=>[3,2,2,1,1,1]
[10,1,3,2,5,6,4,7,9,8]=>[3,2,2,1,1,1]
[10,1,3,2,5,4,7,8,6,9]=>[3,2,2,1,1,1]
[10,1,3,2,5,4,7,6,9,8]=>[3,2,2,2,1]
[10,1,3,2,5,4,6,8,9,7]=>[3,2,2,1,1,1]
[10,1,3,2,4,6,7,8,5,9]=>[3,2,1,1,1,1,1]
[10,1,3,2,4,6,7,5,9,8]=>[3,2,2,1,1,1]
[10,1,3,2,4,6,5,8,9,7]=>[3,2,2,1,1,1]
[10,1,3,2,4,5,7,8,9,6]=>[3,2,1,1,1,1,1]
[10,1,2,4,5,6,3,8,7,9]=>[3,2,1,1,1,1,1]
[10,1,2,4,5,6,3,7,9,8]=>[3,2,1,1,1,1,1]
[10,1,2,4,5,3,7,8,6,9]=>[3,2,1,1,1,1,1]
[10,1,2,4,5,3,7,6,9,8]=>[3,2,2,1,1,1]
[10,1,2,4,5,3,6,8,9,7]=>[3,2,1,1,1,1,1]
[10,1,2,4,3,6,7,8,5,9]=>[3,2,1,1,1,1,1]
[10,1,2,4,3,6,7,5,9,8]=>[3,2,2,1,1,1]
[10,1,2,4,3,6,5,8,9,7]=>[3,2,2,1,1,1]
[10,1,2,4,3,5,7,8,9,6]=>[3,2,1,1,1,1,1]
[10,1,2,3,5,6,7,8,4,9]=>[3,1,1,1,1,1,1,1]
[10,1,2,3,5,6,7,4,9,8]=>[3,2,1,1,1,1,1]
[10,1,2,3,5,6,4,8,9,7]=>[3,2,1,1,1,1,1]
[10,1,2,3,5,4,7,8,9,6]=>[3,2,1,1,1,1,1]
[10,1,2,3,4,6,7,8,9,5]=>[3,1,1,1,1,1,1,1]
[6,7,8,9,1,2,3,4,5,10]=>[2,1,1,1,1,1,1,1,1]
[1,7,8,9,10,2,3,4,5,6]=>[2,1,1,1,1,1,1,1,1]
[5,6,7,8,9,1,2,3,4,10]=>[2,1,1,1,1,1,1,1,1]
[1,6,7,8,9,10,2,3,4,5]=>[2,1,1,1,1,1,1,1,1]
[1,2,4,3,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,4,6,8,10,9,7,5,3]=>[5,1,1,1,1,1]
[2,4,1,5,6,7,8,9,10,3]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,7,9,1,10,8]=>[2,2,1,1,1,1,1,1]
[2,3,5,1,6,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,8,1,9,10,7]=>[2,2,1,1,1,1,1,1]
[2,3,4,6,1,7,8,9,10,5]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,7,1,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[4,1,2,5,6,7,8,9,10,3]=>[2,2,1,1,1,1,1,1]
[4,3,1,5,6,7,8,10,2,9]=>[3,2,1,1,1,1,1]
[2,6,1,5,3,7,8,9,10,4]=>[3,2,1,1,1,1,1]
[5,3,4,1,6,7,9,2,10,8]=>[3,2,2,1,1,1]
[2,3,8,1,6,7,4,9,10,5]=>[3,2,1,1,1,1,1]
[6,3,4,5,1,8,2,9,10,7]=>[3,2,2,1,1,1]
[2,3,4,10,1,7,8,9,5,6]=>[3,1,1,1,1,1,1,1]
[9,2,1,3,4,5,6,7,8,10]=>[3,1,1,1,1,1,1,1]
[8,7,2,4,6,10,1,3,5,9]=>[4,1,1,1,1,1,1]
[2,10,7,9,4,6,8,1,3,5]=>[4,1,1,1,1,1,1]
[6,5,2,4,8,10,1,3,7,9]=>[4,1,1,1,1,1,1]
[2,8,5,7,4,6,10,1,3,9]=>[4,1,1,1,1,1,1]
[10,5,2,4,7,9,6,8,1,3]=>[4,2,1,1,1,1]
[10,9,2,8,5,7,4,6,1,3]=>[6,1,1,1,1]
[8,7,6,5,2,4,10,1,3,9]=>[6,1,1,1,1]
[10,7,2,6,5,9,4,8,1,3]=>[6,1,1,1,1]
[6,10,5,9,8,7,2,4,1,3]=>[6,1,1,1,1]
[4,10,3,9,2,6,8,1,5,7]=>[4,1,1,1,1,1,1]
[4,3,10,7,9,2,6,8,1,5]=>[4,2,1,1,1,1]
[3,6,2,5,4,8,10,1,7,9]=>[4,1,1,1,1,1,1]
[3,6,10,2,5,9,4,8,1,7]=>[4,1,1,1,1,1,1]
[3,5,8,2,4,7,6,10,1,9]=>[4,1,1,1,1,1,1]
[3,5,7,10,2,4,6,9,8,1]=>[4,1,1,1,1,1,1]
[10,9,3,5,8,2,4,7,6,1]=>[6,1,1,1,1]
[8,7,3,6,2,5,4,10,1,9]=>[6,1,1,1,1]
[7,6,3,5,10,2,4,9,8,1]=>[5,2,1,1,1]
[3,6,10,9,8,2,5,7,4,1]=>[6,1,1,1,1]
[10,9,8,7,3,6,2,5,4,1]=>[8,1,1]
[5,4,3,8,2,7,6,10,1,9]=>[5,2,1,1,1]
[5,4,3,7,10,2,6,9,8,1]=>[5,2,1,1,1]
[5,10,4,9,3,8,2,7,6,1]=>[6,1,1,1,1]
[4,8,3,7,6,5,2,10,1,9]=>[6,1,1,1,1]
[4,7,3,6,5,10,2,9,8,1]=>[5,2,1,1,1]
[4,6,10,3,5,9,8,7,2,1]=>[6,1,1,1,1]
[10,9,4,8,3,7,6,5,2,1]=>[8,1,1]
[7,6,5,4,3,10,2,9,8,1]=>[7,2,1]
[6,5,4,10,3,9,8,7,2,1]=>[6,3,1]
[5,10,4,9,8,7,6,3,2,1]=>[8,1,1]
[9,2,3,4,5,6,7,8,1,10]=>[3,1,1,1,1,1,1,1]
[1,10,3,4,5,6,7,8,9,2]=>[3,1,1,1,1,1,1,1]
[1,10,9,4,5,6,7,8,3,2]=>[5,1,1,1,1,1]
[8,1,2,3,4,5,6,7,10,9]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,7,9,8,1,10]=>[3,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,10,9,2]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,6,10,8,9,7]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,10,7,8,9,6]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,10,6,7,8,9,5]=>[3,1,1,1,1,1,1,1]
[1,2,3,10,5,6,7,8,9,4]=>[3,1,1,1,1,1,1,1]
[1,2,10,4,5,6,7,8,9,3]=>[3,1,1,1,1,1,1,1]
[10,2,3,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,6,8,5,7,10,9]=>[2,2,1,1,1,1,1,1]
[1,2,3,4,7,5,8,6,10,9]=>[2,2,2,1,1,1,1]
[1,2,3,5,7,4,6,9,8,10]=>[2,2,1,1,1,1,1,1]
[1,2,3,6,4,7,5,9,8,10]=>[2,2,2,1,1,1,1]
[10,9,8,7,5,6,4,3,2,1]=>[9,1]
[2,1,10,9,8,6,7,5,4,3]=>[7,2,1]
[1,9,8,7,6,5,4,3,2,10]=>[8,1,1]
[2,8,9,10,1,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1]
[8,1,9,2,10,3,4,5,6,7]=>[2,2,2,1,1,1,1]
[7,1,8,2,9,3,10,4,5,6]=>[2,2,2,2,1,1]
[5,1,6,2,7,3,8,4,10,9]=>[2,2,2,2,2]
[4,1,5,2,6,3,8,7,10,9]=>[2,2,2,2,2]
[2,1,3,4,5,6,7,9,10,8]=>[2,2,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,10,9]=>[2,2,1,1,1,1,1,1]
[7,1,2,3,4,5,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[6,1,2,3,4,7,8,9,10,5]=>[2,2,1,1,1,1,1,1]
[5,1,2,3,6,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[9,7,5,4,3,2,1,10,8,6]=>[7,3]
[7,5,3,1,8,6,4,2,9,10]=>[4,4,1,1]
[7,4,1,8,5,2,9,6,3,10]=>[3,3,3,1]
[5,3,1,6,4,2,7,8,9,10]=>[3,3,1,1,1,1]
[5,1,6,2,7,3,8,4,9,10]=>[2,2,2,2,1,1]
[4,1,5,2,6,3,7,8,9,10]=>[2,2,2,1,1,1,1]
[3,1,4,2,5,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]
[1,9,2,3,4,5,6,7,8,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,9,8,10]=>[2,1,1,1,1,1,1,1,1]
[10,3,4,5,6,7,8,9,1,2]=>[3,1,1,1,1,1,1,1]
[9,3,4,5,6,7,8,1,10,2]=>[3,2,1,1,1,1,1]
[8,3,4,5,6,7,1,9,10,2]=>[3,2,1,1,1,1,1]
[7,3,4,5,6,1,8,9,10,2]=>[3,2,1,1,1,1,1]
[6,3,4,5,1,7,8,9,10,2]=>[3,2,1,1,1,1,1]
[5,3,4,1,6,7,8,9,10,2]=>[3,2,1,1,1,1,1]
[4,3,1,5,6,7,8,9,10,2]=>[3,2,1,1,1,1,1]
[10,9,4,5,6,7,8,1,2,3]=>[4,1,1,1,1,1,1]
[10,3,8,5,6,7,1,9,2,4]=>[4,2,1,1,1,1]
[10,3,4,7,6,1,8,9,2,5]=>[4,2,1,1,1,1]
[10,3,4,5,1,7,8,9,2,6]=>[3,2,1,1,1,1,1]
[5,3,4,1,6,10,8,9,2,7]=>[3,3,1,1,1,1]
[4,3,1,5,6,7,10,9,2,8]=>[3,3,1,1,1,1]
[3,1,4,5,6,7,8,10,2,9]=>[2,2,1,1,1,1,1,1]
[9,2,3,4,5,6,7,10,1,8]=>[3,1,1,1,1,1,1,1]
[9,2,10,4,5,6,7,8,1,3]=>[3,2,1,1,1,1,1]
[2,10,4,5,6,7,8,9,1,3]=>[3,1,1,1,1,1,1,1]
[9,8,4,5,6,7,1,2,10,3]=>[4,2,1,1,1,1]
[2,10,9,5,6,7,8,1,3,4]=>[4,1,1,1,1,1,1]
[9,3,8,5,6,7,1,2,10,4]=>[4,2,1,1,1,1]
[9,7,4,5,6,1,8,2,10,3]=>[4,2,2,1,1]
[2,10,4,9,6,7,8,1,3,5]=>[4,1,1,1,1,1,1]
[2,10,8,5,6,7,1,9,3,4]=>[4,2,1,1,1,1]
[1,3,2,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[9,2,3,4,5,6,7,8,10,1]=>[3,1,1,1,1,1,1,1]
[8,2,3,4,5,6,7,10,9,1]=>[3,2,1,1,1,1,1]
[7,2,3,4,5,6,10,8,9,1]=>[3,2,1,1,1,1,1]
[6,2,3,4,5,10,7,8,9,1]=>[3,2,1,1,1,1,1]
[5,2,3,4,10,6,7,8,9,1]=>[3,2,1,1,1,1,1]
[4,2,3,10,5,6,7,8,9,1]=>[3,2,1,1,1,1,1]
[3,2,10,4,5,6,7,8,9,1]=>[3,2,1,1,1,1,1]
[2,10,3,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,6,7,5,8,9,1,10]=>[3,1,1,1,1,1,1,1]
[1,3,4,5,7,8,6,9,10,2]=>[3,1,1,1,1,1,1,1]
[9,7,5,3,1,8,6,4,2,10]=>[5,4,1]
[1,10,8,6,4,2,9,7,5,3]=>[5,4,1]
[3,1,2,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[6,3,5,1,2,4,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[9,7,6,5,4,3,2,1,8,10]=>[8,1,1]
[10,3,2,4,5,6,7,8,9,1]=>[4,1,1,1,1,1,1]
[9,1,2,3,4,5,6,8,7,10]=>[3,1,1,1,1,1,1,1]
[1,10,2,3,4,5,6,7,9,8]=>[3,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,10,2,9]=>[2,1,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,2,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,10,9,7]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,10,9,6]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,7,9,10,8,6]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,7,10,9,8,6]=>[4,1,1,1,1,1,1]
[1,2,3,4,6,7,8,10,9,5]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,6,7,9,10,8,5]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,6,7,10,9,8,5]=>[4,1,1,1,1,1,1]
[1,2,3,4,6,8,10,9,7,5]=>[4,1,1,1,1,1,1]
[1,2,3,4,6,10,9,8,7,5]=>[5,1,1,1,1,1]
[1,2,3,5,6,7,9,10,8,4]=>[3,1,1,1,1,1,1,1]
[1,2,3,5,6,7,10,9,8,4]=>[4,1,1,1,1,1,1]
[1,2,3,5,6,8,9,10,7,4]=>[3,1,1,1,1,1,1,1]
[1,2,3,5,6,8,10,9,7,4]=>[4,1,1,1,1,1,1]
[1,2,3,5,6,10,9,8,7,4]=>[5,1,1,1,1,1]
[1,2,3,5,7,9,10,8,6,4]=>[4,1,1,1,1,1,1]
[1,2,3,5,7,10,9,8,6,4]=>[5,1,1,1,1,1]
[1,2,3,5,10,9,8,7,6,4]=>[6,1,1,1,1]
[1,2,4,5,7,8,10,9,6,3]=>[4,1,1,1,1,1,1]
[1,2,4,5,7,9,10,8,6,3]=>[4,1,1,1,1,1,1]
[1,2,4,5,7,10,9,8,6,3]=>[5,1,1,1,1,1]
[1,2,4,5,10,9,8,7,6,3]=>[6,1,1,1,1]
[1,2,4,6,10,9,8,7,5,3]=>[6,1,1,1,1]
[1,2,4,10,9,8,7,6,5,3]=>[7,1,1,1]
[1,3,5,7,9,10,8,6,4,2]=>[5,1,1,1,1,1]
[1,3,5,7,10,9,8,6,4,2]=>[6,1,1,1,1]
[1,3,5,10,9,8,7,6,4,2]=>[7,1,1,1]
[1,3,10,9,8,7,6,5,4,2]=>[8,1,1]
[9,1,8,2,3,4,5,6,10,7]=>[3,2,1,1,1,1,1]
[9,7,1,2,3,4,5,6,10,8]=>[3,2,1,1,1,1,1]
[2,10,1,9,3,4,5,6,7,8]=>[3,1,1,1,1,1,1,1]
[2,10,8,1,3,4,5,6,7,9]=>[3,1,1,1,1,1,1,1]
[4,1,3,2,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[6,1,2,4,5,3,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[5,4,1,2,3,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[8,1,2,3,5,6,7,4,9,10]=>[3,1,1,1,1,1,1,1]
[4,1,6,3,5,2,7,8,9,10]=>[3,2,1,1,1,1,1]
[8,1,7,3,2,6,4,5,9,10]=>[4,2,1,1,1,1]
[5,7,1,6,2,4,3,8,9,10]=>[4,1,1,1,1,1,1]
[7,3,4,6,1,2,5,8,9,10]=>[3,1,1,1,1,1,1,1]
[6,1,2,9,4,5,7,8,3,10]=>[3,2,1,1,1,1,1]
[4,1,6,3,8,5,7,2,9,10]=>[3,2,2,1,1,1]
[6,8,5,1,7,2,3,4,9,10]=>[3,2,1,1,1,1,1]
[8,3,4,5,7,1,2,6,9,10]=>[3,1,1,1,1,1,1,1]
[10,1,6,3,9,5,2,8,4,7]=>[4,2,2,1,1]
[5,7,1,9,2,8,4,6,3,10]=>[4,2,1,1,1,1]
[7,9,4,6,1,8,2,3,5,10]=>[3,2,1,1,1,1,1]
[9,3,4,5,6,8,1,2,7,10]=>[3,1,1,1,1,1,1,1]
[4,1,6,3,8,5,10,7,9,2]=>[3,2,2,2,1]
[6,8,10,1,7,2,9,3,5,4]=>[4,2,1,1,1,1]
[8,10,4,5,7,1,9,2,3,6]=>[3,2,1,1,1,1,1]
[10,3,4,5,6,7,9,1,2,8]=>[3,1,1,1,1,1,1,1]
[3,5,7,9,1,2,4,6,8,10]=>[2,1,1,1,1,1,1,1,1]
[4,1,2,3,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[5,1,2,3,4,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[8,1,2,3,4,5,6,7,9,10]=>[2,1,1,1,1,1,1,1,1]
[7,1,2,3,4,5,6,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[6,1,2,3,4,5,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[3,4,1,6,2,5,8,7,10,9]=>[2,2,2,2,1,1]
[10,8,6,4,2,1,3,5,7,9]=>[6,1,1,1,1]
[10,8,6,2,1,4,3,5,7,9]=>[5,2,1,1,1]
[10,8,4,2,1,6,3,5,7,9]=>[5,2,1,1,1]
[10,6,4,2,1,8,3,5,7,9]=>[5,2,1,1,1]
[8,6,4,2,1,10,3,5,7,9]=>[5,2,1,1,1]
[8,6,4,2,9,1,3,5,7,10]=>[5,1,1,1,1,1]
[9,6,4,2,7,1,3,5,8,10]=>[5,1,1,1,1,1]
[9,7,4,2,5,1,3,6,8,10]=>[5,1,1,1,1,1]
[9,7,5,2,3,1,4,6,8,10]=>[5,1,1,1,1,1]
[9,7,5,3,1,2,4,6,8,10]=>[5,1,1,1,1,1]
[1,2,10,3,4,5,6,7,9,8]=>[3,1,1,1,1,1,1,1]
[1,2,3,9,4,5,6,10,7,8]=>[2,2,1,1,1,1,1,1]
[1,2,3,4,10,5,6,7,9,8]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,10,6,7,9,8]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,6,9,10,7,8]=>[2,1,1,1,1,1,1,1,1]
[8,1,2,3,4,5,9,6,10,7]=>[2,2,2,1,1,1,1]
[7,10,1,2,3,4,5,9,6,8]=>[3,1,1,1,1,1,1,1]
[6,1,10,2,3,4,5,9,7,8]=>[3,2,1,1,1,1,1]
[5,1,2,3,4,6,9,7,10,8]=>[2,2,2,1,1,1,1]
[4,1,2,3,10,5,6,9,7,8]=>[3,2,1,1,1,1,1]
[3,1,2,4,5,10,6,9,7,8]=>[3,2,1,1,1,1,1]
[9,1,2,3,4,5,7,10,6,8]=>[3,1,1,1,1,1,1,1]
[9,1,2,3,5,7,10,4,6,8]=>[3,1,1,1,1,1,1,1]
[9,1,3,5,7,10,2,4,6,8]=>[3,1,1,1,1,1,1,1]
[7,8,9,6,5,4,3,2,1,10]=>[7,1,1,1]
[7,6,8,9,5,4,3,2,1,10]=>[7,1,1,1]
[7,6,5,8,9,4,3,2,1,10]=>[7,1,1,1]
[7,6,5,4,8,9,3,2,1,10]=>[7,1,1,1]
[7,6,5,4,3,8,9,2,1,10]=>[7,1,1,1]
[7,6,5,4,3,2,8,9,1,10]=>[7,1,1,1]
[9,8,7,6,5,4,2,1,3,10]=>[8,1,1]
[9,8,7,6,5,3,2,1,4,10]=>[8,1,1]
[9,8,7,6,4,3,2,1,5,10]=>[8,1,1]
[9,8,7,5,4,3,2,1,6,10]=>[8,1,1]
[9,8,6,5,4,3,2,1,7,10]=>[8,1,1]
[10,1,3,4,5,6,7,8,9,2]=>[3,1,1,1,1,1,1,1]
[1,9,3,4,5,6,7,10,2,8]=>[3,1,1,1,1,1,1,1]
[9,2,3,4,5,6,1,10,8,7]=>[3,3,1,1,1,1]
[9,1,10,4,5,6,7,8,3,2]=>[4,2,1,1,1,1]
[8,10,3,4,5,6,7,1,9,2]=>[3,2,1,1,1,1,1]
[10,6,1,2,3,4,9,5,7,8]=>[3,2,1,1,1,1,1]
[10,7,1,2,3,4,9,5,6,8]=>[3,2,1,1,1,1,1]
[9,10,1,2,3,4,8,5,6,7]=>[3,1,1,1,1,1,1,1]
[10,1,5,2,3,4,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,1,2,5,3,4,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[5,1,2,3,10,4,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[7,6,1,2,3,4,10,9,5,8]=>[3,3,1,1,1,1]
[9,7,1,2,3,4,8,5,10,6]=>[3,2,2,1,1,1]
[5,9,1,2,3,4,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[10,8,4,9,1,2,3,5,6,7]=>[4,1,1,1,1,1,1]
[2,10,1,5,3,4,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[3,1,5,2,10,4,6,7,8,9]=>[2,2,2,1,1,1,1]
[4,1,2,10,3,5,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[9,10,1,8,7,6,5,4,3,2]=>[8,1,1]
[10,9,1,8,7,6,5,4,3,2]=>[9,1]
[10,9,8,1,7,6,5,4,3,2]=>[9,1]
[10,9,8,7,1,6,5,4,3,2]=>[9,1]
[10,9,8,7,6,1,5,4,3,2]=>[9,1]
[10,9,8,7,6,5,1,4,3,2]=>[9,1]
[10,9,8,7,6,5,4,1,3,2]=>[9,1]
[3,2,5,4,7,6,9,8,1,10]=>[3,2,2,2,1]
[2,4,3,6,5,8,7,10,9,1]=>[3,2,2,2,1]
[3,2,5,4,7,6,1,10,8,9]=>[3,2,2,2,1]
[3,2,5,4,9,8,6,7,1,10]=>[4,2,2,1,1]
[3,2,5,4,1,8,6,10,7,9]=>[3,2,2,2,1]
[3,2,5,4,1,10,9,6,7,8]=>[3,3,2,1,1]
[3,2,7,6,4,5,9,8,1,10]=>[4,2,2,1,1]
[3,2,7,6,4,5,1,10,8,9]=>[4,2,2,1,1]
[3,2,9,6,4,8,5,7,1,10]=>[4,2,2,1,1]
[3,2,1,6,4,8,5,10,7,9]=>[3,2,2,2,1]
[3,2,1,6,4,10,9,5,7,8]=>[3,3,2,1,1]
[3,2,9,8,7,4,5,6,1,10]=>[5,2,1,1,1]
[3,2,1,8,7,4,5,10,6,9]=>[3,3,2,1,1]
[3,2,1,10,7,4,9,5,6,8]=>[3,3,2,1,1]
[3,2,1,10,9,8,4,5,6,7]=>[4,3,1,1,1]
[5,4,2,3,7,6,9,8,1,10]=>[4,2,2,1,1]
[5,4,2,3,7,6,1,10,8,9]=>[4,2,2,1,1]
[5,4,2,3,9,8,6,7,1,10]=>[4,3,1,1,1]
[5,4,2,3,1,8,6,10,7,9]=>[4,2,2,1,1]
[5,4,2,3,1,10,9,6,7,8]=>[4,3,1,1,1]
[7,4,2,6,3,5,9,8,1,10]=>[4,2,2,1,1]
[7,4,2,6,3,5,1,10,8,9]=>[4,2,2,1,1]
[9,4,2,6,3,8,5,7,1,10]=>[4,2,2,1,1]
[1,4,2,6,3,8,5,10,7,9]=>[2,2,2,2,1,1]
[1,4,2,6,3,10,9,5,7,8]=>[3,2,2,1,1,1]
[9,4,2,8,7,3,5,6,1,10]=>[5,2,1,1,1]
[1,4,2,8,7,3,5,10,6,9]=>[3,2,2,1,1,1]
[1,4,2,10,7,3,9,5,6,8]=>[3,2,2,1,1,1]
[1,4,2,10,9,8,3,5,6,7]=>[4,2,1,1,1,1]
[7,6,5,2,3,4,9,8,1,10]=>[5,2,1,1,1]
[7,6,5,2,3,4,1,10,8,9]=>[5,2,1,1,1]
[9,6,5,2,3,8,4,7,1,10]=>[5,2,1,1,1]
[1,6,5,2,3,8,4,10,7,9]=>[3,2,2,1,1,1]
[1,6,5,2,3,10,9,4,7,8]=>[3,3,1,1,1,1]
[9,8,5,2,7,3,4,6,1,10]=>[5,2,1,1,1]
[1,8,5,2,7,3,4,10,6,9]=>[3,2,2,1,1,1]
[1,10,5,2,7,3,9,4,6,8]=>[3,2,2,1,1,1]
[1,10,5,2,9,8,3,4,6,7]=>[4,2,1,1,1,1]
[9,8,7,6,2,3,4,5,1,10]=>[6,1,1,1,1]
[1,8,7,6,2,3,4,10,5,9]=>[4,2,1,1,1,1]
[1,10,7,6,2,3,9,4,5,8]=>[4,2,1,1,1,1]
[1,10,9,6,2,8,3,4,5,7]=>[4,2,1,1,1,1]
[1,10,9,8,7,2,3,4,5,6]=>[5,1,1,1,1,1]
[3,2,5,4,7,6,1,10,9,8]=>[3,3,2,2]
[3,2,5,4,9,8,7,6,1,10]=>[5,2,2,1]
[3,2,5,4,1,8,7,10,9,6]=>[3,3,2,2]
[3,2,5,4,1,10,9,8,7,6]=>[5,3,2]
[3,2,7,6,5,4,9,8,1,10]=>[5,2,2,1]
[3,2,7,6,5,4,1,10,9,8]=>[5,3,2]
[3,2,9,6,5,8,7,4,1,10]=>[5,2,2,1]
[3,2,1,6,5,8,7,10,9,4]=>[3,3,2,2]
[3,2,1,6,5,10,9,8,7,4]=>[5,3,2]
[3,2,1,8,7,6,5,10,9,4]=>[5,3,2]
[3,2,1,10,7,6,9,8,5,4]=>[5,3,2]
[5,4,3,2,7,6,9,8,1,10]=>[5,2,2,1]
[5,4,3,2,7,6,1,10,9,8]=>[5,3,2]
[5,4,3,2,9,8,7,6,1,10]=>[5,4,1]
[5,4,3,2,1,8,7,10,9,6]=>[5,3,2]
[7,4,3,6,5,2,9,8,1,10]=>[5,2,2,1]
[7,4,3,6,5,2,1,10,9,8]=>[5,3,2]
[9,4,3,6,5,8,7,2,1,10]=>[5,2,2,1]
[1,4,3,6,5,8,7,10,9,2]=>[3,2,2,2,1]
[1,4,3,6,5,10,9,8,7,2]=>[5,2,2,1]
[9,4,3,8,7,6,5,2,1,10]=>[7,2,1]
[1,4,3,8,7,6,5,10,9,2]=>[5,2,2,1]
[1,4,3,10,7,6,9,8,5,2]=>[5,2,2,1]
[1,4,3,10,9,8,7,6,5,2]=>[7,2,1]
[7,6,5,4,3,2,9,8,1,10]=>[7,2,1]
[9,6,5,4,3,8,7,2,1,10]=>[7,2,1]
[1,6,5,4,3,8,7,10,9,2]=>[5,2,2,1]
[1,6,5,4,3,10,9,8,7,2]=>[5,4,1]
[9,8,5,4,7,6,3,2,1,10]=>[7,2,1]
[1,8,5,4,7,6,3,10,9,2]=>[5,2,2,1]
[1,10,5,4,7,6,9,8,3,2]=>[5,2,2,1]
[1,10,5,4,9,8,7,6,3,2]=>[7,2,1]
[1,10,7,6,5,4,9,8,3,2]=>[7,2,1]
[1,10,9,6,5,8,7,4,3,2]=>[7,2,1]
[6,5,7,4,8,3,9,2,10,1]=>[6,1,1,1,1]
[6,5,7,4,8,3,10,2,9,1]=>[6,1,1,1,1]
[5,6,4,7,3,8,2,9,1,10]=>[5,1,1,1,1,1]
[9,8,7,6,1,2,3,4,5,10]=>[5,1,1,1,1,1]
[8,10,1,2,3,4,5,9,6,7]=>[3,1,1,1,1,1,1,1]
[10,8,1,9,2,3,4,5,6,7]=>[3,2,1,1,1,1,1]
[8,7,1,2,3,4,5,9,10,6]=>[3,2,1,1,1,1,1]
[2,10,1,5,6,7,8,9,3,4]=>[3,1,1,1,1,1,1,1]
[10,9,2,3,4,5,6,7,8,1]=>[4,1,1,1,1,1,1]
[2,4,3,1,6,5,8,7,10,9]=>[3,2,2,2,1]
[2,1,4,3,6,5,8,10,9,7]=>[3,2,2,2,1]
[2,1,4,3,6,8,7,5,10,9]=>[3,2,2,2,1]
[2,1,4,3,8,10,7,9,5,6]=>[3,2,2,1,1,1]
[2,1,4,3,6,7,10,8,9,5]=>[3,2,2,1,1,1]
[2,1,4,6,5,3,8,7,10,9]=>[3,2,2,2,1]
[2,1,4,6,5,3,8,10,9,7]=>[3,3,2,1,1]
[2,1,6,8,5,7,3,4,10,9]=>[3,2,2,1,1,1]
[2,1,8,7,5,10,4,9,3,6]=>[5,2,1,1,1]
[2,1,6,7,5,10,8,4,9,3]=>[4,2,2,1,1]
[2,1,4,5,8,6,7,3,10,9]=>[3,2,2,1,1,1]
[2,1,8,5,10,6,7,9,3,4]=>[3,2,2,1,1,1]
[2,1,4,7,10,6,9,8,3,5]=>[4,2,1,1,1,1]
[2,1,4,5,6,10,7,8,9,3]=>[3,2,1,1,1,1,1]
[2,4,3,1,6,5,8,10,9,7]=>[3,3,2,1,1]
[2,4,3,1,6,8,7,5,10,9]=>[3,3,2,1,1]
[2,4,3,1,8,10,7,9,5,6]=>[3,3,1,1,1,1]
[2,4,3,1,6,7,10,8,9,5]=>[3,3,1,1,1,1]
[4,6,3,5,1,2,8,7,10,9]=>[3,2,2,1,1,1]
[4,6,3,5,1,2,8,10,9,7]=>[3,3,1,1,1,1]
[6,5,3,8,2,7,1,4,10,9]=>[5,2,1,1,1]
[8,5,3,7,2,10,4,9,1,6]=>[5,2,1,1,1]
[6,5,3,7,2,10,8,4,9,1]=>[5,3,1,1]
[4,5,3,8,6,2,7,1,10,9]=>[4,2,2,1,1]
[8,6,3,5,10,2,7,9,1,4]=>[5,1,1,1,1,1]
[4,7,3,6,10,1,9,8,2,5]=>[4,2,1,1,1,1]
[4,5,3,6,10,7,1,8,9,2]=>[3,2,2,1,1,1]
[2,3,6,4,5,1,8,7,10,9]=>[3,2,2,1,1,1]
[2,3,6,4,5,1,8,10,9,7]=>[3,3,1,1,1,1]
[6,3,8,4,5,7,1,2,10,9]=>[3,2,2,1,1,1]
[8,3,7,4,5,10,2,9,1,6]=>[5,1,1,1,1,1]
[6,3,7,4,5,10,8,2,9,1]=>[4,2,2,1,1]
[2,5,8,4,7,6,1,3,10,9]=>[4,2,1,1,1,1]
[8,5,10,4,7,6,2,9,1,3]=>[5,2,1,1,1]
[2,7,10,4,8,6,9,5,1,3]=>[5,1,1,1,1,1]
[2,5,6,4,10,8,7,3,9,1]=>[5,2,1,1,1]
[2,3,4,8,5,6,7,1,10,9]=>[3,2,1,1,1,1,1]
[8,3,4,10,5,6,7,9,1,2]=>[3,2,1,1,1,1,1]
[2,7,4,10,5,6,9,8,1,3]=>[4,2,1,1,1,1]
[2,3,6,10,5,9,7,8,1,4]=>[4,1,1,1,1,1,1]
[2,3,4,5,10,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,1,8,9,10,7]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,8,9,1,10,7]=>[2,2,1,1,1,1,1,1]
[4,5,6,1,7,8,9,10,2,3]=>[2,2,1,1,1,1,1,1]
[3,5,6,1,7,8,9,10,2,4]=>[2,2,1,1,1,1,1,1]
[3,4,6,1,7,8,9,10,2,5]=>[2,2,1,1,1,1,1,1]
[3,4,5,1,7,8,9,10,2,6]=>[2,2,1,1,1,1,1,1]
[2,1,4,3,6,5,8,9,10,7]=>[2,2,2,2,1,1]
[2,1,4,3,6,7,8,5,10,9]=>[2,2,2,2,1,1]
[2,1,4,3,8,7,9,10,5,6]=>[3,2,2,1,1,1]
[2,1,4,3,6,7,8,9,10,5]=>[2,2,2,1,1,1,1]
[2,1,4,5,6,3,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,4,5,6,3,8,9,10,7]=>[2,2,2,1,1,1,1]
[2,1,6,5,7,8,3,4,10,9]=>[3,2,2,1,1,1]
[2,1,8,5,9,7,3,10,6,4]=>[4,2,2,2]
[2,1,6,5,7,8,9,10,3,4]=>[3,2,1,1,1,1,1]
[2,1,4,5,6,7,8,3,10,9]=>[2,2,2,1,1,1,1]
[2,1,8,5,6,7,9,10,3,4]=>[3,2,1,1,1,1,1]
[2,1,4,7,6,8,9,3,10,5]=>[3,2,2,1,1,1]
[2,1,4,5,6,7,8,9,10,3]=>[2,2,1,1,1,1,1,1]
[2,3,4,1,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[2,3,4,1,6,5,8,9,10,7]=>[2,2,2,1,1,1,1]
[2,3,4,1,6,7,8,5,10,9]=>[2,2,2,1,1,1,1]
[2,3,4,1,8,7,9,10,5,6]=>[3,2,1,1,1,1,1]
[2,3,4,1,6,7,8,9,10,5]=>[2,2,1,1,1,1,1,1]
[4,3,5,6,1,2,8,7,10,9]=>[3,2,2,1,1,1]
[4,3,5,6,1,2,8,9,10,7]=>[3,2,1,1,1,1,1]
[6,3,7,5,1,8,4,2,10,9]=>[4,2,2,2]
[8,3,9,5,1,7,4,10,6,2]=>[4,2,2,2]
[6,3,7,5,1,8,9,10,4,2]=>[4,2,2,1,1]
[4,3,5,6,7,8,1,2,10,9]=>[3,2,1,1,1,1,1]
[8,3,9,5,6,7,1,10,4,2]=>[4,2,2,1,1]
[4,3,7,8,6,10,9,2,5,1]=>[4,2,2,1,1]
[4,3,5,6,7,8,9,10,1,2]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,1,8,7,10,9]=>[2,2,2,1,1,1,1]
[6,3,4,5,7,8,1,2,10,9]=>[3,2,1,1,1,1,1]
[8,3,4,5,9,7,1,10,6,2]=>[4,2,2,1,1]
[6,3,4,5,7,8,9,10,1,2]=>[3,1,1,1,1,1,1,1]
[2,5,4,6,7,1,8,3,10,9]=>[3,2,2,1,1,1]
[8,5,4,6,7,1,9,10,3,2]=>[5,2,1,1,1]
[2,7,4,8,6,1,9,5,10,3]=>[4,2,2,1,1]
[2,5,4,6,7,8,9,1,10,3]=>[3,2,1,1,1,1,1]
[2,3,4,5,6,7,8,1,10,9]=>[2,2,1,1,1,1,1,1]
[8,3,4,5,6,7,9,10,1,2]=>[3,1,1,1,1,1,1,1]
[2,7,4,5,6,8,9,1,10,3]=>[3,2,1,1,1,1,1]
[2,3,6,5,7,8,1,9,10,4]=>[3,2,1,1,1,1,1]
[4,5,2,3,6,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[4,3,2,5,6,7,8,9,10,1]=>[4,1,1,1,1,1,1]
[5,6,7,2,3,4,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[5,3,6,2,4,7,8,9,10,1]=>[4,1,1,1,1,1,1]
[5,4,3,2,6,7,8,9,10,1]=>[5,1,1,1,1,1]
[6,7,8,9,2,3,4,5,10,1]=>[3,1,1,1,1,1,1,1]
[6,3,7,8,2,4,5,9,10,1]=>[4,1,1,1,1,1,1]
[6,7,4,5,2,3,8,9,10,1]=>[4,1,1,1,1,1,1]
[6,4,3,7,2,5,8,9,10,1]=>[5,1,1,1,1,1]
[6,5,4,3,2,7,8,9,10,1]=>[6,1,1,1,1]
[7,8,9,10,1,3,4,5,6,2]=>[3,1,1,1,1,1,1,1]
[7,3,8,9,10,2,4,5,6,1]=>[4,1,1,1,1,1,1]
[7,4,3,8,9,2,5,6,10,1]=>[5,1,1,1,1,1]
[7,5,8,3,6,2,4,9,10,1]=>[5,1,1,1,1,1]
[7,5,4,3,8,2,6,9,10,1]=>[6,1,1,1,1]
[7,6,5,4,3,2,8,9,10,1]=>[7,1,1,1]
[8,5,9,3,6,10,2,4,7,1]=>[5,1,1,1,1,1]
[8,5,4,3,9,10,2,6,7,1]=>[6,1,1,1,1]
[8,9,6,7,4,5,2,3,10,1]=>[5,1,1,1,1,1]
[8,6,4,9,3,7,2,5,10,1]=>[6,1,1,1,1]
[8,6,5,4,3,9,2,7,10,1]=>[7,1,1,1]
[8,7,6,5,4,3,2,9,10,1]=>[8,1,1]
[9,7,5,4,10,3,8,2,6,1]=>[7,1,1,1]
[9,7,6,5,4,3,10,2,8,1]=>[8,1,1]
[10,1,9,2,8,3,7,4,6,5]=>[6,1,1,1,1]
[1,4,3,6,5,10,9,7,8,2]=>[4,2,2,1,1]
[1,4,3,8,7,5,6,10,9,2]=>[4,2,2,1,1]
[1,4,3,10,7,5,9,6,8,2]=>[4,2,2,1,1]
[1,4,3,10,9,8,5,6,7,2]=>[5,2,1,1,1]
[1,6,5,3,4,8,7,10,9,2]=>[4,2,2,1,1]
[1,6,5,3,4,10,9,7,8,2]=>[4,3,1,1,1]
[1,8,5,3,7,4,6,10,9,2]=>[4,2,2,1,1]
[1,10,5,3,7,4,9,6,8,2]=>[4,2,2,1,1]
[1,10,5,3,9,8,4,6,7,2]=>[5,2,1,1,1]
[1,8,7,6,3,4,5,10,9,2]=>[5,2,1,1,1]
[1,10,7,6,3,4,9,5,8,2]=>[5,2,1,1,1]
[1,10,9,6,3,8,4,5,7,2]=>[5,2,1,1,1]
[1,10,9,8,7,3,4,5,6,2]=>[6,1,1,1,1]
[3,1,2,6,5,8,7,10,9,4]=>[3,2,2,2,1]
[3,1,2,6,5,10,9,7,8,4]=>[4,2,2,1,1]
[3,1,2,8,7,5,6,10,9,4]=>[4,2,2,1,1]
[3,1,2,10,7,5,9,6,8,4]=>[4,2,2,1,1]
[3,1,2,10,9,8,5,6,7,4]=>[5,2,1,1,1]
[3,1,5,2,4,8,7,10,9,6]=>[3,2,2,2,1]
[3,1,5,2,4,10,9,7,8,6]=>[4,2,2,1,1]
[3,1,5,2,7,4,6,10,9,8]=>[3,2,2,2,1]
[3,1,5,2,9,8,4,6,7,10]=>[3,2,2,1,1,1]
[3,1,7,6,2,4,5,10,9,8]=>[3,3,2,1,1]
[3,1,7,6,2,4,9,5,8,10]=>[3,2,2,1,1,1]
[3,1,9,6,2,8,4,5,7,10]=>[3,2,2,1,1,1]
[3,1,9,8,7,2,4,5,6,10]=>[4,2,1,1,1,1]
[5,4,1,2,3,8,7,10,9,6]=>[3,3,2,1,1]
[5,4,1,2,3,10,9,7,8,6]=>[4,3,1,1,1]
[5,4,1,2,7,3,6,10,9,8]=>[3,3,2,1,1]
[5,4,1,2,7,3,9,6,8,10]=>[3,2,2,1,1,1]
[5,4,1,2,9,8,3,6,7,10]=>[3,3,1,1,1,1]
[7,4,1,6,2,3,5,10,9,8]=>[3,3,2,1,1]
[7,4,1,6,2,3,9,5,8,10]=>[3,2,2,1,1,1]
[9,4,1,6,2,8,3,5,7,10]=>[3,2,2,1,1,1]
[9,4,1,8,7,2,3,5,6,10]=>[4,2,1,1,1,1]
[7,6,5,1,2,3,4,10,9,8]=>[4,3,1,1,1]
[7,6,5,1,2,3,9,4,8,10]=>[4,2,1,1,1,1]
[9,6,5,1,2,8,3,4,7,10]=>[4,2,1,1,1,1]
[9,8,5,1,7,2,3,4,6,10]=>[4,2,1,1,1,1]
[9,1,2,3,4,5,6,10,8,7]=>[3,2,1,1,1,1,1]
[9,1,2,3,4,5,10,7,8,6]=>[3,2,1,1,1,1,1]
[10,1,2,3,4,9,6,7,8,5]=>[4,1,1,1,1,1,1]
[10,1,9,3,4,5,6,7,8,2]=>[4,1,1,1,1,1,1]
[10,1,2,3,4,5,6,8,9,7]=>[3,1,1,1,1,1,1,1]
[1,9,2,10,3,4,5,6,7,8]=>[2,2,1,1,1,1,1,1]
[1,4,2,3,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[1,3,4,2,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,3,4,5,6,7,10,8,9]=>[2,2,1,1,1,1,1,1]
[10,2,3,4,5,6,7,8,1,9]=>[3,1,1,1,1,1,1,1]
[3,10,1,4,5,6,7,8,9,2]=>[3,1,1,1,1,1,1,1]
[8,1,10,3,4,5,6,7,2,9]=>[3,2,1,1,1,1,1]
[8,2,1,10,4,5,6,7,3,9]=>[3,3,1,1,1,1]
[7,10,8,3,4,5,6,1,2,9]=>[4,1,1,1,1,1,1]
[3,9,1,2,10,5,6,7,8,4]=>[3,2,1,1,1,1,1]
[2,3,4,5,6,7,10,9,8,1]=>[4,1,1,1,1,1,1]
[2,3,4,5,6,9,8,10,7,1]=>[4,1,1,1,1,1,1]
[10,5,9,4,8,3,7,2,6,1]=>[6,1,1,1,1]
[1,3,5,2,4,7,6,9,8,10]=>[2,2,2,1,1,1,1]
[1,4,2,5,3,7,6,9,8,10]=>[2,2,2,2,1,1]
[10,3,1,5,6,7,8,9,2,4]=>[3,2,1,1,1,1,1]
[10,4,1,5,6,7,8,9,2,3]=>[3,2,1,1,1,1,1]
[4,2,6,8,10,1,3,5,7,9]=>[3,1,1,1,1,1,1,1]
[4,6,2,8,10,1,3,5,7,9]=>[3,1,1,1,1,1,1,1]
[4,6,8,2,10,1,3,5,7,9]=>[3,1,1,1,1,1,1,1]
[4,6,8,10,2,1,3,5,7,9]=>[3,1,1,1,1,1,1,1]
[4,6,8,2,9,1,3,5,7,10]=>[3,1,1,1,1,1,1,1]
[4,6,2,7,9,1,3,5,8,10]=>[3,1,1,1,1,1,1,1]
[4,2,5,7,9,1,3,6,8,10]=>[3,1,1,1,1,1,1,1]
[2,3,5,7,9,1,4,6,8,10]=>[2,1,1,1,1,1,1,1,1]
[9,7,10,8,6,5,4,3,2,1]=>[8,2]
[9,7,5,10,8,6,4,3,2,1]=>[7,3]
[8,5,2,9,6,3,10,7,4,1]=>[4,3,3]
[7,3,8,4,9,5,1,10,6,2]=>[3,3,2,2]
[2,3,4,5,6,7,10,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,10,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,10,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,3,10,4,5,6,7,8,9,1]=>[3,1,1,1,1,1,1,1]
[2,1,4,3,6,5,9,8,10,7]=>[3,2,2,2,1]
[2,1,4,3,7,6,8,5,10,9]=>[3,2,2,2,1]
[2,1,4,3,7,6,9,8,10,5]=>[3,2,2,2,1]
[2,1,4,3,8,7,9,6,10,5]=>[4,2,2,1,1]
[2,1,5,4,6,3,8,7,10,9]=>[3,2,2,2,1]
[2,1,5,4,6,3,9,8,10,7]=>[3,3,2,1,1]
[2,1,5,4,7,6,8,3,10,9]=>[3,2,2,2,1]
[2,1,5,4,7,6,9,8,10,3]=>[3,2,2,2,1]
[2,1,5,4,8,7,9,6,10,3]=>[4,2,2,1,1]
[2,1,6,5,7,4,8,3,10,9]=>[4,2,2,1,1]
[2,1,6,5,7,4,9,8,10,3]=>[4,2,2,1,1]
[2,1,6,5,8,7,9,4,10,3]=>[4,2,2,1,1]
[2,1,7,6,8,5,9,4,10,3]=>[5,2,1,1,1]
[3,2,4,1,6,5,8,7,10,9]=>[3,2,2,2,1]
[3,2,4,1,6,5,9,8,10,7]=>[3,3,2,1,1]
[3,2,4,1,7,6,8,5,10,9]=>[3,3,2,1,1]
[3,2,4,1,7,6,9,8,10,5]=>[3,3,2,1,1]
[3,2,4,1,8,7,9,6,10,5]=>[4,3,1,1,1]
[3,2,5,4,6,1,8,7,10,9]=>[3,2,2,2,1]
[3,2,5,4,6,1,9,8,10,7]=>[3,3,2,1,1]
[3,2,5,4,7,6,8,1,10,9]=>[3,2,2,2,1]
[3,2,5,4,7,6,9,8,10,1]=>[3,2,2,2,1]
[3,2,5,4,8,7,9,6,10,1]=>[4,2,2,1,1]
[3,2,6,5,7,4,8,1,10,9]=>[4,2,2,1,1]
[3,2,6,5,7,4,9,8,10,1]=>[4,2,2,1,1]
[3,2,6,5,8,7,9,4,10,1]=>[4,2,2,1,1]
[3,2,7,6,8,5,9,4,10,1]=>[5,2,1,1,1]
[4,3,5,2,6,1,8,7,10,9]=>[4,2,2,1,1]
[4,3,5,2,6,1,9,8,10,7]=>[4,3,1,1,1]
[4,3,5,2,7,6,8,1,10,9]=>[4,2,2,1,1]
[4,3,5,2,7,6,9,8,10,1]=>[4,2,2,1,1]
[4,3,5,2,8,7,9,6,10,1]=>[4,3,1,1,1]
[4,3,6,5,7,2,8,1,10,9]=>[4,2,2,1,1]
[4,3,6,5,7,2,9,8,10,1]=>[4,2,2,1,1]
[4,3,6,5,8,7,9,2,10,1]=>[4,2,2,1,1]
[4,3,7,6,8,5,9,2,10,1]=>[5,2,1,1,1]
[5,4,6,3,7,2,8,1,10,9]=>[5,2,1,1,1]
[5,4,6,3,7,2,9,8,10,1]=>[5,2,1,1,1]
[5,4,6,3,8,7,9,2,10,1]=>[5,2,1,1,1]
[5,4,7,6,8,3,9,2,10,1]=>[5,2,1,1,1]
[1,2,3,4,5,6,9,7,10,8]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,9,10,1,7,8]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,6,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,5,4,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,5,4,7,6,9,8,10]=>[2,2,2,1,1,1,1]
[1,8,9,10,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1]
[1,5,6,7,8,9,10,2,3,4]=>[2,1,1,1,1,1,1,1,1]
[3,4,2,1,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[4,3,1,2,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[6,5,4,3,1,2,7,8,9,10]=>[5,1,1,1,1,1]
[7,6,5,4,3,1,2,8,9,10]=>[6,1,1,1,1]
[9,6,5,4,3,10,1,2,7,8]=>[6,1,1,1,1]
[2,3,4,5,6,7,10,9,1,8]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,10,8,9,1,7]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,10,8,1,9,7]=>[3,2,1,1,1,1,1]
[2,3,4,5,6,10,8,1,7,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,10,1,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,5,10,7,8,9,1,6]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,10,7,8,1,9,6]=>[3,2,1,1,1,1,1]
[2,3,4,5,10,7,8,1,6,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,10,7,1,9,6,8]=>[3,2,1,1,1,1,1]
[2,3,4,5,10,7,1,6,8,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,10,1,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,10,6,7,8,1,9,5]=>[3,2,1,1,1,1,1]
[2,3,4,10,6,7,8,1,5,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,10,6,7,1,8,9,5]=>[3,2,1,1,1,1,1]
[2,3,4,10,6,7,1,9,5,8]=>[3,2,1,1,1,1,1]
[2,3,4,10,6,7,1,5,8,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,10,6,1,8,5,9,7]=>[3,2,2,1,1,1]
[2,3,4,10,6,1,8,5,7,9]=>[3,2,1,1,1,1,1]
[2,3,4,10,6,1,5,7,8,9]=>[3,1,1,1,1,1,1,1]
[2,3,4,10,1,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1]
[2,3,10,5,6,1,8,9,4,7]=>[3,2,1,1,1,1,1]
[2,3,10,5,6,1,8,4,9,7]=>[3,2,2,1,1,1]
[2,3,10,5,6,1,8,4,7,9]=>[3,2,1,1,1,1,1]
[2,3,10,5,6,1,4,7,8,9]=>[3,1,1,1,1,1,1,1]
[2,3,10,5,1,7,4,9,6,8]=>[3,2,2,1,1,1]
[2,3,10,5,1,7,4,6,8,9]=>[3,2,1,1,1,1,1]
[2,3,10,5,1,4,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[2,10,4,1,6,3,8,5,9,7]=>[3,2,2,2,1]
[2,10,4,1,6,3,8,5,7,9]=>[3,2,2,1,1,1]
[2,10,4,1,6,3,5,7,8,9]=>[3,2,1,1,1,1,1]
[2,10,4,1,3,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[8,7,6,5,4,3,2,9,1,10]=>[8,1,1]
[3,4,5,6,8,9,10,1,2,7]=>[2,1,1,1,1,1,1,1,1]
[3,5,6,7,8,9,10,1,2,4]=>[2,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,1,2,9,10]=>[2,1,1,1,1,1,1,1,1]
[8,9,10,1,5,6,7,3,4,2]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,7,1,3,4,2]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,6,3,4,7,2]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,1,3,4,7,2]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,3,4,7,1,2]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,1,3,4,7,2]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,3,4,7,1,2]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,6,7,3,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,7,1,3,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,6,3,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,1,3,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,3,7,1,2,4]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,1,3,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,3,7,1,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,6,3,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,1,3,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,3,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,3,2,4,7,1]=>[5,1,1,1,1,1]
[8,9,5,6,10,1,3,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,3,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,5,6,10,3,2,4,7,1]=>[5,1,1,1,1,1]
[8,9,10,1,5,3,6,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,1,3,6,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,5,3,6,7,1,2,4]=>[4,1,1,1,1,1,1]
[8,9,5,10,1,3,6,7,2,4]=>[4,1,1,1,1,1,1]
[8,9,5,10,3,6,7,1,2,4]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,3,6,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,1,3,6,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,3,6,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,3,6,2,4,7,1]=>[5,1,1,1,1,1]
[8,9,5,10,1,3,6,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,5,10,3,6,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,5,10,3,6,2,4,7,1]=>[5,1,1,1,1,1]
[8,9,5,3,6,10,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,9,5,3,6,10,2,4,7,1]=>[5,1,1,1,1,1]
[8,5,9,10,1,3,6,7,2,4]=>[4,1,1,1,1,1,1]
[8,5,9,10,3,6,7,1,2,4]=>[4,1,1,1,1,1,1]
[8,5,9,10,1,3,6,2,4,7]=>[4,1,1,1,1,1,1]
[8,5,9,10,3,6,1,2,4,7]=>[4,1,1,1,1,1,1]
[8,5,9,10,3,6,2,4,7,1]=>[5,1,1,1,1,1]
[10,1,9,5,6,7,8,2,3,4]=>[4,1,1,1,1,1,1]
[9,1,10,8,6,7,2,3,4,5]=>[4,2,1,1,1,1]
[8,1,9,10,7,2,3,4,5,6]=>[3,2,1,1,1,1,1]
[10,1,8,9,2,3,4,5,6,7]=>[3,1,1,1,1,1,1,1]
[3,1,10,9,6,7,8,2,4,5]=>[4,2,1,1,1,1]
[3,1,9,10,8,7,2,4,5,6]=>[4,2,1,1,1,1]
[3,1,8,9,10,2,4,5,6,7]=>[2,2,1,1,1,1,1,1]
[4,2,5,1,6,3,8,7,10,9]=>[3,2,2,2,1]
[4,2,6,1,7,3,8,5,10,9]=>[3,2,2,2,1]
[4,2,6,1,8,3,9,5,10,7]=>[3,2,2,2,1]
[4,2,6,1,8,3,9,5,7,10]=>[3,2,2,1,1,1]
[4,2,6,1,7,3,5,9,8,10]=>[3,2,2,1,1,1]
[4,2,5,1,3,7,6,9,8,10]=>[3,2,2,1,1,1]
[2,3,4,5,9,7,8,10,6,1]=>[4,1,1,1,1,1,1]
[2,3,4,9,6,7,8,10,1,5]=>[3,1,1,1,1,1,1,1]
[2,3,9,5,6,7,8,10,4,1]=>[4,1,1,1,1,1,1]
[2,9,4,5,6,7,8,10,3,1]=>[4,1,1,1,1,1,1]
[9,3,4,5,6,7,8,10,1,2]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,8,10,1,9,7]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,7,8,1,10,6,9]=>[2,2,1,1,1,1,1,1]
[2,3,4,6,7,1,8,10,5,9]=>[2,2,1,1,1,1,1,1]
[2,3,5,6,1,7,8,10,9,4]=>[3,2,1,1,1,1,1]
[2,4,5,1,6,7,8,10,3,9]=>[2,2,1,1,1,1,1,1]
[3,4,1,5,6,7,8,10,2,9]=>[2,2,1,1,1,1,1,1]
[3,2,4,5,6,7,8,10,9,1]=>[3,2,1,1,1,1,1]
[8,10,6,9,4,7,2,5,3,1]=>[6,1,1,1,1]
[8,10,6,9,4,7,5,2,3,1]=>[6,1,1,1,1]
[8,10,6,9,7,4,5,2,3,1]=>[6,1,1,1,1]
[8,10,9,6,7,4,5,2,3,1]=>[6,1,1,1,1]
[1,3,5,7,2,4,6,9,8,10]=>[2,2,1,1,1,1,1,1]
[2,4,1,5,3,6,7,8,9,10]=>[2,2,1,1,1,1,1,1]
[5,6,2,1,3,7,4,8,9,10]=>[3,2,1,1,1,1,1]
[3,2,5,1,6,4,7,8,9,10]=>[3,2,1,1,1,1,1]
[6,7,2,1,8,3,4,9,5,10]=>[3,2,2,1,1,1]
[3,6,4,1,7,2,8,5,9,10]=>[3,2,2,1,1,1]
[3,6,7,2,1,4,8,5,9,10]=>[3,2,1,1,1,1,1]
[4,2,6,1,7,5,3,8,9,10]=>[3,3,1,1,1,1]
[4,3,2,6,1,7,5,8,9,10]=>[4,2,1,1,1,1]
[3,4,7,1,8,2,9,5,10,6]=>[2,2,2,2,1,1]
[7,8,9,3,2,1,4,5,10,6]=>[4,2,1,1,1,1]
[4,7,2,5,1,8,3,9,6,10]=>[3,2,2,1,1,1]
[4,3,7,8,2,1,5,9,6,10]=>[4,2,1,1,1,1]
[3,5,2,7,1,8,6,4,9,10]=>[3,3,1,1,1,1]
[5,4,3,2,7,1,8,6,9,10]=>[5,2,1,1,1]
[5,8,9,2,1,6,3,10,7,4]=>[3,3,2,1,1]
[5,3,8,6,4,1,9,2,10,7]=>[4,2,2,2]
[3,5,8,2,6,1,9,4,10,7]=>[3,2,2,1,1,1]
[5,4,3,8,9,2,1,6,10,7]=>[5,2,1,1,1]
[6,4,2,8,1,9,7,5,3,10]=>[4,4,1,1]
[4,3,6,2,8,1,9,7,5,10]=>[4,3,1,1,1]
[6,5,4,3,2,8,1,9,7,10]=>[6,2,1,1]
[5,3,7,2,9,1,10,8,6,4]=>[4,4,1,1]
[5,4,3,7,2,9,1,10,8,6]=>[5,3,1,1]
[7,6,5,4,3,2,9,1,10,8]=>[7,2,1]
[2,1,10,3,4,5,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[3,1,2,10,4,5,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[4,1,2,3,10,5,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[5,1,2,3,4,10,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[6,1,2,3,4,5,10,7,8,9]=>[2,2,1,1,1,1,1,1]
[7,1,2,3,4,5,6,10,8,9]=>[2,2,1,1,1,1,1,1]
[10,8,6,4,2,9,7,5,3,1]=>[6,4]
[10,7,4,1,8,5,2,9,6,3]=>[4,3,3]
[9,6,3,8,5,2,10,7,4,1]=>[5,3,2]
[9,5,1,7,3,10,6,2,8,4]=>[4,2,2,2]
[10,6,2,7,3,8,4,9,5,1]=>[4,2,2,2]
[7,3,8,4,10,6,2,9,5,1]=>[4,2,2,2]
[8,4,7,3,10,6,2,9,5,1]=>[5,2,2,1]
[10,5,8,3,6,1,9,4,7,2]=>[5,2,1,1,1]
[9,4,7,2,10,5,8,3,6,1]=>[5,2,1,1,1]
[10,5,7,2,8,3,9,4,6,1]=>[4,2,2,1,1]
[8,3,10,5,7,2,9,4,6,1]=>[4,2,2,1,1]
[8,3,9,4,7,2,10,5,6,1]=>[4,2,2,1,1]
[9,3,5,7,1,10,4,6,8,2]=>[4,2,1,1,1,1]
[10,4,6,8,2,9,3,5,7,1]=>[4,2,1,1,1,1]
[10,4,5,6,7,1,8,2,9,3]=>[3,2,2,1,1,1]
[8,2,9,3,10,4,5,6,7,1]=>[3,2,2,1,1,1]
[9,3,8,2,10,4,5,6,7,1]=>[4,2,1,1,1,1]
[5,6,9,3,7,1,10,4,8,2]=>[4,2,1,1,1,1]
[5,6,10,4,8,2,9,3,7,1]=>[4,2,1,1,1,1]
[5,6,9,3,8,2,10,4,7,1]=>[4,2,1,1,1,1]
[6,5,9,3,8,2,10,4,7,1]=>[5,2,1,1,1]
[9,2,7,6,5,4,10,3,8,1]=>[7,1,1,1]
[10,3,7,6,5,4,8,1,9,2]=>[6,2,1,1]
[9,2,10,3,7,6,5,4,8,1]=>[6,2,1,1]
[7,6,5,4,9,2,10,3,8,1]=>[6,2,1,1]
[6,4,7,5,10,3,9,2,8,1]=>[5,2,1,1,1]
[6,4,7,5,9,2,10,3,8,1]=>[4,2,2,1,1]
[7,5,6,4,9,2,10,3,8,1]=>[5,2,1,1,1]
[6,5,7,4,9,2,10,3,8,1]=>[5,2,1,1,1]
[5,6,7,3,8,4,9,1,10,2]=>[3,2,2,1,1,1]
[5,6,7,3,8,4,10,2,9,1]=>[4,2,1,1,1,1]
[5,6,8,4,7,3,10,2,9,1]=>[5,1,1,1,1,1]
[6,5,8,4,7,3,10,2,9,1]=>[6,1,1,1,1]
[4,2,5,6,7,8,9,10,1,3]=>[3,1,1,1,1,1,1,1]
[7,1,2,3,9,5,6,10,8,4]=>[3,2,2,1,1,1]
[6,1,2,9,4,5,3,10,8,7]=>[3,3,2,1,1]
[9,1,2,3,8,5,10,7,6,4]=>[5,2,1,1,1]
[9,1,2,8,4,3,10,7,5,6]=>[4,3,1,1,1]
[8,1,2,7,4,10,6,5,3,9]=>[5,2,1,1,1]
[9,1,8,3,2,5,10,7,4,6]=>[4,3,1,1,1]
[8,1,7,3,2,10,6,4,5,9]=>[4,3,1,1,1]
[7,1,2,3,10,5,6,9,8,4]=>[4,2,1,1,1,1]
[6,1,2,10,4,5,3,9,8,7]=>[4,2,2,1,1]
[8,1,2,3,10,5,9,6,7,4]=>[4,2,1,1,1,1]
[8,1,2,10,4,3,9,5,7,6]=>[4,2,2,1,1]
[7,1,2,10,4,9,5,3,6,8]=>[4,2,1,1,1,1]
[8,1,10,3,2,5,9,4,7,6]=>[4,2,2,1,1]
[7,1,10,3,2,9,4,5,6,8]=>[3,2,2,1,1,1]
[10,1,2,3,9,5,8,7,6,4]=>[6,1,1,1,1]
[10,1,2,9,4,3,8,7,5,6]=>[5,2,1,1,1]
[10,1,2,9,4,8,3,6,5,7]=>[5,1,1,1,1,1]
[9,1,2,8,4,7,6,5,3,10]=>[6,1,1,1,1]
[10,1,9,3,2,5,8,7,4,6]=>[5,2,1,1,1]
[10,1,9,3,2,8,5,6,4,7]=>[5,2,1,1,1]
[9,1,8,3,2,7,6,4,5,10]=>[5,2,1,1,1]
[8,1,2,3,10,9,5,7,6,4]=>[5,2,1,1,1]
[8,1,2,10,3,9,4,7,6,5]=>[5,2,1,1,1]
[7,1,2,10,9,4,6,3,5,8]=>[4,2,1,1,1,1]
[8,1,10,2,4,9,3,7,6,5]=>[5,2,1,1,1]
[7,1,10,2,9,3,6,4,5,8]=>[4,2,1,1,1,1]
[10,1,2,3,9,8,5,6,7,4]=>[5,1,1,1,1,1]
[10,1,2,9,3,8,4,6,7,5]=>[5,1,1,1,1,1]
[10,1,2,9,8,4,3,5,6,7]=>[5,1,1,1,1,1]
[9,1,2,8,7,4,5,6,3,10]=>[5,1,1,1,1,1]
[10,1,9,2,4,8,3,6,7,5]=>[5,1,1,1,1,1]
[10,1,9,2,8,3,4,5,6,7]=>[4,1,1,1,1,1,1]
[9,1,8,2,7,3,5,6,4,10]=>[5,1,1,1,1,1]
[10,1,9,8,3,2,6,4,5,7]=>[5,2,1,1,1]
[9,1,8,7,3,2,4,5,6,10]=>[5,1,1,1,1,1]
[8,10,1,3,4,9,2,7,6,5]=>[5,1,1,1,1,1]
[7,10,1,3,9,2,6,4,5,8]=>[4,1,1,1,1,1,1]
[10,9,1,3,4,8,2,6,7,5]=>[5,1,1,1,1,1]
[10,9,1,3,8,2,4,5,6,7]=>[4,1,1,1,1,1,1]
[9,8,1,3,7,2,5,6,4,10]=>[5,1,1,1,1,1]
[10,9,1,8,2,3,6,4,5,7]=>[5,1,1,1,1,1]
[9,8,1,7,2,3,4,5,6,10]=>[4,1,1,1,1,1,1]
[7,8,10,1,2,3,4,5,6,9]=>[2,1,1,1,1,1,1,1,1]
[4,5,6,7,8,10,1,2,3,9]=>[2,1,1,1,1,1,1,1,1]
[1,6,7,5,8,4,9,3,10,2]=>[5,1,1,1,1,1]
[1,2,3,4,5,6,8,10,7,9]=>[2,1,1,1,1,1,1,1,1]
[8,9,10,4,5,6,2,3,1,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,6,10,2,3,1,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,5,2,3,6,1,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,10,2,3,6,1,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,2,3,6,10,1,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,10,2,3,6,1,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,2,3,6,10,1,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,5,6,2,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,6,10,2,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,5,2,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,10,2,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,2,6,10,1,3,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,10,2,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,2,6,10,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,5,2,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,10,2,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,2,10,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,5,2,1,3,6,10,7]=>[4,2,1,1,1,1]
[8,4,5,9,10,2,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,2,10,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,4,5,9,2,1,3,6,10,7]=>[4,2,1,1,1,1]
[8,9,10,4,2,5,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,4,10,2,5,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,4,2,5,6,10,1,3,7]=>[4,1,1,1,1,1,1]
[8,4,9,10,2,5,6,1,3,7]=>[4,1,1,1,1,1,1]
[8,4,9,2,5,6,10,1,3,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,2,5,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,10,2,5,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,2,5,10,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,9,4,2,5,1,3,6,10,7]=>[4,2,1,1,1,1]
[8,4,9,10,2,5,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,4,9,2,5,1,3,6,10,7]=>[4,2,1,1,1,1]
[8,4,2,5,9,10,1,3,6,7]=>[4,1,1,1,1,1,1]
[8,4,2,5,9,1,3,6,10,7]=>[4,2,1,1,1,1]
[4,8,9,10,2,5,6,1,3,7]=>[3,1,1,1,1,1,1,1]
[4,8,9,2,5,6,10,1,3,7]=>[3,1,1,1,1,1,1,1]
[4,8,9,10,2,5,1,3,6,7]=>[3,1,1,1,1,1,1,1]
[4,8,9,2,5,10,1,3,6,7]=>[3,1,1,1,1,1,1,1]
[4,8,9,2,5,1,3,6,10,7]=>[3,2,1,1,1,1,1]
[4,8,2,5,9,10,1,3,6,7]=>[3,1,1,1,1,1,1,1]
[4,8,2,5,9,1,3,6,10,7]=>[3,2,1,1,1,1,1]
[6,5,3,1,2,4,8,7,10,9]=>[4,2,2,1,1]
[8,7,5,3,1,2,4,6,10,9]=>[5,2,1,1,1]
[10,9,7,5,3,1,2,4,6,8]=>[6,1,1,1,1]
[7,5,3,1,2,4,6,9,8,10]=>[4,2,1,1,1,1]
[5,3,1,2,4,7,6,9,8,10]=>[3,2,2,1,1,1]
[2,10,9,8,7,6,5,1,4,3]=>[8,1,1]
[9,3,4,5,6,7,1,2,10,8]=>[3,2,1,1,1,1,1]
[1,7,2,8,3,9,4,10,5,6]=>[2,2,2,2,1,1]
[1,7,2,8,3,9,10,4,5,6]=>[2,2,2,1,1,1,1]
[1,7,2,8,9,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[1,7,2,8,9,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[1,7,2,8,9,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[1,7,8,2,3,9,4,10,5,6]=>[2,2,2,1,1,1,1]
[1,7,8,2,3,9,10,4,5,6]=>[2,2,1,1,1,1,1,1]
[1,7,8,2,9,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[1,7,8,2,9,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[1,7,8,2,9,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[1,7,8,9,2,3,4,10,5,6]=>[2,2,1,1,1,1,1,1]
[1,7,8,9,2,3,10,4,5,6]=>[2,2,1,1,1,1,1,1]
[1,7,8,9,2,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,1,2,8,3,9,4,10,5,6]=>[2,2,2,2,1,1]
[7,1,2,8,3,9,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,2,8,9,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[7,1,2,8,9,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,2,8,9,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,1,8,2,3,9,4,10,5,6]=>[2,2,2,2,1,1]
[7,1,8,2,3,9,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,8,2,9,3,4,10,5,6]=>[2,2,2,2,1,1]
[7,1,8,2,9,10,3,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,8,9,2,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[7,1,8,9,2,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,8,9,2,10,3,4,5,6]=>[2,2,2,1,1,1,1]
[7,1,8,9,10,2,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,1,2,3,9,4,10,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,2,3,9,10,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,1,2,9,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,2,9,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,2,9,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,1,9,2,3,4,10,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,9,2,3,10,4,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,9,2,10,3,4,5,6]=>[2,2,2,1,1,1,1]
[7,8,1,9,10,2,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,9,1,2,3,4,10,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,9,1,2,3,10,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,8,9,1,10,2,3,4,5,6]=>[2,2,1,1,1,1,1,1]
[7,2,8,9,10,1,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[9,10,6,4,2,1,3,5,8,7]=>[5,2,1,1,1]
[10,7,8,4,2,1,3,6,5,9]=>[5,2,1,1,1]
[9,7,10,4,2,1,3,6,8,5]=>[5,2,1,1,1]
[8,9,10,4,2,1,3,7,6,5]=>[4,3,1,1,1]
[10,8,5,6,2,1,4,3,7,9]=>[5,2,1,1,1]
[9,10,5,6,2,1,4,3,8,7]=>[4,2,2,1,1]
[10,7,5,8,2,1,4,6,3,9]=>[5,2,1,1,1]
[9,7,5,10,2,1,4,6,8,3]=>[5,2,1,1,1]
[8,9,5,10,2,1,4,7,6,3]=>[4,3,1,1,1]
[10,6,7,8,2,1,5,4,3,9]=>[5,2,1,1,1]
[9,6,7,10,2,1,5,4,8,3]=>[5,2,1,1,1]
[8,6,9,10,2,1,5,7,4,3]=>[5,2,1,1,1]
[7,8,9,10,2,1,6,5,4,3]=>[5,2,1,1,1]
[10,8,6,3,4,2,1,5,7,9]=>[6,1,1,1,1]
[9,10,6,3,4,2,1,5,8,7]=>[5,2,1,1,1]
[10,7,8,3,4,2,1,6,5,9]=>[5,2,1,1,1]
[9,7,10,3,4,2,1,6,8,5]=>[5,2,1,1,1]
[8,9,10,3,4,2,1,7,6,5]=>[4,3,1,1,1]
[10,8,5,3,6,2,4,1,7,9]=>[6,1,1,1,1]
[9,10,5,3,6,2,4,1,8,7]=>[5,2,1,1,1]
[10,7,5,3,8,2,4,6,1,9]=>[6,1,1,1,1]
[9,7,5,3,10,2,4,6,8,1]=>[6,1,1,1,1]
[8,9,5,3,10,2,4,7,6,1]=>[5,2,1,1,1]
[10,6,7,3,8,2,5,4,1,9]=>[5,2,1,1,1]
[9,6,7,3,10,2,5,4,8,1]=>[5,2,1,1,1]
[8,6,9,3,10,2,5,7,4,1]=>[5,2,1,1,1]
[7,8,9,3,10,2,6,5,4,1]=>[5,2,1,1,1]
[10,8,4,5,6,3,2,1,7,9]=>[6,1,1,1,1]
[9,10,4,5,6,3,2,1,8,7]=>[5,2,1,1,1]
[10,7,4,5,8,3,2,6,1,9]=>[6,1,1,1,1]
[9,7,4,5,10,3,2,6,8,1]=>[6,1,1,1,1]
[8,9,4,5,10,3,2,7,6,1]=>[5,2,1,1,1]
[10,6,4,7,8,3,5,2,1,9]=>[6,1,1,1,1]
[9,6,4,7,10,3,5,2,8,1]=>[6,1,1,1,1]
[8,6,4,9,10,3,5,7,2,1]=>[6,1,1,1,1]
[7,8,4,9,10,3,6,5,2,1]=>[5,2,1,1,1]
[10,5,6,7,8,4,3,2,1,9]=>[6,1,1,1,1]
[9,5,6,7,10,4,3,2,8,1]=>[6,1,1,1,1]
[8,5,6,9,10,4,3,7,2,1]=>[6,1,1,1,1]
[7,5,8,9,10,4,6,3,2,1]=>[6,1,1,1,1]
[2,10,4,5,6,7,9,1,3,8]=>[3,1,1,1,1,1,1,1]
[10,3,4,5,6,7,1,9,2,8]=>[3,2,1,1,1,1,1]
[10,9,8,6,4,2,1,3,5,7]=>[7,1,1,1]
[10,8,7,6,4,2,1,3,5,9]=>[7,1,1,1]
[10,7,9,6,4,2,1,3,8,5]=>[6,2,1,1]
[10,9,8,7,6,4,2,1,3,5]=>[8,1,1]
[10,8,6,5,4,2,1,3,7,9]=>[7,1,1,1]
[10,9,8,6,5,4,2,1,3,7]=>[8,1,1]
[10,8,5,7,4,2,1,6,3,9]=>[6,2,1,1]
[10,5,9,7,4,2,1,6,8,3]=>[6,2,1,1]
[10,9,8,5,7,4,2,1,6,3]=>[7,2,1]
[10,8,7,6,5,4,2,1,3,9]=>[8,1,1]
[10,7,9,6,5,4,2,1,8,3]=>[7,2,1]
[10,6,9,8,5,7,2,1,4,3]=>[6,2,1,1]
[10,8,6,4,3,2,1,5,7,9]=>[7,1,1,1]
[10,9,8,6,4,3,2,1,5,7]=>[8,1,1]
[10,8,7,6,4,3,2,1,5,9]=>[8,1,1]
[10,7,9,6,4,3,2,1,8,5]=>[7,2,1]
[10,8,6,3,5,2,4,1,7,9]=>[6,1,1,1,1]
[10,9,8,6,3,5,2,4,1,7]=>[7,1,1,1]
[10,8,3,7,5,2,4,6,1,9]=>[6,1,1,1,1]
[10,3,9,7,5,2,4,6,8,1]=>[6,1,1,1,1]
[10,9,8,3,7,5,2,4,6,1]=>[7,1,1,1]
[10,8,7,6,3,5,2,4,1,9]=>[7,1,1,1]
[10,7,9,6,3,5,2,4,8,1]=>[6,1,1,1,1]
[10,9,3,8,6,5,2,7,4,1]=>[7,2,1]
[10,9,8,7,6,3,5,2,4,1]=>[8,1,1]
[10,8,6,5,4,3,2,1,7,9]=>[8,1,1]
[10,8,5,7,4,3,2,6,1,9]=>[7,1,1,1]
[10,5,9,7,4,3,2,6,8,1]=>[7,1,1,1]
[10,9,8,5,7,4,3,2,6,1]=>[8,1,1]
[10,8,4,7,6,3,5,2,1,9]=>[7,1,1,1]
[10,4,9,7,6,3,5,2,8,1]=>[7,1,1,1]
[10,4,9,6,8,3,5,7,2,1]=>[6,1,1,1,1]
[10,9,8,4,7,6,3,5,2,1]=>[8,1,1]
[10,7,9,6,5,4,3,2,8,1]=>[8,1,1]
[10,6,9,8,5,4,3,7,2,1]=>[8,1,1]
[10,5,9,8,7,4,6,3,2,1]=>[8,1,1]
[3,2,8,9,10,1,4,5,6,7]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,8,9,10,1,6,7]=>[2,1,1,1,1,1,1,1,1]
[2,3,4,7,8,9,10,1,5,6]=>[2,1,1,1,1,1,1,1,1]
[2,3,6,7,8,9,10,1,4,5]=>[2,1,1,1,1,1,1,1,1]
[2,5,6,7,8,9,10,1,3,4]=>[2,1,1,1,1,1,1,1,1]
[1,2,7,3,8,4,9,5,10,6]=>[2,2,2,2,1,1]
[4,1,2,3,6,5,8,7,10,9]=>[2,2,2,2,1,1]
[7,1,2,3,4,5,9,6,10,8]=>[2,2,2,1,1,1,1]
[3,4,5,6,7,1,8,2,10,9]=>[2,2,2,1,1,1,1]
[1,4,5,6,10,7,8,2,9,3]=>[3,2,1,1,1,1,1]
[2,4,5,6,10,7,1,8,3,9]=>[3,2,1,1,1,1,1]
[3,4,5,6,8,7,1,10,2,9]=>[3,2,1,1,1,1,1]
[3,5,6,7,10,8,1,9,2,4]=>[3,2,1,1,1,1,1]
[1,4,5,9,6,7,2,8,10,3]=>[3,2,1,1,1,1,1]
[10,2,3,4,5,6,7,1,9,8]=>[3,2,1,1,1,1,1]
[10,2,3,4,5,6,1,8,9,7]=>[3,2,1,1,1,1,1]
[10,2,3,4,5,1,7,8,9,6]=>[3,2,1,1,1,1,1]
[10,2,3,4,1,6,7,8,9,5]=>[3,2,1,1,1,1,1]
[10,2,3,1,5,6,7,8,9,4]=>[3,2,1,1,1,1,1]
[10,2,1,4,5,6,7,8,9,3]=>[3,2,1,1,1,1,1]
[2,3,4,5,6,7,1,9,8,10]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,1,7,6,9,8,10]=>[2,2,2,1,1,1,1]
[3,4,5,6,7,8,10,1,9,2]=>[3,1,1,1,1,1,1,1]
[7,8,9,6,1,2,3,4,10,5]=>[3,2,1,1,1,1,1]
[2,8,9,10,7,1,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[8,9,7,5,6,1,2,3,10,4]=>[4,2,1,1,1,1]
[2,9,10,8,6,7,1,3,4,5]=>[4,1,1,1,1,1,1]
[7,8,9,5,1,2,3,4,10,6]=>[3,2,1,1,1,1,1]
[7,8,9,1,6,2,3,4,10,5]=>[3,2,1,1,1,1,1]
[2,8,9,10,6,1,3,4,5,7]=>[3,1,1,1,1,1,1,1]
[2,8,9,10,1,7,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[9,10,6,7,4,5,2,3,1,8]=>[5,1,1,1,1,1]
[8,9,4,5,10,1,2,3,6,7]=>[3,1,1,1,1,1,1,1]
[8,4,3,9,10,1,2,5,6,7]=>[4,1,1,1,1,1,1]
[9,6,10,1,3,7,8,2,4,5]=>[4,1,1,1,1,1,1]
[9,10,6,7,4,5,1,2,3,8]=>[4,1,1,1,1,1,1]
[9,6,4,10,3,7,1,2,5,8]=>[5,1,1,1,1,1]
[10,1,8,9,6,7,4,5,2,3]=>[5,1,1,1,1,1]
[10,8,6,1,4,9,3,7,2,5]=>[6,1,1,1,1]
[10,8,6,5,4,1,3,9,2,7]=>[7,1,1,1]
[10,8,7,6,5,4,3,1,2,9]=>[8,1,1]
[1,2,3,4,6,5,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,7,9,10]=>[2,1,1,1,1,1,1,1,1]
[10,7,6,5,4,3,2,1,8,9]=>[8,1,1]
[10,1,2,3,4,5,6,9,8,7]=>[4,1,1,1,1,1,1]
[10,1,2,3,4,5,9,7,8,6]=>[4,1,1,1,1,1,1]
[10,1,2,3,9,5,6,7,8,4]=>[4,1,1,1,1,1,1]
[10,1,2,9,4,5,6,7,8,3]=>[4,1,1,1,1,1,1]
[3,4,5,6,7,9,10,1,8,2]=>[3,1,1,1,1,1,1,1]
[3,4,5,7,8,9,10,1,6,2]=>[3,1,1,1,1,1,1,1]
[3,4,6,7,8,9,10,1,5,2]=>[3,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,1,3,2]=>[3,1,1,1,1,1,1,1]
[6,4,5,7,3,8,2,9,1,10]=>[5,1,1,1,1,1]
[7,5,1,3,2,6,4,8,9,10]=>[4,2,1,1,1,1]
[9,6,1,3,4,2,7,8,5,10]=>[4,2,1,1,1,1]
[8,3,6,1,4,2,7,5,9,10]=>[4,2,1,1,1,1]
[10,1,8,3,2,5,7,4,9,6]=>[4,2,2,1,1]
[10,3,7,1,4,5,2,8,9,6]=>[4,2,1,1,1,1]
[9,3,4,7,1,5,2,8,6,10]=>[4,2,1,1,1,1]
[7,10,1,3,8,2,6,5,9,4]=>[5,1,1,1,1,1]
[10,9,5,1,8,2,4,3,6,7]=>[5,2,1,1,1]
[10,3,4,5,8,1,6,2,9,7]=>[4,2,1,1,1,1]
[9,8,7,5,6,4,3,2,10,1]=>[8,1,1]
[9,10,2,4,6,8,1,3,5,7]=>[3,1,1,1,1,1,1,1]
[7,8,2,4,6,10,1,3,5,9]=>[3,1,1,1,1,1,1,1]
[9,7,10,2,4,6,8,1,3,5]=>[4,1,1,1,1,1,1]
[8,9,10,7,2,4,6,1,3,5]=>[4,1,1,1,1,1,1]
[5,6,2,4,8,10,1,3,7,9]=>[3,1,1,1,1,1,1,1]
[5,6,9,10,2,4,8,1,3,7]=>[3,1,1,1,1,1,1,1]
[7,5,8,2,4,6,10,1,3,9]=>[4,1,1,1,1,1,1]
[7,9,5,10,2,4,6,8,1,3]=>[4,1,1,1,1,1,1]
[5,8,9,10,7,2,4,6,1,3]=>[4,1,1,1,1,1,1]
[6,7,8,5,2,4,10,1,3,9]=>[4,1,1,1,1,1,1]
[9,6,7,5,10,2,4,8,1,3]=>[5,1,1,1,1,1]
[8,9,6,10,5,7,2,4,1,3]=>[5,1,1,1,1,1]
[7,8,9,10,6,5,2,4,1,3]=>[5,1,1,1,1,1]
[3,4,2,6,8,10,1,5,7,9]=>[3,1,1,1,1,1,1,1]
[3,4,9,10,2,6,8,1,5,7]=>[3,1,1,1,1,1,1,1]
[3,4,7,8,2,6,10,1,5,9]=>[3,1,1,1,1,1,1,1]
[9,3,4,7,10,2,6,8,1,5]=>[4,1,1,1,1,1,1]
[8,9,10,3,4,7,2,6,1,5]=>[4,1,1,1,1,1,1]
[5,3,6,2,4,8,10,1,7,9]=>[4,1,1,1,1,1,1]
[5,3,6,9,10,2,4,8,1,7]=>[4,1,1,1,1,1,1]
[5,7,3,8,2,4,6,10,1,9]=>[4,1,1,1,1,1,1]
[5,7,9,3,10,2,4,6,8,1]=>[4,1,1,1,1,1,1]
[8,5,9,10,3,7,2,4,6,1]=>[5,1,1,1,1,1]
[3,6,7,8,5,2,4,10,1,9]=>[4,1,1,1,1,1,1]
[9,3,6,7,5,10,2,4,8,1]=>[5,1,1,1,1,1]
[6,8,3,9,10,5,7,2,4,1]=>[4,2,1,1,1,1]
[7,8,9,10,3,6,5,2,4,1]=>[5,1,1,1,1,1]
[4,5,6,3,2,8,10,1,7,9]=>[4,1,1,1,1,1,1]
[4,5,6,3,9,10,2,8,1,7]=>[4,1,1,1,1,1,1]
[7,4,5,3,8,2,6,10,1,9]=>[5,1,1,1,1,1]
[7,4,5,9,3,10,2,6,8,1]=>[5,1,1,1,1,1]
[4,8,5,9,10,3,7,2,6,1]=>[5,1,1,1,1,1]
[6,7,4,8,3,5,2,10,1,9]=>[5,1,1,1,1,1]
[6,7,9,4,3,5,10,2,8,1]=>[5,1,1,1,1,1]
[8,6,9,4,10,3,5,7,2,1]=>[6,1,1,1,1]
[7,4,8,9,10,6,3,5,2,1]=>[5,2,1,1,1]
[5,6,7,8,4,3,2,10,1,9]=>[5,1,1,1,1,1]
[9,5,6,7,4,3,10,2,8,1]=>[6,1,1,1,1]
[8,9,5,6,4,10,3,7,2,1]=>[6,1,1,1,1]
[7,8,9,5,10,4,6,3,2,1]=>[6,1,1,1,1]
[1,2,4,5,6,8,10,9,3,7]=>[3,1,1,1,1,1,1,1]
[1,2,3,5,7,8,10,6,9,4]=>[3,1,1,1,1,1,1,1]
[1,2,4,5,7,8,10,3,9,6]=>[3,1,1,1,1,1,1,1]
[1,2,4,6,7,5,10,8,3,9]=>[3,2,1,1,1,1,1]
[1,3,4,2,7,8,10,5,9,6]=>[3,2,1,1,1,1,1]
[1,3,4,6,7,2,10,8,5,9]=>[3,2,1,1,1,1,1]
[1,2,3,5,6,9,8,10,7,4]=>[4,1,1,1,1,1,1]
[1,2,4,5,6,9,8,10,3,7]=>[3,1,1,1,1,1,1,1]
[1,2,3,5,7,9,6,10,8,4]=>[3,2,1,1,1,1,1]
[1,2,4,5,7,9,3,10,8,6]=>[3,2,1,1,1,1,1]
[1,2,4,6,5,9,7,10,3,8]=>[3,2,1,1,1,1,1]
[1,3,4,2,7,9,5,10,8,6]=>[3,2,2,1,1,1]
[1,3,4,6,2,9,7,10,5,8]=>[3,2,1,1,1,1,1]
[1,2,3,5,8,7,9,6,10,4]=>[4,1,1,1,1,1,1]
[1,2,4,5,8,7,9,3,10,6]=>[3,2,1,1,1,1,1]
[1,2,4,6,8,5,9,3,10,7]=>[3,2,1,1,1,1,1]
[1,2,4,7,6,8,5,9,3,10]=>[4,1,1,1,1,1,1]
[1,3,4,2,8,7,9,5,10,6]=>[3,2,2,1,1,1]
[1,3,4,6,8,2,9,5,10,7]=>[2,2,2,1,1,1,1]
[1,3,4,7,6,8,2,9,5,10]=>[3,2,1,1,1,1,1]
[1,2,3,6,5,9,7,10,8,4]=>[3,2,2,1,1,1]
[1,2,4,6,3,9,7,10,8,5]=>[3,2,2,1,1,1]
[1,2,5,4,6,9,7,10,3,8]=>[3,2,1,1,1,1,1]
[1,3,2,6,4,9,7,10,8,5]=>[3,2,2,2,1]
[1,3,5,2,6,9,7,10,4,8]=>[3,2,1,1,1,1,1]
[1,2,3,6,8,5,9,7,10,4]=>[3,2,1,1,1,1,1]
[1,2,4,6,8,3,9,7,10,5]=>[3,2,1,1,1,1,1]
[1,2,5,4,8,6,9,3,10,7]=>[3,2,2,1,1,1]
[1,2,5,7,4,8,6,9,3,10]=>[3,2,1,1,1,1,1]
[1,3,2,6,8,4,9,7,10,5]=>[3,2,2,1,1,1]
[1,3,5,2,8,6,9,4,10,7]=>[3,2,2,1,1,1]
[1,3,5,7,2,8,6,9,4,10]=>[3,2,1,1,1,1,1]
[1,4,3,5,8,2,9,6,10,7]=>[3,2,2,1,1,1]
[1,4,3,7,5,8,2,9,6,10]=>[3,2,2,1,1,1]
[2,1,3,6,4,9,7,10,8,5]=>[3,2,2,2,1]
[2,1,5,3,6,9,7,10,4,8]=>[3,2,2,1,1,1]
[2,1,3,6,8,4,9,7,10,5]=>[3,2,2,1,1,1]
[2,1,5,3,8,6,9,4,10,7]=>[3,2,2,2,1]
[2,1,5,7,3,8,6,9,4,10]=>[3,2,2,1,1,1]
[2,4,1,5,8,3,9,6,10,7]=>[2,2,2,2,1,1]
[2,4,1,7,5,8,3,9,6,10]=>[3,2,2,1,1,1]
[5,6,1,2,3,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[2,5,1,3,6,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[3,2,1,5,6,7,8,9,10,4]=>[3,2,1,1,1,1,1]
[6,7,8,1,2,3,4,9,10,5]=>[2,2,1,1,1,1,1,1]
[2,6,7,1,3,4,8,9,10,5]=>[2,2,1,1,1,1,1,1]
[6,3,4,1,2,7,8,9,10,5]=>[3,2,1,1,1,1,1]
[3,2,6,1,4,7,8,9,10,5]=>[3,2,1,1,1,1,1]
[4,3,2,1,6,7,8,9,10,5]=>[4,2,1,1,1,1]
[2,7,8,9,1,3,4,5,10,6]=>[2,2,1,1,1,1,1,1]
[7,3,4,8,1,2,5,9,10,6]=>[3,2,1,1,1,1,1]
[3,2,7,8,1,4,5,9,10,6]=>[3,2,1,1,1,1,1]
[4,7,2,5,1,3,8,9,10,6]=>[3,2,1,1,1,1,1]
[4,3,2,7,1,5,8,9,10,6]=>[4,2,1,1,1,1]
[5,4,3,2,1,7,8,9,10,6]=>[5,2,1,1,1]
[8,3,4,9,10,1,2,5,6,7]=>[3,1,1,1,1,1,1,1]
[8,9,4,5,6,1,2,3,10,7]=>[3,2,1,1,1,1,1]
[4,3,2,8,9,1,5,6,10,7]=>[4,2,1,1,1,1]
[8,5,6,3,4,1,2,9,10,7]=>[4,2,1,1,1,1]
[5,3,8,2,6,1,4,9,10,7]=>[4,2,1,1,1,1]
[5,4,3,2,8,1,6,9,10,7]=>[5,2,1,1,1]
[6,5,4,3,2,1,8,9,10,7]=>[6,2,1,1]
[5,9,10,2,6,7,1,3,4,8]=>[3,1,1,1,1,1,1,1]
[9,5,6,3,4,10,1,2,7,8]=>[4,1,1,1,1,1,1]
[5,3,9,2,6,10,1,4,7,8]=>[4,1,1,1,1,1,1]
[5,4,3,2,9,10,1,6,7,8]=>[5,1,1,1,1,1]
[6,9,4,7,2,5,1,3,10,8]=>[4,2,1,1,1,1]
[6,4,3,9,2,7,1,5,10,8]=>[5,2,1,1,1]
[6,5,4,3,2,9,1,7,10,8]=>[6,2,1,1]
[7,6,5,4,3,2,1,9,10,8]=>[7,2,1]
[10,7,8,5,6,3,4,1,2,9]=>[5,1,1,1,1,1]
[7,5,10,3,8,2,6,1,4,9]=>[5,1,1,1,1,1]
[7,5,4,3,10,2,8,1,6,9]=>[6,1,1,1,1]
[7,6,5,4,3,2,10,1,8,9]=>[7,1,1,1]
[2,1,8,7,4,3,6,5,10,9]=>[4,2,2,2]
[2,1,4,3,6,5,7,9,10,8]=>[2,2,2,2,1,1]
[2,1,4,3,5,7,8,6,10,9]=>[2,2,2,2,1,1]
[2,1,4,3,5,7,6,9,10,8]=>[2,2,2,2,1,1]
[2,1,4,3,5,6,8,9,10,7]=>[2,2,2,1,1,1,1]
[2,1,3,5,6,4,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,3,5,6,4,7,9,10,8]=>[2,2,2,1,1,1,1]
[2,1,3,5,4,7,8,6,10,9]=>[2,2,2,2,1,1]
[2,1,3,5,4,7,6,9,10,8]=>[2,2,2,2,1,1]
[2,1,3,5,4,6,8,9,10,7]=>[2,2,2,1,1,1,1]
[2,1,3,4,6,7,8,5,10,9]=>[2,2,2,1,1,1,1]
[2,1,3,4,6,7,5,9,10,8]=>[2,2,2,1,1,1,1]
[2,1,3,4,6,5,8,9,10,7]=>[2,2,2,1,1,1,1]
[2,1,3,4,5,7,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[1,3,4,2,6,5,7,9,10,8]=>[2,2,2,1,1,1,1]
[1,3,4,2,5,7,8,6,10,9]=>[2,2,2,1,1,1,1]
[1,3,4,2,5,7,6,9,10,8]=>[2,2,2,1,1,1,1]
[1,3,4,2,5,6,8,9,10,7]=>[2,2,1,1,1,1,1,1]
[1,3,2,5,6,4,8,7,10,9]=>[2,2,2,2,1,1]
[1,3,2,5,6,4,7,9,10,8]=>[2,2,2,1,1,1,1]
[1,3,2,5,4,7,8,6,10,9]=>[2,2,2,2,1,1]
[1,3,2,5,4,7,6,9,10,8]=>[2,2,2,2,1,1]
[1,3,2,5,4,6,8,9,10,7]=>[2,2,2,1,1,1,1]
[1,3,2,4,6,7,8,5,10,9]=>[2,2,2,1,1,1,1]
[1,3,2,4,6,7,5,9,10,8]=>[2,2,2,1,1,1,1]
[1,3,2,4,6,5,8,9,10,7]=>[2,2,2,1,1,1,1]
[1,3,2,4,5,7,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[1,2,4,5,6,3,8,7,10,9]=>[2,2,2,1,1,1,1]
[1,2,4,5,6,3,7,9,10,8]=>[2,2,1,1,1,1,1,1]
[1,2,4,5,3,7,8,6,10,9]=>[2,2,2,1,1,1,1]
[1,2,4,5,3,7,6,9,10,8]=>[2,2,2,1,1,1,1]
[1,2,4,5,3,6,8,9,10,7]=>[2,2,1,1,1,1,1,1]
[1,2,4,3,6,7,8,5,10,9]=>[2,2,2,1,1,1,1]
[1,2,4,3,6,7,5,9,10,8]=>[2,2,2,1,1,1,1]
[1,2,4,3,6,5,8,9,10,7]=>[2,2,2,1,1,1,1]
[1,2,4,3,5,7,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[1,2,3,5,6,7,8,4,10,9]=>[2,2,1,1,1,1,1,1]
[1,2,3,5,6,7,4,9,10,8]=>[2,2,1,1,1,1,1,1]
[1,2,3,5,6,4,8,9,10,7]=>[2,2,1,1,1,1,1,1]
[1,2,3,5,4,7,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,6,10,8,9,7,1]=>[4,1,1,1,1,1,1]
[2,3,4,5,10,7,8,9,6,1]=>[4,1,1,1,1,1,1]
[2,3,4,10,6,7,8,9,5,1]=>[4,1,1,1,1,1,1]
[2,3,10,5,6,7,8,9,4,1]=>[4,1,1,1,1,1,1]
[2,10,4,5,6,7,8,9,3,1]=>[4,1,1,1,1,1,1]
[10,3,4,5,6,7,8,9,2,1]=>[4,1,1,1,1,1,1]
[6,5,7,4,8,3,10,1,9,2]=>[5,2,1,1,1]
[6,5,7,4,10,1,9,2,8,3]=>[4,3,1,1,1]
[6,5,10,1,9,2,8,3,7,4]=>[5,2,1,1,1]
[5,10,1,9,2,8,3,7,4,6]=>[5,1,1,1,1,1]
[5,6,4,10,1,9,2,8,3,7]=>[4,2,1,1,1,1]
[5,6,4,7,3,10,1,9,2,8]=>[4,2,1,1,1,1]
[5,6,4,7,3,8,2,10,1,9]=>[5,1,1,1,1,1]
[2,10,1,3,4,5,6,9,7,8]=>[3,1,1,1,1,1,1,1]
[2,9,1,3,4,5,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[10,3,1,2,4,5,6,9,7,8]=>[3,2,1,1,1,1,1]
[3,1,10,2,4,5,6,9,7,8]=>[3,2,1,1,1,1,1]
[9,3,1,2,4,5,6,7,10,8]=>[3,2,1,1,1,1,1]
[3,1,9,2,4,5,6,7,10,8]=>[2,2,2,1,1,1,1]
[10,9,3,4,5,6,7,8,1,2]=>[4,1,1,1,1,1,1]
[10,9,2,3,4,5,6,7,1,8]=>[4,1,1,1,1,1,1]
[10,4,5,6,7,8,9,2,1,3]=>[4,1,1,1,1,1,1]
[10,3,4,5,6,7,8,2,1,9]=>[4,1,1,1,1,1,1]
[1,8,5,2,9,6,3,10,7,4]=>[3,3,3,1]
[10,9,3,8,7,6,5,4,2,1]=>[9,1]
[8,7,6,4,5,3,2,1,10,9]=>[7,2,1]
[10,9,8,6,5,4,7,3,2,1]=>[9,1]
[8,1,9,10,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1]
[5,10,4,9,3,8,2,1,7,6]=>[5,2,1,1,1]
[5,10,4,9,3,2,8,7,1,6]=>[5,2,1,1,1]
[5,10,4,9,3,2,8,1,7,6]=>[5,2,1,1,1]
[5,10,4,9,3,2,1,8,7,6]=>[5,3,1,1]
[5,10,4,3,9,8,2,7,1,6]=>[5,2,1,1,1]
[5,10,4,3,9,8,2,1,7,6]=>[5,2,2,1]
[5,10,4,3,9,2,8,7,1,6]=>[5,2,1,1,1]
[5,10,4,3,9,2,8,1,7,6]=>[5,2,1,1,1]
[5,10,4,3,9,2,1,8,7,6]=>[5,3,1,1]
[5,10,4,3,2,9,8,7,1,6]=>[5,3,1,1]
[5,10,4,3,2,9,8,1,7,6]=>[5,3,1,1]
[5,10,4,3,2,9,1,8,7,6]=>[5,3,1,1]
[5,10,4,3,2,1,9,8,7,6]=>[5,4,1]
[5,4,10,9,3,8,2,7,1,6]=>[5,2,1,1,1]
[5,4,10,9,3,8,2,1,7,6]=>[5,2,2,1]
[5,4,10,9,3,2,8,7,1,6]=>[5,2,2,1]
[5,4,10,9,3,2,8,1,7,6]=>[5,2,2,1]
[5,4,10,9,3,2,1,8,7,6]=>[5,3,2]
[5,4,10,3,9,8,2,7,1,6]=>[5,2,1,1,1]
[5,4,10,3,9,8,2,1,7,6]=>[5,2,2,1]
[5,4,10,3,9,2,8,7,1,6]=>[5,2,1,1,1]
[5,4,10,3,9,2,8,1,7,6]=>[5,2,1,1,1]
[5,4,10,3,9,2,1,8,7,6]=>[5,3,1,1]
[5,4,10,3,2,9,8,7,1,6]=>[5,3,1,1]
[5,4,10,3,2,9,8,1,7,6]=>[5,3,1,1]
[5,4,10,3,2,9,1,8,7,6]=>[5,3,1,1]
[5,4,10,3,2,1,9,8,7,6]=>[5,4,1]
[5,4,3,10,9,8,2,7,1,6]=>[5,3,1,1]
[5,4,3,10,9,8,2,1,7,6]=>[5,3,2]
[5,4,3,10,9,2,8,7,1,6]=>[5,3,1,1]
[5,4,3,10,9,2,8,1,7,6]=>[5,3,1,1]
[5,4,3,10,9,2,1,8,7,6]=>[5,3,2]
[5,4,3,10,2,9,8,7,1,6]=>[5,3,1,1]
[5,4,3,10,2,9,8,1,7,6]=>[5,3,1,1]
[5,4,3,10,2,9,1,8,7,6]=>[5,3,1,1]
[5,4,3,10,2,1,9,8,7,6]=>[5,4,1]
[5,4,3,2,10,9,8,7,1,6]=>[5,4,1]
[5,4,3,2,10,9,8,1,7,6]=>[5,4,1]
[5,4,3,2,10,9,1,8,7,6]=>[5,4,1]
[5,4,3,2,10,1,9,8,7,6]=>[5,4,1]
[3,4,5,6,7,10,1,2,8,9]=>[2,1,1,1,1,1,1,1,1]
[3,4,5,6,9,10,1,2,7,8]=>[2,1,1,1,1,1,1,1,1]
[3,4,5,8,9,10,1,2,6,7]=>[2,1,1,1,1,1,1,1,1]
[3,4,7,8,9,10,1,2,5,6]=>[2,1,1,1,1,1,1,1,1]
[3,6,7,8,9,10,1,2,4,5]=>[2,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,10,7,9,8]=>[3,2,2,2,1]
[2,1,4,3,8,5,7,6,10,9]=>[3,2,2,2,1]
[2,1,4,3,10,9,7,5,6,8]=>[4,2,2,1,1]
[2,1,4,3,10,5,6,8,9,7]=>[3,2,2,1,1,1]
[2,1,6,3,5,4,8,7,10,9]=>[3,2,2,2,1]
[2,1,6,3,5,4,10,7,9,8]=>[3,3,2,1,1]
[2,1,8,7,5,3,4,6,10,9]=>[4,2,2,1,1]
[2,1,10,7,5,9,4,3,6,8]=>[5,2,1,1,1]
[2,1,10,8,5,3,6,4,9,7]=>[4,2,2,2]
[2,1,8,3,4,6,7,5,10,9]=>[3,2,2,1,1,1]
[2,1,10,9,4,6,7,3,5,8]=>[4,2,1,1,1,1]
[2,1,10,3,9,6,4,8,5,7]=>[4,2,2,1,1]
[2,1,10,3,4,5,7,8,9,6]=>[3,2,1,1,1,1,1]
[4,1,3,2,6,5,8,7,10,9]=>[3,2,2,2,1]
[4,1,3,2,6,5,10,7,9,8]=>[3,3,2,1,1]
[4,1,3,2,8,5,7,6,10,9]=>[3,3,2,1,1]
[4,1,3,2,10,9,7,5,6,8]=>[4,3,1,1,1]
[4,1,3,2,10,5,6,8,9,7]=>[3,3,1,1,1,1]
[6,5,3,1,2,4,10,7,9,8]=>[4,3,1,1,1]
[8,5,3,7,2,1,4,6,10,9]=>[5,2,1,1,1]
[10,5,3,7,2,9,4,1,6,8]=>[5,2,1,1,1]
[10,5,3,8,2,1,6,4,9,7]=>[5,2,2,1]
[8,6,3,1,4,2,7,5,10,9]=>[4,2,2,2]
[10,6,3,9,4,2,7,1,5,8]=>[5,2,1,1,1]
[10,6,3,1,9,2,4,8,5,7]=>[4,3,1,1,1]
[10,7,3,1,4,5,2,8,9,6]=>[4,2,2,1,1]
[6,1,2,4,5,3,8,7,10,9]=>[3,2,2,1,1,1]
[6,1,2,4,5,3,10,7,9,8]=>[3,3,1,1,1,1]
[8,7,2,4,5,1,3,6,10,9]=>[4,2,1,1,1,1]
[10,7,2,4,5,9,3,1,6,8]=>[5,1,1,1,1,1]
[10,8,2,4,5,1,6,3,9,7]=>[4,2,2,1,1]
[8,1,7,4,2,6,3,5,10,9]=>[4,2,2,1,1]
[10,9,7,4,2,6,3,1,5,8]=>[6,2,1,1]
[10,1,8,4,9,6,2,3,5,7]=>[4,2,1,1,1,1]
[10,1,8,4,2,5,7,3,9,6]=>[4,2,2,1,1]
[8,1,2,3,5,6,7,4,10,9]=>[3,2,1,1,1,1,1]
[10,9,2,3,5,6,7,1,4,8]=>[4,1,1,1,1,1,1]
[10,1,9,3,5,6,2,8,4,7]=>[4,2,1,1,1,1]
[10,1,2,9,5,3,7,8,4,6]=>[4,2,1,1,1,1]
[10,9,7,6,5,4,3,8,2,1]=>[9,1]
[3,2,4,1,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[3,4,2,5,1,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[4,3,5,2,6,1,7,8,9,10]=>[4,1,1,1,1,1,1]
[4,5,3,6,2,7,1,8,9,10]=>[4,1,1,1,1,1,1]
[5,4,6,3,7,2,8,1,9,10]=>[5,1,1,1,1,1]
[2,1,4,3,6,5,10,7,8,9]=>[2,2,2,2,1,1]
[2,1,4,3,8,5,6,7,10,9]=>[2,2,2,2,1,1]
[2,1,4,3,10,9,6,5,8,7]=>[4,2,2,2]
[2,1,4,3,10,5,6,7,8,9]=>[2,2,2,1,1,1,1]
[2,1,6,3,4,5,8,7,10,9]=>[2,2,2,2,1,1]
[2,1,6,3,4,5,10,7,8,9]=>[2,2,2,1,1,1,1]
[2,1,10,7,4,9,6,3,8,5]=>[4,2,2,2]
[2,1,10,9,4,3,6,7,8,5]=>[4,2,2,1,1]
[2,1,8,3,4,5,6,7,10,9]=>[2,2,2,1,1,1,1]
[2,1,10,9,4,5,6,3,8,7]=>[4,2,2,1,1]
[2,1,10,3,8,5,4,7,6,9]=>[4,2,2,1,1]
[4,1,2,3,6,5,10,7,8,9]=>[2,2,2,1,1,1,1]
[4,1,2,3,8,5,6,7,10,9]=>[2,2,2,1,1,1,1]
[4,1,2,3,10,9,6,5,8,7]=>[4,2,2,1,1]
[6,5,2,1,4,3,8,7,10,9]=>[4,2,2,2]
[6,5,2,1,4,3,10,7,8,9]=>[4,2,2,1,1]
[8,5,2,7,4,1,6,3,10,9]=>[4,2,2,2]
[10,5,2,7,4,9,6,1,8,3]=>[4,2,2,2]
[10,5,2,9,4,1,6,7,8,3]=>[4,2,2,1,1]
[8,7,2,1,4,5,6,3,10,9]=>[4,2,2,1,1]
[10,7,2,9,4,5,6,1,8,3]=>[4,2,2,1,1]
[10,9,2,1,8,5,4,7,6,3]=>[6,2,2]
[10,9,2,1,4,5,6,7,8,3]=>[4,2,1,1,1,1]
[6,1,2,3,4,5,8,7,10,9]=>[2,2,2,1,1,1,1]
[8,7,2,3,4,1,6,5,10,9]=>[4,2,2,1,1]
[10,7,2,3,4,9,6,1,8,5]=>[4,2,2,1,1]
[10,9,2,3,4,1,6,7,8,5]=>[4,2,1,1,1,1]
[8,1,6,3,2,5,4,7,10,9]=>[4,2,2,1,1]
[10,9,6,3,2,5,4,1,8,7]=>[6,2,2]
[10,1,6,3,8,5,2,7,4,9]=>[4,2,2,1,1]
[10,1,8,3,2,5,6,7,4,9]=>[4,2,1,1,1,1]
[10,9,2,3,4,5,6,1,8,7]=>[4,2,1,1,1,1]
[10,1,8,3,4,5,2,7,6,9]=>[4,2,1,1,1,1]
[10,1,2,7,4,3,6,5,8,9]=>[4,2,1,1,1,1]
[1,2,9,7,5,3,10,8,6,4]=>[4,4,1,1]
[2,4,1,5,6,7,8,10,3,9]=>[2,2,1,1,1,1,1,1]
[1,3,5,7,2,9,4,6,8,10]=>[2,2,1,1,1,1,1,1]
[1,3,5,7,2,9,4,10,6,8]=>[2,2,2,1,1,1,1]
[1,3,5,7,2,8,4,9,6,10]=>[2,2,2,1,1,1,1]
[1,3,5,6,2,7,4,9,8,10]=>[2,2,2,1,1,1,1]
[1,3,4,5,2,7,6,9,8,10]=>[2,2,2,1,1,1,1]
[10,1,2,3,4,5,7,8,9,6]=>[3,1,1,1,1,1,1,1]
[8,1,2,3,4,5,10,7,9,6]=>[3,2,1,1,1,1,1]
[8,1,2,3,4,5,9,7,10,6]=>[3,2,1,1,1,1,1]
[9,1,2,3,4,10,6,7,8,5]=>[3,2,1,1,1,1,1]
[8,1,2,3,4,10,6,7,9,5]=>[3,2,1,1,1,1,1]
[8,1,2,3,4,9,6,7,10,5]=>[3,2,1,1,1,1,1]
[7,1,2,3,4,9,6,10,8,5]=>[3,2,2,1,1,1]
[7,1,2,3,4,8,6,9,10,5]=>[3,2,1,1,1,1,1]
[8,1,2,3,10,5,6,7,9,4]=>[3,2,1,1,1,1,1]
[8,1,2,3,9,5,6,7,10,4]=>[3,2,1,1,1,1,1]
[7,1,2,3,10,5,6,8,9,4]=>[3,2,1,1,1,1,1]
[7,1,2,3,8,5,6,9,10,4]=>[3,2,1,1,1,1,1]
[6,1,2,3,8,5,10,7,9,4]=>[3,2,2,1,1,1]
[6,1,2,3,8,5,9,7,10,4]=>[3,2,2,1,1,1]
[6,1,2,3,7,5,8,9,10,4]=>[3,2,1,1,1,1,1]
[6,1,2,9,4,5,10,7,8,3]=>[3,2,2,1,1,1]
[6,1,2,8,4,5,10,7,9,3]=>[3,2,2,1,1,1]
[6,1,2,8,4,5,9,7,10,3]=>[3,2,2,1,1,1]
[6,1,2,7,4,5,8,9,10,3]=>[3,2,1,1,1,1,1]
[5,1,2,7,4,9,6,10,8,3]=>[3,2,2,2,1]
[5,1,2,7,4,8,6,9,10,3]=>[3,2,2,1,1,1]
[5,1,2,6,4,7,8,9,10,3]=>[3,2,1,1,1,1,1]
[4,1,6,3,8,5,9,7,10,2]=>[3,2,2,2,1]
[4,1,6,3,7,5,8,9,10,2]=>[3,2,2,1,1,1]
[4,1,5,3,6,7,8,9,10,2]=>[3,2,1,1,1,1,1]
[1,10,9,8,7,6,5,3,2,4]=>[8,1,1]
[1,10,9,8,7,6,4,3,2,5]=>[8,1,1]
[1,10,9,8,7,5,4,3,2,6]=>[8,1,1]
[1,10,9,8,6,5,4,3,2,7]=>[8,1,1]
[1,10,9,7,6,5,4,3,2,8]=>[8,1,1]
[1,10,8,7,6,5,4,3,2,9]=>[8,1,1]
[9,10,2,3,4,5,6,7,1,8]=>[3,1,1,1,1,1,1,1]
[8,9,10,2,3,4,5,6,1,7]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,2,3,4,5,1,6]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,2,3,1,4]=>[3,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,2,1,3]=>[3,1,1,1,1,1,1,1]
[8,10,3,4,5,6,7,2,1,9]=>[4,1,1,1,1,1,1]
[3,10,2,1,5,6,7,8,9,4]=>[3,2,1,1,1,1,1]
[3,9,1,4,5,6,7,8,2,10]=>[3,1,1,1,1,1,1,1]
[2,10,9,8,7,6,1,5,4,3]=>[8,1,1]
[2,10,9,8,1,7,6,5,4,3]=>[8,1,1]
[2,10,9,1,8,7,6,5,4,3]=>[8,1,1]
[2,1,4,3,10,5,7,6,9,8]=>[3,2,2,2,1]
[2,1,4,3,9,6,10,5,8,7]=>[3,2,2,2,1]
[2,1,8,3,5,4,7,6,10,9]=>[3,2,2,2,1]
[2,1,10,3,5,4,7,6,9,8]=>[3,2,2,2,1]
[2,1,9,6,10,3,5,4,8,7]=>[4,2,2,1,1]
[2,1,7,4,8,3,6,5,10,9]=>[3,2,2,2,1]
[2,1,7,4,10,3,6,5,9,8]=>[3,2,2,2,1]
[2,1,10,3,6,5,9,4,8,7]=>[4,2,2,1,1]
[2,1,9,4,8,5,10,3,7,6]=>[4,2,2,1,1]
[4,1,3,2,10,5,7,6,9,8]=>[3,3,2,1,1]
[4,1,3,2,9,6,10,5,8,7]=>[3,3,2,1,1]
[6,1,3,2,5,4,8,7,10,9]=>[3,2,2,2,1]
[6,1,3,2,5,4,10,7,9,8]=>[3,3,2,1,1]
[8,1,3,2,5,4,7,6,10,9]=>[3,2,2,2,1]
[9,6,10,1,3,2,5,4,8,7]=>[4,2,2,1,1]
[7,4,8,1,3,2,6,5,10,9]=>[4,2,2,1,1]
[7,4,10,1,3,2,6,5,9,8]=>[4,2,2,1,1]
[10,1,3,2,6,5,9,4,8,7]=>[4,2,2,1,1]
[9,4,8,5,10,1,3,2,7,6]=>[5,2,1,1,1]
[5,2,6,1,4,3,8,7,10,9]=>[3,2,2,2,1]
[5,2,6,1,4,3,10,7,9,8]=>[3,3,2,1,1]
[5,2,8,1,4,3,7,6,10,9]=>[3,2,2,2,1]
[5,2,10,1,4,3,7,6,9,8]=>[3,2,2,2,1]
[5,2,9,6,10,1,4,3,8,7]=>[4,2,2,1,1]
[8,1,4,3,7,2,6,5,10,9]=>[4,2,2,1,1]
[10,1,4,3,7,2,6,5,9,8]=>[4,2,2,1,1]
[9,2,6,5,10,1,4,3,8,7]=>[5,2,1,1,1]
[10,1,4,3,8,5,9,2,7,6]=>[4,2,2,1,1]
[7,2,6,3,8,1,5,4,10,9]=>[4,2,2,1,1]
[7,2,6,3,10,1,5,4,9,8]=>[4,2,2,1,1]
[10,1,5,4,9,2,6,3,8,7]=>[4,2,2,1,1]
[8,3,10,1,5,4,9,2,7,6]=>[4,2,2,1,1]
[8,3,9,2,7,4,10,1,6,5]=>[4,2,2,1,1]
[1,2,3,4,5,6,8,9,7,10]=>[2,1,1,1,1,1,1,1,1]
[10,1,2,3,4,5,9,7,6,8]=>[4,1,1,1,1,1,1]
[10,1,2,3,4,9,6,7,5,8]=>[4,1,1,1,1,1,1]
[9,1,2,3,10,5,6,7,4,8]=>[3,2,1,1,1,1,1]
[10,1,2,9,4,5,6,7,3,8]=>[4,1,1,1,1,1,1]
[10,1,9,3,4,5,6,7,2,8]=>[4,1,1,1,1,1,1]
[8,1,2,3,4,5,10,6,9,7]=>[3,2,1,1,1,1,1]
[7,1,2,3,4,9,5,6,10,8]=>[2,2,2,1,1,1,1]
[6,1,2,3,9,4,5,7,10,8]=>[2,2,2,1,1,1,1]
[5,1,2,10,3,4,6,7,9,8]=>[3,2,1,1,1,1,1]
[4,1,9,2,3,5,6,7,10,8]=>[2,2,2,1,1,1,1]
[3,9,1,2,4,5,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[10,2,1,3,4,5,6,7,9,8]=>[3,2,1,1,1,1,1]
[1,2,3,4,5,7,8,6,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,9,6,10]=>[2,1,1,1,1,1,1,1,1]
[2,4,5,6,1,7,8,9,10,3]=>[2,2,1,1,1,1,1,1]
[2,3,5,6,1,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[9,8,10,1,4,5,6,7,2,3]=>[4,1,1,1,1,1,1]
[7,1,10,9,2,3,4,5,6,8]=>[3,2,1,1,1,1,1]
[6,7,9,1,2,3,4,5,10,8]=>[2,2,1,1,1,1,1,1]
[2,8,1,9,10,3,4,5,6,7]=>[2,2,1,1,1,1,1,1]
[8,7,1,10,2,3,4,5,6,9]=>[3,2,1,1,1,1,1]
[1,5,2,8,6,3,10,9,7,4]=>[4,3,2,1]
[4,1,5,2,8,6,3,10,9,7]=>[3,3,2,2]
[1,7,5,2,8,6,3,10,9,4]=>[3,3,3,1]
[4,1,7,5,2,8,3,10,9,6]=>[3,3,2,2]
[6,4,1,7,5,2,8,3,10,9]=>[3,3,2,2]
[3,4,1,7,2,8,5,10,9,6]=>[3,2,2,2,1]
[3,6,4,1,7,2,8,5,10,9]=>[3,2,2,2,1]
[1,5,2,9,8,6,3,10,7,4]=>[4,3,2,1]
[4,1,5,2,9,8,6,3,10,7]=>[4,2,2,2]
[1,7,5,2,9,6,3,10,8,4]=>[3,3,3,1]
[4,1,7,5,2,9,3,10,8,6]=>[3,3,2,2]
[4,1,9,6,5,2,7,3,10,8]=>[4,2,2,2]
[3,4,1,7,2,9,5,10,8,6]=>[3,2,2,2,1]
[3,6,1,9,4,2,7,5,10,8]=>[3,2,2,2,1]
[1,8,7,5,2,9,6,3,10,4]=>[4,3,2,1]
[4,1,8,7,5,2,9,3,10,6]=>[4,2,2,2]
[6,4,1,8,5,2,9,3,10,7]=>[3,3,2,2]
[7,6,4,1,8,5,2,9,3,10]=>[4,3,2,1]
[3,4,1,8,7,2,9,5,10,6]=>[3,2,2,2,1]
[3,6,4,1,8,2,9,5,10,7]=>[3,2,2,2,1]
[3,7,6,4,1,8,2,9,5,10]=>[4,2,2,1,1]
[1,9,6,5,2,7,3,10,8,4]=>[4,3,2,1]
[6,1,9,4,2,7,3,10,8,5]=>[3,3,2,2]
[5,4,1,9,6,2,7,3,10,8]=>[3,3,2,2]
[9,3,1,6,2,7,4,10,8,5]=>[3,3,2,2]
[9,5,3,1,6,2,7,4,10,8]=>[4,2,2,2]
[6,1,8,5,2,9,7,3,10,4]=>[3,3,2,2]
[6,4,1,8,2,9,7,3,10,5]=>[3,3,2,2]
[8,5,4,1,6,2,9,3,10,7]=>[4,2,2,2]
[5,7,4,1,8,6,2,9,3,10]=>[3,3,2,1,1]
[3,6,1,8,2,9,7,4,10,5]=>[3,2,2,2,1]
[5,8,3,1,6,2,9,4,10,7]=>[3,2,2,2,1]
[5,3,7,1,8,6,2,9,4,10]=>[3,3,2,1,1]
[4,3,8,1,9,5,2,6,10,7]=>[3,3,2,1,1]
[7,4,3,5,1,8,2,9,6,10]=>[4,2,2,1,1]
[9,6,2,1,3,7,4,10,8,5]=>[4,3,2,1]
[5,9,2,1,6,3,7,4,10,8]=>[3,2,2,2,1]
[6,8,2,1,3,9,7,4,10,5]=>[3,3,2,1,1]
[8,2,5,1,6,3,9,4,10,7]=>[3,2,2,2,1]
[2,5,7,1,8,6,3,9,4,10]=>[3,2,2,1,1,1]
[2,4,8,1,9,5,3,6,10,7]=>[3,2,2,1,1,1]
[5,6,4,3,2,1,7,8,9,10]=>[5,1,1,1,1,1]
[6,7,5,4,3,2,1,8,9,10]=>[6,1,1,1,1]
[7,8,9,10,1,5,6,3,4,2]=>[4,1,1,1,1,1,1]
[10,9,8,5,7,6,4,3,2,1]=>[9,1]
[10,9,8,4,7,6,5,3,2,1]=>[9,1]
[10,9,4,8,7,6,5,3,2,1]=>[9,1]
[10,3,9,8,7,6,5,4,2,1]=>[9,1]
[10,2,9,8,7,6,5,4,3,1]=>[9,1]
[9,10,2,1,6,4,3,5,7,8]=>[4,2,1,1,1,1]
[7,10,2,1,8,4,3,5,6,9]=>[4,2,1,1,1,1]
[2,9,1,10,7,4,3,5,6,8]=>[4,2,1,1,1,1]
[2,8,1,9,4,3,10,5,6,7]=>[3,2,2,1,1,1]
[10,8,5,2,1,6,3,4,7,9]=>[5,2,1,1,1]
[9,5,2,1,10,6,3,4,7,8]=>[4,3,1,1,1]
[10,7,2,1,8,5,3,4,6,9]=>[4,3,1,1,1]
[9,2,1,10,7,5,3,4,6,8]=>[4,3,1,1,1]
[2,8,1,9,3,10,5,4,6,7]=>[3,2,2,1,1,1]
[10,6,2,1,7,3,8,4,5,9]=>[4,2,2,1,1]
[9,2,1,10,6,3,7,4,5,8]=>[3,3,2,1,1]
[8,2,1,9,3,10,6,4,5,7]=>[3,3,2,1,1]
[7,2,1,8,3,9,4,10,5,6]=>[3,2,2,2,1]
[10,8,6,3,1,4,2,5,7,9]=>[5,2,1,1,1]
[3,9,1,10,6,4,2,5,7,8]=>[4,2,1,1,1,1]
[10,7,3,1,8,4,2,5,6,9]=>[4,3,1,1,1]
[9,3,1,10,7,4,2,5,6,8]=>[4,3,1,1,1]
[8,3,1,9,4,2,10,5,6,7]=>[3,3,2,1,1]
[10,8,5,1,6,3,2,4,7,9]=>[5,2,1,1,1]
[9,5,1,10,6,3,2,4,7,8]=>[4,3,1,1,1]
[10,7,1,8,5,3,2,4,6,9]=>[5,2,1,1,1]
[9,1,10,7,5,3,2,4,6,8]=>[5,2,1,1,1]
[8,3,1,9,2,10,5,4,6,7]=>[3,3,2,1,1]
[10,6,1,7,3,2,8,4,5,9]=>[4,2,2,1,1]
[9,1,10,6,3,2,7,4,5,8]=>[4,2,2,1,1]
[8,1,9,3,2,10,6,4,5,7]=>[3,3,2,1,1]
[7,1,8,3,2,9,4,10,5,6]=>[3,2,2,2,1]
[10,8,4,1,5,2,6,3,7,9]=>[4,2,2,1,1]
[9,4,1,10,5,2,6,3,7,8]=>[3,3,2,1,1]
[10,7,1,8,4,2,5,3,6,9]=>[4,2,2,1,1]
[9,1,10,7,4,2,5,3,6,8]=>[4,2,2,1,1]
[8,1,9,4,2,10,5,3,6,7]=>[3,3,2,1,1]
[10,6,1,7,2,8,4,3,5,9]=>[4,2,2,1,1]
[9,1,10,6,2,7,4,3,5,8]=>[4,2,2,1,1]
[8,1,9,2,10,6,4,3,5,7]=>[4,2,2,1,1]
[7,1,8,2,9,4,3,10,5,6]=>[3,2,2,2,1]
[10,5,1,6,2,7,3,8,4,9]=>[3,2,2,2,1]
[9,1,10,5,2,6,3,7,4,8]=>[3,2,2,2,1]
[8,1,9,2,10,5,3,6,4,7]=>[3,2,2,2,1]
[7,1,8,2,9,3,10,5,4,6]=>[3,2,2,2,1]
[4,2,1,3,6,5,8,7,10,9]=>[3,2,2,2,1]
[10,2,3,1,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,9,8,6,5,7,4,3,2,1]=>[9,1]
[10,9,8,4,5,7,6,3,2,1]=>[8,1,1]
[10,9,8,5,4,6,7,3,2,1]=>[8,1,1]
[1,3,4,2,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,4,5,6,3,7,8,9,10]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,5,6,7,8,4,9,10]=>[2,1,1,1,1,1,1,1,1]
[2,1,5,3,6,7,4,8,9,10]=>[2,2,2,1,1,1,1]
[1,3,5,6,4,2,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[3,5,2,1,6,4,7,8,9,10]=>[3,2,1,1,1,1,1]
[2,1,3,6,4,7,8,9,5,10]=>[2,2,2,1,1,1,1]
[1,3,4,6,7,2,8,5,9,10]=>[2,2,1,1,1,1,1,1]
[3,2,6,1,4,7,8,5,9,10]=>[3,2,1,1,1,1,1]
[2,4,6,1,7,5,3,8,9,10]=>[3,2,1,1,1,1,1]
[4,6,3,2,1,7,5,8,9,10]=>[4,2,1,1,1,1]
[1,3,4,2,7,8,5,9,10,6]=>[2,2,2,1,1,1,1]
[3,2,1,7,4,5,8,9,10,6]=>[3,2,2,1,1,1]
[1,2,4,5,7,8,9,6,3,10]=>[3,1,1,1,1,1,1,1]
[4,3,7,2,1,5,8,9,6,10]=>[4,2,1,1,1,1]
[1,3,5,7,8,6,4,2,9,10]=>[4,1,1,1,1,1,1]
[3,5,7,2,1,8,6,4,9,10]=>[3,3,1,1,1,1]
[5,7,4,3,2,1,8,6,9,10]=>[5,2,1,1,1]
[2,1,5,3,8,6,9,10,7,4]=>[3,2,2,2,1]
[1,3,5,6,8,9,4,2,10,7]=>[3,2,1,1,1,1,1]
[3,5,2,8,1,6,9,4,10,7]=>[3,2,2,1,1,1]
[5,4,8,3,2,1,6,9,10,7]=>[5,2,1,1,1]
[2,4,6,8,1,9,7,5,3,10]=>[4,2,1,1,1,1]
[4,6,8,3,2,1,9,7,5,10]=>[4,3,1,1,1]
[6,8,5,4,3,2,1,9,7,10]=>[6,2,1,1]
[3,5,7,9,2,1,10,8,6,4]=>[4,3,1,1,1]
[5,7,9,4,3,2,1,10,8,6]=>[5,3,1,1]
[7,9,6,5,4,3,2,1,10,8]=>[7,2,1]
[2,3,7,5,6,1,10,9,4,8]=>[3,3,1,1,1,1]
[2,3,4,10,6,9,8,5,1,7]=>[5,1,1,1,1,1]
[2,3,6,5,9,10,8,4,1,7]=>[4,2,1,1,1,1]
[2,3,9,5,8,7,4,1,10,6]=>[5,2,1,1,1]
[2,5,4,9,6,10,8,3,1,7]=>[4,2,2,1,1]
[2,5,4,8,9,7,3,1,10,6]=>[4,2,2,1,1]
[2,3,4,10,6,7,1,9,8,5]=>[4,2,1,1,1,1]
[2,3,7,5,6,1,10,9,8,4]=>[4,3,1,1,1]
[2,3,4,10,6,8,9,1,7,5]=>[4,1,1,1,1,1,1]
[2,3,6,5,8,10,9,1,7,4]=>[4,2,1,1,1,1]
[2,3,8,5,7,9,1,10,6,4]=>[4,2,1,1,1,1]
[2,5,4,8,6,10,9,1,7,3]=>[4,2,2,1,1]
[2,5,4,7,8,9,1,10,6,3]=>[3,3,1,1,1,1]
[2,3,4,10,6,9,8,7,5,1]=>[6,1,1,1,1]
[2,3,6,5,9,10,8,7,4,1]=>[5,2,1,1,1]
[2,3,7,5,9,8,10,6,4,1]=>[5,2,1,1,1]
[2,3,9,5,8,7,6,4,1,10]=>[6,1,1,1,1]
[2,5,4,9,6,10,8,7,3,1]=>[5,2,2,1]
[2,5,4,9,7,8,10,6,3,1]=>[5,2,1,1,1]
[2,5,4,8,9,7,6,3,1,10]=>[5,2,1,1,1]
[2,3,4,10,7,9,8,1,6,5]=>[5,1,1,1,1,1]
[2,3,5,7,10,9,8,1,6,4]=>[5,1,1,1,1,1]
[2,3,8,6,9,7,1,10,5,4]=>[4,2,2,1,1]
[2,4,7,5,10,9,8,1,6,3]=>[5,2,1,1,1]
[2,4,6,8,9,7,1,10,5,3]=>[4,2,1,1,1,1]
[2,3,4,10,7,8,9,6,5,1]=>[5,1,1,1,1,1]
[2,3,5,7,10,8,9,6,4,1]=>[5,1,1,1,1,1]
[2,3,7,6,8,9,10,5,4,1]=>[5,1,1,1,1,1]
[2,3,9,6,7,8,5,4,1,10]=>[5,1,1,1,1,1]
[2,4,7,5,10,8,9,6,3,1]=>[5,2,1,1,1]
[2,4,6,7,8,9,10,5,3,1]=>[4,1,1,1,1,1,1]
[2,4,6,9,7,8,5,3,1,10]=>[5,1,1,1,1,1]
[2,6,5,8,9,7,10,4,3,1]=>[5,2,1,1,1]
[2,6,5,7,8,9,4,3,1,10]=>[5,1,1,1,1,1]
[3,7,4,5,10,9,8,1,6,2]=>[5,2,1,1,1]
[3,6,4,8,9,7,1,10,5,2]=>[4,2,2,1,1]
[3,7,4,5,10,8,9,6,2,1]=>[5,2,1,1,1]
[3,6,4,7,8,9,10,5,2,1]=>[4,2,1,1,1,1]
[3,6,4,9,7,8,5,2,1,10]=>[5,2,1,1,1]
[3,5,6,8,9,7,10,4,2,1]=>[5,1,1,1,1,1]
[3,5,6,7,8,9,4,2,1,10]=>[4,1,1,1,1,1,1]
[4,3,2,7,6,5,1,9,8,10]=>[4,3,2,1]
[4,3,2,1,7,6,9,8,5,10]=>[4,3,2,1]
[4,3,2,7,6,1,9,8,5,10]=>[4,3,2,1]
[4,3,2,7,6,9,8,5,1,10]=>[4,3,2,1]
[4,3,7,6,2,1,9,8,5,10]=>[4,3,2,1]
[4,3,7,6,2,9,8,5,1,10]=>[4,3,2,1]
[4,3,2,1,7,6,5,9,10,8]=>[4,3,2,1]
[4,3,2,7,6,5,1,9,10,8]=>[4,3,2,1]
[4,3,2,1,7,6,9,5,10,8]=>[4,3,2,1]
[4,3,2,7,6,1,9,5,10,8]=>[4,2,2,2]
[4,3,2,7,6,9,5,1,10,8]=>[4,3,2,1]
[4,3,7,6,2,1,9,5,10,8]=>[4,2,2,2]
[4,3,7,6,2,9,5,1,10,8]=>[4,2,2,2]
[4,3,2,1,7,6,9,10,8,5]=>[4,3,2,1]
[4,3,2,7,6,1,9,10,8,5]=>[4,3,2,1]
[4,3,2,7,6,9,1,10,8,5]=>[4,3,2,1]
[4,3,2,7,6,9,10,8,5,1]=>[4,3,2,1]
[4,3,7,6,2,1,9,10,8,5]=>[4,3,2,1]
[4,3,7,6,2,9,1,10,8,5]=>[4,3,2,1]
[4,3,7,6,2,9,10,8,5,1]=>[4,3,2,1]
[4,3,2,1,7,9,6,5,10,8]=>[4,3,2,1]
[4,3,2,7,1,9,6,5,10,8]=>[4,3,2,1]
[4,3,2,7,9,6,5,1,10,8]=>[4,3,2,1]
[4,3,7,2,1,9,6,5,10,8]=>[4,3,2,1]
[4,3,7,2,9,6,5,1,10,8]=>[4,3,2,1]
[4,3,2,1,7,9,6,10,8,5]=>[4,3,2,1]
[4,3,2,7,1,9,6,10,8,5]=>[4,3,2,1]
[4,3,2,7,9,6,1,10,8,5]=>[4,3,2,1]
[4,3,2,7,9,6,10,8,5,1]=>[4,3,2,1]
[4,3,7,2,1,9,6,10,8,5]=>[4,3,2,1]
[4,3,7,2,9,6,1,10,8,5]=>[4,3,2,1]
[4,3,7,2,9,6,10,8,5,1]=>[4,3,2,1]
[4,3,7,9,6,2,1,10,8,5]=>[4,3,2,1]
[4,3,7,9,6,2,10,8,5,1]=>[4,3,2,1]
[4,7,3,2,1,9,6,5,10,8]=>[4,3,2,1]
[4,7,3,2,9,6,5,1,10,8]=>[4,3,2,1]
[4,7,3,2,1,9,6,10,8,5]=>[4,3,2,1]
[4,7,3,2,9,6,1,10,8,5]=>[4,3,2,1]
[4,7,3,2,9,6,10,8,5,1]=>[4,3,2,1]
[4,7,3,9,6,2,1,10,8,5]=>[4,3,2,1]
[5,6,4,7,3,9,1,8,2,10]=>[4,2,1,1,1,1]
[1,6,7,5,8,4,10,2,9,3]=>[4,2,1,1,1,1]
[4,5,6,7,8,9,1,10,2,3]=>[2,2,1,1,1,1,1,1]
[3,2,5,4,7,6,8,10,9,1]=>[3,2,2,2,1]
[3,2,5,4,6,9,7,8,10,1]=>[3,2,2,1,1,1]
[3,2,5,4,6,8,7,10,9,1]=>[3,2,2,2,1]
[3,2,5,4,6,7,10,8,9,1]=>[3,2,2,1,1,1]
[3,2,4,7,5,6,9,8,10,1]=>[3,2,2,1,1,1]
[3,2,4,7,5,6,8,10,9,1]=>[3,2,2,1,1,1]
[3,2,4,6,5,9,7,8,10,1]=>[3,2,2,1,1,1]
[3,2,4,6,5,8,7,10,9,1]=>[3,2,2,2,1]
[3,2,4,6,5,7,10,8,9,1]=>[3,2,2,1,1,1]
[3,2,4,5,9,6,7,8,10,1]=>[3,2,1,1,1,1,1]
[3,2,4,5,8,6,7,10,9,1]=>[3,2,2,1,1,1]
[3,2,4,5,7,6,10,8,9,1]=>[3,2,2,1,1,1]
[3,2,4,5,6,10,7,8,9,1]=>[3,2,1,1,1,1,1]
[2,5,3,4,7,6,9,8,10,1]=>[3,2,2,1,1,1]
[2,5,3,4,7,6,8,10,9,1]=>[3,2,2,1,1,1]
[2,5,3,4,6,9,7,8,10,1]=>[3,2,1,1,1,1,1]
[2,5,3,4,6,8,7,10,9,1]=>[3,2,2,1,1,1]
[2,5,3,4,6,7,10,8,9,1]=>[3,2,1,1,1,1,1]
[2,4,3,7,5,6,9,8,10,1]=>[3,2,2,1,1,1]
[2,4,3,7,5,6,8,10,9,1]=>[3,2,2,1,1,1]
[2,4,3,6,5,9,7,8,10,1]=>[3,2,2,1,1,1]
[2,4,3,6,5,7,10,8,9,1]=>[3,2,2,1,1,1]
[2,4,3,5,9,6,7,8,10,1]=>[3,2,1,1,1,1,1]
[2,4,3,5,8,6,7,10,9,1]=>[3,2,2,1,1,1]
[2,4,3,5,7,6,10,8,9,1]=>[3,2,2,1,1,1]
[2,4,3,5,6,10,7,8,9,1]=>[3,2,1,1,1,1,1]
[2,3,7,4,5,6,9,8,10,1]=>[3,2,1,1,1,1,1]
[2,3,7,4,5,6,8,10,9,1]=>[3,2,1,1,1,1,1]
[2,3,6,4,5,9,7,8,10,1]=>[3,2,1,1,1,1,1]
[2,3,6,4,5,8,7,10,9,1]=>[3,2,2,1,1,1]
[2,3,6,4,5,7,10,8,9,1]=>[3,2,1,1,1,1,1]
[2,3,5,4,9,6,7,8,10,1]=>[3,2,1,1,1,1,1]
[2,3,5,4,8,6,7,10,9,1]=>[3,2,2,1,1,1]
[2,3,5,4,7,6,10,8,9,1]=>[3,2,2,1,1,1]
[2,3,5,4,6,10,7,8,9,1]=>[3,2,1,1,1,1,1]
[2,3,4,9,5,6,7,8,10,1]=>[3,1,1,1,1,1,1,1]
[2,3,4,8,5,6,7,10,9,1]=>[3,2,1,1,1,1,1]
[2,3,4,7,5,6,10,8,9,1]=>[3,2,1,1,1,1,1]
[2,3,4,6,5,10,7,8,9,1]=>[3,2,1,1,1,1,1]
[9,3,10,1,2,4,5,6,7,8]=>[3,1,1,1,1,1,1,1]
[10,3,1,9,2,4,5,6,7,8]=>[3,2,1,1,1,1,1]
[3,1,4,10,2,5,6,7,8,9]=>[2,2,1,1,1,1,1,1]
[10,7,1,2,3,4,8,9,5,6]=>[3,2,1,1,1,1,1]
[6,2,3,4,5,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[2,6,3,4,5,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[2,3,6,4,5,7,8,9,10,1]=>[3,1,1,1,1,1,1,1]
[10,2,3,4,5,6,7,1,8,9]=>[3,1,1,1,1,1,1,1]
[10,2,3,4,5,6,1,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,2,3,4,5,1,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,2,3,4,1,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[2,8,1,3,4,5,6,10,7,9]=>[2,2,1,1,1,1,1,1]
[10,7,1,2,3,4,5,9,6,8]=>[3,2,1,1,1,1,1]
[4,5,6,8,2,9,3,10,7,1]=>[3,2,2,1,1,1]
[10,4,5,6,9,3,8,2,7,1]=>[5,1,1,1,1,1]
[4,5,10,6,9,3,8,2,7,1]=>[5,1,1,1,1,1]
[4,5,8,2,6,10,9,3,7,1]=>[4,2,1,1,1,1]
[10,6,9,5,4,3,8,2,7,1]=>[7,1,1,1]
[8,2,6,10,9,5,4,3,7,1]=>[6,2,1,1]
[8,2,10,4,5,6,7,1,9,3]=>[3,2,2,1,1,1]
[4,5,6,8,2,10,7,1,9,3]=>[3,2,2,1,1,1]
[10,4,5,6,8,2,7,1,9,3]=>[4,2,1,1,1,1]
[4,5,10,6,8,2,7,1,9,3]=>[4,2,1,1,1,1]
[4,5,10,8,2,6,7,1,9,3]=>[4,2,1,1,1,1]
[10,6,8,2,7,1,9,5,4,3]=>[6,2,1,1]
[10,8,2,6,7,1,9,5,4,3]=>[6,2,1,1]
[8,2,7,1,9,3,10,4,5,6]=>[3,2,2,1,1,1]
[4,5,8,2,7,1,9,3,10,6]=>[3,2,2,1,1,1]
[4,5,9,3,10,7,1,8,2,6]=>[3,2,2,1,1,1]
[4,5,7,1,9,3,8,2,6,10]=>[3,2,1,1,1,1,1]
[8,2,7,1,9,5,4,3,10,6]=>[5,2,2,1]
[9,5,4,3,10,7,1,8,2,6]=>[5,2,2,1]
[7,1,9,5,4,3,8,2,6,10]=>[5,2,1,1,1]
[8,2,6,10,4,5,7,1,9,3]=>[4,2,1,1,1,1]
[4,8,2,6,10,5,7,1,9,3]=>[4,2,1,1,1,1]
[4,10,8,2,5,6,7,1,9,3]=>[4,2,1,1,1,1]
[8,2,6,10,5,7,1,9,4,3]=>[5,2,1,1,1]
[10,8,2,5,6,7,1,9,4,3]=>[5,2,1,1,1]
[9,3,10,4,5,7,1,8,2,6]=>[3,2,2,1,1,1]
[4,9,3,10,5,7,1,8,2,6]=>[3,2,2,1,1,1]
[4,9,3,10,7,1,8,2,5,6]=>[3,2,2,1,1,1]
[4,7,1,9,3,8,2,5,6,10]=>[3,2,1,1,1,1,1]
[9,4,3,10,5,7,1,8,2,6]=>[4,2,2,1,1]
[9,4,3,10,7,1,8,2,5,6]=>[4,2,2,1,1]
[7,1,9,4,3,8,2,5,6,10]=>[4,2,1,1,1,1]
[5,10,7,1,8,2,4,3,9,6]=>[4,2,2,1,1]
[5,7,1,8,2,4,3,9,6,10]=>[3,2,2,1,1,1]
[10,5,7,1,9,4,2,6,8,3]=>[4,2,2,1,1]
[9,4,2,5,6,7,1,10,8,3]=>[4,3,1,1,1]
[10,5,7,1,8,3,9,4,2,6]=>[4,2,2,1,1]
[10,7,1,8,3,9,4,2,5,6]=>[4,2,2,1,1]
[7,1,8,3,9,4,2,5,6,10]=>[3,2,2,1,1,1]
[4,2,5,10,7,1,8,3,9,6]=>[3,2,2,2,1]
[4,2,5,7,1,8,3,9,6,10]=>[3,2,2,1,1,1]
[4,5,6,7,8,9,1,2,10,3]=>[2,2,1,1,1,1,1,1]
[10,9,7,3,6,1,2,4,8,5]=>[5,2,1,1,1]
[9,7,3,6,1,2,4,10,8,5]=>[4,3,1,1,1]
[7,3,10,9,6,1,2,4,8,5]=>[4,2,2,1,1]
[7,3,9,6,1,2,4,10,8,5]=>[3,3,2,1,1]
[9,6,1,2,4,10,7,3,8,5]=>[4,2,2,1,1]
[8,4,10,9,7,3,6,1,2,5]=>[5,2,1,1,1]
[10,8,4,9,7,3,6,1,2,5]=>[5,2,1,1,1]
[7,3,8,4,10,9,6,1,2,5]=>[4,2,2,1,1]
[7,3,10,8,4,9,6,1,2,5]=>[4,2,2,1,1]
[10,7,3,8,4,9,6,1,2,5]=>[4,2,2,1,1]
[6,1,2,7,3,8,4,10,9,5]=>[3,2,2,2,1]
[6,1,2,7,3,10,8,4,9,5]=>[3,2,2,2,1]
[6,1,2,10,7,3,8,4,9,5]=>[3,2,2,2,1]
[10,6,1,2,7,3,8,4,9,5]=>[3,2,2,2,1]
[6,1,3,10,9,7,2,4,8,5]=>[4,2,2,1,1]
[6,1,3,9,7,2,4,10,8,5]=>[3,3,2,1,1]
[10,9,6,1,3,7,2,4,8,5]=>[5,2,1,1,1]
[9,6,1,3,7,2,4,10,8,5]=>[4,3,1,1,1]
[10,7,2,4,9,6,1,3,8,5]=>[4,2,2,1,1]
[6,1,3,8,4,10,9,7,2,5]=>[4,2,2,1,1]
[6,1,3,10,8,4,9,7,2,5]=>[4,2,2,1,1]
[8,4,10,9,6,1,3,7,2,5]=>[5,2,1,1,1]
[10,8,4,9,6,1,3,7,2,5]=>[5,2,1,1,1]
[9,6,1,3,8,4,10,7,2,5]=>[4,2,2,1,1]
[7,2,6,1,3,8,4,10,9,5]=>[3,3,2,1,1]
[7,2,6,1,3,10,8,4,9,5]=>[3,3,2,1,1]
[10,7,2,6,1,3,8,4,9,5]=>[4,2,2,1,1]
[7,2,10,6,1,3,8,4,9,5]=>[3,2,2,2,1]
[8,3,6,1,4,10,9,7,2,5]=>[4,3,1,1,1]
[10,8,3,6,1,4,9,7,2,5]=>[5,2,1,1,1]
[10,9,6,1,4,8,3,7,2,5]=>[6,1,1,1,1]
[9,6,1,4,10,8,3,7,2,5]=>[5,2,1,1,1]
[8,3,9,6,1,4,10,7,2,5]=>[4,2,2,1,1]
[8,3,7,2,6,1,4,10,9,5]=>[4,3,1,1,1]
[10,8,3,7,2,6,1,4,9,5]=>[5,2,1,1,1]
[8,3,10,7,2,6,1,4,9,5]=>[4,2,2,1,1]
[7,2,8,3,10,6,1,4,9,5]=>[3,2,2,2,1]
[9,4,10,8,3,7,2,6,1,5]=>[5,2,1,1,1]
[8,3,9,4,10,7,2,6,1,5]=>[4,2,2,1,1]
[7,2,8,3,9,4,10,6,1,5]=>[3,2,2,2,1]
[10,3,4,1,2,5,6,7,8,9]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,8,5,9,6,10,7]=>[2,2,2,1,1,1,1]
[1,2,3,4,5,8,6,10,9,7]=>[3,2,1,1,1,1,1]
[1,2,3,7,4,8,5,10,9,6]=>[3,2,2,1,1,1]
[1,2,3,4,9,7,5,10,8,6]=>[3,3,1,1,1,1]
[1,2,3,4,7,5,10,9,8,6]=>[4,2,1,1,1,1]
[1,6,2,7,3,8,4,10,9,5]=>[3,2,2,2,1]
[1,2,6,3,9,7,4,10,8,5]=>[3,3,2,1,1]
[1,2,6,3,7,4,10,9,8,5]=>[4,2,2,1,1]
[1,2,3,8,6,4,10,9,7,5]=>[4,3,1,1,1]
[1,2,3,6,4,10,9,8,7,5]=>[5,2,1,1,1]
[5,1,6,2,9,7,3,10,8,4]=>[3,3,2,2]
[5,1,6,2,7,3,10,9,8,4]=>[4,2,2,2]
[1,5,2,6,3,10,9,8,7,4]=>[5,2,2,1]
[1,2,7,5,3,10,9,8,6,4]=>[5,3,1,1]
[1,2,5,3,10,9,8,7,6,4]=>[6,2,1,1]
[7,4,1,8,5,2,10,9,6,3]=>[4,3,3]
[4,1,9,7,5,2,10,8,6,3]=>[4,4,2]
[4,1,7,5,2,10,9,8,6,3]=>[5,3,2]
[4,1,5,2,10,9,8,7,6,3]=>[6,2,2]
[1,8,6,4,2,10,9,7,5,3]=>[5,4,1]
[1,6,4,2,10,9,8,7,5,3]=>[6,3,1]
[1,4,2,10,9,8,7,6,5,3]=>[7,2,1]
[7,5,3,1,10,9,8,6,4,2]=>[6,4]
[5,3,1,10,9,8,7,6,4,2]=>[7,3]
[1,4,2,5,6,7,8,10,9,3]=>[3,2,1,1,1,1,1]
[2,1,4,5,6,7,10,8,3,9]=>[3,2,1,1,1,1,1]
[3,1,5,2,6,10,7,8,9,4]=>[3,2,2,1,1,1]
[4,5,1,6,7,9,8,10,2,3]=>[3,2,1,1,1,1,1]
[7,2,8,3,9,4,10,5,1,6]=>[3,2,2,2,1]
[7,2,8,3,9,4,10,1,5,6]=>[3,2,2,1,1,1]
[7,2,8,3,9,10,4,5,1,6]=>[3,2,2,1,1,1]
[7,2,8,3,9,10,4,1,5,6]=>[3,2,2,1,1,1]
[7,2,8,3,9,10,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,2,8,9,3,4,10,5,1,6]=>[3,2,2,1,1,1]
[7,2,8,9,3,4,10,1,5,6]=>[3,2,1,1,1,1,1]
[7,2,8,9,3,10,4,5,1,6]=>[3,2,2,1,1,1]
[7,2,8,9,3,10,4,1,5,6]=>[3,2,2,1,1,1]
[7,2,8,9,3,10,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,2,8,9,10,3,4,5,1,6]=>[3,2,1,1,1,1,1]
[7,2,8,9,10,3,4,1,5,6]=>[3,2,1,1,1,1,1]
[7,2,8,9,10,3,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,3,9,4,10,5,1,6]=>[3,2,2,1,1,1]
[7,8,2,3,9,4,10,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,3,9,10,4,5,1,6]=>[3,2,1,1,1,1,1]
[7,8,2,3,9,10,4,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,3,9,10,1,4,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,2,9,3,4,10,5,1,6]=>[3,2,2,1,1,1]
[7,8,2,9,3,4,10,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,9,3,10,4,5,1,6]=>[3,2,2,1,1,1]
[7,8,2,9,3,10,4,1,5,6]=>[3,2,2,1,1,1]
[7,8,2,9,3,10,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,9,10,3,4,5,1,6]=>[3,2,1,1,1,1,1]
[7,8,2,9,10,3,4,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,9,10,3,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,8,2,9,10,1,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,2,3,4,10,5,1,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,3,4,10,1,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,2,3,10,4,5,1,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,3,10,4,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,3,10,1,4,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,2,10,3,4,5,1,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,10,3,4,1,5,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,10,3,1,4,5,6]=>[3,2,1,1,1,1,1]
[7,8,9,2,10,1,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,2,3,4,1,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,2,3,1,4,5,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,2,1,3,4,5,6]=>[3,1,1,1,1,1,1,1]
[5,9,8,7,6,4,3,2,1,10]=>[8,1,1]
[10,9,8,6,1,7,5,4,3,2]=>[8,2]
[1,2,9,3,4,5,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[1,2,3,4,5,9,6,7,10,8]=>[2,2,1,1,1,1,1,1]
[1,10,6,2,3,4,9,5,7,8]=>[3,2,1,1,1,1,1]
[1,5,2,9,3,10,4,6,7,8]=>[2,2,2,1,1,1,1]
[1,2,4,3,10,9,5,6,7,8]=>[3,2,1,1,1,1,1]
[1,3,2,4,5,10,9,6,7,8]=>[3,2,1,1,1,1,1]
[2,1,3,4,5,9,6,10,7,8]=>[2,2,2,1,1,1,1]
[9,8,7,6,5,4,1,10,3,2]=>[8,2]
[9,8,7,6,5,2,10,1,3,4]=>[7,1,1,1]
[9,8,7,6,3,10,2,1,4,5]=>[7,1,1,1]
[9,8,7,4,10,3,2,1,6,5]=>[7,2,1]
[9,8,5,10,4,3,2,1,6,7]=>[7,1,1,1]
[9,6,10,5,4,3,2,1,7,8]=>[7,1,1,1]
[7,10,6,5,4,3,2,1,9,8]=>[7,2,1]
[10,7,8,1,2,3,4,5,6,9]=>[3,1,1,1,1,1,1,1]
[6,7,10,1,2,3,4,5,8,9]=>[2,1,1,1,1,1,1,1,1]
[1,10,2,3,4,7,5,6,8,9]=>[3,1,1,1,1,1,1,1]
[10,9,8,6,7,5,4,3,2,1]=>[9,1]
[10,9,7,6,8,5,4,3,2,1]=>[9,1]
[10,8,7,6,9,5,4,3,2,1]=>[9,1]
[9,8,7,6,4,3,2,5,1,10]=>[8,1,1]
[9,8,7,6,4,3,5,2,1,10]=>[8,1,1]
[3,1,4,5,6,7,9,2,10,8]=>[2,2,2,1,1,1,1]
[2,4,3,1,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[2,3,6,4,5,1,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[3,4,5,2,1,6,7,8,9,10]=>[3,1,1,1,1,1,1,1]
[2,3,4,8,5,6,7,1,9,10]=>[3,1,1,1,1,1,1,1]
[3,5,4,7,2,6,1,8,9,10]=>[4,1,1,1,1,1,1]
[2,6,4,1,5,3,7,8,9,10]=>[3,2,1,1,1,1,1]
[4,5,2,6,3,1,7,8,9,10]=>[3,2,1,1,1,1,1]
[3,6,4,5,9,2,7,8,1,10]=>[4,1,1,1,1,1,1]
[2,5,4,7,8,6,3,1,9,10]=>[4,2,1,1,1,1]
[4,6,2,5,8,3,7,1,9,10]=>[4,1,1,1,1,1,1]
[3,5,7,6,1,4,2,8,9,10]=>[4,1,1,1,1,1,1]
[5,6,2,3,7,4,1,8,9,10]=>[3,2,1,1,1,1,1]
[2,5,4,8,6,10,7,3,9,1]=>[4,2,2,1,1]
[4,7,2,5,6,10,3,8,9,1]=>[4,1,1,1,1,1,1]
[2,3,9,5,6,1,7,8,4,10]=>[3,2,1,1,1,1,1]
[5,7,2,3,6,9,4,8,1,10]=>[4,1,1,1,1,1,1]
[2,8,4,1,6,3,7,5,9,10]=>[3,2,2,1,1,1]
[4,6,7,8,3,1,5,2,9,10]=>[3,2,1,1,1,1,1]
[6,7,2,3,4,8,5,1,9,10]=>[3,2,1,1,1,1,1]
[3,6,4,10,8,7,1,5,9,2]=>[5,2,1,1,1]
[2,7,4,9,6,3,10,8,5,1]=>[4,3,2,1]
[4,6,8,7,3,9,10,5,2,1]=>[5,2,1,1,1]
[6,8,2,3,4,7,10,5,9,1]=>[4,1,1,1,1,1,1]
[3,5,9,7,1,8,2,6,4,10]=>[4,2,1,1,1,1]
[5,7,8,3,9,4,1,6,2,10]=>[3,2,2,1,1,1]
[7,8,2,3,4,5,9,6,1,10]=>[3,2,1,1,1,1,1]
[4,6,8,10,9,1,5,2,7,3]=>[4,2,1,1,1,1]
[6,8,9,3,4,10,5,1,7,2]=>[3,2,2,1,1,1]
[8,9,2,3,4,5,6,10,7,1]=>[3,2,1,1,1,1,1]
[10,1,2,9,6,3,4,5,7,8]=>[4,1,1,1,1,1,1]
[4,1,2,10,3,5,9,6,7,8]=>[3,2,1,1,1,1,1]
[1,10,9,8,5,6,7,4,3,2]=>[7,1,1,1]
[1,10,9,5,6,7,8,4,3,2]=>[6,1,1,1,1]
[1,10,4,5,6,7,8,9,3,2]=>[4,1,1,1,1,1,1]
[5,3,1,2,6,7,8,9,10,4]=>[3,2,1,1,1,1,1]
[7,3,4,5,1,2,8,9,10,6]=>[3,2,1,1,1,1,1]
[8,3,4,5,6,1,2,9,10,7]=>[3,2,1,1,1,1,1]
[2,6,7,8,9,10,1,3,4,5]=>[2,1,1,1,1,1,1,1,1]
[10,8,9,7,6,5,4,3,2,1]=>[9,1]
[10,8,6,4,9,7,5,3,2,1]=>[7,3]
[10,8,6,4,2,1,9,7,5,3]=>[6,4]
[10,8,9,6,5,4,3,2,1,7]=>[8,1,1]
[9,7,10,8,5,4,3,2,1,6]=>[7,2,1]
[9,7,4,3,2,1,5,10,8,6]=>[6,3,1]
[9,7,5,10,8,6,3,2,1,4]=>[6,3,1]
[10,8,6,4,9,7,5,2,1,3]=>[6,3,1]
[10,8,6,4,1,2,9,7,5,3]=>[5,4,1]
[2,5,1,6,3,7,4,8,9,10]=>[2,2,2,1,1,1,1]
[3,4,5,1,6,2,7,8,9,10]=>[2,2,1,1,1,1,1,1]
[2,6,1,7,3,8,4,9,5,10]=>[2,2,2,2,1,1]
[3,4,6,1,7,2,8,5,9,10]=>[2,2,2,1,1,1,1]
[3,2,6,1,7,4,8,5,9,10]=>[3,2,2,1,1,1]
[4,2,5,6,1,7,3,8,9,10]=>[3,2,1,1,1,1,1]
[3,4,2,6,1,7,5,8,9,10]=>[3,2,1,1,1,1,1]
[3,2,7,1,8,4,9,5,10,6]=>[3,2,2,2,1]
[4,5,6,7,1,8,2,9,3,10]=>[2,2,2,1,1,1,1]
[3,4,2,7,1,8,5,9,6,10]=>[3,2,2,1,1,1]
[5,3,6,4,7,1,8,2,9,10]=>[3,2,2,1,1,1]
[3,5,2,6,7,1,8,4,9,10]=>[3,2,1,1,1,1,1]
[4,3,5,2,7,1,8,6,9,10]=>[4,2,1,1,1,1]
[5,2,6,7,8,1,9,3,10,4]=>[3,2,2,1,1,1]
[5,3,6,4,8,1,9,2,10,7]=>[3,2,2,2,1]
[3,5,2,6,8,1,9,4,10,7]=>[3,2,2,1,1,1]
[4,3,5,2,8,1,9,6,10,7]=>[4,2,2,1,1]
[4,6,2,7,5,8,1,9,3,10]=>[3,2,2,1,1,1]
[4,3,6,2,7,8,1,9,5,10]=>[4,2,1,1,1,1]
[4,5,3,6,2,8,1,9,7,10]=>[4,2,1,1,1,1]
[5,3,7,2,8,6,9,1,10,4]=>[4,2,2,1,1]
[4,5,3,7,2,8,9,1,10,6]=>[4,2,1,1,1,1]
[5,4,6,3,7,2,9,1,10,8]=>[5,2,1,1,1]
[5,1,6,7,8,9,10,2,3,4]=>[2,2,1,1,1,1,1,1]
[5,6,7,8,9,10,1,3,4,2]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,1,4,3,2]=>[4,1,1,1,1,1,1]
[7,8,9,10,1,4,5,6,2,3]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,1,4,5,6,3,2]=>[4,1,1,1,1,1,1]
[7,8,9,10,1,5,6,4,3,2]=>[5,1,1,1,1,1]
[7,8,9,10,1,6,5,4,3,2]=>[6,1,1,1,1]
[8,9,10,1,4,5,6,7,2,3]=>[3,1,1,1,1,1,1,1]
[8,9,10,1,4,5,6,7,3,2]=>[4,1,1,1,1,1,1]
[8,9,10,1,5,6,7,2,3,4]=>[3,1,1,1,1,1,1,1]
[8,9,10,1,5,6,7,4,3,2]=>[5,1,1,1,1,1]
[8,9,10,1,6,7,4,5,2,3]=>[4,1,1,1,1,1,1]
[8,9,10,1,6,7,4,5,3,2]=>[5,1,1,1,1,1]
[8,9,10,1,6,7,5,4,3,2]=>[6,1,1,1,1]
[8,9,10,1,7,6,5,4,3,2]=>[7,1,1,1]
[9,10,1,6,7,8,3,4,5,2]=>[4,1,1,1,1,1,1]
[9,10,1,6,7,8,4,5,2,3]=>[4,1,1,1,1,1,1]
[9,10,1,6,7,8,4,5,3,2]=>[5,1,1,1,1,1]
[9,10,1,6,7,8,5,4,3,2]=>[6,1,1,1,1]
[9,10,1,7,8,5,6,3,4,2]=>[5,1,1,1,1,1]
[9,10,1,7,8,5,6,4,3,2]=>[6,1,1,1,1]
[9,10,1,7,8,6,5,4,3,2]=>[7,1,1,1]
[10,1,8,9,6,7,4,5,3,2]=>[6,1,1,1,1]
[10,1,8,9,6,7,5,4,3,2]=>[7,1,1,1]
[10,1,8,9,7,6,5,4,3,2]=>[8,1,1]
[6,10,9,8,7,5,4,3,1,2]=>[8,1,1]
[2,3,4,5,6,7,1,9,10,8]=>[2,2,1,1,1,1,1,1]
[2,3,4,5,1,7,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[2,3,1,5,6,7,8,9,10,4]=>[2,2,1,1,1,1,1,1]
[4,2,5,3,7,6,9,8,1,10]=>[3,2,2,2,1]
[4,2,6,3,7,5,9,8,1,10]=>[3,2,2,2,1]
[4,2,6,3,8,5,9,7,1,10]=>[3,2,2,2,1]
[4,2,6,3,8,5,10,7,1,9]=>[3,2,2,2,1]
[4,2,6,3,8,5,10,7,9,1]=>[3,2,2,2,1]
[4,2,6,3,8,5,7,10,9,1]=>[3,2,2,2,1]
[4,2,6,3,5,8,7,10,9,1]=>[3,2,2,2,1]
[4,2,3,6,5,8,7,10,9,1]=>[3,2,2,2,1]
[3,4,5,6,7,10,2,1,9,8]=>[3,2,1,1,1,1,1]
[3,4,5,6,9,2,10,1,8,7]=>[3,2,1,1,1,1,1]
[3,4,5,8,2,9,10,1,6,7]=>[3,1,1,1,1,1,1,1]
[3,4,7,2,8,9,10,1,6,5]=>[3,2,1,1,1,1,1]
[3,6,2,7,8,9,10,1,5,4]=>[3,2,1,1,1,1,1]
[5,2,6,7,8,9,10,1,3,4]=>[3,1,1,1,1,1,1,1]
[9,10,8,7,6,5,4,1,3,2]=>[8,1,1]
[10,8,7,6,5,4,3,2,9,1]=>[9,1]
[2,9,4,5,6,7,8,1,10,3]=>[3,2,1,1,1,1,1]
[4,3,10,5,6,7,8,9,2,1]=>[4,2,1,1,1,1]
[3,2,9,5,6,7,8,1,10,4]=>[3,2,2,1,1,1]
[8,9,4,5,6,7,1,3,10,2]=>[4,1,1,1,1,1,1]
[3,4,1,10,6,7,8,9,2,5]=>[3,2,1,1,1,1,1]
[4,9,10,5,6,7,8,2,1,3]=>[4,1,1,1,1,1,1]
[9,1,2,3,6,4,5,7,8,10]=>[3,1,1,1,1,1,1,1]
[5,6,7,8,9,10,3,2,1,4]=>[4,1,1,1,1,1,1]
[7,8,9,10,3,4,5,1,2,6]=>[3,1,1,1,1,1,1,1]
[7,8,9,10,3,4,5,2,1,6]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,2,3,1,6]=>[4,1,1,1,1,1,1]
[7,8,9,10,4,5,3,2,1,6]=>[5,1,1,1,1,1]
[7,8,9,10,5,4,3,2,1,6]=>[6,1,1,1,1]
[8,9,10,3,4,5,6,1,2,7]=>[3,1,1,1,1,1,1,1]
[8,9,10,3,4,5,6,2,1,7]=>[4,1,1,1,1,1,1]
[8,9,10,4,5,6,1,2,3,7]=>[3,1,1,1,1,1,1,1]
[8,9,10,4,5,6,3,2,1,7]=>[5,1,1,1,1,1]
[8,9,10,5,6,3,4,1,2,7]=>[4,1,1,1,1,1,1]
[8,9,10,5,6,3,4,2,1,7]=>[5,1,1,1,1,1]
[8,9,10,5,6,4,3,2,1,7]=>[6,1,1,1,1]
[8,9,10,6,5,4,3,2,1,7]=>[7,1,1,1]
[9,10,5,6,7,2,3,4,1,8]=>[4,1,1,1,1,1,1]
[9,10,5,6,7,3,4,1,2,8]=>[4,1,1,1,1,1,1]
[9,10,5,6,7,3,4,2,1,8]=>[5,1,1,1,1,1]
[9,10,5,6,7,4,3,2,1,8]=>[6,1,1,1,1]
[9,10,6,7,4,5,3,2,1,8]=>[6,1,1,1,1]
[9,10,6,7,5,4,3,2,1,8]=>[7,1,1,1]
[9,10,7,6,5,4,3,2,1,8]=>[8,1,1]
[10,7,8,5,6,3,4,2,1,9]=>[6,1,1,1,1]
[10,7,8,5,6,4,3,2,1,9]=>[7,1,1,1]
[10,7,8,6,5,4,3,2,1,9]=>[8,1,1]
[10,9,1,2,3,7,8,4,5,6]=>[4,1,1,1,1,1,1]
[10,9,1,2,8,7,3,4,5,6]=>[5,1,1,1,1,1]
[9,8,1,10,7,2,3,4,5,6]=>[4,2,1,1,1,1]
[8,6,1,2,3,4,5,9,10,7]=>[3,2,1,1,1,1,1]
[5,7,1,2,3,4,8,9,10,6]=>[2,2,1,1,1,1,1,1]
[10,4,1,2,3,7,8,9,5,6]=>[3,2,1,1,1,1,1]
[10,3,1,2,9,7,8,4,5,6]=>[4,2,1,1,1,1]
[2,9,1,10,8,7,3,4,5,6]=>[4,2,1,1,1,1]
[4,2,6,1,3,5,8,7,10,9]=>[3,2,2,1,1,1]
[4,2,6,1,8,3,5,7,10,9]=>[3,2,2,1,1,1]
[4,2,6,1,8,3,10,5,7,9]=>[3,2,2,1,1,1]
[2,3,4,10,6,7,8,9,1,5]=>[3,1,1,1,1,1,1,1]
[2,3,10,5,6,7,8,9,1,4]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,10,1,9,7,8]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,10,1,8,9,6,7]=>[3,1,1,1,1,1,1,1]
[2,3,10,1,6,7,8,9,4,5]=>[3,1,1,1,1,1,1,1]
[1,4,2,6,5,8,7,10,9,3]=>[3,2,2,2,1]
[1,5,2,6,4,8,7,10,9,3]=>[3,2,2,2,1]
[1,5,2,7,4,8,6,10,9,3]=>[3,2,2,2,1]
[1,5,2,7,4,9,6,10,8,3]=>[3,2,2,2,1]
[1,5,2,7,4,9,6,8,10,3]=>[3,2,2,1,1,1]
[1,5,2,7,4,6,9,8,10,3]=>[3,2,2,1,1,1]
[1,5,2,4,7,6,9,8,10,3]=>[3,2,2,1,1,1]
[1,2,5,4,7,6,9,8,10,3]=>[3,2,2,1,1,1]
[3,4,5,6,7,9,10,8,1,2]=>[3,1,1,1,1,1,1,1]
[3,4,5,6,8,9,10,7,1,2]=>[3,1,1,1,1,1,1,1]
[3,4,6,7,8,9,10,5,1,2]=>[3,1,1,1,1,1,1,1]
[3,5,6,7,8,9,10,4,1,2]=>[3,1,1,1,1,1,1,1]
[3,4,5,6,7,10,1,8,9,2]=>[3,1,1,1,1,1,1,1]
[3,4,5,6,9,1,10,8,7,2]=>[4,2,1,1,1,1]
[3,4,5,8,1,9,10,7,6,2]=>[4,2,1,1,1,1]
[3,4,7,1,8,9,10,5,6,2]=>[3,2,1,1,1,1,1]
[3,6,1,7,8,9,10,5,4,2]=>[4,2,1,1,1,1]
[5,1,6,7,8,9,10,4,3,2]=>[4,2,1,1,1,1]
[6,10,5,1,2,3,4,7,8,9]=>[3,1,1,1,1,1,1,1]
[10,5,4,1,2,3,6,7,8,9]=>[4,1,1,1,1,1,1]
[10,9,3,4,5,6,8,7,2,1]=>[6,1,1,1,1]
[10,9,4,3,5,6,7,8,2,1]=>[6,1,1,1,1]
[10,3,4,5,6,7,9,8,2,1]=>[5,1,1,1,1,1]
[10,4,3,5,6,7,8,9,2,1]=>[5,1,1,1,1,1]
[1,7,5,6,8,4,9,3,10,2]=>[5,1,1,1,1,1]
[1,2,3,4,5,8,6,9,7,10]=>[2,2,1,1,1,1,1,1]
[1,2,3,4,5,9,6,10,7,8]=>[2,2,1,1,1,1,1,1]
[10,8,7,6,5,4,3,9,2,1]=>[9,1]
[10,9,7,6,5,4,8,3,2,1]=>[9,1]
[1,2,3,4,5,6,7,8,9,11,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1]
[11,1,2,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[10,1,2,3,4,5,6,7,8,11,9]=>[2,2,1,1,1,1,1,1,1]
[11,1,2,3,4,5,6,7,10,8,9]=>[3,1,1,1,1,1,1,1,1]
[11,1,2,3,4,5,6,10,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[10,1,2,3,4,5,11,6,7,8,9]=>[2,2,1,1,1,1,1,1,1]
[11,1,2,3,4,10,5,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[11,1,2,3,10,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[10,1,2,11,3,4,5,6,7,8,9]=>[2,2,1,1,1,1,1,1,1]
[11,1,10,2,3,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[11,10,1,2,3,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[10,9,8,7,6,5,4,3,2,1,11]=>[10,1]
[1,11,10,9,8,7,6,5,4,3,2]=>[10,1]
[2,3,4,5,6,7,8,9,10,11,1]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,11,1,10]=>[2,1,1,1,1,1,1,1,1,1]
[3,1,4,5,6,7,8,9,10,11,2]=>[2,2,1,1,1,1,1,1,1]
[11,3,4,5,6,7,8,9,1,2,10]=>[3,1,1,1,1,1,1,1,1]
[11,1,4,5,6,7,8,9,10,2,3]=>[3,1,1,1,1,1,1,1,1]
[10,1,2,3,4,5,6,7,8,9,11]=>[2,1,1,1,1,1,1,1,1,1]
[1,11,2,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[10,9,8,7,6,5,4,3,1,11,2]=>[9,2]
[9,11,8,7,6,5,4,3,2,1,10]=>[9,1,1]
[10,11,9,8,7,6,5,4,3,2,1]=>[10,1]
[11,10,9,8,7,6,5,4,3,1,2]=>[10,1]
[2,3,4,5,6,7,8,9,10,1,11]=>[2,1,1,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,10,11,2]=>[2,1,1,1,1,1,1,1,1,1]
[2,11,1,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[11,3,1,2,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1,1]
[11,4,1,2,3,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1,1]
[5,11,1,2,3,4,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[11,6,1,2,3,4,5,7,8,9,10]=>[3,1,1,1,1,1,1,1,1]
[11,7,1,2,3,4,5,6,8,9,10]=>[3,1,1,1,1,1,1,1,1]
[8,11,1,2,3,4,5,6,7,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[11,9,1,2,3,4,5,6,7,8,10]=>[3,1,1,1,1,1,1,1,1]
[11,9,8,7,6,5,4,3,2,1,10]=>[10,1]
[10,9,8,7,6,5,4,3,2,11,1]=>[10,1]
[9,8,10,7,6,5,4,3,2,1,11]=>[9,1,1]
[9,8,7,10,6,5,4,3,2,1,11]=>[9,1,1]
[9,8,7,6,11,5,4,3,2,1,10]=>[9,1,1]
[9,8,7,6,5,10,4,3,2,1,11]=>[9,1,1]
[9,8,7,6,5,4,10,3,2,1,11]=>[9,1,1]
[9,8,7,6,5,4,3,11,2,1,10]=>[9,1,1]
[9,8,7,6,5,4,3,2,10,1,11]=>[9,1,1]
[9,8,7,6,5,4,3,2,1,10,11]=>[9,1,1]
[3,4,5,6,7,8,9,10,11,2,1]=>[3,1,1,1,1,1,1,1,1]
[10,1,11,9,8,7,6,5,4,3,2]=>[9,2]
[2,11,10,9,8,7,6,5,4,1,3]=>[9,1,1]
[10,2,1,9,8,7,6,5,4,3,11]=>[8,2,1]
[3,2,10,9,8,7,6,5,4,1,11]=>[8,2,1]
[6,7,8,9,10,1,2,3,4,5,11]=>[2,1,1,1,1,1,1,1,1,1]
[1,7,8,9,10,11,2,3,4,5,6]=>[2,1,1,1,1,1,1,1,1,1]
[2,4,1,5,6,7,8,9,10,11,3]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,10,1,11,9]=>[2,2,1,1,1,1,1,1,1]
[2,3,5,1,6,7,8,9,10,11,4]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,9,1,10,11,8]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,6,1,7,8,9,10,11,5]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,5,6,8,1,9,10,11,7]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,5,7,1,8,9,10,11,6]=>[2,2,1,1,1,1,1,1,1]
[1,2,3,4,6,8,5,7,10,9,11]=>[2,2,1,1,1,1,1,1,1]
[1,2,3,4,7,5,8,6,10,9,11]=>[2,2,2,1,1,1,1,1]
[11,10,9,8,7,6,5,4,3,2,1]=>[11]
[2,1,11,10,9,8,7,6,5,4,3]=>[9,2]
[1,2,3,4,5,6,7,8,10,11,9]=>[2,1,1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,10,9,11]=>[2,2,2,2,1,1,1]
[11,3,4,5,6,7,8,9,10,1,2]=>[3,1,1,1,1,1,1,1,1]
[10,3,4,5,6,7,8,9,1,11,2]=>[3,2,1,1,1,1,1,1]
[9,3,4,5,6,7,8,1,10,11,2]=>[3,2,1,1,1,1,1,1]
[8,3,4,5,6,7,1,9,10,11,2]=>[3,2,1,1,1,1,1,1]
[7,3,4,5,6,1,8,9,10,11,2]=>[3,2,1,1,1,1,1,1]
[6,3,4,5,1,7,8,9,10,11,2]=>[3,2,1,1,1,1,1,1]
[5,3,4,1,6,7,8,9,10,11,2]=>[3,2,1,1,1,1,1,1]
[4,3,1,5,6,7,8,9,10,11,2]=>[3,2,1,1,1,1,1,1]
[2,11,4,5,6,7,8,9,10,1,3]=>[3,1,1,1,1,1,1,1,1]
[10,9,4,5,6,7,8,1,2,11,3]=>[4,2,1,1,1,1,1]
[2,11,10,5,6,7,8,9,1,3,4]=>[4,1,1,1,1,1,1,1]
[11,2,3,4,5,6,7,8,9,10,1]=>[3,1,1,1,1,1,1,1,1]
[10,9,1,2,3,4,5,6,7,11,8]=>[3,2,1,1,1,1,1,1]
[2,11,10,1,3,4,5,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[2,4,1,6,3,5,8,7,10,9,11]=>[2,2,2,2,1,1,1]
[10,1,2,3,4,5,6,7,11,8,9]=>[2,2,1,1,1,1,1,1,1]
[1,11,2,3,4,5,6,7,8,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,11,3,4,5,6,7,8,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,10,4,5,6,7,11,8,9]=>[2,2,1,1,1,1,1,1,1]
[1,2,3,4,11,5,6,7,8,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,4,5,11,6,7,8,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,10,7,11,8,9]=>[2,2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,11,8,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,11,10,9]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,11,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[11,1,3,4,5,6,7,8,9,10,2]=>[3,1,1,1,1,1,1,1,1]
[10,2,3,4,5,6,7,8,11,1,9]=>[3,1,1,1,1,1,1,1,1]
[10,11,3,4,5,6,7,8,9,1,2]=>[3,1,1,1,1,1,1,1,1]
[7,1,2,3,4,5,11,6,8,9,10]=>[2,2,1,1,1,1,1,1,1]
[11,1,2,3,4,5,8,6,7,9,10]=>[3,1,1,1,1,1,1,1,1]
[11,1,2,3,4,5,9,6,7,8,10]=>[3,1,1,1,1,1,1,1,1]
[11,10,5,1,2,3,4,6,7,8,9]=>[4,1,1,1,1,1,1,1]
[11,10,1,5,2,3,4,6,7,8,9]=>[4,1,1,1,1,1,1,1]
[5,11,1,2,10,3,4,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[5,11,1,2,3,10,4,6,7,8,9]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,10,11,1,9]=>[2,1,1,1,1,1,1,1,1,1]
[2,4,5,6,7,8,9,10,11,1,3]=>[2,1,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,10,11,1,2]=>[2,1,1,1,1,1,1,1,1,1]
[10,11,1,9,2,3,4,5,6,7,8]=>[3,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,10,11]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,1,11,2,3,4,5,6,7,8,9]=>[2,2,1,1,1,1,1,1,1]
[10,11,1,2,3,4,5,6,7,8,9]=>[2,1,1,1,1,1,1,1,1,1]
[3,1,4,2,6,5,8,7,10,9,11]=>[2,2,2,2,2,1]
[1,2,3,4,5,6,7,8,10,9,11]=>[2,1,1,1,1,1,1,1,1,1]
[11,2,3,4,5,6,7,8,9,1,10]=>[3,1,1,1,1,1,1,1,1]
[3,11,1,4,5,6,7,8,9,10,2]=>[3,1,1,1,1,1,1,1,1]
[9,1,11,3,4,5,6,7,8,2,10]=>[3,2,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,11,10,1]=>[3,1,1,1,1,1,1,1,1]
[3,1,11,5,6,7,8,9,10,2,4]=>[3,2,1,1,1,1,1,1]
[2,3,1,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1]
[3,1,2,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,10,1,2,11]=>[2,1,1,1,1,1,1,1,1,1]
[3,4,5,6,7,9,10,11,1,2,8]=>[2,1,1,1,1,1,1,1,1,1]
[3,4,6,7,8,9,10,11,1,2,5]=>[2,1,1,1,1,1,1,1,1,1]
[11,1,10,5,6,7,8,9,2,3,4]=>[4,1,1,1,1,1,1,1]
[10,1,11,9,6,7,8,2,3,4,5]=>[4,2,1,1,1,1,1]
[9,1,10,11,8,7,2,3,4,5,6]=>[4,2,1,1,1,1,1]
[8,1,9,10,11,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1]
[11,1,10,9,2,3,4,5,6,7,8]=>[4,1,1,1,1,1,1,1]
[9,8,7,6,5,4,3,2,1,11,10]=>[9,2]
[2,3,4,5,6,7,10,9,11,8,1]=>[4,1,1,1,1,1,1,1]
[2,3,4,5,6,10,8,9,11,7,1]=>[4,1,1,1,1,1,1,1]
[2,3,4,5,10,7,8,9,11,1,6]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,10,6,7,8,9,11,5,1]=>[4,1,1,1,1,1,1,1]
[2,3,10,5,6,7,8,9,11,4,1]=>[4,1,1,1,1,1,1,1]
[2,10,4,5,6,7,8,9,11,1,3]=>[3,1,1,1,1,1,1,1,1]
[10,3,4,5,6,7,8,9,11,2,1]=>[4,1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,9,8,11,10]=>[2,2,2,2,2,1]
[3,4,5,6,7,8,9,10,1,11,2]=>[2,2,1,1,1,1,1,1,1]
[6,5,7,4,8,3,9,2,10,1,11]=>[6,1,1,1,1,1]
[1,7,6,8,5,9,4,10,3,11,2]=>[6,1,1,1,1,1]
[2,3,4,5,6,7,8,11,10,1,9]=>[3,1,1,1,1,1,1,1,1]
[11,3,4,5,6,7,8,10,1,2,9]=>[3,1,1,1,1,1,1,1,1]
[3,2,4,5,6,7,8,9,10,11,1]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,1,9,2,11,10]=>[2,2,2,1,1,1,1,1]
[1,4,5,6,7,11,8,9,2,10,3]=>[3,2,1,1,1,1,1,1]
[8,9,10,7,6,1,2,3,4,11,5]=>[4,2,1,1,1,1,1]
[2,9,10,11,8,7,1,3,4,5,6]=>[4,1,1,1,1,1,1,1]
[7,8,9,10,1,2,3,4,5,11,6]=>[2,2,1,1,1,1,1,1,1]
[2,8,9,10,11,1,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,11,1,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,11,1,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,11,1,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,5,11,1,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,4,11,1,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[2,3,11,1,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1]
[3,1,4,5,6,7,8,9,11,2,10]=>[2,2,1,1,1,1,1,1,1]
[2,11,1,3,4,5,6,7,10,8,9]=>[3,1,1,1,1,1,1,1,1]
[2,10,1,3,4,5,6,7,8,11,9]=>[2,2,1,1,1,1,1,1,1]
[11,2,1,3,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1,1]
[11,10,2,3,4,5,6,7,8,9,1]=>[4,1,1,1,1,1,1,1]
[11,3,4,5,6,7,8,9,10,2,1]=>[4,1,1,1,1,1,1,1]
[9,11,1,2,3,4,5,6,7,8,10]=>[2,1,1,1,1,1,1,1,1,1]
[11,10,9,8,6,7,5,4,3,2,1]=>[10,1]
[11,1,2,3,4,5,6,10,8,7,9]=>[4,1,1,1,1,1,1,1]
[11,1,2,3,4,5,10,7,8,6,9]=>[4,1,1,1,1,1,1,1]
[10,1,2,3,4,11,6,7,8,5,9]=>[3,2,1,1,1,1,1,1]
[11,1,2,3,10,5,6,7,8,4,9]=>[4,1,1,1,1,1,1,1]
[11,1,2,10,4,5,6,7,8,3,9]=>[4,1,1,1,1,1,1,1]
[10,1,11,3,4,5,6,7,8,2,9]=>[3,2,1,1,1,1,1,1]
[11,10,2,3,4,5,6,7,8,1,9]=>[4,1,1,1,1,1,1,1]
[11,10,2,1,4,5,6,7,8,9,3]=>[4,2,1,1,1,1,1]
[10,11,8,1,2,3,4,5,6,7,9]=>[3,1,1,1,1,1,1,1,1]
[6,7,5,4,3,2,1,8,9,10,11]=>[6,1,1,1,1,1]
[7,6,5,4,3,1,2,8,9,10,11]=>[6,1,1,1,1,1]
[11,10,9,8,5,7,6,4,3,2,1]=>[10,1]
[11,10,9,8,6,5,7,4,3,2,1]=>[10,1]
[8,9,1,2,3,4,5,6,10,11,7]=>[2,2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,1,11,10]=>[2,2,1,1,1,1,1,1,1]
[3,4,1,5,6,7,8,9,10,11,2]=>[2,2,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,11,2,10]=>[2,1,1,1,1,1,1,1,1,1]
[1,4,2,5,6,7,8,9,11,10,3]=>[3,2,1,1,1,1,1,1]
[1,2,10,3,4,5,6,7,8,11,9]=>[2,2,1,1,1,1,1,1,1]
[1,2,3,4,5,10,6,7,8,11,9]=>[2,2,1,1,1,1,1,1,1]
[10,9,8,7,6,5,4,2,1,3,11]=>[9,1,1]
[10,9,8,7,6,5,3,2,1,4,11]=>[9,1,1]
[10,9,8,7,6,4,3,2,1,11,5]=>[9,2]
[10,9,8,7,5,4,3,2,1,6,11]=>[9,1,1]
[10,9,8,6,5,4,3,2,1,7,11]=>[9,1,1]
[10,9,7,6,5,4,3,2,1,11,8]=>[9,2]
[10,8,7,6,5,4,3,2,1,9,11]=>[9,1,1]
[11,9,10,8,7,6,5,4,3,2,1]=>[10,1]
[10,8,11,9,7,6,5,4,3,2,1]=>[9,2]
[10,8,6,5,4,3,2,1,11,9,7]=>[8,3]
[10,8,6,11,9,7,5,4,3,2,1]=>[8,3]
[11,9,7,5,10,8,6,4,3,2,1]=>[8,3]
[11,9,7,5,3,2,1,10,8,6,4]=>[7,4]
[11,9,7,5,3,10,8,6,4,2,1]=>[7,4]
[10,8,6,4,2,11,9,7,5,3,1]=>[6,5]
[5,6,7,8,9,11,1,2,3,4,10]=>[2,1,1,1,1,1,1,1,1,1]
[6,1,7,8,9,10,11,2,3,4,5]=>[2,2,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,11,1,10,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,10,11,1,9,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,6,8,9,10,11,1,7,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,7,8,9,10,11,1,6,2]=>[3,1,1,1,1,1,1,1,1]
[3,5,6,7,8,9,10,11,1,4,2]=>[3,1,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,11,1,3,2]=>[3,1,1,1,1,1,1,1,1]
[10,2,3,4,5,6,7,8,9,11,1]=>[3,1,1,1,1,1,1,1,1]
[2,10,4,5,6,7,8,9,1,11,3]=>[3,2,1,1,1,1,1,1]
[4,3,11,5,6,7,8,9,10,2,1]=>[4,2,1,1,1,1,1]
[8,11,1,2,3,4,5,9,10,6,7]=>[3,1,1,1,1,1,1,1,1]
[10,11,1,2,3,4,8,9,5,6,7]=>[3,1,1,1,1,1,1,1,1]
[10,11,1,2,3,9,8,4,5,6,7]=>[4,1,1,1,1,1,1,1]
[10,9,1,2,11,8,3,4,5,6,7]=>[4,2,1,1,1,1,1]
[9,8,1,10,11,2,3,4,5,6,7]=>[3,2,1,1,1,1,1,1]
[11,8,9,10,1,2,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,11,9,10,1,8]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,5,6,11,8,9,10,1,7]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,5,11,7,8,9,10,1,6]=>[3,1,1,1,1,1,1,1,1]
[2,3,4,11,6,7,8,9,10,1,5]=>[3,1,1,1,1,1,1,1,1]
[2,3,11,5,6,7,8,9,10,1,4]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,10,11,9,1,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,6,7,9,10,11,8,1,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,5,7,8,9,10,11,6,1,2]=>[3,1,1,1,1,1,1,1,1]
[3,4,6,7,8,9,10,11,5,1,2]=>[3,1,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,11,3,1,2]=>[3,1,1,1,1,1,1,1,1]
[4,5,6,7,8,9,10,11,2,1,3]=>[3,1,1,1,1,1,1,1,1]
[11,10,3,4,5,6,7,9,8,2,1]=>[6,1,1,1,1,1]
[11,10,4,3,5,6,7,8,9,2,1]=>[6,1,1,1,1,1]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,2]
[2,1,4,3,6,5,8,7,12,11,10,9]=>[4,2,2,2,2]
[2,1,4,3,6,5,10,9,8,7,12,11]=>[4,2,2,2,2]
[2,1,4,3,6,5,12,9,8,11,10,7]=>[4,2,2,2,2]
[2,1,4,3,6,5,12,11,10,9,8,7]=>[6,2,2,2]
[2,1,4,3,8,7,6,5,10,9,12,11]=>[4,2,2,2,2]
[2,1,4,3,8,7,6,5,12,11,10,9]=>[4,4,2,2]
[2,1,4,3,10,7,6,9,8,5,12,11]=>[4,2,2,2,2]
[2,1,4,3,12,7,6,9,8,11,10,5]=>[4,2,2,2,2]
[2,1,4,3,12,7,6,11,10,9,8,5]=>[6,2,2,2]
[2,1,4,3,10,9,8,7,6,5,12,11]=>[6,2,2,2]
[2,1,4,3,12,9,8,7,6,11,10,5]=>[6,2,2,2]
[2,1,4,3,12,11,8,7,10,9,6,5]=>[6,2,2,2]
[2,1,4,3,12,11,10,9,8,7,6,5]=>[8,2,2]
[2,1,6,5,4,3,8,7,10,9,12,11]=>[4,2,2,2,2]
[2,1,6,5,4,3,8,7,12,11,10,9]=>[4,4,2,2]
[2,1,6,5,4,3,10,9,8,7,12,11]=>[4,4,2,2]
[2,1,6,5,4,3,12,9,8,11,10,7]=>[4,4,2,2]
[2,1,6,5,4,3,12,11,10,9,8,7]=>[6,4,2]
[2,1,8,5,4,7,6,3,10,9,12,11]=>[4,2,2,2,2]
[2,1,8,5,4,7,6,3,12,11,10,9]=>[4,4,2,2]
[2,1,10,5,4,7,6,9,8,3,12,11]=>[4,2,2,2,2]
[2,1,12,5,4,7,6,9,8,11,10,3]=>[4,2,2,2,2]
[2,1,12,5,4,7,6,11,10,9,8,3]=>[6,2,2,2]
[2,1,10,5,4,9,8,7,6,3,12,11]=>[6,2,2,2]
[2,1,12,5,4,9,8,7,6,11,10,3]=>[6,2,2,2]
[2,1,12,5,4,11,8,7,10,9,6,3]=>[6,2,2,2]
[2,1,12,5,4,11,10,9,8,7,6,3]=>[8,2,2]
[2,1,8,7,6,5,4,3,10,9,12,11]=>[6,2,2,2]
[2,1,8,7,6,5,4,3,12,11,10,9]=>[6,4,2]
[2,1,10,7,6,5,4,9,8,3,12,11]=>[6,2,2,2]
[2,1,12,7,6,5,4,9,8,11,10,3]=>[6,2,2,2]
[2,1,12,7,6,5,4,11,10,9,8,3]=>[6,4,2]
[2,1,10,9,6,5,8,7,4,3,12,11]=>[6,2,2,2]
[2,1,12,9,6,5,8,7,4,11,10,3]=>[6,2,2,2]
[2,1,12,11,6,5,8,7,10,9,4,3]=>[6,2,2,2]
[2,1,12,11,6,5,10,9,8,7,4,3]=>[8,2,2]
[2,1,10,9,8,7,6,5,4,3,12,11]=>[8,2,2]
[2,1,12,9,8,7,6,5,4,11,10,3]=>[8,2,2]
[2,1,12,11,8,7,6,5,10,9,4,3]=>[8,2,2]
[2,1,12,11,10,7,6,9,8,5,4,3]=>[8,2,2]
[2,1,12,11,10,9,8,7,6,5,4,3]=>[10,2]
[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,2,2,2,2]
[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,4,2,2]
[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,4,2,2]
[4,3,2,1,6,5,12,9,8,11,10,7]=>[4,4,2,2]
[4,3,2,1,6,5,12,11,10,9,8,7]=>[6,4,2]
[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,4,2,2]
[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,4,4]
[4,3,2,1,10,7,6,9,8,5,12,11]=>[4,4,2,2]
[4,3,2,1,12,7,6,9,8,11,10,5]=>[4,4,2,2]
[4,3,2,1,12,7,6,11,10,9,8,5]=>[6,4,2]
[4,3,2,1,10,9,8,7,6,5,12,11]=>[6,4,2]
[4,3,2,1,12,9,8,7,6,11,10,5]=>[6,4,2]
[4,3,2,1,12,11,8,7,10,9,6,5]=>[6,4,2]
[4,3,2,1,12,11,10,9,8,7,6,5]=>[8,4]
[6,3,2,5,4,1,8,7,10,9,12,11]=>[4,2,2,2,2]
[6,3,2,5,4,1,8,7,12,11,10,9]=>[4,4,2,2]
[6,3,2,5,4,1,10,9,8,7,12,11]=>[4,4,2,2]
[6,3,2,5,4,1,12,9,8,11,10,7]=>[4,4,2,2]
[6,3,2,5,4,1,12,11,10,9,8,7]=>[6,4,2]
[8,3,2,5,4,7,6,1,10,9,12,11]=>[4,2,2,2,2]
[8,3,2,5,4,7,6,1,12,11,10,9]=>[4,4,2,2]
[10,3,2,5,4,7,6,9,8,1,12,11]=>[4,2,2,2,2]
[12,3,2,5,4,7,6,9,8,11,10,1]=>[4,2,2,2,2]
[12,3,2,5,4,7,6,11,10,9,8,1]=>[6,2,2,2]
[10,3,2,5,4,9,8,7,6,1,12,11]=>[6,2,2,2]
[12,3,2,5,4,9,8,7,6,11,10,1]=>[6,2,2,2]
[12,3,2,5,4,11,8,7,10,9,6,1]=>[6,2,2,2]
[12,3,2,5,4,11,10,9,8,7,6,1]=>[8,2,2]
[8,3,2,7,6,5,4,1,10,9,12,11]=>[6,2,2,2]
[8,3,2,7,6,5,4,1,12,11,10,9]=>[6,4,2]
[10,3,2,7,6,5,4,9,8,1,12,11]=>[6,2,2,2]
[12,3,2,7,6,5,4,9,8,11,10,1]=>[6,2,2,2]
[12,3,2,7,6,5,4,11,10,9,8,1]=>[6,4,2]
[10,3,2,9,6,5,8,7,4,1,12,11]=>[6,2,2,2]
[12,3,2,9,6,5,8,7,4,11,10,1]=>[6,2,2,2]
[12,3,2,11,6,5,8,7,10,9,4,1]=>[6,2,2,2]
[12,3,2,11,6,5,10,9,8,7,4,1]=>[8,2,2]
[10,3,2,9,8,7,6,5,4,1,12,11]=>[8,2,2]
[12,3,2,9,8,7,6,5,4,11,10,1]=>[8,2,2]
[12,3,2,11,8,7,6,5,10,9,4,1]=>[8,2,2]
[12,3,2,11,10,7,6,9,8,5,4,1]=>[8,2,2]
[12,3,2,11,10,9,8,7,6,5,4,1]=>[10,2]
[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,2,2,2]
[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,4,2]
[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,4,2]
[6,5,4,3,2,1,12,9,8,11,10,7]=>[6,4,2]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,6]
[8,5,4,3,2,7,6,1,10,9,12,11]=>[6,2,2,2]
[8,5,4,3,2,7,6,1,12,11,10,9]=>[6,4,2]
[10,5,4,3,2,7,6,9,8,1,12,11]=>[6,2,2,2]
[12,5,4,3,2,7,6,9,8,11,10,1]=>[6,2,2,2]
[12,5,4,3,2,7,6,11,10,9,8,1]=>[6,4,2]
[10,5,4,3,2,9,8,7,6,1,12,11]=>[6,4,2]
[12,5,4,3,2,9,8,7,6,11,10,1]=>[6,4,2]
[12,5,4,3,2,11,8,7,10,9,6,1]=>[6,4,2]
[12,5,4,3,2,11,10,9,8,7,6,1]=>[8,4]
[8,7,4,3,6,5,2,1,10,9,12,11]=>[6,2,2,2]
[8,7,4,3,6,5,2,1,12,11,10,9]=>[6,4,2]
[10,7,4,3,6,5,2,9,8,1,12,11]=>[6,2,2,2]
[12,7,4,3,6,5,2,9,8,11,10,1]=>[6,2,2,2]
[12,7,4,3,6,5,2,11,10,9,8,1]=>[6,4,2]
[10,9,4,3,6,5,8,7,2,1,12,11]=>[6,2,2,2]
[12,9,4,3,6,5,8,7,2,11,10,1]=>[6,2,2,2]
[12,11,4,3,6,5,8,7,10,9,2,1]=>[6,2,2,2]
[12,11,4,3,6,5,10,9,8,7,2,1]=>[8,2,2]
[10,9,4,3,8,7,6,5,2,1,12,11]=>[8,2,2]
[12,9,4,3,8,7,6,5,2,11,10,1]=>[8,2,2]
[12,11,4,3,8,7,6,5,10,9,2,1]=>[8,2,2]
[12,11,4,3,10,7,6,9,8,5,2,1]=>[8,2,2]
[12,11,4,3,10,9,8,7,6,5,2,1]=>[10,2]
[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,2,2]
[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,4]
[10,7,6,5,4,3,2,9,8,1,12,11]=>[8,2,2]
[12,7,6,5,4,3,2,9,8,11,10,1]=>[8,2,2]
[12,7,6,5,4,3,2,11,10,9,8,1]=>[8,4]
[10,9,6,5,4,3,8,7,2,1,12,11]=>[8,2,2]
[12,9,6,5,4,3,8,7,2,11,10,1]=>[8,2,2]
[12,11,6,5,4,3,8,7,10,9,2,1]=>[8,2,2]
[12,11,6,5,4,3,10,9,8,7,2,1]=>[8,4]
[10,9,8,5,4,7,6,3,2,1,12,11]=>[8,2,2]
[12,9,8,5,4,7,6,3,2,11,10,1]=>[8,2,2]
[12,11,8,5,4,7,6,3,10,9,2,1]=>[8,2,2]
[12,11,10,5,4,7,6,9,8,3,2,1]=>[8,2,2]
[12,11,10,5,4,9,8,7,6,3,2,1]=>[10,2]
[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,2]
[12,9,8,7,6,5,4,3,2,11,10,1]=>[10,2]
[12,11,8,7,6,5,4,3,10,9,2,1]=>[10,2]
[12,11,10,7,6,5,4,9,8,3,2,1]=>[10,2]
[12,11,10,9,6,5,8,7,4,3,2,1]=>[10,2]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[12]
[2,4,6,8,10,12,1,3,5,7,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,6,8,11,12,1,3,5,7,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,6,9,10,12,1,3,5,7,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,6,9,11,12,1,3,5,7,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,6,10,11,12,1,3,5,7,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,7,8,10,12,1,3,5,6,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,7,8,11,12,1,3,5,6,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,7,9,10,12,1,3,5,6,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,7,9,11,12,1,3,5,6,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,7,10,11,12,1,3,5,6,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,8,9,10,12,1,3,5,6,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,8,9,11,12,1,3,5,6,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,8,10,11,12,1,3,5,6,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,4,9,10,11,12,1,3,5,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,6,8,10,12,1,3,4,7,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,6,8,11,12,1,3,4,7,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,6,9,10,12,1,3,4,7,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,6,9,11,12,1,3,4,7,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,6,10,11,12,1,3,4,7,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,7,8,10,12,1,3,4,6,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,7,8,11,12,1,3,4,6,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,7,9,10,12,1,3,4,6,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,7,9,11,12,1,3,4,6,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,7,10,11,12,1,3,4,6,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,8,9,10,12,1,3,4,6,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,8,9,11,12,1,3,4,6,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,8,10,11,12,1,3,4,6,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,5,9,10,11,12,1,3,4,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,7,8,10,12,1,3,4,5,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,7,8,11,12,1,3,4,5,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,7,9,10,12,1,3,4,5,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,7,9,11,12,1,3,4,5,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,7,10,11,12,1,3,4,5,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,8,9,10,12,1,3,4,5,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,8,9,11,12,1,3,4,5,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,8,10,11,12,1,3,4,5,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,6,9,10,11,12,1,3,4,5,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,7,8,9,10,12,1,3,4,5,6,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,7,8,9,11,12,1,3,4,5,6,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,7,8,10,11,12,1,3,4,5,6,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,7,9,10,11,12,1,3,4,5,6,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,8,9,10,11,12,1,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,6,8,10,12,1,2,5,7,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,6,8,11,12,1,2,5,7,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,6,9,10,12,1,2,5,7,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,6,9,11,12,1,2,5,7,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,6,10,11,12,1,2,5,7,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,7,8,10,12,1,2,5,6,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,7,8,11,12,1,2,5,6,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,7,9,10,12,1,2,5,6,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,7,9,11,12,1,2,5,6,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,7,10,11,12,1,2,5,6,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,8,9,10,12,1,2,5,6,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,8,9,11,12,1,2,5,6,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,8,10,11,12,1,2,5,6,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,4,9,10,11,12,1,2,5,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,6,8,10,12,1,2,4,7,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,6,8,11,12,1,2,4,7,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,6,9,10,12,1,2,4,7,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,6,9,11,12,1,2,4,7,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,6,10,11,12,1,2,4,7,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,7,8,10,12,1,2,4,6,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,7,8,11,12,1,2,4,6,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,7,9,10,12,1,2,4,6,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,7,9,11,12,1,2,4,6,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,7,10,11,12,1,2,4,6,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,8,9,10,12,1,2,4,6,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,8,9,11,12,1,2,4,6,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,8,10,11,12,1,2,4,6,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,5,9,10,11,12,1,2,4,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,7,8,10,12,1,2,4,5,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,7,8,11,12,1,2,4,5,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,7,9,10,12,1,2,4,5,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,7,9,11,12,1,2,4,5,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,7,10,11,12,1,2,4,5,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,8,9,10,12,1,2,4,5,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,8,9,11,12,1,2,4,5,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,8,10,11,12,1,2,4,5,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,6,9,10,11,12,1,2,4,5,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,7,8,9,10,12,1,2,4,5,6,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,7,8,9,11,12,1,2,4,5,6,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,7,8,10,11,12,1,2,4,5,6,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,7,9,10,11,12,1,2,4,5,6,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,8,9,10,11,12,1,2,4,5,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,6,8,10,12,1,2,3,7,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,6,8,11,12,1,2,3,7,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,6,9,10,12,1,2,3,7,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,6,9,11,12,1,2,3,7,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,6,10,11,12,1,2,3,7,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,7,8,10,12,1,2,3,6,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,7,8,11,12,1,2,3,6,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,7,9,10,12,1,2,3,6,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,7,9,11,12,1,2,3,6,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,7,10,11,12,1,2,3,6,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,8,9,10,12,1,2,3,6,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,8,9,11,12,1,2,3,6,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,8,10,11,12,1,2,3,6,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,5,9,10,11,12,1,2,3,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,7,8,10,12,1,2,3,5,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,7,8,11,12,1,2,3,5,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,7,9,10,12,1,2,3,5,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,7,9,11,12,1,2,3,5,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,7,10,11,12,1,2,3,5,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,8,9,10,12,1,2,3,5,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,8,9,11,12,1,2,3,5,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,8,10,11,12,1,2,3,5,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,6,9,10,11,12,1,2,3,5,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,7,8,9,10,12,1,2,3,5,6,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,7,8,9,11,12,1,2,3,5,6,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,7,8,10,11,12,1,2,3,5,6,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,7,9,10,11,12,1,2,3,5,6,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[4,8,9,10,11,12,1,2,3,5,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,7,8,10,12,1,2,3,4,9,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,7,8,11,12,1,2,3,4,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,7,9,10,12,1,2,3,4,8,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,7,9,11,12,1,2,3,4,8,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,7,10,11,12,1,2,3,4,8,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,8,9,10,12,1,2,3,4,7,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,8,9,11,12,1,2,3,4,7,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,8,10,11,12,1,2,3,4,7,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,6,9,10,11,12,1,2,3,4,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,7,8,9,10,12,1,2,3,4,6,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,7,8,9,11,12,1,2,3,4,6,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,7,8,10,11,12,1,2,3,4,6,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,7,9,10,11,12,1,2,3,4,6,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[5,8,9,10,11,12,1,2,3,4,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[6,7,8,9,10,12,1,2,3,4,5,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[6,7,8,9,11,12,1,2,3,4,5,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[6,7,8,10,11,12,1,2,3,4,5,9]=>[2,1,1,1,1,1,1,1,1,1,1]
[6,7,9,10,11,12,1,2,3,4,5,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[6,8,9,10,11,12,1,2,3,4,5,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[7,8,9,10,11,12,1,2,3,4,5,6]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,10,12,1,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[3,1,4,5,6,7,8,9,10,11,12,2]=>[2,2,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,11,12,10,9]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,9,10,8,7,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,9,11,8,12,10,7]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,10,11,12,9,8,7]=>[4,2,2,2,1,1]
[2,1,4,3,7,8,6,5,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,7,8,6,5,11,12,10,9]=>[3,3,2,2,1,1]
[2,1,4,3,7,9,6,10,8,5,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,7,9,6,11,8,12,10,5]=>[3,2,2,2,2,1]
[2,1,4,3,7,10,6,11,12,9,8,5]=>[4,2,2,2,1,1]
[2,1,4,3,8,9,10,7,6,5,12,11]=>[4,2,2,2,1,1]
[2,1,4,3,8,9,11,7,6,12,10,5]=>[4,2,2,2,1,1]
[2,1,4,3,8,10,11,7,12,9,6,5]=>[4,2,2,2,1,1]
[2,1,4,3,9,10,11,12,8,7,6,5]=>[5,2,2,1,1,1]
[2,1,5,6,4,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,5,6,4,3,8,7,11,12,10,9]=>[3,3,2,2,1,1]
[2,1,5,6,4,3,9,10,8,7,12,11]=>[3,3,2,2,1,1]
[2,1,5,6,4,3,9,11,8,12,10,7]=>[3,3,2,2,1,1]
[2,1,5,6,4,3,10,11,12,9,8,7]=>[4,3,2,1,1,1]
[2,1,5,7,4,8,6,3,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,5,7,4,8,6,3,11,12,10,9]=>[3,3,2,2,1,1]
[2,1,5,7,4,9,6,10,8,3,12,11]=>[3,2,2,2,2,1]
[2,1,5,7,4,9,6,11,8,12,10,3]=>[3,2,2,2,2,1]
[2,1,5,7,4,10,6,11,12,9,8,3]=>[4,2,2,2,1,1]
[2,1,5,8,4,9,10,7,6,3,12,11]=>[4,2,2,2,1,1]
[2,1,5,8,4,9,11,7,6,12,10,3]=>[4,2,2,2,1,1]
[2,1,5,8,4,10,11,7,12,9,6,3]=>[4,2,2,2,1,1]
[2,1,5,9,4,10,11,12,8,7,6,3]=>[5,2,2,1,1,1]
[2,1,6,7,8,5,4,3,10,9,12,11]=>[4,2,2,2,1,1]
[2,1,6,7,8,5,4,3,11,12,10,9]=>[4,3,2,1,1,1]
[2,1,6,7,9,5,4,10,8,3,12,11]=>[4,2,2,2,1,1]
[2,1,6,7,9,5,4,11,8,12,10,3]=>[4,2,2,2,1,1]
[2,1,6,7,10,5,4,11,12,9,8,3]=>[4,3,2,1,1,1]
[2,1,6,8,9,5,10,7,4,3,12,11]=>[4,2,2,2,1,1]
[2,1,6,8,9,5,11,7,4,12,10,3]=>[4,2,2,2,1,1]
[2,1,6,8,10,5,11,7,12,9,4,3]=>[4,2,2,2,1,1]
[2,1,6,9,10,5,11,12,8,7,4,3]=>[5,2,2,1,1,1]
[2,1,7,8,9,10,6,5,4,3,12,11]=>[5,2,2,1,1,1]
[2,1,7,8,9,11,6,5,4,12,10,3]=>[5,2,2,1,1,1]
[2,1,7,8,10,11,6,5,12,9,4,3]=>[5,2,2,1,1,1]
[2,1,7,9,10,11,6,12,8,5,4,3]=>[5,2,2,1,1,1]
[2,1,8,9,10,11,12,7,6,5,4,3]=>[6,2,1,1,1,1]
[3,4,2,1,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[3,4,2,1,6,5,8,7,11,12,10,9]=>[3,3,2,2,1,1]
[3,4,2,1,6,5,9,10,8,7,12,11]=>[3,3,2,2,1,1]
[3,4,2,1,6,5,9,11,8,12,10,7]=>[3,3,2,2,1,1]
[3,4,2,1,6,5,10,11,12,9,8,7]=>[4,3,2,1,1,1]
[3,4,2,1,7,8,6,5,10,9,12,11]=>[3,3,2,2,1,1]
[3,4,2,1,7,8,6,5,11,12,10,9]=>[3,3,3,1,1,1]
[3,4,2,1,7,9,6,10,8,5,12,11]=>[3,3,2,2,1,1]
[3,4,2,1,7,9,6,11,8,12,10,5]=>[3,3,2,2,1,1]
[3,4,2,1,7,10,6,11,12,9,8,5]=>[4,3,2,1,1,1]
[3,4,2,1,8,9,10,7,6,5,12,11]=>[4,3,2,1,1,1]
[3,4,2,1,8,9,11,7,6,12,10,5]=>[4,3,2,1,1,1]
[3,4,2,1,8,10,11,7,12,9,6,5]=>[4,3,2,1,1,1]
[3,4,2,1,9,10,11,12,8,7,6,5]=>[5,3,1,1,1,1]
[3,5,2,6,4,1,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[3,5,2,6,4,1,8,7,11,12,10,9]=>[3,3,2,2,1,1]
[3,5,2,6,4,1,9,10,8,7,12,11]=>[3,3,2,2,1,1]
[3,5,2,6,4,1,9,11,8,12,10,7]=>[3,3,2,2,1,1]
[3,5,2,6,4,1,10,11,12,9,8,7]=>[4,3,2,1,1,1]
[3,5,2,7,4,8,6,1,10,9,12,11]=>[3,2,2,2,2,1]
[3,5,2,7,4,8,6,1,11,12,10,9]=>[3,3,2,2,1,1]
[3,5,2,7,4,9,6,10,8,1,12,11]=>[3,2,2,2,2,1]
[3,5,2,7,4,9,6,11,8,12,10,1]=>[3,2,2,2,2,1]
[3,5,2,7,4,10,6,11,12,9,8,1]=>[4,2,2,2,1,1]
[3,5,2,8,4,9,10,7,6,1,12,11]=>[4,2,2,2,1,1]
[3,5,2,8,4,9,11,7,6,12,10,1]=>[4,2,2,2,1,1]
[3,5,2,8,4,10,11,7,12,9,6,1]=>[4,2,2,2,1,1]
[3,5,2,9,4,10,11,12,8,7,6,1]=>[5,2,2,1,1,1]
[3,6,2,7,8,5,4,1,10,9,12,11]=>[4,2,2,2,1,1]
[3,6,2,7,8,5,4,1,11,12,10,9]=>[4,3,2,1,1,1]
[3,6,2,7,9,5,4,10,8,1,12,11]=>[4,2,2,2,1,1]
[3,6,2,7,9,5,4,11,8,12,10,1]=>[4,2,2,2,1,1]
[3,6,2,7,10,5,4,11,12,9,8,1]=>[4,3,2,1,1,1]
[3,6,2,8,9,5,10,7,4,1,12,11]=>[4,2,2,2,1,1]
[3,6,2,8,9,5,11,7,4,12,10,1]=>[4,2,2,2,1,1]
[3,6,2,8,10,5,11,7,12,9,4,1]=>[4,2,2,2,1,1]
[3,6,2,9,10,5,11,12,8,7,4,1]=>[5,2,2,1,1,1]
[3,7,2,8,9,10,6,5,4,1,12,11]=>[5,2,2,1,1,1]
[3,7,2,8,9,11,6,5,4,12,10,1]=>[5,2,2,1,1,1]
[3,7,2,8,10,11,6,5,12,9,4,1]=>[5,2,2,1,1,1]
[3,7,2,9,10,11,6,12,8,5,4,1]=>[5,2,2,1,1,1]
[3,8,2,9,10,11,12,7,6,5,4,1]=>[6,2,1,1,1,1]
[4,5,6,3,2,1,8,7,10,9,12,11]=>[4,2,2,2,1,1]
[4,5,6,3,2,1,8,7,11,12,10,9]=>[4,3,2,1,1,1]
[4,5,6,3,2,1,9,10,8,7,12,11]=>[4,3,2,1,1,1]
[4,5,6,3,2,1,9,11,8,12,10,7]=>[4,3,2,1,1,1]
[4,5,6,3,2,1,10,11,12,9,8,7]=>[4,4,1,1,1,1]
[4,5,7,3,2,8,6,1,10,9,12,11]=>[4,2,2,2,1,1]
[4,5,7,3,2,8,6,1,11,12,10,9]=>[4,3,2,1,1,1]
[4,5,7,3,2,9,6,10,8,1,12,11]=>[4,2,2,2,1,1]
[4,5,7,3,2,9,6,11,8,12,10,1]=>[4,2,2,2,1,1]
[4,5,7,3,2,10,6,11,12,9,8,1]=>[4,3,2,1,1,1]
[4,5,8,3,2,9,10,7,6,1,12,11]=>[4,3,2,1,1,1]
[4,5,8,3,2,9,11,7,6,12,10,1]=>[4,3,2,1,1,1]
[4,5,8,3,2,10,11,7,12,9,6,1]=>[4,3,2,1,1,1]
[4,5,9,3,2,10,11,12,8,7,6,1]=>[5,3,1,1,1,1]
[4,6,7,3,8,5,2,1,10,9,12,11]=>[4,2,2,2,1,1]
[4,6,7,3,8,5,2,1,11,12,10,9]=>[4,3,2,1,1,1]
[4,6,7,3,9,5,2,10,8,1,12,11]=>[4,2,2,2,1,1]
[4,6,7,3,9,5,2,11,8,12,10,1]=>[4,2,2,2,1,1]
[4,6,7,3,10,5,2,11,12,9,8,1]=>[4,3,2,1,1,1]
[4,6,8,3,9,5,10,7,2,1,12,11]=>[4,2,2,2,1,1]
[4,6,8,3,9,5,11,7,2,12,10,1]=>[4,2,2,2,1,1]
[4,6,8,3,10,5,11,7,12,9,2,1]=>[4,2,2,2,1,1]
[4,6,9,3,10,5,11,12,8,7,2,1]=>[5,2,2,1,1,1]
[4,7,8,3,9,10,6,5,2,1,12,11]=>[5,2,2,1,1,1]
[4,7,8,3,9,11,6,5,2,12,10,1]=>[5,2,2,1,1,1]
[4,7,8,3,10,11,6,5,12,9,2,1]=>[5,2,2,1,1,1]
[4,7,9,3,10,11,6,12,8,5,2,1]=>[5,2,2,1,1,1]
[4,8,9,3,10,11,12,7,6,5,2,1]=>[6,2,1,1,1,1]
[5,6,7,8,4,3,2,1,10,9,12,11]=>[5,2,2,1,1,1]
[5,6,7,8,4,3,2,1,11,12,10,9]=>[5,3,1,1,1,1]
[5,6,7,9,4,3,2,10,8,1,12,11]=>[5,2,2,1,1,1]
[5,6,7,9,4,3,2,11,8,12,10,1]=>[5,2,2,1,1,1]
[5,6,7,10,4,3,2,11,12,9,8,1]=>[5,3,1,1,1,1]
[5,6,8,9,4,3,10,7,2,1,12,11]=>[5,2,2,1,1,1]
[5,6,8,9,4,3,11,7,2,12,10,1]=>[5,2,2,1,1,1]
[5,6,8,10,4,3,11,7,12,9,2,1]=>[5,2,2,1,1,1]
[5,6,9,10,4,3,11,12,8,7,2,1]=>[5,3,1,1,1,1]
[5,7,8,9,4,10,6,3,2,1,12,11]=>[5,2,2,1,1,1]
[5,7,8,9,4,11,6,3,2,12,10,1]=>[5,2,2,1,1,1]
[5,7,8,10,4,11,6,3,12,9,2,1]=>[5,2,2,1,1,1]
[5,7,9,10,4,11,6,12,8,3,2,1]=>[5,2,2,1,1,1]
[5,8,9,10,4,11,12,7,6,3,2,1]=>[6,2,1,1,1,1]
[6,7,8,9,10,5,4,3,2,1,12,11]=>[6,2,1,1,1,1]
[6,7,8,9,11,5,4,3,2,12,10,1]=>[6,2,1,1,1,1]
[6,7,8,10,11,5,4,3,12,9,2,1]=>[6,2,1,1,1,1]
[6,7,9,10,11,5,4,12,8,3,2,1]=>[6,2,1,1,1,1]
[6,8,9,10,11,5,12,7,4,3,2,1]=>[6,2,1,1,1,1]
[7,8,9,10,11,12,6,5,4,3,2,1]=>[7,1,1,1,1,1]
[11,12,9,10,7,8,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[9,10,12,11,7,8,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,7,8,10,9,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[7,10,12,8,11,9,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[7,8,9,12,11,10,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,5,6,8,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[9,10,12,11,5,6,8,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,5,8,10,6,9,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[5,10,12,8,11,6,9,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[5,8,9,12,11,6,10,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,5,6,7,10,9,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[5,10,12,6,7,11,9,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[5,6,9,12,7,11,10,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[5,6,7,8,12,11,10,9,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,3,4,6,5,1,2]=>[6,1,1,1,1,1,1]
[9,10,12,11,7,8,3,4,6,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,7,8,10,9,3,4,6,5,1,2]=>[6,1,1,1,1,1,1]
[7,10,12,8,11,9,3,4,6,5,1,2]=>[6,1,1,1,1,1,1]
[7,8,9,12,11,10,3,4,6,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,3,6,8,4,7,5,1,2]=>[6,1,1,1,1,1,1]
[9,10,12,11,3,6,8,4,7,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,3,8,10,6,9,4,7,5,1,2]=>[6,1,1,1,1,1,1]
[3,10,12,8,11,6,9,4,7,5,1,2]=>[6,1,1,1,1,1,1]
[3,8,9,12,11,6,10,4,7,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,3,6,7,10,9,4,8,5,1,2]=>[6,1,1,1,1,1,1]
[3,10,12,6,7,11,9,4,8,5,1,2]=>[6,1,1,1,1,1,1]
[3,6,9,12,7,11,10,4,8,5,1,2]=>[6,1,1,1,1,1,1]
[3,6,7,8,12,11,10,4,9,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,3,4,5,8,7,6,1,2]=>[6,1,1,1,1,1,1]
[9,10,12,11,3,4,5,8,7,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,3,8,10,4,5,9,7,6,1,2]=>[6,1,1,1,1,1,1]
[3,10,12,8,11,4,5,9,7,6,1,2]=>[6,1,1,1,1,1,1]
[3,8,9,12,11,4,5,10,7,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,3,4,7,10,5,9,8,6,1,2]=>[6,1,1,1,1,1,1]
[3,10,12,4,7,11,5,9,8,6,1,2]=>[6,1,1,1,1,1,1]
[3,4,9,12,7,11,5,10,8,6,1,2]=>[6,1,1,1,1,1,1]
[3,4,7,8,12,11,5,10,9,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,3,4,5,6,10,9,8,7,1,2]=>[6,1,1,1,1,1,1]
[3,10,12,4,5,6,11,9,8,7,1,2]=>[6,1,1,1,1,1,1]
[3,4,9,12,5,6,11,10,8,7,1,2]=>[6,1,1,1,1,1,1]
[3,4,5,8,12,6,11,10,9,7,1,2]=>[6,1,1,1,1,1,1]
[3,4,5,6,7,12,11,10,9,8,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,5,6,1,2,4,3]=>[6,1,1,1,1,1,1]
[9,10,12,11,7,8,5,6,1,2,4,3]=>[6,1,1,1,1,1,1]
[11,12,7,8,10,9,5,6,1,2,4,3]=>[6,1,1,1,1,1,1]
[7,10,12,8,11,9,5,6,1,2,4,3]=>[6,1,1,1,1,1,1]
[7,8,9,12,11,10,5,6,1,2,4,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,5,6,8,7,1,2,4,3]=>[6,1,1,1,1,1,1]
[9,10,12,11,5,6,8,7,1,2,4,3]=>[6,1,1,1,1,1,1]
[11,12,5,8,10,6,9,7,1,2,4,3]=>[6,1,1,1,1,1,1]
[5,10,12,8,11,6,9,7,1,2,4,3]=>[6,1,1,1,1,1,1]
[5,8,9,12,11,6,10,7,1,2,4,3]=>[6,1,1,1,1,1,1]
[11,12,5,6,7,10,9,8,1,2,4,3]=>[6,1,1,1,1,1,1]
[5,10,12,6,7,11,9,8,1,2,4,3]=>[6,1,1,1,1,1,1]
[5,6,9,12,7,11,10,8,1,2,4,3]=>[6,1,1,1,1,1,1]
[5,6,7,8,12,11,10,9,1,2,4,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,1,4,6,2,5,3]=>[6,1,1,1,1,1,1]
[9,10,12,11,7,8,1,4,6,2,5,3]=>[6,1,1,1,1,1,1]
[11,12,7,8,10,9,1,4,6,2,5,3]=>[6,1,1,1,1,1,1]
[7,10,12,8,11,9,1,4,6,2,5,3]=>[6,1,1,1,1,1,1]
[7,8,9,12,11,10,1,4,6,2,5,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,1,6,8,4,7,2,5,3]=>[6,1,1,1,1,1,1]
[9,10,12,11,1,6,8,4,7,2,5,3]=>[6,1,1,1,1,1,1]
[11,12,1,8,10,6,9,4,7,2,5,3]=>[6,1,1,1,1,1,1]
[1,10,12,8,11,6,9,4,7,2,5,3]=>[6,1,1,1,1,1,1]
[1,8,9,12,11,6,10,4,7,2,5,3]=>[6,1,1,1,1,1,1]
[11,12,1,6,7,10,9,4,8,2,5,3]=>[6,1,1,1,1,1,1]
[1,10,12,6,7,11,9,4,8,2,5,3]=>[6,1,1,1,1,1,1]
[1,6,9,12,7,11,10,4,8,2,5,3]=>[6,1,1,1,1,1,1]
[1,6,7,8,12,11,10,4,9,2,5,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,1,4,5,8,7,2,6,3]=>[6,1,1,1,1,1,1]
[9,10,12,11,1,4,5,8,7,2,6,3]=>[6,1,1,1,1,1,1]
[11,12,1,8,10,4,5,9,7,2,6,3]=>[6,1,1,1,1,1,1]
[1,10,12,8,11,4,5,9,7,2,6,3]=>[6,1,1,1,1,1,1]
[1,8,9,12,11,4,5,10,7,2,6,3]=>[6,1,1,1,1,1,1]
[11,12,1,4,7,10,5,9,8,2,6,3]=>[6,1,1,1,1,1,1]
[1,10,12,4,7,11,5,9,8,2,6,3]=>[6,1,1,1,1,1,1]
[1,4,9,12,7,11,5,10,8,2,6,3]=>[6,1,1,1,1,1,1]
[1,4,7,8,12,11,5,10,9,2,6,3]=>[6,1,1,1,1,1,1]
[11,12,1,4,5,6,10,9,8,2,7,3]=>[6,1,1,1,1,1,1]
[1,10,12,4,5,6,11,9,8,2,7,3]=>[6,1,1,1,1,1,1]
[1,4,9,12,5,6,11,10,8,2,7,3]=>[6,1,1,1,1,1,1]
[1,4,5,8,12,6,11,10,9,2,7,3]=>[6,1,1,1,1,1,1]
[1,4,5,6,7,12,11,10,9,2,8,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,1,2,3,6,5,4]=>[6,1,1,1,1,1,1]
[9,10,12,11,7,8,1,2,3,6,5,4]=>[6,1,1,1,1,1,1]
[11,12,7,8,10,9,1,2,3,6,5,4]=>[6,1,1,1,1,1,1]
[7,10,12,8,11,9,1,2,3,6,5,4]=>[6,1,1,1,1,1,1]
[7,8,9,12,11,10,1,2,3,6,5,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,1,6,8,2,3,7,5,4]=>[6,1,1,1,1,1,1]
[9,10,12,11,1,6,8,2,3,7,5,4]=>[6,1,1,1,1,1,1]
[11,12,1,8,10,6,9,2,3,7,5,4]=>[6,1,1,1,1,1,1]
[1,10,12,8,11,6,9,2,3,7,5,4]=>[6,1,1,1,1,1,1]
[1,8,9,12,11,6,10,2,3,7,5,4]=>[6,1,1,1,1,1,1]
[11,12,1,6,7,10,9,2,3,8,5,4]=>[6,1,1,1,1,1,1]
[1,10,12,6,7,11,9,2,3,8,5,4]=>[6,1,1,1,1,1,1]
[1,6,9,12,7,11,10,2,3,8,5,4]=>[6,1,1,1,1,1,1]
[1,6,7,8,12,11,10,2,3,9,5,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,1,2,5,8,3,7,6,4]=>[6,1,1,1,1,1,1]
[9,10,12,11,1,2,5,8,3,7,6,4]=>[6,1,1,1,1,1,1]
[11,12,1,8,10,2,5,9,3,7,6,4]=>[6,1,1,1,1,1,1]
[1,10,12,8,11,2,5,9,3,7,6,4]=>[6,1,1,1,1,1,1]
[1,8,9,12,11,2,5,10,3,7,6,4]=>[6,1,1,1,1,1,1]
[11,12,1,2,7,10,5,9,3,8,6,4]=>[6,1,1,1,1,1,1]
[1,10,12,2,7,11,5,9,3,8,6,4]=>[6,1,1,1,1,1,1]
[1,2,9,12,7,11,5,10,3,8,6,4]=>[6,1,1,1,1,1,1]
[1,2,7,8,12,11,5,10,3,9,6,4]=>[6,1,1,1,1,1,1]
[11,12,1,2,5,6,10,9,3,8,7,4]=>[6,1,1,1,1,1,1]
[1,10,12,2,5,6,11,9,3,8,7,4]=>[6,1,1,1,1,1,1]
[1,2,9,12,5,6,11,10,3,8,7,4]=>[6,1,1,1,1,1,1]
[1,2,5,8,12,6,11,10,3,9,7,4]=>[6,1,1,1,1,1,1]
[1,2,5,6,7,12,11,10,3,9,8,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,1,2,3,4,8,7,6,5]=>[6,1,1,1,1,1,1]
[9,10,12,11,1,2,3,4,8,7,6,5]=>[6,1,1,1,1,1,1]
[11,12,1,8,10,2,3,4,9,7,6,5]=>[6,1,1,1,1,1,1]
[1,10,12,8,11,2,3,4,9,7,6,5]=>[6,1,1,1,1,1,1]
[1,8,9,12,11,2,3,4,10,7,6,5]=>[6,1,1,1,1,1,1]
[11,12,1,2,7,10,3,4,9,8,6,5]=>[6,1,1,1,1,1,1]
[1,10,12,2,7,11,3,4,9,8,6,5]=>[6,1,1,1,1,1,1]
[1,2,9,12,7,11,3,4,10,8,6,5]=>[6,1,1,1,1,1,1]
[1,2,7,8,12,11,3,4,10,9,6,5]=>[6,1,1,1,1,1,1]
[11,12,1,2,3,6,10,4,9,8,7,5]=>[6,1,1,1,1,1,1]
[1,10,12,2,3,6,11,4,9,8,7,5]=>[6,1,1,1,1,1,1]
[1,2,9,12,3,6,11,4,10,8,7,5]=>[6,1,1,1,1,1,1]
[1,2,3,8,12,6,11,4,10,9,7,5]=>[6,1,1,1,1,1,1]
[1,2,3,6,7,12,11,4,10,9,8,5]=>[6,1,1,1,1,1,1]
[11,12,1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1,1,1]
[1,10,12,2,3,4,5,11,9,8,7,6]=>[6,1,1,1,1,1,1]
[1,2,9,12,3,4,5,11,10,8,7,6]=>[6,1,1,1,1,1,1]
[1,2,3,8,12,4,5,11,10,9,7,6]=>[6,1,1,1,1,1,1]
[1,2,3,4,7,12,5,11,10,9,8,6]=>[6,1,1,1,1,1,1]
[1,2,3,4,5,6,12,11,10,9,8,7]=>[6,1,1,1,1,1,1]
[10,12,9,11,7,8,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,8,10,7,9,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[10,12,8,11,7,9,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[9,12,8,11,7,10,5,6,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,6,8,5,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[10,12,9,11,6,8,5,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,8,10,6,9,5,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[10,12,8,11,6,9,5,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[9,12,8,11,6,10,5,7,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,7,10,6,9,5,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[10,12,7,11,6,9,5,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[9,12,7,11,6,10,5,8,3,4,1,2]=>[6,1,1,1,1,1,1]
[8,12,7,11,6,10,5,9,3,4,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,4,6,3,5,1,2]=>[6,1,1,1,1,1,1]
[10,12,9,11,7,8,4,6,3,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,8,10,7,9,4,6,3,5,1,2]=>[6,1,1,1,1,1,1]
[10,12,8,11,7,9,4,6,3,5,1,2]=>[6,1,1,1,1,1,1]
[9,12,8,11,7,10,4,6,3,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,6,8,4,7,3,5,1,2]=>[6,1,1,1,1,1,1]
[10,12,9,11,6,8,4,7,3,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,8,10,6,9,4,7,3,5,1,2]=>[6,1,1,1,1,1,1]
[10,12,8,11,6,9,4,7,3,5,1,2]=>[6,1,1,1,1,1,1]
[9,12,8,11,6,10,4,7,3,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,7,10,6,9,4,8,3,5,1,2]=>[6,1,1,1,1,1,1]
[10,12,7,11,6,9,4,8,3,5,1,2]=>[6,1,1,1,1,1,1]
[9,12,7,11,6,10,4,8,3,5,1,2]=>[6,1,1,1,1,1,1]
[8,12,7,11,6,10,4,9,3,5,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,5,8,4,7,3,6,1,2]=>[6,1,1,1,1,1,1]
[10,12,9,11,5,8,4,7,3,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,8,10,5,9,4,7,3,6,1,2]=>[6,1,1,1,1,1,1]
[10,12,8,11,5,9,4,7,3,6,1,2]=>[6,1,1,1,1,1,1]
[9,12,8,11,5,10,4,7,3,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,7,10,5,9,4,8,3,6,1,2]=>[6,1,1,1,1,1,1]
[10,12,7,11,5,9,4,8,3,6,1,2]=>[6,1,1,1,1,1,1]
[9,12,7,11,5,10,4,8,3,6,1,2]=>[6,1,1,1,1,1,1]
[8,12,7,11,5,10,4,9,3,6,1,2]=>[6,1,1,1,1,1,1]
[11,12,6,10,5,9,4,8,3,7,1,2]=>[6,1,1,1,1,1,1]
[10,12,6,11,5,9,4,8,3,7,1,2]=>[6,1,1,1,1,1,1]
[9,12,6,11,5,10,4,8,3,7,1,2]=>[6,1,1,1,1,1,1]
[8,12,6,11,5,10,4,9,3,7,1,2]=>[6,1,1,1,1,1,1]
[7,12,6,11,5,10,4,9,3,8,1,2]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,5,6,2,4,1,3]=>[6,1,1,1,1,1,1]
[10,12,9,11,7,8,5,6,2,4,1,3]=>[6,1,1,1,1,1,1]
[11,12,8,10,7,9,5,6,2,4,1,3]=>[6,1,1,1,1,1,1]
[10,12,8,11,7,9,5,6,2,4,1,3]=>[6,1,1,1,1,1,1]
[9,12,8,11,7,10,5,6,2,4,1,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,6,8,5,7,2,4,1,3]=>[6,1,1,1,1,1,1]
[10,12,9,11,6,8,5,7,2,4,1,3]=>[6,1,1,1,1,1,1]
[11,12,8,10,6,9,5,7,2,4,1,3]=>[6,1,1,1,1,1,1]
[10,12,8,11,6,9,5,7,2,4,1,3]=>[6,1,1,1,1,1,1]
[9,12,8,11,6,10,5,7,2,4,1,3]=>[6,1,1,1,1,1,1]
[11,12,7,10,6,9,5,8,2,4,1,3]=>[6,1,1,1,1,1,1]
[10,12,7,11,6,9,5,8,2,4,1,3]=>[6,1,1,1,1,1,1]
[9,12,7,11,6,10,5,8,2,4,1,3]=>[6,1,1,1,1,1,1]
[8,12,7,11,6,10,5,9,2,4,1,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,4,6,2,5,1,3]=>[6,1,1,1,1,1,1]
[10,12,9,11,7,8,4,6,2,5,1,3]=>[6,1,1,1,1,1,1]
[11,12,8,10,7,9,4,6,2,5,1,3]=>[6,1,1,1,1,1,1]
[10,12,8,11,7,9,4,6,2,5,1,3]=>[6,1,1,1,1,1,1]
[9,12,8,11,7,10,4,6,2,5,1,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,6,8,4,7,2,5,1,3]=>[6,1,1,1,1,1,1]
[10,12,9,11,6,8,4,7,2,5,1,3]=>[6,1,1,1,1,1,1]
[11,12,8,10,6,9,4,7,2,5,1,3]=>[6,1,1,1,1,1,1]
[10,12,8,11,6,9,4,7,2,5,1,3]=>[6,1,1,1,1,1,1]
[9,12,8,11,6,10,4,7,2,5,1,3]=>[6,1,1,1,1,1,1]
[11,12,7,10,6,9,4,8,2,5,1,3]=>[6,1,1,1,1,1,1]
[10,12,7,11,6,9,4,8,2,5,1,3]=>[6,1,1,1,1,1,1]
[9,12,7,11,6,10,4,8,2,5,1,3]=>[6,1,1,1,1,1,1]
[8,12,7,11,6,10,4,9,2,5,1,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,5,8,4,7,2,6,1,3]=>[6,1,1,1,1,1,1]
[10,12,9,11,5,8,4,7,2,6,1,3]=>[6,1,1,1,1,1,1]
[11,12,8,10,5,9,4,7,2,6,1,3]=>[6,1,1,1,1,1,1]
[10,12,8,11,5,9,4,7,2,6,1,3]=>[6,1,1,1,1,1,1]
[9,12,8,11,5,10,4,7,2,6,1,3]=>[6,1,1,1,1,1,1]
[11,12,7,10,5,9,4,8,2,6,1,3]=>[6,1,1,1,1,1,1]
[10,12,7,11,5,9,4,8,2,6,1,3]=>[6,1,1,1,1,1,1]
[9,12,7,11,5,10,4,8,2,6,1,3]=>[6,1,1,1,1,1,1]
[8,12,7,11,5,10,4,9,2,6,1,3]=>[6,1,1,1,1,1,1]
[11,12,6,10,5,9,4,8,2,7,1,3]=>[6,1,1,1,1,1,1]
[10,12,6,11,5,9,4,8,2,7,1,3]=>[6,1,1,1,1,1,1]
[9,12,6,11,5,10,4,8,2,7,1,3]=>[6,1,1,1,1,1,1]
[8,12,6,11,5,10,4,9,2,7,1,3]=>[6,1,1,1,1,1,1]
[7,12,6,11,5,10,4,9,2,8,1,3]=>[6,1,1,1,1,1,1]
[11,12,9,10,7,8,3,6,2,5,1,4]=>[6,1,1,1,1,1,1]
[10,12,9,11,7,8,3,6,2,5,1,4]=>[6,1,1,1,1,1,1]
[11,12,8,10,7,9,3,6,2,5,1,4]=>[6,1,1,1,1,1,1]
[10,12,8,11,7,9,3,6,2,5,1,4]=>[6,1,1,1,1,1,1]
[9,12,8,11,7,10,3,6,2,5,1,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,6,8,3,7,2,5,1,4]=>[6,1,1,1,1,1,1]
[10,12,9,11,6,8,3,7,2,5,1,4]=>[6,1,1,1,1,1,1]
[11,12,8,10,6,9,3,7,2,5,1,4]=>[6,1,1,1,1,1,1]
[10,12,8,11,6,9,3,7,2,5,1,4]=>[6,1,1,1,1,1,1]
[9,12,8,11,6,10,3,7,2,5,1,4]=>[6,1,1,1,1,1,1]
[11,12,7,10,6,9,3,8,2,5,1,4]=>[6,1,1,1,1,1,1]
[10,12,7,11,6,9,3,8,2,5,1,4]=>[6,1,1,1,1,1,1]
[9,12,7,11,6,10,3,8,2,5,1,4]=>[6,1,1,1,1,1,1]
[8,12,7,11,6,10,3,9,2,5,1,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,5,8,3,7,2,6,1,4]=>[6,1,1,1,1,1,1]
[10,12,9,11,5,8,3,7,2,6,1,4]=>[6,1,1,1,1,1,1]
[11,12,8,10,5,9,3,7,2,6,1,4]=>[6,1,1,1,1,1,1]
[10,12,8,11,5,9,3,7,2,6,1,4]=>[6,1,1,1,1,1,1]
[9,12,8,11,5,10,3,7,2,6,1,4]=>[6,1,1,1,1,1,1]
[11,12,7,10,5,9,3,8,2,6,1,4]=>[6,1,1,1,1,1,1]
[10,12,7,11,5,9,3,8,2,6,1,4]=>[6,1,1,1,1,1,1]
[9,12,7,11,5,10,3,8,2,6,1,4]=>[6,1,1,1,1,1,1]
[8,12,7,11,5,10,3,9,2,6,1,4]=>[6,1,1,1,1,1,1]
[11,12,6,10,5,9,3,8,2,7,1,4]=>[6,1,1,1,1,1,1]
[10,12,6,11,5,9,3,8,2,7,1,4]=>[6,1,1,1,1,1,1]
[9,12,6,11,5,10,3,8,2,7,1,4]=>[6,1,1,1,1,1,1]
[8,12,6,11,5,10,3,9,2,7,1,4]=>[6,1,1,1,1,1,1]
[7,12,6,11,5,10,3,9,2,8,1,4]=>[6,1,1,1,1,1,1]
[11,12,9,10,4,8,3,7,2,6,1,5]=>[6,1,1,1,1,1,1]
[10,12,9,11,4,8,3,7,2,6,1,5]=>[6,1,1,1,1,1,1]
[11,12,8,10,4,9,3,7,2,6,1,5]=>[6,1,1,1,1,1,1]
[10,12,8,11,4,9,3,7,2,6,1,5]=>[6,1,1,1,1,1,1]
[9,12,8,11,4,10,3,7,2,6,1,5]=>[6,1,1,1,1,1,1]
[11,12,7,10,4,9,3,8,2,6,1,5]=>[6,1,1,1,1,1,1]
[10,12,7,11,4,9,3,8,2,6,1,5]=>[6,1,1,1,1,1,1]
[9,12,7,11,4,10,3,8,2,6,1,5]=>[6,1,1,1,1,1,1]
[8,12,7,11,4,10,3,9,2,6,1,5]=>[6,1,1,1,1,1,1]
[11,12,6,10,4,9,3,8,2,7,1,5]=>[6,1,1,1,1,1,1]
[10,12,6,11,4,9,3,8,2,7,1,5]=>[6,1,1,1,1,1,1]
[9,12,6,11,4,10,3,8,2,7,1,5]=>[6,1,1,1,1,1,1]
[8,12,6,11,4,10,3,9,2,7,1,5]=>[6,1,1,1,1,1,1]
[7,12,6,11,4,10,3,9,2,8,1,5]=>[6,1,1,1,1,1,1]
[11,12,5,10,4,9,3,8,2,7,1,6]=>[6,1,1,1,1,1,1]
[10,12,5,11,4,9,3,8,2,7,1,6]=>[6,1,1,1,1,1,1]
[9,12,5,11,4,10,3,8,2,7,1,6]=>[6,1,1,1,1,1,1]
[8,12,5,11,4,10,3,9,2,7,1,6]=>[6,1,1,1,1,1,1]
[7,12,5,11,4,10,3,9,2,8,1,6]=>[6,1,1,1,1,1,1]
[6,12,5,11,4,10,3,9,2,8,1,7]=>[6,1,1,1,1,1,1]
[7,1,8,2,9,3,10,4,11,5,12,6]=>[2,2,2,2,2,2]
[7,1,8,2,9,3,10,4,11,12,5,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,3,10,11,4,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,3,10,11,4,12,5,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,3,10,11,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,3,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,10,3,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,3,11,4,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,10,3,11,4,12,5,6]=>[2,2,2,2,2,1,1]
[7,1,8,2,9,10,3,11,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,2,9,10,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,2,3,10,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,9,2,3,10,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,3,10,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,3,10,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,3,10,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,2,10,3,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,9,2,10,3,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,10,3,11,4,5,12,6]=>[2,2,2,2,2,1,1]
[7,1,8,9,2,10,3,11,4,12,5,6]=>[2,2,2,2,2,1,1]
[7,1,8,9,2,10,3,11,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,10,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,10,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,10,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,2,10,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,2,3,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,3,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,2,3,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,3,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,3,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,2,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,1,8,9,10,2,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,11,2,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,11,2,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,11,2,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,11,2,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,1,8,9,10,11,12,2,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,1,2,9,3,10,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,8,1,2,9,3,10,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,3,10,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,3,10,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,3,10,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,3,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,10,3,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,3,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,10,3,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,2,9,10,3,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,11,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,11,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,11,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,2,9,10,11,12,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,1,9,2,3,10,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,8,1,9,2,3,10,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,3,10,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,3,10,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,3,10,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,2,10,3,4,11,5,12,6]=>[2,2,2,2,2,1,1]
[7,8,1,9,2,10,3,4,11,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,10,3,11,4,5,12,6]=>[2,2,2,2,2,1,1]
[7,8,1,9,2,10,3,11,4,12,5,6]=>[2,2,2,2,2,1,1]
[7,8,1,9,2,10,3,11,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,10,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,10,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,10,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,2,10,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,2,3,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,3,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,2,3,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,3,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,3,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,2,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,1,9,10,2,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,11,2,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,11,2,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,11,2,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,11,2,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,1,9,10,11,12,2,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,1,2,3,10,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,2,3,10,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,3,10,11,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,3,10,11,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,3,10,11,12,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,1,2,10,3,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,2,10,3,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,3,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,2,10,3,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,2,10,3,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,11,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,11,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,11,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,2,10,11,12,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,1,10,2,3,4,11,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,3,4,11,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,2,3,11,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,3,11,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,3,11,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,2,11,3,4,5,12,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,11,3,4,12,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,11,3,12,4,5,6]=>[2,2,2,2,1,1,1,1]
[7,8,9,1,10,2,11,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,11,2,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,11,2,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,11,2,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,11,2,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,1,10,11,12,2,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,1,2,3,4,11,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,3,4,11,12,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,1,2,3,11,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,3,11,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,3,11,12,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,1,2,11,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,11,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,11,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,2,11,12,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,1,11,2,3,4,5,12,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,11,2,3,4,12,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,11,2,3,12,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,11,2,12,3,4,5,6]=>[2,2,2,1,1,1,1,1,1]
[7,8,9,10,1,11,12,2,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,11,1,2,3,4,5,12,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,11,1,2,3,4,12,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,11,1,2,3,12,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,11,1,2,12,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[7,8,9,10,11,1,12,2,3,4,5,6]=>[2,2,1,1,1,1,1,1,1,1]
[9,10,11,12,7,8,5,6,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[11,12,7,8,9,10,5,6,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[7,10,11,8,9,12,5,6,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[7,8,9,10,11,12,5,6,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,9,10,5,6,7,8,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,5,6,7,8,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,5,8,9,6,7,10,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[5,10,11,8,9,6,7,12,3,4,1,2]=>[5,1,1,1,1,1,1,1]
[5,8,9,10,11,6,7,12,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,5,6,7,8,9,10,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[5,10,11,6,7,8,9,12,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[5,6,9,10,7,8,11,12,3,4,1,2]=>[4,1,1,1,1,1,1,1,1]
[5,6,7,8,9,10,11,12,3,4,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,3,4,5,6,1,2]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,7,8,3,4,5,6,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,7,8,9,10,3,4,5,6,1,2]=>[4,1,1,1,1,1,1,1,1]
[7,10,11,8,9,12,3,4,5,6,1,2]=>[4,1,1,1,1,1,1,1,1]
[7,8,9,10,11,12,3,4,5,6,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,3,6,7,4,5,8,1,2]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,3,6,7,4,5,8,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,3,8,9,6,7,4,5,10,1,2]=>[5,1,1,1,1,1,1,1]
[3,10,11,8,9,6,7,4,5,12,1,2]=>[5,1,1,1,1,1,1,1]
[3,8,9,10,11,6,7,4,5,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[11,12,3,6,7,8,9,4,5,10,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,10,11,6,7,8,9,4,5,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,6,9,10,7,8,11,4,5,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,6,7,8,9,10,11,4,5,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,3,4,5,6,7,8,1,2]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,3,4,5,6,7,8,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,3,8,9,4,5,6,7,10,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,10,11,8,9,4,5,6,7,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,8,9,10,11,4,5,6,7,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,3,4,7,8,5,6,9,10,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,10,11,4,7,8,5,6,9,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,4,9,10,7,8,5,6,11,12,1,2]=>[4,1,1,1,1,1,1,1,1]
[3,4,7,8,9,10,5,6,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,3,4,5,6,7,8,9,10,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[3,10,11,4,5,6,7,8,9,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,9,10,5,6,7,8,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,5,8,9,6,7,10,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,5,6,7,8,9,10,11,12,1,2]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,5,6,1,2,3,4]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,7,8,5,6,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[11,12,7,8,9,10,5,6,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[7,10,11,8,9,12,5,6,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[7,8,9,10,11,12,5,6,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,5,6,7,8,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,5,6,7,8,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,5,8,9,6,7,10,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[5,10,11,8,9,6,7,12,1,2,3,4]=>[4,1,1,1,1,1,1,1,1]
[5,8,9,10,11,6,7,12,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,5,6,7,8,9,10,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[5,10,11,6,7,8,9,12,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[5,6,9,10,7,8,11,12,1,2,3,4]=>[3,1,1,1,1,1,1,1,1,1]
[5,6,7,8,9,10,11,12,1,2,3,4]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,1,4,5,2,3,6]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,7,8,1,4,5,2,3,6]=>[4,1,1,1,1,1,1,1,1]
[11,12,7,8,9,10,1,4,5,2,3,6]=>[4,1,1,1,1,1,1,1,1]
[7,10,11,8,9,12,1,4,5,2,3,6]=>[4,1,1,1,1,1,1,1,1]
[7,8,9,10,11,12,1,4,5,2,3,6]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,1,6,7,4,5,2,3,8]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,1,6,7,4,5,2,3,8]=>[4,1,1,1,1,1,1,1,1]
[11,12,1,8,9,6,7,4,5,2,3,10]=>[5,1,1,1,1,1,1,1]
[1,10,11,8,9,6,7,4,5,2,3,12]=>[5,1,1,1,1,1,1,1]
[1,8,9,10,11,6,7,4,5,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[11,12,1,6,7,8,9,4,5,2,3,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,6,7,8,9,4,5,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[1,6,9,10,7,8,11,4,5,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[1,6,7,8,9,10,11,4,5,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,1,4,5,6,7,2,3,8]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,1,4,5,6,7,2,3,8]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,8,9,4,5,6,7,2,3,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,8,9,4,5,6,7,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[1,8,9,10,11,4,5,6,7,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,4,7,8,5,6,9,2,3,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,4,7,8,5,6,9,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[1,4,9,10,7,8,5,6,11,2,3,12]=>[4,1,1,1,1,1,1,1,1]
[1,4,7,8,9,10,5,6,11,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,4,5,6,7,8,9,2,3,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,4,5,6,7,8,9,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,4,9,10,5,6,7,8,11,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,4,5,8,9,6,7,10,11,2,3,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,4,5,6,7,8,9,10,11,2,3,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,1,2,3,4,5,6]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,7,8,1,2,3,4,5,6]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,7,8,9,10,1,2,3,4,5,6]=>[3,1,1,1,1,1,1,1,1,1]
[7,10,11,8,9,12,1,2,3,4,5,6]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,9,10,1,6,7,2,3,4,5,8]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,1,6,7,2,3,4,5,8]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,8,9,6,7,2,3,4,5,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,8,9,6,7,2,3,4,5,12]=>[4,1,1,1,1,1,1,1,1]
[1,8,9,10,11,6,7,2,3,4,5,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,6,7,8,9,2,3,4,5,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,6,7,8,9,2,3,4,5,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,6,9,10,7,8,11,2,3,4,5,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,6,7,8,9,10,11,2,3,4,5,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,1,2,5,6,3,4,7,8]=>[4,1,1,1,1,1,1,1,1]
[9,10,11,12,1,2,5,6,3,4,7,8]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,8,9,2,5,6,3,4,7,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,8,9,2,5,6,3,4,7,12]=>[4,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,5,6,3,4,7,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,2,7,8,5,6,3,4,9,10]=>[4,1,1,1,1,1,1,1,1]
[1,10,11,2,7,8,5,6,3,4,9,12]=>[4,1,1,1,1,1,1,1,1]
[1,2,9,10,7,8,5,6,3,4,11,12]=>[4,1,1,1,1,1,1,1,1]
[1,2,7,8,9,10,5,6,3,4,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,1,2,5,6,7,8,3,4,9,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,2,5,6,7,8,3,4,9,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,9,10,5,6,7,8,3,4,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,5,8,9,6,7,10,3,4,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,5,6,7,8,9,10,3,4,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,1,2,3,4,5,6,7,8]=>[3,1,1,1,1,1,1,1,1,1]
[9,10,11,12,1,2,3,4,5,6,7,8]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,1,8,9,2,3,4,5,6,7,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,8,9,2,3,4,5,6,7,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,3,4,5,6,7,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,1,2,7,8,3,4,5,6,9,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,2,7,8,3,4,5,6,9,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,9,10,7,8,3,4,5,6,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,7,8,9,10,3,4,5,6,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,1,2,3,6,7,4,5,8,9,10]=>[3,1,1,1,1,1,1,1,1,1]
[1,10,11,2,3,6,7,4,5,8,9,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,9,10,3,6,7,4,5,8,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,3,8,9,6,7,4,5,10,11,12]=>[3,1,1,1,1,1,1,1,1,1]
[1,2,3,6,7,8,9,4,5,10,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,10,11,2,3,4,5,6,7,8,9,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,2,9,10,3,4,5,6,7,8,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,2,3,8,9,4,5,6,7,10,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,2,3,4,7,8,5,6,9,10,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[11,1,12,10,9,8,7,6,5,4,3,2]=>[10,2]
[2,12,11,10,9,8,7,6,5,4,1,3]=>[10,1,1]
[11,1,2,3,4,5,6,7,8,9,12,10]=>[2,2,1,1,1,1,1,1,1,1]
[2,12,1,3,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[12,2,1,4,3,6,5,8,7,10,9,11]=>[3,2,2,2,2,1]
[12,2,1,4,3,6,5,8,7,9,11,10]=>[3,2,2,2,2,1]
[12,2,1,4,3,6,5,7,9,10,8,11]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,6,5,7,9,8,11,10]=>[3,2,2,2,2,1]
[12,2,1,4,3,6,5,7,8,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,7,8,6,10,9,11]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,7,8,6,9,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,7,6,9,10,8,11]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[12,2,1,4,3,5,7,6,8,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,6,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,4,3,5,6,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,6,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,4,3,5,6,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,5,6,4,8,7,10,9,11]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,6,4,8,7,9,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,6,4,7,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,5,6,4,7,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,6,4,7,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,5,4,7,8,6,10,9,11]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,7,8,6,9,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,7,6,9,10,8,11]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[12,2,1,3,5,4,7,6,8,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,6,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,5,4,6,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,6,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,3,5,4,6,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,7,8,5,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,7,8,5,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,7,5,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,7,5,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,4,6,7,5,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,5,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,6,5,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,2,1,3,4,6,5,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,2,1,3,4,6,5,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,5,7,8,9,10,6,11]=>[3,2,1,1,1,1,1,1,1]
[12,2,1,3,4,5,7,8,9,6,11,10]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,5,7,8,6,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,5,7,6,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,2,1,3,4,5,6,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[12,1,3,4,2,6,5,8,7,10,9,11]=>[3,2,2,2,1,1,1]
[12,1,3,4,2,6,5,8,7,9,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,4,2,6,5,7,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,6,5,7,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,4,2,6,5,7,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,7,8,6,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,7,8,6,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,7,6,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,7,6,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,4,2,5,7,6,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,6,8,9,10,7,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,3,4,2,5,6,8,9,7,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,6,8,7,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,4,2,5,6,7,9,10,11,8]=>[3,2,1,1,1,1,1,1,1]
[12,1,3,2,5,6,4,8,7,10,9,11]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,6,4,8,7,9,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,6,4,7,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,5,6,4,7,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,6,4,7,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,5,4,7,8,6,10,9,11]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,7,8,6,9,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,7,6,9,10,8,11]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[12,1,3,2,5,4,7,6,8,10,11,9]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,6,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,5,4,6,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,6,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,1,3,2,5,4,6,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,7,8,5,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,7,8,5,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,7,5,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,7,5,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,4,6,7,5,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,5,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,6,5,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,1,3,2,4,6,5,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,1,3,2,4,6,5,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,5,7,8,9,10,6,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,3,2,4,5,7,8,9,6,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,5,7,8,6,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,5,7,6,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,3,2,4,5,6,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,5,6,3,8,7,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,6,3,8,7,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,6,3,7,9,10,8,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,5,6,3,7,9,8,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,6,3,7,8,10,11,9]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,5,3,7,8,6,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,7,8,6,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,7,6,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,7,6,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,2,4,5,3,7,6,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,6,8,9,10,7,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,5,3,6,8,9,7,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,6,8,7,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,5,3,6,7,9,10,11,8]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,3,6,7,8,5,10,9,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,6,7,8,5,9,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,6,7,5,9,10,8,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,6,7,5,9,8,11,10]=>[3,2,2,2,1,1,1]
[12,1,2,4,3,6,7,5,8,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,6,5,8,9,10,7,11]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,6,5,8,9,7,11,10]=>[3,2,2,2,1,1,1]
[12,1,2,4,3,6,5,8,7,10,11,9]=>[3,2,2,2,1,1,1]
[12,1,2,4,3,6,5,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,5,7,8,9,10,6,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,4,3,5,7,8,9,6,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,5,7,8,6,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,5,7,6,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,2,4,3,5,6,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,7,8,4,10,9,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,7,8,4,9,11,10]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,7,4,9,10,8,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,7,4,9,8,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,6,7,4,8,10,11,9]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,4,8,9,10,7,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,6,4,8,9,7,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,6,4,8,7,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,6,4,7,9,10,11,8]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,4,7,8,9,10,6,11]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,5,4,7,8,9,6,11,10]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,4,7,8,6,10,11,9]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,4,7,6,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[12,1,2,3,5,4,6,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,4,6,7,8,9,10,5,11]=>[3,1,1,1,1,1,1,1,1,1]
[12,1,2,3,4,6,7,8,9,5,11,10]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,4,6,7,8,5,10,11,9]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,4,6,7,5,9,10,11,8]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,4,6,5,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[12,1,2,3,4,5,7,8,9,10,11,6]=>[3,1,1,1,1,1,1,1,1,1]
[12,11,2,4,6,8,10,1,3,5,7,9]=>[4,1,1,1,1,1,1,1,1]
[10,9,2,4,6,8,12,1,3,5,7,11]=>[4,1,1,1,1,1,1,1,1]
[2,12,9,11,4,6,8,10,1,3,5,7]=>[4,1,1,1,1,1,1,1,1]
[12,11,10,9,2,4,6,8,1,3,5,7]=>[6,1,1,1,1,1,1]
[8,7,2,4,6,10,12,1,3,5,9,11]=>[4,1,1,1,1,1,1,1,1]
[8,12,7,11,2,4,6,10,1,3,5,9]=>[4,1,1,1,1,1,1,1,1]
[2,10,7,9,4,6,8,12,1,3,5,11]=>[4,1,1,1,1,1,1,1,1]
[2,4,12,7,9,11,6,8,10,1,3,5]=>[4,1,1,1,1,1,1,1,1]
[12,11,2,10,7,9,4,6,8,1,3,5]=>[6,1,1,1,1,1,1]
[10,9,8,7,2,4,6,12,1,3,5,11]=>[6,1,1,1,1,1,1]
[12,9,2,8,7,11,4,6,10,1,3,5]=>[6,1,1,1,1,1,1]
[8,12,7,11,10,9,2,4,6,1,3,5]=>[6,1,1,1,1,1,1]
[12,11,10,9,8,7,2,4,6,1,3,5]=>[8,1,1,1,1]
[6,5,2,4,8,10,12,1,3,7,9,11]=>[4,1,1,1,1,1,1,1,1]
[6,12,5,11,2,4,8,10,1,3,7,9]=>[4,1,1,1,1,1,1,1,1]
[6,10,5,9,2,4,8,12,1,3,7,11]=>[4,1,1,1,1,1,1,1,1]
[6,5,12,9,11,2,4,8,10,1,3,7]=>[4,2,1,1,1,1,1,1]
[12,11,6,10,5,9,2,4,8,1,3,7]=>[6,1,1,1,1,1,1]
[2,8,5,7,4,6,10,12,1,3,9,11]=>[4,1,1,1,1,1,1,1,1]
[2,8,12,5,7,11,4,6,10,1,3,9]=>[4,1,1,1,1,1,1,1,1]
[10,5,2,4,7,9,6,8,12,1,3,11]=>[4,2,1,1,1,1,1,1]
[12,5,7,2,4,6,9,11,8,10,1,3]=>[4,2,1,1,1,1,1,1]
[12,5,11,10,2,4,7,9,6,8,1,3]=>[6,1,1,1,1,1,1]
[10,9,2,8,5,7,4,6,12,1,3,11]=>[6,1,1,1,1,1,1]
[12,5,9,8,2,4,7,11,6,10,1,3]=>[6,1,1,1,1,1,1]
[2,12,5,11,8,10,7,9,4,6,1,3]=>[6,1,1,1,1,1,1]
[12,11,10,9,2,8,5,7,4,6,1,3]=>[8,1,1,1,1]
[8,7,6,5,2,4,10,12,1,3,9,11]=>[6,1,1,1,1,1,1]
[8,7,6,12,5,11,2,4,10,1,3,9]=>[6,1,1,1,1,1,1]
[10,7,2,6,5,9,4,8,12,1,3,11]=>[6,1,1,1,1,1,1]
[7,6,12,5,2,4,9,11,8,10,1,3]=>[5,2,1,1,1,1,1]
[2,12,7,11,6,10,5,9,4,8,1,3]=>[6,1,1,1,1,1,1]
[6,10,5,9,8,7,2,4,12,1,3,11]=>[6,1,1,1,1,1,1]
[2,12,6,9,5,8,7,11,4,10,1,3]=>[6,1,1,1,1,1,1]
[6,8,12,5,7,11,10,9,2,4,1,3]=>[6,1,1,1,1,1,1]
[12,11,6,10,5,9,8,7,2,4,1,3]=>[8,1,1,1,1]
[10,9,8,7,6,5,2,4,12,1,3,11]=>[8,1,1,1,1]
[12,9,8,7,2,6,5,11,4,10,1,3]=>[8,1,1,1,1]
[8,7,6,12,5,11,10,9,2,4,1,3]=>[6,3,1,1,1]
[7,12,6,11,10,9,8,5,2,4,1,3]=>[8,1,1,1,1]
[12,11,10,9,8,7,6,5,2,4,1,3]=>[10,1,1]
[4,3,2,6,8,10,12,1,5,7,9,11]=>[4,1,1,1,1,1,1,1,1]
[4,12,3,11,2,6,8,10,1,5,7,9]=>[4,1,1,1,1,1,1,1,1]
[4,10,3,9,2,6,8,12,1,5,7,11]=>[4,1,1,1,1,1,1,1,1]
[4,3,12,9,11,2,6,8,10,1,5,7]=>[4,2,1,1,1,1,1,1]
[12,11,4,10,3,9,2,6,8,1,5,7]=>[6,1,1,1,1,1,1]
[4,8,3,7,2,6,10,12,1,5,9,11]=>[4,1,1,1,1,1,1,1,1]
[4,8,12,3,7,11,2,6,10,1,5,9]=>[4,1,1,1,1,1,1,1,1]
[4,3,10,7,9,2,6,8,12,1,5,11]=>[4,2,1,1,1,1,1,1]
[4,3,7,9,12,11,2,6,8,10,1,5]=>[4,2,1,1,1,1,1,1]
[12,4,11,3,10,7,9,2,6,8,1,5]=>[6,1,1,1,1,1,1]
[10,9,4,8,3,7,2,6,12,1,5,11]=>[6,1,1,1,1,1,1]
[12,4,9,3,8,7,11,2,6,10,1,5]=>[6,1,1,1,1,1,1]
[4,8,12,11,10,3,7,9,2,6,1,5]=>[6,1,1,1,1,1,1]
[12,11,10,9,4,8,3,7,2,6,1,5]=>[8,1,1,1,1]
[3,6,2,5,4,8,10,12,1,7,9,11]=>[4,1,1,1,1,1,1,1,1]
[3,6,12,2,5,11,4,8,10,1,7,9]=>[4,1,1,1,1,1,1,1,1]
[3,6,10,2,5,9,4,8,12,1,7,11]=>[4,1,1,1,1,1,1,1,1]
[3,12,6,2,5,9,11,4,8,10,1,7]=>[5,1,1,1,1,1,1,1]
[12,11,3,6,10,2,5,9,4,8,1,7]=>[6,1,1,1,1,1,1]
[3,5,8,2,4,7,6,10,12,1,9,11]=>[4,1,1,1,1,1,1,1,1]
[3,5,8,12,2,4,7,11,6,10,1,9]=>[4,1,1,1,1,1,1,1,1]
[3,5,7,10,2,4,6,9,8,12,1,11]=>[4,1,1,1,1,1,1,1,1]
[3,5,7,9,12,2,4,6,8,11,10,1]=>[4,1,1,1,1,1,1,1,1]
[12,11,3,5,7,10,2,4,6,9,8,1]=>[6,1,1,1,1,1,1]
[10,9,3,5,8,2,4,7,6,12,1,11]=>[6,1,1,1,1,1,1]
[9,8,3,5,7,12,2,4,6,11,10,1]=>[5,2,1,1,1,1,1]
[3,5,12,11,8,10,2,4,7,9,6,1]=>[6,1,1,1,1,1,1]
[12,11,10,9,3,5,8,2,4,7,6,1]=>[8,1,1,1,1]
[8,7,3,6,2,5,4,10,12,1,9,11]=>[6,1,1,1,1,1,1]
[8,7,3,6,12,2,5,11,4,10,1,9]=>[6,1,1,1,1,1,1]
[7,6,3,5,10,2,4,9,8,12,1,11]=>[5,2,1,1,1,1,1]
[7,6,3,5,9,12,2,4,8,11,10,1]=>[5,2,1,1,1,1,1]
[7,12,6,11,3,5,10,2,4,9,8,1]=>[6,1,1,1,1,1,1]
[3,6,10,9,8,2,5,7,4,12,1,11]=>[6,1,1,1,1,1,1]
[3,9,6,8,5,7,12,2,4,11,10,1]=>[5,2,1,1,1,1,1]
[3,2,12,6,8,11,10,5,7,9,4,1]=>[6,2,1,1,1,1]
[12,11,3,6,10,9,8,2,5,7,4,1]=>[8,1,1,1,1]
[10,9,8,7,3,6,2,5,4,12,1,11]=>[8,1,1,1,1]
[9,8,7,6,3,5,12,2,4,11,10,1]=>[7,2,1,1,1]
[8,7,3,6,12,11,10,2,5,9,4,1]=>[6,3,1,1,1]
[3,12,7,11,10,9,6,8,2,5,4,1]=>[8,1,1,1,1]
[12,11,10,9,8,7,3,6,2,5,4,1]=>[10,1,1]
[6,5,4,3,2,8,10,12,1,7,9,11]=>[6,1,1,1,1,1,1]
[6,5,4,12,3,11,2,8,10,1,7,9]=>[6,1,1,1,1,1,1]
[6,5,4,10,3,9,2,8,12,1,7,11]=>[6,1,1,1,1,1,1]
[6,12,5,4,3,9,11,2,8,10,1,7]=>[6,1,1,1,1,1,1]
[5,4,3,8,2,7,6,10,12,1,9,11]=>[5,2,1,1,1,1,1]
[5,4,3,8,12,2,7,11,6,10,1,9]=>[5,2,1,1,1,1,1]
[5,4,3,7,10,2,6,9,8,12,1,11]=>[5,2,1,1,1,1,1]
[5,4,3,7,9,12,2,6,8,11,10,1]=>[5,2,1,1,1,1,1]
[5,12,4,11,3,7,10,2,6,9,8,1]=>[6,1,1,1,1,1,1]
[5,10,4,9,3,8,2,7,6,12,1,11]=>[6,1,1,1,1,1,1]
[5,9,4,8,3,7,12,2,6,11,10,1]=>[5,2,1,1,1,1,1]
[12,11,5,4,3,8,10,2,7,9,6,1]=>[7,2,1,1,1]
[12,11,5,10,4,9,3,8,2,7,6,1]=>[8,1,1,1,1]
[4,8,3,7,6,5,2,10,12,1,9,11]=>[6,1,1,1,1,1,1]
[4,8,3,7,6,12,5,11,2,10,1,9]=>[6,1,1,1,1,1,1]
[4,7,3,6,5,10,2,9,8,12,1,11]=>[5,2,1,1,1,1,1]
[4,7,3,6,5,9,12,2,8,11,10,1]=>[5,2,1,1,1,1,1]
[4,7,12,3,6,11,5,10,2,9,8,1]=>[6,1,1,1,1,1,1]
[4,6,10,3,5,9,8,7,2,12,1,11]=>[6,1,1,1,1,1,1]
[4,6,9,3,5,8,7,12,2,11,10,1]=>[5,2,1,1,1,1,1]
[4,6,8,12,3,5,7,11,10,9,2,1]=>[6,1,1,1,1,1,1]
[12,11,4,6,10,3,5,9,8,7,2,1]=>[8,1,1,1,1]
[10,9,4,8,3,7,6,5,2,12,1,11]=>[8,1,1,1,1]
[9,8,4,7,3,6,5,12,2,11,10,1]=>[7,2,1,1,1]
[8,7,4,6,12,3,5,11,10,9,2,1]=>[6,3,1,1,1]
[4,7,12,11,10,3,6,9,8,5,2,1]=>[8,1,1,1,1]
[12,11,10,9,4,8,3,7,6,5,2,1]=>[10,1,1]
[8,7,6,5,4,3,2,10,12,1,9,11]=>[8,1,1,1,1]
[8,7,6,5,4,12,3,11,2,10,1,9]=>[8,1,1,1,1]
[7,6,5,4,3,10,2,9,8,12,1,11]=>[7,2,1,1,1]
[7,6,5,4,3,9,12,2,8,11,10,1]=>[7,2,1,1,1]
[7,6,5,12,4,11,3,10,2,9,8,1]=>[7,2,1,1,1]
[6,5,4,10,3,9,8,7,2,12,1,11]=>[6,3,1,1,1]
[6,5,4,9,3,8,7,12,2,11,10,1]=>[6,2,2,1,1]
[6,5,4,8,12,3,7,11,10,9,2,1]=>[6,3,1,1,1]
[6,12,5,11,4,10,3,9,8,7,2,1]=>[8,1,1,1,1]
[5,10,4,9,8,7,6,3,2,12,1,11]=>[8,1,1,1,1]
[5,9,4,8,7,6,3,12,2,11,10,1]=>[7,2,1,1,1]
[5,8,4,7,6,12,3,11,10,9,2,1]=>[6,3,1,1,1]
[5,7,12,4,6,11,10,9,8,3,2,1]=>[8,1,1,1,1]
[12,11,5,10,4,9,8,7,6,3,2,1]=>[10,1,1]
[10,9,8,7,6,5,4,3,2,12,1,11]=>[10,1,1]
[9,8,7,6,5,4,3,12,2,11,10,1]=>[9,2,1]
[8,7,6,5,4,12,3,11,10,9,2,1]=>[8,3,1]
[7,6,5,12,4,11,10,9,8,3,2,1]=>[8,3,1]
[6,12,5,11,10,9,8,7,4,3,2,1]=>[10,1,1]
[12,10,9,8,7,6,5,4,3,2,1,11]=>[11,1]
[11,3,4,5,6,7,8,9,10,1,12,2]=>[3,2,1,1,1,1,1,1,1]
[2,12,4,5,6,7,8,9,10,11,1,3]=>[3,1,1,1,1,1,1,1,1,1]
[3,1,2,4,5,6,7,8,9,10,11,12]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,11,12,9,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,9,10,7,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,9,11,7,12,8,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,10,11,12,7,8,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,7,8,5,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,7,8,5,6,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,7,9,5,10,6,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,7,9,5,11,6,12,8,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,7,10,5,11,12,6,8,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,8,9,10,5,6,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,8,9,11,5,6,12,7,10]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,8,10,11,5,12,6,7,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,9,10,11,12,5,6,7,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,5,6,3,4,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,5,6,3,4,8,7,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,5,6,3,4,9,11,7,12,8,10]=>[2,2,2,2,1,1,1,1]
[2,1,5,6,3,4,10,11,12,7,8,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,5,7,3,8,4,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,5,7,3,8,4,6,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[2,1,5,7,3,9,4,10,6,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,5,7,3,9,4,11,6,12,8,10]=>[2,2,2,2,2,1,1]
[2,1,5,7,3,10,4,11,12,6,8,9]=>[2,2,2,2,1,1,1,1]
[2,1,5,8,3,9,10,4,6,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,5,8,3,9,11,4,6,12,7,10]=>[2,2,2,2,1,1,1,1]
[2,1,5,8,3,10,11,4,12,6,7,9]=>[2,2,2,2,1,1,1,1]
[2,1,5,9,3,10,11,12,4,6,7,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,6,7,8,3,4,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,6,7,8,3,4,5,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[2,1,6,7,9,3,4,10,5,8,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,6,7,9,3,4,11,5,12,8,10]=>[2,2,2,2,1,1,1,1]
[2,1,6,7,10,3,4,11,12,5,8,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,6,8,9,3,10,4,5,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,6,8,9,3,11,4,5,12,7,10]=>[2,2,2,2,1,1,1,1]
[2,1,6,8,10,3,11,4,12,5,7,9]=>[2,2,2,2,1,1,1,1]
[2,1,6,9,10,3,11,12,4,5,7,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,7,8,9,10,3,4,5,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,7,8,9,11,3,4,5,12,6,10]=>[2,2,2,1,1,1,1,1,1]
[2,1,7,8,10,11,3,4,12,5,6,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,7,9,10,11,3,12,4,5,6,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,8,9,10,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[3,4,1,2,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[3,4,1,2,6,5,8,7,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,6,5,9,10,7,8,12,11]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,6,5,9,11,7,12,8,10]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,6,5,10,11,12,7,8,9]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,7,8,5,6,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,7,8,5,6,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,7,9,5,10,6,8,12,11]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,7,9,5,11,6,12,8,10]=>[2,2,2,2,1,1,1,1]
[3,4,1,2,7,10,5,11,12,6,8,9]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,8,9,10,5,6,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,8,9,11,5,6,12,7,10]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,8,10,11,5,12,6,7,9]=>[2,2,2,1,1,1,1,1,1]
[3,4,1,2,9,10,11,12,5,6,7,8]=>[2,2,1,1,1,1,1,1,1,1]
[3,5,1,6,2,4,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[3,5,1,6,2,4,8,7,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[3,5,1,6,2,4,9,10,7,8,12,11]=>[2,2,2,2,1,1,1,1]
[3,5,1,6,2,4,9,11,7,12,8,10]=>[2,2,2,2,1,1,1,1]
[3,5,1,6,2,4,10,11,12,7,8,9]=>[2,2,2,1,1,1,1,1,1]
[3,5,1,7,2,8,4,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[3,5,1,7,2,8,4,6,11,12,9,10]=>[2,2,2,2,1,1,1,1]
[3,5,1,7,2,9,4,10,6,8,12,11]=>[2,2,2,2,2,1,1]
[3,5,1,7,2,9,4,11,6,12,8,10]=>[2,2,2,2,2,1,1]
[3,5,1,7,2,10,4,11,12,6,8,9]=>[2,2,2,2,1,1,1,1]
[3,5,1,8,2,9,10,4,6,7,12,11]=>[2,2,2,2,1,1,1,1]
[3,5,1,8,2,9,11,4,6,12,7,10]=>[2,2,2,2,1,1,1,1]
[3,5,1,8,2,10,11,4,12,6,7,9]=>[2,2,2,2,1,1,1,1]
[3,5,1,9,2,10,11,12,4,6,7,8]=>[2,2,2,1,1,1,1,1,1]
[3,6,1,7,8,2,4,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[3,6,1,7,8,2,4,5,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[3,6,1,7,9,2,4,10,5,8,12,11]=>[2,2,2,2,1,1,1,1]
[3,6,1,7,9,2,4,11,5,12,8,10]=>[2,2,2,2,1,1,1,1]
[3,6,1,7,10,2,4,11,12,5,8,9]=>[2,2,2,1,1,1,1,1,1]
[3,6,1,8,9,2,10,4,5,7,12,11]=>[2,2,2,2,1,1,1,1]
[3,6,1,8,9,2,11,4,5,12,7,10]=>[2,2,2,2,1,1,1,1]
[3,6,1,8,10,2,11,4,12,5,7,9]=>[2,2,2,2,1,1,1,1]
[3,6,1,9,10,2,11,12,4,5,7,8]=>[2,2,2,1,1,1,1,1,1]
[3,7,1,8,9,10,2,4,5,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[3,7,1,8,9,11,2,4,5,12,6,10]=>[2,2,2,1,1,1,1,1,1]
[3,7,1,8,10,11,2,4,12,5,6,9]=>[2,2,2,1,1,1,1,1,1]
[3,7,1,9,10,11,2,12,4,5,6,8]=>[2,2,2,1,1,1,1,1,1]
[3,8,1,9,10,11,12,2,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[4,5,6,1,2,3,8,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[4,5,6,1,2,3,8,7,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[4,5,6,1,2,3,9,10,7,8,12,11]=>[2,2,2,1,1,1,1,1,1]
[4,5,6,1,2,3,9,11,7,12,8,10]=>[2,2,2,1,1,1,1,1,1]
[4,5,6,1,2,3,10,11,12,7,8,9]=>[2,2,1,1,1,1,1,1,1,1]
[4,5,7,1,2,8,3,6,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[4,5,7,1,2,8,3,6,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[4,5,7,1,2,9,3,10,6,8,12,11]=>[2,2,2,2,1,1,1,1]
[4,5,7,1,2,9,3,11,6,12,8,10]=>[2,2,2,2,1,1,1,1]
[4,5,7,1,2,10,3,11,12,6,8,9]=>[2,2,2,1,1,1,1,1,1]
[4,5,8,1,2,9,10,3,6,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[4,5,8,1,2,9,11,3,6,12,7,10]=>[2,2,2,1,1,1,1,1,1]
[4,5,8,1,2,10,11,3,12,6,7,9]=>[2,2,2,1,1,1,1,1,1]
[4,5,9,1,2,10,11,12,3,6,7,8]=>[2,2,1,1,1,1,1,1,1,1]
[4,6,7,1,8,2,3,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[4,6,7,1,8,2,3,5,11,12,9,10]=>[2,2,2,1,1,1,1,1,1]
[4,6,7,1,9,2,3,10,5,8,12,11]=>[2,2,2,2,1,1,1,1]
[4,6,7,1,9,2,3,11,5,12,8,10]=>[2,2,2,2,1,1,1,1]
[4,6,7,1,10,2,3,11,12,5,8,9]=>[2,2,2,1,1,1,1,1,1]
[4,6,8,1,9,2,10,3,5,7,12,11]=>[2,2,2,2,1,1,1,1]
[4,6,8,1,9,2,11,3,5,12,7,10]=>[2,2,2,2,1,1,1,1]
[4,6,8,1,10,2,11,3,12,5,7,9]=>[2,2,2,2,1,1,1,1]
[4,6,9,1,10,2,11,12,3,5,7,8]=>[2,2,2,1,1,1,1,1,1]
[4,7,8,1,9,10,2,3,5,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[4,7,8,1,9,11,2,3,5,12,6,10]=>[2,2,2,1,1,1,1,1,1]
[4,7,8,1,10,11,2,3,12,5,6,9]=>[2,2,2,1,1,1,1,1,1]
[4,7,9,1,10,11,2,12,3,5,6,8]=>[2,2,2,1,1,1,1,1,1]
[4,8,9,1,10,11,12,2,3,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[5,6,7,8,1,2,3,4,10,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[5,6,7,8,1,2,3,4,11,12,9,10]=>[2,2,1,1,1,1,1,1,1,1]
[5,6,7,9,1,2,3,10,4,8,12,11]=>[2,2,2,1,1,1,1,1,1]
[5,6,7,9,1,2,3,11,4,12,8,10]=>[2,2,2,1,1,1,1,1,1]
[5,6,7,10,1,2,3,11,12,4,8,9]=>[2,2,1,1,1,1,1,1,1,1]
[5,6,8,9,1,2,10,3,4,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[5,6,8,9,1,2,11,3,4,12,7,10]=>[2,2,2,1,1,1,1,1,1]
[5,6,8,10,1,2,11,3,12,4,7,9]=>[2,2,2,1,1,1,1,1,1]
[5,6,9,10,1,2,11,12,3,4,7,8]=>[2,2,1,1,1,1,1,1,1,1]
[5,7,8,9,1,10,2,3,4,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[5,7,8,9,1,11,2,3,4,12,6,10]=>[2,2,2,1,1,1,1,1,1]
[5,7,8,10,1,11,2,3,12,4,6,9]=>[2,2,2,1,1,1,1,1,1]
[5,7,9,10,1,11,2,12,3,4,6,8]=>[2,2,2,1,1,1,1,1,1]
[5,8,9,10,1,11,12,2,3,4,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[6,7,8,9,10,1,2,3,4,5,12,11]=>[2,2,1,1,1,1,1,1,1,1]
[6,7,8,9,11,1,2,3,4,12,5,10]=>[2,2,1,1,1,1,1,1,1,1]
[6,7,8,10,11,1,2,3,12,4,5,9]=>[2,2,1,1,1,1,1,1,1,1]
[6,7,9,10,11,1,2,12,3,4,5,8]=>[2,2,1,1,1,1,1,1,1,1]
[6,8,9,10,11,1,12,2,3,4,5,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,12,10,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[12,1,3,4,5,6,7,8,9,10,11,2]=>[3,1,1,1,1,1,1,1,1,1]
[3,2,5,4,7,6,9,8,11,10,1,12]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,9,8,1,12,10,11]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,11,10,8,9,1,12]=>[4,2,2,2,1,1]
[3,2,5,4,7,6,1,10,8,12,9,11]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,1,12,11,8,9,10]=>[3,3,2,2,1,1]
[3,2,5,4,9,8,6,7,11,10,1,12]=>[4,2,2,2,1,1]
[3,2,5,4,9,8,6,7,1,12,10,11]=>[4,2,2,2,1,1]
[3,2,5,4,11,8,6,10,7,9,1,12]=>[4,2,2,2,1,1]
[3,2,5,4,1,8,6,10,7,12,9,11]=>[3,2,2,2,2,1]
[3,2,5,4,1,8,6,12,11,7,9,10]=>[3,3,2,2,1,1]
[3,2,5,4,11,10,9,6,7,8,1,12]=>[5,2,2,1,1,1]
[3,2,5,4,1,10,9,6,7,12,8,11]=>[3,3,2,2,1,1]
[3,2,5,4,1,12,9,6,11,7,8,10]=>[3,3,2,2,1,1]
[3,2,5,4,1,12,11,10,6,7,8,9]=>[4,3,2,1,1,1]
[3,2,7,6,4,5,9,8,11,10,1,12]=>[4,2,2,2,1,1]
[3,2,7,6,4,5,9,8,1,12,10,11]=>[4,2,2,2,1,1]
[3,2,7,6,4,5,11,10,8,9,1,12]=>[4,3,2,1,1,1]
[3,2,7,6,4,5,1,10,8,12,9,11]=>[4,2,2,2,1,1]
[3,2,7,6,4,5,1,12,11,8,9,10]=>[4,3,2,1,1,1]
[3,2,9,6,4,8,5,7,11,10,1,12]=>[4,2,2,2,1,1]
[3,2,9,6,4,8,5,7,1,12,10,11]=>[4,2,2,2,1,1]
[3,2,11,6,4,8,5,10,7,9,1,12]=>[4,2,2,2,1,1]
[3,2,1,6,4,8,5,10,7,12,9,11]=>[3,2,2,2,2,1]
[3,2,1,6,4,8,5,12,11,7,9,10]=>[3,3,2,2,1,1]
[3,2,11,6,4,10,9,5,7,8,1,12]=>[5,2,2,1,1,1]
[3,2,1,6,4,10,9,5,7,12,8,11]=>[3,3,2,2,1,1]
[3,2,1,6,4,12,9,5,11,7,8,10]=>[3,3,2,2,1,1]
[3,2,1,6,4,12,11,10,5,7,8,9]=>[4,3,2,1,1,1]
[3,2,9,8,7,4,5,6,11,10,1,12]=>[5,2,2,1,1,1]
[3,2,9,8,7,4,5,6,1,12,10,11]=>[5,2,2,1,1,1]
[3,2,11,8,7,4,5,10,6,9,1,12]=>[5,2,2,1,1,1]
[3,2,1,8,7,4,5,10,6,12,9,11]=>[3,3,2,2,1,1]
[3,2,1,8,7,4,5,12,11,6,9,10]=>[3,3,3,1,1,1]
[3,2,11,10,7,4,9,5,6,8,1,12]=>[5,2,2,1,1,1]
[3,2,1,10,7,4,9,5,6,12,8,11]=>[3,3,2,2,1,1]
[3,2,1,12,7,4,9,5,11,6,8,10]=>[3,3,2,2,1,1]
[3,2,1,12,7,4,11,10,5,6,8,9]=>[4,3,2,1,1,1]
[3,2,11,10,9,8,4,5,6,7,1,12]=>[6,2,1,1,1,1]
[3,2,1,10,9,8,4,5,6,12,7,11]=>[4,3,2,1,1,1]
[3,2,1,12,9,8,4,5,11,6,7,10]=>[4,3,2,1,1,1]
[3,2,1,12,11,8,4,10,5,6,7,9]=>[4,3,2,1,1,1]
[3,2,1,12,11,10,9,4,5,6,7,8]=>[5,3,1,1,1,1]
[5,4,2,3,7,6,9,8,11,10,1,12]=>[4,2,2,2,1,1]
[5,4,2,3,7,6,9,8,1,12,10,11]=>[4,2,2,2,1,1]
[5,4,2,3,7,6,11,10,8,9,1,12]=>[4,3,2,1,1,1]
[5,4,2,3,7,6,1,10,8,12,9,11]=>[4,2,2,2,1,1]
[5,4,2,3,7,6,1,12,11,8,9,10]=>[4,3,2,1,1,1]
[5,4,2,3,9,8,6,7,11,10,1,12]=>[4,3,2,1,1,1]
[5,4,2,3,9,8,6,7,1,12,10,11]=>[4,3,2,1,1,1]
[5,4,2,3,11,8,6,10,7,9,1,12]=>[4,3,2,1,1,1]
[5,4,2,3,1,8,6,10,7,12,9,11]=>[4,2,2,2,1,1]
[5,4,2,3,1,8,6,12,11,7,9,10]=>[4,3,2,1,1,1]
[5,4,2,3,11,10,9,6,7,8,1,12]=>[5,3,1,1,1,1]
[5,4,2,3,1,10,9,6,7,12,8,11]=>[4,3,2,1,1,1]
[5,4,2,3,1,12,9,6,11,7,8,10]=>[4,3,2,1,1,1]
[5,4,2,3,1,12,11,10,6,7,8,9]=>[4,4,1,1,1,1]
[7,4,2,6,3,5,9,8,11,10,1,12]=>[4,2,2,2,1,1]
[7,4,2,6,3,5,9,8,1,12,10,11]=>[4,2,2,2,1,1]
[7,4,2,6,3,5,11,10,8,9,1,12]=>[4,3,2,1,1,1]
[7,4,2,6,3,5,1,10,8,12,9,11]=>[4,2,2,2,1,1]
[7,4,2,6,3,5,1,12,11,8,9,10]=>[4,3,2,1,1,1]
[9,4,2,6,3,8,5,7,11,10,1,12]=>[4,2,2,2,1,1]
[9,4,2,6,3,8,5,7,1,12,10,11]=>[4,2,2,2,1,1]
[11,4,2,6,3,8,5,10,7,9,1,12]=>[4,2,2,2,1,1]
[1,4,2,6,3,8,5,10,7,12,9,11]=>[2,2,2,2,2,1,1]
[1,4,2,6,3,8,5,12,11,7,9,10]=>[3,2,2,2,1,1,1]
[11,4,2,6,3,10,9,5,7,8,1,12]=>[5,2,2,1,1,1]
[1,4,2,6,3,10,9,5,7,12,8,11]=>[3,2,2,2,1,1,1]
[1,4,2,6,3,12,9,5,11,7,8,10]=>[3,2,2,2,1,1,1]
[1,4,2,6,3,12,11,10,5,7,8,9]=>[4,2,2,1,1,1,1]
[9,4,2,8,7,3,5,6,11,10,1,12]=>[5,2,2,1,1,1]
[9,4,2,8,7,3,5,6,1,12,10,11]=>[5,2,2,1,1,1]
[11,4,2,8,7,3,5,10,6,9,1,12]=>[5,2,2,1,1,1]
[1,4,2,8,7,3,5,10,6,12,9,11]=>[3,2,2,2,1,1,1]
[1,4,2,8,7,3,5,12,11,6,9,10]=>[3,3,2,1,1,1,1]
[11,4,2,10,7,3,9,5,6,8,1,12]=>[5,2,2,1,1,1]
[1,4,2,10,7,3,9,5,6,12,8,11]=>[3,2,2,2,1,1,1]
[1,4,2,12,7,3,9,5,11,6,8,10]=>[3,2,2,2,1,1,1]
[1,4,2,12,7,3,11,10,5,6,8,9]=>[4,2,2,1,1,1,1]
[11,4,2,10,9,8,3,5,6,7,1,12]=>[6,2,1,1,1,1]
[1,4,2,10,9,8,3,5,6,12,7,11]=>[4,2,2,1,1,1,1]
[1,4,2,12,9,8,3,5,11,6,7,10]=>[4,2,2,1,1,1,1]
[1,4,2,12,11,8,3,10,5,6,7,9]=>[4,2,2,1,1,1,1]
[1,4,2,12,11,10,9,3,5,6,7,8]=>[5,2,1,1,1,1,1]
[7,6,5,2,3,4,9,8,11,10,1,12]=>[5,2,2,1,1,1]
[7,6,5,2,3,4,9,8,1,12,10,11]=>[5,2,2,1,1,1]
[7,6,5,2,3,4,11,10,8,9,1,12]=>[5,3,1,1,1,1]
[7,6,5,2,3,4,1,10,8,12,9,11]=>[5,2,2,1,1,1]
[7,6,5,2,3,4,1,12,11,8,9,10]=>[5,3,1,1,1,1]
[9,6,5,2,3,8,4,7,11,10,1,12]=>[5,2,2,1,1,1]
[9,6,5,2,3,8,4,7,1,12,10,11]=>[5,2,2,1,1,1]
[11,6,5,2,3,8,4,10,7,9,1,12]=>[5,2,2,1,1,1]
[1,6,5,2,3,8,4,10,7,12,9,11]=>[3,2,2,2,1,1,1]
[1,6,5,2,3,8,4,12,11,7,9,10]=>[3,3,2,1,1,1,1]
[11,6,5,2,3,10,9,4,7,8,1,12]=>[5,3,1,1,1,1]
[1,6,5,2,3,10,9,4,7,12,8,11]=>[3,3,2,1,1,1,1]
[1,6,5,2,3,12,9,4,11,7,8,10]=>[3,3,2,1,1,1,1]
[1,6,5,2,3,12,11,10,4,7,8,9]=>[4,3,1,1,1,1,1]
[9,8,5,2,7,3,4,6,11,10,1,12]=>[5,2,2,1,1,1]
[9,8,5,2,7,3,4,6,1,12,10,11]=>[5,2,2,1,1,1]
[11,8,5,2,7,3,4,10,6,9,1,12]=>[5,2,2,1,1,1]
[1,8,5,2,7,3,4,10,6,12,9,11]=>[3,2,2,2,1,1,1]
[1,8,5,2,7,3,4,12,11,6,9,10]=>[3,3,2,1,1,1,1]
[11,10,5,2,7,3,9,4,6,8,1,12]=>[5,2,2,1,1,1]
[1,10,5,2,7,3,9,4,6,12,8,11]=>[3,2,2,2,1,1,1]
[1,12,5,2,7,3,9,4,11,6,8,10]=>[3,2,2,2,1,1,1]
[1,12,5,2,7,3,11,10,4,6,8,9]=>[4,2,2,1,1,1,1]
[11,10,5,2,9,8,3,4,6,7,1,12]=>[6,2,1,1,1,1]
[1,10,5,2,9,8,3,4,6,12,7,11]=>[4,2,2,1,1,1,1]
[1,12,5,2,9,8,3,4,11,6,7,10]=>[4,2,2,1,1,1,1]
[1,12,5,2,11,8,3,10,4,6,7,9]=>[4,2,2,1,1,1,1]
[1,12,5,2,11,10,9,3,4,6,7,8]=>[5,2,1,1,1,1,1]
[9,8,7,6,2,3,4,5,11,10,1,12]=>[6,2,1,1,1,1]
[9,8,7,6,2,3,4,5,1,12,10,11]=>[6,2,1,1,1,1]
[11,8,7,6,2,3,4,10,5,9,1,12]=>[6,2,1,1,1,1]
[1,8,7,6,2,3,4,10,5,12,9,11]=>[4,2,2,1,1,1,1]
[1,8,7,6,2,3,4,12,11,5,9,10]=>[4,3,1,1,1,1,1]
[11,10,7,6,2,3,9,4,5,8,1,12]=>[6,2,1,1,1,1]
[1,10,7,6,2,3,9,4,5,12,8,11]=>[4,2,2,1,1,1,1]
[1,12,7,6,2,3,9,4,11,5,8,10]=>[4,2,2,1,1,1,1]
[1,12,7,6,2,3,11,10,4,5,8,9]=>[4,3,1,1,1,1,1]
[11,10,9,6,2,8,3,4,5,7,1,12]=>[6,2,1,1,1,1]
[1,10,9,6,2,8,3,4,5,12,7,11]=>[4,2,2,1,1,1,1]
[1,12,9,6,2,8,3,4,11,5,7,10]=>[4,2,2,1,1,1,1]
[1,12,11,6,2,8,3,10,4,5,7,9]=>[4,2,2,1,1,1,1]
[1,12,11,6,2,10,9,3,4,5,7,8]=>[5,2,1,1,1,1,1]
[11,10,9,8,7,2,3,4,5,6,1,12]=>[7,1,1,1,1,1]
[1,10,9,8,7,2,3,4,5,12,6,11]=>[5,2,1,1,1,1,1]
[1,12,9,8,7,2,3,4,11,5,6,10]=>[5,2,1,1,1,1,1]
[1,12,11,8,7,2,3,10,4,5,6,9]=>[5,2,1,1,1,1,1]
[1,12,11,10,7,2,9,3,4,5,6,8]=>[5,2,1,1,1,1,1]
[1,12,11,10,9,8,2,3,4,5,6,7]=>[6,1,1,1,1,1,1]
[3,2,5,4,7,6,9,8,1,12,11,10]=>[3,3,2,2,2]
[3,2,5,4,7,6,11,10,9,8,1,12]=>[5,2,2,2,1]
[3,2,5,4,7,6,1,10,9,12,11,8]=>[3,3,2,2,2]
[3,2,5,4,7,6,1,12,11,10,9,8]=>[5,3,2,2]
[3,2,5,4,9,8,7,6,11,10,1,12]=>[5,2,2,2,1]
[3,2,5,4,9,8,7,6,1,12,11,10]=>[5,3,2,2]
[3,2,5,4,11,8,7,10,9,6,1,12]=>[5,2,2,2,1]
[3,2,5,4,1,8,7,10,9,12,11,6]=>[3,3,2,2,2]
[3,2,5,4,1,8,7,12,11,10,9,6]=>[5,3,2,2]
[3,2,5,4,11,10,9,8,7,6,1,12]=>[7,2,2,1]
[3,2,5,4,1,10,9,8,7,12,11,6]=>[5,3,2,2]
[3,2,5,4,1,12,9,8,11,10,7,6]=>[5,3,2,2]
[3,2,5,4,1,12,11,10,9,8,7,6]=>[7,3,2]
[3,2,7,6,5,4,9,8,11,10,1,12]=>[5,2,2,2,1]
[3,2,7,6,5,4,9,8,1,12,11,10]=>[5,3,2,2]
[3,2,7,6,5,4,11,10,9,8,1,12]=>[5,4,2,1]
[3,2,7,6,5,4,1,10,9,12,11,8]=>[5,3,2,2]
[3,2,7,6,5,4,1,12,11,10,9,8]=>[5,5,2]
[3,2,9,6,5,8,7,4,11,10,1,12]=>[5,2,2,2,1]
[3,2,9,6,5,8,7,4,1,12,11,10]=>[5,3,2,2]
[3,2,11,6,5,8,7,10,9,4,1,12]=>[5,2,2,2,1]
[3,2,1,6,5,8,7,10,9,12,11,4]=>[3,3,2,2,2]
[3,2,1,6,5,8,7,12,11,10,9,4]=>[5,3,2,2]
[3,2,11,6,5,10,9,8,7,4,1,12]=>[7,2,2,1]
[3,2,1,6,5,10,9,8,7,12,11,4]=>[5,3,2,2]
[3,2,1,6,5,12,9,8,11,10,7,4]=>[5,3,2,2]
[3,2,1,6,5,12,11,10,9,8,7,4]=>[7,3,2]
[3,2,9,8,7,6,5,4,11,10,1,12]=>[7,2,2,1]
[3,2,9,8,7,6,5,4,1,12,11,10]=>[7,3,2]
[3,2,11,8,7,6,5,10,9,4,1,12]=>[7,2,2,1]
[3,2,1,8,7,6,5,10,9,12,11,4]=>[5,3,2,2]
[3,2,1,8,7,6,5,12,11,10,9,4]=>[5,4,3]
[3,2,11,10,7,6,9,8,5,4,1,12]=>[7,2,2,1]
[3,2,1,10,7,6,9,8,5,12,11,4]=>[5,3,2,2]
[3,2,1,12,7,6,9,8,11,10,5,4]=>[5,3,2,2]
[3,2,1,12,7,6,11,10,9,8,5,4]=>[7,3,2]
[3,2,11,10,9,8,7,6,5,4,1,12]=>[9,2,1]
[3,2,1,10,9,8,7,6,5,12,11,4]=>[7,3,2]
[3,2,1,12,9,8,7,6,11,10,5,4]=>[7,3,2]
[3,2,1,12,11,8,7,10,9,6,5,4]=>[7,3,2]
[3,2,1,12,11,10,9,8,7,6,5,4]=>[9,3]
[5,4,3,2,7,6,9,8,11,10,1,12]=>[5,2,2,2,1]
[5,4,3,2,7,6,9,8,1,12,11,10]=>[5,3,2,2]
[5,4,3,2,7,6,11,10,9,8,1,12]=>[5,4,2,1]
[5,4,3,2,7,6,1,10,9,12,11,8]=>[5,3,2,2]
[5,4,3,2,7,6,1,12,11,10,9,8]=>[5,5,2]
[5,4,3,2,9,8,7,6,11,10,1,12]=>[5,4,2,1]
[5,4,3,2,9,8,7,6,1,12,11,10]=>[5,4,3]
[5,4,3,2,11,8,7,10,9,6,1,12]=>[5,4,2,1]
[5,4,3,2,1,8,7,10,9,12,11,6]=>[5,3,2,2]
[5,4,3,2,1,8,7,12,11,10,9,6]=>[5,5,2]
[5,4,3,2,11,10,9,8,7,6,1,12]=>[7,4,1]
[5,4,3,2,1,10,9,8,7,12,11,6]=>[5,5,2]
[5,4,3,2,1,12,9,8,11,10,7,6]=>[5,5,2]
[5,4,3,2,1,12,11,10,9,8,7,6]=>[7,5]
[7,4,3,6,5,2,9,8,11,10,1,12]=>[5,2,2,2,1]
[7,4,3,6,5,2,9,8,1,12,11,10]=>[5,3,2,2]
[7,4,3,6,5,2,11,10,9,8,1,12]=>[5,4,2,1]
[7,4,3,6,5,2,1,10,9,12,11,8]=>[5,3,2,2]
[7,4,3,6,5,2,1,12,11,10,9,8]=>[5,5,2]
[9,4,3,6,5,8,7,2,11,10,1,12]=>[5,2,2,2,1]
[9,4,3,6,5,8,7,2,1,12,11,10]=>[5,3,2,2]
[11,4,3,6,5,8,7,10,9,2,1,12]=>[5,2,2,2,1]
[1,4,3,6,5,8,7,10,9,12,11,2]=>[3,2,2,2,2,1]
[1,4,3,6,5,8,7,12,11,10,9,2]=>[5,2,2,2,1]
[11,4,3,6,5,10,9,8,7,2,1,12]=>[7,2,2,1]
[1,4,3,6,5,10,9,8,7,12,11,2]=>[5,2,2,2,1]
[1,4,3,6,5,12,9,8,11,10,7,2]=>[5,2,2,2,1]
[1,4,3,6,5,12,11,10,9,8,7,2]=>[7,2,2,1]
[9,4,3,8,7,6,5,2,11,10,1,12]=>[7,2,2,1]
[9,4,3,8,7,6,5,2,1,12,11,10]=>[7,3,2]
[11,4,3,8,7,6,5,10,9,2,1,12]=>[7,2,2,1]
[1,4,3,8,7,6,5,10,9,12,11,2]=>[5,2,2,2,1]
[1,4,3,8,7,6,5,12,11,10,9,2]=>[5,4,2,1]
[11,4,3,10,7,6,9,8,5,2,1,12]=>[7,2,2,1]
[1,4,3,10,7,6,9,8,5,12,11,2]=>[5,2,2,2,1]
[1,4,3,12,7,6,9,8,11,10,5,2]=>[5,2,2,2,1]
[1,4,3,12,7,6,11,10,9,8,5,2]=>[7,2,2,1]
[11,4,3,10,9,8,7,6,5,2,1,12]=>[9,2,1]
[1,4,3,10,9,8,7,6,5,12,11,2]=>[7,2,2,1]
[1,4,3,12,9,8,7,6,11,10,5,2]=>[7,2,2,1]
[1,4,3,12,11,8,7,10,9,6,5,2]=>[7,2,2,1]
[1,4,3,12,11,10,9,8,7,6,5,2]=>[9,2,1]
[7,6,5,4,3,2,9,8,11,10,1,12]=>[7,2,2,1]
[7,6,5,4,3,2,9,8,1,12,11,10]=>[7,3,2]
[7,6,5,4,3,2,11,10,9,8,1,12]=>[7,4,1]
[7,6,5,4,3,2,1,10,9,12,11,8]=>[7,3,2]
[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,5]
[9,6,5,4,3,8,7,2,11,10,1,12]=>[7,2,2,1]
[9,6,5,4,3,8,7,2,1,12,11,10]=>[7,3,2]
[11,6,5,4,3,8,7,10,9,2,1,12]=>[7,2,2,1]
[1,6,5,4,3,8,7,10,9,12,11,2]=>[5,2,2,2,1]
[1,6,5,4,3,8,7,12,11,10,9,2]=>[5,4,2,1]
[11,6,5,4,3,10,9,8,7,2,1,12]=>[7,4,1]
[1,6,5,4,3,10,9,8,7,12,11,2]=>[5,4,2,1]
[1,6,5,4,3,12,9,8,11,10,7,2]=>[5,4,2,1]
[1,6,5,4,3,12,11,10,9,8,7,2]=>[7,4,1]
[9,8,5,4,7,6,3,2,11,10,1,12]=>[7,2,2,1]
[9,8,5,4,7,6,3,2,1,12,11,10]=>[7,3,2]
[11,8,5,4,7,6,3,10,9,2,1,12]=>[7,2,2,1]
[1,8,5,4,7,6,3,10,9,12,11,2]=>[5,2,2,2,1]
[1,8,5,4,7,6,3,12,11,10,9,2]=>[5,4,2,1]
[11,10,5,4,7,6,9,8,3,2,1,12]=>[7,2,2,1]
[1,10,5,4,7,6,9,8,3,12,11,2]=>[5,2,2,2,1]
[1,12,5,4,7,6,9,8,11,10,3,2]=>[5,2,2,2,1]
[1,12,5,4,7,6,11,10,9,8,3,2]=>[7,2,2,1]
[11,10,5,4,9,8,7,6,3,2,1,12]=>[9,2,1]
[1,10,5,4,9,8,7,6,3,12,11,2]=>[7,2,2,1]
[1,12,5,4,9,8,7,6,11,10,3,2]=>[7,2,2,1]
[1,12,5,4,11,8,7,10,9,6,3,2]=>[7,2,2,1]
[1,12,5,4,11,10,9,8,7,6,3,2]=>[9,2,1]
[9,8,7,6,5,4,3,2,11,10,1,12]=>[9,2,1]
[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,3]
[11,8,7,6,5,4,3,10,9,2,1,12]=>[9,2,1]
[1,8,7,6,5,4,3,10,9,12,11,2]=>[7,2,2,1]
[1,8,7,6,5,4,3,12,11,10,9,2]=>[7,4,1]
[11,10,7,6,5,4,9,8,3,2,1,12]=>[9,2,1]
[1,10,7,6,5,4,9,8,3,12,11,2]=>[7,2,2,1]
[1,12,7,6,5,4,9,8,11,10,3,2]=>[7,2,2,1]
[1,12,7,6,5,4,11,10,9,8,3,2]=>[7,4,1]
[11,10,9,6,5,8,7,4,3,2,1,12]=>[9,2,1]
[1,10,9,6,5,8,7,4,3,12,11,2]=>[7,2,2,1]
[1,12,9,6,5,8,7,4,11,10,3,2]=>[7,2,2,1]
[1,12,11,6,5,8,7,10,9,4,3,2]=>[7,2,2,1]
[1,12,11,6,5,10,9,8,7,4,3,2]=>[9,2,1]
[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,1]
[1,10,9,8,7,6,5,4,3,12,11,2]=>[9,2,1]
[1,12,9,8,7,6,5,4,11,10,3,2]=>[9,2,1]
[1,12,11,8,7,6,5,10,9,4,3,2]=>[9,2,1]
[1,12,11,10,7,6,9,8,5,4,3,2]=>[9,2,1]
[1,12,11,10,9,8,7,6,5,4,3,2]=>[11,1]
[2,3,4,5,6,7,8,9,10,11,12,1]=>[2,1,1,1,1,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,10,12,11,9]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,8,10,9,7,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,10,12,9,11,7,8]=>[3,2,2,2,1,1,1]
[2,1,4,3,6,5,8,9,12,10,11,7]=>[3,2,2,2,1,1,1]
[2,1,4,3,6,8,7,5,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,6,8,7,5,10,12,11,9]=>[3,3,2,2,1,1]
[2,1,4,3,8,10,7,9,5,6,12,11]=>[3,2,2,2,1,1,1]
[2,1,4,3,10,9,7,12,6,11,5,8]=>[5,2,2,1,1,1]
[2,1,4,3,8,9,7,12,10,6,11,5]=>[4,2,2,2,1,1]
[2,1,4,3,6,7,10,8,9,5,12,11]=>[3,2,2,2,1,1,1]
[2,1,4,3,10,7,12,8,9,11,5,6]=>[3,2,2,2,1,1,1]
[2,1,4,3,6,9,12,8,11,10,5,7]=>[4,2,2,1,1,1,1]
[2,1,4,3,6,7,8,12,9,10,11,5]=>[3,2,2,1,1,1,1,1]
[2,1,4,6,5,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,4,6,5,3,8,7,10,12,11,9]=>[3,3,2,2,1,1]
[2,1,4,6,5,3,8,10,9,7,12,11]=>[3,3,2,2,1,1]
[2,1,4,6,5,3,10,12,9,11,7,8]=>[3,3,2,1,1,1,1]
[2,1,4,6,5,3,8,9,12,10,11,7]=>[3,3,2,1,1,1,1]
[2,1,6,8,5,7,3,4,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,1,6,8,5,7,3,4,10,12,11,9]=>[3,3,2,1,1,1,1]
[2,1,8,7,5,10,4,9,3,6,12,11]=>[5,2,2,1,1,1]
[2,1,10,7,5,9,4,12,6,11,3,8]=>[5,2,2,1,1,1]
[2,1,8,7,5,9,4,12,10,6,11,3]=>[5,3,2,1,1]
[2,1,6,7,5,10,8,4,9,3,12,11]=>[4,2,2,2,1,1]
[2,1,10,8,5,7,12,4,9,11,3,6]=>[5,2,1,1,1,1,1]
[2,1,6,9,5,8,12,3,11,10,4,7]=>[4,2,2,1,1,1,1]
[2,1,6,7,5,8,12,9,3,10,11,4]=>[3,2,2,2,1,1,1]
[2,1,4,5,8,6,7,3,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,1,4,5,8,6,7,3,10,12,11,9]=>[3,3,2,1,1,1,1]
[2,1,8,5,10,6,7,9,3,4,12,11]=>[3,2,2,2,1,1,1]
[2,1,10,5,9,6,7,12,4,11,3,8]=>[5,2,1,1,1,1,1]
[2,1,8,5,9,6,7,12,10,4,11,3]=>[4,2,2,2,1,1]
[2,1,4,7,10,6,9,8,3,5,12,11]=>[4,2,2,1,1,1,1]
[2,1,10,7,12,6,9,8,4,11,3,5]=>[5,2,2,1,1,1]
[2,1,4,9,12,6,10,8,11,7,3,5]=>[5,2,1,1,1,1,1]
[2,1,4,7,8,6,12,10,9,5,11,3]=>[5,2,2,1,1,1]
[2,1,4,5,6,10,7,8,9,3,12,11]=>[3,2,2,1,1,1,1,1]
[2,1,10,5,6,12,7,8,9,11,3,4]=>[3,2,2,1,1,1,1,1]
[2,1,4,9,6,12,7,8,11,10,3,5]=>[4,2,2,1,1,1,1]
[2,1,4,5,8,12,7,11,9,10,3,6]=>[4,2,1,1,1,1,1,1]
[2,1,4,5,6,7,12,8,9,10,11,3]=>[3,2,1,1,1,1,1,1,1]
[2,4,3,1,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[2,4,3,1,6,5,8,7,10,12,11,9]=>[3,3,2,2,1,1]
[2,4,3,1,6,5,8,10,9,7,12,11]=>[3,3,2,2,1,1]
[2,4,3,1,6,5,10,12,9,11,7,8]=>[3,3,2,1,1,1,1]
[2,4,3,1,6,5,8,9,12,10,11,7]=>[3,3,2,1,1,1,1]
[2,4,3,1,6,8,7,5,10,9,12,11]=>[3,3,2,2,1,1]
[2,4,3,1,6,8,7,5,10,12,11,9]=>[3,3,3,1,1,1]
[2,4,3,1,8,10,7,9,5,6,12,11]=>[3,3,2,1,1,1,1]
[2,4,3,1,10,9,7,12,6,11,5,8]=>[5,3,1,1,1,1]
[2,4,3,1,8,9,7,12,10,6,11,5]=>[4,3,2,1,1,1]
[2,4,3,1,6,7,10,8,9,5,12,11]=>[3,3,2,1,1,1,1]
[2,4,3,1,10,7,12,8,9,11,5,6]=>[3,3,2,1,1,1,1]
[2,4,3,1,6,9,12,8,11,10,5,7]=>[4,3,1,1,1,1,1]
[2,4,3,1,6,7,8,12,9,10,11,5]=>[3,3,1,1,1,1,1,1]
[4,6,3,5,1,2,8,7,10,9,12,11]=>[3,2,2,2,1,1,1]
[4,6,3,5,1,2,8,7,10,12,11,9]=>[3,3,2,1,1,1,1]
[4,6,3,5,1,2,8,10,9,7,12,11]=>[3,3,2,1,1,1,1]
[4,6,3,5,1,2,10,12,9,11,7,8]=>[3,3,1,1,1,1,1,1]
[4,6,3,5,1,2,8,9,12,10,11,7]=>[3,3,1,1,1,1,1,1]
[6,5,3,8,2,7,1,4,10,9,12,11]=>[5,2,2,1,1,1]
[6,5,3,8,2,7,1,4,10,12,11,9]=>[5,3,1,1,1,1]
[8,5,3,7,2,10,4,9,1,6,12,11]=>[5,2,2,1,1,1]
[10,5,3,7,2,9,4,12,6,11,1,8]=>[5,2,2,1,1,1]
[8,5,3,7,2,9,4,12,10,6,11,1]=>[5,3,2,1,1]
[6,5,3,7,2,10,8,4,9,1,12,11]=>[5,3,2,1,1]
[10,5,3,8,2,7,12,4,9,11,1,6]=>[5,2,1,1,1,1,1]
[6,5,3,9,2,8,12,1,11,10,4,7]=>[5,3,1,1,1,1]
[6,5,3,7,2,8,12,9,1,10,11,4]=>[5,2,2,1,1,1]
[4,5,3,8,6,2,7,1,10,9,12,11]=>[4,2,2,2,1,1]
[4,5,3,8,6,2,7,1,10,12,11,9]=>[4,3,2,1,1,1]
[8,6,3,5,10,2,7,9,1,4,12,11]=>[5,2,1,1,1,1,1]
[10,6,3,5,9,2,7,12,4,11,1,8]=>[5,2,1,1,1,1,1]
[8,6,3,5,9,2,7,12,10,4,11,1]=>[5,3,1,1,1,1]
[4,7,3,6,10,1,9,8,2,5,12,11]=>[4,2,2,1,1,1,1]
[10,6,3,7,12,2,9,8,4,11,1,5]=>[5,3,1,1,1,1]
[4,9,3,6,12,1,10,8,11,7,2,5]=>[5,2,1,1,1,1,1]
[4,7,3,6,8,1,12,10,9,5,11,2]=>[5,3,1,1,1,1]
[4,5,3,6,10,7,1,8,9,2,12,11]=>[3,2,2,2,1,1,1]
[10,7,3,5,6,12,2,8,9,11,1,4]=>[5,1,1,1,1,1,1,1]
[4,9,3,7,6,12,1,8,11,10,2,5]=>[4,3,1,1,1,1,1]
[4,5,3,8,7,12,2,11,9,10,1,6]=>[4,2,2,1,1,1,1]
[4,5,3,6,7,12,8,2,9,10,11,1]=>[4,2,1,1,1,1,1,1]
[2,3,6,4,5,1,8,7,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,3,6,4,5,1,8,7,10,12,11,9]=>[3,3,2,1,1,1,1]
[2,3,6,4,5,1,8,10,9,7,12,11]=>[3,3,2,1,1,1,1]
[2,3,6,4,5,1,10,12,9,11,7,8]=>[3,3,1,1,1,1,1,1]
[2,3,6,4,5,1,8,9,12,10,11,7]=>[3,3,1,1,1,1,1,1]
[6,3,8,4,5,7,1,2,10,9,12,11]=>[3,2,2,2,1,1,1]
[6,3,8,4,5,7,1,2,10,12,11,9]=>[3,3,2,1,1,1,1]
[8,3,7,4,5,10,2,9,1,6,12,11]=>[5,2,1,1,1,1,1]
[10,3,7,4,5,9,2,12,6,11,1,8]=>[5,2,1,1,1,1,1]
[8,3,7,4,5,9,2,12,10,6,11,1]=>[5,3,1,1,1,1]
[6,3,7,4,5,10,8,2,9,1,12,11]=>[4,2,2,2,1,1]
[10,3,8,4,5,7,12,2,9,11,1,6]=>[5,1,1,1,1,1,1,1]
[6,3,9,4,5,8,12,1,11,10,2,7]=>[4,2,2,1,1,1,1]
[6,3,7,4,5,8,12,9,1,10,11,2]=>[3,2,2,2,1,1,1]
[2,5,8,4,7,6,1,3,10,9,12,11]=>[4,2,2,1,1,1,1]
[2,5,8,4,7,6,1,3,10,12,11,9]=>[4,3,1,1,1,1,1]
[8,5,10,4,7,6,2,9,1,3,12,11]=>[5,2,2,1,1,1]
[10,5,9,4,7,6,2,12,3,11,1,8]=>[6,2,1,1,1,1]
[8,5,9,4,7,6,2,12,10,3,11,1]=>[5,3,2,1,1]
[2,7,10,4,8,6,9,5,1,3,12,11]=>[5,2,1,1,1,1,1]
[10,7,12,4,8,6,9,5,2,11,1,3]=>[6,2,1,1,1,1]
[2,9,8,4,12,6,10,3,11,7,1,5]=>[5,2,2,1,1,1]
[2,7,8,4,12,6,9,10,1,3,11,5]=>[3,2,2,1,1,1,1,1]
[2,5,6,4,10,8,7,3,9,1,12,11]=>[5,2,2,1,1,1]
[10,5,6,4,12,8,7,3,9,11,1,2]=>[5,3,1,1,1,1]
[2,9,8,4,6,12,7,3,11,10,1,5]=>[5,2,2,1,1,1]
[2,5,8,4,12,9,7,11,6,10,3,1]=>[6,2,1,1,1,1]
[2,5,6,4,7,12,9,8,1,10,11,3]=>[4,2,2,1,1,1,1]
[2,3,4,8,5,6,7,1,10,9,12,11]=>[3,2,2,1,1,1,1,1]
[2,3,4,8,5,6,7,1,10,12,11,9]=>[3,3,1,1,1,1,1,1]
[8,3,4,10,5,6,7,9,1,2,12,11]=>[3,2,2,1,1,1,1,1]
[10,3,4,9,5,6,7,12,2,11,1,8]=>[5,1,1,1,1,1,1,1]
[8,3,4,9,5,6,7,12,10,2,11,1]=>[4,2,2,1,1,1,1]
[2,7,4,10,5,6,9,8,1,3,12,11]=>[4,2,2,1,1,1,1]
[10,7,4,12,5,6,9,8,2,11,1,3]=>[5,3,1,1,1,1]
[2,9,4,12,5,6,10,8,11,7,1,3]=>[5,2,1,1,1,1,1]
[2,7,4,8,5,6,12,10,9,3,11,1]=>[5,2,2,1,1,1]
[2,3,6,10,5,9,7,8,1,4,12,11]=>[4,2,1,1,1,1,1,1]
[10,3,6,12,5,9,7,8,2,11,1,4]=>[5,2,1,1,1,1,1]
[2,9,6,12,5,11,7,8,10,1,3,4]=>[4,2,1,1,1,1,1,1]
[2,3,8,12,5,10,7,11,9,6,1,4]=>[5,2,1,1,1,1,1]
[2,3,6,7,5,12,10,8,9,4,11,1]=>[5,2,1,1,1,1,1]
[2,3,4,5,10,6,7,8,9,1,12,11]=>[3,2,1,1,1,1,1,1,1]
[10,3,4,5,12,6,7,8,9,11,1,2]=>[3,2,1,1,1,1,1,1,1]
[2,9,4,5,12,6,7,8,11,10,1,3]=>[4,2,1,1,1,1,1,1]
[2,3,8,5,12,6,7,11,9,10,1,4]=>[4,2,1,1,1,1,1,1]
[2,3,4,7,12,6,11,8,9,10,1,5]=>[4,1,1,1,1,1,1,1,1]
[2,3,4,5,6,12,7,8,9,10,11,1]=>[3,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,10,11,12,9]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,8,9,10,7,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,10,9,11,12,7,8]=>[3,2,2,2,1,1,1]
[2,1,4,3,6,5,8,9,10,11,12,7]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,6,7,8,5,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,7,8,5,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,8,7,9,10,5,6,12,11]=>[3,2,2,2,1,1,1]
[2,1,4,3,10,7,11,9,5,12,8,6]=>[4,2,2,2,2]
[2,1,4,3,8,7,9,10,11,12,5,6]=>[3,2,2,1,1,1,1,1]
[2,1,4,3,6,7,8,9,10,5,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,10,7,8,9,11,12,5,6]=>[3,2,2,1,1,1,1,1]
[2,1,4,3,6,9,8,10,11,5,12,7]=>[3,2,2,2,1,1,1]
[2,1,4,3,6,7,8,9,10,11,12,5]=>[2,2,2,1,1,1,1,1,1]
[2,1,4,5,6,3,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,5,6,3,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,5,6,3,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,5,6,3,10,9,11,12,7,8]=>[3,2,2,1,1,1,1,1]
[2,1,4,5,6,3,8,9,10,11,12,7]=>[2,2,2,1,1,1,1,1,1]
[2,1,6,5,7,8,3,4,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,1,6,5,7,8,3,4,10,11,12,9]=>[3,2,2,1,1,1,1,1]
[2,1,8,5,9,7,3,10,6,4,12,11]=>[4,2,2,2,2]
[2,1,10,5,11,7,3,9,6,12,8,4]=>[4,2,2,2,2]
[2,1,8,5,9,7,3,10,11,12,6,4]=>[4,2,2,2,1,1]
[2,1,6,5,7,8,9,10,3,4,12,11]=>[3,2,2,1,1,1,1,1]
[2,1,10,5,11,7,8,9,3,12,6,4]=>[4,2,2,2,1,1]
[2,1,6,5,9,10,8,12,11,4,7,3]=>[4,2,2,2,1,1]
[2,1,6,5,7,8,9,10,11,12,3,4]=>[3,2,1,1,1,1,1,1,1]
[2,1,4,5,6,7,8,3,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,5,6,7,8,3,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,8,5,6,7,9,10,3,4,12,11]=>[3,2,2,1,1,1,1,1]
[2,1,10,5,6,7,11,9,3,12,8,4]=>[4,2,2,2,1,1]
[2,1,8,5,6,7,9,10,11,12,3,4]=>[3,2,1,1,1,1,1,1,1]
[2,1,4,7,6,8,9,3,10,5,12,11]=>[3,2,2,2,1,1,1]
[2,1,10,7,6,8,9,3,11,12,5,4]=>[5,2,2,1,1,1]
[2,1,4,9,6,10,8,3,11,7,12,5]=>[4,2,2,2,1,1]
[2,1,4,7,6,8,9,10,11,3,12,5]=>[3,2,2,1,1,1,1,1]
[2,1,4,5,6,7,8,9,10,3,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,10,5,6,7,8,9,11,12,3,4]=>[3,2,1,1,1,1,1,1,1]
[2,1,4,9,6,7,8,10,11,3,12,5]=>[3,2,2,1,1,1,1,1]
[2,1,4,5,8,7,9,10,3,11,12,6]=>[3,2,2,1,1,1,1,1]
[2,1,4,5,6,7,8,9,10,11,12,3]=>[2,2,1,1,1,1,1,1,1,1]
[2,3,4,1,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,3,4,1,6,5,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,3,4,1,6,5,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,3,4,1,6,5,10,9,11,12,7,8]=>[3,2,2,1,1,1,1,1]
[2,3,4,1,6,5,8,9,10,11,12,7]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,1,6,7,8,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,3,4,1,6,7,8,5,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,1,8,7,9,10,5,6,12,11]=>[3,2,2,1,1,1,1,1]
[2,3,4,1,10,7,11,9,5,12,8,6]=>[4,2,2,2,1,1]
[2,3,4,1,8,7,9,10,11,12,5,6]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,1,6,7,8,9,10,5,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,1,10,7,8,9,11,12,5,6]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,1,6,9,8,10,11,5,12,7]=>[3,2,2,1,1,1,1,1]
[2,3,4,1,6,7,8,9,10,11,12,5]=>[2,2,1,1,1,1,1,1,1,1]
[4,3,5,6,1,2,8,7,10,9,12,11]=>[3,2,2,2,1,1,1]
[4,3,5,6,1,2,8,7,10,11,12,9]=>[3,2,2,1,1,1,1,1]
[4,3,5,6,1,2,8,9,10,7,12,11]=>[3,2,2,1,1,1,1,1]
[4,3,5,6,1,2,10,9,11,12,7,8]=>[3,3,1,1,1,1,1,1]
[4,3,5,6,1,2,8,9,10,11,12,7]=>[3,2,1,1,1,1,1,1,1]
[6,3,7,5,1,8,4,2,10,9,12,11]=>[4,2,2,2,2]
[6,3,7,5,1,8,4,2,10,11,12,9]=>[4,2,2,2,1,1]
[8,3,9,5,1,7,4,10,6,2,12,11]=>[4,2,2,2,2]
[10,3,11,5,1,7,4,9,6,12,8,2]=>[4,2,2,2,2]
[8,3,9,5,1,7,4,10,11,12,6,2]=>[4,2,2,2,1,1]
[6,3,7,5,1,8,9,10,4,2,12,11]=>[4,2,2,2,1,1]
[10,3,11,5,1,7,8,9,4,12,6,2]=>[4,2,2,2,1,1]
[6,3,9,5,2,10,8,12,11,4,7,1]=>[4,3,2,2,1]
[6,3,7,5,1,8,9,10,11,12,4,2]=>[4,2,2,1,1,1,1]
[4,3,5,6,7,8,1,2,10,9,12,11]=>[3,2,2,1,1,1,1,1]
[4,3,5,6,7,8,1,2,10,11,12,9]=>[3,2,1,1,1,1,1,1,1]
[8,3,9,5,6,7,1,10,4,2,12,11]=>[4,2,2,2,1,1]
[10,3,11,5,6,7,1,9,4,12,8,2]=>[4,2,2,2,1,1]
[8,3,9,5,6,7,1,10,11,12,4,2]=>[4,2,2,1,1,1,1]
[4,3,7,8,6,10,9,2,5,1,12,11]=>[4,2,2,2,1,1]
[10,3,11,7,6,8,9,4,1,12,5,2]=>[5,3,2,1,1]
[4,3,9,10,6,12,8,2,11,7,5,1]=>[5,2,2,2,1]
[4,3,7,8,6,9,10,12,11,5,1,2]=>[4,2,2,1,1,1,1]
[4,3,5,6,7,8,9,10,1,2,12,11]=>[3,2,1,1,1,1,1,1,1]
[10,3,11,5,6,7,8,9,1,12,4,2]=>[4,2,2,1,1,1,1]
[4,3,9,10,6,7,8,12,11,2,5,1]=>[4,2,2,1,1,1,1]
[4,3,5,8,9,7,12,10,1,11,6,2]=>[4,2,2,2,1,1]
[4,3,5,6,7,8,9,10,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[2,3,4,5,6,1,8,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,3,4,5,6,1,8,7,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,5,6,1,8,9,10,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,5,6,1,10,9,11,12,7,8]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,6,1,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[6,3,4,5,7,8,1,2,10,9,12,11]=>[3,2,2,1,1,1,1,1]
[6,3,4,5,7,8,1,2,10,11,12,9]=>[3,2,1,1,1,1,1,1,1]
[8,3,4,5,9,7,1,10,6,2,12,11]=>[4,2,2,2,1,1]
[10,3,4,5,11,7,1,9,6,12,8,2]=>[4,2,2,2,1,1]
[8,3,4,5,9,7,1,10,11,12,6,2]=>[4,2,2,1,1,1,1]
[6,3,4,5,7,8,9,10,1,2,12,11]=>[3,2,1,1,1,1,1,1,1]
[10,3,4,5,11,7,8,9,1,12,6,2]=>[4,2,2,1,1,1,1]
[6,3,4,5,9,10,8,12,11,2,7,1]=>[4,2,2,1,1,1,1]
[6,3,4,5,7,8,9,10,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[2,5,4,6,7,1,8,3,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,5,4,6,7,1,8,3,10,11,12,9]=>[3,2,2,1,1,1,1,1]
[8,5,4,6,7,1,9,10,3,2,12,11]=>[5,2,2,1,1,1]
[10,5,4,6,7,1,11,9,3,12,8,2]=>[5,3,2,1,1]
[8,5,4,6,7,1,9,10,11,12,3,2]=>[5,2,1,1,1,1,1]
[2,7,4,8,6,1,9,5,10,3,12,11]=>[4,2,2,2,1,1]
[10,7,4,8,6,1,9,5,11,12,3,2]=>[6,2,2,1,1]
[2,9,4,10,6,1,8,5,11,7,12,3]=>[4,2,2,2,1,1]
[2,7,4,8,6,1,9,10,11,5,12,3]=>[4,2,2,1,1,1,1]
[2,5,4,6,7,8,9,1,10,3,12,11]=>[3,2,2,1,1,1,1,1]
[10,5,4,6,7,8,9,1,11,12,3,2]=>[5,2,1,1,1,1,1]
[2,9,4,10,6,7,8,1,11,5,12,3]=>[4,2,2,1,1,1,1]
[2,5,4,8,9,7,11,10,3,6,12,1]=>[4,2,2,1,1,1,1]
[2,5,4,6,7,8,9,10,11,1,12,3]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,1,10,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,3,4,5,6,7,8,1,10,11,12,9]=>[2,2,1,1,1,1,1,1,1,1]
[8,3,4,5,6,7,9,10,1,2,12,11]=>[3,2,1,1,1,1,1,1,1]
[10,3,4,5,6,7,11,9,1,12,8,2]=>[4,2,2,1,1,1,1]
[8,3,4,5,6,7,9,10,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[2,7,4,5,6,8,9,1,10,3,12,11]=>[3,2,2,1,1,1,1,1]
[10,7,4,5,6,8,9,1,11,12,3,2]=>[5,2,1,1,1,1,1]
[2,9,4,5,6,10,8,1,11,7,12,3]=>[4,2,2,1,1,1,1]
[2,7,4,5,6,8,9,10,11,1,12,3]=>[3,2,1,1,1,1,1,1,1]
[2,3,6,5,7,8,1,9,10,4,12,11]=>[3,2,2,1,1,1,1,1]
[10,3,6,5,7,8,1,9,11,12,4,2]=>[5,2,1,1,1,1,1]
[2,9,6,5,7,8,1,10,11,4,12,3]=>[5,2,1,1,1,1,1]
[2,3,8,5,9,7,1,10,6,11,12,4]=>[4,2,2,1,1,1,1]
[2,3,6,5,7,8,9,10,1,11,12,4]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,6,7,8,9,10,1,12,11]=>[2,2,1,1,1,1,1,1,1,1]
[10,3,4,5,6,7,8,9,11,12,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[2,9,4,5,6,7,8,10,11,1,12,3]=>[3,2,1,1,1,1,1,1,1]
[2,3,8,5,6,7,9,10,1,11,12,4]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,7,6,8,9,1,10,11,12,5]=>[3,2,1,1,1,1,1,1,1]
[1,4,3,6,5,8,7,12,11,9,10,2]=>[4,2,2,2,1,1]
[1,4,3,6,5,10,9,7,8,12,11,2]=>[4,2,2,2,1,1]
[1,4,3,6,5,12,9,7,11,8,10,2]=>[4,2,2,2,1,1]
[1,4,3,6,5,12,11,10,7,8,9,2]=>[5,2,2,1,1,1]
[1,4,3,8,7,5,6,10,9,12,11,2]=>[4,2,2,2,1,1]
[1,4,3,8,7,5,6,12,11,9,10,2]=>[4,3,2,1,1,1]
[1,4,3,10,7,5,9,6,8,12,11,2]=>[4,2,2,2,1,1]
[1,4,3,12,7,5,9,6,11,8,10,2]=>[4,2,2,2,1,1]
[1,4,3,12,7,5,11,10,6,8,9,2]=>[5,2,2,1,1,1]
[1,4,3,10,9,8,5,6,7,12,11,2]=>[5,2,2,1,1,1]
[1,4,3,12,9,8,5,6,11,7,10,2]=>[5,2,2,1,1,1]
[1,4,3,12,11,8,5,10,6,7,9,2]=>[5,2,2,1,1,1]
[1,4,3,12,11,10,9,5,6,7,8,2]=>[6,2,1,1,1,1]
[1,6,5,3,4,8,7,10,9,12,11,2]=>[4,2,2,2,1,1]
[1,6,5,3,4,8,7,12,11,9,10,2]=>[4,3,2,1,1,1]
[1,6,5,3,4,10,9,7,8,12,11,2]=>[4,3,2,1,1,1]
[1,6,5,3,4,12,9,7,11,8,10,2]=>[4,3,2,1,1,1]
[1,6,5,3,4,12,11,10,7,8,9,2]=>[5,3,1,1,1,1]
[1,8,5,3,7,4,6,10,9,12,11,2]=>[4,2,2,2,1,1]
[1,8,5,3,7,4,6,12,11,9,10,2]=>[4,3,2,1,1,1]
[1,10,5,3,7,4,9,6,8,12,11,2]=>[4,2,2,2,1,1]
[1,12,5,3,7,4,9,6,11,8,10,2]=>[4,2,2,2,1,1]
[1,12,5,3,7,4,11,10,6,8,9,2]=>[5,2,2,1,1,1]
[1,10,5,3,9,8,4,6,7,12,11,2]=>[5,2,2,1,1,1]
[1,12,5,3,9,8,4,6,11,7,10,2]=>[5,2,2,1,1,1]
[1,12,5,3,11,8,4,10,6,7,9,2]=>[5,2,2,1,1,1]
[1,12,5,3,11,10,9,4,6,7,8,2]=>[6,2,1,1,1,1]
[1,8,7,6,3,4,5,10,9,12,11,2]=>[5,2,2,1,1,1]
[1,8,7,6,3,4,5,12,11,9,10,2]=>[5,3,1,1,1,1]
[1,10,7,6,3,4,9,5,8,12,11,2]=>[5,2,2,1,1,1]
[1,12,7,6,3,4,9,5,11,8,10,2]=>[5,2,2,1,1,1]
[1,12,7,6,3,4,11,10,5,8,9,2]=>[5,3,1,1,1,1]
[1,10,9,6,3,8,4,5,7,12,11,2]=>[5,2,2,1,1,1]
[1,12,9,6,3,8,4,5,11,7,10,2]=>[5,2,2,1,1,1]
[1,12,11,6,3,8,4,10,5,7,9,2]=>[5,2,2,1,1,1]
[1,12,11,6,3,10,9,4,5,7,8,2]=>[6,2,1,1,1,1]
[1,10,9,8,7,3,4,5,6,12,11,2]=>[6,2,1,1,1,1]
[1,12,9,8,7,3,4,5,11,6,10,2]=>[6,2,1,1,1,1]
[1,12,11,8,7,3,4,10,5,6,9,2]=>[6,2,1,1,1,1]
[1,12,11,10,7,3,9,4,5,6,8,2]=>[6,2,1,1,1,1]
[1,12,11,10,9,8,3,4,5,6,7,2]=>[7,1,1,1,1,1]
[3,1,2,6,5,8,7,10,9,12,11,4]=>[3,2,2,2,2,1]
[3,1,2,6,5,8,7,12,11,9,10,4]=>[4,2,2,2,1,1]
[3,1,2,6,5,10,9,7,8,12,11,4]=>[4,2,2,2,1,1]
[3,1,2,6,5,12,9,7,11,8,10,4]=>[4,2,2,2,1,1]
[3,1,2,6,5,12,11,10,7,8,9,4]=>[5,2,2,1,1,1]
[3,1,2,8,7,5,6,10,9,12,11,4]=>[4,2,2,2,1,1]
[3,1,2,8,7,5,6,12,11,9,10,4]=>[4,3,2,1,1,1]
[3,1,2,10,7,5,9,6,8,12,11,4]=>[4,2,2,2,1,1]
[3,1,2,12,7,5,9,6,11,8,10,4]=>[4,2,2,2,1,1]
[3,1,2,12,7,5,11,10,6,8,9,4]=>[5,2,2,1,1,1]
[3,1,2,10,9,8,5,6,7,12,11,4]=>[5,2,2,1,1,1]
[3,1,2,12,9,8,5,6,11,7,10,4]=>[5,2,2,1,1,1]
[3,1,2,12,11,8,5,10,6,7,9,4]=>[5,2,2,1,1,1]
[3,1,2,12,11,10,9,5,6,7,8,4]=>[6,2,1,1,1,1]
[3,1,5,2,4,8,7,10,9,12,11,6]=>[3,2,2,2,2,1]
[3,1,5,2,4,8,7,12,11,9,10,6]=>[4,2,2,2,1,1]
[3,1,5,2,4,10,9,7,8,12,11,6]=>[4,2,2,2,1,1]
[3,1,5,2,4,12,9,7,11,8,10,6]=>[4,2,2,2,1,1]
[3,1,5,2,4,12,11,10,7,8,9,6]=>[5,2,2,1,1,1]
[3,1,5,2,7,4,6,10,9,12,11,8]=>[3,2,2,2,2,1]
[3,1,5,2,7,4,6,12,11,9,10,8]=>[4,2,2,2,1,1]
[3,1,5,2,7,4,9,6,8,12,11,10]=>[3,2,2,2,2,1]
[3,1,5,2,7,4,9,6,11,8,10,12]=>[2,2,2,2,2,1,1]
[3,1,5,2,7,4,11,10,6,8,9,12]=>[3,2,2,2,1,1,1]
[3,1,5,2,9,8,4,6,7,12,11,10]=>[3,3,2,2,1,1]
[3,1,5,2,9,8,4,6,11,7,10,12]=>[3,2,2,2,1,1,1]
[3,1,5,2,11,8,4,10,6,7,9,12]=>[3,2,2,2,1,1,1]
[3,1,5,2,11,10,9,4,6,7,8,12]=>[4,2,2,1,1,1,1]
[3,1,7,6,2,4,5,10,9,12,11,8]=>[3,3,2,2,1,1]
[3,1,7,6,2,4,5,12,11,9,10,8]=>[4,3,2,1,1,1]
[3,1,7,6,2,4,9,5,8,12,11,10]=>[3,3,2,2,1,1]
[3,1,7,6,2,4,9,5,11,8,10,12]=>[3,2,2,2,1,1,1]
[3,1,7,6,2,4,11,10,5,8,9,12]=>[3,3,2,1,1,1,1]
[3,1,9,6,2,8,4,5,7,12,11,10]=>[3,3,2,2,1,1]
[3,1,9,6,2,8,4,5,11,7,10,12]=>[3,2,2,2,1,1,1]
[3,1,11,6,2,8,4,10,5,7,9,12]=>[3,2,2,2,1,1,1]
[3,1,11,6,2,10,9,4,5,7,8,12]=>[4,2,2,1,1,1,1]
[3,1,9,8,7,2,4,5,6,12,11,10]=>[4,3,2,1,1,1]
[3,1,9,8,7,2,4,5,11,6,10,12]=>[4,2,2,1,1,1,1]
[3,1,11,8,7,2,4,10,5,6,9,12]=>[4,2,2,1,1,1,1]
[3,1,11,10,7,2,9,4,5,6,8,12]=>[4,2,2,1,1,1,1]
[3,1,11,10,9,8,2,4,5,6,7,12]=>[5,2,1,1,1,1,1]
[5,4,1,2,3,8,7,10,9,12,11,6]=>[3,3,2,2,1,1]
[5,4,1,2,3,8,7,12,11,9,10,6]=>[4,3,2,1,1,1]
[5,4,1,2,3,10,9,7,8,12,11,6]=>[4,3,2,1,1,1]
[5,4,1,2,3,12,9,7,11,8,10,6]=>[4,3,2,1,1,1]
[5,4,1,2,3,12,11,10,7,8,9,6]=>[5,3,1,1,1,1]
[5,4,1,2,7,3,6,10,9,12,11,8]=>[3,3,2,2,1,1]
[5,4,1,2,7,3,6,12,11,9,10,8]=>[4,3,2,1,1,1]
[5,4,1,2,7,3,9,6,8,12,11,10]=>[3,3,2,2,1,1]
[5,4,1,2,7,3,9,6,11,8,10,12]=>[3,2,2,2,1,1,1]
[5,4,1,2,7,3,11,10,6,8,9,12]=>[3,3,2,1,1,1,1]
[5,4,1,2,9,8,3,6,7,12,11,10]=>[3,3,3,1,1,1]
[5,4,1,2,9,8,3,6,11,7,10,12]=>[3,3,2,1,1,1,1]
[5,4,1,2,11,8,3,10,6,7,9,12]=>[3,3,2,1,1,1,1]
[5,4,1,2,11,10,9,3,6,7,8,12]=>[4,3,1,1,1,1,1]
[7,4,1,6,2,3,5,10,9,12,11,8]=>[3,3,2,2,1,1]
[7,4,1,6,2,3,5,12,11,9,10,8]=>[4,3,2,1,1,1]
[7,4,1,6,2,3,9,5,8,12,11,10]=>[3,3,2,2,1,1]
[7,4,1,6,2,3,9,5,11,8,10,12]=>[3,2,2,2,1,1,1]
[7,4,1,6,2,3,11,10,5,8,9,12]=>[3,3,2,1,1,1,1]
[9,4,1,6,2,8,3,5,7,12,11,10]=>[3,3,2,2,1,1]
[9,4,1,6,2,8,3,5,11,7,10,12]=>[3,2,2,2,1,1,1]
[11,4,1,6,2,8,3,10,5,7,9,12]=>[3,2,2,2,1,1,1]
[11,4,1,6,2,10,9,3,5,7,8,12]=>[4,2,2,1,1,1,1]
[9,4,1,8,7,2,3,5,6,12,11,10]=>[4,3,2,1,1,1]
[9,4,1,8,7,2,3,5,11,6,10,12]=>[4,2,2,1,1,1,1]
[11,4,1,8,7,2,3,10,5,6,9,12]=>[4,2,2,1,1,1,1]
[11,4,1,10,7,2,9,3,5,6,8,12]=>[4,2,2,1,1,1,1]
[11,4,1,10,9,8,2,3,5,6,7,12]=>[5,2,1,1,1,1,1]
[7,6,5,1,2,3,4,10,9,12,11,8]=>[4,3,2,1,1,1]
[7,6,5,1,2,3,4,12,11,9,10,8]=>[4,4,1,1,1,1]
[7,6,5,1,2,3,9,4,8,12,11,10]=>[4,3,2,1,1,1]
[7,6,5,1,2,3,9,4,11,8,10,12]=>[4,2,2,1,1,1,1]
[7,6,5,1,2,3,11,10,4,8,9,12]=>[4,3,1,1,1,1,1]
[9,6,5,1,2,8,3,4,7,12,11,10]=>[4,3,2,1,1,1]
[9,6,5,1,2,8,3,4,11,7,10,12]=>[4,2,2,1,1,1,1]
[11,6,5,1,2,8,3,10,4,7,9,12]=>[4,2,2,1,1,1,1]
[11,6,5,1,2,10,9,3,4,7,8,12]=>[4,3,1,1,1,1,1]
[9,8,5,1,7,2,3,4,6,12,11,10]=>[4,3,2,1,1,1]
[9,8,5,1,7,2,3,4,11,6,10,12]=>[4,2,2,1,1,1,1]
[11,8,5,1,7,2,3,10,4,6,9,12]=>[4,2,2,1,1,1,1]
[11,10,5,1,7,2,9,3,4,6,8,12]=>[4,2,2,1,1,1,1]
[11,10,5,1,9,8,2,3,4,6,7,12]=>[5,2,1,1,1,1,1]
[9,8,7,6,1,2,3,4,5,12,11,10]=>[5,3,1,1,1,1]
[9,8,7,6,1,2,3,4,11,5,10,12]=>[5,2,1,1,1,1,1]
[11,8,7,6,1,2,3,10,4,5,9,12]=>[5,2,1,1,1,1,1]
[11,10,7,6,1,2,9,3,4,5,8,12]=>[5,2,1,1,1,1,1]
[11,10,9,6,1,8,2,3,4,5,7,12]=>[5,2,1,1,1,1,1]
[11,10,9,8,7,1,2,3,4,5,6,12]=>[6,1,1,1,1,1,1]
[2,4,3,6,5,8,7,10,9,12,11,1]=>[3,2,2,2,2,1]
[12,2,3,4,5,6,7,8,9,10,1,11]=>[3,1,1,1,1,1,1,1,1,1]
[3,12,1,4,5,6,7,8,9,10,11,2]=>[3,1,1,1,1,1,1,1,1,1]
[12,3,4,5,6,7,8,9,10,11,1,2]=>[3,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,11,10,12,9]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,9,8,10,7,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,9,8,11,10,12,7]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,10,9,11,8,12,7]=>[4,2,2,2,1,1]
[2,1,4,3,7,6,8,5,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,7,6,8,5,11,10,12,9]=>[3,3,2,2,1,1]
[2,1,4,3,7,6,9,8,10,5,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,7,6,9,8,11,10,12,5]=>[3,2,2,2,2,1]
[2,1,4,3,7,6,10,9,11,8,12,5]=>[4,2,2,2,1,1]
[2,1,4,3,8,7,9,6,10,5,12,11]=>[4,2,2,2,1,1]
[2,1,4,3,8,7,9,6,11,10,12,5]=>[4,2,2,2,1,1]
[2,1,4,3,8,7,10,9,11,6,12,5]=>[4,2,2,2,1,1]
[2,1,4,3,9,8,10,7,11,6,12,5]=>[5,2,2,1,1,1]
[2,1,5,4,6,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,5,4,6,3,8,7,11,10,12,9]=>[3,3,2,2,1,1]
[2,1,5,4,6,3,9,8,10,7,12,11]=>[3,3,2,2,1,1]
[2,1,5,4,6,3,9,8,11,10,12,7]=>[3,3,2,2,1,1]
[2,1,5,4,6,3,10,9,11,8,12,7]=>[4,3,2,1,1,1]
[2,1,5,4,7,6,8,3,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,5,4,7,6,8,3,11,10,12,9]=>[3,3,2,2,1,1]
[2,1,5,4,7,6,9,8,10,3,12,11]=>[3,2,2,2,2,1]
[2,1,5,4,7,6,9,8,11,10,12,3]=>[3,2,2,2,2,1]
[2,1,5,4,7,6,10,9,11,8,12,3]=>[4,2,2,2,1,1]
[2,1,5,4,8,7,9,6,10,3,12,11]=>[4,2,2,2,1,1]
[2,1,5,4,8,7,9,6,11,10,12,3]=>[4,2,2,2,1,1]
[2,1,5,4,8,7,10,9,11,6,12,3]=>[4,2,2,2,1,1]
[2,1,5,4,9,8,10,7,11,6,12,3]=>[5,2,2,1,1,1]
[2,1,6,5,7,4,8,3,10,9,12,11]=>[4,2,2,2,1,1]
[2,1,6,5,7,4,8,3,11,10,12,9]=>[4,3,2,1,1,1]
[2,1,6,5,7,4,9,8,10,3,12,11]=>[4,2,2,2,1,1]
[2,1,6,5,7,4,9,8,11,10,12,3]=>[4,2,2,2,1,1]
[2,1,6,5,7,4,10,9,11,8,12,3]=>[4,3,2,1,1,1]
[2,1,6,5,8,7,9,4,10,3,12,11]=>[4,2,2,2,1,1]
[2,1,6,5,8,7,9,4,11,10,12,3]=>[4,2,2,2,1,1]
[2,1,6,5,8,7,10,9,11,4,12,3]=>[4,2,2,2,1,1]
[2,1,6,5,9,8,10,7,11,4,12,3]=>[5,2,2,1,1,1]
[2,1,7,6,8,5,9,4,10,3,12,11]=>[5,2,2,1,1,1]
[2,1,7,6,8,5,9,4,11,10,12,3]=>[5,2,2,1,1,1]
[2,1,7,6,8,5,10,9,11,4,12,3]=>[5,2,2,1,1,1]
[2,1,7,6,9,8,10,5,11,4,12,3]=>[5,2,2,1,1,1]
[2,1,8,7,9,6,10,5,11,4,12,3]=>[6,2,1,1,1,1]
[3,2,4,1,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[3,2,4,1,6,5,8,7,11,10,12,9]=>[3,3,2,2,1,1]
[3,2,4,1,6,5,9,8,10,7,12,11]=>[3,3,2,2,1,1]
[3,2,4,1,6,5,9,8,11,10,12,7]=>[3,3,2,2,1,1]
[3,2,4,1,6,5,10,9,11,8,12,7]=>[4,3,2,1,1,1]
[3,2,4,1,7,6,8,5,10,9,12,11]=>[3,3,2,2,1,1]
[3,2,4,1,7,6,8,5,11,10,12,9]=>[3,3,3,1,1,1]
[3,2,4,1,7,6,9,8,10,5,12,11]=>[3,3,2,2,1,1]
[3,2,4,1,7,6,9,8,11,10,12,5]=>[3,3,2,2,1,1]
[3,2,4,1,7,6,10,9,11,8,12,5]=>[4,3,2,1,1,1]
[3,2,4,1,8,7,9,6,10,5,12,11]=>[4,3,2,1,1,1]
[3,2,4,1,8,7,9,6,11,10,12,5]=>[4,3,2,1,1,1]
[3,2,4,1,8,7,10,9,11,6,12,5]=>[4,3,2,1,1,1]
[3,2,4,1,9,8,10,7,11,6,12,5]=>[5,3,1,1,1,1]
[3,2,5,4,6,1,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[3,2,5,4,6,1,8,7,11,10,12,9]=>[3,3,2,2,1,1]
[3,2,5,4,6,1,9,8,10,7,12,11]=>[3,3,2,2,1,1]
[3,2,5,4,6,1,9,8,11,10,12,7]=>[3,3,2,2,1,1]
[3,2,5,4,6,1,10,9,11,8,12,7]=>[4,3,2,1,1,1]
[3,2,5,4,7,6,8,1,10,9,12,11]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,8,1,11,10,12,9]=>[3,3,2,2,1,1]
[3,2,5,4,7,6,9,8,10,1,12,11]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,9,8,11,10,12,1]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,10,9,11,8,12,1]=>[4,2,2,2,1,1]
[3,2,5,4,8,7,9,6,10,1,12,11]=>[4,2,2,2,1,1]
[3,2,5,4,8,7,9,6,11,10,12,1]=>[4,2,2,2,1,1]
[3,2,5,4,8,7,10,9,11,6,12,1]=>[4,2,2,2,1,1]
[3,2,5,4,9,8,10,7,11,6,12,1]=>[5,2,2,1,1,1]
[3,2,6,5,7,4,8,1,10,9,12,11]=>[4,2,2,2,1,1]
[3,2,6,5,7,4,8,1,11,10,12,9]=>[4,3,2,1,1,1]
[3,2,6,5,7,4,9,8,10,1,12,11]=>[4,2,2,2,1,1]
[3,2,6,5,7,4,9,8,11,10,12,1]=>[4,2,2,2,1,1]
[3,2,6,5,7,4,10,9,11,8,12,1]=>[4,3,2,1,1,1]
[3,2,6,5,8,7,9,4,10,1,12,11]=>[4,2,2,2,1,1]
[3,2,6,5,8,7,9,4,11,10,12,1]=>[4,2,2,2,1,1]
[3,2,6,5,8,7,10,9,11,4,12,1]=>[4,2,2,2,1,1]
[3,2,6,5,9,8,10,7,11,4,12,1]=>[5,2,2,1,1,1]
[3,2,7,6,8,5,9,4,10,1,12,11]=>[5,2,2,1,1,1]
[3,2,7,6,8,5,9,4,11,10,12,1]=>[5,2,2,1,1,1]
[3,2,7,6,8,5,10,9,11,4,12,1]=>[5,2,2,1,1,1]
[3,2,7,6,9,8,10,5,11,4,12,1]=>[5,2,2,1,1,1]
[3,2,8,7,9,6,10,5,11,4,12,1]=>[6,2,1,1,1,1]
[4,3,5,2,6,1,8,7,10,9,12,11]=>[4,2,2,2,1,1]
[4,3,5,2,6,1,8,7,11,10,12,9]=>[4,3,2,1,1,1]
[4,3,5,2,6,1,9,8,10,7,12,11]=>[4,3,2,1,1,1]
[4,3,5,2,6,1,9,8,11,10,12,7]=>[4,3,2,1,1,1]
[4,3,5,2,6,1,10,9,11,8,12,7]=>[4,4,1,1,1,1]
[4,3,5,2,7,6,8,1,10,9,12,11]=>[4,2,2,2,1,1]
[4,3,5,2,7,6,8,1,11,10,12,9]=>[4,3,2,1,1,1]
[4,3,5,2,7,6,9,8,10,1,12,11]=>[4,2,2,2,1,1]
[4,3,5,2,7,6,9,8,11,10,12,1]=>[4,2,2,2,1,1]
[4,3,5,2,7,6,10,9,11,8,12,1]=>[4,3,2,1,1,1]
[4,3,5,2,8,7,9,6,10,1,12,11]=>[4,3,2,1,1,1]
[4,3,5,2,8,7,9,6,11,10,12,1]=>[4,3,2,1,1,1]
[4,3,5,2,8,7,10,9,11,6,12,1]=>[4,3,2,1,1,1]
[4,3,5,2,9,8,10,7,11,6,12,1]=>[5,3,1,1,1,1]
[4,3,6,5,7,2,8,1,10,9,12,11]=>[4,2,2,2,1,1]
[4,3,6,5,7,2,8,1,11,10,12,9]=>[4,3,2,1,1,1]
[4,3,6,5,7,2,9,8,10,1,12,11]=>[4,2,2,2,1,1]
[4,3,6,5,7,2,9,8,11,10,12,1]=>[4,2,2,2,1,1]
[4,3,6,5,7,2,10,9,11,8,12,1]=>[4,3,2,1,1,1]
[4,3,6,5,8,7,9,2,10,1,12,11]=>[4,2,2,2,1,1]
[4,3,6,5,8,7,9,2,11,10,12,1]=>[4,2,2,2,1,1]
[4,3,6,5,8,7,10,9,11,2,12,1]=>[4,2,2,2,1,1]
[4,3,6,5,9,8,10,7,11,2,12,1]=>[5,2,2,1,1,1]
[4,3,7,6,8,5,9,2,10,1,12,11]=>[5,2,2,1,1,1]
[4,3,7,6,8,5,9,2,11,10,12,1]=>[5,2,2,1,1,1]
[4,3,7,6,8,5,10,9,11,2,12,1]=>[5,2,2,1,1,1]
[4,3,7,6,9,8,10,5,11,2,12,1]=>[5,2,2,1,1,1]
[4,3,8,7,9,6,10,5,11,2,12,1]=>[6,2,1,1,1,1]
[5,4,6,3,7,2,8,1,10,9,12,11]=>[5,2,2,1,1,1]
[5,4,6,3,7,2,8,1,11,10,12,9]=>[5,3,1,1,1,1]
[5,4,6,3,7,2,9,8,10,1,12,11]=>[5,2,2,1,1,1]
[5,4,6,3,7,2,9,8,11,10,12,1]=>[5,2,2,1,1,1]
[5,4,6,3,7,2,10,9,11,8,12,1]=>[5,3,1,1,1,1]
[5,4,6,3,8,7,9,2,10,1,12,11]=>[5,2,2,1,1,1]
[5,4,6,3,8,7,9,2,11,10,12,1]=>[5,2,2,1,1,1]
[5,4,6,3,8,7,10,9,11,2,12,1]=>[5,2,2,1,1,1]
[5,4,6,3,9,8,10,7,11,2,12,1]=>[5,3,1,1,1,1]
[5,4,7,6,8,3,9,2,10,1,12,11]=>[5,2,2,1,1,1]
[5,4,7,6,8,3,9,2,11,10,12,1]=>[5,2,2,1,1,1]
[5,4,7,6,8,3,10,9,11,2,12,1]=>[5,2,2,1,1,1]
[5,4,7,6,9,8,10,3,11,2,12,1]=>[5,2,2,1,1,1]
[5,4,8,7,9,6,10,3,11,2,12,1]=>[6,2,1,1,1,1]
[6,5,7,4,8,3,9,2,10,1,12,11]=>[6,2,1,1,1,1]
[6,5,7,4,8,3,9,2,11,10,12,1]=>[6,2,1,1,1,1]
[6,5,7,4,8,3,10,9,11,2,12,1]=>[6,2,1,1,1,1]
[6,5,7,4,9,8,10,3,11,2,12,1]=>[6,2,1,1,1,1]
[6,5,8,7,9,4,10,3,11,2,12,1]=>[6,2,1,1,1,1]
[7,6,8,5,9,4,10,3,11,2,12,1]=>[7,1,1,1,1,1]
[1,8,2,9,3,10,4,11,5,12,6,7]=>[2,2,2,2,2,1,1]
[1,8,2,9,3,10,4,11,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,3,10,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,3,10,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,3,10,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,10,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,10,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,2,9,10,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,2,9,10,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,2,3,10,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,9,2,3,10,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,3,10,11,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,3,10,11,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,3,10,11,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,2,10,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,9,2,10,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,10,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,9,2,10,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[1,8,9,2,10,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,10,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,10,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,10,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,2,10,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,2,3,4,11,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,3,4,11,12,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,2,3,11,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,3,11,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,3,11,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,2,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[1,8,9,10,2,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,3,4,5,12,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,3,4,12,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,3,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,11,2,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,8,9,10,11,12,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[8,1,2,9,3,10,4,11,5,12,6,7]=>[2,2,2,2,2,1,1]
[8,1,2,9,3,10,4,11,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,3,10,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,3,10,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,3,10,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,10,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,10,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,2,9,10,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,9,10,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,1,9,2,3,10,4,11,5,12,6,7]=>[2,2,2,2,2,1,1]
[8,1,9,2,3,10,4,11,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,3,10,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,3,10,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,3,10,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,2,10,3,4,11,5,12,6,7]=>[2,2,2,2,2,1,1]
[8,1,9,2,10,3,4,11,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,10,3,11,4,5,12,6,7]=>[2,2,2,2,2,1,1]
[8,1,9,2,10,3,11,4,12,5,6,7]=>[2,2,2,2,2,1,1]
[8,1,9,2,10,3,11,12,4,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,10,11,3,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,10,11,3,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,10,11,3,12,4,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,2,10,11,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,2,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,2,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,2,11,3,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,11,3,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,11,3,12,4,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,1,9,10,2,11,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,11,2,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,11,2,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,11,2,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,11,2,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,1,9,10,11,12,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,1,2,3,10,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,2,3,10,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,3,10,11,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,3,10,11,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,3,10,11,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,1,2,10,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,2,10,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,10,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,2,10,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,2,10,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,10,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,10,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,10,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,2,10,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,1,10,2,3,4,11,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,3,4,11,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,2,3,11,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,3,11,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,3,11,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,2,11,3,4,5,12,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,11,3,4,12,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,11,3,12,4,5,6,7]=>[2,2,2,2,1,1,1,1]
[8,9,1,10,2,11,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,11,2,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,11,2,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,11,2,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,11,2,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,1,10,11,12,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,1,2,3,4,11,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,3,4,11,12,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,1,2,3,11,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,3,11,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,3,11,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,1,2,11,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,11,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,11,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,2,11,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,1,11,2,3,4,5,12,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,11,2,3,4,12,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,11,2,3,12,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,11,2,12,3,4,5,6,7]=>[2,2,2,1,1,1,1,1,1]
[8,9,10,1,11,12,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,1,2,3,4,5,12,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,1,2,3,4,12,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,1,2,3,12,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,1,2,12,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,1,12,2,3,4,5,6,7]=>[2,2,1,1,1,1,1,1,1,1]
[8,9,10,11,12,1,2,3,4,5,6,7]=>[2,1,1,1,1,1,1,1,1,1,1]
[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,1,1,1,1]
[11,12,8,6,4,2,1,3,5,7,10,9]=>[6,2,1,1,1,1]
[12,9,10,6,4,2,1,3,5,8,7,11]=>[6,2,1,1,1,1]
[11,9,12,6,4,2,1,3,5,8,10,7]=>[6,2,1,1,1,1]
[10,11,12,6,4,2,1,3,5,9,8,7]=>[5,3,1,1,1,1]
[12,10,7,8,4,2,1,3,6,5,9,11]=>[6,2,1,1,1,1]
[11,12,7,8,4,2,1,3,6,5,10,9]=>[5,2,2,1,1,1]
[12,9,7,10,4,2,1,3,6,8,5,11]=>[6,2,1,1,1,1]
[11,9,7,12,4,2,1,3,6,8,10,5]=>[6,2,1,1,1,1]
[10,11,7,12,4,2,1,3,6,9,8,5]=>[5,3,1,1,1,1]
[12,8,9,10,4,2,1,3,7,6,5,11]=>[5,3,1,1,1,1]
[11,8,9,12,4,2,1,3,7,6,10,5]=>[5,3,1,1,1,1]
[10,8,11,12,4,2,1,3,7,9,6,5]=>[5,3,1,1,1,1]
[9,10,11,12,4,2,1,3,8,7,6,5]=>[5,3,1,1,1,1]
[12,10,8,5,6,2,1,4,3,7,9,11]=>[6,2,1,1,1,1]
[11,12,8,5,6,2,1,4,3,7,10,9]=>[5,2,2,1,1,1]
[12,9,10,5,6,2,1,4,3,8,7,11]=>[5,2,2,1,1,1]
[11,9,12,5,6,2,1,4,3,8,10,7]=>[5,2,2,1,1,1]
[10,11,12,5,6,2,1,4,3,9,8,7]=>[4,3,2,1,1,1]
[12,10,7,5,8,2,1,4,6,3,9,11]=>[6,2,1,1,1,1]
[11,12,7,5,8,2,1,4,6,3,10,9]=>[5,2,2,1,1,1]
[12,9,7,5,10,2,1,4,6,8,3,11]=>[6,2,1,1,1,1]
[11,9,7,5,12,2,1,4,6,8,10,3]=>[6,2,1,1,1,1]
[10,11,7,5,12,2,1,4,6,9,8,3]=>[5,3,1,1,1,1]
[12,8,9,5,10,2,1,4,7,6,3,11]=>[5,3,1,1,1,1]
[11,8,9,5,12,2,1,4,7,6,10,3]=>[5,3,1,1,1,1]
[10,8,11,5,12,2,1,4,7,9,6,3]=>[5,3,1,1,1,1]
[9,10,11,5,12,2,1,4,8,7,6,3]=>[5,3,1,1,1,1]
[12,10,6,7,8,2,1,5,4,3,9,11]=>[6,2,1,1,1,1]
[11,12,6,7,8,2,1,5,4,3,10,9]=>[5,2,2,1,1,1]
[12,9,6,7,10,2,1,5,4,8,3,11]=>[6,2,1,1,1,1]
[11,9,6,7,12,2,1,5,4,8,10,3]=>[6,2,1,1,1,1]
[10,11,6,7,12,2,1,5,4,9,8,3]=>[5,2,2,1,1,1]
[12,8,6,9,10,2,1,5,7,4,3,11]=>[6,2,1,1,1,1]
[11,8,6,9,12,2,1,5,7,4,10,3]=>[6,2,1,1,1,1]
[10,8,6,11,12,2,1,5,7,9,4,3]=>[6,2,1,1,1,1]
[9,10,6,11,12,2,1,5,8,7,4,3]=>[5,3,1,1,1,1]
[12,7,8,9,10,2,1,6,5,4,3,11]=>[6,2,1,1,1,1]
[11,7,8,9,12,2,1,6,5,4,10,3]=>[6,2,1,1,1,1]
[10,7,8,11,12,2,1,6,5,9,4,3]=>[6,2,1,1,1,1]
[9,7,10,11,12,2,1,6,8,5,4,3]=>[6,2,1,1,1,1]
[8,9,10,11,12,2,1,7,6,5,4,3]=>[6,2,1,1,1,1]
[12,10,8,6,3,4,2,1,5,7,9,11]=>[7,1,1,1,1,1]
[11,12,8,6,3,4,2,1,5,7,10,9]=>[6,2,1,1,1,1]
[12,9,10,6,3,4,2,1,5,8,7,11]=>[6,2,1,1,1,1]
[11,9,12,6,3,4,2,1,5,8,10,7]=>[6,2,1,1,1,1]
[10,11,12,6,3,4,2,1,5,9,8,7]=>[5,3,1,1,1,1]
[12,10,7,8,3,4,2,1,6,5,9,11]=>[6,2,1,1,1,1]
[11,12,7,8,3,4,2,1,6,5,10,9]=>[5,2,2,1,1,1]
[12,9,7,10,3,4,2,1,6,8,5,11]=>[6,2,1,1,1,1]
[11,9,7,12,3,4,2,1,6,8,10,5]=>[6,2,1,1,1,1]
[10,11,7,12,3,4,2,1,6,9,8,5]=>[5,3,1,1,1,1]
[12,8,9,10,3,4,2,1,7,6,5,11]=>[5,3,1,1,1,1]
[11,8,9,12,3,4,2,1,7,6,10,5]=>[5,3,1,1,1,1]
[10,8,11,12,3,4,2,1,7,9,6,5]=>[5,3,1,1,1,1]
[9,10,11,12,3,4,2,1,8,7,6,5]=>[5,3,1,1,1,1]
[12,10,8,5,3,6,2,4,1,7,9,11]=>[7,1,1,1,1,1]
[11,12,8,5,3,6,2,4,1,7,10,9]=>[6,2,1,1,1,1]
[12,9,10,5,3,6,2,4,1,8,7,11]=>[6,2,1,1,1,1]
[11,9,12,5,3,6,2,4,1,8,10,7]=>[6,2,1,1,1,1]
[10,11,12,5,3,6,2,4,1,9,8,7]=>[5,3,1,1,1,1]
[12,10,7,5,3,8,2,4,6,1,9,11]=>[7,1,1,1,1,1]
[11,12,7,5,3,8,2,4,6,1,10,9]=>[6,2,1,1,1,1]
[12,9,7,5,3,10,2,4,6,8,1,11]=>[7,1,1,1,1,1]
[11,9,7,5,3,12,2,4,6,8,10,1]=>[7,1,1,1,1,1]
[10,11,7,5,3,12,2,4,6,9,8,1]=>[6,2,1,1,1,1]
[12,8,9,5,3,10,2,4,7,6,1,11]=>[6,2,1,1,1,1]
[11,8,9,5,3,12,2,4,7,6,10,1]=>[6,2,1,1,1,1]
[10,8,11,5,3,12,2,4,7,9,6,1]=>[6,2,1,1,1,1]
[9,10,11,5,3,12,2,4,8,7,6,1]=>[5,3,1,1,1,1]
[12,10,6,7,3,8,2,5,4,1,9,11]=>[6,2,1,1,1,1]
[11,12,6,7,3,8,2,5,4,1,10,9]=>[5,2,2,1,1,1]
[12,9,6,7,3,10,2,5,4,8,1,11]=>[6,2,1,1,1,1]
[11,9,6,7,3,12,2,5,4,8,10,1]=>[6,2,1,1,1,1]
[10,11,6,7,3,12,2,5,4,9,8,1]=>[5,2,2,1,1,1]
[12,8,6,9,3,10,2,5,7,4,1,11]=>[6,2,1,1,1,1]
[11,8,6,9,3,12,2,5,7,4,10,1]=>[6,2,1,1,1,1]
[10,8,6,11,3,12,2,5,7,9,4,1]=>[6,2,1,1,1,1]
[9,10,6,11,3,12,2,5,8,7,4,1]=>[5,3,1,1,1,1]
[12,7,8,9,3,10,2,6,5,4,1,11]=>[6,2,1,1,1,1]
[11,7,8,9,3,12,2,6,5,4,10,1]=>[6,2,1,1,1,1]
[10,7,8,11,3,12,2,6,5,9,4,1]=>[6,2,1,1,1,1]
[9,7,10,11,3,12,2,6,8,5,4,1]=>[6,2,1,1,1,1]
[8,9,10,11,3,12,2,7,6,5,4,1]=>[6,2,1,1,1,1]
[12,10,8,4,5,6,3,2,1,7,9,11]=>[7,1,1,1,1,1]
[11,12,8,4,5,6,3,2,1,7,10,9]=>[6,2,1,1,1,1]
[12,9,10,4,5,6,3,2,1,8,7,11]=>[6,2,1,1,1,1]
[11,9,12,4,5,6,3,2,1,8,10,7]=>[6,2,1,1,1,1]
[10,11,12,4,5,6,3,2,1,9,8,7]=>[5,3,1,1,1,1]
[12,10,7,4,5,8,3,2,6,1,9,11]=>[7,1,1,1,1,1]
[11,12,7,4,5,8,3,2,6,1,10,9]=>[6,2,1,1,1,1]
[12,9,7,4,5,10,3,2,6,8,1,11]=>[7,1,1,1,1,1]
[11,9,7,4,5,12,3,2,6,8,10,1]=>[7,1,1,1,1,1]
[10,11,7,4,5,12,3,2,6,9,8,1]=>[6,2,1,1,1,1]
[12,8,9,4,5,10,3,2,7,6,1,11]=>[6,2,1,1,1,1]
[11,8,9,4,5,12,3,2,7,6,10,1]=>[6,2,1,1,1,1]
[10,8,11,4,5,12,3,2,7,9,6,1]=>[6,2,1,1,1,1]
[9,10,11,4,5,12,3,2,8,7,6,1]=>[5,3,1,1,1,1]
[12,10,6,4,7,8,3,5,2,1,9,11]=>[7,1,1,1,1,1]
[11,12,6,4,7,8,3,5,2,1,10,9]=>[6,2,1,1,1,1]
[12,9,6,4,7,10,3,5,2,8,1,11]=>[7,1,1,1,1,1]
[11,9,6,4,7,12,3,5,2,8,10,1]=>[7,1,1,1,1,1]
[10,11,6,4,7,12,3,5,2,9,8,1]=>[6,2,1,1,1,1]
[12,8,6,4,9,10,3,5,7,2,1,11]=>[7,1,1,1,1,1]
[11,8,6,4,9,12,3,5,7,2,10,1]=>[7,1,1,1,1,1]
[10,8,6,4,11,12,3,5,7,9,2,1]=>[7,1,1,1,1,1]
[9,10,6,4,11,12,3,5,8,7,2,1]=>[6,2,1,1,1,1]
[12,7,8,4,9,10,3,6,5,2,1,11]=>[6,2,1,1,1,1]
[11,7,8,4,9,12,3,6,5,2,10,1]=>[6,2,1,1,1,1]
[10,7,8,4,11,12,3,6,5,9,2,1]=>[6,2,1,1,1,1]
[9,7,10,4,11,12,3,6,8,5,2,1]=>[6,2,1,1,1,1]
[8,9,10,4,11,12,3,7,6,5,2,1]=>[6,2,1,1,1,1]
[12,10,5,6,7,8,4,3,2,1,9,11]=>[7,1,1,1,1,1]
[11,12,5,6,7,8,4,3,2,1,10,9]=>[6,2,1,1,1,1]
[12,9,5,6,7,10,4,3,2,8,1,11]=>[7,1,1,1,1,1]
[11,9,5,6,7,12,4,3,2,8,10,1]=>[7,1,1,1,1,1]
[10,11,5,6,7,12,4,3,2,9,8,1]=>[6,2,1,1,1,1]
[12,8,5,6,9,10,4,3,7,2,1,11]=>[7,1,1,1,1,1]
[11,8,5,6,9,12,4,3,7,2,10,1]=>[7,1,1,1,1,1]
[10,8,5,6,11,12,4,3,7,9,2,1]=>[7,1,1,1,1,1]
[9,10,5,6,11,12,4,3,8,7,2,1]=>[6,2,1,1,1,1]
[12,7,5,8,9,10,4,6,3,2,1,11]=>[7,1,1,1,1,1]
[11,7,5,8,9,12,4,6,3,2,10,1]=>[7,1,1,1,1,1]
[10,7,5,8,11,12,4,6,3,9,2,1]=>[7,1,1,1,1,1]
[9,7,5,10,11,12,4,6,8,3,2,1]=>[7,1,1,1,1,1]
[8,9,5,10,11,12,4,7,6,3,2,1]=>[6,2,1,1,1,1]
[12,6,7,8,9,10,5,4,3,2,1,11]=>[7,1,1,1,1,1]
[11,6,7,8,9,12,5,4,3,2,10,1]=>[7,1,1,1,1,1]
[10,6,7,8,11,12,5,4,3,9,2,1]=>[7,1,1,1,1,1]
[9,6,7,10,11,12,5,4,8,3,2,1]=>[7,1,1,1,1,1]
[8,6,9,10,11,12,5,7,4,3,2,1]=>[7,1,1,1,1,1]
[2,3,4,5,6,7,8,9,12,11,1,10]=>[3,1,1,1,1,1,1,1,1,1]
[12,11,10,8,6,4,2,1,3,5,7,9]=>[8,1,1,1,1]
[12,10,9,8,6,4,2,1,3,5,7,11]=>[8,1,1,1,1]
[12,9,11,8,6,4,2,1,3,5,10,7]=>[7,2,1,1,1]
[12,11,10,9,8,6,4,2,1,3,5,7]=>[9,1,1,1]
[12,10,8,7,6,4,2,1,3,5,9,11]=>[8,1,1,1,1]
[12,11,10,8,7,6,4,2,1,3,5,9]=>[9,1,1,1]
[12,10,7,9,6,4,2,1,3,8,5,11]=>[7,2,1,1,1]
[12,7,11,9,6,4,2,1,3,8,10,5]=>[7,2,1,1,1]
[12,11,10,7,9,6,4,2,1,3,8,5]=>[8,2,1,1]
[12,10,9,8,7,6,4,2,1,3,5,11]=>[9,1,1,1]
[12,9,11,8,7,6,4,2,1,3,10,5]=>[8,2,1,1]
[12,8,11,10,7,9,4,2,1,3,6,5]=>[7,2,1,1,1]
[12,11,10,9,8,7,6,4,2,1,3,5]=>[10,1,1]
[12,10,8,6,5,4,2,1,3,7,9,11]=>[8,1,1,1,1]
[12,11,10,8,6,5,4,2,1,3,7,9]=>[9,1,1,1]
[12,10,9,8,6,5,4,2,1,3,7,11]=>[9,1,1,1]
[12,9,11,8,6,5,4,2,1,3,10,7]=>[8,2,1,1]
[12,11,10,9,8,6,5,4,2,1,3,7]=>[10,1,1]
[12,10,8,5,7,4,2,1,6,3,9,11]=>[7,2,1,1,1]
[12,11,10,8,5,7,4,2,1,6,3,9]=>[8,2,1,1]
[12,10,5,9,7,4,2,1,6,8,3,11]=>[7,2,1,1,1]
[12,5,11,9,7,4,2,1,6,8,10,3]=>[7,2,1,1,1]
[12,11,10,5,9,7,4,2,1,6,8,3]=>[8,2,1,1]
[12,10,9,8,5,7,4,2,1,6,3,11]=>[8,2,1,1]
[12,9,11,8,5,7,4,2,1,6,10,3]=>[7,2,1,1,1]
[12,11,5,10,8,7,4,2,1,9,6,3]=>[8,3,1]
[12,11,10,9,8,5,7,4,2,1,6,3]=>[9,2,1]
[12,10,8,7,6,5,4,2,1,3,9,11]=>[9,1,1,1]
[12,11,10,8,7,6,5,4,2,1,3,9]=>[10,1,1]
[12,10,7,9,6,5,4,2,1,8,3,11]=>[8,2,1,1]
[12,7,11,9,6,5,4,2,1,8,10,3]=>[8,2,1,1]
[12,11,10,7,9,6,5,4,2,1,8,3]=>[9,2,1]
[12,10,6,9,8,5,7,2,1,4,3,11]=>[7,2,1,1,1]
[12,6,11,9,8,5,7,2,1,4,10,3]=>[7,2,1,1,1]
[12,6,11,8,10,5,7,2,1,9,4,3]=>[6,3,1,1,1]
[12,11,10,6,9,8,5,7,2,1,4,3]=>[8,2,1,1]
[12,10,9,8,7,6,5,4,2,1,3,11]=>[10,1,1]
[12,9,11,8,7,6,5,4,2,1,10,3]=>[9,2,1]
[12,8,11,10,7,6,5,9,2,1,4,3]=>[8,2,1,1]
[12,7,11,10,9,6,8,5,2,1,4,3]=>[8,2,1,1]
[12,11,10,9,8,7,6,5,4,2,1,3]=>[11,1]
[12,10,8,6,4,3,2,1,5,7,9,11]=>[8,1,1,1,1]
[12,11,10,8,6,4,3,2,1,5,7,9]=>[9,1,1,1]
[12,10,9,8,6,4,3,2,1,5,7,11]=>[9,1,1,1]
[12,9,11,8,6,4,3,2,1,5,10,7]=>[8,2,1,1]
[12,11,10,9,8,6,4,3,2,1,5,7]=>[10,1,1]
[12,10,8,7,6,4,3,2,1,5,9,11]=>[9,1,1,1]
[12,11,10,8,7,6,4,3,2,1,5,9]=>[10,1,1]
[12,10,7,9,6,4,3,2,1,8,5,11]=>[8,2,1,1]
[12,7,11,9,6,4,3,2,1,8,10,5]=>[8,2,1,1]
[12,11,10,7,9,6,4,3,2,1,8,5]=>[9,2,1]
[12,10,9,8,7,6,4,3,2,1,5,11]=>[10,1,1]
[12,9,11,8,7,6,4,3,2,1,10,5]=>[9,2,1]
[12,8,11,10,7,9,4,3,2,1,6,5]=>[8,2,1,1]
[12,11,10,9,8,7,6,4,3,2,1,5]=>[11,1]
[12,10,8,6,3,5,2,4,1,7,9,11]=>[7,1,1,1,1,1]
[12,11,10,8,6,3,5,2,4,1,7,9]=>[8,1,1,1,1]
[12,10,9,8,6,3,5,2,4,1,7,11]=>[8,1,1,1,1]
[12,9,11,8,6,3,5,2,4,1,10,7]=>[7,2,1,1,1]
[12,11,10,9,8,6,3,5,2,4,1,7]=>[9,1,1,1]
[12,10,8,3,7,5,2,4,6,1,9,11]=>[7,1,1,1,1,1]
[12,11,10,8,3,7,5,2,4,6,1,9]=>[8,1,1,1,1]
[12,10,3,9,7,5,2,4,6,8,1,11]=>[7,1,1,1,1,1]
[12,3,11,9,7,5,2,4,6,8,10,1]=>[7,1,1,1,1,1]
[12,11,10,3,9,7,5,2,4,6,8,1]=>[8,1,1,1,1]
[12,10,9,8,3,7,5,2,4,6,1,11]=>[8,1,1,1,1]
[12,9,11,8,3,7,5,2,4,6,10,1]=>[7,1,1,1,1,1]
[12,11,3,10,8,7,5,2,4,9,6,1]=>[8,2,1,1]
[12,11,10,9,8,3,7,5,2,4,6,1]=>[9,1,1,1]
[12,10,8,7,6,3,5,2,4,1,9,11]=>[8,1,1,1,1]
[12,11,10,8,7,6,3,5,2,4,1,9]=>[9,1,1,1]
[12,10,7,9,6,3,5,2,4,8,1,11]=>[7,1,1,1,1,1]
[12,7,11,9,6,3,5,2,4,8,10,1]=>[7,1,1,1,1,1]
[12,11,10,7,9,6,3,5,2,4,8,1]=>[8,1,1,1,1]
[12,10,9,3,8,6,5,2,7,4,1,11]=>[8,2,1,1]
[12,9,11,3,8,6,5,2,7,4,10,1]=>[7,2,1,1,1]
[12,11,3,8,10,6,5,2,7,9,4,1]=>[7,2,1,1,1]
[12,11,10,9,3,8,6,5,2,7,4,1]=>[9,2,1]
[12,10,9,8,7,6,3,5,2,4,1,11]=>[9,1,1,1]
[12,9,11,8,7,6,3,5,2,4,10,1]=>[8,1,1,1,1]
[12,8,11,10,7,6,3,5,2,9,4,1]=>[8,2,1,1]
[12,11,10,3,9,7,6,8,2,5,4,1]=>[9,1,1,1]
[12,11,10,9,8,7,6,3,5,2,4,1]=>[10,1,1]
[12,10,8,6,5,4,3,2,1,7,9,11]=>[9,1,1,1]
[12,11,10,8,6,5,4,3,2,1,7,9]=>[10,1,1]
[12,10,9,8,6,5,4,3,2,1,7,11]=>[10,1,1]
[12,9,11,8,6,5,4,3,2,1,10,7]=>[9,2,1]
[12,11,10,9,8,6,5,4,3,2,1,7]=>[11,1]
[12,10,8,5,7,4,3,2,6,1,9,11]=>[8,1,1,1,1]
[12,11,10,8,5,7,4,3,2,6,1,9]=>[9,1,1,1]
[12,10,5,9,7,4,3,2,6,8,1,11]=>[8,1,1,1,1]
[12,5,11,9,7,4,3,2,6,8,10,1]=>[8,1,1,1,1]
[12,11,10,5,9,7,4,3,2,6,8,1]=>[9,1,1,1]
[12,10,9,8,5,7,4,3,2,6,1,11]=>[9,1,1,1]
[12,9,11,8,5,7,4,3,2,6,10,1]=>[8,1,1,1,1]
[12,11,5,10,8,7,4,3,2,9,6,1]=>[9,2,1]
[12,11,10,9,8,5,7,4,3,2,6,1]=>[10,1,1]
[12,10,8,4,7,6,3,5,2,1,9,11]=>[8,1,1,1,1]
[12,11,10,8,4,7,6,3,5,2,1,9]=>[9,1,1,1]
[12,10,4,9,7,6,3,5,2,8,1,11]=>[8,1,1,1,1]
[12,4,11,9,7,6,3,5,2,8,10,1]=>[8,1,1,1,1]
[12,11,10,4,9,7,6,3,5,2,8,1]=>[9,1,1,1]
[12,10,4,9,6,8,3,5,7,2,1,11]=>[7,1,1,1,1,1]
[12,4,11,9,6,8,3,5,7,2,10,1]=>[7,1,1,1,1,1]
[12,4,11,6,10,8,3,5,7,9,2,1]=>[7,1,1,1,1,1]
[12,11,10,4,9,6,8,3,5,7,2,1]=>[8,1,1,1,1]
[12,10,9,8,4,7,6,3,5,2,1,11]=>[9,1,1,1]
[12,9,11,8,4,7,6,3,5,2,10,1]=>[8,1,1,1,1]
[12,8,11,10,4,7,6,3,5,9,2,1]=>[8,1,1,1,1]
[12,11,4,10,7,9,6,3,8,5,2,1]=>[8,2,1,1]
[12,11,10,9,8,4,7,6,3,5,2,1]=>[10,1,1]
[12,10,8,7,6,5,4,3,2,1,9,11]=>[10,1,1]
[12,11,10,8,7,6,5,4,3,2,1,9]=>[11,1]
[12,10,7,9,6,5,4,3,2,8,1,11]=>[9,1,1,1]
[12,7,11,9,6,5,4,3,2,8,10,1]=>[9,1,1,1]
[12,11,10,7,9,6,5,4,3,2,8,1]=>[10,1,1]
[12,10,6,9,8,5,4,3,7,2,1,11]=>[9,1,1,1]
[12,6,11,9,8,5,4,3,7,2,10,1]=>[9,1,1,1]
[12,6,11,8,10,5,4,3,7,9,2,1]=>[8,1,1,1,1]
[12,11,10,6,9,8,5,4,3,7,2,1]=>[10,1,1]
[12,10,5,9,8,7,4,6,3,2,1,11]=>[9,1,1,1]
[12,5,11,9,8,7,4,6,3,2,10,1]=>[9,1,1,1]
[12,5,11,8,10,7,4,6,3,9,2,1]=>[8,1,1,1,1]
[12,5,11,7,10,9,4,6,8,3,2,1]=>[8,1,1,1,1]
[12,11,10,5,9,8,7,4,6,3,2,1]=>[10,1,1]
[12,9,11,8,7,6,5,4,3,2,10,1]=>[10,1,1]
[12,8,11,10,7,6,5,4,3,9,2,1]=>[10,1,1]
[12,7,11,10,9,6,5,4,8,3,2,1]=>[10,1,1]
[12,6,11,10,9,8,5,7,4,3,2,1]=>[10,1,1]
[8,9,10,11,7,1,2,3,4,5,12,6]=>[3,2,1,1,1,1,1,1,1]
[2,9,10,11,12,8,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[11,12,2,4,6,8,10,1,3,5,7,9]=>[3,1,1,1,1,1,1,1,1,1]
[9,10,2,4,6,8,12,1,3,5,7,11]=>[3,1,1,1,1,1,1,1,1,1]
[11,9,12,2,4,6,8,10,1,3,5,7]=>[4,1,1,1,1,1,1,1,1]
[10,11,12,9,2,4,6,8,1,3,5,7]=>[4,1,1,1,1,1,1,1,1]
[7,8,2,4,6,10,12,1,3,5,9,11]=>[3,1,1,1,1,1,1,1,1,1]
[7,8,11,12,2,4,6,10,1,3,5,9]=>[3,1,1,1,1,1,1,1,1,1]
[9,7,10,2,4,6,8,12,1,3,5,11]=>[4,1,1,1,1,1,1,1,1]
[9,11,7,12,2,4,6,8,10,1,3,5]=>[4,1,1,1,1,1,1,1,1]
[7,10,11,12,9,2,4,6,8,1,3,5]=>[4,1,1,1,1,1,1,1,1]
[8,9,10,7,2,4,6,12,1,3,5,11]=>[4,1,1,1,1,1,1,1,1]
[11,8,9,7,12,2,4,6,10,1,3,5]=>[5,1,1,1,1,1,1,1]
[10,11,8,12,7,9,2,4,6,1,3,5]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,8,7,2,4,6,1,3,5]=>[5,1,1,1,1,1,1,1]
[5,6,2,4,8,10,12,1,3,7,9,11]=>[3,1,1,1,1,1,1,1,1,1]
[5,6,11,12,2,4,8,10,1,3,7,9]=>[3,1,1,1,1,1,1,1,1,1]
[5,6,9,10,2,4,8,12,1,3,7,11]=>[3,1,1,1,1,1,1,1,1,1]
[11,5,6,9,12,2,4,8,10,1,3,7]=>[4,1,1,1,1,1,1,1,1]
[10,11,12,5,6,9,2,4,8,1,3,7]=>[4,1,1,1,1,1,1,1,1]
[7,5,8,2,4,6,10,12,1,3,9,11]=>[4,1,1,1,1,1,1,1,1]
[7,5,8,11,12,2,4,6,10,1,3,9]=>[4,1,1,1,1,1,1,1,1]
[7,9,5,10,2,4,6,8,12,1,3,11]=>[4,1,1,1,1,1,1,1,1]
[7,9,11,5,12,2,4,6,8,10,1,3]=>[4,1,1,1,1,1,1,1,1]
[10,7,11,12,5,9,2,4,6,8,1,3]=>[5,1,1,1,1,1,1,1]
[5,8,9,10,7,2,4,6,12,1,3,11]=>[4,1,1,1,1,1,1,1,1]
[11,5,8,9,7,12,2,4,6,10,1,3]=>[5,1,1,1,1,1,1,1]
[8,10,5,11,12,7,9,2,4,6,1,3]=>[4,2,1,1,1,1,1,1]
[9,10,11,12,5,8,7,2,4,6,1,3]=>[5,1,1,1,1,1,1,1]
[6,7,8,5,2,4,10,12,1,3,9,11]=>[4,1,1,1,1,1,1,1,1]
[6,7,8,5,11,12,2,4,10,1,3,9]=>[4,1,1,1,1,1,1,1,1]
[9,6,7,5,10,2,4,8,12,1,3,11]=>[5,1,1,1,1,1,1,1]
[9,6,7,11,5,12,2,4,8,10,1,3]=>[5,1,1,1,1,1,1,1]
[6,10,7,11,12,5,9,2,4,8,1,3]=>[5,1,1,1,1,1,1,1]
[8,9,6,10,5,7,2,4,12,1,3,11]=>[5,1,1,1,1,1,1,1]
[8,9,11,6,5,7,12,2,4,10,1,3]=>[5,1,1,1,1,1,1,1]
[10,8,11,6,12,5,7,9,2,4,1,3]=>[6,1,1,1,1,1,1]
[9,6,10,11,12,8,5,7,2,4,1,3]=>[5,2,1,1,1,1,1]
[7,8,9,10,6,5,2,4,12,1,3,11]=>[5,1,1,1,1,1,1,1]
[11,7,8,9,6,5,12,2,4,10,1,3]=>[6,1,1,1,1,1,1]
[10,11,7,8,6,12,5,9,2,4,1,3]=>[6,1,1,1,1,1,1]
[9,10,11,7,12,6,8,5,2,4,1,3]=>[6,1,1,1,1,1,1]
[8,9,10,11,12,7,6,5,2,4,1,3]=>[6,1,1,1,1,1,1]
[3,4,2,6,8,10,12,1,5,7,9,11]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,11,12,2,6,8,10,1,5,7,9]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,9,10,2,6,8,12,1,5,7,11]=>[3,1,1,1,1,1,1,1,1,1]
[11,3,4,9,12,2,6,8,10,1,5,7]=>[4,1,1,1,1,1,1,1,1]
[10,11,12,3,4,9,2,6,8,1,5,7]=>[4,1,1,1,1,1,1,1,1]
[3,4,7,8,2,6,10,12,1,5,9,11]=>[3,1,1,1,1,1,1,1,1,1]
[3,4,7,8,11,12,2,6,10,1,5,9]=>[3,1,1,1,1,1,1,1,1,1]
[9,3,4,7,10,2,6,8,12,1,5,11]=>[4,1,1,1,1,1,1,1,1]
[9,11,3,4,7,12,2,6,8,10,1,5]=>[4,1,1,1,1,1,1,1,1]
[3,10,11,12,4,7,9,2,6,8,1,5]=>[4,1,1,1,1,1,1,1,1]
[8,9,10,3,4,7,2,6,12,1,5,11]=>[4,1,1,1,1,1,1,1,1]
[11,8,9,3,4,7,12,2,6,10,1,5]=>[5,1,1,1,1,1,1,1]
[10,11,8,12,3,4,7,9,2,6,1,5]=>[5,1,1,1,1,1,1,1]
[9,10,11,12,8,3,4,7,2,6,1,5]=>[5,1,1,1,1,1,1,1]
[5,3,6,2,4,8,10,12,1,7,9,11]=>[4,1,1,1,1,1,1,1,1]
[5,3,6,11,12,2,4,8,10,1,7,9]=>[4,1,1,1,1,1,1,1,1]
[5,3,6,9,10,2,4,8,12,1,7,11]=>[4,1,1,1,1,1,1,1,1]
[5,11,3,6,9,12,2,4,8,10,1,7]=>[4,1,1,1,1,1,1,1,1]
[5,10,11,12,3,6,9,2,4,8,1,7]=>[4,1,1,1,1,1,1,1,1]
[5,7,3,8,2,4,6,10,12,1,9,11]=>[4,1,1,1,1,1,1,1,1]
[5,7,3,8,11,12,2,4,6,10,1,9]=>[4,1,1,1,1,1,1,1,1]
[5,7,9,3,10,2,4,6,8,12,1,11]=>[4,1,1,1,1,1,1,1,1]
[5,7,9,11,3,12,2,4,6,8,10,1]=>[4,1,1,1,1,1,1,1,1]
[10,5,7,11,12,3,9,2,4,6,8,1]=>[5,1,1,1,1,1,1,1]
[8,5,9,10,3,7,2,4,6,12,1,11]=>[5,1,1,1,1,1,1,1]
[8,11,5,9,3,7,12,2,4,6,10,1]=>[5,1,1,1,1,1,1,1]
[8,10,11,5,12,3,7,9,2,4,6,1]=>[5,1,1,1,1,1,1,1]
[5,9,10,11,12,8,3,7,2,4,6,1]=>[5,1,1,1,1,1,1,1]
[3,6,7,8,5,2,4,10,12,1,9,11]=>[4,1,1,1,1,1,1,1,1]
[3,6,7,8,5,11,12,2,4,10,1,9]=>[4,1,1,1,1,1,1,1,1]
[9,3,6,7,5,10,2,4,8,12,1,11]=>[5,1,1,1,1,1,1,1]
[9,3,6,7,11,5,12,2,4,8,10,1]=>[5,1,1,1,1,1,1,1]
[6,10,3,7,11,12,5,9,2,4,8,1]=>[5,1,1,1,1,1,1,1]
[6,8,3,9,10,5,7,2,4,12,1,11]=>[4,2,1,1,1,1,1,1]
[6,8,9,3,11,5,7,12,2,4,10,1]=>[4,2,1,1,1,1,1,1]
[10,6,8,3,11,12,5,7,9,2,4,1]=>[5,2,1,1,1,1,1]
[9,6,10,11,12,3,8,5,7,2,4,1]=>[5,2,1,1,1,1,1]
[7,8,9,10,3,6,5,2,4,12,1,11]=>[5,1,1,1,1,1,1,1]
[11,7,8,9,3,6,5,12,2,4,10,1]=>[6,1,1,1,1,1,1]
[10,11,7,8,3,6,12,5,9,2,4,1]=>[6,1,1,1,1,1,1]
[9,10,11,7,12,3,6,8,5,2,4,1]=>[6,1,1,1,1,1,1]
[8,9,10,11,12,7,3,6,5,2,4,1]=>[6,1,1,1,1,1,1]
[4,5,6,3,2,8,10,12,1,7,9,11]=>[4,1,1,1,1,1,1,1,1]
[4,5,6,3,11,12,2,8,10,1,7,9]=>[4,1,1,1,1,1,1,1,1]
[4,5,6,3,9,10,2,8,12,1,7,11]=>[4,1,1,1,1,1,1,1,1]
[4,5,6,11,3,9,12,2,8,10,1,7]=>[4,1,1,1,1,1,1,1,1]
[4,5,6,10,11,12,3,9,2,8,1,7]=>[4,1,1,1,1,1,1,1,1]
[7,4,5,3,8,2,6,10,12,1,9,11]=>[5,1,1,1,1,1,1,1]
[7,4,5,3,8,11,12,2,6,10,1,9]=>[5,1,1,1,1,1,1,1]
[7,4,5,9,3,10,2,6,8,12,1,11]=>[5,1,1,1,1,1,1,1]
[7,4,5,9,11,3,12,2,6,8,10,1]=>[5,1,1,1,1,1,1,1]
[7,10,4,5,11,12,3,9,2,6,8,1]=>[5,1,1,1,1,1,1,1]
[4,8,5,9,10,3,7,2,6,12,1,11]=>[5,1,1,1,1,1,1,1]
[4,8,11,5,9,3,7,12,2,6,10,1]=>[5,1,1,1,1,1,1,1]
[4,8,10,11,5,12,3,7,9,2,6,1]=>[5,1,1,1,1,1,1,1]
[4,5,9,10,11,12,8,3,7,2,6,1]=>[5,1,1,1,1,1,1,1]
[6,7,4,8,3,5,2,10,12,1,9,11]=>[5,1,1,1,1,1,1,1]
[6,7,4,8,3,5,11,12,2,10,1,9]=>[5,1,1,1,1,1,1,1]
[6,7,9,4,3,5,10,2,8,12,1,11]=>[5,1,1,1,1,1,1,1]
[6,7,9,4,11,3,5,12,2,8,10,1]=>[5,1,1,1,1,1,1,1]
[10,6,7,4,11,12,3,5,9,2,8,1]=>[6,1,1,1,1,1,1]
[8,6,9,4,10,3,5,7,2,12,1,11]=>[6,1,1,1,1,1,1]
[8,6,9,11,4,3,5,7,12,2,10,1]=>[6,1,1,1,1,1,1]
[8,10,6,11,4,12,3,5,7,9,2,1]=>[6,1,1,1,1,1,1]
[6,9,4,10,11,12,8,3,5,7,2,1]=>[5,2,1,1,1,1,1]
[7,4,8,9,10,6,3,5,2,12,1,11]=>[5,2,1,1,1,1,1]
[7,11,4,8,9,6,3,5,12,2,10,1]=>[6,1,1,1,1,1,1]
[7,8,10,4,11,6,12,3,5,9,2,1]=>[5,2,1,1,1,1,1]
[9,7,10,4,11,12,6,8,3,5,2,1]=>[6,2,1,1,1,1]
[4,8,9,10,11,12,7,6,3,5,2,1]=>[6,1,1,1,1,1,1]
[5,6,7,8,4,3,2,10,12,1,9,11]=>[5,1,1,1,1,1,1,1]
[5,6,7,8,4,3,11,12,2,10,1,9]=>[5,1,1,1,1,1,1,1]
[9,5,6,7,4,3,10,2,8,12,1,11]=>[6,1,1,1,1,1,1]
[9,5,6,7,4,11,3,12,2,8,10,1]=>[6,1,1,1,1,1,1]
[5,10,6,7,4,11,12,3,9,2,8,1]=>[6,1,1,1,1,1,1]
[8,9,5,6,4,10,3,7,2,12,1,11]=>[6,1,1,1,1,1,1]
[8,9,5,6,11,4,3,7,12,2,10,1]=>[6,1,1,1,1,1,1]
[10,8,5,6,11,4,12,3,7,9,2,1]=>[7,1,1,1,1,1]
[9,5,10,6,11,12,4,8,3,7,2,1]=>[6,2,1,1,1,1]
[7,8,9,5,10,4,6,3,2,12,1,11]=>[6,1,1,1,1,1,1]
[7,8,9,11,5,4,6,3,12,2,10,1]=>[6,1,1,1,1,1,1]
[10,7,8,11,5,4,6,12,3,9,2,1]=>[7,1,1,1,1,1]
[9,10,7,11,5,12,4,6,8,3,2,1]=>[7,1,1,1,1,1]
[8,9,5,10,11,12,7,4,6,3,2,1]=>[6,2,1,1,1,1]
[6,7,8,9,10,5,4,3,2,12,1,11]=>[6,1,1,1,1,1,1]
[11,6,7,8,9,5,4,3,12,2,10,1]=>[7,1,1,1,1,1]
[10,11,6,7,8,5,4,12,3,9,2,1]=>[7,1,1,1,1,1]
[9,10,11,6,7,5,12,4,8,3,2,1]=>[7,1,1,1,1,1]
[8,9,10,11,6,12,5,7,4,3,2,1]=>[7,1,1,1,1,1]
[6,5,2,1,4,3,12,11,8,7,10,9]=>[4,4,2,2]
[2,1,4,3,6,5,8,7,9,11,12,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,7,9,10,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,7,9,8,11,12,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,7,8,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,7,8,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,5,7,8,6,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,7,6,9,10,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,5,7,6,9,8,11,12,10]=>[2,2,2,2,2,1,1]
[2,1,4,3,5,7,6,8,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,6,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,6,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,6,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,5,6,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,5,6,4,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,3,5,6,4,8,7,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,6,4,7,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,6,4,7,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,6,4,7,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,5,4,7,8,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,3,5,4,7,8,6,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,4,7,6,9,10,8,12,11]=>[2,2,2,2,2,1,1]
[2,1,3,5,4,7,6,9,8,11,12,10]=>[2,2,2,2,2,1,1]
[2,1,3,5,4,7,6,8,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,4,6,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,4,6,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,4,6,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,3,5,4,6,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,6,7,8,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,7,8,5,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,6,7,5,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,7,5,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,7,5,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,6,5,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,5,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,5,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[2,1,3,4,6,5,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,5,7,8,9,10,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,5,7,8,9,6,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,5,7,8,6,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,5,7,6,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[2,1,3,4,5,6,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,3,4,2,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[1,3,4,2,6,5,8,7,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,6,5,7,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,6,5,7,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,6,5,7,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,7,8,6,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,5,7,8,6,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,7,6,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,5,7,6,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,4,2,5,7,6,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,6,8,9,10,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,6,8,9,7,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,6,8,7,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,4,2,5,6,7,9,10,11,12,8]=>[2,2,1,1,1,1,1,1,1,1]
[1,3,2,5,6,4,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[1,3,2,5,6,4,8,7,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,6,4,7,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,6,4,7,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,6,4,7,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,5,4,7,8,6,10,9,12,11]=>[2,2,2,2,2,1,1]
[1,3,2,5,4,7,8,6,9,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,4,7,6,9,10,8,12,11]=>[2,2,2,2,2,1,1]
[1,3,2,5,4,7,6,9,8,11,12,10]=>[2,2,2,2,2,1,1]
[1,3,2,5,4,7,6,8,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,4,6,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,4,6,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,4,6,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[1,3,2,5,4,6,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,6,7,8,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,7,8,5,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,6,7,5,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,7,5,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,7,5,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,6,5,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,5,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,5,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[1,3,2,4,6,5,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,5,7,8,9,10,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,5,7,8,9,6,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,5,7,8,6,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,5,7,6,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,3,2,4,5,6,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,4,5,6,3,8,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,5,6,3,8,7,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,6,3,7,9,10,8,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,6,3,7,9,8,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,6,3,7,8,10,11,12,9]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,4,5,3,7,8,6,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,5,3,7,8,6,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,3,7,6,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,5,3,7,6,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,2,4,5,3,7,6,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,3,6,8,9,10,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,3,6,8,9,7,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,3,6,8,7,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,5,3,6,7,9,10,11,12,8]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,4,3,6,7,8,5,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,7,8,5,9,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,6,7,5,9,10,8,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,7,5,9,8,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,7,5,8,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,6,5,8,9,10,7,12,11]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,5,8,9,7,11,12,10]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,5,8,7,10,11,12,9]=>[2,2,2,2,1,1,1,1]
[1,2,4,3,6,5,7,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,5,7,8,9,10,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,5,7,8,9,6,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,5,7,8,6,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,5,7,6,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,2,4,3,5,6,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,5,6,7,8,4,10,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,7,8,4,9,11,12,10]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,5,6,7,4,9,10,8,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,7,4,9,8,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,7,4,8,10,11,12,9]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,5,6,4,8,9,10,7,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,4,8,9,7,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,4,8,7,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,6,4,7,9,10,11,12,8]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,5,4,7,8,9,10,6,12,11]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,4,7,8,9,6,11,12,10]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,4,7,8,6,10,11,12,9]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,4,7,6,9,10,11,12,8]=>[2,2,2,1,1,1,1,1,1]
[1,2,3,5,4,6,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,9,10,5,12,11]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,9,5,11,12,10]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,5,10,11,12,9]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,7,5,9,10,11,12,8]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,6,5,8,9,10,11,12,7]=>[2,2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,9,10,11,12,6]=>[2,1,1,1,1,1,1,1,1,1,1]
[12,1,2,3,4,5,6,7,8,11,9,10]=>[3,1,1,1,1,1,1,1,1,1]
[12,11,1,2,3,4,5,6,7,8,9,10]=>[3,1,1,1,1,1,1,1,1,1]
[12,2,1,3,4,5,6,7,8,9,10,11]=>[3,1,1,1,1,1,1,1,1,1]
[6,12,5,11,4,10,3,9,2,1,8,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,10,3,2,9,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,10,3,2,9,1,8,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,10,3,2,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,11,4,3,10,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,3,10,9,2,1,8,7]=>[6,2,2,1,1]
[6,12,5,11,4,3,10,2,9,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,3,10,2,9,1,8,7]=>[6,2,1,1,1,1]
[6,12,5,11,4,3,10,2,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,11,4,3,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,12,5,11,4,3,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,12,5,11,4,3,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,11,4,3,2,1,10,9,8,7]=>[6,4,1,1]
[6,12,5,4,11,10,3,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,4,11,10,3,9,2,1,8,7]=>[6,2,2,1,1]
[6,12,5,4,11,10,3,2,9,8,1,7]=>[6,2,2,1,1]
[6,12,5,4,11,10,3,2,9,1,8,7]=>[6,2,2,1,1]
[6,12,5,4,11,10,3,2,1,9,8,7]=>[6,3,2,1]
[6,12,5,4,11,3,10,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,4,11,3,10,9,2,1,8,7]=>[6,2,2,1,1]
[6,12,5,4,11,3,10,2,9,8,1,7]=>[6,2,1,1,1,1]
[6,12,5,4,11,3,10,2,9,1,8,7]=>[6,2,1,1,1,1]
[6,12,5,4,11,3,10,2,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,4,11,3,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,12,5,4,11,3,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,12,5,4,11,3,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,4,11,3,2,1,10,9,8,7]=>[6,4,1,1]
[6,12,5,4,3,11,10,9,2,8,1,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,10,9,2,1,8,7]=>[6,3,2,1]
[6,12,5,4,3,11,10,2,9,8,1,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,10,2,9,1,8,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,10,2,1,9,8,7]=>[6,3,2,1]
[6,12,5,4,3,11,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,12,5,4,3,11,2,1,10,9,8,7]=>[6,4,1,1]
[6,12,5,4,3,2,11,10,9,8,1,7]=>[6,4,1,1]
[6,12,5,4,3,2,11,10,9,1,8,7]=>[6,4,1,1]
[6,12,5,4,3,2,11,10,1,9,8,7]=>[6,4,1,1]
[6,12,5,4,3,2,11,1,10,9,8,7]=>[6,4,1,1]
[6,12,5,4,3,2,1,11,10,9,8,7]=>[6,5,1]
[6,5,12,11,4,10,3,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,5,12,11,4,10,3,9,2,1,8,7]=>[6,2,2,1,1]
[6,5,12,11,4,10,3,2,9,8,1,7]=>[6,2,2,1,1]
[6,5,12,11,4,10,3,2,9,1,8,7]=>[6,2,2,1,1]
[6,5,12,11,4,10,3,2,1,9,8,7]=>[6,3,2,1]
[6,5,12,11,4,3,10,9,2,8,1,7]=>[6,2,2,1,1]
[6,5,12,11,4,3,10,9,2,1,8,7]=>[6,2,2,2]
[6,5,12,11,4,3,10,2,9,8,1,7]=>[6,2,2,1,1]
[6,5,12,11,4,3,10,2,9,1,8,7]=>[6,2,2,1,1]
[6,5,12,11,4,3,10,2,1,9,8,7]=>[6,3,2,1]
[6,5,12,11,4,3,2,10,9,8,1,7]=>[6,3,2,1]
[6,5,12,11,4,3,2,10,9,1,8,7]=>[6,3,2,1]
[6,5,12,11,4,3,2,10,1,9,8,7]=>[6,3,2,1]
[6,5,12,11,4,3,2,1,10,9,8,7]=>[6,4,2]
[6,5,12,4,11,10,3,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,5,12,4,11,10,3,9,2,1,8,7]=>[6,2,2,1,1]
[6,5,12,4,11,10,3,2,9,8,1,7]=>[6,2,2,1,1]
[6,5,12,4,11,10,3,2,9,1,8,7]=>[6,2,2,1,1]
[6,5,12,4,11,10,3,2,1,9,8,7]=>[6,3,2,1]
[6,5,12,4,11,3,10,9,2,8,1,7]=>[6,2,1,1,1,1]
[6,5,12,4,11,3,10,9,2,1,8,7]=>[6,2,2,1,1]
[6,5,12,4,11,3,10,2,9,8,1,7]=>[6,2,1,1,1,1]
[6,5,12,4,11,3,10,2,9,1,8,7]=>[6,2,1,1,1,1]
[6,5,12,4,11,3,10,2,1,9,8,7]=>[6,3,1,1,1]
[6,5,12,4,11,3,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,5,12,4,11,3,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,5,12,4,11,3,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,5,12,4,11,3,2,1,10,9,8,7]=>[6,4,1,1]
[6,5,12,4,3,11,10,9,2,8,1,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,10,9,2,1,8,7]=>[6,3,2,1]
[6,5,12,4,3,11,10,2,9,8,1,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,10,2,9,1,8,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,10,2,1,9,8,7]=>[6,3,2,1]
[6,5,12,4,3,11,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,5,12,4,3,11,2,1,10,9,8,7]=>[6,4,1,1]
[6,5,12,4,3,2,11,10,9,8,1,7]=>[6,4,1,1]
[6,5,12,4,3,2,11,10,9,1,8,7]=>[6,4,1,1]
[6,5,12,4,3,2,11,10,1,9,8,7]=>[6,4,1,1]
[6,5,12,4,3,2,11,1,10,9,8,7]=>[6,4,1,1]
[6,5,12,4,3,2,1,11,10,9,8,7]=>[6,5,1]
[6,5,4,12,11,10,3,9,2,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,11,10,3,9,2,1,8,7]=>[6,3,2,1]
[6,5,4,12,11,10,3,2,9,8,1,7]=>[6,3,2,1]
[6,5,4,12,11,10,3,2,9,1,8,7]=>[6,3,2,1]
[6,5,4,12,11,10,3,2,1,9,8,7]=>[6,3,3]
[6,5,4,12,11,3,10,9,2,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,11,3,10,9,2,1,8,7]=>[6,3,2,1]
[6,5,4,12,11,3,10,2,9,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,11,3,10,2,9,1,8,7]=>[6,3,1,1,1]
[6,5,4,12,11,3,10,2,1,9,8,7]=>[6,3,2,1]
[6,5,4,12,11,3,2,10,9,8,1,7]=>[6,3,2,1]
[6,5,4,12,11,3,2,10,9,1,8,7]=>[6,3,2,1]
[6,5,4,12,11,3,2,10,1,9,8,7]=>[6,3,2,1]
[6,5,4,12,11,3,2,1,10,9,8,7]=>[6,4,2]
[6,5,4,12,3,11,10,9,2,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,10,9,2,1,8,7]=>[6,3,2,1]
[6,5,4,12,3,11,10,2,9,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,10,2,9,1,8,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,10,2,1,9,8,7]=>[6,3,2,1]
[6,5,4,12,3,11,2,10,9,8,1,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,2,10,9,1,8,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,2,10,1,9,8,7]=>[6,3,1,1,1]
[6,5,4,12,3,11,2,1,10,9,8,7]=>[6,4,1,1]
[6,5,4,12,3,2,11,10,9,8,1,7]=>[6,4,1,1]
[6,5,4,12,3,2,11,10,9,1,8,7]=>[6,4,1,1]
[6,5,4,12,3,2,11,10,1,9,8,7]=>[6,4,1,1]
[6,5,4,12,3,2,11,1,10,9,8,7]=>[6,4,1,1]
[6,5,4,12,3,2,1,11,10,9,8,7]=>[6,5,1]
[6,5,4,3,12,11,10,9,2,8,1,7]=>[6,4,1,1]
[6,5,4,3,12,11,10,9,2,1,8,7]=>[6,4,2]
[6,5,4,3,12,11,10,2,9,8,1,7]=>[6,4,1,1]
[6,5,4,3,12,11,10,2,9,1,8,7]=>[6,4,1,1]
[6,5,4,3,12,11,10,2,1,9,8,7]=>[6,4,2]
[6,5,4,3,12,11,2,10,9,8,1,7]=>[6,4,1,1]
[6,5,4,3,12,11,2,10,9,1,8,7]=>[6,4,1,1]
[6,5,4,3,12,11,2,10,1,9,8,7]=>[6,4,1,1]
[6,5,4,3,12,11,2,1,10,9,8,7]=>[6,4,2]
[6,5,4,3,12,2,11,10,9,8,1,7]=>[6,4,1,1]
[6,5,4,3,12,2,11,10,9,1,8,7]=>[6,4,1,1]
[6,5,4,3,12,2,11,10,1,9,8,7]=>[6,4,1,1]
[6,5,4,3,12,2,11,1,10,9,8,7]=>[6,4,1,1]
[6,5,4,3,12,2,1,11,10,9,8,7]=>[6,5,1]
[6,5,4,3,2,12,11,10,9,8,1,7]=>[6,5,1]
[6,5,4,3,2,12,11,10,9,1,8,7]=>[6,5,1]
[6,5,4,3,2,12,11,10,1,9,8,7]=>[6,5,1]
[6,5,4,3,2,12,11,1,10,9,8,7]=>[6,5,1]
[6,5,4,3,2,12,1,11,10,9,8,7]=>[6,5,1]
[2,1,4,3,6,5,8,7,12,9,11,10]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,10,7,9,8,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,12,11,9,7,8,10]=>[4,2,2,2,1,1]
[2,1,4,3,6,5,12,7,8,10,11,9]=>[3,2,2,2,1,1,1]
[2,1,4,3,8,5,7,6,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,8,5,7,6,12,9,11,10]=>[3,3,2,2,1,1]
[2,1,4,3,10,9,7,5,6,8,12,11]=>[4,2,2,2,1,1]
[2,1,4,3,12,9,7,11,6,5,8,10]=>[5,2,2,1,1,1]
[2,1,4,3,12,10,7,5,8,6,11,9]=>[4,2,2,2,2]
[2,1,4,3,10,5,6,8,9,7,12,11]=>[3,2,2,2,1,1,1]
[2,1,4,3,12,11,6,8,9,5,7,10]=>[4,2,2,1,1,1,1]
[2,1,4,3,12,5,11,8,6,10,7,9]=>[4,2,2,2,1,1]
[2,1,4,3,12,5,6,7,9,10,11,8]=>[3,2,2,1,1,1,1,1]
[2,1,6,3,5,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,6,3,5,4,8,7,12,9,11,10]=>[3,3,2,2,1,1]
[2,1,6,3,5,4,10,7,9,8,12,11]=>[3,3,2,2,1,1]
[2,1,6,3,5,4,12,11,9,7,8,10]=>[4,3,2,1,1,1]
[2,1,6,3,5,4,12,7,8,10,11,9]=>[3,3,2,1,1,1,1]
[2,1,8,7,5,3,4,6,10,9,12,11]=>[4,2,2,2,1,1]
[2,1,8,7,5,3,4,6,12,9,11,10]=>[4,3,2,1,1,1]
[2,1,10,7,5,9,4,3,6,8,12,11]=>[5,2,2,1,1,1]
[2,1,12,7,5,9,4,11,6,3,8,10]=>[5,2,2,1,1,1]
[2,1,12,7,5,10,4,3,8,6,11,9]=>[5,2,2,2,1]
[2,1,10,8,5,3,6,4,9,7,12,11]=>[4,2,2,2,2]
[2,1,12,8,5,11,6,4,9,3,7,10]=>[5,2,2,1,1,1]
[2,1,12,8,5,3,11,4,6,10,7,9]=>[4,3,2,1,1,1]
[2,1,12,9,5,3,6,7,4,10,11,8]=>[4,2,2,2,1,1]
[2,1,8,3,4,6,7,5,10,9,12,11]=>[3,2,2,2,1,1,1]
[2,1,8,3,4,6,7,5,12,9,11,10]=>[3,3,2,1,1,1,1]
[2,1,10,9,4,6,7,3,5,8,12,11]=>[4,2,2,1,1,1,1]
[2,1,12,9,4,6,7,11,5,3,8,10]=>[5,2,1,1,1,1,1]
[2,1,12,10,4,6,7,3,8,5,11,9]=>[4,2,2,2,1,1]
[2,1,10,3,9,6,4,8,5,7,12,11]=>[4,2,2,2,1,1]
[2,1,12,11,9,6,4,8,5,3,7,10]=>[6,2,2,1,1]
[2,1,12,3,10,6,11,8,4,5,7,9]=>[4,2,2,1,1,1,1]
[2,1,12,3,10,6,4,7,9,5,11,8]=>[4,2,2,2,1,1]
[2,1,10,3,4,5,7,8,9,6,12,11]=>[3,2,2,1,1,1,1,1]
[2,1,12,11,4,5,7,8,9,3,6,10]=>[4,2,1,1,1,1,1,1]
[2,1,12,3,11,5,7,8,4,10,6,9]=>[4,2,2,1,1,1,1]
[2,1,12,3,4,11,7,5,9,10,6,8]=>[4,2,2,1,1,1,1]
[2,1,12,3,4,5,6,8,9,10,11,7]=>[3,2,1,1,1,1,1,1,1]
[4,1,3,2,6,5,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[4,1,3,2,6,5,8,7,12,9,11,10]=>[3,3,2,2,1,1]
[4,1,3,2,6,5,10,7,9,8,12,11]=>[3,3,2,2,1,1]
[4,1,3,2,6,5,12,11,9,7,8,10]=>[4,3,2,1,1,1]
[4,1,3,2,6,5,12,7,8,10,11,9]=>[3,3,2,1,1,1,1]
[4,1,3,2,8,5,7,6,10,9,12,11]=>[3,3,2,2,1,1]
[4,1,3,2,8,5,7,6,12,9,11,10]=>[3,3,3,1,1,1]
[4,1,3,2,10,9,7,5,6,8,12,11]=>[4,3,2,1,1,1]
[4,1,3,2,12,9,7,11,6,5,8,10]=>[5,3,1,1,1,1]
[4,1,3,2,12,10,7,5,8,6,11,9]=>[4,3,2,2,1]
[4,1,3,2,10,5,6,8,9,7,12,11]=>[3,3,2,1,1,1,1]
[4,1,3,2,12,11,6,8,9,5,7,10]=>[4,3,1,1,1,1,1]
[4,1,3,2,12,5,11,8,6,10,7,9]=>[4,3,2,1,1,1]
[4,1,3,2,12,5,6,7,9,10,11,8]=>[3,3,1,1,1,1,1,1]
[6,5,3,1,2,4,8,7,10,9,12,11]=>[4,2,2,2,1,1]
[6,5,3,1,2,4,8,7,12,9,11,10]=>[4,3,2,1,1,1]
[6,5,3,1,2,4,10,7,9,8,12,11]=>[4,3,2,1,1,1]
[6,5,3,1,2,4,12,11,9,7,8,10]=>[4,4,1,1,1,1]
[6,5,3,1,2,4,12,7,8,10,11,9]=>[4,3,1,1,1,1,1]
[8,5,3,7,2,1,4,6,10,9,12,11]=>[5,2,2,1,1,1]
[8,5,3,7,2,1,4,6,12,9,11,10]=>[5,3,1,1,1,1]
[10,5,3,7,2,9,4,1,6,8,12,11]=>[5,2,2,1,1,1]
[12,5,3,7,2,9,4,11,6,1,8,10]=>[5,2,2,1,1,1]
[12,5,3,7,2,10,4,1,8,6,11,9]=>[5,2,2,2,1]
[10,5,3,8,2,1,6,4,9,7,12,11]=>[5,2,2,2,1]
[12,5,3,8,2,11,6,4,9,1,7,10]=>[5,3,1,1,1,1]
[12,5,3,8,2,1,11,4,6,10,7,9]=>[5,3,1,1,1,1]
[12,5,3,9,2,1,6,7,4,10,11,8]=>[5,2,2,1,1,1]
[8,6,3,1,4,2,7,5,10,9,12,11]=>[4,2,2,2,2]
[8,6,3,1,4,2,7,5,12,9,11,10]=>[4,3,2,2,1]
[10,6,3,9,4,2,7,1,5,8,12,11]=>[5,2,2,1,1,1]
[12,6,3,9,4,2,7,11,5,1,8,10]=>[5,2,2,1,1,1]
[12,6,3,10,4,2,7,1,8,5,11,9]=>[5,2,2,2,1]
[10,6,3,1,9,2,4,8,5,7,12,11]=>[4,3,2,1,1,1]
[12,6,3,11,9,2,4,8,5,1,7,10]=>[6,2,1,1,1,1]
[12,6,3,1,10,2,11,8,4,5,7,9]=>[4,3,2,1,1,1]
[12,6,3,1,10,2,4,7,9,5,11,8]=>[4,3,2,1,1,1]
[10,7,3,1,4,5,2,8,9,6,12,11]=>[4,2,2,2,1,1]
[12,7,3,11,4,5,2,8,9,1,6,10]=>[5,2,1,1,1,1,1]
[12,7,3,1,11,5,2,8,4,10,6,9]=>[4,3,2,2,1]
[12,7,3,1,4,11,2,5,9,10,6,8]=>[4,3,1,1,1,1,1]
[12,8,3,1,4,5,6,2,9,10,11,7]=>[4,2,2,1,1,1,1]
[6,1,2,4,5,3,8,7,10,9,12,11]=>[3,2,2,2,1,1,1]
[6,1,2,4,5,3,8,7,12,9,11,10]=>[3,3,2,1,1,1,1]
[6,1,2,4,5,3,10,7,9,8,12,11]=>[3,3,2,1,1,1,1]
[6,1,2,4,5,3,12,11,9,7,8,10]=>[4,3,1,1,1,1,1]
[6,1,2,4,5,3,12,7,8,10,11,9]=>[3,3,1,1,1,1,1,1]
[8,7,2,4,5,1,3,6,10,9,12,11]=>[4,2,2,1,1,1,1]
[8,7,2,4,5,1,3,6,12,9,11,10]=>[4,3,1,1,1,1,1]
[10,7,2,4,5,9,3,1,6,8,12,11]=>[5,2,1,1,1,1,1]
[12,7,2,4,5,9,3,11,6,1,8,10]=>[5,2,1,1,1,1,1]
[12,7,2,4,5,10,3,1,8,6,11,9]=>[5,2,2,1,1,1]
[10,8,2,4,5,1,6,3,9,7,12,11]=>[4,2,2,2,1,1]
[12,8,2,4,5,11,6,3,9,1,7,10]=>[5,2,1,1,1,1,1]
[12,8,2,4,5,1,11,3,6,10,7,9]=>[4,3,1,1,1,1,1]
[12,9,2,4,5,1,6,7,3,10,11,8]=>[4,2,2,1,1,1,1]
[8,1,7,4,2,6,3,5,10,9,12,11]=>[4,2,2,2,1,1]
[8,1,7,4,2,6,3,5,12,9,11,10]=>[4,3,2,1,1,1]
[10,9,7,4,2,6,3,1,5,8,12,11]=>[6,2,2,1,1]
[12,9,7,4,2,6,3,11,5,1,8,10]=>[6,2,2,1,1]
[12,10,7,4,2,6,3,1,8,5,11,9]=>[6,2,2,2]
[10,1,8,4,9,6,2,3,5,7,12,11]=>[4,2,2,1,1,1,1]
[12,11,8,4,9,6,2,3,5,1,7,10]=>[6,2,1,1,1,1]
[12,1,8,4,10,6,11,3,2,5,7,9]=>[5,2,1,1,1,1,1]
[12,1,9,4,10,6,2,7,3,5,11,8]=>[4,2,2,2,1,1]
[10,1,8,4,2,5,7,3,9,6,12,11]=>[4,2,2,2,1,1]
[12,11,8,4,2,5,7,3,9,1,6,10]=>[6,2,1,1,1,1]
[12,1,8,4,11,5,7,3,2,10,6,9]=>[5,2,2,1,1,1]
[12,1,9,4,2,11,7,5,3,10,6,8]=>[5,3,2,1,1]
[12,1,9,4,2,5,6,8,3,10,11,7]=>[4,2,2,1,1,1,1]
[8,1,2,3,5,6,7,4,10,9,12,11]=>[3,2,2,1,1,1,1,1]
[8,1,2,3,5,6,7,4,12,9,11,10]=>[3,3,1,1,1,1,1,1]
[10,9,2,3,5,6,7,1,4,8,12,11]=>[4,2,1,1,1,1,1,1]
[12,9,2,3,5,6,7,11,4,1,8,10]=>[5,1,1,1,1,1,1,1]
[12,10,2,3,5,6,7,1,8,4,11,9]=>[4,2,2,1,1,1,1]
[10,1,9,3,5,6,2,8,4,7,12,11]=>[4,2,2,1,1,1,1]
[12,11,9,3,5,6,2,8,4,1,7,10]=>[6,2,1,1,1,1]
[12,1,10,3,5,6,11,8,2,4,7,9]=>[4,2,1,1,1,1,1,1]
[12,1,10,3,5,6,2,7,9,4,11,8]=>[4,2,2,1,1,1,1]
[10,1,2,9,5,3,7,8,4,6,12,11]=>[4,2,2,1,1,1,1]
[12,11,2,9,5,3,7,8,4,1,6,10]=>[6,2,1,1,1,1]
[12,1,11,10,5,3,7,8,2,4,6,9]=>[6,1,1,1,1,1,1]
[12,1,2,10,5,11,7,3,9,4,6,8]=>[4,2,2,1,1,1,1]
[12,1,2,10,5,3,6,8,9,4,11,7]=>[4,2,2,1,1,1,1]
[10,1,2,3,4,6,7,8,9,5,12,11]=>[3,2,1,1,1,1,1,1,1]
[12,11,2,3,4,6,7,8,9,1,5,10]=>[4,1,1,1,1,1,1,1,1]
[12,1,11,3,4,6,7,8,2,10,5,9]=>[4,2,1,1,1,1,1,1]
[12,1,2,11,4,6,7,3,9,10,5,8]=>[4,2,1,1,1,1,1,1]
[12,1,2,3,11,6,4,8,9,10,5,7]=>[4,2,1,1,1,1,1,1]
[2,1,4,3,6,5,8,7,12,9,10,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,10,7,8,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,6,5,12,11,8,7,10,9]=>[4,2,2,2,2]
[2,1,4,3,6,5,12,7,8,9,10,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,8,5,6,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,4,3,8,5,6,7,12,9,10,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,10,9,6,5,8,7,12,11]=>[4,2,2,2,2]
[2,1,4,3,12,9,6,11,8,5,10,7]=>[4,2,2,2,2]
[2,1,4,3,12,11,6,5,8,9,10,7]=>[4,2,2,2,1,1]
[2,1,4,3,10,5,6,7,8,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,4,3,12,11,6,7,8,5,10,9]=>[4,2,2,2,1,1]
[2,1,4,3,12,5,10,7,6,9,8,11]=>[4,2,2,2,1,1]
[2,1,4,3,12,5,6,7,8,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,6,3,4,5,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[2,1,6,3,4,5,8,7,12,9,10,11]=>[2,2,2,2,1,1,1,1]
[2,1,6,3,4,5,10,7,8,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,6,3,4,5,12,11,8,7,10,9]=>[4,2,2,2,1,1]
[2,1,6,3,4,5,12,7,8,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,8,7,4,3,6,5,10,9,12,11]=>[4,2,2,2,2]
[2,1,8,7,4,3,6,5,12,9,10,11]=>[4,2,2,2,1,1]
[2,1,10,7,4,9,6,3,8,5,12,11]=>[4,2,2,2,2]
[2,1,12,7,4,9,6,11,8,3,10,5]=>[4,2,2,2,2]
[2,1,12,7,4,11,6,3,8,9,10,5]=>[4,2,2,2,1,1]
[2,1,10,9,4,3,6,7,8,5,12,11]=>[4,2,2,2,1,1]
[2,1,12,9,4,11,6,7,8,3,10,5]=>[4,2,2,2,1,1]
[2,1,12,11,4,3,10,7,6,9,8,5]=>[6,2,2,2]
[2,1,12,11,4,3,6,7,8,9,10,5]=>[4,2,2,1,1,1,1]
[2,1,8,3,4,5,6,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[2,1,8,3,4,5,6,7,12,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,10,9,4,5,6,3,8,7,12,11]=>[4,2,2,2,1,1]
[2,1,12,9,4,5,6,11,8,3,10,7]=>[4,2,2,2,1,1]
[2,1,12,11,4,5,6,3,8,9,10,7]=>[4,2,2,1,1,1,1]
[2,1,10,3,8,5,4,7,6,9,12,11]=>[4,2,2,2,1,1]
[2,1,12,11,8,5,4,7,6,3,10,9]=>[6,2,2,2]
[2,1,12,3,8,5,10,7,4,9,6,11]=>[4,2,2,2,1,1]
[2,1,12,3,10,5,4,7,8,9,6,11]=>[4,2,2,1,1,1,1]
[2,1,10,3,4,5,6,7,8,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[2,1,12,11,4,5,6,7,8,3,10,9]=>[4,2,2,1,1,1,1]
[2,1,12,3,10,5,6,7,4,9,8,11]=>[4,2,2,1,1,1,1]
[2,1,12,3,4,9,6,5,8,7,10,11]=>[4,2,2,1,1,1,1]
[2,1,12,3,4,5,6,7,8,9,10,11]=>[2,2,1,1,1,1,1,1,1,1]
[4,1,2,3,6,5,8,7,10,9,12,11]=>[2,2,2,2,2,1,1]
[4,1,2,3,6,5,8,7,12,9,10,11]=>[2,2,2,2,1,1,1,1]
[4,1,2,3,6,5,10,7,8,9,12,11]=>[2,2,2,2,1,1,1,1]
[4,1,2,3,6,5,12,11,8,7,10,9]=>[4,2,2,2,1,1]
[4,1,2,3,6,5,12,7,8,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[4,1,2,3,8,5,6,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[4,1,2,3,8,5,6,7,12,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[4,1,2,3,10,9,6,5,8,7,12,11]=>[4,2,2,2,1,1]
[4,1,2,3,12,9,6,11,8,5,10,7]=>[4,2,2,2,1,1]
[4,1,2,3,12,11,6,5,8,9,10,7]=>[4,2,2,1,1,1,1]
[4,1,2,3,10,5,6,7,8,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[4,1,2,3,12,11,6,7,8,5,10,9]=>[4,2,2,1,1,1,1]
[4,1,2,3,12,5,10,7,6,9,8,11]=>[4,2,2,1,1,1,1]
[4,1,2,3,12,5,6,7,8,9,10,11]=>[2,2,1,1,1,1,1,1,1,1]
[6,5,2,1,4,3,8,7,10,9,12,11]=>[4,2,2,2,2]
[6,5,2,1,4,3,8,7,12,9,10,11]=>[4,2,2,2,1,1]
[6,5,2,1,4,3,10,7,8,9,12,11]=>[4,2,2,2,1,1]
[6,5,2,1,4,3,12,7,8,9,10,11]=>[4,2,2,1,1,1,1]
[8,5,2,7,4,1,6,3,10,9,12,11]=>[4,2,2,2,2]
[8,5,2,7,4,1,6,3,12,9,10,11]=>[4,2,2,2,1,1]
[10,5,2,7,4,9,6,1,8,3,12,11]=>[4,2,2,2,2]
[12,5,2,7,4,9,6,11,8,1,10,3]=>[4,2,2,2,2]
[12,5,2,7,4,11,6,1,8,9,10,3]=>[4,2,2,2,1,1]
[10,5,2,9,4,1,6,7,8,3,12,11]=>[4,2,2,2,1,1]
[12,5,2,9,4,11,6,7,8,1,10,3]=>[4,2,2,2,1,1]
[12,5,2,11,4,1,10,7,6,9,8,3]=>[6,2,2,2]
[12,5,2,11,4,1,6,7,8,9,10,3]=>[4,2,2,1,1,1,1]
[8,7,2,1,4,5,6,3,10,9,12,11]=>[4,2,2,2,1,1]
[8,7,2,1,4,5,6,3,12,9,10,11]=>[4,2,2,1,1,1,1]
[10,7,2,9,4,5,6,1,8,3,12,11]=>[4,2,2,2,1,1]
[12,7,2,9,4,5,6,11,8,1,10,3]=>[4,2,2,2,1,1]
[12,7,2,11,4,5,6,1,8,9,10,3]=>[4,2,2,1,1,1,1]
[10,9,2,1,8,5,4,7,6,3,12,11]=>[6,2,2,2]
[12,9,2,11,8,5,4,7,6,1,10,3]=>[6,2,2,2]
[12,11,2,1,8,5,10,7,4,9,6,3]=>[6,2,2,2]
[12,11,2,1,10,5,4,7,8,9,6,3]=>[6,2,2,1,1]
[10,9,2,1,4,5,6,7,8,3,12,11]=>[4,2,2,1,1,1,1]
[12,9,2,11,4,5,6,7,8,1,10,3]=>[4,2,2,1,1,1,1]
[12,11,2,1,10,5,6,7,4,9,8,3]=>[6,2,2,1,1]
[12,11,2,1,4,9,6,5,8,7,10,3]=>[6,2,2,1,1]
[12,11,2,1,4,5,6,7,8,9,10,3]=>[4,2,1,1,1,1,1,1]
[6,1,2,3,4,5,8,7,10,9,12,11]=>[2,2,2,2,1,1,1,1]
[6,1,2,3,4,5,8,7,12,9,10,11]=>[2,2,2,1,1,1,1,1,1]
[6,1,2,3,4,5,10,7,8,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[6,1,2,3,4,5,12,11,8,7,10,9]=>[4,2,2,1,1,1,1]
[6,1,2,3,4,5,12,7,8,9,10,11]=>[2,2,1,1,1,1,1,1,1,1]
[8,7,2,3,4,1,6,5,10,9,12,11]=>[4,2,2,2,1,1]
[8,7,2,3,4,1,6,5,12,9,10,11]=>[4,2,2,1,1,1,1]
[10,7,2,3,4,9,6,1,8,5,12,11]=>[4,2,2,2,1,1]
[12,7,2,3,4,9,6,11,8,1,10,5]=>[4,2,2,2,1,1]
[12,7,2,3,4,11,6,1,8,9,10,5]=>[4,2,2,1,1,1,1]
[10,9,2,3,4,1,6,7,8,5,12,11]=>[4,2,2,1,1,1,1]
[12,9,2,3,4,11,6,7,8,1,10,5]=>[4,2,2,1,1,1,1]
[12,11,2,3,4,1,10,7,6,9,8,5]=>[6,2,2,1,1]
[12,11,2,3,4,1,6,7,8,9,10,5]=>[4,2,1,1,1,1,1,1]
[8,1,6,3,2,5,4,7,10,9,12,11]=>[4,2,2,2,1,1]
[8,1,6,3,2,5,4,7,12,9,10,11]=>[4,2,2,1,1,1,1]
[10,9,6,3,2,5,4,1,8,7,12,11]=>[6,2,2,2]
[12,9,6,3,2,5,4,11,8,1,10,7]=>[6,2,2,2]
[12,11,6,3,2,5,4,1,8,9,10,7]=>[6,2,2,1,1]
[10,1,6,3,8,5,2,7,4,9,12,11]=>[4,2,2,2,1,1]
[12,11,6,3,8,5,2,7,4,1,10,9]=>[6,2,2,2]
[12,1,6,3,8,5,10,7,2,9,4,11]=>[4,2,2,2,1,1]
[12,1,6,3,10,5,2,7,8,9,4,11]=>[4,2,2,1,1,1,1]
[10,1,8,3,2,5,6,7,4,9,12,11]=>[4,2,2,1,1,1,1]
[12,11,8,3,2,5,6,7,4,1,10,9]=>[6,2,2,1,1]
[12,1,8,3,10,5,6,7,2,9,4,11]=>[4,2,2,1,1,1,1]
[12,1,10,3,2,9,6,5,8,7,4,11]=>[6,2,2,1,1]
[12,1,10,3,2,5,6,7,8,9,4,11]=>[4,2,1,1,1,1,1,1]
[8,1,2,3,4,5,6,7,10,9,12,11]=>[2,2,2,1,1,1,1,1,1]
[8,1,2,3,4,5,6,7,12,9,10,11]=>[2,2,1,1,1,1,1,1,1,1]
[10,9,2,3,4,5,6,1,8,7,12,11]=>[4,2,2,1,1,1,1]
[12,9,2,3,4,5,6,11,8,1,10,7]=>[4,2,2,1,1,1,1]
[12,11,2,3,4,5,6,1,8,9,10,7]=>[4,2,1,1,1,1,1,1]
[10,1,8,3,4,5,2,7,6,9,12,11]=>[4,2,2,1,1,1,1]
[12,11,8,3,4,5,2,7,6,1,10,9]=>[6,2,2,1,1]
[12,1,8,3,4,5,10,7,2,9,6,11]=>[4,2,2,1,1,1,1]
[12,1,10,3,4,5,2,7,8,9,6,11]=>[4,2,1,1,1,1,1,1]
[10,1,2,7,4,3,6,5,8,9,12,11]=>[4,2,2,1,1,1,1]
[12,11,2,7,4,3,6,5,8,1,10,9]=>[6,2,2,1,1]
[12,1,10,7,4,3,6,5,2,9,8,11]=>[6,2,2,1,1]
[12,1,2,7,4,9,6,3,8,5,10,11]=>[4,2,2,1,1,1,1]
[12,1,2,9,4,3,6,7,8,5,10,11]=>[4,2,1,1,1,1,1,1]
[10,1,2,3,4,5,6,7,8,9,12,11]=>[2,2,1,1,1,1,1,1,1,1]
[12,11,2,3,4,5,6,7,8,1,10,9]=>[4,2,1,1,1,1,1,1]
[12,1,10,3,4,5,6,7,2,9,8,11]=>[4,2,1,1,1,1,1,1]
[12,1,2,9,4,5,6,3,8,7,10,11]=>[4,2,1,1,1,1,1,1]
[12,1,2,3,8,5,4,7,6,9,10,11]=>[4,2,1,1,1,1,1,1]
[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,1,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,12,7,9,8,11,10]=>[3,2,2,2,2,1]
[2,1,4,3,6,5,11,8,12,7,10,9]=>[3,2,2,2,2,1]
[2,1,4,3,10,5,7,6,9,8,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,12,5,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[2,1,4,3,11,8,12,5,7,6,10,9]=>[4,2,2,2,1,1]
[2,1,4,3,9,6,10,5,8,7,12,11]=>[3,2,2,2,2,1]
[2,1,4,3,9,6,12,5,8,7,11,10]=>[3,2,2,2,2,1]
[2,1,4,3,12,5,8,7,11,6,10,9]=>[4,2,2,2,1,1]
[2,1,4,3,11,6,10,7,12,5,9,8]=>[4,2,2,2,1,1]
[2,1,6,3,5,4,12,7,9,8,11,10]=>[3,3,2,2,1,1]
[2,1,6,3,5,4,11,8,12,7,10,9]=>[3,3,2,2,1,1]
[2,1,8,3,5,4,7,6,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,8,3,5,4,7,6,12,9,11,10]=>[3,3,2,2,1,1]
[2,1,10,3,5,4,7,6,9,8,12,11]=>[3,2,2,2,2,1]
[2,1,12,3,5,4,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[2,1,11,8,12,3,5,4,7,6,10,9]=>[4,2,2,2,1,1]
[2,1,9,6,10,3,5,4,8,7,12,11]=>[4,2,2,2,1,1]
[2,1,9,6,12,3,5,4,8,7,11,10]=>[4,2,2,2,1,1]
[2,1,12,3,5,4,8,7,11,6,10,9]=>[4,2,2,2,1,1]
[2,1,11,6,10,7,12,3,5,4,9,8]=>[5,2,2,1,1,1]
[2,1,7,4,8,3,6,5,10,9,12,11]=>[3,2,2,2,2,1]
[2,1,7,4,8,3,6,5,12,9,11,10]=>[3,3,2,2,1,1]
[2,1,7,4,10,3,6,5,9,8,12,11]=>[3,2,2,2,2,1]
[2,1,7,4,12,3,6,5,9,8,11,10]=>[3,2,2,2,2,1]
[2,1,7,4,11,8,12,3,6,5,10,9]=>[4,2,2,2,1,1]
[2,1,10,3,6,5,9,4,8,7,12,11]=>[4,2,2,2,1,1]
[2,1,12,3,6,5,9,4,8,7,11,10]=>[4,2,2,2,1,1]
[2,1,11,4,8,7,12,3,6,5,10,9]=>[5,2,2,1,1,1]
[2,1,12,3,6,5,10,7,11,4,9,8]=>[4,2,2,2,1,1]
[2,1,9,4,8,5,10,3,7,6,12,11]=>[4,2,2,2,1,1]
[2,1,9,4,8,5,12,3,7,6,11,10]=>[4,2,2,2,1,1]
[2,1,12,3,7,6,11,4,8,5,10,9]=>[4,2,2,2,1,1]
[2,1,10,5,12,3,7,6,11,4,9,8]=>[4,2,2,2,1,1]
[2,1,10,5,11,4,9,6,12,3,8,7]=>[4,2,2,2,1,1]
[4,1,3,2,6,5,12,7,9,8,11,10]=>[3,3,2,2,1,1]
[4,1,3,2,6,5,11,8,12,7,10,9]=>[3,3,2,2,1,1]
[4,1,3,2,10,5,7,6,9,8,12,11]=>[3,3,2,2,1,1]
[4,1,3,2,12,5,7,6,9,8,11,10]=>[3,3,2,2,1,1]
[4,1,3,2,11,8,12,5,7,6,10,9]=>[4,3,2,1,1,1]
[4,1,3,2,9,6,10,5,8,7,12,11]=>[3,3,2,2,1,1]
[4,1,3,2,9,6,12,5,8,7,11,10]=>[3,3,2,2,1,1]
[4,1,3,2,12,5,8,7,11,6,10,9]=>[4,3,2,1,1,1]
[4,1,3,2,11,6,10,7,12,5,9,8]=>[4,3,2,1,1,1]
[6,1,3,2,5,4,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[6,1,3,2,5,4,8,7,12,9,11,10]=>[3,3,2,2,1,1]
[6,1,3,2,5,4,10,7,9,8,12,11]=>[3,3,2,2,1,1]
[6,1,3,2,5,4,12,7,9,8,11,10]=>[3,3,2,2,1,1]
[6,1,3,2,5,4,11,8,12,7,10,9]=>[3,3,2,2,1,1]
[8,1,3,2,5,4,7,6,10,9,12,11]=>[3,2,2,2,2,1]
[8,1,3,2,5,4,7,6,12,9,11,10]=>[3,3,2,2,1,1]
[10,1,3,2,5,4,7,6,9,8,12,11]=>[3,2,2,2,2,1]
[11,8,12,1,3,2,5,4,7,6,10,9]=>[4,2,2,2,1,1]
[9,6,10,1,3,2,5,4,8,7,12,11]=>[4,2,2,2,1,1]
[9,6,12,1,3,2,5,4,8,7,11,10]=>[4,2,2,2,1,1]
[12,1,3,2,5,4,8,7,11,6,10,9]=>[4,2,2,2,1,1]
[11,6,10,7,12,1,3,2,5,4,9,8]=>[5,2,2,1,1,1]
[7,4,8,1,3,2,6,5,10,9,12,11]=>[4,2,2,2,1,1]
[7,4,8,1,3,2,6,5,12,9,11,10]=>[4,3,2,1,1,1]
[7,4,10,1,3,2,6,5,9,8,12,11]=>[4,2,2,2,1,1]
[7,4,12,1,3,2,6,5,9,8,11,10]=>[4,2,2,2,1,1]
[7,4,11,8,12,1,3,2,6,5,10,9]=>[4,2,2,2,1,1]
[10,1,3,2,6,5,9,4,8,7,12,11]=>[4,2,2,2,1,1]
[12,1,3,2,6,5,9,4,8,7,11,10]=>[4,2,2,2,1,1]
[11,4,8,7,12,1,3,2,6,5,10,9]=>[5,2,2,1,1,1]
[12,1,3,2,6,5,10,7,11,4,9,8]=>[4,2,2,2,1,1]
[9,4,8,5,10,1,3,2,7,6,12,11]=>[5,2,2,1,1,1]
[9,4,8,5,12,1,3,2,7,6,11,10]=>[5,2,2,1,1,1]
[12,1,3,2,7,6,11,4,8,5,10,9]=>[4,2,2,2,1,1]
[10,5,12,1,3,2,7,6,11,4,9,8]=>[4,3,2,1,1,1]
[10,5,11,4,9,6,12,1,3,2,8,7]=>[5,2,2,1,1,1]
[5,2,6,1,4,3,8,7,10,9,12,11]=>[3,2,2,2,2,1]
[5,2,6,1,4,3,8,7,12,9,11,10]=>[3,3,2,2,1,1]
[5,2,6,1,4,3,10,7,9,8,12,11]=>[3,3,2,2,1,1]
[5,2,6,1,4,3,12,7,9,8,11,10]=>[3,3,2,2,1,1]
[5,2,6,1,4,3,11,8,12,7,10,9]=>[3,3,2,2,1,1]
[5,2,8,1,4,3,7,6,10,9,12,11]=>[3,2,2,2,2,1]
[5,2,8,1,4,3,7,6,12,9,11,10]=>[3,3,2,2,1,1]
[5,2,10,1,4,3,7,6,9,8,12,11]=>[3,2,2,2,2,1]
[5,2,12,1,4,3,7,6,9,8,11,10]=>[3,2,2,2,2,1]
[5,2,11,8,12,1,4,3,7,6,10,9]=>[4,2,2,2,1,1]
[5,2,9,6,10,1,4,3,8,7,12,11]=>[4,2,2,2,1,1]
[5,2,9,6,12,1,4,3,8,7,11,10]=>[4,2,2,2,1,1]
[5,2,12,1,4,3,8,7,11,6,10,9]=>[4,2,2,2,1,1]
[5,2,11,6,10,7,12,1,4,3,9,8]=>[5,2,2,1,1,1]
[8,1,4,3,7,2,6,5,10,9,12,11]=>[4,2,2,2,1,1]
[8,1,4,3,7,2,6,5,12,9,11,10]=>[4,3,2,1,1,1]
[10,1,4,3,7,2,6,5,9,8,12,11]=>[4,2,2,2,1,1]
[12,1,4,3,7,2,6,5,9,8,11,10]=>[4,2,2,2,1,1]
[11,8,12,1,4,3,7,2,6,5,10,9]=>[5,2,2,1,1,1]
[9,2,6,5,10,1,4,3,8,7,12,11]=>[5,2,2,1,1,1]
[9,2,6,5,12,1,4,3,8,7,11,10]=>[5,2,2,1,1,1]
[12,1,4,3,8,7,11,2,6,5,10,9]=>[5,2,2,1,1,1]
[11,2,6,5,10,7,12,1,4,3,9,8]=>[5,2,2,1,1,1]
[10,1,4,3,8,5,9,2,7,6,12,11]=>[4,2,2,2,1,1]
[12,1,4,3,8,5,9,2,7,6,11,10]=>[4,2,2,2,1,1]
[11,2,7,6,12,1,4,3,8,5,10,9]=>[5,2,2,1,1,1]
[10,5,11,2,7,6,12,1,4,3,9,8]=>[5,2,2,1,1,1]
[10,5,12,1,4,3,9,6,11,2,8,7]=>[5,2,2,1,1,1]
[7,2,6,3,8,1,5,4,10,9,12,11]=>[4,2,2,2,1,1]
[7,2,6,3,8,1,5,4,12,9,11,10]=>[4,3,2,1,1,1]
[7,2,6,3,10,1,5,4,9,8,12,11]=>[4,2,2,2,1,1]
[7,2,6,3,12,1,5,4,9,8,11,10]=>[4,2,2,2,1,1]
[7,2,6,3,11,8,12,1,5,4,10,9]=>[4,3,2,1,1,1]
[10,1,5,4,9,2,6,3,8,7,12,11]=>[4,2,2,2,1,1]
[12,1,5,4,9,2,6,3,8,7,11,10]=>[4,2,2,2,1,1]
[11,2,6,3,8,7,12,1,5,4,10,9]=>[5,2,2,1,1,1]
[12,1,5,4,10,7,11,2,6,3,9,8]=>[5,2,2,1,1,1]
[8,3,10,1,5,4,9,2,7,6,12,11]=>[4,2,2,2,1,1]
[8,3,12,1,5,4,9,2,7,6,11,10]=>[4,2,2,2,1,1]
[8,3,11,2,7,6,12,1,5,4,10,9]=>[5,2,2,1,1,1]
[11,2,7,6,12,1,5,4,10,3,9,8]=>[6,2,1,1,1,1]
[12,1,5,4,10,3,9,6,11,2,8,7]=>[5,2,2,1,1,1]
[8,3,9,2,7,4,10,1,6,5,12,11]=>[4,2,2,2,1,1]
[8,3,9,2,7,4,12,1,6,5,11,10]=>[4,2,2,2,1,1]
[8,3,12,1,6,5,11,2,7,4,10,9]=>[4,2,2,2,1,1]
[12,1,6,5,11,2,7,4,10,3,9,8]=>[5,2,2,1,1,1]
[10,3,9,4,12,1,6,5,11,2,8,7]=>[5,2,2,1,1,1]
[10,3,9,4,11,2,8,5,12,1,7,6]=>[5,2,2,1,1,1]
[11,12,8,2,1,6,4,3,5,7,9,10]=>[5,2,1,1,1,1,1]
[12,2,9,1,10,6,4,3,5,7,8,11]=>[5,2,1,1,1,1,1]
[11,12,2,1,9,6,4,3,5,7,8,10]=>[5,2,1,1,1,1,1]
[10,2,4,1,11,3,12,6,5,7,8,9]=>[3,3,2,1,1,1,1]
[7,12,10,2,1,8,4,3,5,6,9,11]=>[5,2,1,1,1,1,1]
[2,11,7,1,12,8,4,3,5,6,9,10]=>[4,3,1,1,1,1,1]
[9,12,2,1,10,7,4,3,5,6,8,11]=>[5,2,1,1,1,1,1]
[2,11,1,12,9,7,4,3,5,6,8,10]=>[5,2,1,1,1,1,1]
[10,11,2,1,4,3,12,7,5,6,8,9]=>[3,3,2,1,1,1,1]
[8,12,2,1,9,4,3,10,5,6,7,11]=>[4,2,2,1,1,1,1]
[2,11,1,12,8,4,3,9,5,6,7,10]=>[4,2,2,1,1,1,1]
[2,10,1,11,4,3,12,8,5,6,7,9]=>[3,3,2,1,1,1,1]
[2,9,1,10,4,3,11,5,12,6,7,8]=>[3,2,2,2,1,1,1]
[12,10,8,5,2,1,6,3,4,7,9,11]=>[6,2,1,1,1,1]
[5,11,2,1,12,8,6,3,4,7,9,10]=>[4,3,1,1,1,1,1]
[12,9,5,2,1,10,6,3,4,7,8,11]=>[5,3,1,1,1,1]
[11,5,2,1,12,9,6,3,4,7,8,10]=>[4,4,1,1,1,1]
[10,11,2,1,5,3,12,6,4,7,8,9]=>[3,3,2,1,1,1,1]
[12,10,7,2,1,8,5,3,4,6,9,11]=>[5,3,1,1,1,1]
[11,7,2,1,12,8,5,3,4,6,9,10]=>[4,4,1,1,1,1]
[12,9,2,1,10,7,5,3,4,6,8,11]=>[5,3,1,1,1,1]
[11,2,1,12,9,7,5,3,4,6,8,10]=>[5,3,1,1,1,1]
[10,11,2,1,3,12,7,5,4,6,8,9]=>[4,3,1,1,1,1,1]
[8,9,2,1,12,3,10,5,4,6,7,11]=>[4,3,1,1,1,1,1]
[11,8,2,1,12,3,9,5,4,6,7,10]=>[4,4,1,1,1,1]
[2,10,1,11,3,12,8,5,4,6,7,9]=>[4,2,2,1,1,1,1]
[2,9,1,10,3,11,5,4,12,6,7,8]=>[3,2,2,2,1,1,1]
[12,10,6,2,1,7,3,8,4,5,9,11]=>[5,2,2,1,1,1]
[11,6,2,1,12,7,3,8,4,5,9,10]=>[4,3,2,1,1,1]
[12,9,2,1,10,6,3,7,4,5,8,11]=>[4,3,2,1,1,1]
[11,2,1,12,9,6,3,7,4,5,8,10]=>[4,3,2,1,1,1]
[10,2,1,11,6,3,12,7,4,5,8,9]=>[3,3,3,1,1,1]
[12,8,2,1,9,3,10,6,4,5,7,11]=>[4,3,2,1,1,1]
[11,2,1,12,8,3,9,6,4,5,7,10]=>[4,3,2,1,1,1]
[10,2,1,11,3,12,8,6,4,5,7,9]=>[4,3,2,1,1,1]
[2,9,1,10,3,11,4,12,6,5,7,8]=>[3,2,2,2,1,1,1]
[12,7,2,1,8,3,9,4,10,5,6,11]=>[4,2,2,2,1,1]
[11,2,1,12,7,3,8,4,9,5,6,10]=>[3,3,2,2,1,1]
[10,2,1,11,3,12,7,4,8,5,6,9]=>[3,3,2,2,1,1]
[9,2,1,10,3,11,4,12,7,5,6,8]=>[3,3,2,2,1,1]
[8,2,1,9,3,10,4,11,5,12,6,7]=>[3,2,2,2,2,1]
[12,10,8,6,3,1,4,2,5,7,9,11]=>[6,2,1,1,1,1]
[11,12,3,1,8,6,4,2,5,7,9,10]=>[5,2,1,1,1,1,1]
[9,12,3,1,10,6,4,2,5,7,8,11]=>[5,2,1,1,1,1,1]
[3,11,1,12,9,6,4,2,5,7,8,10]=>[5,2,1,1,1,1,1]
[3,10,4,1,11,2,12,6,5,7,8,9]=>[3,3,2,1,1,1,1]
[12,10,7,3,1,8,4,2,5,6,9,11]=>[5,3,1,1,1,1]
[11,7,3,1,12,8,4,2,5,6,9,10]=>[4,4,1,1,1,1]
[12,9,3,1,10,7,4,2,5,6,8,11]=>[5,3,1,1,1,1]
[11,3,1,12,9,7,4,2,5,6,8,10]=>[5,3,1,1,1,1]
[3,10,1,11,4,2,12,7,5,6,8,9]=>[3,3,2,1,1,1,1]
[12,8,3,1,9,4,2,10,5,6,7,11]=>[4,3,2,1,1,1]
[11,3,1,12,8,4,2,9,5,6,7,10]=>[4,3,2,1,1,1]
[10,3,1,11,4,2,12,8,5,6,7,9]=>[3,3,3,1,1,1]
[9,3,1,10,4,2,11,5,12,6,7,8]=>[3,3,2,2,1,1]
[12,10,8,5,1,6,3,2,4,7,9,11]=>[6,2,1,1,1,1]
[5,11,1,12,8,6,3,2,4,7,9,10]=>[5,2,1,1,1,1,1]
[12,9,5,1,10,6,3,2,4,7,8,11]=>[5,3,1,1,1,1]
[11,5,1,12,9,6,3,2,4,7,8,10]=>[5,3,1,1,1,1]
[3,10,1,11,5,2,12,6,4,7,8,9]=>[3,3,2,1,1,1,1]
[12,10,7,1,8,5,3,2,4,6,9,11]=>[6,2,1,1,1,1]
[11,7,1,12,8,5,3,2,4,6,9,10]=>[5,3,1,1,1,1]
[12,9,1,10,7,5,3,2,4,6,8,11]=>[6,2,1,1,1,1]
[11,1,12,9,7,5,3,2,4,6,8,10]=>[6,2,1,1,1,1]
[3,10,1,11,2,12,7,5,4,6,8,9]=>[4,2,2,1,1,1,1]
[8,9,1,12,3,2,10,5,4,6,7,11]=>[4,2,2,1,1,1,1]
[11,8,1,12,3,2,9,5,4,6,7,10]=>[4,3,2,1,1,1]
[10,3,1,11,2,12,8,5,4,6,7,9]=>[4,3,2,1,1,1]
[9,3,1,10,2,11,5,4,12,6,7,8]=>[3,3,2,2,1,1]
[12,10,6,1,7,3,2,8,4,5,9,11]=>[5,2,2,1,1,1]
[11,6,1,12,7,3,2,8,4,5,9,10]=>[4,3,2,1,1,1]
[12,9,1,10,6,3,2,7,4,5,8,11]=>[5,2,2,1,1,1]
[11,1,12,9,6,3,2,7,4,5,8,10]=>[5,2,2,1,1,1]
[10,1,11,6,3,2,12,7,4,5,8,9]=>[4,3,2,1,1,1]
[12,8,1,9,3,2,10,6,4,5,7,11]=>[4,3,2,1,1,1]
[11,1,12,8,3,2,9,6,4,5,7,10]=>[4,3,2,1,1,1]
[10,1,11,3,2,12,8,6,4,5,7,9]=>[4,3,2,1,1,1]
[9,3,1,10,2,11,4,12,6,5,7,8]=>[3,3,2,2,1,1]
[12,7,1,8,3,2,9,4,10,5,6,11]=>[4,2,2,2,1,1]
[11,1,12,7,3,2,8,4,9,5,6,10]=>[4,2,2,2,1,1]
[10,1,11,3,2,12,7,4,8,5,6,9]=>[3,3,2,2,1,1]
[9,1,10,3,2,11,4,12,7,5,6,8]=>[3,3,2,2,1,1]
[8,1,9,3,2,10,4,11,5,12,6,7]=>[3,2,2,2,2,1]
[12,10,8,4,1,5,2,6,3,7,9,11]=>[5,2,2,1,1,1]
[4,11,1,12,8,5,2,6,3,7,9,10]=>[4,2,2,1,1,1,1]
[12,9,4,1,10,5,2,6,3,7,8,11]=>[4,3,2,1,1,1]
[11,4,1,12,9,5,2,6,3,7,8,10]=>[4,3,2,1,1,1]
[10,4,1,11,5,2,12,6,3,7,8,9]=>[3,3,3,1,1,1]
[12,10,7,1,8,4,2,5,3,6,9,11]=>[5,2,2,1,1,1]
[11,7,1,12,8,4,2,5,3,6,9,10]=>[4,3,2,1,1,1]
[12,9,1,10,7,4,2,5,3,6,8,11]=>[5,2,2,1,1,1]
[11,1,12,9,7,4,2,5,3,6,8,10]=>[5,2,2,1,1,1]
[10,4,1,11,2,12,7,5,3,6,8,9]=>[4,3,2,1,1,1]
[12,8,1,9,4,2,10,5,3,6,7,11]=>[4,3,2,1,1,1]
[11,1,12,8,4,2,9,5,3,6,7,10]=>[4,3,2,1,1,1]
[10,1,11,4,2,12,8,5,3,6,7,9]=>[4,3,2,1,1,1]
[9,1,10,4,2,11,5,3,12,6,7,8]=>[3,3,2,2,1,1]
[12,10,6,1,7,2,8,4,3,5,9,11]=>[5,2,2,1,1,1]
[11,6,1,12,7,2,8,4,3,5,9,10]=>[4,3,2,1,1,1]
[12,9,1,10,6,2,7,4,3,5,8,11]=>[5,2,2,1,1,1]
[11,1,12,9,6,2,7,4,3,5,8,10]=>[5,2,2,1,1,1]
[10,1,11,6,2,12,7,4,3,5,8,9]=>[4,3,2,1,1,1]
[12,8,1,9,2,10,6,4,3,5,7,11]=>[5,2,2,1,1,1]
[11,1,12,8,2,9,6,4,3,5,7,10]=>[5,2,2,1,1,1]
[10,1,11,2,12,8,6,4,3,5,7,9]=>[5,2,2,1,1,1]
[9,1,10,4,2,11,3,12,6,5,7,8]=>[3,3,2,2,1,1]
[12,7,1,8,2,9,4,3,10,5,6,11]=>[4,2,2,2,1,1]
[11,1,12,7,2,8,4,3,9,5,6,10]=>[4,2,2,2,1,1]
[10,1,11,2,12,7,4,3,8,5,6,9]=>[4,2,2,2,1,1]
[9,1,10,2,11,4,3,12,7,5,6,8]=>[3,3,2,2,1,1]
[8,1,9,2,10,4,3,11,5,12,6,7]=>[3,2,2,2,2,1]
[12,10,5,1,6,2,7,3,8,4,9,11]=>[4,2,2,2,1,1]
[11,5,1,12,6,2,7,3,8,4,9,10]=>[3,3,2,2,1,1]
[12,9,1,10,5,2,6,3,7,4,8,11]=>[4,2,2,2,1,1]
[11,1,12,9,5,2,6,3,7,4,8,10]=>[4,2,2,2,1,1]
[10,1,11,5,2,12,6,3,7,4,8,9]=>[3,3,2,2,1,1]
[12,8,1,9,2,10,5,3,6,4,7,11]=>[4,2,2,2,1,1]
[11,1,12,8,2,9,5,3,6,4,7,10]=>[4,2,2,2,1,1]
[10,1,11,2,12,8,5,3,6,4,7,9]=>[4,2,2,2,1,1]
[9,1,10,2,11,5,3,12,6,4,7,8]=>[3,3,2,2,1,1]
[12,7,1,8,2,9,3,10,5,4,6,11]=>[4,2,2,2,1,1]
[11,1,12,7,2,8,3,9,5,4,6,10]=>[4,2,2,2,1,1]
[10,1,11,2,12,7,3,8,5,4,6,9]=>[4,2,2,2,1,1]
[9,1,10,2,11,3,12,7,5,4,6,8]=>[4,2,2,2,1,1]
[8,1,9,2,10,3,11,5,4,12,6,7]=>[3,2,2,2,2,1]
[12,6,1,7,2,8,3,9,4,10,5,11]=>[3,2,2,2,2,1]
[11,1,12,6,2,7,3,8,4,9,5,10]=>[3,2,2,2,2,1]
[10,1,11,2,12,6,3,7,4,8,5,9]=>[3,2,2,2,2,1]
[9,1,10,2,11,3,12,6,4,7,5,8]=>[3,2,2,2,2,1]
[8,1,9,2,10,3,11,4,12,6,5,7]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,9,8,10,12,11,1]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,8,11,9,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,7,6,8,10,9,12,11,1]=>[3,2,2,2,2,1]
[3,2,5,4,7,6,8,9,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,9,7,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,9,7,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,8,7,11,9,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,8,7,10,9,12,11,1]=>[3,2,2,2,2,1]
[3,2,5,4,6,8,7,9,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,7,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,5,4,6,7,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,7,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,5,4,6,7,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,7,5,6,9,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,4,7,5,6,9,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,7,5,6,8,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,7,5,6,8,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,7,5,6,8,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,6,5,9,7,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,9,7,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,8,7,11,9,10,12,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,8,7,10,9,12,11,1]=>[3,2,2,2,2,1]
[3,2,4,6,5,8,7,9,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,7,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,6,5,7,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,7,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,6,5,7,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,9,6,7,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,9,6,7,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,8,6,7,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,8,6,7,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,5,8,6,7,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,7,6,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,7,6,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,5,7,6,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[3,2,4,5,7,6,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,6,11,7,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[3,2,4,5,6,10,7,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,6,9,7,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,6,8,7,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[3,2,4,5,6,7,12,8,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,5,3,4,7,6,9,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[2,5,3,4,7,6,9,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[2,5,3,4,7,6,8,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,7,6,8,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,5,3,4,7,6,8,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,9,7,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,9,7,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,8,7,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,8,7,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,5,3,4,6,8,7,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,7,11,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,5,3,4,6,7,10,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,7,9,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,5,3,4,6,7,8,12,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,4,3,7,5,6,9,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[2,4,3,7,5,6,9,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,7,5,6,8,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,7,5,6,8,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,7,5,6,8,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,6,5,9,7,8,11,10,12,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,9,7,8,10,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,8,7,11,9,10,12,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,8,7,9,12,10,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,7,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,6,5,7,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,7,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,6,5,7,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,9,6,7,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,9,6,7,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,8,6,7,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,8,6,7,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,5,8,6,7,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,7,6,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,7,6,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,5,7,6,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[2,4,3,5,7,6,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,6,11,7,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,4,3,5,6,10,7,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,6,9,7,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,6,8,7,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,4,3,5,6,7,12,8,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,7,4,5,6,9,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,7,4,5,6,9,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,7,4,5,6,8,11,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,7,4,5,6,8,10,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,7,4,5,6,8,9,12,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,6,4,5,9,7,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,9,7,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,8,7,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,8,7,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,3,6,4,5,8,7,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,7,11,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,6,4,5,7,10,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,7,9,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,6,4,5,7,8,12,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,5,4,9,6,7,8,11,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,9,6,7,8,10,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,8,6,7,11,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,8,6,7,10,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,3,5,4,8,6,7,9,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,7,6,11,8,9,10,12,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,7,6,10,8,9,12,11,1]=>[3,2,2,2,1,1,1]
[2,3,5,4,7,6,9,8,12,10,11,1]=>[3,2,2,2,1,1,1]
[2,3,5,4,7,6,8,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,6,11,7,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,5,4,6,10,7,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,6,9,7,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,6,8,7,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,5,4,6,7,12,8,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,9,5,6,7,8,11,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,9,5,6,7,8,10,12,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,8,5,6,7,11,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,8,5,6,7,10,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,8,5,6,7,9,12,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,7,5,6,11,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,7,5,6,10,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,7,5,6,9,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,7,5,6,8,12,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,6,5,11,7,8,9,10,12,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,6,5,10,7,8,9,12,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,6,5,9,7,8,12,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,6,5,8,7,12,9,10,11,1]=>[3,2,2,1,1,1,1,1]
[2,3,4,6,5,7,12,8,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,11,6,7,8,9,10,12,1]=>[3,1,1,1,1,1,1,1,1,1]
[2,3,4,5,10,6,7,8,9,12,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,9,6,7,8,12,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,8,6,7,12,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[2,3,4,5,7,6,12,8,9,10,11,1]=>[3,2,1,1,1,1,1,1,1]
[12,11,9,5,10,7,1,2,4,8,3,6]=>[6,2,1,1,1,1]
[11,9,5,12,10,7,1,2,4,8,3,6]=>[5,3,1,1,1,1]
[10,7,1,2,4,9,5,12,11,8,3,6]=>[4,3,2,1,1,1]
[12,10,7,1,2,4,9,5,11,8,3,6]=>[5,2,2,1,1,1]
[10,7,1,2,4,12,9,5,11,8,3,6]=>[4,3,2,1,1,1]
[8,3,7,1,2,4,12,11,9,5,10,6]=>[4,3,2,1,1,1]
[8,3,7,1,2,4,11,9,5,12,10,6]=>[3,3,3,1,1,1]
[12,11,8,3,7,1,2,4,9,5,10,6]=>[5,2,2,1,1,1]
[11,8,3,7,1,2,4,9,5,12,10,6]=>[4,3,2,1,1,1]
[12,9,5,11,8,3,7,1,2,4,10,6]=>[5,2,2,1,1,1]
[8,3,12,11,7,1,2,4,9,5,10,6]=>[4,2,2,2,1,1]
[8,3,11,7,1,2,4,9,5,12,10,6]=>[3,3,2,2,1,1]
[8,3,12,9,5,11,7,1,2,4,10,6]=>[4,2,2,2,1,1]
[12,8,3,9,5,11,7,1,2,4,10,6]=>[4,2,2,2,1,1]
[10,7,1,2,5,12,11,9,4,8,3,6]=>[5,3,1,1,1,1]
[12,10,7,1,2,5,11,9,4,8,3,6]=>[6,2,1,1,1,1]
[9,4,10,7,1,2,5,12,11,8,3,6]=>[4,3,2,1,1,1]
[9,4,12,10,7,1,2,5,11,8,3,6]=>[5,2,2,1,1,1]
[12,9,4,10,7,1,2,5,11,8,3,6]=>[5,2,2,1,1,1]
[12,11,9,4,8,3,7,1,2,5,10,6]=>[6,2,1,1,1,1]
[11,9,4,8,3,7,1,2,5,12,10,6]=>[5,3,1,1,1,1]
[9,4,12,11,8,3,7,1,2,5,10,6]=>[5,2,2,1,1,1]
[9,4,11,8,3,7,1,2,5,12,10,6]=>[4,3,2,1,1,1]
[11,8,3,7,1,2,5,12,9,4,10,6]=>[5,2,2,1,1,1]
[8,3,9,4,12,11,7,1,2,5,10,6]=>[4,2,2,2,1,1]
[8,3,9,4,11,7,1,2,5,12,10,6]=>[3,3,2,2,1,1]
[8,3,11,7,1,2,5,12,9,4,10,6]=>[4,2,2,2,1,1]
[11,7,1,2,5,12,8,3,9,4,10,6]=>[4,2,2,2,1,1]
[10,5,12,11,9,4,8,3,7,1,2,6]=>[6,2,1,1,1,1]
[12,10,5,11,9,4,8,3,7,1,2,6]=>[6,2,1,1,1,1]
[9,4,10,5,12,11,8,3,7,1,2,6]=>[5,2,2,1,1,1]
[9,4,12,10,5,11,8,3,7,1,2,6]=>[5,2,2,1,1,1]
[12,9,4,10,5,11,8,3,7,1,2,6]=>[5,2,2,1,1,1]
[8,3,9,4,10,5,12,11,7,1,2,6]=>[4,2,2,2,1,1]
[8,3,9,4,12,10,5,11,7,1,2,6]=>[4,2,2,2,1,1]
[8,3,12,9,4,10,5,11,7,1,2,6]=>[4,2,2,2,1,1]
[12,8,3,9,4,10,5,11,7,1,2,6]=>[4,2,2,2,1,1]
[7,1,2,8,3,9,4,10,5,12,11,6]=>[3,2,2,2,2,1]
[7,1,2,8,3,9,4,12,10,5,11,6]=>[3,2,2,2,2,1]
[7,1,2,8,3,12,9,4,10,5,11,6]=>[3,2,2,2,2,1]
[7,1,2,12,8,3,9,4,10,5,11,6]=>[3,2,2,2,2,1]
[12,7,1,2,8,3,9,4,10,5,11,6]=>[3,2,2,2,2,1]
[8,2,4,12,11,9,5,10,7,1,3,6]=>[5,2,2,1,1,1]
[8,2,4,11,9,5,12,10,7,1,3,6]=>[4,3,2,1,1,1]
[12,11,8,2,4,9,5,10,7,1,3,6]=>[5,2,2,1,1,1]
[11,8,2,4,9,5,12,10,7,1,3,6]=>[4,3,2,1,1,1]
[12,9,5,11,8,2,4,10,7,1,3,6]=>[5,2,2,1,1,1]
[7,1,3,8,2,4,12,11,9,5,10,6]=>[4,3,2,1,1,1]
[7,1,3,8,2,4,11,9,5,12,10,6]=>[3,3,3,1,1,1]
[7,1,3,12,11,8,2,4,9,5,10,6]=>[4,2,2,2,1,1]
[7,1,3,11,8,2,4,9,5,12,10,6]=>[3,3,2,2,1,1]
[7,1,3,12,9,5,11,8,2,4,10,6]=>[4,2,2,2,1,1]
[12,11,7,1,3,8,2,4,9,5,10,6]=>[5,2,2,1,1,1]
[11,7,1,3,8,2,4,9,5,12,10,6]=>[4,3,2,1,1,1]
[12,9,5,11,7,1,3,8,2,4,10,6]=>[5,2,2,1,1,1]
[11,7,1,3,9,5,12,8,2,4,10,6]=>[4,2,2,2,1,1]
[12,11,9,4,8,2,5,10,7,1,3,6]=>[6,2,1,1,1,1]
[11,9,4,8,2,5,12,10,7,1,3,6]=>[5,3,1,1,1,1]
[9,4,12,11,8,2,5,10,7,1,3,6]=>[5,2,2,1,1,1]
[9,4,11,8,2,5,12,10,7,1,3,6]=>[4,3,2,1,1,1]
[11,8,2,5,12,9,4,10,7,1,3,6]=>[5,2,2,1,1,1]
[7,1,3,12,11,9,4,8,2,5,10,6]=>[5,2,2,1,1,1]
[7,1,3,11,9,4,8,2,5,12,10,6]=>[4,3,2,1,1,1]
[7,1,3,9,4,12,11,8,2,5,10,6]=>[4,2,2,2,1,1]
[7,1,3,9,4,11,8,2,5,12,10,6]=>[3,3,2,2,1,1]
[7,1,3,11,8,2,5,12,9,4,10,6]=>[4,2,2,2,1,1]
[9,4,12,11,7,1,3,8,2,5,10,6]=>[5,2,2,1,1,1]
[9,4,11,7,1,3,8,2,5,12,10,6]=>[4,3,2,1,1,1]
[11,7,1,3,8,2,5,12,9,4,10,6]=>[4,3,2,1,1,1]
[12,8,2,5,11,7,1,3,9,4,10,6]=>[4,2,2,2,1,1]
[7,1,3,10,5,12,11,9,4,8,2,6]=>[5,2,2,1,1,1]
[7,1,3,12,10,5,11,9,4,8,2,6]=>[5,2,2,1,1,1]
[7,1,3,9,4,10,5,12,11,8,2,6]=>[4,2,2,2,1,1]
[7,1,3,9,4,12,10,5,11,8,2,6]=>[4,2,2,2,1,1]
[7,1,3,12,9,4,10,5,11,8,2,6]=>[4,2,2,2,1,1]
[9,4,10,5,12,11,7,1,3,8,2,6]=>[5,2,2,1,1,1]
[9,4,12,10,5,11,7,1,3,8,2,6]=>[5,2,2,1,1,1]
[12,9,4,10,5,11,7,1,3,8,2,6]=>[5,2,2,1,1,1]
[11,7,1,3,9,4,10,5,12,8,2,6]=>[4,2,2,2,1,1]
[8,2,7,1,3,9,4,10,5,12,11,6]=>[3,3,2,2,1,1]
[8,2,7,1,3,9,4,12,10,5,11,6]=>[3,3,2,2,1,1]
[8,2,7,1,3,12,9,4,10,5,11,6]=>[3,3,2,2,1,1]
[12,8,2,7,1,3,9,4,10,5,11,6]=>[4,2,2,2,1,1]
[8,2,12,7,1,3,9,4,10,5,11,6]=>[3,2,2,2,2,1]
[10,7,1,4,8,2,5,12,11,9,3,6]=>[4,4,1,1,1,1]
[12,10,7,1,4,8,2,5,11,9,3,6]=>[5,3,1,1,1,1]
[12,11,8,2,5,10,7,1,4,9,3,6]=>[6,2,1,1,1,1]
[11,8,2,5,12,10,7,1,4,9,3,6]=>[5,3,1,1,1,1]
[10,7,1,4,11,8,2,5,12,9,3,6]=>[4,3,2,1,1,1]
[12,11,9,3,7,1,4,8,2,5,10,6]=>[6,2,1,1,1,1]
[11,9,3,7,1,4,8,2,5,12,10,6]=>[5,3,1,1,1,1]
[9,3,7,1,4,12,11,8,2,5,10,6]=>[4,3,2,1,1,1]
[9,3,7,1,4,11,8,2,5,12,10,6]=>[4,3,2,1,1,1]
[11,8,2,5,12,9,3,7,1,4,10,6]=>[5,2,2,1,1,1]
[12,11,7,1,4,9,3,8,2,5,10,6]=>[6,2,1,1,1,1]
[11,7,1,4,9,3,8,2,5,12,10,6]=>[5,3,1,1,1,1]
[12,9,3,8,2,5,11,7,1,4,10,6]=>[5,2,2,1,1,1]
[9,3,12,8,2,5,11,7,1,4,10,6]=>[4,2,2,2,1,1]
[10,5,12,11,9,3,7,1,4,8,2,6]=>[6,2,1,1,1,1]
[12,10,5,11,9,3,7,1,4,8,2,6]=>[6,2,1,1,1,1]
[9,3,7,1,4,10,5,12,11,8,2,6]=>[4,3,2,1,1,1]
[9,3,7,1,4,12,10,5,11,8,2,6]=>[4,3,2,1,1,1]
[12,9,3,7,1,4,10,5,11,8,2,6]=>[5,2,2,1,1,1]
[10,5,12,11,7,1,4,9,3,8,2,6]=>[6,2,1,1,1,1]
[12,10,5,11,7,1,4,9,3,8,2,6]=>[6,2,1,1,1,1]
[11,7,1,4,10,5,12,9,3,8,2,6]=>[5,2,2,1,1,1]
[9,3,11,7,1,4,10,5,12,8,2,6]=>[4,2,2,2,1,1]
[9,3,8,2,7,1,4,10,5,12,11,6]=>[4,3,2,1,1,1]
[9,3,8,2,7,1,4,12,10,5,11,6]=>[4,3,2,1,1,1]
[12,9,3,8,2,7,1,4,10,5,11,6]=>[5,2,2,1,1,1]
[9,3,12,8,2,7,1,4,10,5,11,6]=>[4,2,2,2,1,1]
[8,2,9,3,12,7,1,4,10,5,11,6]=>[3,2,2,2,2,1]
[12,11,9,3,7,1,5,10,4,8,2,6]=>[7,1,1,1,1,1]
[11,9,3,7,1,5,12,10,4,8,2,6]=>[6,2,1,1,1,1]
[10,4,9,3,7,1,5,12,11,8,2,6]=>[5,3,1,1,1,1]
[12,10,4,9,3,7,1,5,11,8,2,6]=>[6,2,1,1,1,1]
[10,4,12,9,3,7,1,5,11,8,2,6]=>[5,2,2,1,1,1]
[12,11,7,1,5,10,4,9,3,8,2,6]=>[7,1,1,1,1,1]
[11,7,1,5,12,10,4,9,3,8,2,6]=>[6,2,1,1,1,1]
[10,4,11,7,1,5,12,9,3,8,2,6]=>[5,2,2,1,1,1]
[9,3,10,4,11,7,1,5,12,8,2,6]=>[4,2,2,2,1,1]
[10,4,9,3,8,2,7,1,5,12,11,6]=>[5,3,1,1,1,1]
[12,10,4,9,3,8,2,7,1,5,11,6]=>[6,2,1,1,1,1]
[10,4,12,9,3,8,2,7,1,5,11,6]=>[5,2,2,1,1,1]
[9,3,10,4,12,8,2,7,1,5,11,6]=>[4,2,2,2,1,1]
[8,2,9,3,10,4,12,7,1,5,11,6]=>[3,2,2,2,2,1]
[12,11,5,10,4,9,3,8,2,7,1,6]=>[7,1,1,1,1,1]
[11,5,12,10,4,9,3,8,2,7,1,6]=>[6,2,1,1,1,1]
[10,4,11,5,12,9,3,8,2,7,1,6]=>[5,2,2,1,1,1]
[9,3,10,4,11,5,12,8,2,7,1,6]=>[4,2,2,2,1,1]
[8,2,9,3,10,4,11,5,12,7,1,6]=>[3,2,2,2,2,1]
[3,4,1,5,6,7,8,9,10,11,12,2]=>[2,2,1,1,1,1,1,1,1,1]
[8,2,9,3,10,4,11,5,12,6,1,7]=>[3,2,2,2,2,1]
[8,2,9,3,10,4,11,5,12,1,6,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,4,11,12,5,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,4,11,12,5,1,6,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,4,11,12,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,4,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,11,4,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,4,12,5,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,11,4,12,5,1,6,7]=>[3,2,2,2,1,1,1]
[8,2,9,3,10,11,4,12,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,3,10,11,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,3,4,11,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,10,3,4,11,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,4,11,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,4,11,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,4,11,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,3,11,4,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,10,3,11,4,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,11,4,12,5,6,1,7]=>[3,2,2,2,1,1,1]
[8,2,9,10,3,11,4,12,5,1,6,7]=>[3,2,2,2,1,1,1]
[8,2,9,10,3,11,4,12,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,11,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,11,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,11,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,3,11,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,3,4,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,4,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,3,4,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,4,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,4,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,3,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,2,9,10,11,3,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,12,3,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,12,3,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,12,3,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,12,3,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,2,9,10,11,12,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,2,3,10,4,11,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,9,2,3,10,4,11,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,4,11,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,4,11,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,4,11,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,4,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,11,4,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,4,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,11,4,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,3,10,11,4,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,12,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,12,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,12,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,3,10,11,12,1,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,2,10,3,4,11,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,9,2,10,3,4,11,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,4,11,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,4,11,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,4,11,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,3,11,4,5,12,6,1,7]=>[3,2,2,2,1,1,1]
[8,9,2,10,3,11,4,5,12,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,11,4,12,5,6,1,7]=>[3,2,2,2,1,1,1]
[8,9,2,10,3,11,4,12,5,1,6,7]=>[3,2,2,2,1,1,1]
[8,9,2,10,3,11,4,12,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,11,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,11,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,11,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,3,11,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,3,4,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,4,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,3,4,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,4,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,4,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,3,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,2,10,11,3,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,12,3,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,12,3,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,12,3,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,12,3,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,2,10,11,12,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,2,3,4,11,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,3,4,11,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,4,11,12,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,4,11,12,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,4,11,12,1,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,2,3,11,4,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,3,11,4,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,11,4,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,3,11,4,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,3,11,4,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,11,12,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,11,12,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,11,12,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,3,11,12,1,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,2,11,3,4,5,12,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,4,5,12,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,3,4,12,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,4,12,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,4,12,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,3,12,4,5,6,1,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,12,4,5,1,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,12,4,1,5,6,7]=>[3,2,2,1,1,1,1,1]
[8,9,10,2,11,3,12,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,12,3,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,12,3,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,12,3,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,12,3,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,2,11,12,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,2,3,4,5,12,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,4,5,12,1,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,2,3,4,12,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,4,12,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,4,12,1,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,2,3,12,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,12,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,12,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,3,12,1,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,2,12,3,4,5,6,1,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,12,3,4,5,1,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,12,3,4,1,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,12,3,1,4,5,6,7]=>[3,2,1,1,1,1,1,1,1]
[8,9,10,11,2,12,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,12,2,3,4,5,6,1,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,12,2,3,4,5,1,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,12,2,3,4,1,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,12,2,3,1,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[8,9,10,11,12,2,1,3,4,5,6,7]=>[3,1,1,1,1,1,1,1,1,1]
[11,2,3,4,5,6,7,8,9,10,12,1]=>[3,1,1,1,1,1,1,1,1,1]
          

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.

References

[1] Lewis, J., Lyu, H., Pylyavskyy, P., Sen, A. Scaling limit of soliton lengths in a multicolor box-ball system arXiv:1911.04458

Properties

surjective, graded

Sage code

def mapping(pi):
    to_standard = sage.combinat.permutation.to_standard
    def llis(u):
        if len(u) == 1:
            return 1
        if len(u) == 2:
            if u[0] < u[1]:
                return 2
            return 1
        if len(u) == 3:
            if u[0] < u[1] < u[2]:
                return 3
            if u[0] > u[1] > u[2]:
                return 1
            return 2

        return to_standard(u).longest_increasing_subsequence_length()

    la = []
    n = len(pi)
    t = 0
    pi = pi.reverse()
    for k in range(1, n+1):
        a = 0
        for p in Compositions(n, length=k):
            b = [sum(p[:i]) for i in range(k+1)]
            s = sum(llis(pi[b[i]:b[i+1]]) for i in range(k))
            a = max(a, s)
        d = a - t
        if a == t:
            return Partition(la)
        la.append(d)
        t = a

    return Partition(la)

Weight

Created

Jan 28, 2021 at 12:18 by Martin Rubey

Updated

Feb 01, 2021 at 12:27 by Martin Rubey